Solve the systems of equations using the substitution method.
5y-6=x
Y=-x

Answer:

x= 40°

Step-by-step explanation:

Please see attached picture for full solution.

Key concepts:

- Corresponding angles are equal to each other

- The sum of the angles in a triangle add up to 180°

Answer;

Given that;

n/8=9

Here n is the numerator and 8 is the denominator we know that 8 is divided here so when we take it to the left side we get;

n=9 * 8. (9 multiplied with 8)

n=72

Hence answer only;

n/8=9

n=9 *8

n=72

Hence answer only;

n=72

After solving  n/8=9 you will get n = 72.

To solve the equation n/8 = 9 for n, we need to isolate the variable by performing inverse operations.

Step 1: Multiply both sides of the equation by 8 to eliminate the fraction:

8 * (n/8) = 8 * 9

This simplifies to n = 72.

Therefore, the solution to the equation n/8 = 9 is n = 72. When n is divided by 8, the result is 9. This means that 72 is the value that satisfies the equation and makes it true.

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Answer:

20

Step-by-step explanation:

add all of them together and divide by 7

Answer: 20

Step-by-step explanation: The mean of a data set is equal to the sum of the set of numbers divided by how many numbers are in the set.

So to find the mean of the data set shown here, let's begin by adding the numbers.

15 + 28 + 25 + 22 + 11 + 12 + 27

This will be divided by how many numbers are in the set which is 7.

So we have [tex]\frac{15 + 28 + 25 + 22 + 11 + 12 + 27}{7}[/tex]

Adding the numbers, we get 140.

140 is divided by the number of numbers in the set or 7.

140 divided by 7 is 20.

So the mean of the set of data shown here is 20.

Answer:

Step-by-step explanation:

y ∞ 1/x

y = k/x

Where k is the constant of proportionality

When x = 3 and y = 5

5 = k/3

Cross multiply

k = 5×3

k = 15

The equation is y = 15/x

The given relationship Y varies inversely with X and when X is equal to 3, Y equals to 5 which leads us to the equation Y = 15/X which illustrates this inverse variation.

The given question states that Y varies inversely with X and provides us with a pair of values - X = 3, Y = 5. In mathematics, when one quantity Y varies inversely as another X, it can be represented by the equation Y = k/X where k is the constant of variation. To find k, we will substitute the given X and Y values into the equation leading to 5 = k/3. Simplifying, we find k = 5*3, that is, k equals 15. Therefore, the equation that represents this inverse variation is Y = 15/X.

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Answer:

(0,5)

Step-by-step explanation:

we have

[tex]2x+3y > 12[/tex] ----> inequality A

[tex]x-y\leq 1[/tex] ----> inequality B

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities of the system (makes true both inequalities)

Verify each ordered pair

Substitute the value of x and the value of y of each ordered pair in the inequality A and in the inequality B and then compare the results

case 1) (0,5)

For x=0,y=5

Inequality A

[tex]2(0)+3(5) > 12[/tex]

[tex]15 > 12[/tex] ----> is true

so

The ordered pair satisfy inequality A

Inequality B

[tex]0-5\leq 1[/tex]

[tex]-5\leq 1[/tex] ---> is true

so

The ordered pair satisfy inequality B

therefore

The ordered pair would be a solution of the system

case 2) (5,2)

For x=5,y=2

Inequality A

[tex]2(5)+3(2) > 12[/tex]

[tex]16 > 12[/tex] ----> is true

so

The ordered pair satisfy inequality A

Inequality B

[tex]5-2\leq 1[/tex]

[tex]3\leq 1[/tex] ---> is not true

so

The ordered pair not satisfy inequality B

therefore

The ordered pair is not a solution of the system

case 3) (0,4)

For x=0,y=4

Inequality A

[tex]2(0)+3(4) > 12[/tex]

[tex]12 > 12[/tex] ----> is not true

so

The ordered pair not satisfy inequality A

therefore

The ordered pair is not a solution of the system

case 4) (6,0)

For x=6,y=0

Inequality A

[tex]2(6)+3(0) > 12[/tex]

[tex]12 > 12[/tex] ----> is not true

so

The ordered pair not satisfy inequality A

therefore

The ordered pair is not a solution of the system

Answer:

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

Step-by-step explanation:

For this case the transformation of f (x) is given by

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

To prove it, we must verify that equality is met by replacing the ordered pairs shown in the function g (x)

For (-2,1)

g (-2) = 2 ^ ( -2 + 2)

g(-2)=1

For (-1,2)

g (-1) = 2 ^ ( -1+ 2)

g(-1)=2

For (0,4)

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

g(0)=4

15 ft by 6 ft is the aswerk

15 ft by 6 ft. is the answer

Answer:

[tex]\large\boxed{x=\dfrac{1}{2}=0.5}[/tex]

Step-by-step explanation:

[tex]15-0.5(4x-2)+4x=17\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\15+(-0.5)(4x)+(-0.5)(-2)+4x=17\\\\15-2x+1+4x=17\qquad\text{combine like terms}\\\\(-2x+4x)+(15+1)=17\\\\2x+16=17\qquad\text{subtract 16 from both sides}\\\\2x+16-16=17-16\\\\2x=1\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{1}{2}\\\\x=\dfrac{1}{2}[/tex]

Answer:

Step-by-step explanation:

It takes 9 minutes to fill a depth of [tex]\frac{3}{5}[/tex] meters.

Filling  [tex]\frac{3}{5}[/tex] meters take 9 minutes time.

Filling 3 meters of the aquarium takes [tex]5\times9[/tex] = 45 minutes time (Multiplying by 5 both the numbers).

In order to fill 1 meter of the aquarium it will take [tex]\frac{9\times5}{3} = 15[/tex] minutes (Dividing by 3 both the numerical values).

Answer:

The rate is 15 minutes per meter.

Step-by-step explanation: please give brainliest

1x + 2y = (The answer/money spent)

The total cost that Rahmi spent can be represented by an equation c = j + 2t, with 'c' representing the total cost, 'j' the price of jeans, and 't' the price of a T-shirt. Actual costs can't be determined without specific prices.

To figure out how much Rahmi spent, let's set up an equation with the unknown quantities. Let's assume the cost of one pair of jeans is represented by 'j' and the cost of one T-shirt is represented by 't'. Since Rahmi bought 1 pair of jeans and 2 T-shirts, the total cost, 'c', can be represented as:

c = j + 2t

Unfortunately, without specific prices for the jeans and the T-shirts, we cannot calculate the exact total cost. However, this equation will help Rahmi to determine the cost once the prices are known.

Answer:

4u+16

Step-by-step explanation:

first multiply the outside bumber(in this case its 4) by each of the numbers and variables inside. (making u turn into 4u) and ( making 4 turn into 16 bcs 4x4=16

Answer:

[tex]\$973.80[/tex]  

Step-by-step explanation:

The complete question is

How much money will Alondra make if she invests $900 in an account that pays 8.2% interest compounded annually for one year?

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=1\ year\\ P=\$900\\ r=8.2\%=8.2/100=0.082\\n=1[/tex]

substitute in the formula above

[tex]A=900(1+\frac{0.082}{1})^{1*1}[/tex]  

[tex]A=900(1.082)^{1}[/tex]  

[tex]A=\$973.80[/tex]  

Answer:

See explanation!

Step-by-step explanation:

Due to the way the question is expressed we will assume that it means to find the product of this expression (thus simplify or factor our the equation).

So let us solve as following:

[tex](3g+2)(3g-2)=0\\\\(3g)(3g)+(3g)(-2)+(2)(3g)+(2)(-2)=0\\\\9g^2-6g+6g-4=0\\\\9g^2-4=0\\9g^2=4\\\\g^2=\frac{4}{9}\\ \\g=(+/-)\sqrt{\frac{4}{9} } \\\\g=(+/-)\frac{2}{3}[/tex]

So we have factored our the expression and solve for the values of [tex]g[/tex] which since its squared, the solution can be either positive or negative. Thus

[tex]g=\frac{2}{3}\\[/tex] and [tex]g=-\frac{2}{3}[/tex]

Answer:

d forms a proportion

Step-by-step explanation:

3x5=15,4×5=20

so they both increase protionally

therefore they are protional

The ratios that form a proportion out of the given options are: D. 3:4 and 15:20.

A proportion, in mathematics, can be defined as when two ratios are set equal to each other.

The ratios in option D is proportional, because:

3:4 = 15:20

3/4 = (3 × 5)/(4 × 5)

3/4 = 3/4

Therefore, the ratios that form a proportion out of the given options are: D. 3:4 and 15:20.

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Answer:

Biased; conveince sample response.

Explanation:

THE HOMEROOM might have the sam intrests for the theme

The sampling method most likely to result in self-selection bias is the voluntary response sample. It involves individuals choosing to respond to the survey and may result in a biased sample as those who participate may not represent the overall opinion of the student body.

In the context of the homecoming dance committee's survey, the method that is most likely to result in self-selection bias is the voluntary response sample. This sampling method involves allowing individuals to choose to respond to the survey on their own. The bias comes from the fact that those who choose to respond may not be representative of the entire student body due to differences in interest or motivation related to the theme of the dance. For example, students with strong opinions on the theme or are more involved in the dance may be more likely to respond, leading to a self-selected and therefore potentially biased sample.

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Burt can research other careers in the publishing field.

As Burt is thinking about a career in publishing he can research other careers in the publishing field. Burt can work on cutting-edge research from top academics. The articles and books Burt publish will help teach new generations of students, and may even revolution the field.

Surely, Burt's discovery will enrich the pool of literature on a given subject. Burt's findings will strengthen the arguments of others while it will refute others. It will help shed light on issues that need resolution and it will also help build theories.

If Burt will publish a lot of research on a specific topic or issue, will gain credibility and become a recognized expert in that particular field. If ever there will be government or non-government organizations who will need consultants along the area focus Burt's research on, will have an edge over others who have not published anything.

The correct answer is option C.

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Answer:

The smallest amount is [tex]\£6,911[/tex]

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=3\ years\\ A=\£8,000\\ r=5\%=5/100=0.05\\n=1[/tex]  

substitute in the formula above

[tex]8,000=P(1+\frac{0.05}{1})^{1*3}[/tex]  

solve for P

[tex]8,000=P(1.05)^{3}[/tex]  

[tex]P=8,000/(1.05)^{3}[/tex]  

[tex]P=\£6,910.70[/tex]  

Round to the nearest pound she can invest

The smallest amount is [tex]\£6,911[/tex]

Answer:

(e) =1/2x^3y^4      (f)=y/3x^2

Answer: X = 8.67

Step-by-step explanation:

Area of wooden support is 36 square inches

Solution:

Given that, carpenter cut out a small trapezoid as a wooden support for the front step

The area of trapezoid is given as:

[tex]area = \frac{a+b}{2} \times h[/tex]

Where, "h" is the height

"a" and 'b" are the length of base

Here given that,

Height = h = 4 inches

a = 6 inches

b = 12 inches

Substituting the values we get,

[tex]area = \frac{6+12}{2} \times 4\\\\area = 18 \times 2\\\\area = 36[/tex]

Thus area of wooden support is 36 square inches

Answer:

$ 16.84

Step-by-step explanation:

First take 40 percent of 26 by doing 26 times .4 which gives you 10.4 and then do 26- 10.4 (because it was marked down) which gives you 15.6 and then you multiply 15.6 by .08 giving you 1.248 and then you add 1.248 + 15.6 to give you 16.84

Answer:

y = -21

Step-by-step explanation:

Answer:

No he doesnt have enough

Step-by-step explanation:

Answer:

Step-by-step explanation:

f = v + at....solving for t

f = v + at....subtract v from both sides

f - v = at....divide both sides by a

(f - v) / a = t or could also be : t = f/a - v/a <==

The equivalent equation for the given expression f = v + at  is (f - v) / a = t. The correct option is C.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

The given expression is f = v + at, where, the final velocity of an object, f, with an initial velocity, V, and an acceleration rate, a, over time, t.

The given expression for ' t ' is calculated as:-

f = v + at....solving for t

f = v + at....subtract v from both sides

f - v = at....divide both sides by a

(f - v) / a = t

The above expression can also be written as given below:-

t = f/a - v/a <==

Hence, the expression  f = v + at for t will be equal to (f - v) / a = t. Then the correct option is C.

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Each new term is found by multiplying the last term by 2

1*2 = 2

2*2 = 4

2*4 = 8

2*8 = 16

and so on

Therefore the common ratio is r = 2.

The starting term is a = 1

The general nth term is [tex]a*(r)^{n-1} = 1*(2)^{n-1} = 2^{n-1}[/tex] where n is an integer (aka whole number) and n starts at n = 1.

Answer:

Step-by-step explanation:

8+?=19

19-8=11

Y=11

Final answer:

To solve the equation 19 = 8 + y for y, you subtract 8 from both sides which gives you y = 11.

Explanation:

The equation provided, 19 = 8 + y, is a simple linear equation where you are solving for the variable y. To find the value of y, you need to isolate y on one side of the equation.

Here is the step-by-step process:

Start with the original equation: 19 = 8 + y.

To isolate y, you need to get rid of the 8 on the right side of the equation. You can do this by subtracting 8 from both sides of the equation.

Subtracting 8 from both sides gives us: 19 - 8 = y.

Simplify the left side: 11 = y.

Therefore, y equals 11.

Answer:terminating

Step-by-step explanation:

Answer:11.128

Step-by-step explanation:

The number 28 is divided by the number 3 in fraction form is  9 1/3.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, The number 28 is divided by the number 3.

This can be written in fraction form as 28/3.

Now, 3×9 = 27.

Therefore, 28/3.

= 9 1/3.

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Answer:

n*54/100

Step-by-step explanation:

it depend on your class students number. if your class number is n, n*54/100 is your answer and it must be a natural number so u must rond it. for example if n was 20 so 20*54/100 = 10.8 that must rond it to number 10. 10 is the answer.

54% as a decimal is 0.54. This is found by converting the percent (per hundred) to the fraction 54/100, and then dividing the numerator by the denominator.

To write 54% as a decimal, you need to convert the percent into a fraction and then to a decimal. The word 'percent' means 'per hundred,' so 54% can be written as 54/100. To convert this fraction to a decimal, you divide the numerator by the denominator.

Here's the conversion step by step:

Therefore, 54% as a decimal is 0.54%.. This means that 54% of the students in the class have moved at least one time, which is equivalent to 0.54 when expressed as a