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Combine the following fractions. a. 3/5 + 4/15 b. 5/6 - 1/4

Ne4ueva [31]

Hello there! :)

Answer:

1. $\boxed{\frac{13}{15} }$

2. $\boxed{\frac{7}{12} }$

Step-by-step explanation:

1. 3/5+4/15

First, you multiply by numerator and denominator.

3*3=9

5*3=15

$=\frac{9}{15}$

Then, you had to combine by the fractions.

$\frac{9}{15}+\frac{4}{15}$

Add by the numbers from left to right.

9+4=13

13/15 is the final answer.

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2. 5/6-1/4

First, you multiply by 2 both sides of numerator and denominator.

5*2=10

6*2=12

10/12

3/12

$\frac{10}{12}-\frac{3}{12}$

Subtract by the numerator.

10-3=7

7/12 is the final answer.

______________________________

Hope this helps!

Thanks!

Have a nice day! :)

:D

-Charlie

7 0

3 years ago

What are the roots to the equation 2x² + 6x-1=0?

lys-0071 [83]

Answer:

The roots of equations are as m = $\frac{-3}{2} + \frac{\sqrt{11} }{2}$ And n = $\frac{-3}{2} - \frac{\sqrt{11} }{2}$

Step-by-step explanation:

The given quadratic equation is 2 x² + 6 x - 1 = 0

This equation is in form of a x² + b x + c = 0

Let the roots of the equation are ( m , n )

Now , sum of roots = $\frac{ - b}{a}$

And products of roots = $\frac{c}{a}$

So, m + n = $\frac{ - 6}{2}$ = - 3

And m × n = $\frac{ - 1}{2}$

Or, (m - n)² = (m + n)² - 4mn

Or, (m - n)² = (-3)² - 4 ( $\frac{ - 1}{2}$ )

Or, (m - n)² = 9 + 2 = 11

I.e m - n = $\sqrt{11}$

Again m + n = - 3 And m - n = $\sqrt{11}$

Solving this two equation

(m + n) + ( m - n) = - 3 + $\sqrt{11}$

I.e 2 m = - 3 + $\sqrt{11}$

Or, m = $\frac{-3}{2} + \frac{\sqrt{11} }{2}$

Similarly n = $\frac{-3}{2} - \frac{\sqrt{11} }{2}$

Hence the roots of equations are as m = $\frac{-3}{2} + \frac{\sqrt{11} }{2}$ And n = $\frac{-3}{2} - \frac{\sqrt{11} }{2}$ Answer

6 0

3 years ago

Factor completely 2x^3y^4-8x^2y^3+6xy^2

Maru [420]

Answer:

2 x y^2 (x y - 1) (x y - 3)

Step-by-step explanation:

2x^3y^4-8x^2y^3+6xy^2

each term contains 2xy^2 so factor that out

2xy^2(x^2y^2 -4xy+3)

then lets factor the inside

what terms multiply together to give us +3 and add to -4

-3* -1 = 3 -3+-1 =-4

2 x y^2 (x y - 1) (x y - 3)

6 0

2 years ago

A publishing company claims that in fall 2019, the average price of college textbooks for a single semester is $385. Suppose you

hram777 [196]

Answer:

We accept H₀ . We don´t have enough evidence to express the publisher claim is not true

Step by Step explanation:

We must evaluate if the mean of the price of college textbooks is different from the value claimed by the publisher

n < 30 then we must use t - distrbution

degree of freedom n - 1 df = 22 - 1 df = 21

As the question mentions " different " that means, a two-tail test

At 0,01 significance level α = 0,01 α/2 = 0,005

and t(c) = 2,831

Test Hypothesis

Null Hypothesis H₀ μ = μ₀

Alternative hypothesis Hₐ μ ≠ μ₀

To calculate t(s)

t(s) = ( μ - μ₀ ) /σ/√n

t(s) = ( 433,50 - 385 ) / 86,92 / √22

t(s) = 2,6171

Comparing t(c) and t(s)

t(s) < t(c)

Then t(s) is in the acceptance region we accept H₀. We don´t have enough evidence to claim that mean price differs from publisher claim

6 0

3 years ago

El resultado de la operación combinada 70-25+9-2x10÷2 corresponde a: A) 9 B)44 C)80

AlexFokin [52]

Answer:

B) 44

Step-by-step explanation:

70 - 25 + 9 - 2 × 10 ÷ 2

70 - 25 + 9 - 20 ÷ 2

70 - 25 + 9 - 10

45 + 9 - 10

54 - 10

44

3 0

2 years ago