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3 years ago

Need with number 17 please

Mathematics

1 answer:

solniwko [45]3 years ago

8 0

Hey there :)

We know that the area formula of a rectangle is:
Area = width x length

The given are :
Width = p
Length = 5 + p
Area = 104 ft²

Let us substitute and find p

104 = ( p ) ( 5 + p )
104 = 5p + p²
p² + 5p - 104 = 0

Factor it
Product = - 104 and Sum = 5
Factors = - 8 and 13

( p + 13 )( p - 8 ) = 0
p = -13 p = 8
↓
We reject the negative value since a side can never be negative

Therefore,
Width = p = 8 ft
Length = 5 + p = 5 + 8 = 13 ft

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Two triangles are similar.The the smaller triangle has side 10,20 and 15 units the larger triangles longest side is 52 units.Wha

Oliga [24]

Answer: The perimeter of the largest triangle = 117 units.

Step-by-step explanation:

Sides of smaller triangle = 10,20 and 15 units

Longest side = 20 units

Longest side of larger triangle = 52 units

Sides of two similar triangles are proportional.

Let k be proportionality constant.

$k=\dfrac{\text{Length in larger triangle}}{\text{Length in smaller triangle}}$

$k=\dfrac{52}{20}\\\\\Rightarrow\ k=\dfrac{13}{5}$

Length of other two sides,

$10\times\dfrac{13}{5}, 15\times\dfrac{13}{5}\ i.e.\ 26\text{ units}, 39\text{ units.}$

So sides of larger triangle = 52 units, 26 units , 39 units

Perimeter of largest triangle = 52 +26+39 = 117 units

Hence, the perimeter of the largest triangle = 117 units.

4 0

3 years ago

Please help i don't understand

alexira [117]

Answer:

Step-by-step explanation:

The diagonals of a parallelogram bisect each other. Hence, the two shorter sides created on diagonal RT ("6x-7" and "x+28" ) are equal.

We can set them equal and solve for x:

$6x-7=x+28\\6x-x=28+7\\5x=35\\x=\frac{35}{5}\\x=7$

So the side length of 6x -7 is:

6(7)-7 = 35

and the side length of x + 28 is:

7 + 28 = 35

THus, the diagonal RT = 35 + 35 = 70 units

Answer choice A is right.

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3 years ago

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olganol [36]

Answer:

Step-by-step explanation:

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3 years ago

Read 2 more answers

Find the length of the arc and express your answer as a fraction times pie

Elina [12.6K]

Solution:

Given a circle of center, A with radius, r (AB) = 6 units

Where, the area, A, of the shaded sector, ABC, is 9π

To find the length of the arc, firstly we will find the measure of the angle subtended by the sector.

To find the area, A, of a sector, the formula is

$\begin{gathered} A=\frac{\theta}{360\degree}\times\pi r^2 \\ Where\text{ r}=AB=6\text{ units} \\ A=9\pi\text{ square units} \end{gathered}$

Substitute the values of the variables into the formula above to find the angle, θ, subtended by the sector.

$\begin{gathered} 9\pi=\frac{\theta}{360\degree}\times\pi\times6^2 \\ Crossmultiply \\ 9\pi\times360=36\pi\times\theta \\ 3240\pi=36\pi\theta \\ Divide\text{ both sides by 36}\pi \\ \frac{3240\pi}{36\pi}=\frac{36\pi\theta}{36\pi} \\ 90\degree=\theta \\ \theta=90\degree \end{gathered}$

To find the length of the arc, s, the formula is

$\begin{gathered} s=\frac{\theta}{360\degree}\times2\pi r \\ Where \\ \theta=90\degree \\ r=6\text{ units} \end{gathered}$

Substitute the variables into the formula to find the length of an arc, s above

$\begin{gathered} s=\frac{\theta}{360}\times2\pi r \\ s=\frac{90\degree}{360\degree}\times2\times\pi\times6 \\ s=\frac{12\pi}{4}=3\pi\text{ units} \\ s=3\pi\text{ units} \end{gathered}$

Hence, the length of the arc, s, is 3π units.

4 0

1 year ago

What does 2 (p -q) +5 (p+q) equal when p = 7 and q = -2? Answer:

salantis [7]

Answer:

Step-by-step explanation:

Given

2(p - q) + 5(p + q) ← substitute p = 7 and q = - 2 into the expression

= 2(7 - (- 2)) + 5(7 + (- 2))

= 2(7 + 2) + 5(7 - 2)

= 2(9) + 5(5)

= 18 + 25

= 43

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4 years ago