Mathematics High School

shawna and amanda are selling pies for a school fundraiser. customers can buy cherry pies and pumpkin pies. shawna sold 1 cherry pie and 3 pumpkin pies for a total of $55. amanda sold 3 cherry pies and 3 pumpkin pies for a total of $69. what is the cost of each one cherry pie and one pumpkin pie?
PLEASE SHOW WORK

Answers

Answer 1
Let the cherry pies be c and the pumpkin pies be p:
Shawna: c + 3p = 55
Amanda: 3c + 3p = 69
We want to find the cost of c + p. To do this, the easiest way is to divide the second equation by 3:
(3c + 3p)/3 = 69/3
c + p = 23
Therefore, 1 cherry pie & 1 pumpkin pie cost $23.

Related Questions

Use substitution to determine which of the following points is a solution to the standard form equation below. 2y = 5

Answers

The question is incomplete.

This is the complete question as I found in internet:

Use substitution to determine which of the following points is a solution to the standard form equation below 5x-2y = 10

these are the points:

-1,5

1,5

0,-5

0,5

Answer: (0, -5)

Explanation:


point          x           y        5x - 2y = 10 ?


-1,5         -1           5         5(-1) - 2(5) = - 5 - 10 = - 15 ≠ 10 ⇒ not a solution

1,5            1          5         5(1) - 2(5) = 5 - 10 = 5 ≠ 10 ⇒ not a solution
 
0,-5           0        -5           0 -2(-5) = 10 ⇒ a solution

0,5             0         5          0 - 2(5) = - 10 ≠ 10 ⇒ not a solution

Answer:

(10,5/2) answer is A

Step-by-step explanation:

just took test.

Quadrilateral ABCD has the following vertices: A(-4, -3), B(2, -3), C(4, -6), and D(-4, -6). Quadrilateral ABCD is a

A. trapezoid
B. parallelogram
C. square
D. rectangle

Answers

In order to get the figure, you have to plot it.

Quadlirateral ABCDwith vertices: A(-4, -3), B(2, -3), C(4, -6), and D(-4, -6) is s A. TRAPEZOID

the answer is TRAPEZOID

PLEASE ANSWER ASAP Becky purchased a home entertainment center for $2,254 using an 18-month deferred payment plan with an interest rate of 22.48%. She did not make any payments during the deferment period. What will Becky's monthly payment be if she must pay off the home entertainment center within three years after the deferment period?

$121.01

$87.45

$62.61

$113.72

Answers

The correct answer for your problem would be $62.61

Answer:

$62.61

Step-by-step explanation:

Data:

The price of home entertainment = $ 2 254

Time to pay = 18 months

interest rate  = 22.48 %

monthly payment  = $ 2254/ 18

                              =  $ 125. 22

                              =   - 22.48 (2254)/18

                              = $ 62.61

Sophia and Tyler are running around a 400-meter track. They start running from the same place, at the same time. Sophia runs at a speed of 5 m/s and Tyler runs at a speed of 4 m/s. How long will it take Sophia to lap Tyler?

Answers

We will call:

S: Runner Sophia.
T: Runner Tyler.

At the beginning the distance between both runners is 400m

At t = 1s Sophia runs 5m and Tyler 4m
At t = 2s Sophia runs 10m and Tyler 8m

and so on.

So, for example at t = 1s, the distance between both runner is:

D = 400m - 5m(the advantage of Sophia) + 4m(what Tyler recovers)

So, we can find a general equation for this matter. Knowing that the distance, velocity and time are related by this equation:

[tex]d=vt[/tex]

Then, the distance between both runners, at any time, is given by:

[tex]D = 400-5t+4t[/tex]

So we need to find the how long it will take Sophia to lap Tyler. This happens when D = 0:

[tex]0 = 400 - 5t+4t[/tex]
∴ [tex]400-t = 0[/tex]
∴ [tex]t = 400s[/tex]

Answer: 400 seconds

Step-by-step explanation:

5x = 400 + y

4x = y

take 4x and add it to the top so it looks like this:

5x = 400 + 4x

cancel 4x if you don't know how to do it  you do it like this you take +4x and instead you do -4x to cancel.

and you do it to 5x so you cancel 4x and 5x - 4x = x so x = 400

x = 400

Students washed cars to raise funds for their school. they collected $291 by charging $3.00 per car. how many cars did they wash?

Answers

Divide total money collected by amount charged per car to find number of cars washed.

=$291 total ÷ $3 a car
=97 cars


ANSWER: They washed 97 cars.

Hope this helps! :)

The expression 8x + 2y

Answers

You can do 2(4x + 1y)

A ball is rolling in a circular path that has a radius of 10 inches as shown in

Answers

the complete question in the attached figure

we know that
[circumference]=2*pi*r
for r=10 in
[circumference]=2*pi*10-----> 62.8 in

if 360° (full circle) has a length of --------> 62.8 in

 54°------------------------------> X
x=54*62.8/360-----> x=9.42 in

the answer is 9.42 in

Hamilton received a 75 on his algebra exam. The professor is allowing students to take a 7-question bonus quiz to improve their algebra exam score. Each question answered correctly on the bonus quiz will add 3 points to the exam score. Hamilton needs to receive at least a 90 on his exam score in order to make an "A" for the semester. If x represents the number of questions answered correctly on the bonus quiz, which of the following inequalities symbolizes this situation?


A. 3x + 75 < 90
B. 7x + 75 > 90
C. 3x + 75 > 90
D. 7x + 75 < 90




Answers

The answer is A.

Since each question answered right would add 3 points, the amount of questions answered correctly would be x. You then going to add that to his original score, 75. He needs at least a 90, so 90 is the lowest test grade he can afford. Therefore, 90 is should be the greatest number since there are no less than, equal to and such. Knowing that, the answer would be A

Hope this helps!

Final answer:

The correct inequality should be 3x + 75 ≥ 90 to indicate Hamilton needs at least 90 on his exam. The closest option given, which is not entirely accurate, is C. 3x + 75 > 90.

Explanation:

To determine the inequality that represents Hamilton’s situation, we need to calculate how many points he requires to reach a score of at least an “A”, which is 90. Each correct bonus question adds 3 points to his exam score of 75. We need to find the number of questions, x, Hamilton must answer correctly to achieve a total score of 90 or more. Therefore, the inequality that encompasses this scenario is 3x + 75 ≥ 90 because each correct answer contributes 3 points towards closing the 15-point gap between his current score and the desired score of 90.

However, the options given do not include the correct representation which would be 3x + 75 ≥ 90. Instead, the closest option is C. 3x + 75 > 90, which would imply that Hamilton must score more than 90, which is not a requirement for making an “A” (as “A” can include exactly 90).

triangle XYZ is obtuse which list could represent the angle measures of triangle XYZ?

A. 20 60 100
B. 30 60 90
C. 50 50 80
D. 60 60 60

Answers

An obtuse triangle must have an angle greater than 90degrees (cannot equal 90). Therefore, A. would be the correct answer. This is because A. is the only set of angles that includes an angle greater than 90. Also, all angle measures add up to equal 180degrees.

If x varies directly as y, and x = 48 when y = 16, find x when y = 5.

A) 5/3

B) 153.6

C) 15

Answers

x =k y
48 = k* 16
k = 3

x=3*5
x=15

Answer:

15

Step-by-step explanation:

x =ky

48 = k16

divide by 16

k = 3

plug k into x=ky

x=3*5

x=15

What is the standard deviation of the following data set rounded to the nearest tenth? 52.1, 45.5, 51, 48.8, 43.6

Answers

The standard deviation of a set of data is given by
[tex]\sigma = \sqrt{ \frac{1}{N} \sum (x_i - \mu)^2} [/tex]
where
N is the number of data (in this case, N=5)
[tex]x_i[/tex] are the data
[tex]\mu[/tex] is the average value

Let's calculate the average value:
[tex]\mu = \frac{52.1+45.5+51+48.8+43.6}{5}=48.2 [/tex]

And now we can apply the formula to calculate the standard deviation:
[tex]\sigma = \sqrt{ \frac{1}{5} \sum ( x_i - 48.2 )^2} =[/tex]
[tex]= \sqrt{ \frac{1}{5} ( (3.9)^2 + (-2.7)^2 + (2.8)^2 + (0.6)^2 + (-4.6)^2 ) } =[/tex]
[tex]= \sqrt{ \frac{1}{5} (51.86) } =3.2[/tex]

Answer:

Standard deviation is 3.2.

Step-by-step explanation:

Given data is,

52.1, 45.5, 51, 48.8, 43.6,

Let x represents the data points,

Now, mean of the data is,

[tex]\mu = \frac{52.1 + 45.5 + 51 + 48.8 + 43.6}{5}=48.2[/tex]

Population size, N = 5,

Hence, the standard deviation of the following data set is,

[tex]\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N} (x_i-\mu )^2[/tex]

[tex]=\sqrt{\frac{1}{5}\sum_{i=1}^{5} (x_i-48.2 )^2[/tex]

[tex]=\sqrt{\frac{1}{5} (15.21+7.29+7.84+0.36+21.16)}[/tex]

[tex]=\sqrt{10.372}[/tex]

[tex]=3.2205589577[/tex]

[tex]\approx 3.2[/tex]

Jason was hired to mow a lawn that covers an area of acres 2 3/4. It took him 4 1/8 hours to complete the job. What was his unit rate in hours per acre?

I understand the steps where I am stuck is how did you get 2/3/

Answers

Divide the area by the time:

Divide 2 3/4 acres by 4 1/8 hours:

Divide 2.75 acres by 4.125 hours:

2.75 acres
--------------- = 2.667 acres/hour, or 2 2/3 acres / hour.
4.125 hrs

If this is not entirely clear to you, please share the work you've done yourself and I will respond.

A bin is constructed from sheet metal with a square base and 4 equal rectangular sides. if the bin is constructed from 48 square feet of sheet metal, then what is the largest volume of such a bin? what are its dimensions?

Answers

This is a problem of maxima and minima using derivative.

In the figure shown below we have the representation of this problem, so we know that the base of this bin is square. We also know that there are four square rectangles sides. This bin is a cube, therefore the volume is:

V = length x width x height

That is:

[tex]V = xxy = x^{2}y[/tex]

We also know that the bin is constructed from 48 square feet of sheet metal, so:

Surface area of the square base = [tex]x^{2}[/tex]

Surface area of the rectangular sides = [tex]4xy[/tex]

Therefore, the total area of the cube is:

[tex]A = 48 ft^{2} = x^{2} + 4xy[/tex]

Isolating the variable y in terms of x:

[tex]y = \frac{48- x^{2} }{4x}[/tex]

Substituting this value in V:

[tex]V = x^{2}( \frac{48- x^{2} }{x}) = 48x- x^{3} [/tex]

Getting the derivative and finding the maxima. This happens when the derivative is equal to zero:

[tex]\frac{dv}{dx} = 48-3x^{2} =0[/tex]

Solving for x:

[tex]x = \sqrt{\frac{48}{3}} = \sqrt{16} = 4[/tex]

Solving for y:

[tex]y = \frac{48- 4^{2} }{(4)(4)} = 2[/tex]

Then, the dimensions of the largest volume of such a bin is:

Length = 4 ft
Width =  4 ft
Height = 2 ft

And its volume is:

[tex]V = (4^{2} )(2) = 32 ft^{3}[/tex]

Line RS is tangent to circle Q at point R.


What is the measure of ∠SQR ?

Enter your answer in the box.

Answers

If the line RS is tangent to the circle, then it is at a 90 degree angle to the circle at the point of contact.

Now that we know 2 angles, we can find the 3rd:

180 - 90 - 32 = 58

Using the tangent and radius theorem, the measure of ∠SQR is 58°.

What is Circle Geometry??

From the question, we are to determine the measure of ∠SQR

In the given diagram, QR is a radius

By the tangent and radius theorem,

If a tangent and a radius meet at the point of tangency, then they are perpendicular to one another

∴ ∠QRS = 90°

∠SQR + ∠RSQ + ∠QRS = 180° (Sum of angles in a triangle)

∠SQR + 32° + 90° = 180°

∠SQR + 122° = 180°

∠SQR  = 180° -  122°

∠SQR  = 58°

Hence, the measure of ∠SQR is 58°.

Learn more on Circle geometry here: https://brainly.com/question/21872415

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Solve the system of equations and choose the correct answer from the list of options. (4 points) x − y = 7 y = 3x + 12

Answers

x = -19/2
y = -33/2

Start by plugging in the second equation for y in the first equation. Then solve for x. After you can use that value to solve for y. 

What is cos 45? Please HELP !!!

Answers

Answer:

A) Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].

Step-by-step explanation:

Given  : Triangle 90 -45 -45 .

To find : What is cos 45.

Solution : We have given

Triangle 90 -45 -45  

Hypotenuse = √2 ,

Adjacent side to 45 degree = 1 .

By the trigonometric ratio : cosine is the ratio of the adjacent side to angle  to the hypotenuse .

Cos ( theta) = [tex]\frac{Adjacent}{hypotenuse}[/tex].

Plug the values  Hypotenuse = √2 , Adjacent side to 45 degree = 1 .

Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].

Therefore, A) Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].

The cosine of 45° is √2 / 2.

In a triangle with angles of 90°, 45°, and 45°, we can use the trigonometric functions to find the ratios of the sides.

In this case, we want to find the cosine of 45°.

The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse.

In the given triangle, the adjacent side to the 45° angle is 1, and the hypotenuse is √2.

Using the formula for cosine, we have:

cos 45° = adjacent side / hypotenuse

Substituting the values, we get:

cos 45° = 1 / √2

To rationalize the denominator, we multiply both the numerator and denominator by √2:

cos 45° = (1 / √2) * (√2 / √2) = √2 / 2

Therefore, the cosine of 45° is √2 / 2.

To learn more about cosine function;

https://brainly.com/question/29277391

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Identify a counterexample to disprove 6n>n^2/6,where n is a real number.

Answers

A counterexample to disprove the inequality [tex]6n > n^2/6[/tex] is n = 12, because when plugged into the inequality, it results in 72 > 24, which is false.

The question is asking for a counterexample to disprove the inequality [tex]6n > n^2/6[/tex], where n is a real number. To find a counterexample, let's test an arbitrary positive number, such as n = 7, to see if the inequality holds.

Substituting 7 for n, we get:

6 x 7 > 72/6

42 > 49/6

42 > 8.167

This is indeed true, so 7 is not a counterexample. However, we can think of a larger value of n. Let's try n = 12:

6 x 12 > 122/6

72 > 144/6

72 > 24

This is false. Hence, n = 12 serves as a counterexample to disprove the given inequality. So, the inequality does not hold for all real numbers.

Can anyone help me with this problem?

Answers

[tex]\tan\Theta=\dfrac{|BC|}{|CA|}[/tex]

Use Pythagorean theorem:
[tex]|AB|^2=|BC|^2+|CA|^2\\\\9^2=6^2+|CA|^2\\\\81=36+|CA|^2\ \ \ \ |-36\\\\|CA|^2=45\to|CA|=\sqrt{45}\\\\|CA|=\sqrt{9\cdot5}\\\\|CA|=\sqrt9\cdot\sqrt5\\\\|CA|=3\sqrt5[/tex]
[tex]\tan\Theta=\dfrac{6}{3\sqrt5}=\dfrac{2}{\sqrt5}\cdot\dfrac{\sqrt5}{\sqrt5}=\dfrac{2\sqrt5}{5}[/tex]

Need help to write equations for 5, 6 & 7

Answers

5)
The x-values go up by 1: -2, -1, 0, 1, 2
The y values are always 3 times the previous value.
This is an exponential function.

[tex] y = a(b)^x [/tex]

We need to find a and b.
Look at x = 0.
For x = 0, y = 4.

[tex] y = a(b)^x [/tex]

[tex] 4 = a(b)^0 [/tex]

Since b^0 = 1, this simplifies to

[tex] 4 = a [/tex]

Now we know a = 4. We have

[tex] y = 4(b)^x [/tex]

Look at x = 1. For x = 1, y = 12.

[tex] 12 = 4(b)^1 [/tex]

[tex] 12 = 4b [/tex]

[tex] b = 3 [/tex]

Now that we know a and b, we can write the function.

[tex] y = 4(3)^x [/tex]

Now that you have the function written out, notice the following.
In the exponential equation we found, the number raised to x
is the number you multiply each y value to get the next y value.
In this case, each y value is 3 times the previous one, so you have 3^x.
The way you find "a" in the exponential equation is to look at the y-coordinate
when x = 0. When x = 0, b^x is 1, so b^x drops out, and you get "a" equal to
the y-value. In this case, when x = 0, y = 4, so "a" is 4.
With b = 3, and a = 4, you can quickly write:
y = 4(3)^x.

Simplify the trigonometric expression.

Answers

First we are going to find the common denominator of both fractions. To do that, we are going to multiply their denominators:
[tex](1+sin \alpha )(1-sin \alpha )=1-sin^2 \alpha [/tex]

Now we can rewrite our expression using the common denominator:
[tex]\frac{1-sin \alpha }{1-sin^2 \alpha } + \frac{1+sin \alpha }{1-sin^2 \alpha} = \frac{2}{1-sin^2 \alpha} [/tex]

Finally, we can use the trig identities: [tex]1-sin^2 \alpha =cos^2 \alpha [/tex] and [tex]sec \alpha = \frac{1}{cos \alpha } [/tex] to simplify our trig expression:
[tex]\frac{2}{cos^2\alpha}=2sec^2 \alpha [/tex]

We can conclude that the correct answer is the fourth one.
1/(1+sin theta) + 1/(1-sin theta) 

THe answer is letter D. 2 sec^2 theta

Hope it help! Goodluck! 

Need this geometry answer quick!

Answers

Since it is a 90° angle it is equal to the sum of 6x° and 4x°, so 6+4=10 and the answer is the second one.
Adjacent angles on a straight line sum up to 180:
90 + 6x + 4x = 180

Combine like terms:
90 + 10x = 180

Subtract 90 from both sides:
10x = 90

Divide both sides by 10:
x = 9

Answer: 9

PLS HELP ME ASAP WITH 3, 4, AND 5! PLS! (Read directions carefully :)

(BRAINLIEST WILL BE GIVEN HOPEFULLY!)

(Random answers gets moderated!)

Answers

3) It is a matter of reading the value from the graph. I read the graph as ...
a. d(0) = 20
b. d(2) = 18
c. d(4) = 12
d. d(6) = 10
e. d(9) = 15
f. d(3) = 15, or d(9) = 15

4) The domain is the horizontal extent: 0 to 12.
The range is the vertical extent: 10 to 20.

5)
a. f(7) = -2*7 +5 = -9
b. f(-3) = -2(-3) +5 = 11
c. -2x +5 = 17; -2x = 12; x = -6, so f(-6) = 17

The area of the rectangle shown is given by the function A(x) = 2x2 - 5x. If the width of the rectangle is 13, what is the area?

Answers

we know that
area of rectangle=length*width
let
x-----> the length side
y-----> the width side
y=13 units

A=2x²-5x
A=x*y------> 2x²-5x=x*13------> 2x²-18x=0-----> x²-9x=0
x*(x-9)=0
the solutions are
x=0
x=9

hence
the dimensions of the rectangle are
length is 9 units
width is 13 units

the area of rectangle is -----> 9*13-----> 117 units²

the answer is 
117 units²

An investment of $450 increases at a rate of 6.5% per year. What is the growth factor, b?

Answers

[tex]\bf \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\to &450\\ r=rate\to 6.5\%\to \frac{6.5}{100}\to &0.065\\ t=\textit{elapsed time}\\ \end{cases} \\\\\\ A=450(1+0.065)^t\implies A=450(\stackrel{growth~factor}{1.065})^t[/tex]

find the greatest common factor 6x^2a + 6xa^2

Answers

The greatest common factor is 6xa

If you multiply 6xa with a and x ---->  6xa(x+a), you'll get 6x^2a + 6xa^2 

The square root of 136 is between which two whole numbers?

Answers

The square root of 136 is between 11 and 12. Hope I helped!
The square root is between 11 and 12 but closer to 12. 
Hope this helps! 

Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the length of the chord whose endpoints are the points of tangency.

2r
r²
r√2

Answers

r^2
.......................
The answer is r squared. Hope it helped!

Find the sum of the summation of 2 i minus 12, from i equals 7 to 16.

22
110
220
440

Answers

Sum: S
S=[2(7)-12]+[2(8)-12]+[2(9)-12]+[2(10)-12]+[2(11)-12]+[2(12)-12]+[2(13)-12]+[2(14)-12]+[2(15)-12]+[2(16)-12]

S=2(7+8+9+10+11+12+13+14+15+16)-10(12)
S=2(115)-120
S=230-120
S=110

Answer: Second option 110

Answer: Second option is correct.

Step-by-step explanation:

Since we have given that

[tex]\sum_{7}^{16}(2i-12)\\\\=\sum_{7}^{16}2(i-6)\\\\=2\sum_{7}^{16}(i-6)\\\\=2[(16-6)+(15-6)+(14-6)+(13-6)+(12-6)+(11-6)+(10-6)+(9-6)+(8-6)+(7-6)]\\\\=2[10+9+8+7+6+5+4+3+2+1]\\\\\text{Sum of n natural numbers }\\\\=2(\frac{10\times (10+1)}{2})\\\\\=\frac{n(n+1)}{2}\\\\=2\times \frac{10\times 11}{2}\\\\=10\times 11\\\\=110[/tex]

Hence, the value of summation is 110.

Therefore, Second option is correct.

Find the slope of the line on the graph

Answers

find 2 points on the graph where the blue line crosses an X and Y that we know

1st point ( -4,0)
 2nd point (0,3)

slope = change in y over change in x

change in y = 3-0 = 3

change in x = 0 - -4 = 0+4 = 4

slope = 3/4




_________________ lines are lines that never intersect and are not coplanar. A) Parallel B) Perpendicular C) Skew D) Transversal

Answers

the answer is c- skew lines
Hey There! I'll be glad too help you.



Skew lines are lines that never intersect and are not coplanar.



So the answer would be C. ^-^
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