The zeros of a quadratic function are 1 and 7. To which factored quadratic expression is this function related?

Answer:

✅The table can be represented by the equation, [tex] y = 4x + 4 [/tex]

✅The relation is a function.

✅The graph of the function is linear.

Step-by-step explanation:

✍️The first statement: The table can be represented by the equation, [tex] y = 4x + 4 [/tex].

To check if the first statement is correct let's find the equation that can represent the table by finding the slope (m) and y-intercept (b).

Using two pairs, (1, 8) and (2, 12),

Slope = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 8}{2 - 1} = \frac{4}{1} = 4 [/tex].

Substitute, x = 1, y = 8, and m = 4 into y = mx + b to solve for b.

Thus:

8 = (4)(1) + b

8 = 4 + b

Subtract 4 from each side

8 - 4 = b

4 = b

Plug in the values of b and m into y = mx + b.

Thus, the equation that represents the table would be:

[tex] y = 4x + 4 [/tex].

✅Therefore, the first statement is correct.

✍️The second statement: The graph of the function is non-linear.

This is NOT TRUE because the equation of the function, [tex] y = 4x + 4 [/tex], represents the equation of a linear graph in the slope-intercept form. When graphed, it will give us a straight line.

✍️The Third statement: The relation is a function.

This is TRUE because each input value (x-value) has exactly one output value (y-value).

✍️The Fourth statement: The rate of change is NOT constant.

This standby is NOT TRUE.

The rate of change is the slope (m) that we have calculated above to be 4. Between any two pairs, the rate of change remains 4.

Therefore, this statement is not correct.

✍️The Fifth statement: The graph of the function is linear.

This is TRUE. As stated earlier, from the equation generated, it is safe to say that the equation represents graph of a linear function. The graph will be a straight line graph.

The true statements are:

(a) The equation of the function

Start by calculating the slope (m)

[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 -x_1}}[/tex]

So, we have:

[tex]\mathbf{m = \frac{12 - 8}{2 -1}}[/tex]

[tex]\mathbf{m = 4}[/tex]

The equation is then calculated as:

[tex]\mathbf{y = m(x -x_1) + y_1}[/tex]

So, we have:

[tex]\mathbf{y = 4(x -1) + 8}[/tex]

[tex]\mathbf{y = 4x -4 + 8}[/tex]

[tex]\mathbf{y = 4x +4}[/tex]

Hence, this statement is true

(b) The graph is nonlinear

Because of (a) above, the graph is linear

Hence, this statement is false

(c) The relation is a function

A linear relation is a function

Hence, this statement is true

(d) The rate of change is not constant

Because of (a) above, the rate of change is constant

Hence, this statement is false

(e) The graph is linear

Because of (a) above, the graph is linear

Hence, this statement is true

Read more about linear relations at:

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Answer:

2(x+y)

Step-by-step explanation:

Step-by-step explanation:

multiply both the variable

BEING CAREFUL WHILE USING THE INTERNET

Answer:

Answer:

Happy to help!

Answer:

C

Step-by-step explanation:

Answer:  3. Distributive

Step-by-step explanation:

3(x -2y) = 3x - 6y   To get from  left to rigth, you have to multiply them which is the same as distribitue.

3(x) - 3(2y) = 3x - 6y

18. Perimeter of rectangle = 2(l + b)

l = 16m

b = 12m

Perimeter of rectangular park = 2 (12 + 16)

= 24 + 32

= 56m

Perimeter of square park = 56m

(given that, perimeter of rectangular and square park are equal)

Perimeter of square = 4a

4a = 56

a = 56/4

a = 14m

Area of square park = a²

= 14²

= 196m²

Answer:

n = 6, a = 5, b = 60

Step-by-step explanation:

In a binomial function (a + b)ⁿ expression that represents the terms,

(a + b)ⁿ = [tex]\sum_{k=0}^{n}\binom{n}{k}a^{n-k}b^k[/tex]

By this formula,

1st term = [tex]\binom{n}{0}a^{n-0}b^0[/tex] = aⁿ

2nd term = [tex]\binom{n}{1}a^{n-1}b^1[/tex] = [tex]n.a^{n-1}b^1[/tex]

3rd term = [tex]\binom{n}{2}a^{n-2}b^2[/tex] = [tex]\frac{n(n-1)}{2}.a^{n-2}.b^2[/tex]

For the binomial expansion initial 3 terms of (2 - ax)ⁿ = 64 - 16bx + 100bx²

Terms of (2 - ax)ⁿ = [tex]2^n+n(2)^{n-1}(-ax)+\frac{n(n-1)}{2}(2)^{n-2}(-ax)^2[/tex]

                             = [tex]2^n-n(2)^{n-1}(ax)+n(n-1)(2)^{n-3}(a^2x^2)[/tex]

Comparing the terms of both the expansions,

1st term

2ⁿ = 64

2ⁿ = 2⁶

n = 6

2d term

[tex]n(2)^{n-1}(ax)=16bx[/tex]

[tex]6(2)^{6-1}(a)=16b[/tex]

192a = 16b

b = 12a -----(1)

3rd term

[tex]n(n-1)2^{n-3}(a^2x^2)=100bx^2[/tex]

[tex]6(6-1)2^{(6-3)}(a^2)=100b[/tex]

[tex]30(2)^3(a^2)=100b[/tex]

240a² = 100b

b = 2.4a² -----(2)

From equation (1) and (2),

b = 12a = 2.4a²

a = [tex]\frac{12}{2.4}=5[/tex]

From equation (1)

b = 12a = 60

Therefore, n = 6, a = 5, b = 60

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

If there are 1500 total students.

75% or 1125 are boys

25% or 375 are girls.

Answer:

13 and 5

Step-by-step explanation:

x+y=18

x-y=8

_____

2x=26

x=13

So the first number must be 13

13+y=18

y=5

And the second number must be 5

When we write out the system of equations, we will get:

x+y=18

x-y=8

 We can then use elimination to get just one variable.

 x+y=18

+x-y=  8

 Which gives us:   2x=26

 We then divide by 2 and get:    x=13

 We next plug that into one of the two equations and solve for the other variable:    (13)+y=18

We subtract 13 from both sides and get:   y=5

So the two numbers are 13 and 5.

~ I hope this helped, and I would appreciate Brainliest. ♡ ~ ( I request this to all the lengthy answers I give ! )

Answer:

g(4)=7

Step-by-step explanation:

1/2(4) = 2

2+5 = 7

g(4)=7

Answer:

y= - 13/15x + 6/5

Step-by-step explanation:

Answer:

X = 1

Step-by-step explanation:

HOPE THIS HELPS

am i answering the same question over and over again?

whatever

PLZ MARK BRAINLIEST

-14 is right after -15

-3 is the 3rd point left of 0

-8 is the 8th point left of 0

Answer:

40 customers

Step-by-step explanation:

Trimming = 1/4 hours

Styling = 1/6 hours

Working hours per day = 3 1/3 hours

Working days per week = 5

Total work time per week :

3 1/3 * 5 = 10/3 * 5 = 50 / 3 hours

Time taken for styling and trimming :

1/4 + 1/6 = (3 + 2) / 12 = 5/12

Number of appointments stylist can schedule each week :

Total work time / time taken per person

(50 / 3) ÷ (5 / 12)

(50 /3) * (12 /5)

(50 * 12) / (3 * 5)

= 600 / 15

= 40

Answer:

0.25

Step-by-step explanation:

Following the law of segregation which states that only one of the two gene copies noticeable in an organism is diffused to each gamete (egg or sperm cell) and gene allocation is random.

A heterozygous gene for Q = Qq

If these two individuals mate and produce gametes by meiosis,

The probability that both the egg and sperm will carry the recessive allele is determined as follows:

Qq    ×    Qq

             Q              q

Q           QQ          Qq

q            Qq            qq

The probability that both the egg and sperm will carry the recessive allele qq is 25% or 0.25

Answer:

f(x) = [tex]-\frac{1}{4}[/tex] x - 2

Step-by-step explanation:

Slope of the line: m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )

f(x) = mx + b (b - is y-intercept)

(0, - 2) Coordinates of y-intercept

(4, - 3)

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

f(x) = [tex]-\frac{1}{4}[/tex] x - 2

9514 1404 393

Answer:

Step-by-step explanation:

The end result after the final transformation is ...

  (x, y) ⇒ (-x, y)

so, each x-coordinate is negated. The transformed coordinates are ...

  S(-5, -3) ⇒ S''(5, -3)

  T(-1, 0) ⇒ T''(1, 0)

  U(-4, 1) ⇒ U''(4, 1)

  V(-4, 0) ⇒ V''(4, 0)

Answer:

-3/2

Step-by-step explanation:

You can do this using slope formula, y2-y1/x2-x1.

We first substitute in the numbers--> -2 - 13/ 6 - (-4)

Then we simplify to get--> -15/10 = -3/2

You could also graph the points and find the rise over run.

Hope this helps!

Answer:

The answer is 6.454

mark brainliest,

Answer:0.9

Step-by-step explanation:

The speed of an object is defined as the ratio of distance travelled by it to the time taken. It will take a person 0.9 hours to walk end and back .

Speed is the ratio of distance and time. It is a measure of how fast or slow an object is moving. A high speed object takes less time to travel the same distance as compared to a low speed object.

Given length of island is 2.7 miles.

Speed of the person is 6 mph.

Thus total length for travelling end and back  2.7 + 2.7 =5.4 miles.

Time taken = distance/speed

Therefore, time taken by the person is given as, time is 5.4/6 = 0.9 hours.

Hence, the person will have to take 0.9 hours to walk island end and back.

To learn more about speed click on the following link

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Answer:

scalene obtuse

Step-by-step explanation:

all sides are different and it has an angle 90 or greater

Answer:

Scalene obtuse I guess?

Answer:

slope(m)=-1

Step-by-step explanation:

let the point (8,8) and (12,12) be ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2} , y_{2}[/tex])

slope of point([tex]m_{1}[/tex])=[tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

                             =(12-8)/(12-8)

                            =1

let the slope of perpendicular line to given point be [tex]m_{2}[/tex]

now ,

    [tex]m_{1} m_{2}[/tex]=-1

  so [tex]m_{2}[/tex]=-1