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2 years ago

Solving Multi Step Equations: Solve for the variable~y/5 - 9 = 11

1 answer:

6 0

$\frac{y}{5}-9=11$
Isolate y-terms:
$\frac{y}{5}-9+9=11+9$
$\frac{y}{5}=18$
Isolate 'y':
$\frac{y}{5}5=18\times 5$
$y=90$

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Find a cubic function f(x) = ax^3 + bx^2 + cx + d that has a local maximum value of 3 at x = −3 and a local minimum value of 0 a

Ahat [919]

Answer:

f(x) = (3x³ + 9x² - 27x + 15)/32

Step-by-step explanation:

f'(x) = 3ax² + 2bx + c

Maximum or minimum: f'(x) = 0

Maximum: f'(-3) = 0 and f(-3) = 3

Minimum: f'(1) = 0 and f(1) = 0

f'(-3) = 0 leads 27a - 6b + c = 0 (1)

f'(1) = 0 leads 3a + 2b + c = 0 (2)

f(-3) = 3 leads -27a + 9b -3c + d = 3 (3)

f(1) = 0 leads a + b + c + d = 0 (4)

(1) - (2): 24a - 8b = 0, or 3a - b = 0, b = 3a

(3) - (4) -28a + 8b - 4c = 3 (5)

(1) * 4 + (5): 80a - 16b = 3,

use b = 3a, get 80a - 16*3a = 3, 32a = 3, a = 3/32, b = 3a = 9/32

From (2): c = -3a - 2b = -9/32 - 18/32 = -27/32

From (4): d = -a - b - c = -3/32 - 9/32 + 27/32 = 15/32

f(x) = (3x³ + 9x² - 27x + 15)/32

3 0

2 years ago

PLEASE someone help its due tonight im almost done

marusya05 [52]

<h3>Answers:</h3>

48 seconds
3624 feet

========================================================

Explanation:

x = number of seconds that elapse

y = altitude (aka height) of the plane

The equation for plane A is

y = 20.25x+2652

because it starts off at 2652 ft in the air, and then adds on 20.25 feet per second which is what the 20.25x describes

The equation for plane B is

y = 75.5x

The y intercept is zero because plane B starts on the ground, aka height 0.

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

The system of equations is

$\begin{cases}y = 20.25x+2652\\y = 75.5x\end{cases}$

If we want to know when they'll reach the same height (y), then we can set the two right hand sides equal to each other and solve for x.

75.5x = 20.25x+2652

75.5x-20.25x = 2652

55.25x = 2652

x = (2652)/(55.25)

x = 48

The two planes reach the same altitude at exactly <u>48 seconds</u>

That altitude is <u>3624 feet</u> because

y = 20.25*x + 2652 = 20.25*48+2652 = 3624
y = 75.5*x = 75.5*48 = 3624

Notice I plugged x = 48 into each equation and I got the same y value of y = 3624. This helps confirm the answers.

7 0

1 year ago

If you travel at a rate of 45 mph how many minutes will you will it take you to travel 1 mile

stiks02 [169]

It'd take you<span>, 1 minute and 33 secounds.
45 miles = 60 minutes
1 mile = 60/45 = 4/3 = 1.33 minutes </span>

7 0

3 years ago

Rewrite the fraction in the sentence below as a percentage 21/25

Paul [167]

21/25

Change to decimal:-

Divide numerator by denominator.

21/25

21 ÷ 25 = 0.84

21/25 = 0.84

Change to a percentage:-

0.84 × 100 = 84

21/25 = 0.84 = 84%

6 0

3 years ago

Brittany went grocery shopping , she spent 4/7 of her money on fresh foods. she spent 2/3 of the remainder of her money on froze

pychu [463]

Answer:

$44

Step-by-step explanation:

Let the total amount of money be represented by Y

Amount spent on fresh food =

$\frac{4}{7} \times y$

Remainder =

$y - \frac{4}{7}y = \frac{3}{7} y$

Amount spent on frozen foods = two-thirds of remainder = $22

$= \frac{2}{3} \times \frac{3}{7} y = \frac{2}{7} y$

$\frac{2}{7} y = 22 \\ y = 22 \times \frac{7}{2} \\ y = 77$

The total amount for grocery shopping is $77

Therefore, Brittany spent $44 on fresh foods

$= \frac{4}{7} \times 77 \\ = 4 \times 11 \\ = 44$

5 0

2 years ago

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