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3 years ago

4 1/4 divided by 2/7 (x+8)-(3x- 5) Explain how you got the answer!!!!!

Mathematics

1 answer:

Dmitry_Shevchenko [17]3 years ago

8 0

Turn it to improper fractions.

4 1/4 divided by 2/7

Divide them.

17/4 divided by 2/7

17 2 17 x 7

--- ÷ --- = --------- = 119/8 OR 14 7/8

4 7 4 x 2

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

Distribute to take out the parentheses.

(x + 8) - (-3x - 5)

Combine like terms.

x + 8 + 3x + 5

Answer.

4x + 13

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What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?

mrs_skeptik [129]

Answer:

x <3

Step-by-step explanation:

–2(5 – 4x) < 6x – 4

Distribute

-10 +8x < 6x-4

Subtract 6x from each side

-10+8x-6x < 6x-6x-4

-10 +2x < -4

Add 10 to each side

-10+2x+10 < -4+10

2x< 6

Divide by 2

2x/2 < 6/2

x <3

4 0

3 years ago

Help me please please help please

Dominik [7]

Answer:

Step-by-step explanation:

180-81 = 99

Hope this helps!

7 0

3 years ago

Read 2 more answers

Light travels at 3.0 x 108 km/s. How far does light travel in 5 minutes? A) 1.5 x 1010 km B) 1.5 x 1011 km C) 9.0 x 109 km D) 9.

MaRussiya [10]

D) 9.0 x 10^10 km This is more an exercise in handling scientific notation than anything else. Since we have the distance that light travels in 1 second and we want to calculate how far it travels in 5 minutes, we must first calculate how many seconds are in 5 minutes. Simply multiplying 5 by 60 gives us 300 seconds. Now we need to multiply 300 by 3.0x10^8 km. So 300 * 3.0x10^8 = ? We could first convert 300 into scientific notion, but it's easier to just leave it along and assume that it's 300 x 10^0. So 300 times 3 is 900. And since 0 plus 8 is 8, we have as the answer: 900 x 10^8 But we're not done. The significand has to be greater than or equal to 1 and less than 10. So let's divide 900 by 100 and add 2 to the exponent. So we get 9 x 10^10 Finally, since our data had 2 significant figures, our result should have that as well. So let's add the 2nd digit getting: 9.0 x 10^10 So we know that light travels 9.0x10^10 km in 5 minutes, and that answer matches option "D" from the available choices.

4 0

3 years ago

If anyone knows about definite integrals for calculus then please I request help! I

kicyunya [14]

Answer:

$\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{1}{8} \bigg( e^\Big{\frac{4}{25}} - e^\Big{\frac{4}{81}} \bigg)$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

U-Substitution

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution.

Set u: $\displaystyle u = 4x^{-2}$
[u] Differentiate [Basic Power Rule, Derivative Properties]: $\displaystyle du = \frac{-8}{x^3} \ dx$
[Bounds] Switch: $\displaystyle \left \{ {{x = 9 ,\ u = 4(9)^{-2} = \frac{4}{81}} \atop {x = 5 ,\ u = 4(5)^{-2} = \frac{4}{25}}} \right.$

Step 3: Integrate Pt. 2

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}\int\limits^9_5 {\frac{-8}{x^3}e^\big{4x^{-2}}} \, dx$
[Integral] U-Substitution: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}\int\limits^{\frac{4}{81}}_{\frac{4}{25}} {e^\big{u}} \, du$
[Integral] Exponential Integration: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}(e^\big{u}) \bigg| \limits^{\frac{4}{81}}_{\frac{4}{25}}$
Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8} \bigg( e^\Big{\frac{4}{81}} - e^\Big{\frac{4}{25}} \bigg)$
Simplify: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{1}{8} \bigg( e^\Big{\frac{4}{25}} - e^\Big{\frac{4}{81}} \bigg)$