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4 years ago

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Mathematics

1 answer:

Gnoma [55]4 years ago

4 0

Answer:

x=4

Step-by-step explanation:

DE+EF=DF

(x-1)+(3x+3)=(5x-2)

x-1+3x+3=5x-2

4x+2=5x-2

-x=-4

x=4

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A pre-paid cell phone company charges $18.5 as a monthly access fee and $0.11 per minute of calling time. Express the monthly co

Shalnov [3]

Answer:

c=54.69

Step-by-step explanation:

so this is a two step problem

c=18.5+0.11x

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4 years ago

The cube of the sum of 4 and 9 times x divided by the product of 5 times x and the difference of x and 1

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3 years ago

a 16 inch wire is to be cut. one piece is to be bent into the shape of a square, whereas the other piece is to be bent into the

Lyrx [107]

1. Let x be a length of square side, then the square perimeter is 4x (you need to cut 4x from 16 in. to make a square with side x in.). Then 16-4x is remained length of wire and you have to make form this piece a rectangle with sides one of which is twice bigger than another. If y is length of the smaller side, then 2y is length of the bigger side and rectangle perimeter is y+2y+y+2y=6y. You have 16-4x in. of wire left, so 6y=16-4x and $y= \frac{16-4x}{6}$ .

2.
$A_{square}=x^2 \\ A_{rectangle}=y\cdot 2y=\frac{16-4x}{6}\cdot2\cdot\frac{16-4x}{6}= \frac{(16-4x)^2}{18} \\ A(x)=A_{square}+A_{rectangle}=x^2+\frac{(16-4x)^2}{18}$ .

3. Find the derivative of the function A(x):
$A'(x)=2x+ \dfrac{2(16-4x)\cdot(-4)}{18} =2x- \dfrac{4(16-4x )}{9}$ .

4. Solve the equation A'(x)=0:
$2x- \dfrac{4(16-4x )}{9}=0 \\ 18x-64+16x=0 \\ 34x=64 \\ x= \frac{32}{17}$

5. Since $y= \frac{16-4x}{6}$ you have

$y= \dfrac{16-4 \frac{32}{17} }{6} = \dfrac{16\cdot17-4\cdot32}{6\cdot 17} = \dfrac{24}{17}$ .

Answer: <span>the width of the rectangle is $\frac{24}{17}$ </span>

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4 years ago

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Zarrin [17]

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3 years ago

Recall that two angles are complementary if the sum of their measures is 90. Find the measures of two complementary angles if on

dsp73

Answer: 25° and 65°

Step-by-step explanation:

Let the smaller angle of the complementary angle be represented by x.

Since the other angle is 15 degree more than two times the other angle, this will be:

= (2 × x) + 15°

= 2x + 15°.

Then we add both angles together and equate them to 90° and this will be:

x + 2x + 15° = 90°

3x + 15° = 90°

3x = 90° - 15°

3x = 75°

x = 75°/3

x = 25°

Then the other angle will be:

= 2x + 15°

= (2 × 25°) + 15°

= 50° + 15°

= 65°

Therefore, the angles are 25° and 65°.

8 0

3 years ago

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