Find the missing side length. Show all work.
first right answer with right work gets 500 points

Answer:

45f.

Step-by-step explanation:

home is 60f.cold

we turn heat in order to raise the temprature by15

and 60minus 15 is 50

Answer:

75f

Step-by-step explanation:

since you raise the temperature you need to add those 2numbers together so 60+15=75f degrees

We can represent the expression (62−42)×3 in phrase as "three times the difference of 62 and 42".

In the given question we have to write a phrase that represent a given expression.

The given expression is (62−42)×3.

We can phrase a given expression by writing expression in to words. We write epression in to word according to the given expression.

As we can see that we subrating 62 by 42

So we can write it as difference of 62 and 42.

Then we multiplying with 3. So the expression in phrase is;

"three times the difference of 62 and 42"

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ANSWER:

D. 44

STEP-BY-STEP EXPLANATION:

The percentage of a number is calculated by multiplying the percentage number in its decimal form by the number whose percentage is to be calculated.

A percentage number is converted to a decimal by dividing that number by 100, so it would finally look like this:

So the correct answer is D. 44

Answer:

slope = - 14

Step-by-step explanation:

calculate the slope m using the slope formula

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

with (x₁, y₁ ) = (- 92, 21 ) and (x₂, y₂ ) = (- 93, 35 )

m = [tex]\frac{35-21}{-93-(-92)}[/tex] = [tex]\frac{14}{-93+92}[/tex] = [tex]\frac{14}{-1}[/tex] = - 14

Answer:

The answer will

be 0

Step-by-step explanation:

=9+4×8-8

=13×0

=0

The average rate of change over the interval x = 3 and x = 7 is 30

The average rate of change of a function, graph, table or ordered pair is simply the slope of the relation

The equation is given as

g(x) = 2ˣ - 1

The interval is given as:

x = 3 and x = 7

Start by calculating g(3) and g(7)

So, we have

g(3) = 2³ - 1 = 7

g(7) = 2⁷ - 1 = 127

So, the average rate over these intervals is calculated as:

Average rate = [g(b) - g(a)]/[b - a]

This gives

Average rate = [g(7) - g(3)]/[7 - 3]

Substitute known values

Average rate = [127 - 7]/[7 - 3]

Simplify

Average rate = 120/4

Average rate = 30

Hence, the average rate of change is 30

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Answer:

exponents / the little x next to the 5

Answer: You move "x"s to one side, numbers to another and so the first operation is moving +4 to another side and making it -4

The number of gallons of paints that will be made if 28 drops is used is 20 gallons

A rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

The total number of drops used to make 5 gallons is 7drops, i.e 4+3=7

this means to make 1 gallon 5/7 drops of color will be used

Therefore for 28 drops , 5/7×20 gallons will be made

= 20gallons

Therefore the gallons made with 28drops is 20gallons.

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The function given is,

The graph of the function will be shown below

a) The zeros of a function, also referred to as roots or x-intercepts, occur at x-values where the value of the function is 0 (f(x) = 0).

Hence, from the graph above the zeros of the function is at

b) The function's domain is

c) The function's long-run behaviour is that:

Hence, the answer is

In the triangle LMN angle N is 76 degree.

Given,

In the question:

There is two isosceles triangle in the figure:

Triangle JKL and Triangle LMN

Angle J = 64 degree

To find the angle Angle N

Now, According to the question:

The triangle is isosceles.

<J = 64 degrees

All triangles have 180

<JLK = 180 - 64 - 64

Angle JLK = 52degree.

Angle JLK = MLN  = 52 degree (Vertical opposite angle )

M is the left over from the 2 equal angles.

N = 180 - <M - < MLN                      

N = 180 - 52 - 52

N = 76 degree

Hence, In the triangle LMN angle N is 76 degree.

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SOLUTION

From the equation, to find the time in minutes which is y, we plugging 5 (from 5 days) for x into the equation, we have

Hence the answer is option B

Answer:  360,000

Reason:

Think of 360 as 360.0

We move the decimal point 3 spots to the right to get to 360,000.0 or simply 360,000; this movement of 3 to the right is directly because of the exponent over the 10.

The 10^3 represents "thousand", so "360 x 10^3" is "360 thousand" = 360,000.

To evaluate f(x) at x = -4 we substiitute x in the equation with -4. Doing this gives

which is our answer!

Current price of go-kart = $2,589

Price of go-kart next month = $2,119

If Rafael decides to buy the go-kart next month,

He will save $2,589 - $2,119 = $470

By definition of estimation

Estimation is an approximate calculation or judgment of the value, number, quantity, or extent of something

Approximating to the nearest hundred

$470 = $500

Therefore, Rafael will save an estimate of $500 if he wants to buy the go-kart next month

Solution:

Given:

An exponential function is of the form:

To get the exponential function for the relation;

Part A:

Relating this to the parameters given:

The exponential function that models the problem is;

Part B:

On the twenty-third day,

Therefore, he would have saved 4,194,304 pennies on the twenty-third day.

The given information is:

- They surveied 164 pet owners

- 61 own a dog

- 66 own a cat

- 11 own both a dog and a cat

We have to find how many owned neither a cat nor a dog.

We can represent this survey in the following diagram:

To find the solution we need to subtract the number of people who said they own a dog, own a cat, and own both, from the total number of people in the survey, so:

The people who own neither a dog nor a cat are 26.

Given:

Principal Amount, P = $4,400

Interest rate, r = 90%

Here, Camilla needs to create an exponential equation that allows her tract the interest earned over time.

This is a Compound interest problem.

To find create an exponential equation, apply the formula below:

WHere:

P is the principal amount = $4,400

r is the rate = 90% = 0.90

t is the time (number of years)

Input values into the equation above:

Therefore, the exponential equation that allows her to track the interest earned over time is:

Plugging the value for the number of years for t, you will get the interest earned over time, t.

ANSWRER:

Answer:

Any value other than 3 will work.

The value of equation is  x = [tex]2\sqrt{2} and x = - 2\sqrt{2}[/tex] and method is used "Direct keeping Method".

Given,

In the question:

The equation is :

2[tex]x^{2}[/tex] – 7 = 9

To solve the above equation and explain which method to solve the equation?

Now, According to the question:

2[tex]x^{2}[/tex] – 7 = 9

2[tex]x^{2}[/tex] = 9 + 7

2[tex]x^{2}[/tex] = 16

[tex]x^{2}[/tex] = 8

x = [tex]2\sqrt{2} and x = - 2\sqrt{2}[/tex]

{There is no one- time item}

The method is used for solving equation is the "Direct keeping Method"

Hence, The value of equation is  x = [tex]2\sqrt{2} and x = - 2\sqrt{2}[/tex] and method is used "Direct keeping Method".

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Answer:

Use the square root property of equality.

There is no x term.

Add and divide to isolate x^2.

Step-by-step explanation:

By using properties of angles, it is obtained that

x = 20°,

What is an Angle?

When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.

Here,

[tex]m\angle DOB =m\angle DOE +m\angle EOB[/tex] [ Addition of two angles]

[tex]m\angle DOB =90+x[/tex] [ Substitution]

[tex]m\angle AOC = m\angle DOB[/tex] [Vertically opposite angle]

[tex]110 = 90 + x[/tex] [ Substitution]

[tex]x = 20^{\circ}[/tex] [Algebra]

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Answer:

I hope I did it right

Answer: ∠WZY=150°

Step-by-step explanation:

Analysis :

ΔWXY is an isosceles triangle

perpendicular to WX intersecting:

XY at A

∠XWA = 21°

∠WXA = 90°-21° = 69°

Now, ΔXYZ is equilateral,

∠XYZ = ∠YXZ = 60°

Then,

∠WXZ = ∠WXA - ∠YXZ

= 69°-60°

= 9°

Since the angles of a triangle = 180°

∠WZY = ∠WZX = 180° - ∠XWA - ∠WXZ

= 180° - 21° - 9°

= 150°

You have to calculate the probability of obtaining an odd number after rolling the die and obtaining tail after tossing a coin, symbolically:

Where

"O" represents the event " rolling an odd number"

"T" represents the event "tossing a coin and obtaining tail"

The events are independent, which means that the intersection between both events is equal to the product of the individual probability of each event:

So, first, we have to calculate the probabilities of "rolling an odd number" P(O) and "tossing a coin and obtaining tail" P(T)

-The die is six-sided and numbered from 1 to 6, assuming that each possible outcome has the same probability, we can calculate the probability of rolling one number (N) as follows:

The possible outcomes when you roll a die are {1, 2, 3, 4, 5, 6}

Out of these six numbers, three are odd numbers {1, 3, 5}, this is the number of favorable outcomes of the event "O", and the probability can be calculated as follows:

So, the probability of rolling an odd number is P(O)=1/2

-When you toss a coin, there are two possible outcomes: "Head" and "Tail", assuming that both outcomes are equally possible.

For the event "toss a coin and obtain tail" there is only one favorable outcome out of the two possible ones, so the probability can be calculated as:

The probability of tossing a coin and obtaining a tail is P(T)=1/2

Once calculated the individual probabilities you can determine the asked probability:

Monetary value of 120 square foot piece of plastic wrap is $0.64

Direct variation means when ratio of two variable say cost and item always remains same.

example if cost of 2 pen is $1

then it will cost $2 for 4 pens

Given :

A 4500 square foot roll of plastic wrap costs $23.95

we have to find cost of 120 square foot roll of plastic for party game

Cost of 4500 square foot roll = $23.95

Cost of 1 square foot roll = [tex]\frac{23.95}{4500}[/tex]

=  $0.00532

Cost of 120 square foot long roll = cost of 1 square foot roll × 120

= 0.00532 × 120

=0.63833

rounding off

$0.64 is cost of 120 square foot long plastic roll

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Answer:

y=1/3x-3

Step-by-step explanation:

Let x be the number of teachers that go on the school trip

1 : 18 = x : 72

1/18 = x/72

cross-multiply

18x = 72

Divide both-side of the equation by 18

x = 4

Therefore, 4 teachers went on the school trip

Since f is the number of female cousins and the number of male cousins is 4 less than the number of female cousins, we can write the following expression to represent the number of male cousins:

For example, if the number of female cousins is 7, we can use this value (f = 7) in the expression above to find the number of male cousins:

So if the number of female cousins is 7, the number of male cousins is 3.

Therefore the expression for the number of boy cousins is f - 4.

Answer:

[tex]a_n=n^2 + 3[/tex]

Step-by-step explanation:

To find the nth term of a quadratic sequence, we need to determine the quadratic function that generates the sequence.

Given quadratic sequence:

4, 7, 12, 19, 28, ...

Begin by calculating the first differences between consecutive terms:

[tex]4 \underset{+3}{\longrightarrow}7 \underset{+5}{\longrightarrow} 12\underset{+7}{\longrightarrow} 19\underset{+9}{\longrightarrow} 28[/tex]

As the first differences are not the same, we need to calculate the second differences (the differences between the first differences):

[tex]3\underset{+2}{\longrightarrow} 5 \underset{+2}{\longrightarrow} 7\underset{+2}{\longrightarrow}9[/tex]

As the second differences are the same, the sequence is quadratic and will contain an n² term.

The coefficient of the n² term is half of the second difference.

As the second difference is 2, the coefficient of the n² term is 1.

Now we need to compare n² with the given sequence (where n is the position of the term in the sequence).

[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6}n&1&2&3&4&5\\\cline{1-6}n^2&1&4&9&16&25\\\cline{1-6}\sf operation&+3&+3&+3&+3&+3\\\cline{1-6}\sf sequence&4&7&12&19&28\\\cline{1-6}\end{array}[/tex]

We can clearly see that the algebraic operation that takes n² to the terms of the sequence is add 3.

Therefore, the expression to find the the nth term of the given quadratic sequence is:

[tex]\boxed{a_n=n^2 +3}[/tex]

From the information available, the initial population was 16,007. That figure was taken as at the year zero which is January 1, 2014.

This means

This trend would be used until we get to January 1, 2030, when we would calculate as follows;

Note that the years count from Jan 1 to Jan 1.

The function that models the yearly growth is;

Using the first year, 2014 which is year zero, the result would remain 16,007. That is;

For the 16th year, which is year 2030, we woud now have the following;

Rounded to the nearest whole number, this figure becomes;

ANSWER: