Slope =
y-intercept = (0,

The linear function f with f (- 1/2) = 1 and f (0) = -4 would be ; y = -5x -4.

Linear equation is equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c

Linear equation with two variables, when graphed on cartesian plane with axes of those variables, give a straight line.

We are asked to write the linear function f with f (- 1/2) = 1 and f (0) = -4

Let the equation in variable x and y can be written in the form y = mx + c

So f (- 1/2) = 1

this gives, 1 = -1/2m+c      -----------eq 1

Also f (0) = -4

This gives -4 = c.            --------------eq2

Now Putting value of c in equation in eq1 we get m=0.

So 1 = -1/2m+c  

1 = -1/2m - 4

m = -5

Then we get;

y = -5x -4.

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Solution

Since the diagram given is a Triangle, therefore, the sum of it's interior angles is 180 degrees

However, the Triangle is a right angle Triangle since on of its angles is 90 degrees.

The sum of its Interior angles is given by;

subtracting 142 from both sides,

Therefore, z = 38

To make a plot of the data you first must choose your axis. In this case we've chosen the X axis to be the average cost of the jeans and the Y axis to be the number of copies sold. To graph the data we match the information we're given in the table as shown in the drawing.

First step: Simplify everything

[tex]2(10-a) + 4a + 4a+7 = 48[/tex]

Next: Distribute required values

[tex]20-2a+4a+4a+7=48[/tex]

Next: Time to add like terms

[tex]6a = 21[/tex]

Final Step: Divide 6 on both sides to isolate variable

[tex]a = \frac{21}{6}[/tex]

Thus, the value "a" = [tex]\frac{21}{6}[/tex]

Hope this helps :)

The standard form of a linear equation in two variables is given by the expresssion:

So, rewriting the equation:

y-10=2x-16

y-2x=-16+10

y-2x=-6

2x-y=6

Okay, here we have this:

Considering that a real number is said to be irrational if it cannot be expressed as a quotient of whole numbers. ✓2 is an irrational number, and as all the irrational number are real numbers ✓2 is also a real number.

Answer:

Explanation:

We were given the following information:

This is a normal distribution curve

Mean = 53

Standard deviation = 9

We are to find the area right of x = 71

This is calculated as shown below:

We will proceed to plot this on a graph as sown below:

The area to the right of x = 71 (highlighted in red above) is given by using a Standard z-score table:

Therefore, the area that lies to the right of x = 71 is 0.0228 or 2.28%

ANSWER

x = 5 and x = -7

EXPLANATION

We want to solve the equation by factoring.

The equation is:

First, there is a greatest common factor that we can use to simplify the equation. That is -2, so, first we divide through by -2.

It becomes:

Now, factorise:

We were told that volume of water that flows over the fall each second is 2.9 x 10^5 gallons.

Recall, 1 hour = 3600 seconds

If 1 second = 2.9 x 10^5 gallons, then

3600 seconds = 3600 x 2.9 x 10^5

= 1.044 x 10^9 gallons

Thus, 1.044 x 10^9 gallons of water will flow over the falls in an hour.

y - 6 = - 5/2 (x + 4)

To write in slope-intercept form means to write in the form;

y= mx + b

where m is the slope and b is the intercept

y - 6 = - 5/2 (x + 4)

open the parenthesis

y - 6 = -5/2 x - 10

add 6 to both-side of the equation

y = - 5/2 x - 10 + 6

y = -5/2 x - 4

Next is to check whether 5y = 2x + 6 is perpendicular to the above

To do that, we have to make the equation to be in the form y=mx+ b

5y = 2x + 6

Divid through by 5

y = 2/5 x + 6/5

The slope of perpendicular equation, when multiply gives minus one (-1)

The slope of the first equation = -5/2

The slope of the second equation is 2/5

Multiplying the two slopes;

(-5/2) (2/5) = -1

Hence the lines are perpendicular

The formula to calculate compound interest is given to be:

where:

The following parameters are given in the question:

We can substitute these values into the formula to calculate the final amount as follows:

Solving, we get:

The amount after 17 years is $154,577.64

Answer:

  y = 4/9x +10/3

Step-by-step explanation:

You want the slope-intercept equation of the line through point (-3, 2) that is perpendicular to the line y = -9/4x +1.

The slope-intercept form of the equation for a line is ...

  y = mx + b . . . . . . m is the slope, b is the y-intercept

In order to write the desired equation, we need to know the desired slope and the y-intercept that makes the line go through the given point.

The slope of the perpendicular line is the opposite reciprocal of the slope of the given line. The given line equation is in slope-intercept form, so the coefficient of x is the slope of it: -9/4.

The slope of the perpendicular line is the opposite reciprocal of this:

  m = -1/(-9/4) = 4/9

Solving the slope-intercept form equation for b, we find ...

  b = y - mx

Using the values of x and y for the given point, and the slope we just found, we have ...

  b = 2 -(4/9)(-3) = 2 +4/3 = 10/3

The slope-intercept equation for a line with slope 4/9 and y-intercept 2/3 is ...

  y = 4/9x +10/3

__

Additional comment

It can also be useful to start from the point-slope equation:

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

Your line is ...

  y -2 = 4/9(x +3) . . . . . . use m=opposite reciprocal of -9/4; (h, k) = (-3, 2)

  y = 4/9x +(4/9)(3) +2 = 4/9x +10/3 . . . . . . add 2 and simplify

Answer

Algebraic equation that shows the relationship is

P = 20S

Explanation

Number of college professors = P

Number of students = S

There are 20 times as many students as professors.

P = (S) (20)

P = 20S

Hope this Helps!!!

In order to write an inequality we can read the original statement in small parts.

In this case, the statement is:

"the product of c and 9 is greater than 16"

We have that "the product" is a multiplication

Then, "the product of c and 9" is the multiplication between c and 9:

9 · c

And, "the product of c and 9 is greater than 16" means that 9 · c is greater than 16:

9 · c > 16

The amount of fiber in the banana is 2.9 grams of fiber.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

From the. information, she has raisin bran cereal, which contains 3.8 grams of fiber and in all, Leslie eats 6.7 grams of fiber at breakfast.

Let the fiber in banana be b. This will be illustrated as:

b + 3.8 = 6.7

Collect like terms

b = 6.7 - 3.8

b.= 2.9

The fiber is 2.9 grams

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Given:

Dimensions and weight of a solid is given.

Height (h) of a cylinder (in cm) =

Radius (r) of a cylinder (in cm) =

Mass (m) of solid (in grams)=

Density of several elements is given.

Cobalt=8.86, Copper=8.96, Gold=19.3, Iron=7.87, Lead 11.3, Platinum=21.5, Silver=10.5, Nickel=8.90.

Required:

What element is the solid made up of.

Answer:

Let us find the volume (V) of cylinder (in cubic cm).

Using formula of density (D), we get,

Hence, the density of the solid is 7.87 grams per cubic cm.

From the given information of density of several elements, we see that the solid is made up of Iron.

Final Answer:

The solid is made up of Iron.

Answer:

• Plan B, by $4

• 140 minutes

Explanation:

Part A

From the graph, at 40 minutes, the costs of the plans are:

• Plan A: $4

• Plan B: $8

Plan B costs more by $4.

Part B

The point where the costs are the same is the time at which the two graphs intersect.

When the number of minutes = 140 minutes

• Cost of Plan A = $14

• Cost of Plan B = $14

Thus, the two plans cost the same for 140 minutes of long-distance call.

• If the time spent is less than this amount, Plan B costs more.

Since x is the larger number and y is the smaller number

Since their sum is 56

That means add x and y then equate them by 56

Since the difference between them is 28

That means subtract y from x and equate the answer by 28

Look at the answer to find the correct answer

It is B

x - y = 28 and x + y = 56

Answer:

Step-by-step explanation:

To know the price to

Answer:

P = 0.04

Explanation:

The probability is equal to the number of options where the first spinner is landing on the color pink and the second spinner is landing on the number 5 divided by the total number of options.

Since there is only one option that satisfies the condition P5 and there are 25 possible outcomes, the probability is:

So, the answer is P = 0.04

Answer:

6

Explanation:

First, we find the squares of 5 and 6.

We conclude therefore that the square root of 31 is closer to 6 since it has a smaller difference.

The dotted plot representing how much a customer spends in a store from the attached diagram is Option D.

Step 1: Write out the frequency distribution of the population in tabular form

x | f

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

5 | 17

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

| 17

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

Using mathematical operations we know that total tickets of 2 children ($31.9) and 7 adults ($306.95) were purchased which cost the total amount of $338.85.

So, a number of adults and children who purchased the tickets:

Now, the equation can be:

Now, the second equation will be:

43.85a + 15.95c = 338.85

Now, substitute a = 9 - c in equation (2) as follows:

Hence:

Then:

Therefore, using mathematical operations we know that total tickets of 2 children ($31.9) and 7 adults ($306.95) were purchased which cost the total amount of $338.85.

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Suppose the given coordinates are represented as,

Then, the formula for slope can be expressed as,

Solving it,

The slope is 1.5.

The formula of (10, 8) anjd (-5,8) is

The equation is represented by:

0.5 + 10b + 4 = 19.5

In which 19.5 is the total weight of the box and it's contents.

0.5 is the weight of the cardboard box.

4 is the weight of the jar of peanut butter.

10b is the weight of all loaves of bread.

And b is the weight of a single loaf of bread

The answer is:

The solution of the equation, which is the value of b, represents the weight of a single loaf of bread.

Answer:

The range of values of x for which the function is < 0 is:

2<x<3.

Step-by-step explanation:

x²-5x+6<0

First find the critical points:

x^2 - 5x + 6 = 0

(x - 2)(x - 3) = 0.

x = 2, 3.

The critical points are 2 and 3.

Make a table of values:

x                      x<2      2<x<3          x >3

x -2                  < 0          >0             >0

x -3                   <0           <0             >0

(x - 2)(x - 3)       >0          <0             >0

Answer:

The answer is C.

Step-by-step explanation:

In order to solve this, you must use an inequality from one side of the equation.

Inequality is the growing inequality between rich and poor.

First thing you do is divide by 4 from both sides.

[tex]\sf{\dfrac{4x}{4} > \dfrac{-8}{4}}[/tex]

Solve.

Divide these numbers goes from left to right.

-8/4=-2

[tex]\boxed{\sf{x > -2}}[/tex]

Therefore, the graph represents the solution set of the inequality of 4x>-8 is C, which is our answer.

I hope this helps, let me know if you have any questions.

The correct answer is  A. 90 - d

Since the sum of all the angles in a triangle is 180° and one of the angle is 90° because the triangle is a right triangle. So the sum of the remaining angles is 90°.

And to find the other acute angle we use 90° - d.

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Given the modulus function expressed as:

Since the function is a modulus function, the dependent variables "y" will all be a positive value

Using the values of x to be -5, 8, and 13 to determine the ordered pairs

When x = -5

y = |-5 - 8|

y = |-13|

y = 13

The first ordered pair will be (-5, 13)

If x = 8

y = |8 - 8|

y = |0|

y = 0

The second ordered pair will be (8, 0)

If x = 13

y = |13 - 8|

y = |5|

y = 5

The third ordered pair will be at (13, 5)

The graph of the function is as shown below: