I need to find the one real answer

I Need To Find The One Real Answer

Answers

Answer 1

The missing value for which there is one solution of the equation are 13, -11 and 11.

What is defined as the solution of the equation?A mathematical equation expresses that two expressions seem to be equal. 4+4=8 is a mathematical formula. A mathematical formula with one or more variables is known as an algebraic equation. It has a first-degree variable (x) and a straight line graph.The method of identifying the number that what a variable represents is known as solving an equation. The value obtained is known as the equation's solution. An equation is a mathematical language that claims that two algebraic expressions has to be equal in nature.

For the given question,

The expression is given as;

(4/3)(-9x + 12) - x = _x - 9

Putting, 13, -11 and 11 will given the one solution of the equation.

Except -13 as expression is not defined for it.

Put -13 at the blank space and solve it,

-12x + 48 - x = - 13 x - 9

- 13x + 48 = -13x - 9

-13x will get cancelled.

Thus,

48 = -9

But,

48 ≠ -9

Thus, -13 is not a solution of the expression.

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Related Questions

In 25 minutes Shiloh can In 10 laps around the track. Determine the number of
laps he can run
per minute.
A.
Find the constant of proportionality in this situation.
Answer:
B. Write an equation to represent the relationship.
Answer:

Answers

Shiloh can run 04 laps per minute if in 25 minutes Shiloh can run in 10 laps around the track and it is Laps per minute is simply division.

What is constant of proportionality?

The ratio that is connecting two given numbers is what is known as the exact proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names that can be given for the constant of proportionality.

To represent the equation in laps per min,

L/m = 10/25

= 2/5

= 0.4 laps per minute

The constant of proportionality in this situation

10/25 = 0.4

The equation to represent the relationship.

y = 0.4x

How do you determine the proportionality constant?

Identifying the same x and y variables is the first step in determining the proportionality constant. X will be the weight and Y will be the number of butter sticks in order to calculate the exact weight to stick ratio.

Then to determine the proportionality constant, we can use the constant equation k = y x.

Why is K the proportionality constant?

When two variables are directly or indirectly proportional to one another, their relationship can be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables. The proportionality constant, k, is often used.

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pls help
what are the coordinates of Y if 5,12 is 1/3 of the way from X to Y

Answers

The coordinates of the point Y at the other endpoint is 41

How to determine the coordinates of the point Y?

From the question, the given parameters are

Point X = 5The location of the point between X and Y = 12Proportion = 1/3

Because there is not y coordinates in the coordinates, we can make use of only the x coordinate

So, we have the following equation

Point = Proportion * (Y - X)

Substitute the known values in the above equation

So, we have the following equation

12 = 1/3 * (Y - 5)

Multiply through the equation by 3

So, we have the following equation

36 = Y - 5

Add 5 to both sides of the equation

So, we have the following equation

Y = 41

This means that the conclusion is the coordinate of the point Y is 41

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Find the savings plan balance after 6 months with an APR of 8% and monthly payments of $200

Answers

The savings account balance after six months with an 8% annual percentage rate and $200 monthly contributions is $202.6.

What does a savings plan formula serve?

Savings Plan Formula

The future worth of a savings or investment account in which you make regular deposits can be calculated using the formula below.

EXAMPLE 1 Assume you put $100 into a savings account each month that pays 7.3% interest that is compounded monthly.

To determine the saving plan balance after 6 month

First of all we have to calculate the growth factor

Growth factor =(1+(0.08/6)) per month

Growth factor= 1.013

Now let calculate the savings plan balance after 6 month

Saving plan balance after 6

Months =$200.00x1.0133

             = $202.6

From conclusion the saving plan balance after 6 month is=$202.6

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go quick if you have a good brain

see attachment beloww.

Answers

Answer:y=21°

x=8°

Step-by-step explanation:

3y+27=90

3y=63

y=21°

x+90°+8x+18°=180°

9x+108°=180°

9x=72°

x=8°

I need the answer to this with an explanation. This is ratio.

Answers

Given that 2500 students entered the Teacher Education Program.

[tex]\text{Number of male students + Number of female students = 2500}[/tex]

20% of the students are male. Thus,

[tex]\begin{gathered} \text{Number of male students = 20\% of 2500} \\ \Rightarrow\frac{20}{100}\times2500 \\ \text{Number of male students = 500} \end{gathered}[/tex]

Thus,

[tex]\begin{gathered} \text{Number of male students + Number of female students = 2500} \\ 500\text{ + Number of female students =2500} \\ \Rightarrow Number\text{ of female students = 2500 -500 = 2000 } \end{gathered}[/tex]

Thus, the ratio of the number of males to the number of females is evaluated as

[tex]\begin{gathered} \text{Number of female : Number of male} \\ 2000\text{ : 500} \\ reducing\text{ to the lowest term gives} \\ 4\colon1 \end{gathered}[/tex]

Hence, the ratio of the number of females to the number of males is thus 4:1

The slope of a line is

Answers

Answer:

-2

Step-by-step explanation:

You have to use rise over run. For example, to go from (-1,0) to (-2,2), you have to go up 2 squares and go left 1. That gives you 2/-1, which is -2. Hope this helps!

) Which problem below would require that you use the distributive property to help yousimplify it? Explain why the distributive property is required for that problem. What wouldyou use to simplify the other problem?2 (x+4)5+ 9(5-1)

Answers

Given the expressions:

[tex]\begin{gathered} 2(x+4) \\ 5+9\mleft(5-1\mright) \end{gathered}[/tex]

You need to remember that the Distributive Property states that:

[tex]a(b\pm c)=ab\pm ac[/tex]

• In order to simplify the first expression, you only need to apply the Distributive Property, because there is a number multiplying a Sum. Therefore, get:

[tex]\begin{gathered} =(2)(x)+(2)(4) \\ =2x+8 \end{gathered}[/tex]

• In order to simplify the second expression, you need to follow these steps:

1. Apply the Distributive Property:

[tex]=5+(9)(5)-(9)(1)[/tex]

[tex]=5+45-9[/tex]

2. Solve the Addition:

[tex]=41[/tex]

Hence, the answers are:

• The first problem requires to use only the Distributive Property to simplify it. It is required because there is a number multiplying a Sum:

[tex]2(x+4)[/tex]

Notice that the second expression can be simplified using the Distributive Property as the first step.

• The second problem can be simplified by applying the Distributive Property and then adding the numbers.

Find a smart way to compute.1 8/11 x 5/12 + 5/12 x 3/11

Answers

On simplifying the given equation, the answer is [tex]\frac{5}{6}[/tex]

How an equation can be simplified?

The fundamental guidelines and procedures to simplify any statement are as follows:

By multiplying factors, remove any grouping symbols like brackets and parenthesis.

If the words contain exponents, use the exponent rule to eliminate grouping.

Add or subtract like terms to combine them.

Add the constants together.

Given,

1 8/11 x 5/12 + 5/12 x 3/11

[tex]\frac{19}{11}[/tex]  ×  [tex]\frac{5}{12}[/tex]    +  [tex]\frac{5}{12}[/tex]   × [tex]\frac{3}{11}[/tex]

Taking [tex]\frac{5}{11 * 12}[/tex] as a common factor,

⇒ [tex]\frac{5}{11 * 12}[/tex] ( [tex]19 + 3[/tex])

⇒ [tex]\frac{5}{11 * 12}[/tex] × 22

On simplifying,

⇒ [tex]\frac{5}{6}[/tex]

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the functions f and g are defined as follows.
f (x) = -2x^3 - 3 g (x) = 2x + 4.
find f (-2) and g (-6)
Simplify your answers as much as possible.

Answers

Answer: [tex]f(-2)=13, g(-6)=-8[/tex]

Step-by-step explanation:

[tex]f(-2)=-2(-2)^3 -3=13\\\\g(-6)=2(-6)+4=-8[/tex]

The values of functions f(-2) and g(-6) are 13 and -8 respectively.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

It is given in the question  that:-

[tex]f (x) = -2x^3 - 3[/tex]

g(x) = 2x + 4

We have to find the values of f(-2) and g(-6).

Putting x = -2 in f(x), we get,

f(-2) = [tex]-2(-2)^3 - 3[/tex] = -2*(-8) - 3 = 16 - 3 = 13

Putting x = -6 in g(x), we get,

g(-6) = 2(-6) + 4 = -12 + 4 = -8

Hence, the values of functions f(-2) and g(-6) are 13 and -8 respectively.

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A friend lends you $720, which you agree to repay with 4% interest. How much will you have to repay? How much was the interest?

Answers

Answer: $16081.60

Step-by-step explanation:

1)

FV=3000(1.03)=$3090

2)

240*1.04=$249.60

3)

FV=14000(1.02)^7

FV=14000(1.1487)

FV=$16081.60

I need help with question #8

Answers

There is no picture provided. Make sure when you make a question with a specific understanding of the photo, you press choose file, or add a photo. Also, remember to double check!!



Hope this helps!!

A sales representative receive a monthly salary of $1600 plus a commission of 3% of the total monthly sales. write a linear model that relates total monthly wages W to sales S

Answers

Answer:

The equation is W = 1600 + .03S

2x-5>3 and -4x+7<-25

whats the compound inequality and how would it be graphed

Answers

Answer:

  8 < x

  see attached for the graph

Step-by-step explanation:

You want the compound inequality and the graph that represents the solution to the system ...

  2x-5>3 and -4x+7<-25

Solution

The first inequality has the solution ...

  2x -5 > 3 . . . . . given

  2x > 8 . . . . . . . add 5

  x > 4 . . . . . . . divide by 2

The second inequality has the solution ...

  -4x +7 < -25

  -4x < -32 . . . . . . subtract 7

  x > 8 . . . . . . . . divide by -4

The solution is the intersection of these solution spaces:

  4 < x    and   8 < x

The intersection is ...

  8 < x . . . . . solution to the compound inequality

The graph is attached.

Increase 10kg by 20%

I'm genuinely tonta right now please help

Answers

When 10kg is increased by 20%, the number becomes 24%

What is the result of the percentage increase?

Percentage is a measure of frequency that is used to express a quantity as a number out of 100. The sign that is used to represent percentages is %. In order to convert a number to a percentage, multiply the number by 100.

The new increased number = (100% + percentage increase) x initial number

(100 + 20%) x 20%

120% x 20%

1.20 x 20% = 24%

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in a large bag of marbles, 20% of them are red. A child chooses 14 marbles from his bag. If the child uses the marbles at random what is a chance that the child gets less than six red marbles?

Answers

If the child uses the marbles at random what is the chance that the child gets less than six red marbles is given as   0.9561. See the calculation below.



What is the explanation given for the above solution?

Note that we are given the following:

p = 20% = 0.20

1 - p = 1 - 0.20 = 0.80

n = 14

Utilizing the binomial formula, we have:

P(X = x) = ((n! / x! (n - x)!) * px * (1 - p)n - x

P(X < 6) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)+  P(x = 4) + P(x = 5)  

Plugging in the value of n, we have:

=  ((14! / 0! (14)!) * 0.200 * (0.80)14 + ((14! / 1! (13)!) * 0.201 * (0.80)13 + ((14! / 2! (12)!) * 0.202 * (0.80)12 + ((14! / 3! (11)!) * 0.203 * (0.80)11 + ((14! / 4! (10)!) * 0.204 * (0.80)10 + ((14! / 5! (9)!) * 0.205 * (0.80)9

=  0.9561

As a result, the probability that the youngster would receive less than six red marbles is provided as 0.9561 if the marbles are used at random.

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Fråga 5 20 poäng A farmer wants to plant a small rectangular plot of ornamental blue corn. He has enough fencing material to enclose a space with a perimeter of 144 feet. He wants to know the dimensions of the largest rectangle that can be enclosed with 144 feet of fence. To help find them, he graphed the following equation. Area = x (72 - x) What are the dimensions of the largest area the farmer can enclose with 144 feet of fence?

Answers

The maximum dimensions is a square of sides 36 ft by 36 ft;

The maximum area is 1,296 ft^2

Here, we want to know the diemensions of the largest area the farmer can enclose within the perimeter

Mathematically, the greatest dimension that can maximize the area of the plot is the shape being a square

In other words, we need the diemnsions of both sides to be equal so as to get the area

If the dimensions are equal, we can say the length and width are represented by x

The length is thus as follows;

[tex]\begin{gathered} 4\text{ }\times\text{ x = 144} \\ 4x\text{ = 144} \\ \text{ x = 144/4} \\ x\text{ = 36 ft} \end{gathered}[/tex]

The greatest possible or the maximum area is thus;

[tex]36\times36=1,296ft^2[/tex]

On Monday, your English teacher gives you a list of twenty-five vocabulary terms to be memorized. You memorize all of them Monday night and do not look at the list again. Because you do not study again, you forget 6% of the list each day.a. Does this problem represent exponential growth or decay? How do you know?b. Which exponential formula below will you use for this problem? Why?(Your choices are f(x) = a (1 + r) or f(x) = a (1-ry')c. Write the formula for this specific problem. Explain how you know where each number goes in the formula.d. How many terms will you remember seven days later for the test? Show all your work and explain your computations.

Answers

Answer:

a. Exponential decay

b. f(x) = a (1 - r)^x

c. f(x) = 25(1 - 0.06)^x

d. 16 terms

Explanation:

a. Does this problem represent exponential growth or decay? How do you know?

Each day the number of terms that you know is less than the day before, so there is a decrease in the vocabulary terms memorized. It means that the problem represents exponential decay.

b. Which exponential formula below will you use for this problem? Why?

The formula for the exponential decay is:

[tex]f(x)=a(1-r)^x[/tex]

Where a is the initial value and r is the rate of decay.

So, the formula that you will use is f(x) = a (1 - r)^x

c. Write the formula for this specific problem. Explain how you know where each number goes in the formula.

The initial value is 25 terms and the decay rate is 6%, so the specific equation is:

[tex]f(x)=25(1-0.06)^x[/tex]

d. How many terms will you remember seven days later for the test? Show all your work and explain your computations.​

Now, we need to replace the value of x by 7, so:

[tex]\begin{gathered} f(7)=25(1-0.06)^7 \\ f(7)=25(0.94)^7 \\ f(7)=25(0.6485) \\ f(7)=16.21 \end{gathered}[/tex]

Therefore, you will remember 16 terms seven days later.

Help me pls with this fast!

Answers

Answer:

Step-by-step explanation:

...

Answer:

2x+9=7

Step-by-step explanation:

"Sum" means addition

"2 times a number" since the number is unknown we use a letter, since its a letter we usually don't need parentheses

"and" is usually used ror addition so another clue

"is" just means equals

1/4(n-6)= 1/4n-3/2

Hint: undo the fraction

Answers

1/4(n-6)=1/4n-3/2. We can say left side is equal to right side.

Given that,

1/4(n-6)=1/4n-3/2

We have to find the n value.

We have to 1st prove left side is equal to right side

We can split an equation into two parts, the left hand side and the right hand side. We refer to the LHS and RHS of the equation in abbreviated form. If the LHS and RHS are equal, then the equation is true; otherwise, the equation does not hold for at least some real number values.

First take the left side which is

1/4(n-6)

We multiply 1/4 to n-6

1/4n-1/4(6)

Now we divide 6/4

1/4n-3/2

See the right side

1/4n-3/2

Therefore,

left side is equal to right side.

1/4(n-6)=1/4n-3/2

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ASAP!! The Brown family baked 3 pies for Thanksgiving. They made a pumpkin pie, an apple pie, and a cherry pie. They ate 0.75 of the pumpkin pie, 0.5 of the apple pie, and 0.6 of the cherry pie How many pies did the Brown family eat in all? Record your answer as a decimal number.

Answers

Answer: The Brown family ate 1.85 pies in all

Step-by-step explanation: If you think about it all you have to do is 0.75+0.5= 1.25 and then you do 1.25+ 0.6  and then get 1.85 so they ate 1.85 pies in all

Hope this helped!!!!

At The Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 28 fencers at The Fencing Center. We are interested in the numbers that do not use the foil as their main weapon. How many fencers are expected to not use the foil as their main weapon? (Round your answer to the nearest whole number.)

Answers

Based on the percentage of fencers who said they used foil as their main weapon when surveyed, the number of fencers out of 28 fencers who would not use foil as their main weapon is 11 fencers

How to find the number of fencers?

The random survey showed that in a given sample, there would be 60% of fencers who would prefer to use foil as their main weapon. This means that the percentage of fencers who would not use foil as their main weapon is:

= 1 - percentage who use foil as main weapon

= 1 - 60%
= 40%

If 28 fencers are randomly surveyed, the percentage of them who would not use foil as their main weapon would be expected to be:

= Number of fencers x Percentage who don't use foil as main weapon:

= 28 x 40%

= 11.2 fencers

= 11 fencers to the nearest whole number

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Is the package late? A shipping company claims that 90% of its shipments arrive on time.
Suppose this claim is true. If we take a random sample of 20 shipments made by the
company, what's the probability that at least 1 of them arrives late?

Answers

Using the binomial distribution, there is a 0.8784 = 87.84% probability that at least 1 of them arrives late.

Binomial distribution

The probability mass function, giving the the probability of x successes is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters of the distribution are given as follows:

n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.

In the context of this problem, of 20% shipments with 90% on time, the parameters are:

p = 0.9, n = 20.

The probability that all arrive on time is:

P(X = 20) = (0.9)^20 = 0.1216.

All on time and least one late are complementary events, hence the probability of at least one package arriving late is given as follows:

P(X < 20) = 1 - P(X = 10) = 1 - 0.1216 = 0.8784.

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Solve: (6x2 + 5x + 1) ÷ (x + 2).

A.) 6x - 7
B.) 6x - 7 - x/15 + 2
C.) 6x + 8
D.) 6x - 7 + 15/ x+ 2

Answers

Answer:

d

Step-by-step explanation:

Divide

6x2+5x+1

x+2

=6x−7+

15

x+2

What’s the correct answer answer asap

Answers

the answers is a. bones to bones

divide and round to the nearest hundredths place. 4.05 divided 0.07

Answers

We have the next operation

[tex]\frac{4.05}{0.07}=57.857=57.86[/tex]

the result of this operation rounded to nearest hundredths place is 57.86

2. Solve the following addition problem. Remember to carry as necessary.
6 cu yd 9 cu ft
134 cu in
+ 1 cu yd 12 cu ft
200 cu in

Answers

The solution to the given addition problem is 150.6 ft^9.

Converting everything to the same unit is the simplest solution to this problem.

The conversions are:

1 cubic yard = (27 cubic feet)

1 cubic inch = (0.000578704 cubic feet)

The addition can be performed as,

(6 cu yd × 9 cu ft × 134 cu in) + (1 cu yd × 12 cu ft × 200 cu in)

=  [6(27 cu ft) × 9 cu ft × 134(0.000578704 cu ft)] + [1(27 cu ft) × 12 cu ft × 200(0.000578704 cu ft)]

= 150.6 ft^9

The result of the addition is 150.6 ft^9.

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Molly grows corn on her farm to sell for pig feed. one of her fields produced 176.4 bushels of corn this year . if corn is currently selling 3.75 per bushel, how much will molly earn from this field

Answers

This year, one of her fields yielded 176.4 bushels of corn. $661.5 will Molly make from this field if corn is now selling for $3.75 per bushel.

Given that,

On her farm, Molly raises corn that she sells for pig food. This year, one of her fields yielded 176.4 bushels of corn.

We have to find how much will Molly make from this field if corn is now selling for $3.75 per bushel.

We have to multiply

=176.4×3.75

=661.5

Therefore, $661.5 will Molly make from this field if corn is now selling for $3.75 per bushel.

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Consider the graph of the function f(x) = 2^x Which statements describe key features of function g if g(x) = f(x + 2)?

Answers

The statements that describe key features of function g if g(x) = f(x + 2) are;

a. y-intercept at (0,4)

b. domain of {x|-∞ < x < ∞}

c. horizontal asymptote of y = 0

What are the features of the Function?

We are given the function f(x) = 2^(x)

We want to find the features of the function g if;

g(x) = f(x + 2)

Let us first find f(x + 2);

g(x) = f(x + 2) = 2^(x + 2)

The y-intercept is when x = 0;

g(0) = 2^(0 + 2)

g(0) = 4

Some features in a function that limit the x values are: roots, fractions, etc.

g(x) = 2^(x + 2) does not have any restricting value of x.

This means the value of x ranges from negative infinity to positive infinity.

Hence, the domain is: (-∞, ∞)

Next, calculate the horizontal asymptote.

To do this, we plot the graph of g(x) --> see attachment

Then we trace a horizontal line from the horizontal part of the curve of g(x) till it gets to the y-axis.

From the attached graph of g(x), the line touches the y-axis at y = 0

So, the horizontal asymptote is: y = 0

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The missing options are;

a. y-intercept at (0,4)

b. domain of {x|-∞ < x < ∞}

c. horizontal asymptote of y = 0

d. horizontal asymptote of y=2

e. y-intercept at (0,1)​

Answer:

see photo

Step-by-step explanation:

Plato/Edmentum

Solve for x: |x − 2| + 10 = 12 (1 point)

x = 0 and x = 4
x = −4 and x = 0
x = −20 and x = 4
No solution

Answers

Answer:

x=20 and x=4

Step-by-step explanation:

at birth,a male baby giraffe stands almost 2 feet tall.at 3 years of age ,the male giraffe will be about three times as tallas at birth.

Answers

Answer: if you're asking how tall it will stand at 3 years of age it would be 6.

Step-by-step explanation: 2 times 3 equals 6.

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Information is given about a polynomial f(x) whose coefficients are realnumbers. Find the remaining zeros of f.Degree 3; zeros: -4, -2- iThe remaining zero(s) of f is(Use a comma to separate answers as needed.) How long does it take for a person that is walking at 2 meters per second to travel 1200 meters Find the volume of a solid bounded by the paraboloids [tex]\displaystyle{z=4x^2+4y^2}[/tex] and [tex]\displaystyle{z=5-6x^2-y^2}[/tex] 2 Cmo le naci a Marcos Andrs Antil la ideade "Caf con Causa"?(A) Quera que su empresa obtuviera msingresos y ganancias.(B) Quera encontrar una iniciativa sostenible.(C) A sus clientes les gustaba el caf que les daba,pero no tenan dnde comprarlo.(D) Record que las ganancias del caf noregresan a las comunidades. Which sentence is a formal revision of the informal example sentence? Informal sentence: In my opinion, Hercules is pretty much the best character because he shows more strength and courage than any other mortal man. Everyone knows that Hercules is the strongest and most courageous of the mythical characters. Hercules shows important character traits, such as strength and courage. Sometimes, like in the case of Hercules, its really all about how strong and courageous you are. Hercules is the best character because hes stronger and more courageous than other mortals. what is the ratios of 29:1, and the math eqation. 3 5/11 as a decimal exspansion NO LINKS!!! Part 2 Please help me with this Similarity Practice Solve for x.(x - 2) = 2 9. Students studying the hydrologic cycle plan to use several rain gauges to compareaverage annual precipitation in several Texas stare parks. Which of these variablesshould be the independent variable? How did Nero and Diocletian influence early Christianity?They spread the epistles to people who had converted.They murdered non-Christians, often throwing them to the lions.They persecuted early Christians in the Roman Empire.They accepted Christianity and all other religions. pioneer farmers settling the american west often built houses of sod, while early settlers of the eastern forests built wooden structures such as log cabins. this suggests that the choice of building materials A match-seller arranges his matchboxes in atriangular pattern as shown in Fig. 18.4. Hecontinues until there are 11 matchboxes inthe bottom row of the triangle. How manymatchboxes are in the complete pattern?MATOMATCHESMATCHESFig. 18.4MATCHESMATCHESMATCHESMATCHESMATCHESMATCHESMATCHESMATCHES Evaluate the expression when a = 2 and x = -4.2a-x Learning Task 5: Get an article, journal or any other online sources. Copy or cut-and-paste it in your notebook. Then, highlight each modal used in the article. Then identify if the highlighted modals express permission, obligation or prohibition. The subtraction of 8 from a number is 2. What is the number? Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels 12 miles per hour slower than the westbound train. If the two trains are 300 miles apart after 2 hours, what is the rate of the westbound train? answer these 2 questions for a cookie What role does Wiglaf play in the poem? Why is he important to the story of Beowulf? the aroma of freshly brewed coffee hung in the air. is this a dependent or independent clause