Solve the equation. Then check your solution
Please select the best answer from the choices provided

Answer:

[tex]x=40^o[/tex]

Step-by-step explanation:

the picture of the question in the attached figure

step 1

Find the measure of the interior angle of a regular nonagon

The formula to calculate the measure of the interior angle in any polygon is given by

[tex]\frac{(n-2)180^o}{n}[/tex]

where

n is the number of sides

In this problem we have

n=9 sides

substitute

[tex]\frac{(9-2)180^o}{9}=140^o[/tex]

step 2

Find the value of x

Remember that

The sum of the interior angle and the exterior angle in any vertex of the polygon must be equal to 180 degrees

so

[tex]x+140^o=180^o[/tex]

solve for x

[tex]x=180^o-140^o=40^o[/tex]

The scale factor for the transformation of the pre-image ABC to A'B'C' shown in the figure is 5/2

How to estimate the scale factor of the dilation

From the question, we have the following parameters that can be used in our computation:

The transformation of the pre-image ABC to A'B'C'

By definition, the scale factor is simply the ratio of sides of two corresponding figures

So, the scale factor (S) would be:

S = A'B'C'/ABC

The actual measurements are given as

ABC = 2

A'B'C' = 5

Substitute the known values into the equation

S = 5/2

Hence, the estimated scale factor is 5/2

Answer:

she incorrectly multiplied 90 times 0.9

Step-by-step explanation:

The volume of the tent is option A) 226 ft³

Step-by-step explanation:

The given data are,

To find the volume of the tent :

The volume of the tent can be found using the formula for volume of the cone, since the tent is in the shape of a cone.

Volume of the cone = (1/3)πr²h

where, r is the radius of the cone. The diameter is given as 12 ft. Therefore, to find the radius = diameter /2 = 12/2 = 6 ft.

The radius, r = 6 ft.

The height h of the cone is h= 6 ft.

Volume of the cone = (1/3)× 3.14× 6²× 6.

⇒ (1/3)× 3.14× 216

⇒ 678.24 / 3

⇒ 226.08 (which is approximately 226)

⇒ 226 cubic. ft

Therefore, the volume of the tent is option A) 226 ft³

Answer:

Each shirt cost $12

Step-by-step explanation:

First, we have to interpret this question and turn each to an equation, letting shirts represent the letter s and ties represent the letter t.

6 shirts and 3 ties cost $79.50 would be interpreted to 6s+3t=79.5 ,and 3 shirts and 2 ties cost $41 would be interpreted to 3s+2t=41

Hence we have two equations, and we solve them simultaneously.

6s+3t=79.5 (Equation 1)

3s+2t=41 (Equation 2)

We can either use the substitution method or the elimination method but for the sake of this question, we use the Elimination method.

6s+3t=79.5 (Equation 1)

3s+2t=41 (Equation 2)

We multiply equation 1 by 2 and we multiply equation 2 by 3, I'm prefer to eliminate the

2(6s+3t=79.5)

12s+6t=159 Equation 3

3(3s+2t=41)

9s+6t=123 Equation 4

We subtract equation 4 from equation 3.

12s+6t=159

9s+6t=123

12s-9s=3s

6t-6t=0

159-123=36

We therefore have

3s=36

Divide both sides by 3

s=36/3

s=12

One shirt cost $12

For the given triangle, x = 5.1 cm and y = 6.1 cm.

Step-by-step explanation:  

Step 1:  

In the given triangle, the angle is 50°. It is given that the opposite side has a length of y cm and the adjacent side has a length of y cm.   The hypotenuse of the triangle measures 8 cm.

To determine the length of the opposite side of the triangle, we use the sin of the given angle.  

To determine the length of the adjacent side of the triangle, we use the cos of the given angle.  

[tex]sin \theta = \frac{oppositeside}{hypotenuse} , cos \theta = \frac{adjacentside}{hypotenuse}.[/tex]

Step 2:  

In the given triangle,  

The length of the opposite side = y cm,  

The length of the adjacent side = x cm,  

The length of the hypotenuse = 8 cm,  

The angle of the triangle = 50°.

[tex]sin \theta = \frac{oppositeside}{hypotenuse} , sin 50 = \frac{y}{8}.[/tex]

[tex]y = 0.7660 (8) = 6.128.[/tex]

[tex]cos \theta = \frac{adjacentside}{hypotenuse} , cos 50 = \frac{x}{8}.[/tex]

[tex]x = 0.6427 (8) = 5.1416.[/tex]

So x = 5.1416 cm and y = 6.128 cm. Rounding these off to one decimal place, we get x = 5.1 cm and y = 6.1 cm.

Answer:

17,810.58

Step-by-step explanation:

A = $ 17,810.58

A = P + I where

P (principal) = $ 10,000.00

I (interest) = $ 7,810.58

Step-by-step explanation:

we can write it in %form:

100% of the total income Annual income= $32,000 (given in question)

1%=$320. (divide both sides by 100 to solve by 1%)

8%=$320×8

(multiply by 8 both side to get money saved)

8%= *$2,560*

Answer:

By assuming that shortest feather has a length of 1/4 inches, the length of the longest feather is 2 inches.

Step-by-step explanation:

A mathematical translation of the statement of the problem is:

[tex]x - y = \frac{7}{4}[/tex]

Where x, y represent the lengths of the longest and shortest feathers, respectively. Let assume that length of the shortest feather is 1/4 inches. Then, the length of the longest feather is:

[tex]x = y + \frac{7}{4}[/tex]

[tex]x = 2[/tex]

By assuming that shortest feather has a length of 1/4 inches, the length of the longest feather is 2 inches.

The length of the new feather that made the difference between the longest and shortest feathers is 1 3/4 inches.

The question is asking for the possible length of the new feather that made the difference between the longest and shortest feathers. We know that the difference between these feathers is 1 3/4 inches.

To find the length of the new feather, we need to consider the lengths of the longest and shortest feathers.

Let's say the length of the shortest feather is x inches. Then, the length of the longest feather would be x + 1 3/4 inches. So, the equation would be: (x + 1 3/4) - x = 1 3/4 inches.

Simplifying the equation, we get: 1 3/4 = 1 3/4 inches.

Therefore, the length of the new feather is 1 3/4 inches.

Answer:

100 degrees

Step-by-step explanation:

A straight line pretty much means you have 180 degrees.

180 - 115 = 65

A triangle has 180 degrees

x = 180 - 15 - 65 = 100

Answer:

-8

Step-by-step explanation:

The answer is -8 because y=4 so 4-12=-8

The mean absolute deviation for the given data set is 45.1.

To find the mean absolute deviation for a given data set, follow these steps:

Find the mean of the data set by adding up all the values and dividing by the total number of values.

For each value in the data set, find the absolute difference between the value and the mean.

Find the average of these absolute differences by summing them up and dividing by the total number of values.

In this case, the data set is {122,132,155,198,213,225,261,280}.

The mean of this data set is 196. The absolute differences from the mean are: 74, 64, 41, 2, 17, 29, 65, 84.

The average of these absolute differences is 45.1. Therefore, the mean absolute deviation for the data set is 45.1.

Answer: 1/100 or 0.01

Answer:

1 cm = 0.01 m

Step-by-step explanation:

Divide both sides of 1 meter = 100 centimeters by 100 to obtain an expression for the value of 1 cm:

  1 meter        100 cm

---------------- = -------------

 100                 100

Reducing this, we find that:  1 cm = 0.01 m

Answer:

-36/7 or -5.14287

Step-by-step explanation:

so I would get rid of parentheses you do not need them

[tex]\frac{-6+-30}{5--2}[/tex]=[tex]\frac{-36}{7}[/tex](because when two negative come before two numbers like -x-y they are being added but negative is present to the result of the sum, when one negative sign comes after a number and the other negative sign comes before a number, like x--y they are being added as well but negative is not present to the result of the sum)

-36/7=-5.1428

hope this helps!

Answer:

[tex]-5 \frac{4}{5}[/tex]

Step-by-step explanation:

That's the answer

Answer:

I guess the answer would be -5 and 4/5.

Hope this helps!

The length of the side of the hexagon or square is 24 units.

Step-by-step explanation:

It is given that, a square and a regular hexagon have side of the same length.

The length is not given in the problem. So, let us assume the length of the side of hexagon or square as 'x'.

The additional information given is that, the perimeter of the square increased by 48 units will be equal to the perimeter of the hexagon.

To calculate the length x of square and hexagon :

Comparing both the perimeters of square and hexagon,

⇒ (4x + 48) = 6x

⇒ 48 = 6x-4x

⇒ 2x = 48

⇒ x = 48/2

⇒ x = 24 units.

The length of the side of the hexagon or square is 24 units.

Graphs of proportional relationships visually depict how two or more variables are interrelated using line graphs, pie graphs, and bar graphs. Line graphs show direct relationships with a constant rate of change, pie graphs represent portions of a whole, and bar graphs compare quantities through the height of bars.

When interpreting graphs of proportional relationships, it's essential to recognize that these graphs illustrate how two variables correlate with one another. In line graphs, a straight line that passes through the origin indicates a direct proportionality, meaning as one variable increases, the other increases at a constant rate. For instance, if a line graph shows the relationship between hours worked and income earned, the line's slope denotes the rate of earning per hour, showcasing a proportional increase in income with more hours worked.

Pie graphs are used to represent how a whole is divided into parts, with the size of each 'slice' showing the percentage of the total. An example could be a budget allotment where each slice represents what percentage of the budget is spent on specific categories, like marketing or research and development.

Lastly, bar graphs can also indicate proportional relationships through the height of the bars. For example, if a bar graph displays the population sizes of different countries, each bar's height is proportional to the population of that country. When bars are segmented, they can show subgroups within that population, such as age demographics or income brackets.

Answer:

40

Step-by-step explanation:

Plug x=-9 in. -9-8+(-9×(-8)) -15=-17+72-15=-17+72-15=40. I hope this helped!

Answer:

40

Step-by-step explanation:

72-32=40

Answer:

D

Step-by-step explanation:

To find Volume, you multiply length, width and height.

10x4=40

40x5=200

Answer:

D)200yd^3

Step-by-step explanation:

all you have to do is times 4*5*10=200 to get the volume

Answer:

A..., 1, 1/2", 1/4", 1/8"...

Step-by-step explanation:

Answer:   17lbs of carrots

Step-by-step explanation:

Answer:

[tex]3y + 2 [/tex]

Step-by-step explanation:

We want to find a common factor for

[tex]3 {y}^{3} + 2 {y}^{2} [/tex]

and

[tex]6 {y}^{4} + 4 {y}^{3} [/tex]

We factor each of them to get;

[tex]3 {y}^{3} + 2 {y}^{2} = {y}^{2} (3y + 2)[/tex]

and

[tex]6 {y}^{4} + 4 {y}^{3} = 2 {y}^{3} (3y + 2)[/tex]

We can observe now that;

The factor common to both expression is

[tex]3y + 2[/tex]

Equation of the line is [tex]y=\frac{2}{3}x-\frac{8}{3}[/tex].

Solution:

Slope (m) = [tex]\frac{2}{3}[/tex]

Point [tex](x_1, y_1)=(-5, -6)[/tex]

Point - slope form:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]$y-(-6)=\frac{2}{3}(x-(-5))[/tex]

[tex]$y+6=\frac{2}{3}(x+5)[/tex]

[tex]$y+6=\frac{2}{3}x+\frac{10}{3}[/tex]

Subtract 6 from both sides.

[tex]$y+6-6=\frac{2}{3}x+\frac{10}{3}-6[/tex]

[tex]$y=\frac{2}{3}x+\frac{10-18}{3}[/tex]

[tex]$y=\frac{2}{3}x-\frac{8}{3}[/tex]

Equation of the line is [tex]y=\frac{2}{3}x-\frac{8}{3}[/tex].

The image of the graph is attached below.

Answer:

Equation of the line is

Step-by-step explanation:

Answer:

D. $306.

Step-by-step explanation:

If the dishwasher originally cost $450, then after applying 15% off, its price will be 100% - 15% = 85% of the original price:

[tex]\dfrac{85\%}{100\%} *\$450[/tex]

[tex]0.85*\$450 = \$382.5[/tex]

Thus, during the 15% off sale, the dishwasher will cost $382.5.

Now, the employees of the discount appliance store receive an additional 20% off; therefore, the price of the dishwasher will be 100% - 20% = 80% of $382.5:

[tex]\dfrac{80\%}{100\%} *\$382.5[/tex]

[tex]0.8*\$382.5=\$306[/tex]

Therefore, the employee will purchase the dishwasher at a price of $306, which is choice D.

Final answer:

The employee will pay $306 for the dishwasher, which corresponds to answer choice D.

Explanation:

The subject of this question is Mathematics, and it pertains to the calculation of cumulative discounts on an item. The question is designed to test the student's understanding of how to apply successive percentage discounts to an original price.

Original price of the dishwasher: $450

15% off sale discount: 0.15 × $450 = $67.50

Price after sale discount: $450 - $67.50 = $382.50

Employees receive an additional 20% off the lowest price: 0.20 × $382.50 = $76.50

Price after employee discount: $382.50 - $76.50 = $306

Therefore, the employee will pay $306 for the dishwasher, which corresponds to answer choice D.

Answer:

James is 58 and Tyson is 39 years old.

Step-by-step explanation:

x + y = 97

x - y = 19    +

--------------

2x = 116

x = 58

--------------

y = 97 - 58

y = 39

To find the ages of two friends based on the sum and difference of their ages.

James and Tyson are two friends whose ages sum up to 97 and have a difference of 19. To find their ages, we can set up a system of equations:

Therefore, James is 58 years old, and Tyson is 39 years old.

Answer:

<A=<G

so <CAB=<EGF

Step-by-step explanation:

Answer:

B.  

∠CAB and ∠GEF

Answer:

what are you looking for

Step-by-step explanation:

Answer:

Step-by-step explanation:

(x 3)(x – 3)

(x5 3)(x – 3)

(x3 3)(x2 – 3)

(x3 3)(x3 – 3)

Answer:

(x3 + 3)(x3 – 3)

Step-by-step explanation:

Answer:

(6 + 9 + 24)/3

Step-by-step explanation:

First, you must add 6, 9, and 24.

6 + 9 + 24

Now you need to divide that sum by 3.

You must use parentheses to show the sum being divided by 3.

(6 + 9 + 24)/3

None of your expressions contain a division sign, so there is no answer contained in the choices. Did you use the equal sign to mean a division sign?