MATHEMATICS HIGH SCHOOL

Find the x-intercept of the parabola with vertex (6,27) and y-intercept (0,-81)

Answers

Answer 1
Answer: The vertex form of the equation of a parabola with the vertex (h,k):
y=a(x-h)^2+k

The parabola has the vertex at (6,27).
y=a(x-6)^2+27

The y-intercept is (0,-81).
x=0, \ y=-81 \n\Downarrow \n-81=a(0-6)^2+27 \n-81=a(-6)^2+27 \n-81=36a+27 \n-81-27=36a \n-108=36a \n(-108)/(36)=a \na=-3

The equation of the parabola is:
y=-3(x-6)^2+27

y=0 at the x-intercepts.
0=-3(x-6)^2+27 \n-27=-3(x-6)^2 \n(-27)/(-3)=(x-6)^2 \n9=(x-6)^2 \n√(9)=√((x-6)^2) \n3=|x-6| \nx-6=3 \ \lor \ x-6=-3 \nx=3+6 \ \lor \ x=-3+6 \nx=9 \ \lor \ x=3

The x-intercepts are x=3 and x=9.

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A shopper thought shoes marked $40 the sales tax is 8% how much the shopper pay in all

Answers

so, if I understand correctly the prize before sales tax is 40 dollars and the sales tax is 8%. how much is this?

(8)/(100) *40= (8)/(10) *4=(4)/(5) *4= (16)/(5) =3.2

so the final prize is 40+3.2=43.2

A 16- ounce bottle of fresh water is $1.76. A 20-ounce bottle of spring water is $2.40. Which statement about the unit price is true? A. Spring water has a lower unit price of $0.12/ounce
B. Fresh water has a lower unit price of $0.11/ounce
C. Fresh water has a lower unit price of $0.12/ounce
D. Spring water has a lower unit price of $0.11/ounce

Answers

To find the unit price of each item you want to divide:

Fresh water:

$1.76 / 16 = $0.11

Spring water:

$2.40 / 20 = $0.12

So the statement that is true is B) Fresh water has a lower unit price of $0.11/ounce.

Hope this Helps!!

What is the distance between point A and point B? Round to nearest tenth.

Answers

Answer:

d \approx 12.6

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Algebra II

  • Distance Formula: d = √((x_2-x_1)^2+(y_2-y_1)^2)

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point A (-4, 2)

Point B (8, 6)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d.

  1. Substitute [DF]:                    d = √((8+4)^2+(6-2)^2)
  2. Add/Subtract:                       d = √((12)^2+(4)^2)
  3. Exponents:                           d = √(144+16)
  4. Add:                                      d = √(160)
  5. Simplify:                                d = 4√(10)
  6. Evaluate:                              d = 12.6491
  7. Round:                                 d \approx 12.6

Find f^(-1) (-2) =

Answers

Answer:

f(2) = - 2

{f}^( - 1) ( - 2) = 2

Show your working for the following questions:-18 divided by -3

Two sevenths times eight thirds

Three eights plus one twelth

Answers

(-18)/(-3) (divide 3 from numerator and denominator) = (6)/(1) = 6

(2)/(7) × (8)/(3) = (16)/(21)

(3)/(8) + (1)/(12) = (9)/(24) + (2)/(24) = (11)/(24)

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Solve for the following equation step by step and justify your steps when using an exponential property.
(7^x)^4= 7^2*7^3/7^x3

Answers

hope this helps you note only if it is the correct question then the answer will be correct

Answer:

(7^x)^4 = (7^2 * 7^3)/7^3x

7^4x = 7^5/7^3x

7^4x = 7^5-3x

4x = 5 - 3x

7x = 5

​x = 5/7

PLEASE MARK BRAINLIEST!
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