Given the function f(x) = 2x + 6| – 4, for what values of x is f() = 6?

What is the following product? Assume x>/=0 ^3sqrt(x^2)*^sqrtx^3

RoseWind [281]

Answer:

$x(\sqrt[12]{x^5} )$

Step-by-step explanation:

We need to remember 2 rules when doing these:

1. $\sqrt[n]{x^a} =x^{\frac{a}{n}}$

2. $x^a*x^b=x^{ab}$

Using these 2 rules, we can simplify the product (steps shown below):

$\sqrt[3]{x^2} *\sqrt[4]{x^3} \\=x^{\frac{2}{3}}*x^{\frac{3}{4}}\\=x^{\frac{2}{3}+\frac{3}{4}}\\=x^{\frac{17}{12}}\\=x^{\frac{12}{12}+\frac{5}{12}}\\=x(x^{\frac{5}{12}})\\=x(\sqrt[12]{x^5} )$

Rearranging, we see that it is the third choice.

7 0

3 years ago

What is the volume of a cone that has a height of 10 feet and a base with a diameter of 2 and half feet?

lyudmila [28]

Volume of a cone: 1/3 $\pi$ r²h
r is the radius (diameter ÷ 2) and h is the height.

Find the radius first using the diameter: 2 $\frac{1} {2}$ ÷ 2 = 1.25

Now plug in the numbers into the formula.

1/3 $\pi$ 1.25²10 = <span>16.4
</span>
The volume of the cone is 16.4 cubic feet.

6 0

3 years ago

Hi can you help with some ratio and proportion questions

pochemuha

Answer:

1a. 12 : 40

1b. 15 : 21

1c. 24 : 44

1d. 2 : 25

2. 40 boys and 100 girls

3. 96 girls

4. £71.43

5a. 9 : 4

5b. 3 : 1

5c. 3 : 5

6. 210 : 90

7. Sorry, I couldn't figure out how to solve this question :(

Step-by-step explanation:

Since I'll be using a similar method to solve these questions, I won't go into a detailed explanation for how I solved every single question. If you do need extra help, please ask in the comments below my answer.

1. Let's use part (a) as an example. The ratio is 3:10. To new ratio is ?:40. So, 10 becomes 40. What number multiplied by 10 equals 40? The answer is 4. If 10 is multiplied by 4, then 3 must be multiplied by 4 as well. 3*4 = 12, so the ratio is 12:40.

In part b the ratio is multiplied by 3, part c is 4, and part d is 1/2.

2. To solve this, add the values on both sides of the ratio together: 2 + 5 = 7. Now, divide the total number of pupils, 140, by 7: 140/7 = 20. Finally, multiply 20 by both sides of the ratio: 2 * 20:5 * 20 = 40:100. There are 40 boys and 100 girls.

3. To solve this I used the same method as the one I used in question 1.

4. The ratio is 5:140, where 140 becomes 2000. To solve, use the method used in question 1.

5. Simplifying ratios is the same as simplifying fractions. Find the greatest common factor of the values on both sides of the ratio and divide both sides by that factor. For example, in part a the factor for 45:20 is 5. 45/5 = 9 and 20/5 = 4. The ratio becomes 9:4.

For part b the factor is 9 and for part c the factor is 50.

6. Same method as was used in question 2.

Hope this helps :)

5 0

3 years ago

Awnser Find the slope of the line that passes through (-34, 81) and (32, 12).

icang [17]

Answer:

-23/22

Step-by-step explanation:

Slope m = (y2-y1)/(x2-x1)

m = (12 - 81)/(32 - -34) = (-69)/(66) = -23/22

7 0

2 years ago

6.493 rounded to the hundredths

Nana76 [90]

The answer is 6. 49 you welcome :)

7 0

3 years ago

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