QUESTION 3 (3 points)
Convert the following quadratic into standard form. Show all work.
f(x) = 3(x - 5)² - 40​

Answer:

8.9

Step-by-step explanation:

Use Pemdas or Bedmas ( Brackets, Exponents, Division, Multiplication, Addition, Subtraction.

First add 4.5 and 7.6, you get 12.1

Now do the division, 8/2.5 = 3.2

Lastly you subtract, 12.1-3.2 = 8.9

Answer:

B

Step-by-step explanation:

☺

Answer:

c) y= 2x +4

Step-by-step explanation:

Slope-intercept form:

y= mx +c, where m is the gradient and c is the y-intercept.

Parallel lines have the same gradient.

Gradient of given line= 2

m= 2

y= 2x +c

To find the value of c, substitute a pair of coordinates into the equation.

when x= -1, y=2,

2= 2(-1) +c

2= c -2

c= 2 +2

c= 4

Thus, the equation of the line is y= 2x +4.

Answer:

Step-by-step explanation:

To complete the square, we need to add and subtract a constant term that will allow us to write the function in the form f(x) = a(x + h)^2 + k. Here's how we can rewrite f(x) = 2x^2 + 3x - 2 using completing the square:

f(x) = 2x^2 + 3x - 2

First, we factor out the coefficient of x^2:

f(x) = 2(x^2 + (3/2)x) - 2

Next, we take half of the coefficint of x and square it, then add and subtract it inside the parentheses:

f(x) = 2(x^2 + (3/2)x + (3/4)^2 - (3/4)^2) - 2

Simplifying the expression inside the parentheses:

f(x) = 2[(x + 3/4)^2 - 9/16] - 2

Expanding the brackets and simplifying:

f(x) = 2(x + 3/4)^2 - 17/8

Therefore, f(x) = 2x^2 + 3x - 2 can be written in the form f(x) = 2(x + 3/4)^2 - 17/8.

Hope that helps

Answer:

Bottom left

Step-by-step explanation:

For it to be scalene, all 3 sides must be of different length, so cross off D. Acute means all angles are less then 90°, so cross off the top 2.

Answer:

{0.3, 3, 30, 300, 3000}

Step-by-step explanation:

Here a(1) = 0.3, and

        a(2) = 3, and

         a(3) = 30, and

          a(4) = 300, and

          a(5) = 3000

The first term (given) is 0.3, and the common ratio is 10.

Answer: 42

Step-by-step explanation: 35 divided by 5=7 so 35+7=42

Answer:

7 > x > 6

Step-by-step explanation:

- 8 x > 67 > x > 6 will become  -8 x > 6 when you cancel out the 67 and the x .

Then you will calculate - 8 x > 6 which will equal to 7 > x > 6 .

So your answer would be your last option

I hope this helps :)

Answer:

$535.78

Step-by-step explanation:

First find out the annual earnings. So multiply 3.4% by 445

0.034 x 445 = 15.13

That's what the account earns every year. Now multiply it by 6 to know what it'll get in 6 years.

15.13 x 6 = 90.78

Now add that to the initial value.

90.78 + 445 = 535.78

That's the balance in the account after 6 years...

$535.78

Answer:

5.38%

966/52 = 0.05383022774

Step-by-step explanation:

5.38 can also be 5.4%

As proved.

We can write this as 52>52.2

To find  52>52.49 we only have to divide it by the larger number.

52.49/966 = 0.05433747412

or multiply to check.

966 x 0.054 = 52.164   sales tax  =  5.4% paid

966 x 0.053835 = 52.00461 = 5.38 % paid  

Both these amounts or in-between would be sales tax percentage

But exact would be 5.38%

Answer:

5.383%

Step-by-step explanation:

To find what percent a part is of a number, divide the part by the number and multiply by 100%.

part = 52

number = 966

percent = 52/966 * 100% = 5.383%

Answer:

9.696

Step-by-step explanation:

Answer:

x = 9.7 feet

Step-by-step explanation:

Use tan to find the value of x

tan 22 = [tex]\frac{x}{24}[/tex]       Simplify

0.404 = [tex]\frac{x}{24}[/tex]       Multiply both sides by 24

x = 9.696        Round this answer to the nearest tenth of a foot

x = 9.7 feet

Answer: B

Step-by-step explanation:

Given that the scatter plot with points going down from about zero comma 4 to the right to about 7 comma zero. That is, (0 , 4 ) to ( 7, 0 )

Let's first find the slope M

M = (0 - 4)/( 7 - 0)

M = - 4/7

Since the line of best fit is linear, let adopt general equation of straight line

Y = MX + C

As the line passes through ( 0 , 4 )

Substitutes for Y and X

4 = - 4/7 (0) + C

C = 4

Where C = intercept

The equation for the line of best fit to represent the data will be:

Y = - 4/7 X + 4

Y equals negative two thirds times x plus 4

Answer:

It is B.

Step-by-step explanation:

I took the test...  :)

The closest lower value would be 10.

10^2 = 100

So the two consecutive numbers would be 10 and 11

Answer:

A(3,11)

Step-by-step explanation:

[tex]y = 2x + 5[/tex]

[tex]2×3 = 6[/tex]

[tex]6 + 5 = 11[/tex]

Answer

7 Units left and 3 units up

Step-by-step explanation:

Rise over Run

Up 3 and to the left 7

Answer:

5x⁵4x³+2x²+5x+3

Polynomials will be closed under an operation if the operation produces another polynomial. (2x2 + 3x + 4) + (x2 - 5x - 3) = 3x2 - 2x + 1

Step-by-step explanation:

Answer:

its b i checked it

Step-by-step explanation:

The equivalent rational exponent form of the expression [tex]\sqrt{10}[/tex] is [tex]10^{\frac{1}{2}[/tex].

We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,

The other type of radicals are indices where a number is raised to such power that is greater than one.

We know the square root of a number indicated the number has been raised by half.

Given, An expression [tex]\sqrt{10}[/tex].

So, The rational form of the expression [tex]\sqrt{10}[/tex] should be [tex]10^{\frac{1}{2}[/tex].

learn more about radical expressions here :

https://brainly.com/question/1369233

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Answer:

y = 3x - 9

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 4 ← is in slope- intercept form

with slope m = 3

Parallel lines have equal slopes, thus

y = 3x + c ← is the partial equation

To find c substitute (2, - 3) into the partial equation

- 3 = 6 + c ⇒ c = - 3 - 6 = - 9

y = 3x - 9 ← equation of parallel line

Answer:

see explanation

Step-by-step explanation:

cos150°

= - cos(180 - 150)°

= - cos30°

= - [tex]\frac{\sqrt{3} }{2}[/tex]

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

sin150°

= sin (180 - 150)°

= sin30°

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

The trigonometric values for cos(150°) and sin(150°) are -√3/2 and 1/2, respectively.

To find the trigonometric values of cos(150°) and sin(150°), we can use the unit circle and the angle sum formulas.

cos(150°):

We know that cos(180° - θ) = -cos(θ). Therefore, we can rewrite cos(150°) as cos(180° - 30°). Since cos(30°) = √3/2, we have:

cos(150°) = -cos(30°) = -√3/2.

sin(150°):

We know that sin(180° - θ) = sin(θ). Therefore, we can rewrite sin(150°) as sin(180° - 30°). Since sin(30°) = 1/2, we have:

sin(150°) = sin(30°) = 1/2.

Learn more about trigonometric values on:

https://brainly.com/question/15227398

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Answer:

It will take her 28 months

Step-by-step explanation:

You first subtract 682.20 and 150.40 to get 576.80. Then you divide 576.80 by 20.60 to get 28.

Answer:

The Answer you are looking for is 28 months.

Answer:

Step-by-step explanation:

The volume of figure 1 is 45 cm greater than the volume of figure 2.

The volume of figure 2 is 45 cm greater than the volume of figure 1.

The volume of fioure 1 is 10mg areater than the volume of figure 2

______________________________

Hey!!!

-22-(-26)

= -22+26

= 4

So the answer is 4.

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

____________________________

-22 - (-26)​ = -22+26=4

So the answer is 4

If this helped mark me as brainliest plss

Hope this helps! Good luck!!

Answer:

The leading coefficient is 15

The constant is -6

Step-by-step explanation:

So first open up all the parentheses:

[tex]8r^3+2r^2+1-7+7r^3-3r^2 = 15r^3-r^2-6[/tex]

The leading coefficient is 15

The constant is -6

Answer:

5 units

Step-by-step explanation:

see the picture

Answer:

The answer is 5 units

Step-by-step explanation:

Answer:

x= 1.27, y= 11.4 (to 3s.f.)

Step-by-step explanation:

5x -y= -5 -----(1)

3x -5y= -3 -----(2)

From (1):

-y= -5x -5

divide by -1 throughout:

y= 5x +5 -----(3)

Subst. (3) into (2):

3x -5(5x +5)= -3

3x -25x +25= -3 (expand)

-22x= -3 -25

-22x= -28

divide by -22 throughout:

x= 1.2727 (5 s.f.)

x= 1.27 (3 s.f.)

subst. into (3):

y= 5(1.2727) +5

y= 11.4 (3 s.f.)

Answer:

it is an acute triangle

Step-by-step explanation:

angle M is 180 - 44 - 77 = 59

since all angles are less than 90 degree, thus is an acute triangle

Answer:

x>-2

Step-by-step explanation:

13+x>11

Subtract 13 from each side

13-13+x>11-13

x>-2

Answer:

Step-by-step explanation:

Since 20% is taken off, 100%-20% or 80% remains.

80% of $65 is 0.80�$65 or $52.  That's the price without tax.  

The tax on $52 is 0.06�$52 or $3.12,

$52 + $3.12 = $55.12

Answer:

d

Step-by-step explanation:

Answer:

8: +4

9: *3 + 5

10: *(-9)+1

11: *(-8)

Answer:

8. Y=x+4, 11. y= X (x) -8

Step-by-step explanation:

Unsure about 9 and 10