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nataly862011 [7]
3 years ago
5

Jenny is diving into a swimming pool from a diving board. The expression below represents Jenny's vertical height x, in feet, ab

ove the surface of the water.
-16x^2+12x+10
Which statement best describes the term 10?
A).Jenny's initial height above the surface of the water
B).the time it takes Jenny to reach the surface of the water
C).the horizontal distance from the diving board Jenny travels
D).the maximum height Jenny reaches
NextReset
Mathematics
1 answer:
fredd [130]3 years ago
4 0

Answer:

A

Step-by-step explanation:

The projectile motion of Jenny's dive can be represented by -at^2 + v_0t + h_0 where a is acceleration, v_0 is velocity, t is time, and h_0 is initial height.

Jenny's vertical height above the water is represented by -16x^2+12x+10. 10 is h_0 and is Jenny's initial height.

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A student is asked to find the length of the hypotenuse of a right triangle. The length of one leg is 38 ​centimeters, and the l
a_sh-v [17]
Answer:
Hypotenuse = 43.4 cm
4 0
2 years ago
A man bought a lot for 1200 and sold it for 1500. his percent of gain based on his purchase was
jok3333 [9.3K]

Answer: The percent gain was 25%.

Step-by-step explanation:

Given, Cost price of lot = $1,200

Selling price of lot = $1,500

The percent gain = \dfrac{\text{selling price- cost price}}{\text{cost price}}\times100

⇒ Percent gain =\dfrac{1500-1200}{1200}\times100\%

\Rightarrow\text{ Percent gain}=\dfrac{300}{1200}\times100\%\\\\\Rightarrow\text{ Percent gain}=\dfrac{1}{4}\times100\%\\\\\Rightarrow\text{ Percent gain}=25\%

Hence, the percent gain was 25% based on his purchase.

5 0
3 years ago
1.) Determine the type of solutions for the function (Picture 1)
NNADVOKAT [17]

Answer:

1) 2 nonreal complex roots

2) 1 Real Solution

3) 16

4) Reflected, narrower by a factor of 2/5, slides right 4 units and slides up 6 (units)

Step-by-step explanation:

1) The graph does not intercept the x-axis, therefore, there are no real solutions at the point y = 0

We get;

y = a·x² + b·x + c

At y = 6, x = -2

Therefore;

6 = a·(-2)² - 2·b + c = 4·a - 2·b + c

6 = 4·a - 2·b + c...(1)

At y = 8, x = 0

8 = a·(0)² + b·0 + c

∴ c = 8...(2)

Similarly, we have;

At y = 8, x = -4

8 = a·(-4)² - 4·b + c = 16·a - 4·b + 8

16·a - 4·b = 0

∴ b = 16·a/4 = 4·a

b = 4·a...(3)

From equation (1), (2) and (3), we have;

6 = 4·a - 2·b + c

∴ 6 = b - 2·b + 8 = -b + 8

6 - 8 = -b

∴ -b = -2

b = 2

b = 4·a

∴ a = b/4 = 2/4 = 1/2

The equation is therefor;

y = (1/2)·x² + 2·x + 8

Solving we get;

x = (-2 ± √(2² - 4 × (1/2) × 8))/(2 × (1/2))

x =( -2 ± √(-12))/1 = -2 ± √(-12)

Therefore, we have;

2 nonreal complex roots

2) Give that the graph of the function touches the x-axis once, we have;

1 Real Solution

3) The given function is f(x) = 2·x² + 8·x + 6

The general form of the quadratic function is f(x) = a·x² + b·x + c

Comparing, we have;

a = 2, b = 8, c = 6

The discriminant of the function, D = b² - 4·a·c, therefore, for the function, we have;

D = 8² - 4 × 2 × 6 = 16

The discriminant of the function, D = 16

4.) The given function is g(x) = (-2/5)·(x - 4)² + 6

The parent function of a quadratic equation is y = x²

A vertical translation is given by the following equation;

y = f(x) + b

A horizontal to the right by 'a' translation is given by an equation of the form; y = f(x - a)

A vertical reflection is given by an equation of the form; y = -f(x) = -x²

A narrowing is given by an equation of the form; y = b·f(x), where b < 1

Therefore, the transformations of g(x) from the parent function are;

g(x) is a reflection of the parent function, with the graph of g(x) being narrower by 2/5 than the graph of the parent function. The graph of g(x) is shifted right by 4 units and is then slides up by 6 units.

7 0
2 years ago
7)
Lady_Fox [76]
They pay $10.74 each
3 0
3 years ago
Luke has two summer jobs. During the week he works in the grocery store, and on the
TiliK225 [7]

Hello! First, let's get some important information:

Luke works in the:

  • week → grocery store → $16/hour
  • weekend → nursery → $22/hour

Now, let's analyze the questions:

<h3>a) How much does he earn if he works 5 hours at the grocery store and 8 hours at the nursery? </h3>

To find the amount he will receive, you must multiply the amount of 1 hour by the number of hours worked. Look:

\mathrm{Grocery\:Store}\\\\\$16 \cdot 5 \:\mathrm{hours}= \$80\\\$22 \cdot 8\:\mathrm{hours}=\$176

<h3>b) How much does he earn if he works g hours at the grocery store and n hours at the nursery?</h3>

\$16 \cdot \mathrm{g} \:\mathrm{hours}= \$16\cdot\mathrm{g}\\\$22 \cdot \mathrm{n}\:\mathrm{hours}=\$22\cdot\mathrm{n}

<h3>c) Total pay, 5 hours at the grocery store and 8 hours at the nursery:</h3>

You'll just have to just add the value in each of the jobs:

$80 + $176 = $256

<h3>d) Total pay, g hours at the grocery store and n hours at the nursery:</h3>

Adding the values of each job:

$16g + $22n

Hope this helps!

8 0
3 years ago
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