Write an equation in slope-intercept form
to represent the relationship between x
and y shown in the table.
X
Y
-10 -5 0 5
55
20
-15
-50
10
-85

Answer:

1: x^2+y^2-6x-4y-3=0

2: x^2+y^2-10x+4y=0

3: x^2+y^2-10x+2y+1=0

The minimum amount of fence needed to enclose the lots is 120ft.

Adding areas of both fields, the combined area comes about to be 600sq ft.

The dimensions of the new plot are x length and y breadth. According to the question, there is a fence in the middle with y breadth.

g(x, y, z) = xy - 600

g(x, y, z) = 2x + 3y

∇g = ∇ (xy - 600) = (y, x)

∇f = ∇(2x + 3y) = (2, 3)

Now from the Lagrange method,

∇f = λ∇g

2 = λy

3 = λx

Now to get the value of lambda,

(2/y) = (3/x) = λ

x = 1.5y

Solving now we get,

1.5y² = 600

y = 20

x = 1.5 × 20 = 30

Thus after getting (x,y) we can put the value in the function to get the answer as 120ft.

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Answer:

Any equation that has the same slope as this line will be parallel to it. The slope is -1/4, so whichever equation has -1/4 x in it will be parallel to the line.

The solution set for the inequality is.

-113 ≤ y ≤ 131

Here we have the following inequality:

|y - 9| ≤ 122

Any absolute value inequality can just be decomposed as follows:

|y - 9| ≤ 122

to:

-122 ≤  y - 9 ≤  122

Now we can solve this for y by adding 9 in all places:

-122 + 9 ≤ y - 9 + 9 ≤  122 + 9

-113 ≤ y ≤ 131

That is the solution set.

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For the given figure, angle 3 will be equal to angle 2.

According to the question,

We have the following information:

We have a figure where some angles are marked in form of numbers and  the measure of angle 3 is equal to the sum of the measures of angle 6.

Now, we know that vertically opposite angles are equal and angle 1 and angle 4 are vertically opposite angles like angle 2 and angle 3.

(More to know: the sum of three angles of a triangle is equal to 180°.)

Hence, for the given figure, angle 3 will be equal to angle 2.

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The solution to the algebraic equation 8x - 8 = 4x is x = 2

Algebra: This is the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.

8x - 8 = 4x

8x - 4x = 8

4x = 8

x = 8/4

x = 2

Check:

8x - 8 = 4x

substitute x = 2 into the equation

8(2) - 8 = 4(2)

16 - 8 = 8

8 = 8

Other examples of algebraic equation

3x + 5 = 11

substract 5 from both sides

3x = 11 - 5

3x = 6

divide both sides by 3

x = 6/3

x = 2

Therefore, the value of x from the equation is given by 2

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a) The margin of error associated with a 95% confidence interval is 4.

b) The 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77,$37.77)

a) We are given with the information that the mean for 54 discount brokers is $50 for 100 shares is $33.77 Also the population standard deviation is $15.

The formula for margin of error is Z  = zα/2 σ √ n

Now we know from our z-table that value of zα/2 for 95% confidence interval is 1.96

So, the value of error margin is  zα/2 σ √ n =1.96 (15/√54) = 1.96 x 2.04

= 4

b) We know from part a that margin of error is 4.

Also, the mean price charged for a trade of 100shares at 50 per share was $33. 77

The value of confidence interval for population mean is,

x ± zα/2 σ √ n = 33.77 ± 4 = (29.77,37.77)

Thus, the 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77,$37.77)

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Mr. Harrington will need $510.75  to buy the TV

The correct answer is an option (a)

In this question, Mr. Harrington wants to buy a new TV for $500

He has a 10% off coupon.

After applying this coupon, the cost of TV would be,

500 - (10 percent of $500)

= 500 -[ (10/100) * 500]

= 500 - 50

= 450

He knows the tax be 13.5%.

13.5 percent of 450 would be,

(13.5/100) * 450

= 60.75

So, the amount he will need to save to buy the TV,

$450 + $60.75 = $510.75

Therefore, Mr. Harrington will need $510.75  to buy the TV

The correct answer is an option (a)

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The linear functions representing the systems of equations in each case are given as follows:

8. (D) 6x − y = 8 3x + 2y = 9

9. (C) a + o = 72 a = o + 8.

10. (C) 4x + 3y = −12 2x − 5y = 10.

The slope-intercept representation of a linear function is presented by the rule as follows:

y = mx + b

The coefficients of the function and their meaning are listed as follows:

For the line m, we have that when x increases by 6, y increases by 36, hence the slope is:

m = 36/6 = 6.

Considering the positive slope of 6, at x = 0, the numeric value is 12 less than the numeric value at x = 2, hence the intercept is:

b = 4 - 2 x 6 = -8.

Hence the equation is:

y = 6x - 8.

6x - y - 8.

Thus option d is correct.

For item 9, we use the variables a and o. The total is of 72, hence:

a + o = 72.

Suppose that a crate has 8 more apples than oranges, hence:

a = o + 8.

Thus option c is correct.

For line r in item 10, when x increases by 3, y decays by 4, hence the slope is:

m = -4/3.

When x = 0, y = -4, hence the intercept is:

b = -4.

Thus the equation is:

y = -4x/3 - 4

3y = -4x - 4.

4x + 3y = -12.

Meaning that option c is correct.

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Answer:

14.5 feet

Step-by-step explanation:

     To make the subject as 'w', isolate w.

              2L + 2W =P

                      2W = P - 2L

                        [tex]\sf W = \dfrac{P-2L}{2}\\\\W =\dfrac{P}{2}-\dfrac{2L}{2}\\\\ \boxed{W = \dfrac{P}{2}-L}[/tex]

   P = 37 feet

   L = 4 feet

           [tex]\sf W =\dfrac{37}{2}-4\\\\[/tex]

                = 18.5 - 4

           W = 14.5 feet

When the divisor is missing, you divide the dividend (3.472) by the quotient (0.112)

So, we will do 3.472 divided by 0.112

3.472/0.112 = 31

Another method is multiplication. Multiplication is the opposite of division. We'd multiply 0.112 by 31.

0.112 x 31 = 3.472

In conclusion,

3.472/31 = 0.122

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Answer: 3.472/31 = 0.122

Step-by-step explanation: I hope this helps:)

First, break down the problem.  

Someone can skate 3 miles in 9 minutes.

What is their speed?  How far would they go if they did that speed for 1 minute?

To find speed given time and distance, divide distance by time.

3/9 = 1/3

Speed is 1/3 mile per minute

if they travel one minute, they will travel 1/3 of a mile

hope this helps :)

Answer:

11

Step-by-step explanation:

Distance formula is square root of (x2-x1)^2+(y2-y1)^2

square root of (6-(-5))^2+(7-7)^2

square root of (11)^2+(0)^2

square root of 121+0

square root of 121

11

distance is 11

The required expression of the reflection of the point is (-x, y).

Given that,
A line segment has endpoints at (–4, –6) and (–6, 4). Which reflection will produce an image with endpoints at (4, –6) and (6, 4) is to be determined.

The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
A line segment has endpoints at (–4, –6) and (–6, 4) and an image with endpoints at (4, –6) and (6, 4) is produced the equation of the reflection is given as,
(x, y) ----> (-x, y)

Thus, the required expression of the reflection of the point is (-x, y).

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Answer:

45.47

Step-by-step explanation:

The constant of proportionality is known to be the ratio of two proportional values that is said to be in a constant value.

The constant of proportionality is a term that is defined as the rate or the ratio of two proportional values which are known to be at the same value.

constant of proportionality = 2.5

Given  :  y = 2.5x.

To find : What is constant of Proportionality in the equation.

Solution : We have given

y = 2.5x.

On comparing with equation of proportionality : y = kx,

Where,   k is the constant of proportionality.

On comparing y = 2.5 x  by y = kx .

We get  k = 2.5

So, constant of proportionality = 2.5

Therefore, constant of proportionality = 2.5

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The value of constant proportionality is 2.5. The constant of proportionality is known to be the ratio of two proportional values that is said to be in a constant value.

The constant of proportionality is a term that is defined as the rate or the ratio of two proportional values which are known to be at the same value.

constant of proportionality = 2.5

Given  :  y = 2.5x.

To find : What is constant of Proportionality in the equation.

Solution : We have given

y = 2.5x.

On comparing with equation of proportionality : y = kx,

Where,   k is the constant of proportionality.

On comparing y = 2.5 x  by y = kx .

We get  k = 2.5

So, constant of proportionality = 2.5

Therefore, constant of proportionality = 2.5

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Answer:

The guy under me is correct

Step-by-step explanation:

Answer:

x - 5

Step-by-step explanation:

Factor the expressions that are not already factored

(x^2 - 9x + 20) / (x - 4)

Cancel out x - 4 in both numerator and denominator

[tex]\frac{(x-5)(x-4)}{x-4}[/tex]

x - 5

The solution of the double-ended inequality is -7/2 < x < -5/2

From the question, we are to solve the doubled ended inequality.

The given inequality is

2x - 5 < 4x + 2 < 2x -3

From the inequality, we can write that

2x - 5 < 4x + 2 and 4x + 2 < 2x - 3

Now, we will solve each of the inequalities separately

Solving 2x - 5 < 4x + 2

Add 5 to both sides

2x - 5 + 5 < 4x + 2 + 5

2x < 4x + 7

Subtract 4x from both sides

2x - 4x < 4x - 4x + 7

-2x < 7

Divide both sides by -2 and reverse the sign

x > -7/2

-7/2 < x

Solving 4x + 2 < 2x - 3

Subtract 2x from both sides of the equation

4x - 2x + 2 < 2x - 2x -3

2x + 2 < -3

Subtract 2 from both sides

2x + 2 -2 < -3 - 2

2x < -5

Divide both sides by 2

x < -5/2

Putting the two solutions together, we get

-7/2 < x and x < -5/2

-7/2 < x < -5/2

Hence, the solution is -7/2 < x < -5/2

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The demand function for a certain is given by the equation p=−0. 01x2−0. 1x+21 then the determined values will be −50.905557, −0.427737,41.333295.

From the given values,

R=px

9 = (−0. 01x2−0. 1x+21) x

0.01x3+0.1x2−21x−9=0

By reducing the equation,

X = −50.905557, −0.427737,41.333295.

Therefore, the determined values will be −50.905557, −0.427737,41.333295.

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The probability that at most 25 tails occur is 0.99999848.

We know that,

P(x = x) = ⁿCₓ × pˣ × [tex]q^{n-x}[/tex]

p = probability of success = 0.5

n = number of trials = 28

q = 1 - p = 0.5

The probability of the tail occurring at most 25 times can be written as

P(X ≤ 25) = P (X = 0) + P(X = 1) + ..... + P(X = 25)

Using a binomial probability calculator,

P(X ≤ 25) = 0.99999848

Therefore the probability that at most 25 tails occur is 0.99999848

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Answer:

SA(surface area) of the rectangular prism is 1,510 in inches

Step-by-step explanation:

SA=2(lh+lw+hw)

2inch=24ft

lh=264

lw=336

wh=154

755*2=1,510

The function has a maximum value of 30 at x = 3.

Given Function:

f(x) = -3[tex]x^{2}[/tex]+18x+3

here a = -3 , b = 18 , c = 3

a is negative so it has maximum value

x = -b/2a

= -18/2*(-3)

= -18/-6

= 18/6

= 3

f(x) = -3*[tex]3^2[/tex] + 18*3 + 3

= -3*9+54+3

= -27+54+3

= 27+3

= 30

Therefore the function has a maximum value of 30 at x = 3.

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Answer: $84.80

Step-by-step explanation:

The actual sales tax was 4.80 because 6% of 80 is 4.80

Then add the 4.80 to the 80 to get your total

Hope this helped :)

Answer:

Question 1: #3 is correct.

Question 2: #4 is correct.

The Excel formula that Bill would use is PMT.

From Bill's situation, he has the following information:

time = NPER = number of periods = 18 years

RATE of the bank

FV = future value = cost of tuition

PMT, is a financial function, computes the loan payment based on constant payments and a constant interest rate. The Excel PMT function is a financial function that computes loan payments based on a fixed interest rate, the number of periods, and the loan amount. The function's name is derived from the acronym "PMT," which stands for "payment."

In conclusion, the correct option is PMT.

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Complete question

Bill wants to save for his son’s college expenses. He knows what tuition will cost in 18 years and knows the interest rate on the bank account. What he doesn’t know is how much to deposit each month to save enough for his son’s college expenses. Which Excel formula would you use? Choose from FV, PV, PMT, NPER, or RATE.

The number of bicycles that must be manufactured to minimize the cost of 250 and the minimum cost is $11,500.

In the given question,

The cost C in dollars of manufacturing x bicyles at a production plant is given by the function shown below;

C(x) = 3x^2-1500x+199,000

(a) In the given question we have to find the number of bicyles that must be  manufactured to minimize the cost.

The given function is

C(x) = 3x^2-1500x+199,000

To find the maximum or minimum value we firstly find the value of f'(x).

C'(x) = 6x-1500

Now put f'(x)=0

6x-1500=0

Add 1500 on both side, we get

6x=1500

Divide by 6 on both side we get

x=250

Hence, the number of bicycles that must be manufactured to minimize the cost of 250.

(b) Now finding the value of function at x=250

C(250) = 3(250)^2-1500*250+199,000

C(250) = 3*62,500-375,000+199,000

C(250) = 187,500-375,000+199,000

C(250) = 11,500

The minimum cost is $11,500.

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We have to prove (cosA−sinA+1)/(cosA-sinA-) = cotA+cosecA using Trigonometric Functions

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

L.H.S=(cosA−sinA+1)/(cosA-sinA-)

dividing by sinA

=cotA+1−cosecA/cotA−1+cosecA

​=(cotA−1+cosecA)(cotA+1+cosecA)/(cotA+1)²-cosec²A

=(cotA+cosec)²-1/2cotA

=cotA+cosecA(R.H.S)

​Hence the above trigonometric function is proved.

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