The rectangle is framed find the area of shaded region if the frame is 2 unit wide
Answers
The area of the shaded region is 20 square units for the given rectangle frame.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
Dimensions of the inside rectangle, are as follows:
Length L₁ = 5 units
Width W₁ = 3 units
Since the frame is 2 units wide,
So, the dimensions of the outside rectangle, are as follows:
Length L₂ = 5 + 2 = 7 units
Width W₂ = 3 + 2 = 5 units
The area of the shaded region = area of the outside rectangle - area of the inside rectangle
The area of the shaded region = L₂ x W₂ - L₁ x W₁
The area of the shaded region = 7 x 5 - 5 x 3
The area of the shaded region = 35 - 15
The area of the shaded region = 20 square units
Thus, the area of the shaded region is 20 square units.
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The question seems incomplete, the missing figure is attached below.
Related Questions
which is a true statement about two numerical sets of data that have negative association
Answers
Answer:
Option D.
Step-by-step explanation:
Negative correlation also called an " inverse correlation " is a relation between 2 variables where-by they behave in opposite manner. When one variable moves ---> in an increasing /\ direction, the other variable moves in a decreasing \/ direction.
Thus, Option D.
The length of the dashed line in the circle
Answers
The length of the dotted line would be 7.922 ft.
What is the diameter of the circle?
The diameter of a circle is the distance across the circle through its center. It is equal to twice the length of the radius, which is the distance from the center of the circle to any point on the circle.
In mathematical terms, if d represents the diameter of a circle, and r represents its radius, we have the formula:
d = 2r
In the given circle, for finding the inner diameter we have to remove the thickness of the circle from outer diameter, we get
q = 17.708 - 4.893 - 4.893
By solving this, we get
q = 7.922
Hence, the length of the dotted line would be 7.922 ft.
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Find the image of the given point
under the given translation.
P(12, 8)
T(x, y) = (x-8, y - 12)
Answers
P(12,8)
Move 8 units to the left (X) and 12 units down(Y).
P'(12-8, 8-12)
P'(4, -4)
If you don't how to do translation try plotting (12,8).
A sample, sized 5, was taken with the following measurements: 5, 10, 2, 7, and 6.
What is the point estimate of the population mean?
Answers
The point estimate of the population mean is 6
What is the point estimate of the population mean?From the question, we have the following parameters that can be used in our computation:
Measurements: 5, 10, 2, 7, and 6.
Sample size = 5
The point estimate of the population mean is the sample size of the mean
Using the above as a guide, we have the following:
Sample mean = Sum/Count
substitute the known values in the above equation, so, we have the following representation
Sample mean = (5 + 10 + 2 + 7 + 6)/5
Evaluate
Sample mean = 6
Hence, the estimate is 6
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To find 15+32,
Kayla adds the ones.
Then she adds the tens.
Then she adds the ones and tens.
5+2=7
1+3=4
7+4=11
Do you agree with Kayla? Yes or No.
Explain by showing your thinking using drawings, numbers, or
words.
Answers
Answer:
no
Step-by-step explanation:
15+32 you would first add the tens
5+2=7
then the ones
1+3 =4
you're answer would then be 47 as the ones come before the tens
PLEASEEE HELP —-> Step 1: Construct a circle through three points not on a line.
a) Points D, E, and F are not in a line. To construct a circle through points D, E, and F, begin by
drawing line segments DE and EF. Then construct the perpendicular bisectors of DE and EF, and
name the point of intersection of the perpendicular bisectors O. How do you know that point O
is the center of the circle that passes through the three points? (10 points)
Answers
Answer:
Step 1: Construct a circle through three points not on a line.
a) Points D, E, and F are not in a line. To construct a circle through points D, E, and F, begin by
drawing line segments DE and EF. Then construct the perpendicular bisectors of DE and EF, and
name the point of intersection of the perpendicular bisectors O. How do you know that point O
is the center of the circle that passes through the three points?
Answer:
Step-by-step explanation:
To show that point O is the center of the circle that passes through points D, E, and F, we can use the property of perpendicular bisectors. The perpendicular bisectors of two chords of a circle bisect the chord and pass through the center of the circle. Since the perpendicular bisectors of DE and EF intersect at point O, it follows that O must be the center of the circle that passes through points D, E, and F.
This property can also be proven using the Pythagorean theorem. Let the radius of the circle be r and let the midpoints of DE and EF be M1 and M2, respectively. Then, OM1 = OM2 = r, and the distance between M1 and M2 is equal to the distance between D and F. By the Pythagorean theorem, the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse, so we have:
OM1^2 + (M1M2)^2 = r^2 + r^2 = 2r^2
Since OM1^2 + (M1M2)^2 is equal to 2r^2, it follows that the distance between M1 and M2 is equal to the diameter of the circle. This means that M1 and M2 are the midpoints of the diameter of the circle, so they must both lie on the circumference of the circle. This, in turn, means that O is the center of the circle that passes through points D, E, and F.
10 inches in 6 hours
80 inches in 2 days
Answers
The relation is a direct variation
How to determine if the relation is a direct variationFrom the question, we have the following parameters that can be used in our computation:
10 inches in 6 hours
80 inches in 2 days
Convert 2 days to hours
So, we have the following representation
10 inches in 6 hours
80 inches in 72 hours
For the relation to be a direct variation, the following must be equal
6/10 = 72/80
Evaluate
0.6 = 0.6
Hence, the relation is a direct variation
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Complete question
Determine if the following relation represents a direct variation
10 inches in 6 hours
80 inches in 2 days
How many solutions does the system have? { � = 5 � + 1 � = − 2 � − 8 ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ y=5x+1 y=−2x−8
Answers
The given system of linear equations has a unique solution.
What are linear equations?A linear equation is an algebraic equation in which each term has an exponent of 1 and when graphed, the result is always a straight line.
Given that, a system of linear equations, y = 5x+1 and y = -2x-8, we are asked to find how many solutions do they have,
The rule for a system of linear equations, a₁x+b₁y+c₁ = 0 and a₂x+b₂y+c₂ = 0 are :-
When the system has a unique solution :-a₁ / a₂ ≠ b₁ / b₂, and the lines intersect at one only point.
When the system has a no solution :-a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂, and the lines are parallel.
When the system has infinite solution :-a₁ / a₂ = b₁ / b₂ = c₁ / c₂, and the lines overlaps.
Checking for the given equations,
y = 5x+1 and y = -2x-8
Converting into standard form of the linear equations,
5x-y +1 = 0 and 2x+y+8 = 0
5/2 ≠ -1
The equation is following the rule of unique solution, also the graph is intersecting at one point, [graph is attached]
Hence, the given system of linear equations has a unique solution.
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Answer:
One solution
Step-by-step explanation:
verify the
identity algebraically.
Answers
Step-by-step explanation:
[tex] \frac{1}{ \sin(x ) } - \frac{1}{ \csc(x) } = \csc(x) - \sin(x) [/tex]
[tex] \frac{ \csc(x) - \sin(x) }{ \csc(x) \sin(x) } [/tex]
[tex] \csc(x) - \sin(x) = \csc(x) - \sin(x) [/tex]
Add Decimals-Instruction - Level E
June makes slime using 1.5 liters of white glue and 0.72 liter of a starch and water mixture.
Find the total volume of the slime.
Are there enough hundredths to make a tenth?
➡ There are ? hundredths. That is
enough to make a tenth.
✓is
is not
Answers
➡ There are 22 hundredths. That is enough to make a tenth.
What is the arithmetic operations?
Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms,[disputed – discuss] which are highly important to the field of mathematical logic today.
The four basic mathematical operations are Addition, subtraction, multiplication, and division.
To find the total volume of the slime, we need to add 1.5 and 0.72:
1.5 + 0.72 = 2.22
There are 22 hundredths, which is enough to make a tenth.
Hence, the answer is:
➡ There are 22 hundredths. That is enough to make a tenth.
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PLEASEEE HELP —-> Step 1: Construct a circle through three points not on a line.
a) Points D, E, and F are not in a line. To construct a circle through points D, E, and F, begin by
drawing line segments DE and EF. Then construct the perpendicular bisectors of DE and EF, and
name the point of intersection of the perpendicular bisectors O. How do you know that point O
is the center of the circle that passes through the three points? (10 points)
Answers
Answer:
Step-by-step explanation:
To show that point O is the center of the circle that passes through points D, E, and F, we can use the property of perpendicular bisectors. The perpendicular bisectors of two chords of a circle bisect the chord and pass through the center of the circle. Since the perpendicular bisectors of DE and EF intersect at point O, it follows that O must be the center of the circle that passes through points D, E, and F.
This property can also be proven using the Pythagorean theorem. Let the radius of the circle be r and let the midpoints of DE and EF be M1 and M2, respectively. Then, OM1 = OM2 = r, and the distance between M1 and M2 is equal to the distance between D and F. By the Pythagorean theorem, the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse, so we have:
OM1^2 + (M1M2)^2 = r^2 + r^2 = 2r^2
Since OM1^2 + (M1M2)^2 is equal to 2r^2, it follows that the distance between M1 and M2 is equal to the diameter of the circle. This means that M1 and M2 are the midpoints of the diameter of the circle, so they must both lie on the circumference of the circle. This, in turn, means that O is the center of the circle that passes through points D, E, and F.
6 3/14 divided by 250 + 5 2/7 divided by 250
Answers
Answer:
The solution is 23/500 or 0,046
Step-by-step explanation:
6 3/14÷250+5 2/7÷250
= 6 3/14×1/250+5 2/7×1/250
= (87/14×1/250)+(37/7×1/250)
= (87/3500)+(37/1750)
= 87+37(2)/3500
= 87+74/3500
= 161/3500
= 161÷7/3500÷7
= 23/500
= 0,046
carrie is cutting sheets of stickers to put in 4 gift bags Each bag will contain the same number of stickers . if each sheet contains 22 stickers then what is the fewwer number of sheets carrie can use so there are no stickers left over
Answers
Carrie is slicing sticker sheets to fit four present bags. There will be an equal quantity of stickers in each bag.
What is fewer number?The word "fewer" is represented by the Greek letter "," which denotes that one thing is less than another. Any number bigger than another is indicated by the sign >. In this case, 6 10 demonstrates that 6 is less than 10. According to this, 6 is less than 10 in size.A rule concerning fewer and less is frequently cited. As an example, "fewer options" and "fewer issues" relate to the quantity or amount among things that are counted, whereas "less time" and "less work" refer to the quantity or amount among things that are measured. Lesser simply indicates "not as many."To learn more about fewer number refer to:
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The accompanying data represent the miles per gallon of a random sample of cars with a three-cylinder, 1.0 liter engine.
(a)
Compute the z-score corresponding to the individual who obtained miles per gallon. Interpret this result.
(b)
Determine the quartiles.
(c)
Compute and interpret the interquartile range, IQR.
(d)
Determine the lower and upper fences. Are there any outliers?
Answers
a) The value of z-score is -0.299.
c) The IQR value is measure of spread of data, IQR = 4.25.
d) There is outliers since observations are not less than 30.375 and greater than 47.375.
What is z- score?The z-score is an example of a standardised score. The standard deviation of a data point's divergence from the mean of the distribution is calculated using a z-score.
Given:
Sample Data = 31.5, 36.0, 37.8, 38.5, 40.1, 42.2, 34.2, 36.2, 38.1, 38.7, 40.6, 42.5, 34.7, 37.3, 38.2, 39.5, 41.4, 43.4, 35.6, 37.6, 38.4, 39.6, 41.7, 49.3
(a) The value of z-score is calculated as follows,
μ = [tex]\sum _{i=1}^n[/tex]/ n = 933.1 /24 = 38.88
σ = 3.61
So, z = X - μ / σ
= 37.8 - 38.88/3.61
= − 0.299
(b) Quartile:
Q₁ = ( n+1/4)th value
= (24+1/4)th
= 6.25th
= 36.2 + 0.25 x ( 37.3 − 36.2 )
= 36.47
and, M = ( n+1/2)th value
= (24+1/2)th
= (24+1/4)th
= 12.5 t h
= 38.4 + 38.5/2
= 38.45
Q₃ = 3( n+1/4)th
= 3(24+1/4)th
= 18.75 t h
= 40.6 + 0.75 x ( 41.4 − 40.6 )
= 41.2
(c) Interquartile range
= Q ₃ − Q ₁
= 41.2 − 36.47
= 4.25
(d) Lower fences = Q₁− 1.5 ( I Q R )
= 36.75 − 1.5 ( 4.25 )
= 30.375
Upper fences = Q ₃+1.5
= 41 + 1.5( 4.25 )
= 47.375
Hence, there is outliers since observations are not less than 30.375 and greater than 47.375.
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Circle the pair of like fractions 4/6and5/6and1/2and3/4and1/3and2/6 and1/10and2/100
Answers
The required pair of the like fraction among the given fraction is given as 1/3 and 2/6.
What is the fraction?A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers.
Here,
For pairs of fraction area given we have to determine that fair of like fraction,
So we have to simplify the fraction given in the pair,
1. 4/6 and 5/6 = 2/3 and 5/6which not like pair of fraction, Similarly pairs [1/2 and 3/4] and [1/10and2/100] are not like fractions.
Now,
3. pair 1/3and2/6 is like fractions because 1/3 = 2/6 (=1/3)
Thus, the required pair of the like fraction among the given fraction is given as 1/3 and 2/6.
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what is statistics?
Answers
Statistics is referred to as a discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
What is Data?This is referred to as information that has been translated into a form that is efficient for movement or processing.
Statistics involves using information that has been translated into a form that is efficient for movement or processing through different tools such as mean standard deviation etc.They help to provide more details about a set of data which makes it use very important.
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Write 15*15*15*15 using an exponent
Answers
Answer:
15^4
Step-by-step explanation:
An exponent refers to the number of times a number is multiplied by itself,
so 15 multiplied 3 more times by itself (15 * 15 * 15 * 15) its 15^4.
[tex]15^{4} .[/tex]
Step-by-step explanation:1. General concept about exponents.When working with positive non fractional exponents, we state that a number A elevated to the n power is that number A in a multiplication of itself n times. For example, when we write [tex]7^{3}[/tex] we're stating that the seven is being multiplied 3 times: [tex]7*7*7[/tex].
2. Use the rule to rewrite the expression.As you may see, the expression "15*15*15*15" is just the number 15 being multiplied by itself four times. Hence, we could say that the number 15 to the power of 4. Thus, we can rewrite it as:
[tex]15^{4} .[/tex]
Charles and some friends ate at the Winterfield Café. Their bill was $50.00$ They paid $60.00. What percentage gratuity did they pay?
Answers
The percentage of gratuity paid is 20%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Amount for the bill = $50
Amount paid = $60
The amount of gratuity.
= 60 - 50
= $10
Now,
The percentage of gratuity.
= 10/50 x 100
= 20%
Thus,
The percentage of gratuity is 20%.
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A bag with 12 marbles has 12 blue marbles,a marble is chosen from the bag,What's the probability is blue
Answers
100%, If 12 of all 12 marbles are blue, its 100%
Can someone please help me with this I can’t figure it out
Answers
Answer:
69
Step-by-step explanation:
if it bisects that mean both angles are equal which tells us we can just divide the whole angle by 2
angle BOA is 138
so when you divide 138 by 2 you get 69
hope it helped
please mark brainiest
The price (in S) of a cookbook is determined by the number of cookbooks x demanded by consumers and supplied by the publisher.
Supply: p=0.003.x
Demand: p= -0.008x+330
(a) Solve the system of equations defined by the supply and demand models.
(b) What is the equilibrium price?
(c) What is the equilibrium quantity?
Answers
The system of equations defined by the supply and demand models solved for equilibrium price is $9 and equilibrium quantity is 3000 units
How to solve system of equation?Supply:
p=0.003x
x = p/0.003
x = 1/0.003p
Demand:
p= -0.008x+330
-0.008x = p - 330
x = (p - 330)/-0.008
Equilibrium price
Equate supply and demand price
0.003x = -0.008x+330
0.003x + 0.008x = 330
0.011x = 330
x = 330/0.11
x = 3,000
Substitute into
p=0.003x
p = 0.003(3000)
p = $9
Consequently, the equilibrium quantity and price is 3000 units and $9
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Find the area of a rectangle with side lengths 5/8ft. and 1/3 ft.
A. 5/11
B. 1 11/12
C. 6/11
D. 5/24
Answers
The area of a rectangle with side lengths 5/8ft. and 1/3 ft is: D. 5/24 ft².
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.W represents the width or base of a rectangle.L represents the length or height of a rectangle.Substituting the given points into the area of rectangle formula, we have the following;
Area of rectangle = 5/8 × 1/3
Area of rectangle = 5/24 square feet.
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Given the function g(n) = 2 n4 + 20 n3 + 42n2
Its g-intercept is
Its n intercepts are
Answers
The g-intercept of the function g(n) is 0.
The n-intercepts of the function g(n) are n = 0, n = -3, and n = -7.
What is a function?
In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the range), such that each input is related to exactly one output.
To find the g-intercept of a function, we need to determine the value of g when n = 0. So, to find the g-intercept of the function g(n) = 2n⁴+ 20 n³ + 42n², we can simply substitute n = 0 into the function:
g(0) = 2(0)⁴ + 20 (0)³ + 42(0)² = 0
Therefore, the g-intercept of the function g(n) is 0.
To find the n-intercepts of a function, we need to determine the values of n for which g(n) = 0. In other words, we need to solve the equation 2n⁴+ 20 n³ + 42n² = 0.
We can factor out a common factor of 2n² to simplify the equation:
2n²(n² + 10n + 21) = 0
This equation is true when either 2n² = 0 (which implies n = 0), or when n² + 10n + 21 = 0. The quadratic equation n² + 10n + 21 = 0 can be factored as (n + 3)(n + 7) = 0, so its solutions are n = -3 and n = -7.
The n-intercepts of the function g(n) are n = 0, n = -3, and n = -7.
Hence,
The g-intercept of the function g(n) is 0.
The n-intercepts of the function g(n) are n = 0, n = -3, and n = -7.
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Find the distance the point P(3, 1, 7), is to the plane through the three points
Q(5, 0, 3), R(0, -1, 7), and S(7, 5, 0).
Answers
The distance between the point P and the plane through the points Q, R, and S is 60/23.
How did we get the value?The distance of a point P(x1, y1, z1) from a plane that passes through the points Q(x2, y2, z2), R(x3, y3, z3), and S(x4, y4, z4) can be found using the following formula:
d = |(A * x1 + B * y1 + C * z1 + D) / sqrt(A^2 + B^2 + C^2)|
Where A, B, and C are the coefficients of the plane's normal vector and D is the constant term in the equation of the plane. The normal vector can be found by taking the cross product of the vectors Q-R and Q-S:
n = (Q-R) x (Q-S)
The coefficients of the normal vector can be found using the following equations:
A = n1
B = n2
C = n3
D = -(A * x2 + B * y2 + C * z2)
Substituting the values of Q, R, and S, we have:
Q-R = (5-0, 0-(-1), 3-7) = (5, 1, -4)
Q-S = (7-5, 5-0, 0-3) = (2, 5, -3)
The cross product of Q-R and Q-S is:
n = (1 * -3 - 5 * -4, -3 * 5 - 2 * -4, -2 * 1 - 5 * 5) = (-23, 29, 17)
So,
A = -23
B = 29
C = 17
D = -(A * x2 + B * y2 + C * z2) = -(-23 * 5 + 29 * 0 + 17 * 3) = -109
Finally, substituting the values of x1, y1, and z1:
d = |(A * x1 + B * y1 + C * z1 + D) / √(A^2 + B^2 + C^2)|
= |(-23 * 3 + 29 * 1 + 17 * 7 + -109) / √(-23^2 + 29^2 + 17^2)|
= |(-69 + 29 + 119 -109) / √(-23^2 + 29^2 + 17^2)|
= |60 / √(-23^2 + 29^2 + 17^2)|
= |60 / √(529)|
= 60 / 23
So the distance between the point P and the plane through the points Q, R, and S is 60/23.
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suppose you are one of 19 people at a dinner party. Find the probability that at least one of the other guests has the same birthday as you and that some pair of guests share the same birthday assume there are 365 days in the year
The probability that at least one other guest shares your birthday is approximately?
The probability that some pair of guests share the same birthday is approximately?
Answers
The solution is 0.3486 or 34.86%, chance that exactly one other guest has the same birthday as you.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
For each guest, the probability that they share a birthday with you is 1 in 365. Aside from you, there are 499 guests.
Therefore, this problem can be modeled by a binomial probability model with probability of success 1/365.
The probability of exactly 1 success in 499 trials is given by:
P(x=1) = 0.3486
There is a 0.3486 or 34.86% chance that exactly one other guest has the same birthday as you.
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If x=3. what is y=?
Y=
X: -3 0 3 6
Y: -5 -4 -3 -3
Answers
Answer:
Step-by-step explanation:
y = -3
Suppose that 71% of the surface of the Earth is covered in water, and a random number generator uses latitude and longitude to select a random location on the Earth. If 7 such locations are generated, what is the probability that the first 5 locations are in water and the last 2 locations are on land?
A. 0.0010
B. 0.0152
C. 0.0910
D. 0.9090
Answers
Answer:
0.0152 is the probability that the first 5 locations are in water and the last 2 locations are on land.
6.88 + 3w= 17.98 find w
Answers
Answer:
3w= 17.98-6.88
3w=11.1
w =3.7
Step-by-step explanation:
After subtracting divide both side by 3
Answer:
w = 3.70
Step-by-step explanation:
Given that,
6.88 + 3w= 17.98 ..........(1)
Now subtracting both sides by 6.88 in equation (1), We have
6.88 + 3w - 6.88 = 17.98 - 6.88
or, 3w + 0 = 11.1
or, 3w = 11.1
Again dividing both sides by 3 in the above equation, We have
[tex]\frac{3w}{3}=\frac{11.1}{3} = 3.70[/tex]
Hence the required answer is w = 3.70
Solve the triangle. Round to the nearest tenth.
Answers
In the given triangle, ∠F=29°, d>15 and e<15.
What exactly is a triangle?
Triangles are polygons in geometry that have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle. The triangle is classified into six forms based on its sides and angles.
A triangle is categorised into three categories based on its sides, namely:
Scalene Triangle - Each side has a distinct length.
Isosceles Triangle - A triangle with two sides of equal length and one side of a different length.
Equilateral Triangle - A triangle has three sides that are of the same length.
A triangle is categorised into three categories based on its angles, namely:
Acute Angle Triangle - A triangle with all of its angles smaller than 90°.
Obtuse Angle Triangle - A triangle with one of its angles larger than 90°.
Triangle with a Right Angle - A triangle with one of its angles equal to 90°.
Now
As sum of all angles of triangle=180°
∠F+127°+24°=180°
∠F=180-151
∠F=29°
and In a triangle Largest angle is opposite to largest side and smallest angle is opposite to smallest side.
Then the sides e and d will be as following d>15 and e<15.
hence,
In the given triangle, ∠F=29°, d>15 and e<15.
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Solve the equation in the complex number system. X^2+x+8=0
(Simplify your answer. Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
Answers
Answer:
Step-by-step explanation:
here's a step-by-step explanation with more detail:
The equation X^2 + X + 8 = 0 can be solved using the Quadratic Formula:
X = (-b ± √(b^2 - 4ac)) / 2a,
where a = 1, b = 1, and c = 8.
Plugging in the values, we get:
X = (-1 ± √(1^2 - 4 * 1 * 8)) / 2 * 1
X = (-1 ± √(-31)) / 2
Since the square root of a negative number is not a real number, the solution to the equation must be expressed using complex numbers. In this case, the square root of -31 can be expressed as the imaginary unit i times the square root of 31.
X = (-1 ± i * √31) / 2
So, the two solutions to the equation are:
X = (-1 + i * √31) / 2 and X = (-1 - i * √31) / 2
And these are the two solutions expressed in terms of the imaginary unit i.
