Find the solution to the system of equations given below using substitution.

A. x = -1, y = -7
B. x = 7, y = -1
C. x = 7, y = 1
D. x = -1, y = 7

Answer:

Step-by-step explanation:

I can't do much more than just give you the answer.

The commutative property of multiplication is turning a and b around.

commutative(a*b) = b*a

answer: b * a

Answer:

b a

Step-by-step explanation:

so the communative property is just switching the numbers ( or letters in this case) around!

ANSWER

y-intercept:

(0,-13)

x-intercept:

[tex](4 \frac{1}{3} ,0)[/tex]

EXPLANATION

The given line has equation

[tex]y + 1 = 3(x - 4)[/tex]

At y-intercept , x=0.

This implies that;

[tex]y + 1 = 3(0 - 4)[/tex]

[tex]y = - 12 - 1[/tex]

[tex]y = - 13[/tex]

The y-intercept is

(0,-13).

At x-intercept y=0,

This implies that;

[tex]0+ 1 = 3(x - 4)[/tex]

[tex] \frac{1}{3} = x - 4[/tex]

[tex] \frac{1}{3} + 4 = x[/tex]

[tex]4 \frac{1}{3} = x[/tex]

The x-intercept is

[tex](4 \frac{1}{3} ,0)[/tex]

Answer:

x-intercept = [tex]\frac{13}{3}[/tex]

y-intercept = [tex]-13[/tex]

Step-by-step explanation:

We are given the following equation of a line and we are to find the x and y intercepts for it:

[tex] y + 1 = 3 ( x - 4 ) [/tex]

In order to find the x-intercept, we will substitute 0 in place of y to get:

[tex] 0 + 1 = 3 ( x - 4 ) \\\\ 1 = 3 x - 12 \\\\ 3 x = 1 + 12 \\\\ x = \frac { 13 } { 3 } [/tex]

And to find the y-intercept, we need to substitute 0 in place of x:

[tex] y + 1 = 3 ( 0 - 4 ) \\\\ y + 1 = -124 \\\\ y = - 12 - 1 \\\\ y = - 13 [/tex]

So the x-intercept is [tex]\frac{13}{3}[/tex] while the y-intercept is [tex]-13[/tex].

Answer:

You add all the scores up, then divide the sum by 24 and you get your answer.

Step-by-step explanation:

Answer:

x=16, x=8

Step-by-step explanation:

since x in |x-12| can be both negative and positive, we have to find two numbers for each senario. if x-12 is negative, we flip them so it becomes 12-x. so 12-x=4 is easily solved and the answer would be 8. if it is positive, we would keep it and x-12 would be 4. we also solve this to get 16. we can check our work by putting them in to get 16-12 is 4 and |8-12| is 4

Answer:

[tex]\large\boxed{f(-3)=3.6}[/tex]

Step-by-step explanation:

[tex]f(x)=0.6(3-x)\\\\f(-3)\to\text{Put x = -3 to the equation of a function:}\\\\f(-3)=0.6(3-(-3))=0.6(3+3)=0.6(6)=3.6[/tex]

Answer:

[tex]\large\boxed{y=-\dfrac{2}{3}x+\dfrac{1}{3}}[/tex]

Step-by-step explanation:

The skope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (2, -1) and (5, -3). Substitute:

[tex]m=\dfrac{-3-(-1)}{5-2}=\dfrac{-3+1}{3}=\dfrac{-2}{3}=-\dfrac{2}{3}[/tex]

We have the equation:

[tex]y=-\dfrac{2}{3}x+b[/tex]

Put the coordinates of the point (2 , -1) to the equation:

[tex]-1=-\dfrac{2}{3}(2)+b[/tex]

[tex]-1=-\dfrac{4}{3}+b[/tex]           add 4/3 to both sides

[tex]\dfrac{1}{3}=b\to b=\dfrac{1}{3}[/tex]

Finally we have:

[tex]y=-\dfrac{2}{3}x+\dfrac{1}{3}[/tex]

The pipes can fill the pool individually in 16 and 20 hours respectively, by solving the simultaneous equations: 1/x + 1/y = 1/5 and 1/2x + 1/2y = 18.

Let's assume one pipe can fill the pool in x hours, while the other pipe can fill it in y hours. When the two pipes work together, they complete one job in 5 hours, which can be expressed as 1/x + 1/y = 1/5.

When each pipe fills half the pool, it takes 18 hours. Since each of them is doing half the work, this can be represented as 1/2x + 1/2y = 18.

To solve these simultaneous equations, it is best to use the substitutive method. We can set the two equations equal to each other to get x = 36 - y. Plugging this into the first equation and solving for y, we find y = 20. Substituting y back into the equation x = 36 - y, we find x = 16.

So, one pipe could fill the pool alone in 16 hours, while the other could do it in 20 hours.

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The first pipe would take approximately 6.92 hours to fill the pool if it were working alone, and the second pipe would take 18 hours to fill the pool if it were working alone.

Let's assume that the first pipe can fill the pool in x hours, and the second pipe can fill the pool in y hours.

When the two pipes fill the pool together, they can complete the job in 5 hours. So, their combined rate of work is 1/5 of the pool per hour.

When the first pipe fills half the pool, it takes over for the second pipe, which then finishes filling the pool. This entire process takes 18 hours. So, the first pipe fills half the pool in 18 hours, which means that its rate of work is 1/18 of the pool per hour.

Using the concept of work done, we can set up the following equation:

1/x + 1/y = 1/5 (equation 1)

1/y = 1/18 (equation 2)

Solving the equations simultaneously, we can find the values of x and y:

From equation 2, y = 18 hours.

Substituting the value of y in equation 1, we get:

1/x = 1/5 - 1/18 = (18 - 5)/90 = 13/90.

Therefore, x = 90/13 hours.

So, the first pipe would take approximately 6.92 hours to fill the pool if it were working alone, and the second pipe would take 18 hours to fill the pool if it were working alone.

Answer:

[tex]\boxed{\bold{2(3a + 4) = 6a + 8}}[/tex]

Step-by-step explanation:

Distributive Property: [tex]\bold{a(b+c) \ = \ (a*b)+(a*c)}[/tex]

2(3a + 4)

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

(2 * 3a) + (2 * 4)

(2 * 3a) = 6a

(2 * 4) = 8

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

6a + 8

Answer:

Step-by-step explanation: 15 + X = 27 Candies

Any Variable Will Work.

Answer:

c + 15 = 27

Step-by-step explanation:

c + 15 = 27

15 is the starting amount.

c is the number of candies her mom put in.

27 is the new total.

Answer: -87

Step-by-step explanation: −27−42−18

Answer:

soda = 35mg

coffee = 81mg

energy = 83mg

Step-by-step explanation:

coffee + energy + soda = 199

coffee = 11 + (2 * soda)

energy = (soda + coffee) - 33

(11 + (2 * soda)) + ((soda + (11 + (2 * soda))) - 33) + soda = 199

11 + 2s + s + 11 + 2s - 33 + s = 199

22 + 6s - 33 = 199

-11 + 6s = 199

6s = 210

s = 35

soda = 35mg

c  = 11 + 2s

c = 11 + 2(35)

c = 11 + 70

c = 81

coffee = 81mg

e = s + c - 33

e = (35) + (81) - 33

e = 116 - 33

e = 83

energy = 83mg

Final answer:

One serving of soda contains 35 mg of caffeine, one serving of coffee contains 81 mg of caffeine, and one serving of energy drink contains 83 mg of caffeine.

Explanation:

Let's solve this problem step by step:

To find the value of x, we can set up an equation:

Simplifying the equation:

Combine like terms:

Add 11 to both sides:

Divide both sides by 6:

Therefore, one serving of soda contains 35 mg of caffeine. Substituting this value into the previous equations:

Answer:

20 miles

Step-by-step explanation:

The formula for distance is

d =rt  where r  is the rate and t is the time

We need to convert the time to hours since the rate is in mph

15 minutes * 1 hour/ 60 minutes = 1/4 hour = .25 hours

d = (80 mph) * .25 hours

d = 20 miles

The train goes 80 miles in an hour which is 60 minutes. 60 minutes divided by 15 minutes equals 4. 80 miles divided by 4 equals 20 miles. The train went 20 miles in 15 minutes.

Answer:

L ∪ (M ∩ N) = {0, 10, 20, 40, 80, 100}

Step-by-step explanation:

L ∪ (M ∩ N) means "take what's common of set M and set N" and then "add it to all the elements of set L".

So, what are the common elements of set M and set N?

They are 10 & 20. So,

M ∩ N = {10,20}

Now, we add it to all the elements of set L. Note that we don't need to count 20 twice.

Thus L ∪ (M ∩ N) = {0, 10, 20, 40, 80, 100}

Answer: second option. (NOTE: If the first option is [tex](-2)^3[/tex], then it would be an equivalent expression too, because:  [tex](-2)(-2)(-2)=-8[/tex])

Step-by-step explanation:

To solve this problem you must keep on mind the following exponents rule:

[tex](\frac{1}{a})^-b=a^b[/tex]

Therfore, you have that:

[tex](-\frac{1}{2})^-3=(-2)^3[/tex]

This means that the number -2 must be multiply by itself three times. Therefore, you obtain the folllowing result:

[tex](-2)(-2)(-2)=-8[/tex]

If the first option is [tex](-2)^3[/tex], then it would be an equivalent expression too, because:

 [tex](-2)(-2)(-2)=-8[/tex]

Answer:

[tex](\frac{-1}{2})^{-3} = -8[/tex].

Step-by-step explanation:

Given :  –8.

To find : Which expression is equivalent.

Solution : We have given  –8.

By the radical rule : [tex](\frac{-1}{x})^{-a} = -x^{a}[/tex].

Then

[tex](\frac{-1}{2})^{-3} = -2^{3}[/tex].

[tex](\frac{-1}{2})^{-3} = -8[/tex].

Therefore,  [tex](\frac{-1}{2})^{-3} = -8[/tex].

Equivalent inequalities are inequalities with the same solutions. They're also the most likely paired together.

Answer:

it is equivalent to the number that you want to find it out

Step-by-step explanation:

Inequalety

Answer:

[tex]\large\boxed{803.8\ cm^2}[/tex]

Step-by-step explanation:

The formula of a surface area of a sphere:

[tex]S.A.=4\pi R^2[/tex]

R - radius

We have R = 8 cm. Substitute:

[tex]S.A.=4\pi(8^2)=4\pi(64)=256\pi\ cm^2[/tex]

[tex]\pi\approx3.14[/tex]

Substitute:

[tex]S.A.\approx256(3.14)=803.84\ cm^2[/tex]

Answer:

Line B will become line A and Line A will become line B.

Step-by-step explanation:

To factor out the greatest common factor from 30 and 42, first, find the GCF. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. The greatest common factor is 6. Using the distributive property, 30 + 42 becomes 6(5 + 7). So, the final answer is 6 times the sum of 5 and 7, which is 72.

To factor out the greatest common factor (GCF) from the expression 30 + 42, we first need to find the GCF of the two numbers, which is 6. Then we can rewrite the expression using the distributive property.

Step 1: Find the GCF of 30 and 42:

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.

The common factors are 1, 2, 3, and 6. The greatest common factor is 6.

Step 2: Rewrite the expression using the GCF:

[tex]\[30 + 42 = 6 \times 5 + 6 \times 7\][/tex]

Step 3: Apply the distributive property:

[tex]\[30 + 42 = 6 \times (5 + 7)\][/tex]

Step 4: Perform the addition inside the parentheses:

[tex]\[30 + 42 = 6 \times 12\][/tex]

Step 5: Multiply:

30 + 42 = 72

So,30 + 42 equals 72 after factoring out the greatest common factor using the distributive property.

Answer:

The correct answer is: descriptive and inferential statistics.

Step-by-step explanation:

The two branches of the study of statistics are generally referred to as descriptive and inferential statistics.

Descriptive statistics are the brief summary statistic which summarizes a given data set, which can be a representation of the entire population or just a sample of it.

While Inferential statistics is the way data analysis is used to deduce the properties of an underlying probability distribution.

The study of statistics generally branches into descriptive statistics, which involves summarizing and displaying data, and inferential statistics, which makes predictions about a population based on sampled data.

The two branches of the study of statistics are generally referred to as descriptive statistics and inferential statistics. Descriptive statistics involves the organization, summarization, and display of data. It seeks to describe a situation or sample population without offering any conclusions or inferences about the data. Examples include calculating averages, measures of central tendency like mean, median, mode, and variability measures such as range, variance, and above all standard deviation.

On the other hand, inferential statistics is a method to make predictions or inferences about a population based on a sample of data. It is used when it is not practical or impossible to examine the entire population. Examples of inferential statistics methods include hypothesis testing, chi-square tests, t-tests, ANOVA, regression analysis etc.

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The answer is the 4th option.

y = -2x - 4 would be the answer

Answer:

A will appear to the left of B.  The answer is B) hope this helps

Step-by-step explanation:

If A < B, A will appear to the left of B on the number line.

A number line is a linear line on which points are marked equidistant from each other and used to represent the position of a certain linear number on it.

Let us take an example where A = 2 and B = 3. Here 2 < 3.

We know that 2 is to the left of 3 on the number line.

Now let us take an example of negative numbers. A = -3 and B = -2.

Here, -3 < -2. - 3 is also to the left of - 2.

Therefore we can say that A is always to the left of B.

Therefore, if A < B, A will appear to the left of B on the number line.

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Anwer:

4b/a=2

Step-by-step explanation:

Lets assume:

a = 4 & b = 2

So a/b would equal 2.

4b/a indicates that you are going to multiply b times 4, meaning that in this scenario you would multiply 2 times 4.

4(2) = 8

and 8 divided by (4) is 2.

Why 4? Because remember a = 4 (in this scenario).

Other examples:

10/5 = 2, -->  4(5) = 20, -->  20/10 = 2.

20/10 = 2. --> 4(10) = 40, --> 40/20 = 2.

Answer:

2

Step-by-step explanation:

a/b = 2

Invert each side of the equation

b/a = ½

Multiply each side by 4

4b/a = 4 × ½ = 2

SOH CAH TOA

CAH

Cosine = Adjacent / Hypotenuse

∆ABC, where lets say B is the right angle.

cos C = adjacent/hypotenuse = BC/AC

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Answer:

The perimeter of rectangle is [tex]18\ cm[/tex]

Step-by-step explanation:

Let

x-----> the length of the rectangle

y----> the width of the rectangle

we know that

[tex]x=y+5[/tex] ----> equation A

[tex]120=xy+2x^{2}+2y^{2}[/tex] ---> equation B (area of the constructed figure)

substitute the equation A in equation B

[tex]120=(y+5)y+2(y+5)^{2}+2y^{2}[/tex]

[tex]120=(y+5)y+2(y+5)^{2}+2y^{2}\\ 120=y^{2}+5y+2(y^{2}+10y+25)+2y^{2}\\ 120=y^{2}+5y+2y^{2}+20y+50+2y^{2}\\120=5y^{2}+25y+50\\5y^{2}+25y-70=0[/tex]

using a graphing calculator -----> solve the quadratic equation

The solution is

[tex]y=2\ cm[/tex]

Find the value of x

[tex]x=y+5 ----> x=2+5=7\ cm[/tex]

Find the perimeter of rectangle

[tex]P=2(x+y)=2(7+2)=18\ cm[/tex]

Answer:

256 Coins

Step-by-step explanation:

On the first day, Jada starts with one coin, so all you have to do here is multiply it by 2.

Day 1: 2 coins

Day 2: 2 x 2 = 4 coins

Day 3: 4 x 2 = 8 coins

Day 4: 8 x 2 = 16 coins

Day 5: 16 x 2 = 32 coins

Day 6: 32 x 2 = 64 coins

Day 7: 64 x 2 = 128 coins

Day 8: 128 x 2 = 256 coins

Hope this helps! Just message me if you have more questions or need more help! :)

The number of coins that Jada will have after 8 days is; 256 coins

We are told that on the first day, Jada starts with one coin and that the number of coins doubles each day. Thus;

Day 1: She has 2 coins

Day 2: She has 2 * 2 = 4 coins

This follows a geometric pattern 2ⁿ

where n is number of days

Thus, for 8 days, she will have; 2⁸ coins = 256 coins

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4^6= 4096

4^3= 64

4096 • 64= 262144

Answer:

262144

Step-by-step explanation:

4^6 = 4 x 4 x 4 x 4 x 4 x 4

4^3 = 4 x 4 x 4

that ends up being 4^9 if you add them up.

4^9 is 262,144

Answer:

 -p5q2 - p3q5 + 2p3 + 2pq2 + 2q3  

 ____________________________

              p3q2              

Step-by-step explanation:

            2

Simplify   ——

           q2

Equation at the end of step  1  :

      (p+q)         2

 (((2•—————)-(q3))+——)-p2

      (p3)         q2

Step  2  :

           p + q

Simplify   —————

            p3   (p + q)             2      

 (((2 • ———————) -  q3) +  ——) -  p2

          p3               q2      

Step  3  :    2 • (p + q)            2      

 ((——————————— -  q3) +  ——) -  p2

       p3                q2               q3     q3 • p3

   q3 =  ——  =  ———————

         1        p3  

Answer:

8*x > 72

x > 72/8

x > 9

The number is any number greater than 9.

It could be 9.5, 10, 11, 12,....

Step-by-step explanation:

The mathematical expression representing the verbal expression given is 8n < 72

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, a verbal expression. eight times a number n less than 72,

We need to convert it in mathematical expression

So, the expression will be

8n < 72

Now, solving for n,

8n < 72

n < 9

Therefore, values of n below 9 is the solution of the inequality.

Hence, the mathematical expression representing the verbal expression given is 8n < 72

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Answer:

Step-by-step explanation:

The area of a triangle is base*height/2

So one triangle is 2*4/2=4

Multiplied by 4 sides, 4*4=16

Finally the base is a square, so 2*2=4

Therefore the entire shape is 16+4=20 square feet

The amount of paper it will take to make each tree, including the bottom is 20 ft²

Find the area that its outer surfaces possess. Sum of all those surfaces' area is the surface area of the considered object.

Surface area of paper tree = sum of areas of those 4 slant standing triangles + area of base

Area of each of those 4 triangles are same (assuming they're symmetric).

Each triangle has height of 4 ft and base of 2 ft. (the base is a square of side length 2 ft).

Thus, we get:

Area of 4 triangles = 4(area of each tree ) = [tex]4\left (\dfrac{1}{2} \times \text{base} \times \text{height}\right) = 4\left (\dfrac{1}{2} \times 2 \times 4\right) = 16 \: \rm ft^2[/tex]

Area of square base = [tex]\text{side}^2 = 2^2 = 4 \: \rm ft^2[/tex]

Thus, we get:

Surface area of paper tree = 16 + 4 = 20 ft²

Thus, the amount of paper it will take to make each tree, including the bottom is  20 ft²

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