Danielle is making a quilt with triangles and squares. There are 4 colored triangles inside each square. The base and height of each triangle is x + 4 inches as shown. Which polynomial represents the area of the colored triangles in square inches?

Answers

Answer 1

Answer:

[tex](2x^2+16x+32)\ \text{sq. inches}[/tex]

Step-by-step explanation:

b = h = Base = Height of triangle = [tex](x+4)\ \text{inches}[/tex]

Area of one triangle

[tex]A=\dfrac{1}{2}bh=\dfrac{1}{2}(x+4)(x+4)[/tex]

There are 4 colored triangles so total area of the triangles is

[tex]4A=4\times \dfrac{1}{2}(x+4)(x+4)\\\Rightarrow 4A=2(x+4)^2\\\Rightarrow 4A=2(x^2+8x+16)\\\Rightarrow 4A=2x^2+16x+32[/tex]

The area of the colored triangles is [tex](2x^2+16x+32)\ \text{sq. inches}[/tex]

Danielle Is Making A Quilt With Triangles And Squares. There Are 4 Colored Triangles Inside Each Square.

Related Questions

There is a sale at your favorite clothing store. They have their jeans priced at $49.99 with a extra 20% off. How much will you pay for three pairs of jeans, not including tax? Exlpain how you got your answer.

Answers

Answer: You need to pay $119.98 for three pairs of jeans.

Step-by-step explanation:

Market price of 1 jeans = $49.99

Discount percent = 20% = 0.20

Market price for 3 jeans = 3 x ($49.99)

= $ 149.97

Discount price = 20% of (Market price for 3 jeans )

= .0.20 x ($149.97)

= $ 29.99

Price of 3 jeans after discount = (Market price for 3 jeans ) - ( Discount price)

= $ (149.97 - 29.99)

= $  119.98

Hence, you need to pay $119.98 for three pairs of jeans.

What is the product of 7/10 and 3 2/3?

1 3/5

1 13/15

2 17/30

3 7/15

Answers

It’s c just to let u know cause 3 is not 7/15

Please help asap- will give brainliest:
See the image attached and choose ONE

Answers

Yellow is the correct answer, I think.
if u have desmos it will help a lot and i think it would be blue

Write the equation of the line in slope-intercept form and general form.

(4, 2) (-3,9)

Answers

Answer:

y = -7x + 30

Step-by-step explanation:

The shoes were $175. They are now 10% off. How much are they now?

Answers

Sale Price = $157.5 (answer). This means the cost of the item to you is $157.5. You will pay $157.5 for a item with original price of $175 when discounted 10%. In this example, if you buy an item at $175 with 10% discount, you will pay 175 - 17.5 = 157.50 dollars.

Hope this helps!

Emily used 27 centimeters of tape to wrap 3 presents. How much tape will Emily need in all if she has to wrap 5 presents? Assume the relationship is directly proportional.

? centimeters

Answers

Answer: 45 centimeters

Step-by-step explanation:

27 - 3

divide both by 3

9 - 1

multiply by 5

45 - 5

Answer:

45 Centimeters.

Step-by-step explanation:

27 / 3 = 9

9 x 5 = 45

Find the slope of this line. *
(5 puntos)
-1
1
3
5
y
-2
0
2
4

Answers

Answer:

1

Step-by-step explanation:

Slope = y2 - y1 / x2 - x1 so, (0 - (-2)) / (1 - (-1)) == 2/2 = 1

1. Solve the system of equations.
2y - 3z=0
x+3y = -4
3x + 4y = 3

Answers

Answer:

1. y = 3/2z

Step-by-step explanation:

1. ,2y-3z + 3z =0 + 3z ,2y=3z, 2y/2 =3z/2=3/2z

Please explain how you answered it along with your answer - thanks

Answers

Answer:

B

Step-by-step explanation:

Because you have to separate the equation. So you get [tex]\frac{2x-4}{3}[/tex]>[tex]\frac{1}{5}[/tex] And [tex]\frac{2x-4}{3}[/tex]<6

Then you have to solve for x so you get x>[tex]\frac{23}{10}[/tex] and x>11

Then you find the intersection so the answer is B

Maine has a cold climate in the winter. Which statement about the probability of temperatures falling below 32F in Maine during the month of January is most likely true? Options: The probability is 100 | The probability is closer to 1 than to 0. The probability cannot be determined before Febuary The probability could be -1.

Answers

Answer:

can't help u..

Step-by-step explanation:

i am so sorry

xbxnxnxn

xnzjznzn

sjziaowoo1i3uo

PLZ MARK ME AS BRAINLIST

What is the value of the equation -2/3x + 9 = 4/3 x -3?​

Answers

Answer:

x = 6

Step-by-step explanation:

[tex]\frac{-2}{3}x+9=\frac{4}{3}x-3\\\\\frac{-2}{3}x-\frac{4}{3}=-3-9\\\\\frac{-2-4}{3}x= - 12\\\\\frac{-6}{3}x = -12\\\\ -2x -12\\\\x = \frac{-12}{-2}\\\\x = 6[/tex]

Solve the proportion:

Answers

Answer:

15

Step-by-step explanation:

Answer:

x = 15

Step-by-step explanation:

cross multiply

9*10=90

90/6=15

What is the image of the point (1,8)(1,8) after a rotation of 180 counterclockwise about the origin?

Answers

Answer:

(- 1, - 8 )

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 180°

a point (x, y ) → (- x, - y ) , thus

(1, 8 ) → (- 1, - 8 )

Which pair of triangles MUST be similar?



A. Triangle 5 has a 25 degree angle and a 75 degree angle. Triangle 6 has a 25 degree angle and a 70 degree angle.

B. Triangles 1 and 2 each have a 40 degree angle.

C. Triangle 7 has a 40 degree angle and a 35 degree angle. Triangle 8 has a 40 degree angle and a 105 degree angle.

D.Triangles 3 and 4 are both scalene. Each have a 65 degree angle.

Answers

Answer:

C

Step-by-step explanation:

The total measurement of a triangle is 180

Triangle 7 has a 40 degree angle and 35 degree angle.

40+35=75

180-75=105

Triangle 8 has the same angle that is 40 degrees and 105. And if you do the same math, you would get 35 for the missing angle of triangle 8

Charlie, Henry, and Patrick went to the movies and each purchased 2
chocolate candy bars from concessions. Charlie ate
1/2 of a candy bar, Henry
ate 1 &
1/6 candy bars, and Patrick ate 1 & 3/4
candy bars.
How many candy bars did
the boys eat altogether? Select all the correct answers.
A. 3 & 5/12

B. 5 & 5/12

C. 41/12

D. 65/12

E. 2 & 5/12

Answers

Answer:

A

Step-by-step explanation:

Olivia got a 72% on her quiz, there are 25 questions how many did she get right and how many did she get right

Answers

Answer:

18

Step-by-step explanation:

72% of 25 is 18.

Hope this helped! :)

what is the (gcf) of 18 and 72?

Answers

Answer:

18

Step-by-step explanation:

The GCF is also known as the greatest common factor. Every number can be written as the product of at least 2 numbers, and almost every number has at least one factor that is a prime number (or a number that is only divisible by 1 and itself).

Let's find the prime factorization of 18 and 72; in other words, let's find what prime numbers make these numbers up.

18 = 2 * 9 = 2 * 3 * 3  ⇒  notice that while 9 isn't a prime number, 2 and 3 are

72 = 2 * 36 = 2 * 2 * 18 = 2 * 2 * 2 * 3 * 3  ⇒  again, 2 and 3 are primes

In finding the GCF, we want to find the largest value of the prime numbers that the two numbers share.

Here, we see that both 18 and 72 have at least one factor of 2 and at least two factors of 3. So, that's the greatest common factor: 2 * 3 * 3 = 18.

18 because 72 can be divided by 18

11) Stephanie makes $ 50 a week babysitting. She spends $ 25, saves $ 15, and uses the rest to pay off a $ 100 loan from her brother. After six weeks, how much has Stephanie spent, how much has she saved, and how much still owes her brother?

Answers

Answer:

She saved 90 dollars and she owes her brother 40 still.

Step-by-step explanation:

45% of _____________is 165

Answers

Answer:

366.666666  

Step-by-step explanation:

Let the number be x

45% of x = 165x*45/100 = 165x = 165*100/45x = 366.666666  

The radius of a cone is increasing at a constant rate of 7 meters per minute, and the volume is decreasing at a rate of 236 cubic meters per minute. At the instant when the radius of the cone is 99 meters and the volume is 180 cubic meters, what is the rate of change of the height? The volume of a cone can be found with the equation V=\frac{1}{3}\pi r^2 h.V= 3 1 ​ πr 2 h. Round your answer to three decimal places.

Answers

Answer:

The rate of change of the height is 0.021 meters per minute

Step-by-step explanation:

From the formula

[tex]V = \frac{1}{3}\pi r^{2}h[/tex]

Differentiate the equation with respect to time t, such that

[tex]\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)[/tex]

[tex]\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)[/tex]

To differentiate the product,

Let r² = u, so that

[tex]\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)[/tex]

Then, using product rule

[tex]\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}][/tex]

Since [tex]u = r^{2}[/tex]

Then, [tex]\frac{du}{dr} = 2r[/tex]

Using the Chain's rule

[tex]\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}[/tex]

∴ [tex]\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})][/tex]

Then,

[tex]\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}][/tex]

Now,

From the question

[tex]\frac{dr}{dt} = 7 m/min[/tex]

[tex]\frac{dV}{dt} = 236 m^{3}/min[/tex]

At the instant when [tex]r = 99 m[/tex]

and [tex]V = 180 m^{3}[/tex]

We will determine the value of h, using

[tex]V = \frac{1}{3}\pi r^{2}h[/tex]

[tex]180 = \frac{1}{3}\pi (99)^{2}h[/tex]

[tex]180 \times 3 = 9801\pi h[/tex]

[tex]h =\frac{540}{9801\pi }[/tex]

[tex]h =\frac{20}{363\pi }[/tex]

Now, Putting the parameters into the equation

[tex]\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}][/tex]

[tex]236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)][/tex]

[tex]236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386][/tex]

[tex]708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}[/tex]

[tex]708 = 30790.75 \frac{dh}{dt} + 76.36[/tex]

[tex]708 - 76.36 = 30790.75\frac{dh}{dt}[/tex]

[tex]631.64 = 30790.75\frac{dh}{dt}[/tex]

[tex]\frac{dh}{dt}= \frac{631.64}{30790.75}[/tex]

[tex]\frac{dh}{dt} = 0.021 m/min[/tex]

Hence, the rate of change of the height is 0.021 meters per minute.

Juan needs to simplify the fraction LaTeX: \frac{32}{52}32 52. He will need to divide the numerator and the denominator by the greatest common factor. What is the greatest common factor of 32 and 52?

Answers

Answer:

4

Step-by-step explanation:

Given the expression, 32/52

Juan need to divide the numerator and the denominator by the greatest common factor

For 32;

32 = 8 * 4

For 53

52 = 13 * 4

Find the ratio

32/52 = (8*4)/(13*4)

32/52 = 8/13

Since 4 is common to both factors, Hence the greatest common factor is 4

A rectangle has a length of x inches and a width 2 inches less than the length. If the dimensions were doubled, what would be the area, in square inches , of the new rectangle in terms of x

Answers

Answer:

Option (4)

Step-by-step explanation:

Area of a rectangle = Length × width

If the dimensions of the given rectangle is doubled,

Area of the new rectangle = 2(Length) × 2(width)

                                            = 4(Length × width)

                                            = 4(x)(x - 2)

                                            = 4[x² - 2x]

                                            = 4x² - 8x

Therefore, Option (4) will be the correct option.

what is the missing term in the factorization?
18m^2-200 2(3m-10)(3m+?)
A). -100
B). -10
C). -3
D). 3
E). 10

Answers

Answer:

2 ( 3m -10) (3m+10)

Step-by-step explanation:

18m^2-200

Factor out 2

2 ( 9m^2 -100)

We recognize that this is the difference of squares ( a^2 -b^2) = (a-b)(a+b)

2 ( ( 3m)^2 - 10^2)

2 ( 3m -10) (3m+10)

Make a reasonable estimate for the situation. A snail moves at a speed of 3.395 inches per minute. If the snail keeps moving at this rate, about how many inches will it travel in 6.187 minutes?

Answers

Answer:

Distance = 21.0049 inches

Step-by-step explanation:

Given the following data;

Speed = 3.395 inches per minute.

Time = 6.187 minutes

To find the distance;

Distance = speed * time

Substituting into the equation, we have;

Distance = 3.395 * 6.187

Distance = 21.0049

Compute the sum of the squares of the shorter lengths. Compute the sum of the squares of the shorter lengths. Compute the square of the longest length. Compute the square of the longest length. What kind of triangle is it? What kind of triangle is it? Acute triangle Acute triangle Right triangle Right triangle Obtuse triangle Obtuse triangle

Answers

The given triangle is a right triangle because it agrees Pythagoras theorem.

In the given triangle, the shorter lengths are 12 and 16.

The sum of square of shorter lengths:

[tex]= 12^2 + 16^2[/tex]

[tex]=144+256[/tex]

[tex]=400[/tex]

The longer length is 20.

Square of the longest length is [tex]20^2.[/tex]

[tex]20^2 = 20 \times 20[/tex]

=400

The sum of squares of shorter lengths is equal to Square of the longest length which obeys Pythagoras theorem.

400 = 400

As this is agreeing Pythagoras theorem it is a right angle triangle.

Hence, option B is correct. right triangle.

To learn more on Triangles click:

https://brainly.com/question/2773823

#SPJ12

PLEASE HELP ME I NEED THE ANSWER ASAP THANK YOU SO MUCH!!

Answers

dark blue is the answer

(3,1) is the answer

[WORTH 100 WHOLE POINTS] !!

I need it soon!!

Answers

1. 1/5
2. 3/5
3. i do not understand
4. 1/2 (even chance)

Answer:

1. 1/5    2. 3/5       4. 1/2    I dont know what 3 is

Step-by-step explanation:

A museum requires a minimum number of chaperones proportional to the number of students on a field trip. The museum requires a minimum of 333 chaperones for a field trip with 242424 students.

Answers

Answer: See explanation

Step-by-step explanation:

Here is the complete question:

A museum requires a minimum number of chaperones proportional to the number of students on a field trip. The museum requires a minimum of 3 chaperones for a field trip with 24 students. Which of the following could be combinations of values for the students and the minimum number of chaperones the museum requires? Choose 2 answers.

A. Students: 72

Minimum of chaperones: 9

B. Students: 16

Minimum of chaperones: 2

C. Students: 60

Minimum of chaperones: 6

D. Students: 45

Minimum of chaperones: 5

E. Students: 40

Minimum of chaperones: 8

Since the museum requires a minimum of 3 chaperones for a field trip with 24 students. This means that there will be 24/3 = 8 students per chaperone.

We then divide the number of students given in the question by the number of chaperone to know our answers. This. Will be:

Students: 72

Minimum of chaperones: 9

This will be: 72/9 = 8

Therefore, this is correct.

B. Students: 16

Minimum of chaperones: 2

This will be: 16/2 = 8

This is correct

C. Students: 60

Minimum of chaperones: 6

This will be: = 60/6 = 10.

Therefore, this is wrong

D. Students: 45

Minimum of chaperones: 5

This will be 45/5 = 9

Therefore, this is wrong.

E. Students: 40

Minimum of chaperones: 8

This will be: 40/5 = 8.

Therefore, this is wrong.

Therefore, options A and B are correct.

Find the solutions of the quadratic equation 3x2 + 9x + 17 = 0.

Answers

Answer: C

Step-by-step explanation: Just did khan academy

Mrs. Wienman baked her family’s favorite pie. There are 5 people in the family. She cut the pie into eight parts. Her family ate four slices. What part of the pie was left?

Answers

Answer:

4/8

Step-by-step explanation:

Answer:

Pie remaining = 1/2 (simplified form of 4/8)

Step-by-step explanation:

Pie = 1 = 8/8 (cut into 8 peices)

Pie ate = 4/8

Pie remaining = 4/8 (8/8 - 4/8)

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