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2 years ago

Type the correct answer in each box. Use numerals instead of words.

Mathematics

1 answer:

malfutka [58]2 years ago

4 0

Answer:

y - 8 = -2(x + 1)^2

Step-by-step explanation:

The vertex of this parabola is (-1, 8). It opens downward, so the x^2 term has a negative coefficient. The zeros are (-3, 0) and (1, 0), and the y-intercept is (0, 7).

Through the vertex form of the equation of a parabola we get:

y - (8) = a(x - (-1)) + 7, or

y - 8 = a(x + 1)^2. Find coefficient a by substituting the coordinates (-3, 0) in this equation:

0 - 8 = a(-3 + 1)^2, or

-8 = a(-2)^2, or a = -2

The desired equation is

y - 8 = -2(x + 1)^2

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Riley’s Rug Warehouse purchases rugs from the manufacturer for $82.00 each. The manager marks the rugs up 150% and then includes

Volgvan

A customer will pay $225.5 for one rug.

Step-by-step explanation:

Given,

Purchase price of rug = $82.00

Mark up = 150%

Amount of mark up = 150% of purchase price

Amount of mark up = $\frac{150}{100}*82$

Amount of mark up = 1.5*82 = $123

Price of rug after mark up = Purchase price + Mark up

Price of rug after mark up = 82+123 = $205

Sales tax = 10%

Amount of sales tax = 10% of price after markup

Amount of sales tax = $\frac{10}{100}*205=\$20.5$

Selling price = Price after markup + Amount of sales tax

Selling price = 205+20.5 = $225.5

A customer will pay $225.5 for one rug.

Keywords: percentage, markup

Learn more about percentages at:

#LearnwithBrainly

5 0

3 years ago

Question 3

Elan Coil [88]

Answer:

Domain: $-3\leq x\leq 1$

Range: $-4\leq y\leq 0$

Step-by-step explanation:

If you find the coordinate of the graph you can get the domain and range

(-3,0), (-2,-4), (-1,-2), (0,0), (1, -4)

Now that we have that find the domain and range

Domain - x coordinate

Range - y coordinate

Domain: (-3, -2, -1, 0, 1)

Range: (-4, -2, 0)

Since the domain ranges from -3 to 1 you can use the inequality $-3\leq x\leq 1$ to represent the domain and $-4\leq y\leq 0$ for the range

7 0

3 years ago

I am four times as old as my daughter. In 20 years time I shall be twice as old as her. How old are we now?

SashulF [63]

Answer:

If x is my daughter's age now, my age now is 4x. So now my daughter is 10 years old, and I'm 40 years old, and in 20 years she'll be 30 and I'll be 60, twice as hers.

Step-by-step explanation:

6 0

3 years ago

A radioactive isotope that was originally 275 grams has decayed to 150 grams. the equation shown can be used to calculate the nu

k0ka [10]

Answer: 4.4 years

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Task 1:

OleMash [197]

Answer:

maximum height is 4.058 metres

Time in air = 0.033 second

Step-by-step explanation:

Given that the equation height h

h = -212t^2 + 7t + 4

What is the toy's maximum height?

Let us assume that the equation is a perfect parabola

Time t at Maximum height will be

t = -b/2a

Where b = 7 and a = - 212

t = -7/ - 212 ×2

t = 7/ 424 = 0.0165s

Substitute t in the main equation

h = - 212(7/424)^2 + 7(7/424) + 4

h = - 0.05778 + 0.115567 + 4

h = 4.058 metres

Therefore the maximum height is 4.058 metres

How long is the toy in the air?

The object will go up and return to the ground.

At ground level, h = 0

-212t^2 + 7t + 4 = 0

212t^2 - 7t - 4 = 0

You can factorize the above equation and pick the positive time t since time can't be negative

Since we have assumed that it's a perfect parabola,

Total time in air = (-b/2a) × 2

Time in air = 0.0165 × 2 = 0.033 s

3 0

3 years ago