Multiply and simplify.
(x + 3)(x - 8)
A) 2x - 24
B) x2 - 5x + 24
C) x2 - 5x - 24
D) x2 - 8x - 24

Answer:A

Step-by-step explanation:took the test

The correct option is a. A rectangular prism measuring 5 feet by 6 feet by 8 feet and a triangular prism with the dimensions of 3 feet by 5 feet by 8 feet describes the correct dimensions of the figures.

A rectangular prism has three dimensions: length, width, and height.

A triangular prism has three dimensions: the base of the triangular face, the height of the triangular face, and the length (or depth) of the prism.

Let's examine each option based on the given dimensions:

Option a is the correct answer. It logically fits the dimensions of the shed with a larger rectangular prism for the base and a reasonably proportioned triangular prism for the roof.

In figure, the dimensions of rectangular prism are 5 feet by 6 feet by 8 feet and the dimensions of triangular prism are 3 feet by 5 feet by 8 feet.

The complete question is

The shed in Adam’s backyard is shown below.

Which correctly describes the dimensions of the figures that make up the shed?

a. a rectangular prism measuring 5 feet by 6 feet by 8 feet and a triangular prism with the dimensions of 3 feet by 5 feet by 8 feet

b. a rectangular prism measuring 3 feet by 5 feet by 8 feet and a triangular prism with the dimensions of 5 feet by 6 feet by 8 feet

c. a rectangular prism measuring 5 feet by 6 feet by 8 feet and a triangular prism with the dimensions of 3 feet by 5 feet by 6 feet

d. a rectangular prism measuring 3 feet by 5 feet by 6 feet and a triangular prism with the dimensions of 5 feet by 6 feet by 8 feet

Answer:

(B) is the homogeneous mixture

Answer:

25 dollars

Step-by-step explanation:

To calculate the cost of a 75 credits card, we first find the cost per credit and the initial cost of the card, which are $0.18 and $8 respectively. The total cost is then $21.5.

We know Jude bought a card with 50 credits for $17 and Audrey got one with 80 credits for $26. We can say that the cost per credit is constant. To find this cost per credit, we first need to calculate the difference between the costs and then divide the result by the difference in number of credits: So, cost per credit = (26-17) / (80-50) = 0.18. This implies for each credit the cost is 18 cents. For a 75 credit card, the price would be 75 * 0.18 = $13.5. However, this doesn't account for the initial cost to purchase the game card. If we say the initial cost is a flat fee included in the price Jude and Audrey paid, we need to subtract the total cost of the credits from their total spend to work this out: Jude’s initial cost = $17 - (50 * $0.18) = $8. Audrey’s initial cost = $26 - (80 * $0.18) = $8. As we supposed, initial cost is a constant of $8. Hence, the cost of a 75 credits card would include this initial cost: 75 credits would cost = $8 + 75 * $0.18 = $21.5.

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Cancel 3 on both sides

-2y + 2y = 0

Simplify -2y + 2y to 0

0 = 0

Since both sides are equal, there are infinitely many solutions;

= Infinitely Many Solutions

The Answer is B

Hope this helps :)

So 25% of $199 is $49.75. If you subtract the promotion off you get 199-49.75=149.25. Then the sales tax is 6% so you take the new cost $149.25 and multiply it by .06 which equals 8.955. so then you add on the tax so $149.25+8.955=$158.205. Your answer is $158.205 or approximately $158.21

Answer:

$94.61

Step-by-step explanation:

Tax is on reduced and not original price

Answer:

Neither A or B

Answer: Option A

Step-by-step explanation:

Given two variables X and Z, it is said that there is a correlation between X and Z if both variables change together.

That is, if when the variable X increases the variabl Z increases also then there is a positive correlation

if when the variable X increases the variable Z decreases then there is a negative correlation.

Now observe the graphs that are shown in the image. Note that in both cases the points are scattered and there is no clear relationship between the variables. Therefore the correlation is zero in both cases

Examples of strong positive and negative correlations are shown in the attached image

Answer:

The correct answer is 13.75

Step-by-step explanation:

4+2= 6

6+1=7

6+7= 13

13+1/2= 13.5

13.5+1/4= 13.75

Answer:

[tex]s_10=\frac{1023}{128}[/tex]

Step-by-step explanation:

4+2+1+1/2+1/4.....

WE need to find out the sum s10

first term is 4 and second term is 2

2/4 = 1/2

1/2= 1/2

1/2 / 1= 1/2

so common ratio is 1/2

The given series is geometric series

we use the sum formula for the geometric series

[tex]s_n= a\frac{(1-r^n)}{1-r}[/tex]

Where 'r' is the common ratio and 'a' is the first term

a= 4  and r= 1/2

Plug in the values in the sum formula'

[tex]s_n= 4\frac{(1-(\frac{1}{2})^n)}{1-(\frac{1}{2})}[/tex]

Given n=10

[tex]s_10= 4\frac{(1-(\frac{1}{2})^{10})}{1-(\frac{1}{2})}=\frac{1023}{128}[/tex]

Answer:

4x + 16

Step-by-step explanation:

Area of a triangle is:

A = ½ bh

Here, b = x+4 and h = 8:

A = ½ (x + 4) (8)

A = 4x + 16

The area of the given triangle with sides 5x,8, and x+4 is 4x + 16.

We have given the diagram.

In the diagram we have,

base(b) = x+4 and height(h) = 8

We have to determine the area of the triangle

[tex]A = 1/2\times b\times h[/tex]

Where b is the base and h is the height of the triangle

Use the given values in the above formula we have,

[tex]A = 1/2(x + 4) (8)\\\\A = 4x + 16[/tex]

Therefore the area of the triangle is 4x + 16.

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Let's assume x is the blank.

The equation is therefore:

[tex]

7\times(5-2)=(7\times5)-(x\times2) \\

7\times3=35-2x \\

21=35-2x \\

21-35=-2x \\

-14=-2x\Longrightarrow x=\frac{-14}{-2}=\boxed{7}

[/tex]

Answer:

Step-by-step explanation:

7x(3) = 21

(7x5) - (7x2) = 21

35-14=21

Answer is (7 x 2)or 7

Because you are required to get a positive number of centimetres we use positive value of x.

[tex]

\mid6.75-x\mid<0.25 \\

6.75-x<0.25\Longrightarrow x>6.5

[/tex]

The answer is B: The length of a part must be greater than 6.5 cm.

Answer:

m<PQR = 80°

Step-by-step explanation:

Points to remember

Sum angles in a linear pair is 180

To find the value of x

It is given that, angle PQR and angle RQS are linear pairs, and

m< PQR =5x+5 and m<RQS =11x-65

m<PQR + m<RQS = 180

5x + 5 + 11x - 65 = 180

16x -60 = 180

16x = 180 + 60

16x = 240

x = 15

To find the value of angle PQR

m<PQR = 5x + 5

 = 5*15 + 5

 = 75 + 5 = 80

Therefore m<PQR = 80°

Subtract 11 from 5 to get -6.

Because the equation is in between two vertical lines, this means the absolute value, which is a positive value, so -6 becomes positive 6.

The answer is 6

Outcome Bag of Gold Magic Wand

Relative frequency 0.32 0.68

The relative frequency of getting a bag of gold is .......... reasonably close

.32 is close to 30% so

Alison's claim about the theoretical probability is likely to be 2............true

Further, this means that the theoretical probability of getting a magic wand is most likely 3............1 - 30% = 70%

what you do I set 45x equal to your two other angles since the sum of those two angles is equal to that angle outside the triangle.

so you have

45x=57+x+25x

combine like terms

45x=57+26x

then subtract 26x on both sides to get

19x=57

lastly divide by 19

x=3

Answer:

3 degrees

Step-by-step explanation:

Answer:

D. Pi

Step-by-step explanation:

Circumference=diameter*pi

Or

Circumference=2*pi*radius

The answer is 3. You would just match up the sides and combine the common things. 3z times z is 3z^2 because it would be the same number twice, not times two. Then 9 times 8 is 72. Z times 8 is 8z because it would be 8 times whatever number the variable was. Then lastly it’s 9 times 3 z. You’ll multiply the 9 times 3 to get 27. Then it would be 27z. 27z and 3z^2 cannot be added together because they are preforming different things. One is multiplying by the variable another is multiplying by 3 and the the variable to the 2nd power.

[tex]

-3x+6y=9 \\

5x+7y=-49 \\ \\

-15x+30y=45 \\

15x+21y=-147 \\ \\

51y=-102 \\

\underline{y=-2} \\ \\

-3x+6\cdot(-2)=9 \\

-3x-12=9 \\

-3x=21 \\

\underline{x=-7} \\ \\

\boxed{(-7, -2)}

[/tex]

The answer is C.

Hope this helps.

r3t40

Answer:

(-7, -2) is the correct answer

For this case we have the following expression:

[tex]7x^{10} + 6x ^ 5 + 5[/tex]

We must rewrite it quadratically:

By definition, a quadratic equation is of the form:

[tex]ax ^ 2 + bx + c = 0[/tex]

Now, suppose [tex]u = x ^ 5[/tex]

Rewriting the given expression with the change of variable we have:

[tex]7u ^ 2 + 6u + 5[/tex]

So, we have a quadratic expression.

Returning the change we have:

[tex]7 (x ^ 5) ^ 2 + 6 (x ^ 5) +5[/tex]

ANswer:

Option B

answer would be the second one: Rectangle that is not a square

Answer:

B.Rectangle that is not a square.

Step-by-step explanation:

We are given that Cecile drew a 4-sides figure. it means a quadrilateral.It had 2 sides that were 3.4cm long and 2 sides that were 3.3 centimeters long.

We are given that a quadrilateral had atleast 3 right angles.

If a quadrilateral had 3 right angles then the IV angle of quadrialteral is also right angle.

In quadrlateral ABCD

[tex]\angle A=90^{\circ}[/tex]

[tex]\angle B=90^{\circ}[/tex]

[tex]\angle C=90^{\circ}[/tex]

[tex]\angle A+\angle B+\angle C+\angle D==360^{\circ}[/tex]

By angle sum property of quadrilateral

[tex]90+90+90+\angle D=360[/tex]

[tex]270+\angle D=360[/tex]

[tex]\angle D=360-270=90^{\circ}[/tex]

Hence, IV angle of quadrilateral is also right angle.

Given two sides of quadrilateral are equal and other two sides of quadrilateral are equal.Therefore, the given quadrilateral can be rectangle not square because in square four sides are of equal lengths.

Hence, the given quadrilateral can be rectangle but not square.Therefore, option B is correct.

Answer:

the graph of the parabola opens upwards.

Step-by-step explanation:

For any quadratic equation of the form

[tex]ax ^ 2 + bx + c[/tex] is true that:

if the main coefficient "a" is negative then the graph of the parabola opens downwards.

If the main coefficient "a" is positive, the parabola opens upwards

In this case the parabola is [tex]y=x^2-6x[/tex]

Note that [tex]a=1[/tex] and [tex]a>0[/tex] therefore the graph of the parabola opens upwards.

Answer:

√55

Step-by-step explanation:

Notice that the small triangle in the bottom corner shares an angle with the overall triangle.  Also, they are both right triangles.  Therefore, they are similar triangles.

Notice that the large triangle at the top shares an angle with the overall triangle and is also a right triangle.  Therefore it is also similar to the overall triangle and the smaller triangle.

Writing a proportion between the small and large triangles:

y / 11 = 5 / y

y² = 55

y = √55

Final answer:

The problem involves finding the base 'b' and height 'h' of a parallelogram with an area of 216 cm², where the height is 2/3 of the base. By substituting h = (2/3)b into the area formula, base x height, and solving, we find that the base is 18 cm and the height is 12 cm.

Explanation:

To find the base and height of the parallelogram given that the area is 216 cm² and the height is 2/3 of its base, we use the formula for the area of a parallelogram:

Base x Height = Area of parallelogram

Let the base be 'b' and the height be 'h'. According to the problem, h = (2/3)b, so we can substitute 'h' in the area

formula:

b x (2/3)b = 216 cm²

Which simplifies to:

(2/3)b² = 216 cm²

Now, solve for 'b' to find the base, and use that to find 'h' (the height):

b² = (216 cm²) x (3/2)

b² = 324 cm²

b = √(324 cm²)

b = 18 cm

Therefore, the base is 18 cm. Now we find the height:

h = (2/3) x 18 cm

h = 12 cm

The base of the parallelogram is 18 cm and the height is 12 cm.

To write the equation for g(x) which is a scaled version of f(x)=x^2, we can use the general form of a quadratic function y=a(x-h)^2+k. The value of a determines the scaling factor.

To write the equation for g(x) which is a scaled version of f(x)=x^2, we can use the general form of a quadratic function y=a(x-h)^2+k. The value of a determines the scaling factor. Since g(x) is a scaled version of f(x), a is the scaling factor. Therefore, the equation for g(x) is g(x)=a(x-h)^2+k, where a is the scaling factor, h is the x-coordinate of the vertex of f(x), and k is the y-coordinate of the vertex of f(x).

The scaled version of the function f(x) = x^2 is g(x) = a * x^2, where a is the scale factor determining the graph's stretch or compression.

If the function g is considered a scaled version of f(x) = x^2, it means that g will also be a quadratic function, but with a constant factor that scales or stretches the graph of f. The general form of a scaled quadratic function is g(x) = a * x^2, where a is the scale factor.

This scale factor a could be any real number. It determines whether the graph of g is narrower or wider compared to f. For example, if a is greater than 1, the graph of g will be narrower; if 0 < a < 1, the graph will be wider; and if a is negative, the graph will be reflected over the x-axis.

Answer:

164 sq. meters

Step-by-step explanation:

So to make it easier, you can break the shape up in a smaller shape. So now it'll look like 2 big rectangles on each side with a small rectangle in the middle. Now you can find the area.

For the big rectangle on the left:

5 × 15 = 75

For the big rectangle on the right:

5 × 15 = 75

For the small rectangle in the middle:

It doesn't say what the length is but if you subtract 8 from 15, that's what the length will be.

15 - 8 = 7

L = 7

7 × 2 = 14

Now add all the areas up.

75 + 75 + 14 = 164

Answer:

The lines are neither parallel nor perpendicular

Step-by-step explanation:

The first step is to re-write the equations in slope-intercept form. The first equation is given as;

y = -4/5x + 3

This equation is already in slope-intercept form. Its slope is -4/5

The second equation is given as;

4x - 5y = -15

We solve for y;

-5y = -4x - 15

y = 4/5x + 3

The slope of the line is thus 4/5

Parallel lines have equal or identical slopes. The slopes of the two lines are not equal implying that the lines are not parallel. Two lines are said to be perpendicular if the product of their slopes is equal to -1.

The product of the slopes of the two lines is;

(-4/5) * (4/5) = -16/25 ≠ -1

The two lines are not perpendicular

By comparing the slopes of the given equations, y = -4/5x + 3 and 4x - 5y = -15, we find that they are negative reciprocals of each other, indicating that the lines are perpendicular.

To determine whether the given pair of equations represent lines that are parallel, perpendicular, or neither, we need to compare their slopes. The slope-intercept form of a line is y = mx + b, where m represents the slope and b represents the y-intercept.

The first equation is already in slope-intercept form: y = -4/5x + 3, so its slope is -4/5.

To put the second equation into slope-intercept form, we solve for y:
4x - 5y = -15
-5y = -4x - 15
y = (4/5)x + 3

The slope of the second line is 4/5.

Since the slopes of the two lines are negative reciprocals of each other, the lines are perpendicular.

Hello There!

“A” 2g+17

“B” 18h-3

Have A Great Day!

Answer:

A) 2g + 17

B) 18h - 3

Step-by-step explanation:

Hello! The reasoning for A is 2 x g + 17  would be the algebraic expression for "the sum of 2 times g and 17.

the reasoning for B is the same reason as a it is the algebraic expression for "the product of 18 and h.

I hope this helped you good luck!

PLEASE GIVE A BRAINLIEST IT WOULD MEAN A LOT!

:)

Suppose there is a function [tex]f(n)=3n^2, n\in\mathbb{N}[/tex].

We start counting by 1 from the first element in domain of natural numbers so: 1, 2, 3, 4.

We assemble the definition set [tex]A=\{1,2,3,4\}[/tex] than use the function f(n) to create transformation set:

[tex]f(A)=3\{1,2,3,4\}^2\Longrightarrow\{3,6,9,12\}^2 \\

\boxed{B=\{9,36,81,144\}}

[/tex]

So the first four terms are defined in transformation set B.

Hope this helps.

r3t40

D

The larger the number the warmer it is

Answer:

D

Step-by-step explanation:

Answer:

c. 32

Step-by-step explanation:

The problem states that we need to assume that segments that appear tangent are actually tangent. From the figure, the tangent segment is the one that measures [tex]x[/tex] while the radius measures 24. The key in this problem is that if a radius of a circle and a tangent line to that circle touch intersect at the same point, then they form a right angle there. Accordingly, we have a right triangle here, so using the Pythagorean theorem, we can find [tex]x[/tex]. Thus:

[tex]x=\sqrt{40^2-24^2} \\ \\ x=\sqrt{1600-576} \\ \\ \boxed{x=32}[/tex]