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3 years ago

What is the solution to 2x+4=6x-16

Mathematics

2 answers:

earnstyle [38]3 years ago

7 0

Answer:

Step-by-step explanation:

2x+4=6x-16

-2x -2x (Subtract 2x from both sides)

***************

4=4x-16

+16 +16 (Add sixteen to both sides)

**********

20=4x

Divide both sides by 4 and the answer is

5=x

Ymorist [56]3 years ago

4 0

Answer:

x=5

Step-by-step explanation:

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Square root of 32 = 25/2 true or false ?

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False, the estimated square root of 32 is 5.65685424... while 25/2 = 12.5

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3 years ago

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Solve for the variable x+9=12

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Answer:

Step-by-step explanation:

subtract 9 from both sides

x=3

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2 years ago

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The students in Mr. Wilson's Physics class are making golf ball catapults. The

Mnenie [13.5K]

Answer:

Part a) About 48.6 feet

Part b) About 8.3 feet

Part c) The domain is $0 \leq x \leq 48.6\ ft$ and the range is $0 \leq y \leq 8.3\ ft$

Step-by-step explanation:

we have

$y=-0.014x^{2} +0.68x$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

where

x is the ball's distance from the catapult in feet

y is the flight of the balls in feet

Part a) How far did the ball fly?

Find the x-intercepts or the roots of the quadratic equation

Remember that

The x-intercept is the value of x when the value of y is equal to zero

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

$-0.014x^{2} +0.68x=0$

$a=-0.014\\b=0.68\\c=0$

substitute in the formula

$x=\frac{-0.68(+/-)\sqrt{0.68^{2}-4(-0.014)(0)}} {2(-0.014)}$

$x=\frac{-0.68(+/-)0.68} {(-0.028)}$

$x=\frac{-0.68(+)0.68} {(-0.028)}=0$

$x=\frac{-0.68(-)0.68} {(-0.028)}=48.6\ ft$

therefore

The ball flew about 48.6 feet

Part b) How high above the ground did the ball fly?

Find the maximum (vertex)

$y=-0.014x^{2} +0.68x$

Find out the derivative and equate to zero

$0=-0.028x +0.68$

Solve for x

$0.028x=0.68$

$x=24.3$

<em>Alternative method</em>

To determine the x-coordinate of the vertex, find out the midpoint between the x-intercepts

$x=(0+48.6)/2=24.3\ ft$

To determine the y-coordinate of the vertex substitute the value of x in the quadratic equation and solve for y

$y=-0.014(24.3)^{2} +0.68(24.3)$

$y=8.3\ ft$

the vertex is the point (24.3,8.3)

therefore

The ball flew above the ground about 8.3 feet

Part c) What is a reasonable domain and range for this function?

we know that

A reasonable domain is the distance between the two x-intercepts

$0 \leq x \leq 48.6\ ft$

All real numbers greater than or equal to 0 feet and less than or equal to 48.6 feet

A reasonable range is all real numbers greater than or equal to zero and less than or equal to the y-coordinate of the vertex

we have the interval -----> [0,8.3]

$0 \leq y \leq 8.3\ ft$

All real numbers greater than or equal to 0 feet and less than or equal to 8.3 feet

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2 years ago

WILL MARK BRAINLEST IF RIGHT. the radius of a circle is 2 feet. what is the area?

kolezko [41]

Answer:

12.57

Step-by-step explanation:

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3 years ago

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The ability to find a job after graduation is very important to GSU students as it is to the students at most colleges and unive

gtnhenbr [62]

Answer: (0.8468, 0.8764)

Step-by-step explanation:

Formula to find the confidence interval for population proportion is given by :-

$\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

, where $\hat{p}$ = sample proportion.

z* = Critical value

n= Sample size.

Let p be the true proportion of GSU Juniors who believe that they will, immediately, be employed after graduation.

Given : Sample size = 3597

Number of students believe that they will find a job immediately after graduation= 3099

Then, $\hat{p}=\dfrac{3099}{3597}\approx0.8616$

We know that , Critical value for 99% confidence interval = z*=2.576 (By z-table)

The 99 % confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation will be

$0.8616\pm(2.576)\sqrt{\dfrac{0.8616(1-0.8616)}{3597}}$

$0.8616\pm (2.576)\sqrt{0.0000331513594662}$

$\approx0.8616\pm0.0148\\\\=(0.8616-0.0148,\ 0.8616+0.0148)=(0.8468,\ 0.8764)$

Hence, the 99 % confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation. = (0.8468, 0.8764)

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3 years ago

What is the solution to 2x+4=6x-16​

What is the solution to 2x+4=6x-16