A function f(x) is defined to be f(x) = X^2 -3x +21 .

What are the solutions to the equation f(x)=0?

Answer:

2y = x + 2

Step-by-step explanation:

Looking at the graph, we can see from one point to the next (from right to left), the x-value rises by 2 and the y-value by 1;

From this we can work out the gradient between two points using the formula, i.e. the change/difference in y divided by the change/difference in x:

[tex]m = \frac{dy}{dx} = \frac{1}{2}[/tex]

Joining the points gives a straight line, which means a constant gradient of ¹/₂

Use the line equation formula to get the function:

y - y₁ = m(x - x₁)

m = ¹/₂

x₁ = 0

y₁ = 1

y - 1 = ¹/₂.(x - 0)

y - 1 = ¹/₂.x

2y - 2 = x

2y = x + 2

Answer:

I think that removing (1, 3) would make the most sense

Answer:

(1,3)

Step-by-step explanation:

Because (1,-2) and (1,3) have the same x value, they do not pass verticle line test, so it is not a function.

Answer:

Albert needs 32 cars to wash to reach his goal.

Step-by-step explanation:

We know that the slope-intercept form of a linear function is

[tex]y = mx+b[/tex]

where m is the slope or rate of change and b is the y-intercept

It is stated that Albert needs $133 to buy a new hard drive.

As earns $4.75 for each car he washes. Thus, $4.75 the rate of change or slope will be.

As he spends $19 on supplies. Since it is an expense, so -19 is basically the y-intercept 'b'.

Let 'x' be the number of cars he needs to wash to reach his goal.

Thus, substituting the value m = 4.75, y = 133, and b=-19 in the slope-intercept form of a linear function

y = mx+b

133 = 4.75x - 19

133+19 = 4.75x

152 = 4.75x

x = 152 / 4.75

x = 32

Therefore, Albert needs 32 cars to wash to reach his goal.

Answer:

The addition expression that represents the situation is;

175 + 100 + 100 - 55 -55

Step-by-step explanation:

Here, we want to write an addition expression to represent the situation

While the deposits are considered positive, the withdrawals are considered negative

So the addition expression will be;

175 + 100 + 100 - 55 - 55

Answer:

5.5 quotient 5 and rest 1

But I would answer quotient is 5 and half

Step-by-step explanation:

11/3 ÷ 2/3 = 11/3 * 3/2 = 11/2= 5.5

So the quotient is 5 and rest is 1

Hope this helps, have a good day

Answer:

5 1/2

Step-by-step explanation:

11/3÷2/3

Applying the fractions formula for division,

=11/3×3/2

=33/6

Simplifying 33/6, the answer is

=5 1/2

Answer:

Q is -7

Step-by-step explanation:

Q×2+5=x

Q-2=x

Q=-7

Answer:

14

Step-by-step explanation:

If you divide -28 and -2, you get 14 which is the constant of proportionality. You can try to multiply -4 and 14 to check which you get -56. The graph shows that and it's the correct answer!

Answer:

21

Step-by-step explanation:

Answer:

4x_2y=5

4x=5+2y

x=5+2y/5

now, y=3x_1

putting value of x in second question

In this way you can do

Answer:d

Step-by-step explanation: tufryvztgv

Answer:

65

Step-by-step explanation:

Answer:

The bag costs 1500, while the umbrella cost 500

Step-by-step explanation:

Let the cost of the bag be b and the cost of the umbrella be u

Total cost is;

b + u = 2,000 •••••(i)

From the second part of the question;

b = 5u-1000 ••••••(ii)

Substitute ii into i

5u-1000 + u = 2000

6u = 2000 + 1000

6u = 3000

u = 3000/6

u = 500

To get b, substitute the value of u into equation ii

b = 5(500)-1000

b = 2500-1000

b = 1500

Answer:

0.25 or 1/4

Step-by-step explanation:

easy - 3250 pounds divided by 13000 students

everyone will get 0.25 or 1/4 of a pound of chicken

hope this helps!!

Have a nice day!

Answer:

a = b = 40°

Step-by-step explanation:

∠ a and 140° are adjacent and are supplementary , thus

a = 180° - 140° = 40°

a and b are alternate angles and are congruent, thus

b = a = 40°

Answer:

b=40 okkkkllllllkkkkkkkkkkkkkkkkkkkkkllllllkkkk

Answer:

the answer is table B

Step-by-step explanation:

Answer:

Table B shows a proportional relationship

Explanation:

In a proportional relationship two quantities vary directly with each other.

So,

y ∝ x

y = kx

Where, k is the constant of variation.

The ordered pairs of table A are (-2,2), (-1,3), (0,0) and (1,5).

From these ordered pairs we can conclude that the value of y-coordinate is not changing according to the x-coordinate because the values of x increased by 1 for each ordered pair but the value of y is not increasing in the same proportion..

The ordered pairs of table B are (-1,-3), (0,0), (1,3) and (2,6). The value of y increasing at a constant rate 3 and the value of y-coordinate is 3 times of x-coordinate.

Choose any two ordered pairs of table B. Let the two points are (0,0) and (1,3).

The proportional relationship is defined as

y = 3x

Therefore, 3 is the constant of variation and rate of change.

So, Table B shows a proportional relationship.

Answer:

4

Step-by-step explanation:

Answer:

18%

Step-by-step explanation:

Subtract $10.50 from $12.30 and you will get 1.8.

Then divide 1.8 to 100 (because 100% = total) and you will get 0.018 which means 18%. Her hourly wage increased by 18%.

Answer:

[tex] - \frac{4}{5} [/tex]

Step-by-step explanation:

Please see the attached picture.

[tex]slope \\ = \frac{1 - ( - 3)}{ - 3 - 2} \\ = \frac{1 + 3}{ - 5} \\ = - \frac{4}{5} [/tex]

☆In the gradient formula,

(x1, y1) is the first coordinate and (x2, y2) is the second coordinate.

Answer:

1/14(the first one)

Step-by-step explanation:

Answer:

[tex]Measurement = 0.75ft[/tex]

Step-by-step explanation:

See attachment for complete question

Method 1:

Considering the width and length of the quilt

Given

[tex]Number\ of\ squares = 24[/tex]

Required

Determine the dimension of 1 square

The width of the quilt is 4.5ft and there are 6 squares in that dimension.

Each measurement is calculated as thus:

[tex]Measurement = \frac{4.5ft}{6}[/tex]

[tex]Measurement = 0.75ft[/tex]

Or

The length of the quilt is 3ft and there are 4 squares in that dimension.

Each measurement is calculated as thus:

[tex]Measurement = \frac{3ft}{4}[/tex]

[tex]Measurement = 0.75ft[/tex]

Method 2:

Calculate the area of the quilt.

[tex]Area = 4.5ft * 3ft[/tex]

[tex]Area = 13.5ft^2[/tex]

The area of 1 of the 24 squares is calculated by dividing the total area by number of squares

[tex]Area = \frac{13.5ft^2}{24}[/tex]

[tex]Area = 0.5625\ ft^2[/tex]

Represent the dimension of individual square with L

Area of a square is:

[tex]Area = L * L[/tex]

This gives:

[tex]L * L = 0.5625[/tex]

[tex]L^2 = 0.5625[/tex]

Take square root of both sides

[tex]L = \sqrt{0.5625[/tex]

[tex]L = 0.75ft[/tex]

Hence, the dimension of each square is 0.75ft

Answer:

4

Step-by-step explanation:

2.50/5=0.5

0.5*8=4

Answer:

3 5

Step-by-step explanation:

It just is trust

Answer:

A. because both variables (y and x) cancel each other out because they are equal. The answer to A is 0=6, which is clearly not true. All other choices have a solution that is possible, because at least 1 of the variables doesn't cancel itself out.

Answer:

[tex]m=\frac{1}{2}[/tex]

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Point (-1, 4)

Point (5, 7)

Step 2: Find slope m

Answer:

x = 2.825

Step-by-step explanation:

-4.3(6.3x + -4.18) = -58.56

-4.3(-4.18 + 6.3x) = -58.56

(-4.18 * -4.3 + 6.3x * -4.3) = -58.56

(17.974 + -27.09x) = -58.56

17.974 + -27.09x = -58.56

17.974 + -17.974 + -27.09x = -58.56 + -17.974

0.000 + -27.09x = -58.56 + -17.974

-27.09x = -58.56 + -17.974

-27.09x = -76.534

x = 2.825175341