The perimeter of the trapezoid shown is 6x+2 units. Find the length of the missing side

The sum of the integers -9, 4, 10, -4, 8, -4 is calculated by adding the numbers together, which totals 5.

To find the sum of the integers -9, 4, 10, -4, 8, -4, we add them together:

-9 + 4 + 10 + (-4) + 8 + (-4) = 5.

We can group the positive and negative numbers to make this simpler:

(4 + 10 + 8) = 22

(-9 - 4 - 4) = -17

Adding the results of the positive and negative groups gives us:

22 + (-17) = 5.

Therefore, the sum of the given integers is 5.

How many classes could Anna take so that the total cost for the month would be the same?

5 classes

What is the total monthly cost when it is the same for both gyms?

$37.50

Step-by-step explanation:

The number of classes Anna could take so the total cost for the month would be the same is 5.

The total monthly cost when it is the same for both gyms would be $37.50.

When the total cost is the same, both equations for the gym would be equal to each other.

7.5x = 5.5x + 10

In order to determine the value of x, take the following steps:

Combine similar terms

7.5x - 5.5x = 10

Add similar terms together

2x = 10

Divide both sides by 2

x = 5

Total cost = 7.5 x 5 = $37.50

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Halving the height halves the volume, but halving the radius quarters it; their effects on volume differ.

It seems there might be a typo or a mistake in your reasoning. Let's reassess the situation:

Original cone:

- Radius, [tex]\( r = 2 \)[/tex]

- Height, [tex]\( h = 6 \)[/tex]

- Volume, [tex]\( V_1 = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (2)^2 (6) = 8\pi \)[/tex] cubic units

Now, you're considering two scenarios:

1. If the height is changed to [tex]\( h = 3 \)[/tex]:

  - New volume, [tex]\( V_2 = \frac{1}{3} \pi (2)^2 (3) = 4\pi \)[/tex] cubic units

2. If the radius is changed to \( r = 1 \):

  - New volume, [tex]\( V_3 = \frac{1}{3} \pi (1)^2 (6) = 2\pi \)[/tex] cubic units

Now, let's analyze the effects:

- Changing the height from 6 to 3 reduces the volume by half (from [tex]\( 8\pi \)[/tex] to [tex]\( 4\pi \)[/tex]).

- Changing the radius from 2 to 1 reduces the volume by a factor of [tex]\( \frac{1}{4} \)[/tex] (from [tex]\( 8\pi \)[/tex] to [tex]\( 2\pi \))[/tex].

So, changing the height to half of its original value reduces the volume by half, while changing the radius to half of its original value does not reduce the volume by half but rather by a quarter. Therefore, the effects are not the same.

Answer:

Observe the attached image

Step-by-step explanation:

We have the graph of a line that passes through the points (0,5) and (2, 1).

The equation of the line that passes through these points is found in the following way:

[tex]y = mx + b[/tex]

Where

m = slope

[tex]m = \frac {y_2-y_1}{x_2-x_1}\\\\m = \frac{1-5}{2-0}\\\\m = -2\\\\b = y_2-mx_2\\\\b = 1 -(-2)(2)\\\\b = 5[/tex]

So

[tex]y = -2x + 5[/tex]

We must apply to this function the transformation[tex]f (x-4)[/tex].

We know that a transformation of the form

[tex]y = f (x + h)[/tex] shifts the graph of the function f(x) h units to the right if [tex]h <0[/tex], or shifts the function f(x) h units towards the left if [tex]h> 0[/tex].

In this case [tex]h = -4 <0[/tex] then the transformation [tex]f(x-4)[/tex] displaces the graph 4 units to the right.

Therefore if f(x) passes through the points (0,5) and (2,1) then [tex]f (x-4)[/tex] passes through the points (4, 5) (6, 1)

And its equation is:

[tex]y = -2(x-4) +5\\\\y = -2x +13[/tex]

Observe the attached image

Answer:

y=x-8 and y=-x+4

Step-by-step explanation:

The slopes of the lines can be anything, as long as they are the opposite reciprocals of each other. Then you can plug in the point for x and y to solve for b in both lines (for y=mx+b where m is the slope)

For this case we must find the inverse of the following function:

[tex]f (x) = x ^ 2 + 7[/tex]

For this we follow the steps below:

Replace f(x) with y:

[tex]y = x ^ 2 + 7[/tex]

We exchange the variables:

[tex]x = y ^ 2 + 7[/tex]

We solve the equation for "y", that is, we clear "y":

[tex]y^ 2 + 7 = x[/tex]

We subtract 7 on both sides of the equation:

[tex]y ^ 2 = x-7[/tex]

We apply square root on both sides of the equation to eliminate the exponent:

[tex]y = \pm\sqrt {x-7}[/tex]

We change y by[tex]f ^ {- 1} (x):[/tex]

[tex]f ^ {- 1} (x) =\pm\sqrt {x-7}[/tex]

Answer;

Option A

I will say 1 block is 1 something okay cause I don’t have a key mini has an area of 2 (2x2=4/2=2) And the giant has an area of 32 (8x8=64/2=32) I don’t know if the small one became big or the big one became small so if the small to big is 16 big to small is 0.0625 or the numbers the other way around

Answer:

Area of left triangle = 2 * 2 / 2 = 2

Area of triangle on the right = 8 * 8 / 2 =32

32 / 2 = 16

Therefore the triangle on the right has 16 times the area than the triangle on the left.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Substitute the values of n into the recursive formula and check result against values in table

A

[tex]a_{2}[/tex] = 3 + 5 = 8 ← correct

[tex]a_{3}[/tex] = 8 + 5 = 13 ← correct

[tex]a_{4}[/tex] = 13 + 5 = 18 ← correct

[tex]a_{5}[/tex] = 18 + 5 = 23 ← correct

Answer:

the answer is A

Step-by-step explanation:

Answer:

[tex]\large\boxed{y=\dfrac{8}{37}}[/tex]

Step-by-step explanation:

[tex]Domain:\ 2+2y\neq0\to y\neq-1\\\\\dfrac{-30+15y}{2+2y}=-11\\\\\dfrac{-30+15y}{2+2y}=\dfrac{-11}{1}\qquad\text{cross multiply}\\\\(-30+15y)(1)=(-11)(2+2y)\qquad\text{use the distributive property}\\\\-30+15y=(-11)(2)+(-11)(2y)\\\\-30+15y=-22-22y\qquad\text{add 30 to both sides}\\\\15y=8-22y\qquad\text{add}\ 22y\ \text{to both sides}\\\\37y=8\qquad\text{divide both sides by 37}\\\\y=\dfrac{8}{37}[/tex]

[tex]5 \times 3 \times 2 + \frac{3}{0} - \frac{45}{3} + 1 = \\ \\ = \frac{3}{0} \\ \\ or \\ \\ 1. \: 30 + \frac{3}{0} - \frac{45}{3} + 1 \\ 2. \: 30 + \infty - \frac{45}{3} + 1 \\ 3. \: 30 + \infty - 15 + 1 \\ 4. \: \infty [/tex]

Yeah it's Impossible

Answer:

Yeah it's Impossible

Step-by-step explanation:

Answer:I THINK 89.3 in.

You can solve this problem with the Pythagorean Theorem. The base is a square. So half way across the middle will the right under the tip of the pyramid.

Answer:

[tex]f * g = 21x ^ 2 + 32x +12[/tex]

Domain: all real numbers [tex](-\infty, \infty)[/tex]

Step-by-step explanation:

We have the functions [tex]f (x) = 3x + 2[/tex] and [tex]g (x) = 7x + 6[/tex]

We want to find f*g. Then we must multiply the function f by the function g.

Note that the function [tex]f (x) = 3x +2[/tex] is a linear function, therefore its domain is all real numbers. In the same way the function [tex]g (x) = 7x + 6[/tex] is also a linear function and its domain is all real numbers.

The multiplication of f * g will be

[tex]f * g = (3x + 2) (7x + 6)\\\\f * g = 21x ^ 2 + 18x + 14x +12\\\\f * g = 21x ^ 2 + 32x +12[/tex]

The function g(x) is a quadratic function and its domain is the intercept of the domain of f(x) with the domain of g(x), that is, all real numbers.

Answer: option c

Step-by-step explanation:

You can use these identities:

[tex]sin\alpha=\frac{opposite}{hypotenuse}\\\\tan\alpha=\frac{opposite}{adjacent}[/tex]

Then, using the angle that measures 30 degrees, you know that:

[tex]\alpha=30\°\\opposite=8\\adjacent=b[/tex]

Substituting:

[tex]tan(30\°)=\frac{8}{b}[/tex]

Now you must solve for b:

[tex]b=\frac{8}{tan(30\°)}\\\\b=8\sqrt{3}[/tex]

Using the angle that measures 30 degrees, you know that:

[tex]\alpha=30\°\\opposite=8\\hypotenuse=c[/tex]

Substituting:

[tex]sin(30\°)=\frac{8}{c}[/tex]

Now you must solve for c:

[tex]c=\frac{8}{sin(30\°)}\\\\c=16[/tex]

ANSWER

The correct answer is C

EXPLANATION

The side adjacent to the 60° angle is 8 units.

The hypotenuse is c.

Using the cosine ratio, we have

[tex] \cos(60 \degree) = \frac{adjacent}{hypotenuse} [/tex]

[tex]\cos(60 \degree) = \frac{8}{c} [/tex]

[tex] \frac{1}{2}= \frac{8}{c} [/tex]

Cross multiply

[tex]c = 8 \times 2 = 16[/tex]

Also

[tex]\cos(30 \degree) = \frac{b}{c} [/tex]

[tex]\cos(30 \degree) = \frac{b}{16} [/tex]

[tex] \frac{ \sqrt{3} }{2} = \frac{b}{16} [/tex]

Multiply both sides by 16

[tex]b = 16 \times \frac{ \sqrt{3} }{2} [/tex]

[tex]b = 8 \sqrt{3} [/tex]

The correct answer is C

Answer:

298

Step-by-step explanation:

Given

(8 - (- 9))² + (-3 - (- 6))² ← evaluate the parenthesis before squaring

= (8 + 9)² + (- 3 + 6)²

= 17² + 3²

= 289 + 9

= 298

Answer: (8+9)^2 + (-3 + 6)^2

= 17^2 + 3^2

= 289 + 9

= 298. ANS.

If a local city collects 8% sales tax if the total purchase was $216 then $17.28 is collected for sales tax.

A relative value indicating hundredth parts of any quantity is known as Percentage.

Given that a  local city collects 8% sales tax

The total purchase was $216.

We need to find the amount collected for sales tax.

To find this we have to find 8% of 216.

Convert 8% to the decimal value.

8/100=0.08

Now multiply 0.08 with 216

0.08×216

$17.28

Hence, if a local city collects 8% sales tax if the total purchase was $216 then $17.28 is collected for sales tax.

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The amount collected for sales tax is $16.

Step 1: Understand the Problem

The total purchase amount ($216) includes the sales tax. We need to find how much of this amount is the sales tax itself.

Step 2: Convert the Percentage to a Decimal

Convert the sales tax rate from a percentage to a decimal.

[tex]\[ \text{Sales Tax Rate} = \frac{8}{100} = 0.08 \][/tex]

Step 3: Set Up the Equation

Let ( P ) be the pre-tax purchase amount and ( T ) be the total amount including tax. The relationship can be written as:

[tex]\[ T = P + \text{Sales Tax} \][/tex]

Since the sales tax is 8% of the pre-tax amount,

[tex]\[ \text{Sales Tax} = 0.08 \times P \][/tex]

Thus, the total amount is:

[tex]\[ T = P + 0.08P = 1.08P \][/tex]

Step 4: Solve for the Pre-Tax Amount

We know the total amount ( T ) is $216.

[tex]\[ 216 = 1.08P \][/tex]

To find ( P ):

[tex]\[ P = \frac{216}{1.08} \][/tex]

[tex]\[ P \approx 200 \][/tex]

Step 5: Calculate the Sales Tax

Now, find the sales tax:

[tex]\[ \text{Sales Tax} = 0.08 \times P \][/tex]

[tex]\[ \text{Sales Tax} = 0.08 \times 200 \][/tex]

[tex]\[ \text{Sales Tax} = 16 \][/tex]

Therefore the amount collected for sales tax is $16.

Answer:

Step-by-step explanation:

The distributive property: a(b + c) = ab + ac

[tex]3(2x-5)=5(x-4)+x\\\\(3)(2x)+(3)(-5)=(5)(x)+(5)(-4)+x\\\\6x-15=5x-20+x\qquad\text{combine like terms}\\\\6x-15=6x-20\qquad\text{subtract}\ 6x\ \text{from both sides}\\\\-15=-20\qquad\bold{FALSE}[/tex]

Answer: 12.20 feet.

Step-by-step explanation:

Observe in the figure attached that a right triangle is formed.

Then, you  need to remember the identity:

[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]

In this case you can identify that:

[tex]adjacent=10\\hypotenuse=x[/tex]

[tex]\alpha=35\°[/tex]

Then, to find the length of the wooden board (x), you need to substitute values and solve for x.

Therefore, you get:

[tex]cos(35\°)=\frac{10}{x}\\\\(x)(cos(35\°))=10\\\\x=\frac{10}{cos(35\°)}\\\\x=12.20[/tex]

The length of the wooden board is: 12.20 feet.

Answer:

8/45

Step-by-step explanation:

Write 4 5/8 as an improper fraction:  45/8.

Then invert this result, obtaining:

 .  This is the "reciprocal" of 4 5/8.

Answer:

37/8

Step-by-step explanation:

attachement ---

ANSWER

[tex]x = \frac{5}{4} - \frac{ \sqrt{ 17} }{4} [/tex]

or

[tex]x = \frac{5}{4} + \frac{ \sqrt{ 17} }{4} [/tex]

EXPLANATION

The given equation is:

[tex]2 {x}^{2} - 5x + 1= 0[/tex]

Comparing this to

[tex]a {x}^{2} + bx + c = 0[/tex]

we have a=2, b=-5, c=1

The quadratic formula is given by

[tex]x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

We substitute the values to get,

[tex]x = \frac{ - - 5 \pm \sqrt{ {( - 5)}^{2} - 4(1)(2)} }{2(2)} [/tex]

[tex]x = \frac{ 5 \pm \sqrt{ 17} }{4} [/tex]

[tex]x = \frac{5}{4} - \frac{ \sqrt{ 17} }{4} [/tex]

or

[tex]x = \frac{5}{4} + \frac{ \sqrt{ 17} }{4} [/tex]

Answer:

B

Step-by-step explanation:

Let x be the number of packages of paper towels.

Each package of paper towels costs $2.79.

Then x packages of paper towels cost $2.79x.

Hence, a function f(x) is

[tex]f(x)=2.79x[/tex]

Practically, you can buy 0 packages, 1 package, 2 packages and so on, only whole numbers of packages, so practical domain is all whole numbers.

ANSWER

A) For all x > 0 the graph will be higher.

EXPLANATION

Jack's graph has equation

y=2x

This graph passes through the origin and has slope 2.

Nina's graph is y=5x.

This graph also passes through the origin and has slope 5.

Since 5 is greater than 2, for all x>0, Nina's graph will be higher.

Answer: A

Step-by-step explanation: Changing the 2 to a 5 makes an exponential growth function increase at a faster rate. Therefore, for all x > 0 the graph will be higher. At x = 0 the graphs will have the same value and for all x < 0, Nina's graph will be lower.

Answer:

Step-by-step explanation:

6,18,8,4,18,20,10,10,21,6,17,18

Arrange the data in ascending order

4,6,6,8,10,10,17,18,18,18,20,21

Part A

Mean = 156/12 = 13 is correct

Median = 15 is incorrect because the data is not arranged. Median when there are even numbers will be: 10+17/2 = 13.5

Mode = 10 is incorrect, because mode is most repeating value and in the data set it is 18 so, Mode = 18

Part B

10,12 and 52 should be added in data set in ascending order

4,6,6,8,10,10,10,12,17,18,18,18,20,21,52

Mean = 230/15 = 15

Median = Middle term as odd numbers = 8th term = 12

Mode = 10 and 18

Part C

Both median and mean are used to measure central tendency.

The best measure of central tendency is considered median because the mean is affected by the presence of outliers while median is not affected by outliers.

Answer:

He is correct.

Step-by-step explanation:

I got 100% on my paper

Answer:

To sum consecutive numbers we use the formula:

n * (n+1) / 2

1 through 55 = (55 * 56) / 2 = 1,540

1 through 9 = (9 * 10) / 2 = 45

10 through 55 = 1,540 -45 = 1,495

********************************************************

EDITED

Gee, it seems I added ALL numbers from 10 through 55

ALL ODD numbers from 10 through 55 sum to

759

Step-by-step explanation:

Answer:

[tex](5y^2+2z)(5y^2-2z)[/tex]

Step-by-step explanation:

Use the difference of squares formula.

[tex]a^2-b^2=(a+b)(a-b)[/tex]

[tex]a=5y^2 \\ b=2z[/tex]

[tex](5y^2+2z)(5y^2-2z)[/tex]

Answer:

(6,-5)

Step-by-step explanation:

As the point is 4 units to the left of X=2, the reflection must be 4 units to the right of X=2

The answer is C: the average reading speed of the science fiction novel.

If x is her reading speed for the historical fiction novel, and her reading speed for the sci-fi novel is just two pages more than that of the historical fiction novel, then the equation to find out how fast she reads the science fiction novel would be x + 2, as you’re adding 2 to the reading speed of the historical fiction book (x)

Answer:

The answer to this question is correct but on PLATO the answer choice is actually A.

Step-by-step explanation:

PLATO

Answer:

Option D.

[tex]A =96\pi\ cm^2[/tex]

Step-by-step explanation:

The area of the circular bases is:

[tex]A_c = 2\pi(a) ^ 2[/tex]

Where

[tex]a=4\ cm[/tex] is the radius of the circle

Then

[tex]A = 2\pi(4) ^ 2[/tex]

[tex]A = 32\pi\ cm^2[/tex]

The area of the rectangle is:

[tex]A_r=b * 2\pi r[/tex]

Where

[tex]b=8\ cm[/tex]

b is the width of the rectangle and [tex]2\pi r[/tex] is the length

Then the area of the rectangle is:

[tex]A_r=8 * 2\pi (4)[/tex]

[tex]A_r=64\pi\ cm^2[/tex]

Finally the total area is:

[tex]A = A_c + A_r\\\\A = 32\pi\ cm^2 + 64\pi\ cm^2\\\\[/tex]

[tex]A =96\pi\ cm^2[/tex]

Answer:

The correct answer is option B.  96π

Step-by-step explanation:

Points to remember

Surface area of cylinder = 2πr(r + h)

Where r is the radius of cylinder and h is the height of cylinder.

From the figure we get r = 4 cm and h = 8 cm

To find the surface area of cylinder

Surface area = 2πr(r + h)

 = 2π * 4(4 + 8)

 = 96π

The correct answer is option B.  96π

Answer:

12.A.) Heptagon

Step-by-step explanation:

Answer:

Option C is correct

Step-by-step explanation:

The relationship between Roberts age and Julia’s age is given by:

r = j+3            ....[1]

where,

r is the Robert's age and j represents the Julia's age in years

We have to find the table of values represents the relationship between Roberts age and Julia’s age

if r = 9 years

then;

[tex]9 = j+3[/tex]

Subtract 3 from both sides we have;

6 = j

or

j = 3 years

Similarly:

if r = 15 years

then;

[tex]15= j+3[/tex]

Subtract 3 from both sides we have;

12 = j

or

j = 12 years

If r = 21 years

then;

[tex]21= j+3[/tex]

Subtract 3 from both sides we have;

18 = j

or

j = 18 years

Therefore, the table of values represents the relationship between Roberts age and Julia’s age is, Table C

option c is the right answer

Answer:

If x is greater than 1 it is growth, if it less than it is decay

Step-by-step explanation: