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3 years ago

Which statement best describes the solutions of this equation? 4/3x+1 = x/2x+10

Mathematics

1 answer:

Komok [63]3 years ago

5 0

Answer:

x= 5

x= 8/3

Step-by-step explanation:

Step one

Given the expression

$\frac{4}{3x+1} =\frac{x}{2x+10}$

cross multiply we have

$4(2x+10)= x(3x+1)$

$8x+40=3x^2+x$

collect like terms

$3x^2+x-8x-40=0$

$3x^2-7x-40=0$

applying the quadratic equation

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-(-7)\pm\sqrt{(-7)^2-4*3(-40)}}{2*3}\\\\x=\frac{7\pm\sqrt{49+480}}{2*3}\\\\x=\frac{7\pm\sqrt{529}}{6}\\\\x=\frac{7\pm 23}{6}\\\\x=\frac{7\+23}{6}\\\\x=\frac{30}{6} \\\\x=5\\\\x=\frac{7-23}{6}\\\\x=\frac{-16}{6} \\\\x=\frac{8}{3}$

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Please help me with this.

JulijaS [17]

The speed intervals such that the mileage of the vehicle described is 20 miles per gallon or less are: v ∈ [10 mi/h, 20 mi/h] ∪ [50 mi/h, 75 mi/h]

<h3>How to determine the range of speed associate to desired gas mileages</h3>

In this question we have a quadratic function of the gas mileage (g), in miles per gallon, in terms of the vehicle speed (v), in miles per hour. Based on the information given in the statement we must solve for v the following quadratic function:

g = 10 + 0.7 · v - 0.01 · v² (1)

An effective approach consists in using a graphing tool, in which a horizontal line (g = 20) is applied on the maximum desired mileage such that we can determine the speed intervals. The speed intervals such that the mileage of the vehicle is 20 miles per gallon or less are: v ∈ [10 mi/h, 20 mi/h] ∪ [50 mi/h, 75 mi/h].

To learn more on quadratic functions: brainly.com/question/5975436

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3 0

2 years ago

Finds the slope of the line

Zinaida [17]

Answer:

Step-by-step explanation:

Slope=rise over run.

From bottom marked point (-3, -3) to the other (-2, 1)...

Rise= 4

Run= 1

4/1=4

Therefore, the slope is 4.

Hope this helps!! Have an amazing day ❤

6 0

3 years ago

PLEASE I NEED HELP WITH THIS

Ber [7]

Given:

The figure of a circle.

To find:

The measure of arc AD and measure of each arc.

Solution:

The measure of arc is equal to the central angle of that arc.

The central angle of arc AD is 105 degrees. So,

$m(arc(AD))=105^\circ$

The central angle of arc BC is 35 degrees. So,

$m(arc(BC))=35^\circ$

The central angle of arc CD is 50 degrees. So,

$m(arc(CD))=50^\circ$

The central angle of a complete circle is 360 degrees. So,

$m(arc(AD))+m(arc(BC))+m(arc(CD))+m(arc(AB))=360^\circ$

$105^\circ+35^\circ+50^\circ+m(arc(AB))=360^\circ$

$190^\circ+m(arc(AB))=360^\circ$

$m(arc(AB))=360^\circ-190^\circ$

$m(arc(AB))=170^\circ$

Therefore, the measure of arc AD is 105°, the measure of arc BC is 35°, the measure of arc CD is 50° and the measure of arc AB is 170°

3 0

3 years ago

In a seafood stew, Erin wants to use lobster, crab, and shrimp. She wants one part lobster, two parts crab, and three parts shri

alukav5142 [94]

Answer:

Answer: (B) 3

Step-by-step explanation:

20x + 15(2x) + 10(3x) = 40

20x + 30x + 30x = 40

80x = 40

x = 40/80

x = 1/2

Find the amount of lobster

Lobster = x = 1/2 pound

Find the amount of crab:

Crab = 2x = 2(1/2) = 1 pound

Find the amount of Shrimp:

Shrimp = 3x = 3(1/2) = 3/2 pounds

Find the total pounds of seafood:

Total = 1/2 + 1 + 3/2 = 3 pounds

Answer: (B) 3

6 0

3 years ago

If A = 3x power 2+2y + 2 and B=6x power 2 - 8y + 1 then A+B and A-B

ollegr [7]

Answer:

see explanation

Step-by-step explanation:

Given A = 3x² + 2y + 2 and B = 6x² - 8y + 1 , then

A + B

= 3x² + 2y + 2 + 6x² - 8y + 1 ← collect like terms

= 9x² - 6y + 3

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

A - B

= 3x² + 2y + 2 - (6x² - 8y + 1) ← distribute parenthesis by - 1

= 3x² + 2y + 2 - 6x² + 8y - 1 ← collect like terms

= - 3x² + 10y + 1

5 0

3 years ago