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4 years ago

Solve x^2–10x+25=35 for x

1 answer:

3 0

First you need to subtract 35 to get one equation =0.

x^2-10x-10=0 then use the quadratic formula (let me know if you need the formula of need to see these steps)

and solve to = approximately 8.87 and 1.12

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When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a ra

Sergeu [11.5K]

Answer:

$r=\sqrt{10}\text{ m}$

Step-by-step explanation:

We have been given that when a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. We are asked to find the approximate radius of tank in meters.

We will use volume of cylinder formula to solve our given problem as:

$V=\pi r^2h$ , where,

r = Radius,

h = Height of cylinder.

Since the level of water in the tank rises at a rate of 0.7 meters per hour, so height of cylinder would be $h = 0.7$ meters at $V=22\text{ m}^3$ .

Upon substituting these values in above formula, we will get:

$22\text{ m}^3=\frac{22}{7}\cdot r^2(0.7\text{ m})$

$22\text{ m}^3=\frac{22}{10}\cdot r^2\text{ m}$

$\frac{10}{22}\cdot\frac{22\text{ m}^3}{\text{m}}=r^2$

$r^2=\frac{10}{22}\cdot\frac{22\text{ m}^3}{\text{m}}$

$r^2=10\text{ m}^2$

Now, we will take positive square root of both sides as radius cannot be negative.

$\sqrt{r^2}=\sqrt{10\text{ m}^2}$

$r=\sqrt{10}\text{ m}$

Therefore, radius of tank would be approximately square root of 10 m.

5 0

3 years ago

Simplify the expression. (16y54y3)12 Enter your answer in the box.

sp2606 [1]

Answer:

Simplify the expression: $(16y^{\frac{5}{4}}y^3)^{\frac{1}{2}}$

Use the exponent power:

$a^n \cdot a^m = a^{n+m}$

$\sqrt[n]{a^n} =a$
$(a^n)^m = a^{nm}$

$(16y^{\frac{5}{4}}y^3)^{\frac{1}{2}}$

Apply the given rules;

$(16y^{\frac{5}{4} +3} )^{\frac{1}{2}}$

Simplify:

$(16y^{\frac{17}{4}} )^{\frac{1}{2}}$

then;

$(16)^{\frac{1}{2}} \cdot (y^{\frac{17}{4}})^{\frac{1}{2}} = 4y^{\frac{17}{8}}$

Therefore, the simplified expression of $(16y^{\frac{5}{4}}y^3)^{\frac{1}{2}}$ is, $4y^{\frac{17}{8}}$

7 0

3 years ago

What is the Greatest Common Factor of x^4 and x^3?

hammer [34]

Judging by the question I noticed that the two both share x^3 in common. You can divide x^4 by x^3 and get x as a result, and x^3 can still divide into itself.

Thus your answer should be C, x^3

5 0

3 years ago

How do u do this please

blagie [28]

Answer: In number 1 the answer is 2. Number 2 the answer is 7. Number 3 you read the problem as 4 x 4 x 4 or 4 to the 3rd. For number 4 it's 2x2x2x2x2x2x2 or 2 to the 7th power. Number 5 is right. For number 6 B. is 5. C is 6

Hope this helps

Step-by-step explanation:

4 0

3 years ago

cole spent $55.00 buying songs and movies at an online store that charges $1.25 for each song and $2.75 for each movie. He purch

Sergeu [11.5K]

If you would like to write and solve a system of equations that represent the situation above, you can do this using the following steps:

s ... number of songs
m ... number of movies

$55.00 = $1.25 * s + $2.75 * m
55 = 1.25 * s + 2.75 * m

26 songs and movies = s + m
26 = s + m
s = 26 - m

55 = 1.25 * s + 2.75 * m
55 = 1.25 * (26 - m) + 2.75 * m
55 = 1.25 * 26 - 1.25 * m + 2.75 * m
55 - 32.5 = 1.5 * m
22.5 = 1.5 * m
m = 22.5 / 1.5 = 15 movies

s = 26 - m = 26 - 15 = 11 songs

The correct result would be 15 movies and 11 songs.

6 0

3 years ago