help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer 1

The percentage of decrease is 20%

How to find the missing percentage?

First, if we have an initial value A, and we increase it by x (a percentage in decimal form) then the new value will be:

A' = A*(1 + x)

Whle a decrease is written as:

A' = A*(1 - x)

In this case we have an increase of the 25%, it is written as:

A' = A*(1 + 0.25)

A' = A*1.25

IF we pass the factor to the other side, will get:

(1/1.25)*A' =  A

(0.8)*A' = A

Now we want to write the coefficient on the left in the form (1 - x)

We will get:

0.8 = 1 - 0.2

0.2 is the percentage (in decimal form) decreased  from A' to get A. Then the answer is 20%.

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Related Questions

PLEASE HELP WITH ALGEBRA!!!

A classmate simplified this rational equation. (Picture attached)

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

a) circle and explain the error in this simplifcation
b) show your work as you correct the error

Answers

Part (a)

The error happens on the 2nd step.

The student multiplied both sides by the LCD (x+3)(x-3) to clear out the fractions, but forgot about the first "1" at the very left.

=================================================

Part (b)

[tex]1 - \frac{2}{x+3} = \frac{x+1}{x-3}\\\\(x+3)(x-3)*1 - (x+3)(x-3)*\frac{2}{x+3} = (x+3)(x-3)*\frac{x+1}{x-3}\\\\(x+3)(x-3) - 2(x-3) = (x+1)(x+3)\\\\x^2-9 - 2x+6 = x^2+4x+3\\\\x^2-2x-3 = x^2+4x+3\\\\x^2-2x-3-x^2-4x-3=0\\\\-6x-6=0\\\\-6x=6\\\\x = 6/(-6)\\\\x = -1[/tex]

The answer is x = -1

Check:

[tex]1 - \frac{2}{x+3} = \frac{x+1}{x-3}\\\\1 - \frac{2}{-1+3} = \frac{-1+1}{-1-3}\\\\1 - \frac{2}{2} = \frac{0}{-4}\\\\1 - 1 = 0\\\\0 = 0\\\\[/tex]

The answer is fully confirmed.

You can use a graphing tool like GeoGebra to visually confirm the answer.

please help me on this

Answers

Answer:

[tex]\frac{4}{90}[/tex]

Step-by-step explanation:

[tex]\frac{4}{9}[/tex]  - [tex]\frac{4}{10}[/tex]

to subtract the fractions we require them to have a common denominator

the LCM of 9 and 10 is 90

= = [tex]\frac{4(10)}{9(10)}[/tex] - [tex]\frac{4(9)}{10(9)}[/tex]

= [tex]\frac{40}{90}[/tex] - [tex]\frac{36}{90}[/tex]

= [tex]\frac{40-36}{90}[/tex]

= [tex]\frac{4}{90}[/tex]

Naomi has taken six science tests so far this year. The tests are out of 100 points, and she has gotten the following scores.

64, 88, 92, 86, 81, 92

What must Naomi score on her seventh test in order to raise her mean to an 85?
88
92
85
95

Answers

Answer:92

Step-by-step explanation:

[tex]\frac{64+88+92+89+81+92+x}{7} =85[/tex]

85 x 7 = 595

595 - 64 - 88 - 92 - 89 - 81 - 92 = 92

Answer:

Naomi needs to score a 92 on her seventh test to raise her mean to an 85.

Step-by-step explanation:

Let's call the score Naomi needs to get on her seventh test "x".

To find out what score she needs to raise her mean to 85, we can set up an equation:

(64 + 88 + 92 + 86 + 81 + 92 + x) / 7 = 85

We add up all her scores so far (64 + 88 + 92 + 86 + 81 + 92) and add the score she needs to get on her seventh test (x). We divide the sum by the total number of tests (7) to get the mean score of 85.

Simplifying the equation, we get:

503 + x = 595

Subtracting 503 from both sides, we get:

x = 92

A group of marine biologists tags 45 great white sharks off the coast of Mexico
to study migratory patterns. All of the tag numbers are unique. Weeks later, the
marine biologists travel to Hawaii. While there, they randomly capture and release
20 great white sharks per day, for three consecutive days. On the first day, 3 of the
sharks have the original tags. On the second day, 2 of the sharks have the original
tags. On the third day, 4 of the sharks have the original tags. Based on the data,
what is the estimated population of great white sharks that have migrated from
Mexico to Hawaii?

Answers

Yall are some cheaters. Quit looking it up on this website like, dang....

I will give you a Brainliest

Answers

Answer:

192

Step-by-step explanation:

2x9=18

18x12=192

A procedure for using sample data to find the estimated regression equation isa. point estimation. b. interval estimation.c. the least squares method. d. extrapolation..

Answers

A procedure for using sample data to find the estimated regression equation is (c) the least squares method.

The least squares method is a commonly used statistical procedure for finding the estimated regression equation by minimizing the sum of the squared differences between the observed and predicted values.

The goal of this method is to find the line of best fit that closely represents the relationship between the independent and dependent variables in the sample data. The regression equation obtained from the least squares method can be used to make predictions about the dependent variable based on the values of the independent variable.

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100 POINTS!
Select the true statement that describes a right circular cone.

A right circular cone does not have a base.
A right circular cone has a rectangular face.
A right circular cone has one apex.
A right circular cone has 7 edges.

Answers

Answer:

C

Step-by-step explanation:

It makes the most sense.

Determine whether each number is an integer, a rational number that is not an integer, or an irrational number. pls help very urgent

Answers

Integer: 12

Irrational numbers: -2√10 and √20

Rational numbers: 17/4, 0.25, and -77/11.

What are integers?

Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."

Given:

There are rational and irrational numbers in the image.

The numbers can be written in the form of p/q, where q is never zero is rational numbers.

And rest of the numbers are irrational numbers.

So, the solutions are given in the image below.

√144 = 12

0.25 = 25/100 = 1/4

Therefore, the solutions are given in the image below.

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How Much Tax Will She Pay

Answers

The total amount of money Tegan paid for tax last year from her income of £48,300 is £4,830

How Much Tax did Tegan Pay?

Tegan's income last year before tax = £48,300

Tegan's earnings is upto £43,000 and in excess of £48,300 - £43,000

= £5,300

Assume, Tegan's tax rate is 10% since her excess is not up to £11,000

Tegan's tax = 10% of £48,300

= 0.10 × 48,300

= £4,830

Ultimately, Tegan paid a total amount of £4,830 as tax last year.

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what is 2 + 2 equal and what are the steps to solving it

Answers

Answer: 4

Step-by-step explanation:

1+1=2 but  if it is 2+2 then it would = 4

Martín did the following work and found his surfing increased 50% from the first week to the second.
Percent of change= amount of change/Original amount = 9-6/6 = 3/6 =0.5.
0.5—->50%. Describe Martin’s method for finding percent change in your own words.

Answers

The surfing increased by 50% from the first week to the second. His method is correct.

What is the percentage change?

The amount of any product is given as if it were a percentage of a hundred. The ratio is one-quarter of one hundred. % is an abbreviation for one hundred percent. It is represented by the character '%'.

The percentage is given as,


Percentage (P) = [Final value - Initial value] / Initial value x 100

The Surfing 6 seconds to reach 9 seconds. Then the percentage is given as,

P = [(9 - 6) / 6] x 100

P = (3 / 6) x 100

P = 0.50 x 100

P = 50%

The surfing increased by 50% from the first week to the second. His method is correct.

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Does a matrix have to be symmetric to be orthogonally diagonalizable?

Answers

No, a matrix does not have to be symmetric to be orthogonally diagonalizable. Orthogonal diagonalization is a property of square matrices that can be used to simplify calculations and solve certain types of problems.

A square matrix A is orthogonally diagonalizable if there exists an orthogonal matrix P and a diagonal matrix D such that A = PDP^T, where D contains the eigenvalues of A and P contains the corresponding eigenvectors.

A symmetric matrix is always orthogonally diagonalizable, meaning that there exists an orthogonal matrix P such that A = PDP^T, where D is a diagonal matrix containing the eigenvalues of A. However, not all matrices are symmetric and still can be orthogonally diagonalizable.

For a non-symmetric matrix, the eigenvectors and eigenvalues may not have certain symmetrical properties that make orthogonal diagonalization straightforward, but it is still possible to diagonalize the matrix. In such cases, we can use other techniques, such as the Schur decomposition, to obtain a similar diagonal form.

In summary, a matrix does not have to be symmetric to be orthogonally diagonalizable, but symmetric matrices are always orthogonally diagonalizable. Other techniques may be used for diagonalizing non-symmetric matrices.

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3. Xavier has $43 in his savings account and plans to save $15 each week. Write an alger
expression to represent how much Xavier will have in his savings account after w weeks.

Answers

An algebraic expression to represent how much Xavier will have in his savings account after w weeks is; y = 15w + 43

How to solve Linear Equation Word problems?

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

We are given that Xavier has $43 in his savings account. Thus;

y-intercept = $43

He plans to save $15 each week. Thus;

Slope = $15

Now, after w weeks, the total savings is expressed as;

y = 15w + 43

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A ramp 22 ft long rises to a platform. The bottom of the platform is 12 ft from the foot of the ramp. Find x, the angle of elevation of the ramp. Round the answer to the nearest tenth of a degree.

Answers

The angle of elevation is 61.34°.

What is angle of elevation?

An angle of elevation is defined as an angle between the horizontal plane and line of sight from the observer's eye to some object above.

here, we have,

Given here, ramp 18 ft long rises to a platform.

The bottom of the platform is 13 ft from the foot of the ramp.

Let the angle be x then angle of elevation is

      tanx =22/12

     x   = tan⁻¹(22/12)

    x   =61.34°

Hence, the angle of elevation is  61.34°

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5/18 + 11/12
fractions
adding fractions with unlike denominators

Answers

Answer:

= 43.

Step-by-step explanation:

[tex] \frac{5}{18} + \frac{11}{12} \\ = 36 \times \frac{5}{18} + 36 \times \frac{11}{12} \\ = 2(5) + 3(11) \\ = 10 + 33 \\ = 43[/tex]

Note// the LCM for 18 and 12 is 36.

What is the value of 1 gallon in kg?

Answers

Answer:

kg = gal × 3.7854 × density.

Step-by-step explanation:

Two furniture salesmen are comparing their salaries. Gert is paid R25,00 per hour plus a 15% commission on his total sales. Ben is paid R29,00 per hour plus a 10% commission on his total sales. Suppose each has sold R5 000 worth of furniture, compare their income over various periods of time to find out when they will earn the same. What will happen after that point? Who would have earned more before that point?​

Answers

When sales are under $15,000, the current job pays less than the new offer. The new job offer is therefore favoured for sales below $15,000.

What is meant by linear equation?A linear equation, according to the definition, is an algebraic equation in which each term has an exponent of one and the graphed value of the equation is a straight line. Y=mx + b is a prime example of a linear equation. Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5. Finding both intercepts of an equation in this format is rather simple (x and y). A two-variable linear equation can be thought of as a linear relationship between x and y, or two variables where the value of one (often y) relies on the value of the other (usually x).

a)   Wc = 2000+.07S

b)  Wn =2300+.05S

c)  When the totals are similar, the sales level at which she would not care

   2000 + .07S = 2300 + .05S

   subtract .05S from both sides

    2000 +.02S = 2300

   subtract 2000 from both sides

    .02S = 300

   divide both sides by .02

   S = 300/.02 = 15000

Sales of $15,000 equate to identical pay.

If we apply the same calculation, substituting less than for the = sign... The result of our equation is

2000 + .07S < 2300 + .05S

S < 15000

The present employment pays less than the new offer when sales are under $15,000. Therefore, the new job offer is preferred for sales below $15,000.

check:  Let S = 10,000

Wc = 2000+.07(10000) = $2700

Wn = 2300 + .05(10000) = $2800

As can be seen, at sales of $10,000 the new job earns more.

The complete question is:

A salesperson receives a monthly salary $2000 plus commission of 7% of sales. she is offered a new job at $2300 per month plus commission of 5% os sales.

a) write a linear equation for her current wage W in terms of her monthly sales S.

b)write a linear equation for her monthly wage W of the job offer in terms of her monthly sales S.

c) what level of sales will make her indifferent between the two jobs? Which scheme is preferred when sales are below this level?

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HJK and RST are supplementary angles. If HJK is 56 , what is the measure of RST?

Answers

Answer: The measure of RST is 124 degrees.

Step-by-step explanation:

If HJK and RST are supplementary angles, it means that their sum is equal to 180 degrees. So we can use this information to find the measure of RST.

HJK + RST = 180

Substituting HJK = 56, we get:

56 + RST = 180

Subtracting 56 from both sides, we get:

RST = 180 - 56

RST = 124

Therefore, the measure of RST is 124 degrees.

In the Diagram segment ad bisects angle bac

Answers

Since segment AD bisects angle BAC, the value of x is equal to 14.6.

What is an angle bisector?

In Mathematics, an angle bisector can be defined as a type of line, ray, or segment, that bisects or divides a line segment exactly into two (2) equal angles.

By applying the angle bisector theorem to this triangle (ΔABC), we have:

AB/BD = AC/DC

19/x = 17/(20 - x)

17x = 19(20 - x)

17x = 380 - 19x

19x + 17x = 380

26x = 380

x = 380/26

x = 14.6.

In conclusion, we can reasonably infer and logically deduce that the value of x in triangle ABC is 14.6.

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what is the value of 5g in mg?

Answers

The value of 5g in mg is 5000mg. This is because 1g is equal to 1000mg, and 5g is equal to 5 times that amount, or 5000mg.

When converting between different metric units of mass, the prefixes are used to denote the multiple of the base unit. In this case, the base unit is the gram, and the prefix we are using is 'milli', which is equal to one thousandth of the base unit. Therefore, in order to convert 5g to mg, the prefix 'milli' is multiplied by the base unit of grams, resulting in a value of 5000mg.When converting between metric units, it is important to remember that the decimal point moves right by a number of places equal to the number of zeroes in the prefix. For example, if we were converting 5g to kg, the prefix 'kilo' has three zeroes, so the decimal point would move three places to the right, resulting in a value of 0.005kg.When converting from a larger unit to a smaller unit, the numerical value will increase, and when converting from a smaller unit to a larger unit, the numerical value will decrease. In this case, we are converting 5g to mg, which is a smaller unit, so the numerical value of 5g increases to 5000mg.

Overall, the value of 5g in mg is 5000mg. This is because 1g is equal to 1000mg, and the prefix 'milli' is multiplied by the base unit of grams, resulting in a value of 5000mg.

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Look at pic for info

40) Given the information in the figure shown, what is the measure of "angle m" in triangle PQR?
P
68
R
111

Oa.) 45 degrees
Ob.) 179 degrees
Oc.) 44 degrees
Od.) 43 degrees

Answers

The measure of angle m is,

⇒ m = 43°

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle PQR is shown in figure.

Now, We know that;

An exterior angle of a triangle is sum of two opposite angle of that triangle.

⇒ m + 68° = 111°

Solve for m;

⇒ m = 111° - 68°

⇒ m = 43°

Thus, The measure of angle m is,

⇒ m = 43°

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In the U.S., shoe sizes are defined differently for men and women, but in Europe, both genders use the same shoe size scale. The accompanying histograrn shows the European shoe sizes of 269 male and female college students, converted from their reported U.S. shoe sizes. a) Describe the shape. b) How many modes does the histogram have? What might explain that?

Answers

the shape is bimodal and symmetric and  histogram have 38 to 40 and 44 to 46.

If the two peaks are mirror reflections of one another, the bimodal distribution may be symmetrical. symmetrical Cauchy distributions exist. These are not likely to be found in basic statistics. These distributions belong to a family where the anticipated value is hypothetical. the long tails of the logistic distribution. If the data is symmetric but contains more extreme values than one would anticipate from a normal distribution, the logistic and Cauchy distributions are utilized. these different distribution types. It is symmetric for the uniform distribution. Since the odds are same at every location, the distribution is essentially a straight line. The distribution is bimodal and nearly symmetric. There are two modes in the distribution, from 38 to 40 and 44 to 46. The existence of data for both men and women may account for this. Women may prefer the lower mode, whereas males may prefer the upper.

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What does t-test assuming equal variances mean?

Answers

The t-test assuming equal variances means Pooled t-test in which variances of the two sample populations are equal.

The pooled t-test is the statistical procedure that assumes that population variances are equal. Finding a weighted average of the two independent sample variances is referred to as pooling. By combining data from samples from populations 1 and 2, we may estimate the common variance when there is solid evidence that population 1's variance is equal to population 2's variance.

Compare the ratio of the two sample standard deviations as a quick way to verify this. The ratio would be compared as: S1/S2. The ratio would be 1, or, in the event that the two are equal.

However, we cannot anticipate the ratio to be exactly 1, as they are samples and as a result, there will be some errors. Thus, the pooled t-test implies whether the null-hypothesis should be accepted or rejected.

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Given f(x) = 2x - 1, find the value of f(-1).

Answers

To find the value of f(-1), we simply need to substitute -1 for x in the function f(x) = 2x - 1 and evaluate:

f(-1) = 2(-1) - 1

= -2 - 1

= -3

Therefore, the value of f(-1) is -3.

Answer:

f=2x-1/x

Step-by-step explanation:

I hope this helps :) <3

Anita uses one sheet of paper to make a calendar showing each month of the year. Draw Anita’s calendar. Show how she can divide her calendar so that each month is given the same space. What fraction of the calendar does each month receive

Answers

The requried, each month receives 1/12 of the calendar or about 8.33% of the total space.

What is the fraction?

A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers.

Here,
Anita can start by drawing a large rectangle on the paper to represent the entire year. Then, she can divide the rectangle into 12 equal parts, each representing a month. One way to do this is to draw four vertical lines to divide the rectangle into five equal columns, and then draw three horizontal lines to divide each column into four equal rows.

Each of the 12 parts represents 1/12 or one-twelfth of the calendar. Therefore, each month receives 1/12 of the calendar, or about 8.33% of the total space.

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Millie is considering a zero closing cost loan. She wants to borrow $600,000 her lending institution is offering her a 3.49% loan for 25 years. She has the option of purchasing negative points, which will increase her apr by 0.125% for each 1% of her principal credited to her. To cover the bank's closing cost she will need to get 2 negative points. Determine Millie's breakeven time. Is this purchase of negative points a wise decision? Explain.

Answers

Breakeven's time is 31.7 years.

The loan term is only 25 years, so it is not a wise decision.

What is a percentage?

The percentage means the required value out of 100.

It is calculated by dividing the required value by the total value and multiplying it by 100.

The percentage change is also calculated using the same method.

In percentage change, we find the difference between the values given.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

To determine if the purchase of negative points is a wise decision, we first need to calculate Millie's monthly payment with and without the negative points.

Without negative points:

Principal = $600,000

Interest rate = 3.49%

Loan term = 25 years or 300 months

Now,

Monthly Payment = $2,967.27

With negative points:

Millie needs to purchase 2 negative points to cover the bank's closing cost. Each negative point will increase her APR by 0.125%, so the new interest rate will be:

New interest rate.

= 3.49% + (2 x 0.125%)

= 3.49/100 + (2 x 0.125/100)

= 3.74%

Monthly Payment = $2,998.84

The breakeven time.

This is the amount of time it takes for the cost of the negative points to be offset by the savings in monthly payments.

The total cost of the negative points.

We see that,

Each negative point costs 1% of the principal.

Cost of negative points,

= 2 x $6,000

= $12,000

The breakeven time.

Monthly savings.

= $2,967.27 - $2,998.84

= -$31.57

i.e

The value is negative because the new monthly payment is higher.

So,

Breakeven time.

= $12,000 ÷ -$31.57

= 380.2 months

This is,

1 year = 12 months

so,

31.7 years

Thus,

Breakeven's time is 31.7 years.

The loan term is only 25 years, so it does not make sense to purchase the negative points.

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in what time will the simple interest on Rs7560 be Rs1102.50 at 25/4% per annum

Answers

The amount of time in which the simple interest on Rs7560 be Rs1102.50 at 25/4% per annum, 5 years

What is simple interest?

Simple interest is an amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider: principal amount(P), rate(R) and time(T).

Every time we calculate simple interest the principal values will be the same unlike compound interest.

Formula;    Simple Interest(I) =  P × R × T/100

To find the time it takes for the simple interest on Rs. 7560 to be Rs. 1102.50 at 25/4% per annum, we can use the formula for simple interest:

We are given I = 1102.50 and P = 7560, and the interest rate is 25/4% per annum, which we can convert to a decimal:

r = 25/4% ÷ 100

 = 0.25/4

 = 0.0625

Now, we can substitute the known values into the formula and solve for t:

1102.50 = 7560 x r x t

1102.50 / 7560 = r x t

t = 1102.50 / (7560 x 0.0625)

t = 5 years

So, it will take 5 years for the simple interest on Rs. 7560 to be Rs. 1102.50 at 25/4% per annum.

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a person is standing exactly 36 ft from a telephone pole there is a 30 degree angle of elevation from the ground to the top of the pole. what is the height of the pole

Answers

Answer:

Therefore, the height of the pole is approximately 20.79 feet.

Step-by-step explanation:

the person is standing at point A, which is 36 ft away from the base of the telephone pole. The angle of elevation from the ground to the top of the pole is 30 degrees. We want to find the height of the pole, which is represented by "h" in the diagram.

To solve for "h", we can use the tangent function, which relates the opposite side (height) to the adjacent side (distance from the pole to the person) of a right triangle:

tan(30°) = h / 36

We can solve for "h" by multiplying both sides by 36 and taking the tangent of 30 degrees:

h = 36 * tan(30°)

h = 36 * 0.5774 (rounded to four decimal places)

h ≈ 20.79

Therefore, the height of the pole is approximately 20.79 feet.

Answer:

20.78460969082652752232935609807

Step-by-step explanation:

;)

1. A slide is 15 ft. high. If the slides makes a 50° angle with theground, how long is the slide?

Answers

The approximate measure of the slide is 20 feet.

What are heights and distances?

Heights and Distances is a study about the applications of Trigonometry. It has many real-life applications, such as measuring the object’s height, depth of the object, the distance between two celestial objects etc. The formulas and the ratios of trigonometry are helpful in the study of heights and distances.

Given that, a slide is 15 feet high and the slides makes a 50° angle with the ground.

Let the length of the slide be x.

Now, sin50° =15/x

0.766=15/x

x=15/0.766

x=19.58

≈ 20 feet

Therefore, the approximate measure of the slide is 20 feet.

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1. draw the graphs of:
a. g(x) = -4x - 5

b. h(x) = - 4x - 12

c. j(x)= -4x -15

2. Write an equation for the linear function with a gradient of - 4 and an
unknown y-intercept of k.

Answers

1. a. The graph for the g(x) = -4x - 5 is mentioned in the image below.

1. b. The graph for the h(x) = - 4x - 12 is mentioned in the image below.

1. c. The graph for the j(x)= -4x -15 is mentioned in the image below.

2. The equation for the linear function with a gradient of - 4 and an unknown y-intercept of k is y = -4x + k.

What is slope intercept form?

A slope-intercept form is an equation that represents a straight line and is written as y = mx + c, where m is the gradient and c is the y-intercept. If c becomes zero, it passes through the origin.

1. a.

The function g(x) = -4x - 5 represents a straight line that has a slope of -4 and a y-intercept of -5.

When x = 0, g(x) = -5. The point is (0,-5).

When x = 1, g(x) = -9. The point is (1,-9).

When x = -1, g(x) = -1. The point is (-1,-1).

The graph of the function is given below.

1. b.

The function h(x) = -4x - 12 represents a straight line that has a slope of -4 and a y-intercept of -12.

When x = 0, h(x) = -12. The point is (0,-12).

When x = 1, h(x) = -16. The point is (1,-16).

When x = -1, h(x) = -8. The point is (-1,-8).

The graph of the function is given below.

1. c.

The function j(x) = -4x - 15 represents a straight line that has a slope of -4 and a y-intercept of -15.

When x = 0, j(x) = -15. The point is (0,-15).

When x = 1, j(x) = -15. The point is (1,-19).

When x = -1, j(x) = -11. The point is (-1,-1).

The graph of the function is given below.

2.

The slope-intercept form of a line is y = mx + c. On substituting m = -4 and c = k into the equation, it gets reduced to y = -4x + k.

Therefore, the obtained answer is y = -4x +k.

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