(Score for Question 2: ___ of 10 points)
2. A room is shaped like a trapezoid as shown.


(a) What is the area of the room? Use the formula . Show your work.
(b) Carpet costs $8.30 per square foot. How much will it cost to carpet the room? Show your work.
(c) Furniture covers 25% of the floor. How many square feet of carpet are covered by furniture? Show your work.

(PLEASE SHOW THE WORK ON HOW TO DO IT FOR EACH ONE)
Answer:

Answers:

bio = 258

sociology = 169

============================================================

Work Shown:

x = number of bio textbooks

y = number of sociology textbooks

x+y = 427 books sold total

y = x-89 since 89 less sociology textbooks were sold compared to bio

Apply substitution to get the following

x+y = 427

x+x-89 = 427 ... replace y with x-89

2x-89 = 427

2x = 427+89

2x = 516

x = 516/2

x = 258 bio textbooks were sold

y = x-89

y = 258-89

y = 169 sociology textbooks were sold

[tex]y = 3x-2\\\\~~~=3(-5) -2\\\\~~~= -15-2\\\\~~~= -17[/tex]

Answer:

y = -17

Step-by-step explanation:

Given values :

⇒ x = -5

Let's substitute in the expression to find y :

⇒ y = 3(-5) - 2

⇒ y = -15 - 2

⇒ y = -17

The distance that would be covered after t seconds = 1.5t meters

The speed of the race=distance/time =1.5m/s

The time given = t seconds

The distance (d) = ?

From the formula of speed = distance/time, make distance the subject of formula,

distance (d) = speed×time

= 1.5×t

= 1.5t meters

Therefore, the distance covered is 1.5t meters after t seconds.

Learn more about distance here:

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Answer:

30° and 60°

Step-by-step explanation:

Let the interior angles be ∠x₁ (smaller) and ∠x₂ (larger), and the exterior angle ∠X.

Making the statements into equations :

Size of an exterior angle of a triangle is the supplement of smaller of two opposite interior angles ⇒ ∠X + ∠x₁ + ∠x₂ = 180° [Equation 1]

Greater of the opposite interior angles exceeds smaller by 30° :

⇒ ∠x₂ = ∠x₁ + 30° [Equation 2]

By exterior angle property :

⇒ ∠x₁ + ∠x₂ = ∠X [Equation 3]

Substituting Equation 3 in Equation 1 :

⇒ ∠x₁ + ∠x₂ + ∠x₁ + ∠x₂ = 180°

⇒ 2 (∠x₁ + ∠x₂) = 180°

⇒ ∠x₁ + ∠x₂ = 90°

⇒ ∠x₂ = 90° - ∠x₁ [Equation 4]

Substituting Equation 4 in Equation 2 :

⇒ 90° - ∠x₁ = ∠x₁ + 30°

⇒ 2∠x₁ = 60°

⇒ ∠x₁ = 30°

Substituting the value of ∠x₁ in Equation 2 :

⇒ ∠x₂ = 30° + 30°

⇒ ∠x₂ = 60°

The measures of the interior angles are 30° and 60°

Answer:

x=48º

Step-by-step explanation:

Using the normal distribution, it is found that 84 people would be expected to have BP > 160.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Researching the problem on the internet, the mean and the standard deviation for the BPs are given, respectively, by:

[tex]\mu = 122, \sigma = 22[/tex].

The proportion of adults with BP > 160 is given by one subtracted by the p-value of Z when X = 160, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{160 - 122}{22}[/tex]

Z = 1.73

Z = 1.73 has a p-value of 0.9582.

1 - 0.9582 = 0.0418.

Out of 2000 people:

0.0418 x 2000 = 83.6.

Rounding to the nearest integer, 84 people would be expected to have BP > 160.

More can be learned about the normal distribution at https://brainly.com/question/24663213

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Step-by-step explanation:

that means the opposite ...

the opposite of

x > 39

is

x <= 39

Answer: [tex]b^{2}(1-21a^{3})[/tex]

Step-by-step explanation:

[tex]b^{2} - 21a^{3} b^{2} \\b^{2}(1-21a^{3})[/tex]

Answer: 160 seconds

Step-by-step explanation:

First let us find the number of seconds per rotation

52 second/65 rotations

52/65

0.8 seconds/1 rotation

0.8 seconds per rotation

Now let us multiply 0.8 by 200 to get our answer

0.8 * 200

160

It takes 160 seconds to do 200 rotations

Answer:

160 seconds

Step-by-step explanation:

We have 65 rotations in 52 seconds, let's represent it like this:

[tex]\frac{52 seconds}{65 rotations}[/tex]

Now, let's multiply this by 200 rotations, and cancel out the rotations on the bottom:

[tex]\frac{52 seconds}{65 rotations} * 200 rotations[/tex]

See how there is rotations on both the top and bottom? This cancels both of them and leaves seconds!

Multiply the above equation and we get:

160 seconds or 2 minutes 40 seconds.

Hope this helps! Good luck and if you have questions please leave them in the comments!

Answer:

the vertex is (-3 , -3)

Step-by-step explanation:

[tex]\frac{1}{2} x^{2}+3x+\frac{3}{2}[/tex]

[tex]=\frac{1}{2} \left( x^{2}+6x+3\right)[/tex]

[tex]=\frac{1}{2} \left[ \left( x+3\right)^{2} -9+3\right][/tex]

[tex]=\frac{1}{2} \left( x+3\right)^{2} -3[/tex]

then the vertex is (-3 , -3)

Answer:

2x + 2y + 3y

Step-by-step explanation:

The others are equations ( containing the = sign).

Answer:

2x+2y+3y

Step-by-step explanation:

an expression is not equated to any number but an equation is equated to any number especially zero

Answer:

Ok I can walk you through if you comment the questions ok?

Step-by-step explanation:

Trust me :-)

Answer:

1. obtuse

2.straight

3.right

4. acute

5. <EAF

6. <DAF

7. <BAF

8. They are perpendicular to each other

Step-by-step explanation:

since there are answer options we don't need to formally solve the system of equations, we only need to try the first point of every option, and see, where the equations are true.

if we cannot find it for the first point, then we would need to try the same thing for the serving points.

let's put (0, 6) into the first equation :

-2×0² + 6 = 6

6 = 6 true

let's put it into the second equation ;

4×0² + 3×6 = 28

18 = 28 false

that eliminates the first 2 answers.

let's put (-1, 4) into the first equation :

-2×(-1)² + 4 = 6

-2×1 + 4 = 6

-2 + 4 = 6

2 = 6 false

that eliminates the third answer.

let's put (-1, 8) into the first equation :

-2×(-1)² + 8 = 6

-2 + 8 = 6

6 = 6 true

let's put it into the second equation :

4×(-1)² + 3×8 = 28

4 + 24 = 28

28 = 28 true

and because the square function delivers the same result for -1 and +1, it is also true for the second point.

and the 4th answer is therefore correct.

The best approximation of the factor by which the population increases over a ten years period will be 6.19.

The exponent denotes that the base will rise to a specific level of strength. The base is X, and the power is n.

A certain buffalo population increases by a factor of 1.2 each year.

Then the best approximation of the factor by which the population increases over a ten years period will be

→ 1.2¹⁰

→ 6.1917

→ 6.19

More about the exponent link is given below.

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Question 1 ) A ray has one endpoint and continues forever in the opposite direction

Question 2)

⇒

IG

Question3)

⇒

DC

Hope this helps!

Step-by-step explanation:

1)

SOLUTION

5(x+5) = 6. (6 +9)

90 = 5x + 25

13 = x

2)

SOLUTION

x (3) = (4) (6)

3x = 24

x= 8

3)

SOLUTION

3 (3 + x + 2) = (x+1)(x + 1 + x – 1) Use Theorem

3x + 15=2x²+2x

0 = 2x² – x – 15

0 = (x – 3) (2x + 5) Solve for x

3 = x Use positivesolution

Answer:

C.

Step-by-step explanation:

-3 7/8 rounds down to -4

4.63 rounds up to 5

-4 x 6 + 5

-24 + 5

-19

her answer (-19.14) also rounds to -19

So yes, it is reasonable and the correct response is C.

Answer:

[tex]6 \frac{2}{13} [/tex]

Step-by-step explanation:

the perimeter is the sum of the 4 individual sides.

if the sides are doubled, so is the sum of them.

therefore, the new perimeter is then

12×2 = 24 cm

Answer:

[tex]\textsf{i)} \quad \text{T} &=2 \pi r^2 + \dfrac{26}{r}[/tex]

ii)  radius = 1.27 cm (3 sf)

   height = 2.55 cm (3 sf)

Step-by-step explanation:

[tex]\text{Volume of a cylinder}=\pi r^2 h \quad \text{(where r is radius and h is height)}[/tex]

Given volume = 13 cm³, rewrite the equation making h the subject:

[tex]\implies 13=\pi r^2 h[/tex]

[tex]\implies h=\dfrac{13}{\pi r^2}[/tex]

Substitute found expression for h into the Surface Area equation to find the expression for the total surface area, T:

[tex]\begin{aligned}\text{Surface Area of a cylinder} & =2 \pi r^2 + 2 \pi r h\\\implies \text{Surface Area} & =2 \pi r^2 + 2 \pi r \left(\dfrac{13}{\pi r^2}\right)\\& =2 \pi r^2 + \dfrac{26 \pi r}{\pi r^2}\\ \implies \text{T} &=2 \pi r^2 + \dfrac{26}{r}\end{aligned}[/tex]

To find the radius of the minimum surface area, differentiate T with respect to r:

[tex]\begin{aligned}\text{T}& =2 \pi r^2 +26r^{-1}\\\implies \dfrac{dT}{dr} & =(2)2 \pi r^{(2-1)}+(-1)26r^{(-1-1)}\\ & =4 \pi r-26r^{-2}\\ & =4 \pi r-\dfrac{26}{r^2}\\ & = \dfrac{4 \pi r^3-26}{r^2} \end{aligned}[/tex]

Set it to zero, and solve for r:

[tex]\begin{aligned}\dfrac{dT}{dr} & = 0 \\\implies \dfrac{4 \pi r^3-26}{r^2} & = 0 \\\impliles 4 \pi r^3-26 & = 0 \\4 \pi r^3 & = 26 \\r^3 & = \dfrac{13}{2 \pi} \\r & = \sqrt[3]{\dfrac{13}{2 \pi}} \end{aligned}[/tex]

To find the height, substitute the found value of r into the equation for height (found previously):

[tex]\begin{aligned}h & =\dfrac{13}{\pi r^2} \\\implies h & =\dfrac{13}{\pi \left(\sqrt[3]{\dfrac{13}{2 \pi}}\right)^2} \\& =2.548499134\end{aligned}[/tex]

Therefore,

Answer:

(x - 1) x - X^2

Hope this helps :)

Answer:

1.09

Step-by-step explanation:

9.81÷3=3.27 This shows the cost of 1 yard

3.27÷3= 1.09 since theres 3 feet in a yard, when you divide by 3 it shows how much 1 foot costs

Answer: Option (c) is correct.

68% of the data points lie between 10 and 18.

Step-by-step explanation: Given :  a normal distribution with a standard deviation of 4 and a mean of 14

We have to choose the  sentence that correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14.

Since, given 68% data.

We know mean of data lies in middle.

And standard deviation is distribute equally about the mean that is 50% of values less than the mean  and 50% greater than the mean.

So, 68% of data lies

mean - standard deviation = 14 - 4 = 10

mean + standard deviation = 14 + 4 = 18

So, 68% of the data points lie between 10 and 18.

Answer:

4x² + 4y² + 8xy

Step-by-step explanation:

( 2x + 2y ) ( 2x + 2y ) = ( 2x + 2y )²

Formula : -

( a + b )² = a² + b² + 2ab

Here,

a = 2x

b = 2y

( 2x + 2y )²

= ( 2x )² + ( 2y )² + 2 ( 2x ) ( 2y )

= 2²x² + 2²y² + 8xy

= 4x² + 4y² + 8xy