Write a two-column proof to prove that vertical angles are congruent.

By solving the equation we can conclude that Bill worked 4 years and Hoang worked 10 years in the hospital.

So, Hoang worked for 6 years longer than her friend.

She spent twice as much time in the hospital two years ago. Then:

Hence, Bill worked for 4 years and Hoang worked (4+6) for 10 years in the hospital.

Therefore, by solving the equation we can conclude that Bill worked for 4 years and Hoang worked for 10 years in the hospital.

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The exponential function given in this problem represents an exponential decay, and it's asymptote is of y = 0.

An exponential function is modeled according to the rule given as follows:

[tex]y = ab^x + c[/tex]

The parameters of the function are defined as follows:

To verify if the function represents growth or decay, we have to check parameter b as follows:

In the context of this problem, the function is defined as follows:

[tex]y = 14\left(\frac{1}{2}\right)^x[/tex]

Hence the parameters of the given function are as follows:

a = 14, b = 0.5, c = 0.

Then:

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Answer:

Answer down bellow

Step-by-step explanation:

Q's asked: Does the function y equals 14 times the quantity 1 over 2 end quantity to the x power represent exponential growth or decay? What is the equation of the asymptote?

Answer: Decay; y = 0

hope this helps

~~Wdfads~~

(x-5) is not a factor of  6) 5x³-28x + 13x³ + 5x² + 27x - 10 and 7) 2x² - 4x² - 10​.

What is the long division method?

You can divide huge numbers into numerous smaller groups or portions with the long division tool. The number of groups that can be formed when a dividend is divided by a divisor is given by the quotient, and the number of elements or integers that will remain ungrouped is given by the remainder.

6) we can simplify the equation 5x³-28x + 13x³ + 5x² + 27x - 10 further,

=  5x³+ 13x³+ 5x²-28x + 27x - 10

=[tex]18x^{3}+5x^{2} -x-10[/tex]

similarly, equation  2x² - 4x² - 10 can further be simplified

= [tex]-2x^{2} +0x-10\\[/tex]

now using the long-division method, in both cases (refer to the photo attached):

After referring to the picture we can conclude that (x-5) is not a factor of  6) 5x³-28x + 13x³ + 5x² + 27x - 10 or 7) 2x² - 4x² - 10​.

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Probability of three youngest student are selected is [tex]\frac{1}{816}[/tex]

The field of mathematics known as probability concerns with numerical representations of the possibility that an event will occur or that a statement is accurate. An event's probability is a number between 0 and 1, where, roughly speaking, 0 indicates the event's impossibility and 1 represents certainty.

Given data

Total number of students available = 17

Number of students selected = 3

C₍₁₈₋₃₎ = [tex]\frac{18!}{3!(18-3)!}[/tex]

C₍₁₈₋₃₎ = [tex]\frac{18(17)(16)}{3(2)(1)}[/tex]

C₍₁₈₋₃₎ = [tex]\frac{4896}{6}[/tex]

C₍₁₈₋₃₎ = 816

Number of ways where students selected are youngest = 1

Probability of three youngest student are selected

= [tex]\frac{1}{C}[/tex]₍₁₈₋₃₎

= [tex]\frac{1}{816}[/tex]

Probability of three youngest student are selected is [tex]\frac{1}{816}[/tex].

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The amount of water that Lucy should drink more is 750 ml.

From the information, Lucy between breakfast and lunch she pours 2 glasses of water each measuring 250ml. This will be:

= 250ml × 2

= 500ml

Between lunch and her dinner she pours 3 glasses also measuring 250 ml. This will be:

= 3 × 250ml

= 750 ml

Since Lucy wants to drink 2L of water, the amount needed to drink more will be:

= 2L - (750 + 500)

= 2000ml - 1250ml

= 750ml

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Answer:

b

Step-by-step explanation:

4x + 28 = 40

4x + 4*7 = 40

4(x+7) = 40

Answer:3

Step-by-step explanation:

(-3/4)/(-2/8)=(-3/4)(-8/2)=(-3/4)(-4)=3

Due to different rates of change in each case, neither graph shows a proportional relationship.

A graph represents a proportional relationship if the output variable y in the y-axis can be written as a product of the input variable x in the x-axis and the constant of proportionality k, as follows:

y = kx.

For the first case, the rate of change is of:

k = 4/10 = 0.4.

For the second case, the rate of change is of:

k = 8/10 = 0.8.

Different rates, hence cannot be written as proportional relationship.

Hence the rates for each interval are given as follows:

Different rates, hence it is not a proportional relationship.

The graphs are missing and are given by the image inserted at the end of the answer.

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The perimeter of the square BCDE is 8√2 cm.

A square is a quadrilateral that has all its sides equal to each other. All the angles in a square are also equal.

Therefore, the perimeter of a square is the sum of the whole sides of the square.

perimeter of the square BCDE = 4l

area of triangle ABC = 2cm²

area of triangle ABC = 1 / 2 bh

2 = 1 / 2 bh

The diagonal of square bisect each other.

The base and height of the triangle ABC are the same.

bh = 4

b² = 4

b = √4

b = 2 cm

Therefore,

BC = √2² + 2²

BC = √8

BC = 2√2 cm

Hence,

perimeter of the square BCDE = 4(2√2)

perimeter of the square BCDE = 8√2 cm

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The expression will be given as -4x² + 3x. Thus, option B is correct answer.

Area may be defined as the total amount of space which is covered by an entity. The area for a square will be given by the product of its sides and the area of the rectangle will be given as the product of its length and breadth. It is given that the area of Maria's garden is 8x² - 3x and the length and breadth of Jamal's garden are 4x - 2 and 3x respectively. The area of Jamal's garden is given by A = l×b  = (4x - 2) × 3x = 12x² - 6x.

Now, difference between Maria's garden and Jamal's garden is given by

(8x² - 3x) - (12x² - 6x)

= 8x² - 3x - 12x² + 6x

=> -4x² + 3x which is the required answer.

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Answer:

Step-by-step explanation:

To solve this problem, use the order of operations.

PEMDAS stands for:

112-38*14÷14+109

First thing you do is multiply.

[tex]\sf{38*14\div14}[/tex]

38*14=532

532÷14=38

112-38+109

Add and subtract the numbers from left to right.

[tex]\sf{112-38+109}[/tex]

[tex]\sf{112-38=74}[/tex]

[tex]\sf{74+109=\boxed{\sf{183}}[/tex]

[tex]\Rightarrow \boxed{\sf{183}}[/tex]

Therefore, the correct answer is A. 183.

I hope this helps, let me know if you have any questions.

Answer:

I’m believing it is A. 183

Step-by-step explanation:

is correct don’t you;)

Answer:

C and D. The x-axis is horizontal, the y-axis is vertical. Quadrant 3 is where you would find a point where the x is positive and the y is negative. Quadrant 3 is below the x-axis and is to the left of the y-axis.

Step-by-step explanation:

Hope it helps! =D

The percent of the people he paid claimed to be his friends is 67.5%

Given,

Mr. McCullough paid 80 people to say they were his friends.

and, After he paid them, 26 of them still did not claim to be his friend.

To find the percent of the people he paid claimed to be his friends

Now, According to the question:

Based on the given condition,

Formulate :

(80- 26) ÷ 80

Calculate:

(80- 26) / 80

= 54/80

Simplify

= 27/40

=0.675

Convert to percentage;

Multiply a number to both the numerator and the denominator

0.675 × 100/100

Calculate

67.5 / 100

= 67.5%

Hence, The percent of the people he paid claimed to be his friends is 67.5%.

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Answer:

99.58

Step-by-step explanation:

Im not sure if its correct but the way I got the answer is 100-0.42

The value of x in the equation given as x - 2(x - 6) = -x + 12 is 0

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the equation is given as

x - 2(x - 6) = -x + 12

Open the bracket

So, we have

x - 2x + 12 = -x + 12

Evaluate the like terms

So, we have

x - 2x = -x

This gives

x = 0

Hence, the solution of x in the equation is 0

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:f{}^{-1}(x) = x +5 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

We need to find the inverse of given function; f(x) = x - 5

[tex]\qquad \tt \rightarrow \: y = x - 5[/tex]

here, write x in terms of y.

[tex]\qquad \tt \rightarrow \: x = y + 5[/tex]

replace x with [tex]{\tt{{f}^{-1} (x)} } [/tex] and y with x, you will get your required inverse function.

[tex]\qquad \tt \rightarrow \: f {}^{ - 1} (x) = x + 5[/tex]

And it's already in slope intercept form

[tex]\qquad \tt \rightarrow \: y = mx + c[/tex]

where, slope (m) = 1 and y intercept (c) = 5

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The equation that represents the proportional relationship between the number of red paint and white paint is: y = 1/4x.

A proportional relationship between two variables, x and y, where k represents the constant of proportionality or unit rate, can be expressed in  slope-intercept form as: y = kx.

To find the value of k, which is the unit rate, the coordinates of any point on the line can be used and solved as: k = y/x.

Given the graph that represents the relationship between the number of red paint and white paint, we can use a point on the line, say (4, 1) to find k:

Unit rate/constant of proportionality, k = y/x = 1/4.

Substitute k = 1/4 into y = kx:

y = 1/4x.

The equation is: y = 1/4x.

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Answer: x < 2

Step-by-step explanation:

    To solve this, we will isolate the variable c.

   Given:

4c < 14 - 3c

   Add 3c to both sides of the equation:

7x < 14

   Divide both sides of the equation by 7:

x < 2

4) The surface area of the square pyramid is; 145 ft²

5) The surface area of the rectangular prism is; 948 ft²

4) For the square pyramid, we see that the faces have been broken down into 4 equal rectangles and one square base.

We know that;

Area of triangle = 1/2 * base * height

Thus

Area of 4 triangles = 4(1/2 * 5 * 12) = 120 ft²

Area of square = 5 * 5 = 25 ft²

Total surface area = 120 + 25 = 145 ft²

5) The surface area of a rectangular prism is;

A = 2(wl + hl + hw)

Thus, Area = 2((20 * 3) + (20 * 18) + (18 * 3))

Area = 2(474)

Surface area = 948 ft²

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Answer: not sure

Step-by-step explanation: this: by this -

Equals this: ur mom

Answer:

b. one dimension

Step-by-step explanation:

0 dimensions would be a point.

1 dimension is a line

2 dimensions is an area

3 dimensions is a volume.

rise over run to find the slope

y = mx+b

we rose 1 and went over by 2

which means the equation is 1/2 x or 0.5x

The number of the smaller squares which would be shaded to represent 0.75% as given in the task content is; 75.

The number of squares to correctly represent 245% on the grid is; 245.

It follows from the task content that; To represent the percent, Don uses a 10 × 10 grid and divides one of the squares in the grid into 100 smaller squares.

Since each Square in the 10 × 10 grid represents 1%, it follows that on division of one of the squares in the grid into 100 smaller squares;

The percentage, 0.75% can be represented by shading 75 smaller squares.

Also, the number of squares to be shaded on 10 × 10 grids to represent 245% according to the task content is; 245. This follows from the fact that, all 100 squares on the on 10 × 10 grids represent 100%.

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The expression for the number of cups of flour Cindy has left in the cupboard is y = 5 - c.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

Let c be the number of cups of flour Cindy needs in her cupboard.

Let y be the number of cups of flour Cindy has left after making the brownies.

Now, the total number of cups in the cupboard is 5.

So, the expression for the total number of cups will be:

c + y = 5

Subtracting c from each side of the equation.

c + y - c = 5 - c

y = 5 - c

Therefore, the expression for the number of cups left is y = 5- c.

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on june 10, 2010 the boston globe reported that in the six years between 2006 and 2012 boston firefighters received raises of 2%, 2.5%, 3%, 3.5%, 2.5%, and 1.5%. then overall raise is 16%

on june 10, 2010 the boston globe reported that in the six years between 2006 and 2012 boston firefighters received raises of 2%, 2.5%, 3%, 3.5%, 2.5%, and 1.5%.

let us assume the amount be 100

in 2007 it increase at 2% then it become 102

in 2008 at rate 2.5% then =102+2.55=104.55

in 2009 at rate 3% then it become =3.1365+104.55= 107.68

in 2010 at rate 3.5% = 3.7690+107.68=111.44

in 2011 at rate 2.5% = 2.786+111.44=114.22

in 2012 at rate 1.5%= 1.71+114.22=115.93

Hence, overall increase is 16%

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The line that passes through the pair of points has the given slope. ( − 2 , 8 ) , ( r , 4 ) , m = − 1 2, then the intersection with the domain is r = -5/3.

The line that passes through the pair of points has the given slope is,

( − 2 , 8 ) , ( r , 4 )  and m = -12

Slope, numerical measure of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).

m = rise/run

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

Where,

m = slope

[tex](x_{1} ,y_{1} )[/tex] = coordinates of first point in the line

[tex](x_{2} ,y_{2} )[/tex] =  coordinates of second point in the line

Then, we can find the [tex]m_{1}[/tex]

We can use these two values, ( − 2 , 8 ) , ( r , 4 )

x1 = -2

y1 = 8

x2 = r

y2 = 4

m = [tex]\frac{4-8}{r-(-2)}[/tex]

[tex]m = \frac{-4}{r+2}[/tex]

We can substitute m= -12 value into m= -(4/r+2)

So,

We can write,

-12 =  [tex]\frac{-4}{r+2}[/tex]

We can find the domain,

If the fraction is defined, the dominator can not be equal to zero.

2 + r ≠ 0

Rearrange variables to the left side of the inequality,

r ≠ -2

Append the inequality as the domain,

r ≠ -2

We can solve the equation,

-12 =  [tex]\frac{-4}{r+2}[/tex]

Multiply both sides of equation by the common denominator,

-12 (r+2) =  -4(r+2)/ (r+2)

Reduce the fractions,

-12 (r+2) = -4

Apply the distributive property,

-12r - 24 = -4

Rearrange variable to the left side of the equation,

-12r = -4 + 24

Calculate the sum or difference,

-12r = 20

Divide both sides of the equation by the coefficient of variables,

r = - 20/12

r = -5/3

Therefore,

The intersection with the domain is r = -5/3, so  the line that passes through the pair of points has the given slope. ( − 2 , 8 ) , ( r , 4 ) , m = − 12.

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Answer:

umm i will explain

Step-by-step explanation:

miguel = 448 in 8 min

jaycee = 700 in 25 min

in 1 min miguel can type=

448/8 = 56 words

in 1 min jaycee can type=

700/25 = 28 words

so miguel can type's faster than jaycee

rjdjdjdufjfjfjfjfuuf

The number of trees that could be saved is 8 trees.

We know that papers are obtained from trees. The trees have to be cut down and then the Malina from the trees could be used in the production of paper.

It is also possible to save the trees by decreasing the number of trees that have to be cut by the recycling of the paper.  The number of trees saved by recycling is directly proportional to the height of a stack of recyclable newspapers.

If  stack of recyclable newspaper 36 inches high will save one tree;

Let the stack of recyclable newspaper = s

Number of trees = n

s α  n

Introducing a constant of proportionality

s = kn

k = s/n

k = 36 inches/1

k = 36 inches

When the height is  24 feet high of 288 inches

n = s/k

n = 288 inches/36 inches

n = 8 trees

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