Answers
Chords AB and CD intersect at E and AE= EB is Semi circle is drawn with diameter CD. EF perpendicular to CD meet this semi circle at F then AE= EF
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Let M be the midpoint of AB, so EM is perpendicular to AB.
Since OF is a diameter of the circle, angle EOF is a right angle.
Triangles EOF and EMA are similar, since they both have a right angle and angle EFM is congruent to angle EAM, being alternate interior angles of parallel lines.
The corresponding sides are proportional:
EF / EA = EO / EM.
EM is half the length of AB, which is the diameter of the semicircle,
EO must be equal to the radius of the semicircle.
Therefore, we have EF / EA = radius / (diameter / 2) = 2 / 2 = 1,
EF = EA.
Hence, chords AB and CD intersect at E and AE= EB is Semi circle is drawn with diameter CD. EF perpendicular to CD meet this semi circle at F then AE= EF
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Related Questions
Two sides of a triangle are
shown. Find the range of
values of the third side.
8, 5
< X <
Answers
The range of values for the third side must be 5 < C < 13 this means that the third side must be a value greater than 5 and less than 13.
What is triangle?
A triangle is a two-dimensional geometric shape with three sides and three angles. It is a basic polygon and one of the simplest shapes in geometry. Triangles come in different types based on the length of their sides or the measure of their angles, such as equilateral triangles (all sides are equal), isosceles triangles (two sides are equal), scalene triangles (no sides are equal), right triangles (one angle measures 90 degrees), and obtuse triangles (one angle measures greater than 90 degrees).
The third side of a triangle must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, for a triangle with sides A, B, and C, we have:
A + B > C
B + C > A
A + C > B
For the given sides of 8 and 5, the range of values for the third side can be found by considering the two inequalities:
5 + C > 8
8 + C > 5
Adding the two inequalities, we get:
13 > C
So the range of values for the third side must be:
5 < C < 13
This means that the third side must be a value greater than 5 and less than 13.
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find the volume of the cylinder 9in and 5in
Answers
706.5 in³
Step-by-step explanation:The volume of a shape describes the amount of space a shape takes up.
Volume Formula
For a cylinder, the volume formula is V = πr²h. In this formula, V represents the total volume. Additionally, π represents the constant pi, which is approximately 3.14. The variable r represents the radius. Remember that radius is the distance from the center of the circle to the edge. Finally, h is the height of the cylinder.
Solving for Volume
The diagram shows that the radius is 5in. We know this because the distance from the center to the edge of the circle is 5in. Additionally, the height is 9in. Now, we can plug these values into the formula.
V = π(5)² * 9V = 225πV ≈ 706.5For this calculation, I used 3.14 for π. The unrounded volume in terms of pi is 225π.
The volume of the cylinder is 706.5 in³.
what do the numbers on a centimeter ruler represent
Answers
The numbers on a centimeter ruler represent that There are 10 millimeters unit for each centimeter.
What is a unit?
Units are the instruments used to measure and compare various things. When all measuring units are the same, comparison is simple. Various units can be categorised based on their intended usage. A couple of the units are classed as follows:
The seven SI basic units (The International System of Units (SI), sometimes known as the metric system, is the international measurement standard) are as follows:
Length - meter (m)
Time - second (s)
Amount of substance - mole (mole)
Electric current - ampere (A)
Temperature - kelvin (K)
Luminous intensity - candela (cd)
Mass - kilogram (kg)
Now,
As we have seen in a ruler from any two numbers 1 and 2 or 4 and 5
there are always 10 vertical lines which represents a millimeter
and 10 lines means 10 millimeter.
hence,
The numbers on a centimeter ruler represent that There are 10 millimeters unit for each centimeter.
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what distance does the tip of the minute hand on a clock travel in 11 minutes if the minute hand is 23 cm long?
Answers
The tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.
What is Circle?
A circle is a two-dimensional geometric shape that is defined as the set of all points in a plane that are a fixed distance away from a given point, called the center of the circle. This distance is known as the radius of the circle.
A circle can also be defined as the locus of a point that moves in a plane in such a way that its distance from a fixed point is constant. The constant distance is the radius of the circle.
The minute hand on a clock makes a full rotation in 60 minutes, which means it travels the circumference of a circle with a radius of 23 cm in 60 minutes. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14.
Therefore, the circumference of the circle traced by the tip of the minute hand is:
C = 2πr = 2 × 3.14 × 23 cm ≈ 144.44 cm
To find out how far the minute hand travels in 11 minutes, we need to calculate what fraction of the circumference it covers in that time. Since 11 minutes is about 18.3% of an hour (60 minutes), the minute hand travels 18.3% of the circumference of the circle in that time:
Distance traveled = 0.183 × 144.44 cm ≈ 26.4 cm
Therefore, the tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.
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To make a strawberry banana smoothie, a recipe calls for 1.75 cups of strawberries and some bananas. TO make
the recipe taste more like banana, ; cup more banana was added to the blender. The smoothie now has 1.4 cups
of bananas. How many cups of bananas were in the original recipe?
cup
Answers
Based on the information, it can be inferred that the original recipe contained 0.9 cups of banana.
How to calculate the original amount of banana contained in the recipe?To calculate the original amount of banana contained in the smoothie recipe we must perform the following mathematical operation:
We know that the final recipe has 1.4 cups of banana and that to make it have a more intense banana flavor they added 1/2 cups of banana, that is, 0.5 cups.
According to the above, we must subtract the amount that was added to the final amount to find how much the recipe has as shown below:
1.4 drinks - 0.5 drinks = 0.9 drinks
According to the above, the original recipe would have 0.9 cups of banana.
Note: This question is incomplete. Here is the complete information:
To make a strawberry banana smoothie, a recipe calls for 1.75L cups of strawberries and some bananas. To make the recipe taste more like banana, 1/2 C cup more banana was added to the blender. The smoothie now has 1.4 cups of bananas. How many cups of bananas were in the original recipe?
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Please answer it’s for school
Answers
Using the vertices given, the area of triangle PQR is 18 squared units
What is the area of the triangleThe area of triangle PQR can be found using the Shoelace Theorem. This theorem states that the area of a polygon can be calculated by taking the sum of the products of the coordinates of its vertices and subtracting the sum of the products of the coordinates of its vertices in reverse order.
In this case, the vertices of triangle PQR are P(-8, 2), Q(-2, 4), and R(-6, 8), so the area can be calculated as follows:
A = 1/2 * |(-8 * 4) + (-2 * 8) + (-6 * 2) - (2 * -2) - (4 * -6) - (8 * -8)| = 1/2 * |-32 + 16 + -12 - 4 + 24 + 64| = 1/2 * |36| = 18 square units
So the area of triangle PQR is 18 square units.
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What is the measure of the smallest angle?
one line has 2x #2 had 3x - 11 #3 had 2x + 9
67°
69°
52°
61°
Answers
In the preceding equation the measure of the smallest angle is 52° in length.
What are the names of angles 2 and 3?Internal angles 2 and 3 are alternate options. Two angles that share a vertex and a side but no interior points in common. two angles that don't have any shared interior points but do have a common vertex and side.
We know that a triangle has 180 angles altogether.
So, 2x + 3x - 11 + 2x + 9 = 180
7x - 2 = 180
7x = 180 + 2
x = 182 / 7
x = 26
Now, magnitude of angles = 2x = 2(26) = 52 [ Smallest ]
3x - 11 = 3(26) - 11 = 78 - 11 = 67 [ Largest ]
2x +9 = 2(26) + 9 = 52 + 9 = 61
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Let f(x) = 2√3x and g(x) = -4√3x. Find (f-g)(x), then evaluate when x = 12.
Answers
The function operation (f-g)(x) in the functions f(x) = 2√3x and g(x) = -4√3x is 6√3x and the value of (f-g)(12) is 36.
What is the function operation (f-g)(x) and value of (f-g)(12)?A function is simply a relationship that maps one input to one output.
Given that;
f(x) = 2√3xg(x) = -4√3x(f-g)(x) = ?(f-g)(12) = ?First, set up the function;
(f - g)(x) = f(x) - g(x)
Replace the function designators with the actual function.
(f - g)(x) = f(x) - g(x)
(f - g)(x) = 2√3x - (-4√3x)
(f - g)(x) = 2√3x + 4√3x
(f - g)(x) = 6√3x
Now, we evaluate when x = 12.
(f - g)(x) = 6√3x
Replace x with 12
(f - g)( 12 ) = 6√3(12)
(f - g)( 12 ) = 6√36
(f - g)( 12 ) = 6 × 6
(f - g)( 12 ) = 36
Therefore, the function operation (f-g)(x) is 6√3x and (f-g)(12) is 36.
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Problem
Aurelia has a coin that she suspects is unfair. She wants to test
H
0
:
p
=
0.5
H
0
:p=0.5H, start subscript, 0, end subscript, colon, p, equals, 0, point, 5 versus
H
a
:
p
≠
0.5
H
a
:p
=0.5H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 5, where
p
pp is the proportion of flips that this coin lands showing heads.
She flipped the coin
100
100100 times and it landed showing heads
43
4343 of those times.
Which of the following represents the P-value for Aurelia's test?
Answers
The correct option is C, P - value is 0.0718.
Describe sample percentageA sample proportion in statistics is a measurement of the proportion or percentage of a sample that demonstrates an important characteristic or quality. It is computed by dividing the sample's overall population by the proportion of participants who exhibit the characteristic.
For instance, if a sample of 100 individuals is chosen to estimate the percentage of people who love chocolate ice cream, and 30 of those individuals state that they do, the sample proportion would be 0.3 or 30%, as 30 out of 100 individuals state that they do.
We must first compute the test statistic in order to determine the P-value for Aurelia's test. The test statistic has a typical normal distribution when the null hypothesis is true.
The sample proportion of heads is:
p' = 43/100 = 0.43
The test statistic is:
[tex]z = \frac{(p' - p)}{ \sqrt{(p(1-p) / n)}}[/tex]
where p is the hypothesized proportion under the null hypothesis, and n is the sample size.
Substituting the given values, we get:
[tex]z = \frac{(0.43 - 0.5)}{/ {sqrt(0.5 \times 0.5 / 100)}} = -1.8[/tex]
Since this is a two-sided test, we need to find the area under the standard normal distribution curve in both tails of the distribution that is more extreme than the observed test statistic.
Using a standard normal distribution table, we find that the area to the left of -1.8 is 0.0359. Therefore, the area in both tails is:
P-value = 2 × 0.0359 = 0.0718
So, the correct answer is:
c) 0.0718
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Answer:C
Step-by-step explanation: Kahn Academy
the base of the rectangle is 7 more than its height x. if the perimeter of the rectangle is greater than 30in find the height
Answers
The height of the rectangle must be greater than 4 inches if the perimeter of the rectangle is greater than 30 inches.
In geometry, a rectangle is a quadrilateral with four right angles, and opposite sides are equal in length. The perimeter of a rectangle is the total distance around it.
Let's assume that the height of the rectangle is x inches. According to the problem, the base is 7 more than its height, which means the base is (x + 7) inches.
Now, we can calculate the perimeter of the rectangle using the formula:
Perimeter = 2(length + width)
In a rectangle, the length and width are the same as the base and height, respectively. So, in our case, the perimeter of the rectangle will be:
Perimeter = 2(x + (x + 7)) = 4x + 14
As we are given that the perimeter of the rectangle is greater than 30 inches, we can write the inequality:
4x + 14 > 30
Solving for x, we get:
4x > 16
x > 4
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Jayden has some dimes and some quarters. He has at most 25 coins worth at least $4.60 combined. If Jayden has 7 dimes, determine all possible values for the number of quarters that he could have. Your answer should be a comma separated list of values.
Answers
The possible values of the number of quarters are at least 14 and more.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
1 dime = $0.10
1 quarter = $0.25
Number of dimes = x
Number of quarters = y
Now,
He has at most 25 coins worth at least $4.60 combined.
This means
we can write two inequalities.
x + y ≤ 25 ____(1)
0.10x + 0.25y ≥ 4.60 _____(2)
Now,
From (1) and (2).
x ≤ 25 - y
Substituting in (2).
0.10x + 0.25y = 4.60
0.10 (25 - y) + 0.25y ≥ 4.60
2.5 - 0.10y + 0.25y ≥ 4.60
2.5 + 0.15y ≥ 4.60
0.15y ≥ 4.60 - 2.5
0.15y ≥ 2.1
y ≥ 2.1/0.15
y ≥ 14
This means,
y is at least 14.
Thus,
The possible values of the number of quarters are at least 14 and more.
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Daniel was given a large box of 36 chocolates for his birthday. If he eats exactly 3
chocolates each day, how many chocolates would Daniel have remaining 8 days after
his birthday?
Answers
Answer:12
Step-by-step explanation:
8 times 3 equals 24.24 subtract36 get 12
PLEASE HELP!!! I WILL GIVE BRAINLIEST!!! :) 20 POINTS!!!
5) There are 5 slices of pepperoni pizza, 1 slice of sausage pizza, and 3 slices of cheese pizza left. Without looking, Douglas took a slice of pizza, ate it, and then took another slice.
What's the probability of Douglas eating two of the same kinds of pizza?
6) A drawer contains 10 blue pens, and 10 red pens. Without looking, Mrs. Stanton is going to take one pen from a drawer, use it, and then put it back in the drawer. Then she is going to take another pen from the drawer to use.
What's the probability Mrs. Stanton takes two red pens?
Answers
PLEASE GIVE BRAINLIEST!
thank you and have a good day :)
Answer:
5)1/12
6) 25%
Step-by-step explanation:
5)The odds of Mr Douglas eating two slices of cheese pizza can be calculated by doing 3/(5 + 1 +3) = 1/3
the second slice's odds can be calculated by doing 2/(5+1+2) = 1/4
Multiply these to get the odds of two being eaten
1/4 times 1/3 is 1/12.
6) the odds of her selecting a red pen the first time is 50%. to do it again would be another 50% chance. 50% times 50% is 25%.
The sum of two numbers is 14. The difference of twice the first and the second is -5. What are the two numbers?
Answers
The two numbers are 3 and 11 respectively
How to determine the numbersFrom the information given, we have that
The first number is x
The second number is y
Also,
2x - y = -5
x + y = 14
Make 'x' the subject from equation 2
x = 14 - y
Make 'x' the subject
2(14-y) - y = -5
28 - 2y - y= -5
collect like terms
-3y = -33
y = 11
Substitute the values
x = 3
Hence, the values are 3 and 11
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plss help!
An ice cream shop sold a combined total of 367 ice cream cones in the flavors of chocolate or vanilla. They sold 95 more vanilla cones than chocolate. How many chocolate ice cream cones did they sell?
Answers
Let's first assign variables to the numbers given.
Let the number of vanilla cones be x and the number of chocolate cones be y.We're given:
[tex]x+y=367[/tex][tex]x=y+95[/tex]Plug the second equation into the first one and solve for y:
[tex]x+y=367\\(y+95)+y=367\\2y+95=367\\2y=272\\y=136[/tex]
Therefore, they sold 136 chocolate cones.
AnswerThey sold 136 chocolate ice cream cones.
Y=Chocolate
X+Y=367
95+Y=X
(95+Y)+Y=367
2Y+95=367
-95. -95
2Y=272
Y=136
Chocolate=136
Vanilla=231
out of the 10,000 people who took their driving test for the first time, it was found that 6500 passed the test on the first attempt. estimate the probability that a randomly selected person would pass the driving test on the first attempt.
Answers
To estimate the probability that a randomly selected person would pass the driving test on the first attempt, we can divide the number of people who passed on the first attempt (6500) by the total number of people who took the test (10,000).
Probability = Number of favorable outcomes / Total number of possible outcomes.In this case, the favorable outcome is passing the test on the first attempt, and the possible outcomes are all the people who took the test.
Probability = 6500 / 10000= 0.65
Therefore, the estimated probability that a randomly selected person would pass the driving test on the first attempt is 0.65 or 65%. This means that there is a 65% chance that a randomly selected person from the group of 10,000 would pass the driving test on their first try.
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a plane ticket to beacelona is £175 the price decreased by 6%
how much is the plane ticket now?
Answers
94/100x175
=£164.5
Question 9 Multiple Choice Worth 2 points) (09.06 MC) Sara's kite flew 48 meters in the air. Tayjen's kite flew 5,860 centimeters in the air. How m 00.16 meters 016 meters O106 centimeters 1,060 centimeters
Answers
The difference in height between Sarah and Tayjen kite is 1060 cm (10.6 m)
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
1 m = 100 cm
Sara's kite flew 48 meters in the air. Hence:
Height of Sarah kite = 48 m = 48 m * 100 cm per m = 4800 cm
Tayjen's kite flew 5,860 centimeters in the air. Therefore:
Difference in height = 5860 - 4800 = 1060 cm = 1060 cm * 1 m per 100 cm = 10.6 m
The difference in height is 1060 cm (10.6 m)
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At soccer practice last night, Leroy made 4 times as many penalty kicks as he missed.
Pick the diagram that models the ratio in the story.
If Leroy made 9 more penalty kicks than he missed, how many penalty kicks did he make?
Penalty kicks:
Answers
The model that would model the ratio is 4 : 1
the penalties made is given as 12
How to solve for the penaltiesTo get the penalty kicks that he made given that he made 9 more penalty kicks than he missed
let the penalty kicks be
= x
if he made more than 9 than missed we would have
x + 9 = 4
x = 1
cross multiply
1 (x + 9) = 4 * X
x + 9 = 4x
9 = 3x
x = 3
since x + 9 penalties made
3 + 9 = 12
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Megan dilates ∆JKL about point J by a scale factor of 3/5 to create ∆JNO.
What is the length of segment NO?
Show all work solving for segment NO.
Answers
The measure of the length NO after dilation will be 15.
What is a scale factor?The scale factor is the ratio of the actual size of the image to the new size of the image. It is used to Map the objects like if you want to increase or decrease the size without changing the original shape of the image it is done by the scale factor.
Given that to make JNO, Megan enlarges JKL by a scale factor of 3/5 around point J.
The measure of side NO will be calculated as:-
NO = 3 / 5 x 25
NO = 3 x 5
NO = 15
Therefore, the length of the side NO is 15.
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PLEASE HELP ASAP??!!!
Andrew factored the polynomial 3x²y 6xy² as 3xy(x – 2y). Determine
if he is correct. If he is incorrect, help him fix his error. If he is correct, explain what
he did to get his answer.
Answers
Answer:
He is correct.
Step-by-step explanation:
Shown in picture.
Hope its clear.
The image of a trapezoid is shown.
An isosceles trapezoid with a short base of 3 meters and a height of 5.8 meters. The portion of the large base from the left vertex to the perpendicular is 4 meters. The portion of the large base from the right vertex to the perpendicular is 7 meters.
What is the area of the trapezoid?
Answers
The area of the trapezoid would be 42.5 m².
What is the area of a trapezoid?
The area of a trapezoid is given by the formula:
Area = (1/2) × (sum of the bases) × height
where the bases are the two parallel sides of the trapezoid and the height is the perpendicular distance between the bases.
The parameters of the trapezoid are;
Short base length = 3 m
Height = 5
Large base length = 4 + 3 + 7 = 14 m
Thus;
Area of a trapezoid = 1/2 * (Short base + Large base) * h
Area = 1/2 * (3 + 14) * 5
= 1/2 * 17 * 5
= 42.5 m²
Hence, the area of the trapezoid would be 42.5 m².
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Sorry for the grease LOL was eating a big mac also this is urgent
Jada's grandparents started a savings account for her in 2010. The table shows the
amount in the account each year.
If this relationship is graphed with the year on the horizontal axis and the amount in
dollars on the vertical axis, what is the vertical intercept? What does it mean in this
context?
2
year
2010
2012
2014
2016
1gnibasi
Seadsh
amount in dollars
Answers
The vertical intercept for the table showing the relationship for Jada's grandparents starting a savings account for her is starting savings amount in the account of $ 600.
What is the vertical intercept in a graph ?The vertical intercept in a graph is the point where a line intersects the vertical axis of the coordinate plane. It represents the value of the dependent variable (y) when the independent variable (x) is equal to zero.
The vertical intercept would therefore be first amount in the savings account by Jada's grandparents which is the $ 600. This is the amount when x = 0 or rather when x was the starting year of 2006.
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GUITAR CLASS, HELP ASAP, WILL GIVE BRAINLIEST,
Five horizontal, parallel, equidistant lines with black oval with stem in 3rd space.
What is the name of the note shown above?
A
B
C
G
Answers
The above-shown note is labeled B based on the information provided.
How do you measure the distance between two lines evenly?A point is considered to really be equidistant from both of two other points when they are equally distanced from one another. The distance between any two given points may be calculated using the distance formula utilizing the coordinates of the two points.
What does equidistant mean?Example: Given that points A and B have the coordinates (1, -2) and (5, 6), respectively, determine the midpoint of line segment AB. Find the midpoint's distance between points A and B to confirm it. The midpoint is confirmed to be equally far from points A and B because both of those places are from it.
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A, B, C and D are points on the circumference of a circle, centre O. ED is a tangent to the circle. Angle ODB= 25degrees. Work out angle BAD. You must give a reason for each stage of your working.
Can someone please help!
Thank you
Answers
the angle BAD is 75 degrees and we used the properties of angles in a circle and the tangent-secant theorem to find angle BAD .
To work out angle BAD, we need to use the properties of angles in a circle and the tangent-secant theorem. Here are the steps to solve the problem:
Identify the relevant angles First, we need to draw a diagram to visualize the problem. We have a circle with center O, points A, B, C, and D on the circumference, and tangent ED. Angle ODB is given as 25 degrees. We need to find angle BAD. We can label the angles in the diagram as follows:
Angle AOB = 2x (angle at the center is twice the angle at the circumference)
Angle BCD = x (angles in the same segment are equal)
Angle OBD = 90 degrees (tangent and radius are perpendicular)
Angle OED = 90 degrees (tangent and radius are perpendicular)
Angle ABD = y (we need to find this angle)
Angle BAD = z (we need to find this angle)
Use the sum of angles in a triangle
We notice that triangle ABD is a right triangle, with right angle at B. Therefore, angles ABD and BAD are complementary. That is, ABD + BAD = 90 degrees. Use the tangent-secant theorem
We can use the tangent-secant theorem to find the value of angle ABD. The tangent-secant theorem states that if a tangent and a secant intersect at a point on a circle, then the angle between the tangent and the secant is equal to the half the difference of the intercepted arcs. In our diagram, ED is a tangent, and BD is a secant. Therefore, angle ODB = 25 degrees is half the difference of the intercepted arcs AD and AB. That is, angle ABD = (2x - x)/2 = x/2.
Solve for x
To find x, we can use the fact that the angles in a triangle add up to 180 degrees. Therefore, x + 2x + 90 = 180 (sum of angles in triangle AOB). Solving for x, we get x = 30 degrees.
Find angle ABD and angle BAD
Using the result from step 3, we get ABD = x/2 = 15 degrees. Using the result from step 2, we get BAD = 90 - ABD = 75 degrees.
Therefore, the angle BAD is 75 degrees. In summary, we used the properties of angles in a circle and the tangent-secant theorem to find angle BAD. We noticed that ABD and BAD are complementary, and we used the tangent-secant theorem to find ABD. Then, we solved for x using the fact that the angles in a triangle add up to 180 degrees. Finally, we used the results from steps 2 and 3 to find BAD.
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3. Find the height of the tree below to the nearest foot.
Answers
The height of the tree to the nearest foot is 27 feet.
How to find the height of a tree?The height of the tree can be found as follows:
The height of the tree can be found using trigonometric ratios. Therefore,
let
tan ∅ = opposite / adjacent
Therefore,
opposite side = adjacent tan ∅
Hence,
height of the tree = 20 + x tan 45° = x tan 75°
20 + x tan 45° = x tan 75°
20 tan 45 + x tan 45° = x tan 75°
20 tan 45 = x tan 75° - x tan 45°
20 tan 45 = x(tan 75 - tan 45)
20 tan 45 = x(3.73205080757 - 1)
2.73205x = 20
x = 20 / 2.73
x = 7.32600732601
x = 7.34
Therefore,
height of the tree = x tan 75°
height of the tree = 7.34 × tan 75°
height of the tree = 27.3186119114
height of the tree = 27 ft
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Problem: Solve the equation AB = BC for A, assuming that A, B, and C are square and B is invertible.
I do know how to solve for A to show that it's invertible which is by finding a matrix C such that AC = CA = i, then C = A^-1
Theorem: If A and B are invertible then AB is invertible
(AB)^-1 = B^-1A^-1
Please help in finding B
Answers
Given the equation AB = BC, we want to find B, assuming that A, B, and C are square matrices and B is invertible. We can conclude that B is invertible.
To do this, we will use the fact that if A is invertible, then we can multiply both sides of the equation by its inverse to isolate B:
AB = BC
[tex]A^-1 AB = A^-1 BC[/tex]
B = A^-1 BC
Here, A^-1 is the inverse of A, and it satisfies the equation[tex]A A^-1 = A^-1 A[/tex]= I, where I is the identity matrix. By multiplying both sides of the equation [tex]AB = BC by A^-1[/tex], we obtain the expression for B.
Now, let's consider the invertibility of B. If A and B are invertible, then the product AB is also invertible. This is because the product of two invertible matrices is invertible, and its inverse is given by the formula [tex](AB)^-1 = B^-1A^-1[/tex]. In this case, since[tex]B = A^-1 BC,[/tex] we can conclude that B is invertible.
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Chandra just spends 15 minutes away or math problems she spends the same amount of time on each problem how many minutes does she spend on each problem
Answers
Chandra spends 3 minutes on each math problem if she spends a total of 15 minutes on math problems and spends the same amount of time on each problem
Chandra spends the same amount of time on each math problem. Let's call the amount of time she spends on each problem "t".
We know that Chandra spends a total of 15 minutes on math problems. If she spends the same amount of time on each problem, then the total time spent on all the problems is equal to the number of problems multiplied by the time spent on each problem.
So, we can write the following equation:
total time spent on all problems = number of problems * time spent on each problem
We know that the total time spent on all problems is 15 minutes, so we can substitute this into the equation:
15 = number of problems * t
We don't know the number of problems, but we can solve for t by rearranging the equation:
t = 15 / number of problems
So, the amount of time Chandra spends on each math problem is equal to 15 divided by the number of problems.
For example, if Chandra works on 5 math problems, then the amount of time she spends on each problem is:
t = 15 / 5 = 3
So, Chandra spends 3 minutes on each math problem if she spends a total of 15 minutes on math problems and spends the same amount of time on each problem.
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A rope is tied from the top of a flag pole to the ground. If the rope is 28 ft long and makes a 15 degree angle with the ground, how far away is where it is tied to the base of the flag pole? Round your answer to the nearest hundredth
Answers
The distance of the rope to the base of the flagpole is 27.05 ft.
How to find the distance of the rope to the flag pole?A rope is tied from the top of a flag pole to the ground. If the rope is 28 ft long and makes a 15 degree angle with the ground, the distance of the rope to the base of the flag pole can be calculated as follows:
The situation forms a right angle triangle.
Hence,
using trigonometric ratios,
cos 15° = adjacent / hypotenuse
cos 15° = x / 28
cross multiply
Therefore,
x = 28 cos 15
x = 28 × 0.96592582628
x = 27.0459231361
x = 27.05 ft
Therefore,
distance of the flagpole to the base of the ground = 27.05 ft
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in a study, the data you collect is weight in pounds. what is the level of measurement? nominal ordinal interval ratio
Answers
The level of measurements that the data we collect is weights in pounds is Ratio level.
The Ratio level of measurement: At this level of measurement, observations can have a value of zero as well as equal intervals. Although the characteristics are similar to those of interval level measurement, the zero in the scale distinguishes this sort of measurement from others. In the ratio level of measurement, the divisions between the points on the scale have an equivalent distance between them. We may confidently assert that 20 pounds are twice as heavy as 10 pounds. Ratio variables also have a meaningful zero-point.
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