Kassidy wants to prove that the interior angles of any triangle sum to 180°. She draws a line through one vertex parallel to the opposite side, and then she labels all the angles formed.

Drag a reason to match each statement in Kassidy's two-column proof in the table below.

Answer:

Step-by-step explanation:

Pounds to Ounces: 1 ounce = 0.625 pounds

12.8 ounces = 0.8 pounds

15/0.8 = 18.75 dollars

18.75 dollars

Answer:

Step-by-step explanation:

3 1/2-1 2/3-1/4

Answer:

A. 10.5h

Step-by-step explanation:

Answer:

Because we have a point and slope, we can use at the beginning the point-slope form: y-y1=m(x-x1)

Step-by-step explanation:

m=3 , x1=1 , y=-3

y-(-3)=3(x-1)

y+3=3x-3      subtract 3 from both sides

y=3x-6    the answer in the slope-intercept form y=mx+b

Answer:

The width is 4 units, and the length is 10 units.

Step-by-step explanation:

area of rectangle = length * width

Let L = length; let W = width.

"The length is 6 units greater than the width.": L = W + 6

area = LW = 40

Since L = W + 6, we substitute L with W + 6.

(W + 6)W = 40

W^2 + 6W = 40

W^2 + 6W - 40 = 0

(W - 4)(W + 10) = 0

W - 4 = 0 or W + 10 = 0

W = 4 or W = -10

A width cannot be a negative number, so we discard the solution W = -10.

W = 4

L = W + 6 = 4 + 6 = 10

The width is 4 units, and the length is 10 units.

Answer:

10 by 4 or B

Step-by-step explanation:

took test on edge

Answer:

(420/2)-10=r

r=200

Step-by-step explanation:

Answer:

r = 200

Step-by-step explanation:

divide both sides by 2

210 = r + 10 ( subtract 10 from both sides )

200 = r ⇒ r = 200

Answer:

100/19400*12105=62.3969072165     100-62.3969072165 = 37.60% (rounded)

Step-by-step explanation:

100% = 19'400 divide and multiply with the current value, this will give you the % deductions. Simply deduct the result from 100.

Answer:

copy paste version

Step-by-step explanation:

we know that the formula to calculate the depreciated value is equal to:

D = P(1-r)^t

where  

D is the depreciated value  

P is the original value  

r is the rate of depreciation  in decimal  

t  is Number of Time Periods  

In this problem we have:

P = $19,400

D = $12,105

t = 3 years

substitute in the formula above and solve for r:

$12,105 = $19,400(1-r)^3

Simplify:

(12,105/19,400) = (1-r)^3

(1-r) = 3√(12,105/19,400)

r = 1 - 3√(12,105/19,400)

r = 0.1455

Convert to percentage:

r = 14.55%

Option C is the answer.

Explanation:

Amount paid per hour = $ 15.60

Total working hours in a week = 15

Hence, total earnings in a week are = 15.60 x 15 = $234

Deductions are =

7.65 % of 234 = [tex]\frac{7.65}{100}*234= 17.90[/tex]

11.15 % of 234 =  $26.09

6.5% of 234 =  $15.21

So totaling all deductions we get $59.20

Hence, earnings per week after deductions become = 234-59.20 = $174.80

As each week, 10% is saved, so amount saved each week is = 174.80 x 0.10 = $ 17.48

So, savings per month (4 weeks in a month) becomes = 17.48 x 4 = $69.92

Hence, option c) $69.92 is the answer.

Answer

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Answer:

Price of single fern is $12

Price of single azalea is $8

Step-by-step explanation:

Let's assume

price of each fern is x

price of each azalea is y

Mark bought six ferns and one azalea for $80

so, we got first equation as

[tex]6x+y=80[/tex]

Melissa bought five ferns and three azaleas for $84

so, we got second equation as

[tex]5x+3y=84[/tex]

now, we can solve it

Firstly, we can solve for y from first equation and then plug that in second equation

[tex]6x+y=80[/tex]

[tex]y=80-6x[/tex]

now, we can plug that into second equation

[tex]5x+3(80-6x)=84[/tex]

[tex]-13x+240=84[/tex]

[tex]-13x=-156[/tex]

[tex]x=12[/tex]

now, we can solve for y

[tex]y=80-6\times 12[/tex]

[tex]y=8[/tex]

The 2x2 square centered at the origin has vertices at (-1,1), (1,1), (-1,-1), and (1,-1). When it is dilated by a factor of 3, the coordinates of the vertices are multiplied by 3, resulting in new vertices at (-3, 3), (3, 3), (-3, -3), and (3, -3).

The subject here is Geometry, specifically dealing with transformations such as dilations on a plane. The starting square is 2x2 and centered at the origin means its vertices are at (-1,1), (1,1), (-1,-1), and (1,-1). A dilation by a factor of 3 from the origin means we are going to multiply every coordinate by 3. Doing this, we get the new vertices as (3*-1, 3*1) = (-3, 3), (3*1, 3*1) = (3, 3), (3*-1, 3*-1) = (-3, -3), and (3*1, 3*-1) = (3, -3). Therefore after the dilation, the vertices of the square will be at positions (-3, 3), (3, 3), (-3, -3), and (3, -3).

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Final answer:

To find the percent increase for the second demand increase when the original price is sextupled and the first increase was 50%, we calculate the ratio of the final price to the price after the first increase. The second price increase was determined to be 300% based on this calculation.

Explanation:

The question asks us to determine the percent increase of the second price change when the price of an item becomes six times its original price, with the first price increase being 50%. To solve this, let's assume the original price is $1 for ease of calculation. After a 50% increase, the new price would be $1.50. Now, we know that after the second increase the new price is 6 times the original, which means the price is now $6.00.

To calculate the percent increase of the second price change, we divide the final price by the price after the first increase: $6.00 / $1.50 equals 4. This means the price was quadrupled. To find the percentage increase, we subtract the initial value (1, since it was multiplied by 4) and then multiply by 100. Therefore, the percent increase for the second time is (4 - 1) × 100% which equals 300%. The second price increase was 300%.

Answer:

The domain of a function is the complete set of possible values of the independent variable.

In plain English, this definition means:

The domain is the set of all possible x-values which will make the function "work", and will output real y-values.

When finding the domain, remember:

The denominator (bottom) of a fraction cannot be zero

The number under a square root sign must be positive in this section

Step-by-step explanation:

Answer and explanation:

The set of all possible values of x that will make the function work, giving an output of real y values is said to be the domain of a function.

The domain of a function is determined by looking for the values of the independent variable (which is usually x) that are allowed to use.

While the complete set of all possible output values of the dependent variable (usually y), when we substitute the x values is called the range.

Range can be determined by the spread of the possible y-values (minimum y-value to maximum y-value).

Answer:

She would have to do 219 haircuts in a month for the costs to be the same, which would be $428.

Step-by-step explanation:

To find this we take the costs of the first place.

$438

Next we can look at the costs of the second place using x as the number of haircuts she'd do.

2x

Now we can set the two equal to each other to find the number of cuts.

438 = 2x

219 = x

Answer: 5, 7, 9

Step-by-step explanation:

1st#: 2k+1

2nd#: 2k+3

3rd#: 2k+5

2(2k+1 + 2k+3 + 2k+5) = 3(2k+5) + 15

2(6k + 9) = 6k + 15 + 15

12k + 18 = 6k + 30

6k           =        12

 k           =         2

1st#: 2k+1  = 2(2) + 1 = 5

2nd#: 2k+3 = 2(2) + 3 = 7

3rd#: 2k+5 = 2(2) + 5 = 9

Answer:

15

Step-by-step explanation:

The square root of 5 times 3 square root of 5 is 5√3

[tex] \sqrt{5 \times 3} \sqrt{5} [/tex]

[tex] = \sqrt{15} \times \sqrt{5} [/tex]

[tex] = \sqrt{75} [/tex]

[tex] = \sqrt{25 \times 3} [/tex]

[tex] = 5 \sqrt{3} [/tex]

The simplification of the square root of 5 times 3 square root of 5 is 5√3

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Answer:

they are both irrational

Step-by-step explanation:

if you add them, then they turn out to be decimals that go on and have no pattern

Answer:

Both will be irrational

Answer:

240

Step-by-step explanation:

Once you divide, using a calculator if possible, you get the exact solution.

Answer:

240

Step-by-step explanation:

1st you gotta turn 3.1 into a whole number by moving the decimal 1 space to the right then add a 0 to 744, next you divide normally

Answer:

Im pretty sure its a. C and G

Step-by-step explanation:

Answer: The answer is (C) C and E.

Step-by-step explanation:  We are given a figure including a plane 'w' and a number of points A, B, C, D, E and F around the plane. We are to select the pair of points from the given options that  lie within the plane 'w'.

We can see in the figure that the points A and F lie above the plane 'w'; the points  B and D lie below the plane 'w'; the points C and E lie on or within the plane 'w'.  

Since we are to find the set of points lying within the plane 'w', so option (C) is the correct option.

Answer:

x must be less than or equal to 5 hours

Step-by-step explanation:

24.   C= 2(x-2) +3

 C must be less than 10

10> 2(x-2) +3

Distribute the 2

10> 2x-4+3

Combine like terms

10> 2x-1

Add 1 to each side

10+1> 2x-1+1

11> 2x

Divide each side by 2

11/2 >2x/2

5.5 >x

We can only have whole hours

x must be less than or equal to 5 hours

Answer:

The price for both senior and child tickets are $9 each

Step-by-step explanation:

Since your just trying to find the price for senior citizen and child  tickets, we'll use the equation for the first day:

4x + x = $45

5x = $45

x = 9

now plug it for 4x and x

4(9) = $36  <<divide $36 by 4 == $9

$9 for each child ticket

Answer:

Q 9:

Because the two polygons are similar so AB ≈ PQ = SR

Scale factor is 25/20 = 1.25

Perimeter of ABCD = 14+20+14+20 = 68

We can find the length of SP by multiplying the scale factor with the AD so

SP = 14 * 1.24= 17.5

Perimeter of PQRS = 17.5+25+17.5+25 = 85

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Q 10:

Because the two polygons are similar so AD ≈. EH

Scale factor is 7/14 = 0.5

Perimeter of ABCD = 12+14+13+26 = 65

Because the two polygons are similar so DC ≈ HG

and our scale factor is 0.5 so HG = 13/2 = 6.5

Perimeter of EFHG = 6 + 7 + 6.5 + 13 =  32.5

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Q 11:

The Geometric Mean is a special type of average where we multiply the numbers together and then take a square root (for two numbers). And the formula for finding the Geometric mean of two numbers a and b is

[tex]\sqrt{a*b}[/tex]

So geometric mean of the 8 and 10 can be found as

[tex]\sqrt{8*2} = \sqrt{16} = 4[/tex]

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Q 12:

Similarly we can using the above formula of finding the geometric mean of 5 and 45 as

[tex]\sqrt{5*45} = \sqrt{225} = 15[/tex]

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

Q 13:

and we can find the geometric mean of 6 and 30 by using the same formula

[tex]\sqrt{6*30} = \sqrt{180} = 13.41[/tex]

First you must simplify the  equation. 7t+(-3t) is equal to 4t. Then we subract 3y from 4t. This brings us to 4t-3y. We also can simplify the first equation. We can move 4t to 8t and we then get 8t-4t-3y which is equal to 4t-3y. We know that 4t-3y=4t-3y.

Hopw this helps. <3

The solution is A = 4t - 3y

The value of the equation A is A = 4t - 3y

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = 8t - 3y - 4t   be equation (1)

Let the equation B = 7t + ( -3t ) - 3y   be equation (2)

Now , on simplifying the equation (1) , we get

A = 8t - 4t - 3y

A = 4t - 3y

So , the value of A is 4t - 3y

Now , on simplifying the equation (2) , we get

B = 7t + ( -3t ) - 3y

B = 7t - 3t - 3y

The value of B = 4t - 3y

Therefore , the value of A is equal to value of B

Hence , the equation A is equivalent to equation B

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Answer:

In order to represent functions as graphs, first we need to make a table of x and y values and plot those x,y values on the graph

Step-by-step explanation:

Suppose we have a statement as below:-

The cost of carrot is $2.50/lb

We can convert this statement into a function as

total cost = price per lb * weight of carrot bought

Let y be the total cost and x be weight of carrot bought

So,

y = 2.50 * x

where x is the independent variable and y is the dependent variable

A function represents an equation that shows the relationship between the input x and the output y.

The input x is also known as the Domain

The output y is also known as the Range

1) We can represent this function as a graph. In order to make a graph we need to begin by making a table containing inputs and their corresponding outputs.

Input, x (lb) Output, y ($)

0                       0

1                       2.50

2                       5.00

3                       7.50

The above table is generated by plugging in the values of x as 0, 1, 2, 3 into the function y=2.50*x and calculating the corresponding value of y

2) Now, we just need to plot the above pair of x,y values on the graph as shown in the attached figure.

Answer:

9

Step-by-step explanation:

In the larger triangle you divided 12 by 2 which gave you the length of its corresponding side. So if you do 12/6 to get 2, you divide 54 by 6 and get 9.

[tex]u(x)=-2x^2+3\\\\v(x)=\dfrac{1}{x}\\\\(u\ \circ\ v)(x)=-2\left(\dfrac{1}{x}\right)^2+3=-2\left(\dfrac{1}{x^2}\right)+3=-\dfrac{1}{x^2}+3\\\\\text{The range of}\ y=\dfrac{1}{x^2}\ \text{is all positive real numbers.}\\\\\text{The range of}\ y=-\dfrac{1}{x^2}\ \text{is all negative real numbers.}\\\\\text{The range of }\ (u\ \circ\ v)(x)=-\dfrac{1}{x^2}+3\ is\ (-\infty,\ 3)[/tex]

Answer:

(-∞,3)

Step-by-step explanation:

Imagine functions as little machines that turn one number into another number, the set of numbers that can enter the machine are called domain and the set of  numbers that can exit the machine are called range.  In this excercise we have to do function composition, which would be like having two machines and take the numbers that exit machine number 2 ([tex]v(x)[/tex]) and enter them into the machine number 1 ([tex]u(x)[/tex]). In math this is done by replacing the [tex]x[/tex] in [tex]u(x)[/tex] with the function [tex]v(x)[/tex] like this:

[tex]u(x)=-2x^{2} +3\\v(x)=\frac{1}{x}\\(u°v)=-2(\frac{2}{x})^{2} +3[/tex]

Now we need the range of the composed function, this will be the numbers that can come out of the machine number 1 when the numbers from the machine number 2 are entered to it.

So first which numbers will come out of machine number 2([tex]v(x)[/tex])? All but 0 because  we there is no number that we can divide 1 by it that will give us the value 0 (not even zero itself because it is and indeterminate form).

We have now which numbers will enter machine number 1 (we dont have any restrictions in [tex]u(x)[/tex] to enter numbers)

The range of the composed function will be then the range of [tex]u(x)[/tex] less the value that we woud obtain by replacing [tex]x[/tex] with 0.

The range of [tex]u(x)[/tex] is (-∞,3] according to the  attached graph and the value that we woud obtain by replacing [tex]x[/tex] with 0 is 3 so we would have (-∞,3).

Answer:

Step-by-step explanation:

did this on my hw got a 100

The area of the circle has a circumference of 11pie is 94.98 ft sq.

The area of the circle is the region enclosed by a circle of radius r.

The area of the circle = [tex]\pi r^{2}[/tex]

It is given that

The circumference of a circle = [tex]2\pi r[/tex] = 11π

         [tex]2\pi r[/tex] =  11π

           r = 11/2

The area of the circle = [tex]\pi r^{2}[/tex]

                                    = [tex]\pi \times (11/2)^{2}[/tex]

                                    = [tex]3.14 \times 121/4\\[/tex]

                                    = 94.98 ft sq

Thus, The area of the circle has a circumference of 11pie is 94.98 ft sq.

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Answer:

3(15)

Step-by-step explanation:

We found that the width is 11 yards and the length is 14 yards.

We are given that the length of a rectangle is 3 yards longer than its width and that the perimeter of the rectangle is 50 yards. To find the length and width, we can set up a system of equations based on the information provided.

Let the width of the rectangle be w yards. Then the length would be w + 3 yards. Because the perimeter of a rectangle is the sum of all its sides, we can express the perimeter P as:

P = 2 * ( L + B)

Substituting the given values:

50 = 2(w + 3) + 2w

Now, let's solve the equation:

50 = 2w + 6 + 2w

50 = 4w + 6

44 = 4w

11 = w

Thus, the width is 11 yards. The length is 14 yards (because it is 3 yards longer than the width).

Answer:

4 feet = 48 inches

Step-by-step explanation:

In one foot there are 12 inches and since we have 4 of them we multiply to find how many total inces there are:

4x12=48

If you wanted to check the other side of it you would divide 48 inches by 12 inches to find out how many feet you have:

48÷12=4

Answer:

They are equal.

Step-by-step explanation:

A foot is made up of 12 inches

4 feet= 12*4 inches

4 feet= 48 inches

There you go!

The two are equal to each other