All categories

3 years ago

Solve for x. 2(x + 14) + x = 70a. 11b. 12c. 14d. 17

Mathematics

1 answer:

Mariulka [41]3 years ago

6 0

Hello!

To solve for the variable x, we need to follow the rules of SADMEP. SADMEP is ONLY used when solving algebraic equations. SADMEP is an acronym for subtraction, addition, division, multiplication, exponents, and parentheses. Also, when solving for x, our main goal is to isolate x to one side of the equation.

2(x + 14) + x = 70 (use the distributive property)

2x + 28 + x = 70 (simplify - add)

3x + 28 = 70 (subtract 28 from both sides)

3x = 42 (divide both sides by 3)

x = 14

When solving ANY algebraic equation, we need check our answer. To check your answer, you substitute the x-value, which is 14 in this case, into the original equation and solve using PEMDAS.

2(x + 14) + x = 70 (substitute x = 14)

2(14 + 14) + 14 = 70 (simplify the terms inside the parentheses)

2(28) + 14 = 70 (simplify - multiply)

56 + 14 = 70 (simplify - add alike term)

70 = 70 | This is correct!

Therefore, your final answer is x = 14, which is choice C.

You might be interested in

You invest $500 in an account that has a annual interest rate of 5%, compounded quarterly for four years. What is the equivalent

posledela

Answer:

1.25% and 16 times

Step-by-step explanation:

Since the interest is compounded quarterly it will be compounded 4 times a year. So 4 x 4 is 16, so it will be compounded 16 times.

Then you have to divide the 5% by four to get how much will be compounded each quarter. So, (0.05 / 4) = 0.0125, which is 1.25%.

3 0

3 years ago

I don't care about getting the answers but rather a step-by-step explanation for this problem: A simple interest, 8-month loan o

alisha [4.7K]

Answer:

Step-by-step explanation:

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

From the information given

T = 8 months = 8/12 = 2/3 years

P = $3000

R = 9.3%

Therefore

I = (3000 × 9.3 × 2/3)/100

I = 18600/100

I = $186

The maturity value (in dollars) of this loan would be

3000 + 186 = $3186

7 0

3 years ago

Find the inverse of f(x)=(x−5)/(−4x−2)

uysha [10]

Answer:

${f}^{ - 1} (x)= \frac{ 5 - 2x }{ 4x + 1}$

Step-by-step explanation:

The given rational function is

$f(x) = \frac{x - 5}{ - 4x - 2}$

Let

$y = \frac{x - 5}{ - 4x - 2}$

Interchange x and y

$x= \frac{y- 5}{ - 4y - 2}$

Cross multiply

$x( - 4y - 2)= y- 5$

Expand

$- 4xy - 2x= y- 5 \\ - 4xy - y= 2x - 5 \\y( - 4x - 1)= 2x - 5$

Solve for y;

$y= \frac{ 2x - 5}{ - 4x - 1}$

$y= \frac{ 5 - 2x }{ 4x + 1}$

Therefore

${f}^{ - 1} (x)= \frac{ 5 - 2x }{ 4x + 1}$

7 0

3 years ago

Triangle ABC has AB=5, BC=7, and AC=9. D is on AC with BD=5. Find the length of DC

e-lub [12.9K]

Answer:

$DC=\frac{8}{3}\ units$

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The triangle ABD is an isosceles triangle

because

AB=BD

The segment BM is a perpendicular bisector segment AD

In the right triangle ABM

Applying the Pythagorean Theorem

$BM^2=AB^2-AM^2$

we have

$AB=5\ units\\AM=x\ units$

substitute

$BM^2=5^2-x^2$

$BM^2=25-x^2$ -----> equation A

In the right triangle BMC

Applying the Pythagorean Theorem

$BM^2=BC^2-MC^2$

we have

$BC=7\ units\\MC=AC-AM=(9-x)\ units$

substitute

$BM^2=7^2-(9-x)^2$

$BM^2=49-(81-18x+x^2)$

$BM^2=49-81+18x-x^2$

$BM^2=-x^2+18x-32$ ----> equation B

equate equation A and equation B

$-x^2+18x-32=25-x^2$

solve for x

$18x=25+32\\18x=57\\\\x=\frac{57}{18}$

Simplify

$x=\frac{19}{6}$

Find the length of DC

$DC=AC-2x$

substitute the given values

$DC=9-2(\frac{19}{6})$

$DC=9-\frac{19}{3}\\\\DC=\frac{8}{3}\ units$

8 0

3 years ago

If a rug is 6 feet wide by 8 feet long and suki makes a diagram that is 1 1/3 feet long how many inches should its width be

soldier1979 [14.2K]

The length in the diagram is 4/3 feet.
(4/3)/8=w/6 where w is the width.
So 4/(3×8)=w/6.
1/6=w/6 so w=1 foot or 12 inches.

4 0

3 years ago