The requried solutions are as follows,
(1) the original price is $450. (2) the original price is $172.40.
Sale price is defined as the price of a product marked including of various price cut such as discounts.
Here,
If the percent of discount is 80% and the sale price is $90, we can use the following formula to find the original price x (let)
Sale price = Original price - Discount
$90 = x - 0.8x
Simplifying the right-hand side:
$90 = 0.2x
x = $450
Therefore, the original price is $450.
If the percent of discount is 15% and the sale price is $146.54, we can use the same formula:
Sale price = Original price - Discount
$146.54 = x - 0.15x
Simplifying the right-hand side:
$146.54 = 0.85x
x = $172.40
Therefore, the original price is $172.40.
Learn more about sale price here:
https://brainly.com/question/2984088
#SPJ9
Last year, Becky's dog weighed 55 pounds. One year later, she had gained p pounds. Which expression gives her weight one year later?'
Answer: 55+p
Step-by-step explanation: Since p is in unlike terms as 55, you can just write that as is an the expression to represent the dog's weight.
Fifteen gallons of gas cost $50.25. What is the price per gallon
Answer:
$3.35
Step-by-step explanation:
$50.25 ÷ 15 gallons = $3.35 a gallon
What is the surface area of the net shown below?
▸
8 ft
3 ft
3 ft
3 ft
The surface area of the net is 108 squate feet
How to determine th surface area of the netThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
A net that has the following shapes
Rectangle: 8ft by 12 ftTwo triangles: 3ft by 4ftThe area of the net is the sum of the individual areas
So, we have
Area = 8 * 12 + 2 * 0.5 * 3 * 4
Evaluate
Area = 108
Hence, teh area is 108 squate feet
Read more about area at
https://brainly.com/question/22972014
#SPJ1
A student has completed 3 tests in biology class. How many points above her present test average must she
score on the fourth test in order to raise her test average 4 points?
OA. 7
OB. 9
OC. 12
O D. 16
OE. 20
The student must she score on the fourth test in order to raise her test average 4 points is 4 points.
What is average?An average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.
Given that, a student has completed 3 tests in biology class, we need to find that how many points above her present test average must she score on the fourth test in order to raise her test average 4 points,
Let the required point be x,
According to question,
x+4×3 / (3+1) = 4
x+12 = 16
x = 4
Hence, the student must she score on the fourth test in order to raise her test average 4 points is 4 points.
Learn more about average, click;
https://brainly.com/question/24057012
#SPJ1
Neeeeeed hellppppppppll
To draw a centroid for ΔABC, follow the steps below.
Draw the triangle ABC with the line segment CD bisecting it. Line segment CD is called a median and it connects the midpoint of side AB to the opposite vertex, C.Using a protractor, measure the distance between B and C, place the protractor on C and make an arc on both sides of the triangle. Place the protractor on B and repeat the same step. place your ruler such that the ruler is actactly in between the twin arcs on both sides of the triangle, mark the point where the ruler crosses the line segment BC.Call this point long BC point x.repeat this for LIne segment AC.Call the point on line AC y.Draw another line segment from point B to the midpoint of side BC, that is point x and repeat same for point y.The intersection point of line segments CD and XY is the centroid of the ΔABC. Label this point as G.
See the sample attached. Note that this is not constructed to scale.
What is a Centroid?The centroid is the point where the three medians of a triangle intersect.
A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. In this case, line segment CD is one of the medians of triangle ABC because it connects the midpoint of AB (which is also the midpoint of CD) to vertex C. The other two medians connect the midpoints of the other two sides to their opposite vertices.
Learn more about Centroid:
https://brainly.com/question/10708357
#SPJ1
next, place point a on the graph to demonstrate how many trips kathy will take if the price is $230 per round-trip ticket. c. if the price of a round-trip ticket is $230, how many trips should kathy take?
Kathy should take 4 trips if the price of a round-trip ticket is 230.
Point A on the graph would be placed at (230, 4). This demonstrates that Kathy should take 4 trips if the price of a round-trip ticket is 230. This can be calculated as follows:
Kathy has a budget of 1,000. Therefore, she can afford 4 round-trip tickets at the price of 230 each. This can be calculated by dividing 1000 by 230, which gives 4. Therefore, Kathy should take 4 trips if the price of a round-trip ticket is 230.
It is important to note that Kathy should also consider other factors such as the cost of other expenses, such as accommodation and food, when deciding how many trips to take. Additionally, Kathy may also want to consider whether the benefits of taking more trips are worth the additional cost.
Learn more about graph here:
https://brainly.com/question/17267403
#SPJ4
A moderately active 40-pound dog needs an average of 1,215 calories per day. Taryn's dog participated in a dog race this morning, so it will need more than the average calories. Taryn's dog has already eaten 729 calories, and she feeds her dog 243 calories per meal.
243x + 729 > 1,215
How many more meals does Taryn need to feed her dog today? A.
x > 3
B.
x > 243
C.
x > 729
D.
x > 2
help please its due today
The amount of extra meals that Taryn needs to feed her dog today is given by the inequality expression; x > 2
How to solve Inequality word problems?The parameters given in the question are;
Weight of dog = 40 pounds
Average amount of calories required per day = 1215 calories
Amount of calories already eaten = 729 calories
Amount of calories fed per meal = 243 calories
The inequality that represents the given word problem is;
243x + 729 > 1215
Subtract 729 from both sides to get;
243x > 486
divide both sides by 243 to get;
x > 2
Read more about Inequality word problems at; https://brainly.com/question/25275758
#SPJ1
amit took part in an cycle race .he started at 1:25 pm and reached the finishing line at 1:50 . what was the duration of the race ?
amit took a part in cycle race .he started at 1:25 and he reached finishing lline at 1:50 pm what was the duration of the race .
Answer:
25 minutes
Step-by-step explanation:
The time difference between 1:25 and 1:50 is 25 min
2. Choose one of the pair of starting angles in the table below::
(a = 50 degrees
y = 110 degrees)
(a= 30 degrees
b=70 degrees)
(c =30 degrees
y=120 degrees)
Please note you are only using 1 of the the selections above, and they will give different results
(a) What is the angle measurement of first unknown angle? Explain the angle relationship you used.
(b) What is the angle measurement of second unknown angle? Explain the angle relationship you used.
Hint: Remember to start with a relationship where you have one unknown.
(a) The angle measurement of first unknown angle is c = 80 degrees
(b) The angle measurement of second unknown angle is y = 110 degrees
How to find the angle measurement of first unknown angle?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
(a) You can pick pair of starting angles a = 30 degrees and b = 70 degrees
The angle measurement of first unknown angle will be:
a + b + c = 180 (sum of angles in a triangle is 180 degrees)
c = 180 - a - b
c = 180 - 30 - 70
c = 80 degrees
(b) The angle measurement of second unknown angle will be:
y = 180 - b (sum of angles on a straight line is 180 degrees)
y = 180 - 70
y = 110 degrees
Learn more about Trigonometry on:
brainly.com/question/11967894
#SPJ1
The t-value changes depending on the number of data points collected.
a. True
b. False
The statement that " t-value changes depending on the number of data points collected" is (b) False because t-value is a statistic that is used in hypothesis testing to determine the difference between 2 sample means is significant or not.
The t-value does depend on the sample size (number of data points) as well as the sample mean and standard deviation, but it does not change "depending on" the number of data points in the sense that the same data set will always produce the same t-value for a given statistical test.
So , it is important to note that the t-value is a fixed value for a given set of data, regardless of the number of data points collected.
Therefore, if the same data set is used to perform a t-test multiple times, the resulting t-value will always be the same.
Learn more about t-Value here
https://brainly.com/question/29844684
#SPJ4
I need help…………………………….
a) The Equation is 7.65x + 50 = 149.45.
b) The customer used the car for 13 hours.
c) If the car used for 2 days i.e., 48 hours then the amount will be $471.12
What is equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given that;
Members of a car sharing program pay a fee of $50 per month plus $7.65 for every hour they use a car.
And, a members bill was $149.45 last month.
a) Let number of hours for the customer use a car last month = x
So, 7.65x + 50 = 149.45
7.65x = 149.45 - 50
7.65x = 99.45
x = 13
b) The customer used the car for 13 hours.
c) If the car used for 2 days i.e., 48 hours
= 7.65x + 50
= 7.65(48)+ 50
= 471.2
Learn more about the Equation here:
https://brainly.com/question/1679555
#SPJ9
help with question 17
Answer:
hundredths
Step-by-step explanation:
a wall street journal subscriber survey asked 46 questions about subscriber characteristics and interests. state whether each of the following questions provides categorical or quantitative data. (a) what is your age? categorical quantitative (b) are you male or female? categorical quantitative (c) when did you first start reading the wsj? high school, college, early career, mid career, late career, or retirement? categorical quantitative (d) how long have you been in your present job or position? categorical quantitative (e) what type of vehicle are you considering for your next purchase? nine response categories include sedan, sports car, suv, minivan, and so on. categorical
a) "What is your age?" is a quantitative data.
b) "Are you male or female?" is a categorical data.
c) "When did you first start reading the wsj?" is a categorical data.
d) "How long have you been in your present job or position?" is a quantitative data.
e) "What type of vehicle are you considering for your next purchase?" is a categorical data.
(a) "What is your age?" - This question provides quantitative data because age is a numerical value that can be measured and ordered in a meaningful way. Respondents could give an answer such as "25", "45", or "70", for example, which can be used to calculate statistics such as the mean or median age of the survey population.
(b) "Are you male or female?" - This question provides categorical data because the responses fall into discrete, non-numeric categories (in this case, "male" or "female"). It's not possible to order the responses in a meaningful way, since there is no inherent numerical value associated with being male or female.
(c) "When did you first start reading the WSJ?" - This question provides categorical data because the possible responses fall into discrete, non-numeric categories (high school, college, early career, mid career, late career, or retirement). While it's possible to order the categories in a logical sequence, they don't represent numerical values.
(d) "How long have you been in your present job or position?" - This question provides quantitative data because the responses can be measured as numerical values (for example, "3 years", "10 years", or "25 years"). The data can be used to calculate statistics such as the average length of time that respondents have been in their current position.
(e) "What type of vehicle are you considering for your next purchase?" - This question provides categorical data because the possible responses fall into discrete, non-numeric categories (sedan, sports car, SUV, minivan, etc.). While it's possible to order the categories in a logical sequence based on size, price, or other factors.
To learn more about data click on,
https://brainly.com/question/13191929
#SPJ4
what number when divided by 15 20 30 the remainder is always 8
The number when divided by 15, 20, and 30 and the remainder is always 8 will be 68.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The number which is divisible by 15, 20, or 30 will be given as,
LCM of the numbers 15, 20, and 30 will be given as,
2 | 15, 20, 30
2 | 15, 10, 15
3 | 15, 5, 15
5 | 5, 1, 5
1, 1, 1
LCM = 2 x 2 x 3 x 5
LCM = 60
The number whose remainder is always 8 is given as,
⇒ 60 + 8
⇒ 68
The number when divided by 15, 20, and 30 and the remainder is always 8 will be 68.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ9
Please help I don't understand.
The surface area of the sphere is 113.2 ft².
Surface area of the Sphere:The area that a sphere's outer surface covers in three dimensions is known as the surface area of the Sphere. A sphere is a three-dimensional solid that resembles a circle in shape and is round.
The formula for a sphere's total surface area is given by
Surface area = 4 π r² square unitsHere we have
The formula for the radius of a sphere r = 1/2 [√S/π]
Diameter of the Moeraki boulder radius = 3 feet
=> 3 feet = 1/2 [√S/π]
=> 6 = [√S/π]
Squaring on both sides
=> 36 = [√S/π]²
=> S/π = 36
=> S = 36π
=> S = 113.2
Therefore,
The surface area of the sphere is 113.2 ft².
Learn more about surface area
https://brainly.com/question/14692728
#SPJ1
A book shop advertises that they will discount their maths book by 3/8 of the retail price what would the sale price of a book with a retail of R 100 and what would be sale price of a book with a retail of R 88
The Selling price of a book with a retail of R 100 and R 88 will be 99.625 and 87.625 respectively.
The selling price of a good or service is the final cost to the seller, or what the buyer actually pays. A commodity or service in a specific amount, weight, or measurement can be exchanged.
It is one of the most crucial things for a business to decide. It is significant since it determines whether or not it will survive. Sales of a product are directly impacted by its price.
According to the question,
Discount = 3/8 of the retail price.
Now,
When retail price is 100,
Selling price [tex]= 100-3/8[/tex]
[tex]=99.625[/tex]
When retail price is 88.
Selling price [tex]= 88-3/8[/tex]
[tex]=87.625[/tex]
To learn more about Selling price visit;
https://brainly.com/question/28017453
#SPJ4
Express 0.10670.10670, point, 1067 as a fraction.
Answer: 1067/10000 is a fraction in simplest form. where, 0.1067 is a decimal, 10.67% is a percentage.
Step-by-step explanation:
Bunolo ran a 10km race her average speed was 6km per hour how long did it take her in minutes to complete the race
It took Bunolo 100 minutes (or 1 hour and 40 minutes) to complete the 10 km race at an average speed of 6 km/h.
To find out how long it took Bunolo to complete a 10 km race with an average speed of 6 km/h, we can use the formula:
time = distance / speed
where "distance" is the distance of the race and "speed" is the average speed at which Bunolo ran. We can convert the speed to km/minute to get the time in minutes.
To do this, we can divide the speed in km/hour by 60 (the number of minutes in an hour) to get the speed in km/minute:
6 km/hour ÷ 60 minutes/hour = 0.1 km/minute
Now, we can substitute the distance and speed values into the formula to get the time in minutes:
time = 10 km / 0.1 km/minute = 100 minutes
Therefore, To complete the 10 km race with the average speed of 6 km/h, it took Bunolo 100 minutes.
To learn more about time click on,
https://brainly.com/question/11164138
#SPJ4
shawna knows that a correlation between calories of sweeteners consumed and mortality rates among women does not, in itself, mean that drinking more soft drinks will lead to a higher chance of her dying. which of the following would not be a lurking variable in the above scenario? a.) shawna's weight b.) the time of day shawna exercises c.) the number of soft drink brands available for purchase d.) the amount of caffeine available in soft drinks
Answer: Musical preferences
A variable is a lurking variable if it can influence an explanatory/response relationship. So it must be related to both the explanatory and response variable. It is not likely your musical preferences affect mortality or how much sweetener you consume.
The number of soft drink brands available for purchase is not a lurking variable in this scenario. Correct option is C.
The statement is asking which of the given variables is not a lurking variable in the scenario where Shawna is considering the correlation between the calories of sweeteners consumed and the mortality rates among women, and is trying to determine whether drinking more soft drinks will lead to a higher chance of her dying.
A lurking variable is a variable that is not included in the analysis, but has an effect on the relationship between the variables being studied. In this case, the variables being studied are the calories of sweeteners consumed and the mortality rates among women, and the effect of drinking more soft drinks on the chances of dying.
Out of the given variables, the number of soft drink brands available for purchase would not be a lurking variable, as it does not have an effect on the relationship being studied.
Shawna's weight, the time of day she exercises, and the amount of caffeine available in soft drinks could all potentially have an effect on the relationship being studied, either as confounding variables or moderators.
For example, Shawna's weight could be a confounding variable, as it is associated with both sweetener consumption and mortality rates. The time of day she exercises could be a moderator, as exercise may affect the metabolism of sweeteners and caffeine, which could in turn affect mortality rates.
The amount of caffeine available in soft drinks could be a confounding variable, as caffeine consumption is associated with both sweetener consumption and mortality rates.
In summary, the number of soft drink brands available for purchase is not a lurking variable in this scenario, while Shawna's weight, the time of day she exercises, and the amount of caffeine available in soft drinks could potentially be confounding variables or moderators that need to be accounted for in the analysis.
To learn more about correlation click on,
https://brainly.com/question/30087784
#SPJ4
Use a graphing calculator to find an equation of the line of best fit for the data. Round the slope to the nearest tenth and the y-
intercept to the nearest integer.
X
y
y =
5 6
12 -2
r=
7
00
8 9 10 11 12
3
-1-4
6
0
Identify the correlation coefficient. Round to the nearest thousandth if necessary.
An equation of the line of best fit for the data is y = -0.9x + 13.6.
The correlation coefficient (r) for the data to the nearest thousandth is -0.964.
How to determine an equation of the line of best fit for the data?In order to determine a linear equation in slope-intercept form for the line of best fit that models the data points described above, we would use a scatter plot (graphing calculator).
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the data set, a linear equation for the line of best fit is given by:
y = -0.895x + 13.600.
Rounding up as required, we have:
y = -0.9x + 13.6.
Read more on scatter plot here: brainly.com/question/28605735
#SPJ1
Complete Question:
Use a graphing calculator to find an equation of the line of best fit for the data in the table. Round the slope and y-intercept to the nearest tenth. Then Identify and interpret the correlation coefficient.
X- 10.1 9.8 9.7 9.4 8.9 8.7 8.4 8.1
Y- 4.3 4.8 5.3 5.2 5.6 5.8 6.1 6.3
The equation of the line of best fit is y=
To the nearest thousandth, the correlation coefficient is r=
What is the GCF of 4454 and 121j²k?
O 4j³k²
O 4j²k4
O 11j³k²
O 11j²4
The required, there is no highest common factor between 4454 and 121j²k. None of the options are correct.
What is the greatest common factor?The highest common factor (HCF) of two or more numbers is the largest number that divides all of the numbers exactly.
Here,
To find the greatest common factor (GCF) of 4454 and 121j²k, we need to factor both numbers into their prime factors and then identify the common factors.
Since 4454 is an even number and 121 is an odd number so there is no prime highest common factor between the given number.
Thus, none of the options are correct.
Learn more about greatest common factors here: https://brainly.com/question/11221202
#SPJ9
describe to use or importance of points , lines , and planes in daily life
Points, lines and planes can be used in different fields like Navigation, Architecture, Art, Engineering, etc.
What are points, lines, and planes?
Point: A point is a basic geometric object that represents a specific location in space.
Line: A line is a straight path that extends infinitely in both directions. It is made up of an infinite number of points that are all collinear, or lie on the same straight path.
Plane: A plane is a two-dimensional flat surface that extends infinitely in all directions.
Navigation: Points and lines are essential for navigation, both on land and in the air. For example, on a map, points represent specific locations, while lines represent roads, highways, and other paths that can be taken to get from one point to another.
Architecture and Design: Points, lines, and planes are critical for architecture and design. Architects use points to specify the locations of walls, columns, and other structural elements, while lines are used to create the edges of rooms and buildings. Planes are used to define the surfaces of walls, floors, and ceilings.
Art: Artists often use points, lines, and planes to create visual effects in their work. Points can be used to create texture, while lines can be used to create movement and depth. Planes can be used to create shapes and form.
Engineering: Points, lines, and planes are fundamental to engineering, which involves the design and construction of structures and machines. Engineers use points to specify the locations of components, while lines are used to create the edges of parts. Planes are used to define the surfaces of structures, such as the wings of an airplane.
Hence, points, lines and planes can be used in different fields like Navigation, Architecture, Art, Engineering, etc.
To learn more about the points, lines, and planes, visit:
https://brainly.com/question/13099718
#SPJ1
What is the slope of a line that contains the points (14,-42) (-48,24)
Enter the correct answer as m=
PLEASE SHOW WORK
The slope on the line containing the points (14,-42) is 1.06, as stated in the preceding sentence (-48,24).
How is slope determined?The % slope is calculated by multiplying the distance between two locations by the differences in elevation above them. The difference in height between two places is referred to as "rise." The distance between it sites is known as the run. Therefore, the formula for percent slope is (rise / run) x 100.
The slope's formula is as follows:
m = (y₂-y₁)/x₂-x₁)
In the formula, replace the point values as follows:
m = (24-(-42))/(-48-14)
Make the fraction simpler:
m = (24-(-42))/(-48-14)
m = 66/-62
m = 1.06
To know more about Slope visit:
https://brainly.com/question/3493733
#SPJ1
I need explanations under similar shapes
The two major properties of similar shapes include the following:
They must have the same shape.They can have different sizes.What are the properties of similar geometric shapes?In Mathematics, two (2) geometric shapes are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
This ultimately implies that, two (2) similar geometric shapes can have different sizes depending on the scale factor that is applied because it would either enlarge (increase) or reduce (decrease) them.
Read more on scale factor here: brainly.com/question/18067651
#SPJ1
2. The product of two rational numbers is 4/25
. If one number is −6/5
, find the other number.
Answer:
Step-by-step explanation:
If the product of two rational numbers is 4/25, we can write the equation:
(x) * (-6/5) = 4/25
where x is the other number.
Expanding the equation:
x * -6/5 = 4/25
Multiplying both sides by 5 to get rid of the fraction on the right-hand side:
5 * x * -6/5 = 5 * 4/25
x * -6 = 4
Dividing both sides by -6:
x = -4/-6
x = 4/6
So, the other number is 4/6.
Answer:
So the other number is -[tex]\frac{4}{3}[/tex].
Step-by-step explanation:
Let x be the number.
We know,
(-[tex]\frac{6}{5}[/tex]) × x = [tex]\frac{4}{25}[/tex]
-[tex]\frac{6}{5}[/tex] × x = [tex]\frac{4}{25}[/tex] (By expanding the left side of the equation)
Dividing both sides by -[tex]\frac{6}{5}[/tex]
x = - [tex]\frac{4}{25}[/tex] × -[tex]\frac{6}{5}[/tex]
After simplifying the equation ,
x = -[tex]\frac{4}{3}[/tex]
So the number is -[tex]\frac{4}{3}[/tex].
Plssssss asap it is due soon
For the given system of equations, the answers are of the given choices (A), (B) and (D).
What exactly is an equation system?A group of two or more equations with shared variables is referred to as a system of linear equations. Finding the value of the unknown variables employed in the equations that must satisfy both equations is necessary to solve a system of equations.
Given equations are -
y - 10 = 2x ⇒ y = 2x + 10
1/2y = x + 5 ⇒ y = 2x + 10
We can observe from the equation, that both the lines are same,
So any pair of values (x, y) that satisfy the equation y = 2x + 10 is a solution to the system. For example:
(0, 10) is a solution, since y = 2(0) + 10 = 10 and (1/2).10 = 0 + 5 =
(1, 12) is a solution, since y = 2(1) + 10 = 12 and (1/2).12 = 6 = 1 + 5
(2, -6) is a not solution, since y = 2(2) + 10 = 14 and (1/2)(-6) = 7 = 2 + 5
(-5, 0) is a solution, since y = 2(-5) + 10 = 0 and (1/2)(0) = 0
Therefore, the answer is of the given choices are (A), (B), (D).
To learn more about the system of equations visit,
brainly.com/question/25976025
#SPJ1
Use the Pythagorean Theorem to find the distance between points F and C.
A. 2 √3
B. √41
C. 4 √3
D. 3 √5
Answer:
D. 3√5
Step-by-step explanation:
The distance between points F and C is the hypotenuse of a right triangle. Therefore we can use Pythagoras Theorem to calculate the distance between these points.
From inspection of the given graph the coordinates of the two points are:
Point C = (2, 2)Point F = (-4, -1)The horizontal difference between the x-coordinates is:
[tex]x_C-x_F=2-(-4)=6\; \sf units[/tex]
The vertical difference between the y-coordinates:
[tex]y_C-y_F=2-(-1)=3\; \sf units[/tex]
Therefore, we have a right triangle with the following dimensions:
Leg a = 3Leg b = 6Hypotenuse c = CF[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
To calculate the length of the hypotenuse, and therefore the distance between points C and F, substitute the values into the Pythagoras Theorem formula and solve for CF:
[tex]\implies a^2+b^2=c^2[/tex]
[tex]\implies 3^2+6^2=CF^2[/tex]
[tex]\implies 9+36=CF^2[/tex]
[tex]\implies CF^2=45[/tex]
[tex]\implies \sqrt{CF^2}=\sqrt{45}[/tex]
[tex]\implies CF=\sqrt{9 \cdot 5}[/tex]
[tex]\implies CF=\sqrt{9} \sqrt{5}[/tex]
[tex]\implies CF=3\sqrt{5}[/tex]
Therefore, the distance between points F and C is 3√5.
A square pyramid is shown. What is the surface area?
A square based pyramid, with bases labeled 3.5 centimeters and side length of triangle labeled 7 centimeters.
(4 points)
19.25 cm2
30.625 cm2
49.625 cm2
61.25 cm2
Answer:
61.25
Step-by-step explanation:
brainlest pls and I hope this helped u :)
The radius of a circle is 5 m. Find its circumference in terms of pie
Briana ha $3 in her piggy bank. She has all quarters and dimes. Write and equation in STANDARD FORM to represent this scenario. Use X and Y as your variables (Ax+By=C)
The equation in standard form representing the scenario where Briana has $3 in her piggy bank and has all quarters and dimes, using x for the number of quarters and y for the number of dimes, is [tex]25x + 10y = 300[/tex].
Let x be the number of quarters and y be the number of dimes Briana has in her piggy bank.
The value of each quarter is 25 cents or 0.25 dollars, and the value of each dime is 10 cents or 0.10 dollars. Therefore, the total value of the coins in Briana's piggy bank can be expressed as:
[tex]0.25x + 0.10y[/tex]
Since Briana has $3 in her piggy bank, we can set up the following equation:
[tex]0.25x + 0.10y = 3.00[/tex]
To write this equation in standard form ([tex]Ax + By = C[/tex]), we need to clear the decimals by multiplying both sides of the equation by 100:
[tex]25x + 10y = 300[/tex]
Therefore, the equation in standard form that represents this scenario is:
[tex]25x + 10y = 300[/tex]
Learn more about equation here:
https://brainly.com/question/29174899
#SPJ4
