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3 years ago

What is the solution to 3(1-3x)=2(-4x+7)?

Mathematics

1 answer:

Inessa05 [86]3 years ago

8 0

Answer:

x = -11

Step-by-step explanation:

3(1 - 3x) = 2(-4x + 7)

Distribute the 3.

(3 - 9x) = 2(-4x + 7)

Distribute the 2.

3 - 9x = -8x + 14

Add 8x to both sides.

3 - x = 14

Subtract 3 from both sides.

-x = 11

Multiply by -1.

x = -11.

Proof:

3(1 - 3x) = 2(-4x + 7)

3(1 - 3(-11)) = 2(-4(-11) + 7)

3(1 + 33) = 2(44 + 7)

3(34) = 2(51)

102 = 102

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Solve for x: 10 - 2x = -5x - 5 (1) X = -5 (3) X= 4 (2) x 15 (4)x= -15

Alekssandra [29.7K]

10 - 2x = -5x -5
+2x +2x
10 = -3x -5
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bagirrra123 [75]

Answer:

Step-by-step explanation:

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3 years ago

Which of the following is an improper integral?

guapka [62]

Answer:

A) $\displaystyle \int\limits^3_0 {\frac{x + 1}{3x - 2}} \, dx$

General Formulas and Concepts:

Calculus

Discontinuities

Removable (Hole)
Jump
Infinite (Asymptote)

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Definite Integrals
Integration Constant C
Improper Integrals

Step-by-step explanation:

Let's define our answer choices:

A) $\displaystyle \int\limits^3_0 {\frac{x + 1}{3x - 2}} \, dx$

B) $\displaystyle \int\limits^3_1 {\frac{x + 1}{3x - 2}} \, dx$

C) $\displaystyle \int\limits^0_{-1} {\frac{x + 1}{3x - 2}} \, dx$

D) None of these

We can see that we would have a infinite discontinuity if x = 2/3, as it would make the denominator 0 and we cannot divide by 0. Therefore, any interval that includes the value 2/3 would have to be rewritten and evaluated as an improper integral.

Of all the answer choices, we can see that A's bounds of integration (interval) includes x = 2/3.

∴ our answer is A.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

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3 years ago

Given: circle k(O), diameter US, measure of arc RU=50, measure of arc UT=30

sleet_krkn [62]

Answer:

angle RUS = 65 degrees

angle STU = 90 degrees

Step-by-step explanation:

(a) find angle RUS

Given arc RU = 50 degrees, so angle RSU = 50/2 = 25 degrees

Since US is the diameter,

angle URS is a right-angle.

Consider triangle RUS,

sum of angles of a triangle = 25+90+RUS = 180

solve for

RUS = 180 - 25 - 90 = 65 degrees.

(b) Find STU

All diameters span a right angle at the circumference,

since we're given US is a diameter, this means that

angle STU is a right angle.

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3 years ago

A laptop computer is purchased for $2050. After each year, the resale value decreases by 30%. What will the resale value be afte

defon

Answer:

492.205

$492

Step-by-step explanation:

2050/100 = ?/ 70 <- repeat four times changing 2050 to the new value.

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3 years ago