Three-quarters of a number is 15. Work out four-fifths of the number.

This parabola has x-intercepts

slega [8]

Answer:

see the explanation

Step-by-step explanation:

we have the quadratic equation

$y=-16x^{2} +32x-10$

This is a vertical parabola open downward

The vertex is a maximum

Find the x-intercepts of the quadratic equation

The x-intercepts are the values of x when the value of y is equal to zero

so

For y=0

$-16x^{2} +32x-10=0$

Solve the quadratic equation

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-16x^{2} +32x-10=0$

so

$a=-16\\b=32\\c=-10$

substitute in the formula

$x=\frac{-32(+/-)\sqrt{32^{2}-4(-16)(-10)}} {2(-16)}$

$x=\frac{-32(+/-)\sqrt{384}} {-32}$

$x=\frac{-32(+/-)8\sqrt{6}}{-32}$

$x=\frac{-32(+)8\sqrt{6}}{-32}=\frac{32(-)8\sqrt{6}}{32}=0.39\ sec$

$x=\frac{-32(-)8\sqrt{6}}{-32}=\frac{32(+)8\sqrt{6}}{32}=1.61\ sec$

therefore

This parabola has two x-intercepts representing the times when the dolphin's height above water is zero feet

8 0

3 years ago

Read 2 more answers

Use compatible numbers to find two estimates

taurus [48]

Use compatible numbers to find two estimates that the quotient is between. For example:

1,624 divided by 3
 1500 / 3 = 500 

1800 / 3 = 600

7 0

3 years ago

Read 2 more answers

Solve 5x^2+2x=1 using either factoring, square root method, completing the square or quadratic formula.

wolverine [178]

Answer:

x = -1 ± √6 / 5

Step-by-step explanation:

Solve $5x^{2}$ + 2x = 1

move 1 to the left side of the equation by subtracting it from both sides.

$5x^{2}$ + 2x - 1 = 0

Use the quadratic formula to find the solutions.

-b± $\sqrt{b^2 - 4 (ac)}$ / 2a

Substitute the values a = 5 , b = 2, and c = -1 into the quadratic formula and solve for x

-2± $\sqrt{2^2 - 4(5 - 1)}$ / 2 ⋅ 5

Simplify.

x = -2 ± 2 $\sqrt{6}$ / 10

x = -1 ± $\sqrt{6}$ / 5

Exact Form:

x = -1 ± $\sqrt{6}$ / 5

4 0

3 years ago

A plumber charges a $70 flat rate for all home repairs. His hourly rate is $15 per half hour. How much would a 2 hour and 26 m

Gnesinka [82]

The plumber's 2 hour and 26 min plumbing bill cost is $73

What is the plumber's per minute rate?

The plumber's per minute rate is the per half-hour rate divided by 30 minutes since the plumber charges $15 for every 30-minute job

per-minute rate=$15/30

per-minute rate=$0.50

Now, let us convert 2hours and 26 minutes to minutes, in other words, every 1 hour is 60 minutes, the two hours equal 120 minutes plus the 26 minutes gives a total of 146 minutes

Total minutes=120 min+26 min

total minutes=146 minutes

Total plumbing bill cost for 146 minutes is $0.50, the per-minute rate multiplied by the number of minutes the plumber needs to work in this case

2 hour and 26 min plumbing bill cost=146*$0.50

2 hour and 26 min plumbing bill cost=$73

Find out more about hourly rate on:brainly.com/question/4468523

#SPJ1

4 0

2 years ago

Dora is building the right square pyramid shown in the diagram.

saul85 [17]

Answer is 4 :) I hope it help you.

8 0

3 years ago