Find the surface area.
24 yd
15 yd
15 yd
+13 yd
15 yd

Answer:3/2

3x3-2x2-7x+6=x+1(Multiply the numbers)

9-4-7x+6=x-1(Calculate)

11-7x=x-1(Move the terms)

-7x-x=-1-11(Collect like terms&calculate)

-8x=-12(Divide both sides by -8)

x=3/2

Synthetic division is a process used to divide a polynomial by a linear expression. Using a step-by-step process, the polynomial 3x^3 - 2x^2 - 7x + 6 is divided by x + 1. The result is a new polynomial, which represents the quotient and a remainder.

Synthetic division is used to divide a polynomial by a linear expression. In this case, we have the polynomial (3x^3 - 2x^2 - 7x + 6) and we want to divide it by (x + 1). Synthetic division follows a specific set of steps:

The numbers at the bottom are the coefficients of the quotient polynomial, and the remainder if any.

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Answer:

Step-by-step explanation:

Let r and j represent Riley's hours and Jace's hours, respectively. The equations could be ...

  25r +30j = 460

  r - j = 3

__

The solution is (r, j) = (10, 7).

The system of equations that could be used to determine the number of hours Riley and Jace worked is: R = J + 3 and 25R + 30J = 460, where R represents the number of hours Riley worked, and J is the number of hours Jace worked.

Let's define our variables first. Let's let J represent the number of hours Jace worked and R represent the number of hours Riley worked.

From the information given, we know that Riley worked 3 more hours than Jace. So we can write this as an equation: R = J + 3.

We also know that between them, they ironed 460 shirts. We can express this as another equation by multiplying their per-hour output by the number of hours they worked, then adding the two together: 25R + 30J = 460.

So our system of equations is: R = J + 3 and 25R + 30J = 460.

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Answer:

x=3

Step-by-step explanation:

9x+5+2x = 38

Combine like terms

9x+2x   +5 = 38

11x+5 = 38

Subtract 5 from each side

11x+5-5 = 38-5

11x = 33

Divide each side by 11

11x/11 = 33/11

x = 3

Answer:

3(2n + 10) = 54

n = 4

Step-by-step explanation:

3(2n + 10) = 54

Divide both sides by 3

2n + 10 = 18

Subtract 10 form both sides

2n = 8

Divide both sides by 2

n = 4

The graph of r = 2cos5theta is symmetric about the x-axis only.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given function:

[tex]r=\ 2\ \cos\ \left(5\theta\right)[/tex]

Here, the graph shown below of this function.

As, seen from the graph.

The graph is symmetric about x- axis  only .

Learn more about graph here:

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Answer:

Angle, [tex]\theta=70.4^{\circ}[/tex]

Step-by-step explanation:

We have, an A-frame house is 45 feet high and 32 feet wide. It is required to find the measure of the angle that the roof makes with the floor.

The attached figure shows the A frame. Let [tex]\theta[/tex] is the angle that the roof makes with the floor. So,

[tex]\tan\theta=\dfrac{45}{16}\\\\\tan\theta=2.81\\\\\theta=\tan^{-1}(2.81)\\\\\theta=70.4^{\circ}[/tex]

So, the angle of 70.4 degrees is the angle that the roof makes with the floor.

Final answer:

To find the angle an A-frame house roof makes with the floor, one needs to use trigonometry. By dividing the width of the house by 2 to work with a right triangle and using the tangent function, the angle is calculated to be approximately 70 degrees.

Explanation:

The question involves finding the angle that an A-frame house roof makes with the floor, given the height of the house is 45 feet and the width is 32 feet. To solve this, we can use trigonometry, specifically the tangent function, as we are dealing with a right-angled triangle where the house's height forms one leg (opposite) and half of the width forms the other leg (adjacent). The formula to find the angle (θ) is θ = arctan(opposite/adjacent).

First, halve the width to work with one side of the A-frame: 32 feet / 2 = 16 feet. Then, use the arctan function: θ = arctan(45 feet / 16 feet). Use a calculator to find θ, which gives us an angle of approximately 70.346 degrees. When rounded to the nearest degree, the angle is 70 degrees.

Therefore, the angle that the roof makes with the floor is 70 degrees.

The two events are Independent events. So, the selection of topics by different students does not influence each other's choices.

This is a question about whether the events of students selecting essay topics independently are dependent or independent. In this context, the two events are independent. Each student's choice of topic does not depend on the choices of other students, as they do not need to inform the teacher or each other beforehand. Therefore, the selection of topics by different students does not influence each other's choices.

Answer:

4.375 a year

Step-by-step explanation:

The formula is

Interest earned= principal ×interest rate×time

I=125×0.035×1=4.375

Kristina could earn $4.375 in simple interest.

To calculate the interest Kristina could earn, we can use the formula:

Interest = Principal × Rate × Time

where Principal is the initial amount, Rate is the interest rate, and Time is the duration in years.

Plugging in the values, we have:

Using the formula, we can calculate the interest:

Interest = $125 × 0.035 × 1 = $4.375

Therefore, Kristina could earn $4.375 in simple interest.

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Answer:

241.402

Step-by-step explanation:

Answer:

241.402

Step-by-step explanation:

Answer:

132 patches

Step-by-step explanation:

First we need to find the area of the rectangular piece, multiplying the length and the width:

Area of fabric: 10 * 6 = 60 cm2

If each triangular patch has 15 cm2 of area, a fabric of 60cm2 can make 60 / 15 = 4 triangular patches.

Then, if Leia uses 33 pieces of fabric, she can make a total of 33 * 4 = 132 patches.

Answer:

132

Step-by-step explanation:

Total area'A' of rectangular piece of fabric is given by

A= length 'l' x width'w'

A= 10 x 6=> 60cm²

As there are 33 such pieces, 33 x 60=1980cm²

In order to evaluate the  umber of triangles that can be made, divide total area by the area of one triangular piece

n= 1980/15

n=132

Therefore, 132 triangles can be made

We have been given that Mr. Hayes has 111 straw bundles to use for bedding in his horse stalls. We are asked to find the greatest number of bundles that he can fill if each stall holds exactly 4 bundles of straw.

To solve our given problem, we will divide 111 by 4.

[tex]\text{Greatest number of stalls that can be filled}=\frac{111}{4}[/tex]

[tex]\text{Greatest number of stalls that can be filled}=27.75[/tex]

Since 0.75 is not an integer, so Mr. Hayes cannot fill 0.75 of a stall. Therefore, the greatest possible number of stalls will be 27.  

Answer:

A -47

Step-by-step explanation:

(2-10)= -8*5= -40-7= -47

Answer:

-47.

Step-by-step explanation:

5(2-10)-7

--> 2-10= -8

5*-8-7

--> 5*-8= -40

--> -40-7 = -47

Triangle ABD and triangle DCA can be proven congruent using the RHS congruence criterion.

To prove that triangle ABD and triangle DCA are congruent using the RHS (Right Angle, Hypotenuse, Side) congruence criterion, we need to show that they have a right angle, an equal hypotenuse, and an equal side adjacent to the right angle.

Therefore, by the RHS criterion, triangle ABD and triangle DCA are congruent.

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Answer:

(-2, 5)

Step-by-step explanation:

The solution of a system is where the lines cross, or a common point they share. The lines meet at (-2, 5), so that is the solution to the system.

Answer:

A

Step-by-step explanation:

The equation is in the standard form of a circle:

(x – h)^2 + (y – k)^2 = r^2

where (h,k) is the center, and r is the radius.

If we compare the 2 equations:

(x – h)^2 + (y – k)^2 = r^2

(x + 10)^2 + (y + 9)^2 = 100

We can see that the center is (-10, -9).

This is because (x- -10) will become (x+10), and (y- -9) will become (x+9).

So, choice A is correct

Answer:

A

Step-by-step explanation:

The equation of a circle in standard form is: [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h, k) is the center and r is the radius.

Here, our equation is: [tex](x+10)^2+(y+9)^2=100[/tex] , which means that h = -10 and k = -9. Then, the center is (-10, -9).

The answer is A.

Answer:

A

Step-by-step explanation:

I got it correct

Answer:

(1) w = 6.4

(2) w = -67

(3) q = 336

(4) z = -14

(5) x = 9

(6) y = 3

(7) x = 8

(8) x = -16

(9) x = 54

(10) x = 13.5

Step-by-step explanation:

Ik u need it quick so mb for not explaining. Good luck

Answer:

the first one is 6.4 i cant help with others srry im not smart either.

Step-by-step explanation:

Answer:

A)Unit prize is $0.162

B)Unit prize is $0.183

Step-by-step explanation:

A) 13.5-ounce bottle cost 2.19

Cost of 13.5 ounce bottle =2.19

Cost of 1 ounce bottle =[tex]\frac{2.19}{13.5}=0.162[/tex]

So, Unit prize is $0.162

B)29.2-ounce bottle costs 5.37

Cost of 29.2 ounce bottle = 5.37

Cost of 1 ounce bottle =[tex]\frac{5.37}{29.2}=0.183[/tex]

So, Unit prize is $0.183

Answer:

$126.5

Step-by-step explanation:

45.18+18.07=67.25

67.25*2=126.5

Answer:

Answer choice d

Step-by-step explanation:

To find the volume of this triangular prism, you first need to find the area of the triangular base. The formula for the area of a triangle is bh/2, which in this case is 3*2/2=3 square units. Multiplying this by the height of the prism, 3.5, you get a total of 10.5 cubic inches, or answer choice d. Hope this helps!

Answer:

Step-by-step explanation:

Is there answer choices? If not here's my answer:

That's all that it should be.

Answer:

6 mangoes

0.38 or 38p

Step-by-step explanation:

Apparently the value of the mango is £ 0.77, which means that to get the number of mangoes you can buy, you must divide this value to the amount of money you have, that is, £ 5

5 / 0.77 = 6.49

which means that it is enough for 6 mangoes.

To know the change, multiply the value of one by 6 and subtract it with £ 5, it would be the change.

6 * 0.77 = 4.62

5 - 4.62 = 0.38

That is, the change is £ 0.38 or 38p

Answer:

(a) 6 mangoes

(b) £0.38

Step-by-step explanation:

(a) The greengocers sell the mangoes for 77 p.

The greatest number of mangoes you can buy for £5 can be gotten by dividing £5 by the price of each mango (77 p). We will only pick the whole number part because number of mangoes can only be whole number.

First, we convert £5 to pence:

£1 = 100 pence

=> £5 = 5 * 100 = 500 pence

Hence, the greatest number of mangoes that can be bought is:

500 / 77 = 6.49

Since we are only picking the whole number part, the answer is 6 mangoes.

(b) The price of 6 mangoes is:

6 * 77 = 462 pence

Hence, if you take £5 (500 pence) to the store, your change should be:

500 - 462 = 38 pence

38 pence is the same as £0.38

Answer:

h(0) = 3600

t=60 when it hits the ground

max height at 4050

at 15 seconds

Step-by-step explanation:

h(t) = -2t^2 + 60t +3600

When it is thrown is t=0

h(0) = -2(0) +60(0) +3600 = 3600

When it hits the ground is h(t) =0

0 =  -2t^2 + 60t +3600

Factor out -2

0 = -2 (t^2 -30t -1800)

Divide by -2

0 = (t^2 -30t -1800)

Factor.  What 2 numbers multiply to -1800 and add to -30

0 = (t+30) (t-60)

Using the zero product property

t+30 = 0   t-60 =0

t = -30     t = 60

Since we do not have negative time

t=60

The maximum occurs halfway between the zeros

(-30+60)/2 = 30/2 = 15

Put this into the function to find the maximum value

h(15) = -2(15)^2 + 60(15) +3600

       = -2 (225) +900+3600

       =4050

Answer:

Thrown at: 3600

Ground after: 60

Max height: 4050

After: 15

Step-by-step explanation:

h(t) = -2t² + 60t + 3600

h(0) = 3600

-2t² + 60t + 3600 = 0

t² - 30t - 1800 = 0

t² - 60t + 30t - 1800 = 0

t(t - 60) + 30(t - 60) = 0

(t - 60)(t + 30) = 0

t = 60, -30(not possible)

h(t) = -2t² + 60t + 3600

-2(t² - 30t) + 3600

-2(t² - 2(t)(15) + 15² - 15²) + 3600

-2[(t - 15)² - 225] + 3600

-2(t - 15)² + 450 + 3600

-2(t - 15)² + 4050

Answer:

a.) [tex](m+6)(m+10)[/tex]

Step-by-step explanation:

Factor [tex]m^2+16m+60[/tex]

Find what two numbers add up to 16, and equal 60 when multiplied:

[tex]6[/tex] and [tex]10[/tex]

[tex]6+10=16\\6*10=60[/tex]

Factor:

[tex](m+6)(m+10)[/tex]

Finito.

Answer:

(m+6)(m+10).

Step-by-step explanation:

To find this answer, we will need to determine factors of 60 that when added, they are equivalent to 16.

We can begin by listing some factors:

30 and 2

4 and 15

12 and 5

6 and 10

...

Then, we can determine which of these factors can be added together to become 16. From this, we can determine that only factors "6 and 10" become 16 when added together.

When we do this, we can see that only answer 1, (m+6)(m+10), is equivalent to the equation given.

Answer:

3 feet

Step-by-step explanation:

There are 36 inches in 3 feet. (there are 12 inches in a foot)

Answer:

3 ft = 36 inches

Step-by-step explanation:

We know that 1 foot = 12 inches

Multiply each side by 3

3 * 1ft = 3 *12 inches

3 ft = 36 inches

Answer:

A = 5      

B= 20

C= 15

D=20

Step-by-step explanation:

Answer:

A = 5      

B= 20

C= 15

D=20

Step-by-step explanation:

Answer: 43feet

Step-by-step explanation:

Perimeter= 135 feet

Since perimeter= 2πr

135 = 2πr

Recall that π = 3.14

135 = 2 × 3.14 × r

135 = 6.28 × r

135 = 6.28r

r = 135/6.28

r = 21.5

d = 2r

d = 2 × 21.5

d = 43 feet

Answer:

42.95 feet

Step-by-step explanation:

In this question, we are tasked with calculating the distance around the dance hall that is the greatest.

Now, to answer this, we must have at the back of our mind that the dance hall is circular in shape. Thus, the greatest distance that could arise is the distance from one edge of the dance hall to the other end of the dance passing exactly through the center of the dance hall.

This distance described above is the diameter of the dance hall.

Notice we were given a length in the question? This length refers to the circumference around the circular dance hall.

Reframing then question, we were just told to calculate the diameter of a circle given the circumference of the circle.

Mathematically, circumference C of a circle = 2 * pi * r

Recall, mathematically also 2r = D

so we can say C = pi * D

Using the value of 22/7 for pi and the value of the circumference in the question, we have;

135 = 22/7 * D

D = (7 * 135)/22

D = 42.95 feet

Answer:

4.9m

Step-by-step explanation:

In circle Y:

Radius=4m

Central Angle of XYZ=70°

Length of an arc[tex]=\frac{\theta}{360^\circ}X2 \pi r [/tex]

Therefore, Length of minor arc XZ

[tex]=\frac{70^\circ}{360^\circ}X2X4 X \pi [/tex]

=4.9m (correct to the nearest tenth)

Final answer:

The total weight of Luigi's inventory if he collects 27 socks is 30 grams.

Explanation:

The equation i = s + 3 represents the scenario where Luigi's inventory weight is represented by i and the number of old socks collected is represented by s. According to the equation, the total weight of Luigi's inventory is equal to the number of socks collected plus 3 grams.

If Luigi collects 27 socks, we can substitute s with 27 in the equation to find the total weight of his inventory.

i = 27 + 3 = 30 grams.