use distributive property then solve for y: 2(8 + y) = 22

Answers

Answer 1

Answer:

The value of y in the given equation is 3.

Step-by-step explanation:

Hey there!

Part 1 - Using the Distributive Property

To use the distributive property, we need to understand the formula to use it. This formula will ensure that you can easily solve any equation.

The distributive property is A(B + C) = AB + AC, where AB is the product of the values A and B and AC is the product of the values A and C.

First, let's notice that we are distributing a 2 into the parentheses, so we will mark this as our A value.

Then, our two values inside the parentheses are B and C respectfully.

Now, we can apply the formula.

\(2(8 + y) = (2 \times 8) + (2 \times y)\)

This can be further simplified using basic algebraic techniques. Simply find the products of 2 × 8 and 2 × y, and then add them together.

\(2(8 + y) = 16 + 2y\)

Since 16 and 2y are not like terms, they cannot be added together. Therefore, we can no further simplify.

Part 2 - Solving for Y

Now, we will replace the 2(8 + y) with our new distributed work:

\(16 + 2y = 22\)

Now, we can solve the equation for y.

First, rearrange the equation so the term with the y-variable is the leading term.

\(2y + 16 = 22\)

Now, we want to get the y-variable by itself, so we will subtract 16 from both sides of the equation.

\(2y = 6\)

Finally, to get y by itself, we can divide by its coefficient of 2 on both sides of the equation.

\(y = 3\)

Therefore, y is equal to 3.

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Answer 2

Hey there!


2(8 + y) = 22

2(8) + 2(y) = 22

16 + 2y = 22

2y + 16 = 22


SUBTRACT 16 to BOTH SIDES

2y + 16 - 16 = 22 - 16

CANCEL out: 16 - 16 because it gives you 0

KEEP: 22 - 16 because it help solve for the y-value


NEW EQUATION: 2y = 22 - 16


SIMPLIFY IT!


2y = 6


DIVIDE 2 to BOTH SIDES

2y/2 = 6/2

CANCEL out: 2/2 because it gives you 1

KEEP: 6/2 because it gives you the y-value


NEW EQUATION: y = 6/2


SIMPLIFY IT!

y = 3


Therefore, your answer is: y = 3


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)


Related Questions

:( CAN SOMEONE PLEASE HELP ME

:( CAN SOMEONE PLEASE HELP ME

Answers

Answer:

I think that Nick is correct because you are going to have to make your answer positive and when you do the two fractions -4/9 + -6/9 are going to be   6/9 + 4/9 and there is already a addition sign in the last problem we are just going to keep it there. And when we add we get 10/9 or 1 1/9

If i get it wrong please don't hate im just in 7 grade ok :(

Answer:

Solution given:

Gobriella is correct.

Nick change - to + in second line.

Find the length of the third side. If necessary, write in simplest radical form.
5
6

Answers

Answer:

     \(c=\sqrt{61}\)

Step-by-step explanation:

Assuming it's a right triangle, you would have to use the Pythagorean Theorem which states:

\(a^{2} +b^{2} =c^{2}\)

Assuming we're looking for the hypotenuse:

\(5^{2} +6^{2} =c^{2}\)

\(25+36=c^{2}\)

\(61=c^{2}\)

\(\sqrt{61} =c\)

use the graphing function on your calculator what is the solution to the system of equations show below y+2x=5 4y+5x=14

Answers

To solve the system of equations y + 2x = 5 and 4y + 5x = 14 using the graphing function on a calculator, follow these steps:

1. Enter the first equation y + 2x = 5 into the calculator in the form of "y = -2x + 5".

2. Enter the second equation 4y + 5x = 14 into the calculator in the form of "y = (-5/4)x + 7/2".

3. Graph both equations on the same coordinate plane by selecting the "graph" function on the calculator.

4. The solution to the system of equations is the point where the two lines intersect on the graph. To find this point, use the "trace" or "intersect" function on the calculator.

5. The solution to the system of equations is (x,y) = (1,3).

Therefore, the solution to the system of equations y + 2x = 5 and 4y + 5x = 14 is (1,3).

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To solve the system of equations y + 2x = 5 and 4y + 5x = 14 using the graphing function on a calculator, follow these steps:

1. Enter the first equation y + 2x = 5 into the calculator in the form of "y = -2x + 5".

2. Enter the second equation 4y + 5x = 14 into the calculator in the form of "y = (-5/4)x + 7/2".

3. Graph both equations on the same coordinate plane by selecting the "graph" function on the calculator.

4. The solution to the system of equations is the point where the two lines intersect on the graph. To find this point, use the "trace" or "intersect" function on the calculator.

5. The solution to the system of equations is (x,y) = (1,3).

Therefore, the solution to the system of equations y + 2x = 5 and 4y + 5x = 14 is (1,3).

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30 timess please only serious awnseresss

Answers

Answer:

120

Step-by-step explanation:

Answer:

30 times ?

let no be x

30×x=30x

30×4=120

solve each system by substitution. y=2x-1 3x+8y=11

Answers

X=1 y=1

Answer:

y=2x-1 ---(1)

3x+8y=11 ---(2)

sub (1) into (2)

3x+8(2x-1)=11

3x+16x-8=11

19x=19

X= 1

sub X= 1 into (1)

y= 2(1)-1

y=1

HEEELP ASAP PLEASEEEEEEEE

Find the slope of the curve f(x) = 2x^2.

2x
x
4x

Answers

Answer:

4x

Step-by-step explanation:

2\(x^{2}\)

The derivative of a\(x^{n}\) is na\(x^{n-1}\)

2 × 2\(x^{2-1}\)

Multiply 2 times 2.

4\(x^{2-1}\)

Subtract 1 from 2.

4\(x^{1}\)

For any term t, \(t^{1}\) = t

4\(x\)

A local bakery called Brianny's makes 100 batches of cookies in 4 hours. If they keep this pace, how many batches of cookies would they make in 16 hours?

Answers

Answer:

400 batches of cookies

Step-by-step explanation:

4 hours = 100 cookies

8 hours = 200 cookies

12 hours = 300 cookies

16 hours = 400 cookies

the national survey of student engagement found that 24% of seniors report that they often or very often went to class without completing readings or assignments.12 assume that the sample size of seniors is 276,000. (a) find the margin of error for 99% confidence.

Answers

Margin of error for 99% confidence interval is 0.0021

What is confidence interval?

he range of values that, should you repeat your experiment or resample the population in the same manner, you would anticipate your estimate to fall within a particular percentage of the time.

Main Body:

Given :

99% Confidence Interval for p

p = 0.24,n = 276000

Significance level = α = 1− confidence = 1 − 0.99 = 0.01

Critical z-value = zα/2 = z0.01/2 = z0.005 = 2.58 (closest value From z table)

Standard e

or of p : SE =

√p× (1 − p)n=√0.24 × 0.76276000

≈ 0.0008129

E = zα/2 ×√p× (1 − p)n

= 2.58 × 0.0008129 ≈ 0.002097

Hence ,Margin of Error or, E = 0.00210

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Solve in simplest form

Solve in simplest form

Answers

Answer:

2

Step-by-step explanation:

Which is ⁴√81x³y⁴z8 with rational exponents?
(a) 3x(¾)yz²
(b) 8x (¾) yz²
(c) 2x (⅓) yz²
(d) 9x (⅓) yz²​

Answers

The expression of ⁴√(81x³y⁴z⁸) with rational exponents is: 3x(¾)yz²

How to solve Laws of Exponents?

The 8 laws of exponents can be listed as follows:

Zero Exponent Law: a^(0) = 1.

Identity Exponent Law: a^(1) = a.

Product Law: a^m × a^n = a^(m+n)

Quotient Law: a^m/a^n = a^(m - n)

Negative Exponents Law: a^(-m) = 1/a^(m)

Power of a Power: (a^m)^n = a^(mn)

Power of a Product: (ab)^m = a^m*b^m

Power of a Quotient: (a/b)^m = a^m/b^m

We are given the algebra expression as:

⁴√81x³y⁴z⁸

This gives us:

81^(1/4) * x^(3/4) * y^(4/4) * z^(8/4)

= 3x^(3/4)yz²

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with the new dough, there were 16 complaints out of 340 pizzas. let p1 be the proportion of customer complaints with the old dough and p2 be the proportion of customer complains with the new dough. based on a 95% confidence for the difference of the proportions, what can be concluded?

Answers

The correct answer is:

Reject null hypothesis H0, we cannot conclude the proportion of customer complaints is more for the old dough.

As given in the question,

Let us consider proportion of customer complaints with old dough is p₁

And proportion of complaints with new dough is p₂

Difference in proportion of complaints in old and new dough

= p₁ - p₂

Null hypothesis : H0 : p1 ≥ p2

p₁ - p₂  ≥ 0

Alternative hypothesis : Ha : p1 < p2

p1 - p2 < 0

Let 'x' represents the number of complaints

Sample size = n

Sample proportion = x/n

Old dough:

Number of complains with old dough 'x₁' = 6

Number of pizzas with old dough 'n₁' = 385

p₁ = 6/385

   = 0.01558

   = 0.016

New dough:

Number of complains with new dough 'x₂' = 16

Number of pizzas with new dough 'n₂' = 340

p₂ = 16/340

   = 0.04705

   = 0.047

Pooled proportion test:

\(\bar{p}\) = (x₁+ x₂)/(n₁ + n₂)

  = (6 + 16)/(385 + 340)

  = 0.0303

  = 0.03

1 -  \(\bar{p}\) = 1 - 0.03

      = 0.97

z = (p₁ - p₂)/√\(\bar{p}\)(1 - \(\bar{p}\))(1/n₁ + 1/n₂)

 = (0.016 - 0.047)/√(0.03)(0.97)(1/385 + 1/340)

 = (-0.031)/ √(0.03)(0.97)(0.0026 + 0.0029)

 = - 0.031/√0.00016005

 = -0.031 / .01265

 = -2.45

It is left tailed test.

p value for the area to the left of the z score using normal distribution table:

p value = 0.007143

Significant level 'α' for  95% confidence level:

= 1 - 0.95

= 0.05

Since 0.05 > 0.0.007143

Reject null hypothesis.

Therefore, reject H0, we cannot conclude the proportion of customer complaints is more for the old dough.

The complete question is :

Paul owns a mobile wood-fired pizza oven operation. A couple of his clients complained about his dough at a recent catering, so he changed his dough to a newer product. Using the old dough, there were 6 complaints out of 385 pizzas. With the new dough, there were 16 complaints out of 340 pizzas. Let p1 be the proportion of customer complaints with the old dough and p2 be the proportion of customer complains with the new dough. Based on a 95% confidence for the difference of the proportions, what can be concluded?

Multiple Choice

A. Reject H0, we can conclude the proportion of customer complaints is more for the old dough

B. Do not reject H0, we cannot conclude the proportion of customer complaints is more for the old dough

C. Do not reject H0, we can conclude the proportion of customer complaints is more for the old dough

D. Reject H0, we cannot conclude the proportion of customer complaints is more for the old dough

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(1 point) find y as a function of t if 8y′′ 27y=0, y(0)=6,y′(0)=3. y(t)=

Answers

The general solution of the differential equation 8y′′ + 27y = 0 is y(t) = c1 cos((3/8)t) + c2 sin((3/8)t), where c1 and c2 are constants determined by the initial conditions.

The given differential equation is a linear homogeneous second-order differential equation with constant coefficients. The characteristic equation is \(8r^2 + 27 = 0\), which has roots r = ±(3i/2√2). Since the roots are complex, the general solution will involve sine and cosine functions.

The general solution is therefore y(t) = c1 cos((3/8)t) + c2 sin((3/8)t), where c1 and c2 are arbitrary constants that can be determined from the initial conditions. Using the initial condition y(0) = 6, we have c1 = 6. To find c2, we differentiate y(t) and use the other initial condition y′(0) = 3:

\(y′(t) = (-3/8)c1 sin((3/8)t) + (3/8)c2 cos((3/8)t)\)

y′(0) = (3/8)c2 = 3

c2 = 8/3

Therefore, the solution to the differential equation with the given initial conditions is:

y(t) = 6 cos((3/8)t) + (8/3) sin((3/8)t)

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need HELP PLEASE
Question 1: Abhasra and Jimmy each improved their yards by planting daylilies and ornamental grass. They bought their supplies from the same store. Abhasra spent $20 on 4 daylilies and 4 bunches of ornamental grass. Jimmy spent $25 on 3 daylilies and 8 bunches of ornamental grass. Find the cost of one daylily and the cost of one bunch of ornamental grass.

Question 2: Rob and Ndiba are selling pies for a school fundraiser. Customers can buy cherry pies and blackberry pies. Rob sold 1 cherry pie and 4 blackberry pies for a total of $60. Ndiba sold 4 cherry pies and 1 blackberry pie for a total of $30. What is the cost each of one cherry pie and one blackberry pie?

Answers

1. The cost of one daylily is $3 and the cost of one bunch of ornamental grass is $2.

2. The cost  of one cherry pie is $4 and one blackberry pie is $14.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Daylily cost=x

grass cost=y

4x+4y=20...(1)

3x+8y=25...(2)

Multiply 3 on equation 1 and multiply with 4 on equation 2

12x+12y=60

12x+32y=100

Subtract both the equations.

12x+12y-12x-32y=60-100

-20y=-40

Divide both sides by 20

y=2

Now plug in y value in any of the equation.

4x+4(2)=20

4x+8=20

4x=12

Divide both sides by 4

x=3

Hence, the cost of one daylily is $3 and the cost of one bunch of ornamental grass is $2.

2. Rob sold 1 cherry pie and 4 blackberry pies for a total of $60.

Ndiba sold 4 cherry pies and 1 blackberry pie for a total of $30.

x+4y=60..(1)

4x+y=30..(2)

x=60-4y

4(60-4y)+y=30

240-16y+y=30

240-15y=30

240-30=15y

210=15y

Divide both sides by 15

y=210/15=14

x=60-4(14)

x=4

4+4y=60

4y=56

y=56/4=14

Hence, the cost of one cherry pie is $4 and one blackberry pie is $14.

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which of the following ordered pairs are a solution to the equation y = 6x -3

(4,61)

(0,-3)

(-4,-27)

(1,3)

Answers

(0,-3)  (-4,-27)  (1,3) are the correct points

(4,61) doesn't work

a calculator is listed for $110 and is on clearence for 35% off. sales tax is 7%. what is the cost of the calculator

Answers

Answer:

$76.51

Step-by-step explanation:

The price after discounting is (1.00 - .35)($110), or 0.65($110) = $71.50.

The price after 7% sales tax has been added in is

(1.00 + 0.07)($71.50) = $76.51.

Answer:

76.50

Step-by-step explanation:

what is the equivalent exponential expression for the radical expression below?
√6​

what is the equivalent exponential expression for the radical expression below?6

Answers

I think the answer would be 6

Answer:

D. \(6^\frac{1}{2}\)

Step-by-step explanation:

I just used a calculator and found the 2nd root of 6. Then I compared it to the answers.

Complete the statement with equal to, greater than, or less than.

2 x 2/9 will be __________ 2

Answers

2 x 2/9 Will Be Less Than 2

Find the average rate of change in the simplest form

Find the average rate of change in the simplest form

Answers

m = (5-15)/(4-2). Rise over run
Slope = -5

Ursula tosses two six-sided number cubes and ADDS the numbers rolled. Which of these is a list of the outcomes of the two row? A) 3, 4, 5, 6, 7, 8 B) 2,4,6,8, 10, 12 C) 5, 8, 11, 14, 17, 20 D) 0/25, 1/25, 3/25, 5/25, 6/25, 25/2

Answers

Answer:

A) 3, 4, 5, 6, 7, 8

Step-by-step explanation:

2+1, 2+2, 2+3, 2+4, 2+5, 2+6= 3, 4, 5, 6, 7, 8

1. Luzcel real estate owns 8000 square meters of lot area and decides to construct two different styles of houses, B and C. The lot area of house B is 250 sq. m. and house C lot area is 200 sq. m. The construction engineer has a maximum of 6400 man-hours of labor for the construction. Let your variables be the number of units of house B and the number of units of house C to be constructed. a) Write an inequality which states that there are 8000 sq. m. of land available. b) A unit of house B requires 160 man-hour and a unit of house C requires 256 man-hour. Write an inequality that the engineer has at most 6400 man-hour available for construction. c) If material cost 600 thousand pesos for a unit of house B and 800 thousand for a unit of house C, write an inequality stating that the engineer has at least 12 million pesos to spend for materials. d) Labor cost 1.1 million pesos for constructing a unit of house B and 1.3 million pesos for constructing a unit of house C. If a unit of house B sells for 3.5 million and a unit of house C selis for 4 million, how many units of house B and house C should be constructed to obtain the maximum profit? Show the graph.

Answers

Inequality stating that there are 8000 sq. m. of land available: Let B be the number of units of house B and C be the number of units of house C.

Therefore,B+C ≤ 8000/200 [Reason: House C requires 200 sq. m. of land]⇒B+C ≤ 40b. Inequality that the engineer has at most 6400 man-hour available for construction:

160B + 256C ≤ 6400c

Inequality stating that the engineer has at least 12 million pesos to spend for materials:

600B + 800C ≤ 12000d

. Let us write down a table to calculate the cost, income and profit as follows:Units of house BLabor Hours per unit of house BUnits of house CLabor Hours per unit of house CTotal Labor HoursMaterial Cost per unit of house BMaterial Cost per unit of house CTotal Material CostIncome per unit of house BIncome per unit of house C

Total IncomeTotal ProfitBC=8000/200-B160CB+256C600000800000+256C12,000,0003,500,0004,000,0003,500,000B+C ≤ 40 160B + 256C ≤ 6400 600B + 800C ≤ 12000 Units of house B requires 160 man-hour and a unit of house C requires 256 man-hour.

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for what values of x and y are the triangles below congruent by HLX=Y=

for what values of x and y are the triangles below congruent by HLX=Y=

Answers

A triangle is congruent by HL if the hypotenuse and one of the legs is equal between the triangles.

\(\begin{gathered} x=y+3 \\ x+1=3y \end{gathered}\)

replace the first equation into the second one

\(\begin{gathered} y+3+1=3y \\ y+4=3y \\ 4=3y-y \\ 4=2y \\ \frac{4}{2}=y \\ y=2 \end{gathered}\)

replace y into one of the equations

\(\begin{gathered} x=2+3 \\ x=5 \end{gathered}\)

x must be equal to 5 and y to 2 in oder for the triangles to be congruent by hl.

If the length of the side of a square is 15 inches. What is the area of the square?

Answers

Answer:

225 inch^2

Step-by-step explanation:

15×15=225

Answer:

225 In²

Step-by-step explanation:

15*15=225 because the square has all sides the same length.

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Please help me respond this

Please help me respond this

Answers

Option 2 is correct that is 1.79

What is third quartile ?

When presented in ascending order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).

The quartiles formula is as follows:

Upper Quartile (Q3) = 3/4(N+1)

Lower Quartile (Q1) = (N+1) * 1/3

Middle Quartile (Q2) = (N+1) * 2/3

Interquartile Range = Q3 -Q1,

1.74, 0.24, 1.56, 2.79, 0.89, 1.16, 0.20, and 1.84 are available.

Sort the data as follows: 0.20, 0.24, 0.89, 1.16, 1.56, 1.74, 1.84, 2.79 in ascending order of magnitude.

The data set has 8 values.

hence, n = 8; third quartile: 3/4 (n+1)th term

Q3 =3/4 of a term (9) term

Q3 =27/4 th term

Q3 = 1.74 + 1.84 / 2 (average of the sixth and seventh terms)

equals 1.76

Thus Q3 is 1.76 that is option 2

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The simple interest on a sum of money invested at 3% per annum for 2 years was $39.75.
Calculate the sum of money invested

Answers

Answer:

$37.50

Step-by-step explanation:

\(P+Prt=39.75 \\ \\ P+P(2)(0.03)=39.75 \\ \\ 1.06P=39.75 \\ \\ P=\$37.50\)

What was the overall shape of the distribution of soldiers’ foot lengths? About where was the center of the distribution?

Answers

The overall shape of the distribution of soldiers' foot lengths was likely symmetric or approximately bell-shaped.

The distribution of soldiers' foot lengths can be described as symmetric or bell-shaped. The majority of foot lengths cluster around the center, with fewer foot lengths deviating significantly. The center of the distribution, representing the average foot length, can be determined using the mean.

Analyzing the shape through a histogram or box plot helps identify symmetry. A symmetric shape with a peak in the middle and evenly tapering tails indicates a bell-shaped distribution.

Understanding the distribution's shape and center allows us to infer the overall characteristics of the soldiers' foot lengths.

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Please help me with this

Please help me with this

Answers

answer is 11

Using pythagorean theorem

{a}^{2} + {b}^{2} = {c}^{2}

c being the hypotenuse.

Plug in 60 and 61, so 60^2 + b^2 = 61^2

then square it, 60^2 = 3,600. 61^2 = 3,721.

plug those numbers in 3,600 + b^2 =3,721

to find b^2 subtract 3600 from 3721, 3,721 - 3600 = 121

then find the square root of 121, which is 11.

suppose the matrix, , has eigenvectors , , and whose eigenvalues are , and respectively. then, using the same order, can be written in the form where

Answers

We can write A = PAP where 1 P= and A= where P is an invertible matrix that maps the null space of A to itself.  

To find the matrix P, we need to solve the following system of linear equations:

λ_1 1 = 1

λ_2 (-4) 1 = 1

λ_3 (-1) 1 = 1

The eigenvalues are real and non-negative, so they can be written as λ = λ_1, λ_2, λ_3 = λ_1, -4, -1 respectively.

Using Cramer's rule, we have:

\(λ_1 * 1^T = 1 * 1^T = 1\)

\(λ_2 * (-4)^T = -4 * 1^T = -4\)

\(λ_3 * (-1)^T = (-1) * 1^T = -1\)

Multiplying the first and third equations, we get:

\(-λ_1 * λ_3 = -4 * (-1) = 4\)

Multiplying the second and third equations, we get:

\(-λ_2 * λ_3 = -4 * (-1) = 4\)

Subtracting the second equation from the first, we get:

\(λ_1^2 - λ_2^2 = 1^2 - (-4)^2 = 5\)

Multiplying the first and third equations, we get:

\(-λ_1 * λ_2 = -4 * (-1) = 4\)

Dividing the third equation by the second equation, we get:

\(-1/λ_2 = -1/λ_3\)

Taking the reciprocal of both sides, we get:λ_2 = λ_3

Substituting this into the second equation, we get:

-\(λ_1 * λ_3 = -4 * (-1) * λ_3 = -4\)

Simplifying, we get:

-4 = -4

This equation has no solution, so the matrix A cannot be written in the form A = PAP where 1 P= and A= Thus, the answer is no.  

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Full Question: the matrix, A, has eigenvectors and whose eigenvalues are 1, –4 and – 1 respectively. Then, using the same order, A can be written in the form A = PAP where 1 P= and A=

What is the equation of the line perpendicular to 2x – 3y = 13 that passes through the point (-6, 5)?
O Y=2/3x+9
O y=-3/2x-4
O y=-3/2x-13
O y=2/3x-1

Answers

Answer:

Option 2, y=-3/2x-4

Step-by-step explanation:

Solve with the point-slope formula: y-y1=m(x-x1). The line is perpendicular, meaning the slope of the new equation will be the oppposite reciprocal of the original slope.

First, we need to rewrite the original equation into standard form.

2x-3y=13

-3y=13-2x

y=-13/3+2/3x

From this, we can see that the slope here is 2/3. Since the line we're looking for is perpendicular, the opposite reciprocal of that slope is -3/2.

Now, we can plug in the coordinates we have into the formula (-6, 5), along with our slope (-3/2).

y-(5)=-3/2(x+6)

y-5=-3/2x-9

y=-3/2x-4

And to check, we can just plug the coordinates into our new equation:

Check:

(5)=-3/2(-6)-4

5=9-4

5=5

Answer: B on edg

Step-by-step explanation:

trust me

Help!!!
a $52 item is marked up 10% and then markdown 10% what is the final price

Answers

Answer: $51.48

Step-by-step explanation:

If a $52 item is marked up by 10%, its new price will be:

$52 + 10% of $52 = $52 + $5.20 = $57.20

Then, if this new price is marked down by 10%, the final price will be:

$57.20 - 10% of $57.20 = $57.20 - $5.72 = $51.48

Therefore, the final price of the item after the markup and markdown is $51.48.

That's driver pays all tall is using only nickels and dimes by throwing one coin at a time into the mechanical toll collector

Answers

Since nickel is 5 cents and a dime is 10 cents, the possible tolls that you can pay need to be multiplies of 5 cents.

Let on represent the number of a ways

for the number of different ways the bus

The driver can pay a toll of 5n rent first case.

The first case used in a nickel then there are ways to pay =

57 - 5 = 5 ( 1 - 1 ) cents

The second case: - The coin used is a dime, then

there is a long way to

pay 5n - 10 2 5 ( 1 - 2 ) cents -

Adding the numbers of sequence of all

In three cases, we then obtain

an = an - 1 an +2

Initially, when n 20 there is exactly I way to pay cents ( using no coins )

when an = 1 there is exactly I to way

to pay 5 cents ( using one tickle )

q =f .

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