Quadrilateral PQRS is a rectangle. What is the length of PQ?

Select the best answer from the choices provided.
А.7
B.19.799
C.24.249
D.28

Answer:

180-87 = 93

Step-by-step explanation:

supplementary angles add up to 180°

so (the other angle + 87)=180°

other angle =180-87=93°

Answer:

93 degrees

Step-by-step explanation:

Supplementary angles add up to 180 degrees. Therefore, the equation for finding the supplementary angle to 87 would be:

[tex]87 + x = 180\\x=180-87\\x=93[/tex]

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Answer:

[tex]\huge\boxed{\sf SG = 31}[/tex]

Step-by-step explanation:

Given:

SW = 3x + 1

WA = 6x

AG = x + 6

SW = AG

Required:

Length of SG = ?

Solution:

Given that:

SW = AG

3x + 1 = x + 6

Combining like terms

3x - x = 6 - 1

2x = 5

x = 5/2

x = 2.5

Now,

SG = SW + WA + AG

SG = 3x + 1 + 6x + x + 6

SG = 3x + 6x + x + 1 + 6

SG = 10x + 6

Put x = 2.5

SG = 10(2.5) + 6

SG = 25 + 6

SG = 31

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

1/4

Step-by-step explanation:

HT represent the probability of tossing a head then Tail.

There is 4 possible results and only 1 give us HT.

We call this theoretical probability. which is

[tex] \frac{x}{y} [/tex]

where x is favorable outcomes and y is total number of outcomes.

So there is a 1/4 probability of getting a head followed by a tail.

Answer:

27 Days

Step-by-step explanation

The rate of her gas consumption is inverse to the time she is driving. This means that if her time spent driving is increased by 66.66% (5/3 of the original rate), then it would inverse to create her decreased gas consumption by 3/5.

3/5 of 45 = 27

27 days

hope this helps :)

Answer:  The guage block height is 4.98 m

The base of the right triangle that is formed is 7.3784 m

The last angle in the triangle is 56 degrees

Step-by-step explanation:

Redraw the triangle formed in the picture and use H for the hypotenuse, O for the block height, and A for the base.  Now we can use trig (SOHCAHTOA) to find the answaers.

Using sine, we can first find the gauge block height, O (Opposite).  Given the Hypotenuse (H) is 8.9 m, we can use the definition of the sine of an angle to find the height, O.

Sine(34) = Opposite/Hypotenuse (O/H), or O = H*Sine(34)

O = (8.9)*(0.5592)

O = 4.98 m, the height of the gauge block,

The base of the triangle, A, can be determined with cosine.

Cosine(34) = A/O, or A = Cosine(34)*O

A = (0.82904)*(8.9)

A = 7.3784 m

The sum of all angles in a triangle is 180 degrees.  

180 = X + 34 + 90

X = 56 degrees

Answer:

D 37.64

Step-by-step explanation:

C=2πr

so 2✘3.14 ✘6

Answer:

The cover has diameter of:

a.

Area of the pool cover:

b.

The length of the rope:

Answer:

Step-by-step explanation:

Add the length of the pool and the extent the pool cover [ 12in = 1ft ] has over the pool.

20 + 2 = 22ft

Part A:

The formula for the area of a circle is πr².

To find the radius just divide by two; 22 / 2 = 11ft

= π(11)²

= 121π

≈ 379.94ft

Part B:

We can use the circumference formula [ dπ ] to find how long the rope is.

= 22(3.14)

= 69.08ft

Best of Luck!

Answer:

see explanation

Step-by-step explanation:

For the triangle to be isosceles it must have 2 equal sides.

Calculate the length of the sides using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = A (- 1, 2) and (x₂, y₂ ) = B (3, 5)

AB = [tex]\sqrt{(3-(-1))^2+(5-2)^2}[/tex]

     = [tex]\sqrt{(3+1)^2+3^2}[/tex]

     = [tex]\sqrt{4^2+9}[/tex]

     = [tex]\sqrt{16+9}[/tex] = [tex]\sqrt{25}[/tex] = 5

Repeat with (x₁, y₁ ) = A (- 1, 2) and (x₂, y₂ ) = C (3, - 1)

AC = [tex]\sqrt{(3+1)^2+(-1-2)^2}[/tex]

      = [tex]\sqrt{4^2+(-3)^2}[/tex]

      = [tex]\sqrt{16+9}[/tex] = [tex]\sqrt{25}[/tex] = 5

Consider B (3, 5) and C (3, - 1)

Since both x- coordinates are 3, this is a vertical line and its length is the difference of the y- coordinates, that is

BC = | - 1 - 5 | = | - 6 | = 6

Then

AB = AC = 5 , BC = 6

Since AB = AC = 5 then the triangle is isosceles

Answer:

Step-by-step explanation:

Answer:

The selling price of 21 articles is equal to the cost price of 18 articles. Find the loss percent. Answer: answer is 100/7 %

I circled the answer and put an example hope it helps

I'm not sure if this is what you meant - 3.12.5.8.6.6, but I'm operating based on that

mean - 6.7

median - 6

mode - 6

range - 9

Answer:

B, D, H, I, J

Step-by-step explanation:

Median: A line segment that joins the vertex of a triangle to the midpoint of the opposite side.

Step-by-step explanation:(2, -3)

[tex]thank \: you[/tex]

[tex]\\ \sf\longmapsto (x,y)=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

[tex]\\ \sf\longmapsto (x,y)=\left(\dfrac{5+8}{2},\dfrac{3.5+10}{2}\right)[/tex]

[tex]\\ \sf\longmapsto (x,y)=\left(\dfrac{13}{2},\dfrac{13.5}{2}\right)[/tex]

Answer:

D) 9.8

Step-by-step explanation:

The geometric mean of two numbers x and y is

[tex]\sqrt{xy}[/tex]

so [tex]\sqrt{8*12}[/tex] = [tex]\sqrt{96}[/tex] [tex]\approx 9.7979[/tex]

Which, since the 9 in the hundredths place is greater than 5, we can round up to 9.8

Answer:

-0.450 as a fraction is -9/20

Step-by-step explanation:

Since there 3 decimal places, divide it by 1000

-450/1000 and simplify it

Answer:

65÷5(18-5)

=65÷5×13

=13×13

=169

The length of the shorter piece is 45 inches.

Let's represent the length of the shorter piece as "x" inches.

According to the information given, the length of the longer piece would be three times the length of the shorter piece, which means it's 3x inches.

Since the total length of the pipe is 180 inches, we can set up an equation:

x (shorter piece) + 3x (longer piece) = 180

Now solve for x:

4x = 180

x = 45

Therefore, the length of the shorter piece is 45 inches.

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Here we go !!

Since it's a regular pentagon, all it's sides are equal so let's solve for x

[tex] \hookrightarrow \: 3(x - 1) = 5x - 6[/tex]

[tex] \hookrightarrow \: 3x - 3 = 5x - 6[/tex]

[tex] \hookrightarrow \: 3x - 5x = - 6 + 3[/tex]

[tex] \hookrightarrow \: - 2x = - 3[/tex]

[tex] \hookrightarrow \: x = \dfrac{ - 3}{ - 2} [/tex]

[tex] \boxed{\boxed{x = \dfrac{3}{2} }}[/tex]

now let's find the measure of each side, i.e

[tex] \hookrightarrow \: 5x - 6[/tex]

[tex] \hookrightarrow \: (5 \times \dfrac{3}{2}) - 6[/tex]

[tex] \hookrightarrow \: \dfrac{15}{2} - 6[/tex]

[tex] \hookrightarrow \: 7.5 - 6[/tex]

[tex] \mathrm{\hookrightarrow \: 1.5 \: units}[/tex]

perimeter = 5 × side length ( for a regular pentagon )

[tex] \hookrightarrow \: 1.5 \times 5[/tex]

[tex] \boxed{ \boxed{ \: \: \: \: \: \: \: \: 7.5 \: \: units \: \: \: \: \: \: \: }}[/tex]

Answer:

The answer is C

Step-by-step explanation:

since the left side reads k times a, the only way to get a by itself is by dividing both sides by k

a.yes

Step-by-step explanation:

a.angle BCD =b because angle BCD is alternate angle of angle ABC

b.the two angles angle BAC and angle ACD is co-interior angle because they are inside a parallel line

Answer:

[tex]13\leq x<4[/tex]

Explanation:

If a side has a bracket [] then it is less than or equal to, meaning that it can reach that exact number.

However, if a side has a parentheses () then it is simply less than. It cannot be that exact number, but it can be even slightly less than that number.

Answer:

The cost of the printer is x=288 and cost of computer is 3x=864

Step-by-step explanation:

Let the cost of the printer be x and cost of computer be 3x

ATQ, x+3x=1152, x=288.

The cost of the printer is x=288 and cost of computer is 3x=864

Explanation:

The given limit notation means we're approaching x = 3 from the left side. So start at say x = 0 and approach x = 3. We don't actually get to x = 3 itself, but instead just get closer and closer. Note how y gets closer to y = 1.5

Answer:

total = 99m² + 39.4m²

= 148.4m²

Answer:

Ok so

Step-by-step explanation:

Yes yes yes yes its C

Answer:

25958400

Step-by-step explanation:

[tex] {8}^{2} \times 6(4 + {8}^{2} \times (10 - 6) {)}^{2} [/tex]

[tex] = 64 \times 6(4 + {2}^{6} \times 4 {)}^{2} [/tex]

[tex] = 64 \times 6(4 + {2}^{6} \times {2}^{2} {)}^{2} [/tex]

[tex] = 64 \times 6(4 + {2}^{8} {)}^{2} [/tex]

[tex] = 64 \times 6(16 + 2048 + 65536)[/tex]

[tex] = 64 \times 6 \times 67600[/tex]

[tex] = 25958400[/tex]

Answer:

sin b = 0.8

Step-by-step explanation:

Since a and b are complementary angles , then

sin b = cos a = 0.8

The sine of angle b is 0.8

"It is a triangle in which one of the angle measures 90° "

"It is the longest side of the right triangle."

"In a right triangle, sine of angle [tex]\theta[/tex] is the ratio of the opposite side of angle  [tex]\theta[/tex] to the hypotenuse."

"In a right triangle, cosine of angle [tex]\theta[/tex] is the ratio of the adjacent side of angle  [tex]\theta[/tex] to the hypotenuse."

"Two angles are complementary if the sum of their measures is equal to 90 degrees."

For given question,

We have been given a right triangle.

here,

∠a + ∠b = 90°

∠b = 90° - ∠a                             ................(i)

This means, a and b are complementary angles.

The cosine of a is 0.8

cos(a) = 0.8

We need to find the sine of angle b.

sin(b)

= sin(90 - a)                        .............(from (i))

= cos(a)                               .............(Since [tex]sin(90-\theta)=cos(\theta)[/tex])

= 0.8                                    ............(Given)

So, sin(b) = 0.8

Therefore, the sine of angle b is 0.8

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Each term has a common factor of x + y + z, so

a (x + y + z) + b (x + y + z) + c (x + y + z) = (a + b + c) (x + y + z)