The net below shows a square pyramid. What is the lateral surface area?
A. 176 in^2
B. 112 in^2
C. 64 in^2
D. 210 in^2

-11+2(4x-1)+6

-11+8x-2+6

-13+8x+6

-7+8x

Answer:

x= 81°

Step-by-step explanation:

the interior angles of a quadrilaterial add up to 360°

143+80+56+x=360

condense left side: 279+x=360

isolate x: 279-279+x=360-279

x= 81°

Answer:

[tex]3^{6-(-2)}[/tex]

Step-by-step explanation:

[tex]~~3^6 \div 3^{-2}\\\\\\=\dfrac{3^6}{3^{-2}}\\\\\\=3^{6-(-2)}[/tex]

Answer:

7(3j+8k)

Step-by-step explanation:

Answer:

y = 3(x - 1)(x + 5)(x + 2)

Step-by-step explanation:

Given points:   (1, 0)   (-5, 0)   (-2, 0)   (-4, 30)

x-intercepts are when y = 0

Therefore, the x-intercepts are x = 1, x = -5 and x = -2

So (x - 1), (x + 5) and (x + 2) are all factors of the polynomial.

Therefore, the equation of the polynomial is:

y = a(x - 1)(x + 5)(x + 2)  where a is a constant to be found

To find the constant a, input the point (-4, 30) into the equation and solve:

⇒ a(-4 - 1)(-4 + 5)(-4 + 2) = 30

⇒ a(-5)(1)(-2) = 30

⇒ 10a = 30

⇒ a = 3

Therefore, the equation of the polynomial is:

y = 3(x - 1)(x + 5)(x + 2)

Answer:

C

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (5, 2 ) and (x₂, y₂ ) = (10, - 3 )

m = [tex]\frac{-3-2}{10-5}[/tex] = [tex]\frac{-5}{5}[/tex] = - 1 , then

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (5, 2 ), then

2 = - 5 + c ⇒ c = 2 + 5 = 7

y = - x + 7 ← equation of line

It is true that you are required to keep a Driving Log and record a minimum of 60 hours of driving time, while on level 1

There are 5 requirements a driver must fulfil before progressing to level 2 of learner permit.

One of these requirements is that the driver must spend at least 60 hours driving.

This means that the minimum driving time is 60 hours

Hence, the statement is true

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Answer:

D

Step-by-step explanation:

[tex]slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ g(t)= 20.9t\qquad \begin{cases} t_1=2\\ t_2=3 \end{cases}\implies \cfrac{g(3)-g(2)}{3-2}\implies \cfrac{20.9(3)~~ - ~~20.9(2)}{1} \\\\\\ 62.7~~ - ~~41.8\implies 20.9[/tex]

Answer:

Answer choice B: 153

Step-by-step explanation:

Problem 1

There are 23 women that drive out of 12+3+23+8+5+32 = 83 people total

Divide the two values: 23/83 = 0.28 approximately

This says about 28% of the total people are women who drive a car.

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Problem 2

The "given" is a very important keyword in probability. In this case, we're given that the employee takes the bus. That means we soly focus on the "bus" column only. Everything else is irrelevant. This is because we know 100% that whoever we selected takes the bus, and we've shrunk down the population just these employees.

We have 8 males who take the bus out of 12+8 = 20 people who take the bus. Therefore, 8/20 = 0.40 represents the relative frequency of males who take the bus out of all bus commuters. In other words, 40% of the bus riders are male.

the probability that a woman selected at random has a blood pressure between 114 and 128 is 0.5588.

A z-table also known as the standard normal distribution table, helps us to know the percentage of values that are below (or to the left of the Distribution) a z-score in the standard normal distribution.

Given the mean is 121 while the standard deviation of the women is 9. Therefore, Using the z-table, the probability can be found.

(a) The probability that a woman selected at random has blood pressures greater than 136.

[tex]P(x > 136) = 1 - P(x < 136)\\\\P(x > 136) = 1 - P(z < \dfrac{x-\mu}{\sigma})[/tex]

                  [tex]=1 - P(z < \dfrac{136-121}{9})\\\\=1 - P(z < 1.667)\\\\=1-0.9515\\\\=0.0485[/tex]

(b) The probability that a woman selected at random has a blood pressure less than 114.

[tex]P(x < 114)= P(z < \dfrac{114-121}{9})\\\\[/tex]

                  [tex]= P(z < -0.77)\\\\= 0.2206[/tex]

(c) The probability that a woman selected at random has a blood pressure between 114 and 128.

[tex]P(114 < x < 128)= P(\dfrac{114-121}{9} < z < \dfrac{128-121}{9})\\\\[/tex]

                  [tex]= P(-0.77 < z < 0.77)\\\\= P(z < 0.77)-P(z < -0.77)\\\\= 0.7794 - 0.2206\\\\=0.5588[/tex]

Hence, the probability that a woman selected at random has a blood pressure between 114 and 128 is 0.5588.

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Answer:

56

Step-by-step explanation:

First I would get the area of the entire figure as if it were a Rectangle

10x7 = 70 Area if the figure was a rectangle.

We can form a triangle with the cut out space, the height of the triangle is 10-6 which is 4 and has a base of 7.

7x4= 28

28/2 = 14 Area of triangle cutout

Now you subtract the two figures

70-14= 56

56 Is the area

The area of the given shape is 56 square units.

The quantity of space within a two-dimensional figure or form is measured by its area. It is a number that describes the size or extent of a surface, like the surface of a flat plane or the contours of an area on a map.

First I would get the area of the entire figure as if it were a Rectangle

10x7 = 70 Area if the figure was a rectangle.

Form a triangle with the cutout space, the height of the triangle is 10-6 which is 4, and has a base of 7.

7 x 4= 28

28/2 = 14 Area of triangle cutout

Now you subtract the two figures

70-14= 56 Square units

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Answer:

x=3

Step-by-step explanation:

I took the test and I got it right but if you want an explanation  see bellow.

so triangle ABC is a 45- 45 -90 and we are given the hypotenuse of [tex]6\sqrt{2}[/tex]

and on a 45-45-90 triangle we know that the hypotenuse is always [tex]s\sqrt{2}[/tex] s  standing for the lengths of both of the legs since they are both equal, so this tells us that line segment AB and BC are equal to 6, SO triangle BCD hypotenuse is equal to 6.Triangle BCD is a 60-90-30 triangle as we can tell by the measures given, and in a 60-90-30 triangle the hypotenuse is equal to S and it's shorter length known as line segment BD on this triangle is equal to [tex]\frac{s}{2}[/tex] and since we know s=6 we can do [tex]\frac{6}{2}[/tex] giving us our answer 3.

Using the sine ratio and the cosine ratio, the value of x in the given triangle is calculated as: x = 6.

Using the sine ratio, find BC:

sin ∅ = opposite/hypotenuse

Given the following:

∅ = 45°

hypotenuse = 6√2

opposite = BC

Substitute:

sin 45 = BC/6√2

sin 45 = BC/6√2

√2 = BC/6√2 [sin 45 = √2]

BC = √2 * 6√2

BC = 12 units

Use the cosine ratio to find x:

cos ∅ = adjacent/hypotenuse

Thus, we have:

cos 60 = x/12

1/2 = x/12 [cos 60 = 1/2]

2x = 12

x = 6.

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Answer:

The answer is given below

Step-by-step explanation:

[tex](5y + 10) = - 3[/tex]

[tex]5y = - 3 - 10[/tex]

[tex]5y = - 13[/tex]

[tex]y = - 13 \div 5[/tex]

This is the velue of y

Answer:

5(y+2)= -3

distribute

5y+10=-3

-10

5y=-13

divide by 5

y=-13/5

Hope This Helps!!!

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the unit rate , divide the total cost by number of books

Cost of 1 book = 26.25 ÷  3

                        = $ 8.75

Maria bought 3 books for a total of $26. 25. How much did each book cost ?

In this question it is given that Maria bought 3 books and the cost of 3 books is $26.25. We are asked to calculate the cost of 1 book.

We can find the cost of 1 book by dividing the total cost by number of books.

Cost of 1 book = $26.25 ÷ 3 = [tex]\dfrac{26.25}{3}[/tex] = 8.75

Cost of 1 book = $8.75

Cost of 3 books = 8.75 × 3 = $26.25

Hence, proved

Applying the pythagroean theorem, the formula to find the horizontal distance, d, is: [tex]\mathbf{d = \sqrt{h^2 - R^2} }[/tex]

The pyhagroean theorem is given as, c² = a² + b², where h is the longest side of the right triangle.

Given  the following:

The formula derived would be:

h² = d² + R²

Make d the subject fo the formula

[tex]\mathbf{d = \sqrt{h^2 - R^2} }[/tex]

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Answer:

A. Minimum = 54, Q1= 69.5, Median = 75, Q3= 106, Maximum = 183

Step-by-step explanation:

Arranging the data set in order from least to greastest we get:

54, 68, 71, 72, 75, 84, 104, 108, 183

From this, we can see that the minimum value is 54 and the maximum value is 183.

Taking a number off one by one on each side of the data set gives the median. In the middle lies 75, so that is our median

To find quartile ranges, split the data set into two where the median lies, then, find the median of those two data sets. The medians will be the values of the upper (Q3) and lower quartiles (Q1).

Q1: 54, 68, 71, 72

68 + 71 = 139
139 ÷ 2 = 69.5

-----

Q3: 84, 104, 108, 183

104 + 108 = 212

212 ÷ 2 = 106

Option A is the only answer with all of these values, therefore, it is the answer.

hope this helps!

Answer:

486kg

Step-by-step explanation:

Answer:

The answer for Q35 is : 176 cubic feet

Step-by-step explanation:

V = 16×3×2+16×5

= 96 + 80

= 176 cubic feet

Answer:

175

Step-by-step explanation:

How would one find a three-digit number which is 5 times as large as the product of its digits?

100a + 10b +c = 5abc

This shows that c must be a multiple of 5. Since it is a digit, c=5 ( c=0 does not work ).

Then:

100a + 10b + 5 = 25ab

This again shows that 10b+5 is a multiple of 25.

By testing all the digits, b=2 or b=7.

If b=2, then

100a + 25 = 50a

which has the solution a= -1/2, not a digit.

if b=7

100a +75 = 175a

Now the solution is a=1, so finally the number is 175. Indeed, 175 = 5*1*7*5.

Does that answer your question..?

Answer:

The option u chose is the correct one

Answer:

v=0g

That's what i got

good luck

Answer:

A.

Step-by-step explanation:

Answer:

The square root of an imperfect square

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

The shortest leg warmer:

4.5

The longest leg warmers:

6 and 6.5

6 + 6.5 = 12.5

12.5 - 4.5 = 8