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3 years ago

F is between E and G. EF=3X, EG= 11x-2, FG= 5x+16. Find the value of the variable

Mathematics

1 answer:

Salsk061 [2.6K]3 years ago

3 0

9514 1404 393

Answer:

x = 6

Step-by-step explanation:

The sum of segments is used:

EF +FG = EG

3x +(5x +16) = 11x -2 . . . . substitute given expressions

8x +18 = 11x . . . . . . . . add 2

18 = 3x . . . . . . . . subtract 8x

6 = x . . . . . . divide by 3

The value of the variable is 6.

Check

The segment lengths are ...

EF = 3x = 3·6 = 18

FG = 5x+16 = 5·6 +16 = 46

EG = 11x -2 = 11·6 -2 = 64 = 18+46 . . . answer is correct

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3x+112=5x+100 what is the answer I don't get it

slega [8]

Reorder the terms
112 + 3x = 100 + 5x
112 + 3x + (-5x) = 100 + 5x + (-5x)

Combine the like terms
5x + (-5x) = 0
112 + (-2x) = 100 + 0
112 + (-2x) = 100

112 + (-112) + (-2x) = 100 + (-112)
Combine like terms again
112 + (-112) =0
0 + (-2x) = 100 + (-112)
100 + (-112) = (-112) = (-12)
-2x = -12
-12 / -2 = 6
x = 6 ✓

Check your work
3 * 6 + 112 = 130
5 * 6 + 110 = 130
130 = 130 ✓

3 0

3 years ago

Find the point of diminishing returns (x comma y )for the function R(x), where R(x) represents revenue (in thousands of doll

riadik2000 [5.3K]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The point of diminishing returns (x , y ) is (11, 21462)

Step-by-step explanation:

From the question we are told that

The function is $R(x) = 10,000 -x^3 - 33x^2 + 800x , \ \ 0 \le x \le 20$

Here R(x) represents revenue (in thousands of dollars) and x represents the amount spent on advertising (in thousands of dollars).

Now differentiating R(x) we have

$R'(x) = -3x^2 +66x + 800$

Finding the second derivative of R(x)

$R''(x) = -6x +66$

at inflection point $R''(x) = 0$

So $-6x +66 = 0$

=> $x= 11$

substituting value of x into R(x)

$R(x) = 10,000 -(11)^3 - 33(11)^2 + 800(11) ,$

$R(x) = 21462$

Now the point of diminishing returns (x , y ) i.e (x , R(x) ) is

(11, 21462)

4 0

3 years ago

Bob is hiking down a 15-mile country trail. He could hike at 5 mph for the first 2 hours and then go the rest of the way at 3 mp

mash [69]

Answer:

1) 11/3 hours or about 3.67 hours.

2) 3.75 hours.

Step-by-step explanation:

Let’s determine the time it will take for Bob to hike for each of the options.

Option 1) Hiking 5mph for 2 hours, then 3mph.

The total distance is 15 miles.

If Bob hiked 5mph for 2 hours, then after two hours, Bob would’ve covered 5(2)=10 miles out of 15.

Therefore, 15-10 or 5 miles still needs to be covered.

To find how long that will take, we can simply divide the distance by the rate.

We are now going at a rate of 3mph. So, 5/3 is about 1.67 hours.

So, it will take another 1.67 hours to complete the hike.

So, the total time it will take is 2+1.67 or abou 3.67 hours. More specifically, it will be 2+5/3 or 11/3 hours.

Option 2) Hiking 4mph the entire way.

The total distance is 15 miles.

If Bob hiked 4mph the entire way, to find how long it will take, we can simply divide the total distance by the rate.

So: 15/4=3.75.

Therefore, it will take 3.75 hours to hike the entire distance going 4mph.

8 0

3 years ago

In the diagram shown, chords AB and CD intersect at E. The measure of (AC) ̂ is 120°, the measure of (DB) ̂ is (2x)° and the mea

Mars2501 [29]

Answer:

The measure of angle < AED is $100\°$

Step-by-step explanation:

we know that

The measure of the interior angle is the semi-sum of the arcs comprising it and its opposite.

$m$

substitute the values and solve for x

$4x=\frac{1}{2}(120\°+2x)$

$8x=(120\°+2x)$

$8x-2x=120\°$

$6x=120\°$

$x=20\°$

$m$

$m$ -----> by supplementary angles

substitute value

$80\°+m$

$m$

4 0

3 years ago

What is the slip of the line shown below ? A - 11/4 B- 4/11 C- -4/11 D- 11/4

RUDIKE [14]

The picture is blurry

5 0

3 years ago