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Vaselesa [24]
3 years ago
15

If DE=4x+10, EF= 2x-1, and DF=9x-15, Find DF

Mathematics
1 answer:
djverab [1.8K]3 years ago
6 0

Answer:

Df=9x-15

Step-by-step explanation:

The answer is on the question

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A supermarket employee wants to construct an open-top box from a 14 by 30 in piece of cardboard. To do this, the employee plans
Tanzania [10]

Answer: The side of the square will be 3 cm.

Step-by-step explanation:

When squares of equal size of side x, are cut from the four corners, we are left with the following dimensions for the cuboid box.

l= 30-2x

b = 14-2x

h= x

Hence, the volume of the cuboid will be ,

V = lbh

= (30-2x)(14-2x)x

Since this volume should be the largest possible, then differentiating volume with x should be equal to zero.

Therefore, \frac{dV}{dx} = 0

\frac{dV}{dx} =-2(14-2x)x -2(30-2x)x+(30-2x)(14-2x)=0

solving we get, x = 3, x = \frac{35}{3}

We can omit x = \frac{35}{3} because 14 - 2x < 0 , which is not possible.

Therefore, x=3.

7 0
4 years ago
The height H of an ball that is thrown straight upward from an initial position 3 feet off the ground with initial velocity of 9
mariarad [96]

Answer:

The ball will be 84 feet above the ground 1.125 seconds and 4.5 seconds after launch.

Step-by-step explanation:

Statement is incorrect. Correct form is presented below:

<em>The height </em>h(t)<em> of an ball that is thrown straight upward from an initial position 3 feet off the ground with initial velocity of 90 feet per second is given by equation </em>h(t) = 3 +90\cdot t -16\cdot t^{2}<em>, where </em>t<em> is time in seconds. After how many seconds will the ball be 84 feet above the ground. </em>

We equalize the kinematic formula to 84 feet and solve the resulting second-order polynomial by Quadratic Formula to determine the instants associated with such height:

3+90\cdot t -16\cdot t^{2} = 84

16\cdot t^{2}-90\cdot t +81 = 0 (1)

By Quadratic Formula:

t_{1,2} = \frac{90\pm \sqrt{(-90)^{2}-4\cdot (16)\cdot (81)}}{2\cdot (16)}

t_{1} = 4.5\,s, t_{2} = 1.125\,s

The ball will be 84 feet above the ground 1.125 seconds and 4.5 seconds after launch.

3 0
3 years ago
For the following right triangle, find the side length x.
lesantik [10]

Answer:

x= 5√7

Step-by-step explanation:

Use the Pythagorean theorem

16^2= 9^2 + x^2

x^2=175

x= √175

x= 5√7

6 0
3 years ago
18+6/-4-16 HELP only d part​
Ivahew [28]

Answer:

\frac{1}{2} is the answer

Step-by-step explanation:

First we need to substitute X and Y with their respective numbers

3\cdot \:6+\frac{6}{-4}-\left(-4\right)^2

Then, following PEMDAS, We just need to simplify

18+\frac{6}{-4} -16

16.5-16=0.5=\frac{1}{2}

3 0
3 years ago
Read 2 more answers
Which is the best approximation of square root of 51
ser-zykov [4K]

Answer: Answer is D.

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
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