If the difference (3x2 - 2x + 5) – (x2 + 3x

Which of the following represents a first step in solving the equation (x - 6)² = 9?

Alik [6]

"B." Because you must do what's in the parenthesis first. So 6² is 36 so that would be x-36=9 then to solve it $x-36=9 \\ +36=x-9 \\ 9+36=45 \\ x=45$

3 0

4 years ago

A chemist has 200 mL of a 10% sucrose solution. She adds x mL of a 40% sucrose solution. The percent concentration, y, of the fi

user100 [1]

Answer:

The chemist needs to add 400mL of 40% solution.

Step-by-step explanation:

The equation

$y=\frac{0.1(200)+0.4x}{200+x} *100$

gives the percent concentration $y$ of the final mixture, when $x$ mL of the 40% solution are added.

Now we are asked, how many milliliters $x$ of the 40% solution should the chemist add to get final percent concentration $y=30$ ; this is just a matter of solving the equation

$30=\frac{0.1(200)+0.4x}{200+x} *100$

and we solve it the following way:

$30=\frac{0.1(200)+0.4x}{200+x} *100\\\\0.3 =\frac{0.1(200)+0.4x}{200+x}\\\\0.3(200+x)=0.1(200)+0.4x\\\\60+0.3x=20+0.4x\\\\40=0.1x\\\\x=\frac{40}{0.1} \\\\\boxed{x=400\:mL}$

Thus, the chemist needs 400mL of 40% solution to get 30% concentration of the final mixture.

7 0

4 years ago

How do you find a volume of a cone?

Dennis_Churaev [7]

Answer:

V = (1/3)πr²h

Step-by-step explanation:

The volume of a cone is 1/3 the volume of a cylinder with the same radius and height.

Cylinder Volume = πr²h

Cone Volume = (1/3)πr²h

where r is the radius (of the base), and h is the height perpendicular to the circular base.

_____

Comment on area and volume in general

You will note the presence of the factor πr² in these formulas. This is the area of the circular base of the object. That is, the volume is the product of the area of the base and the height. In general terms, ...

V = Bh . . . . . for an object with congruent parallel "bases"

V = (1/3)Bh . . . . . for a pointed object with base area B.

This is the case for any cylinder or prism, even if the parallel bases are not aligned with each other. (That is, it works for oblique prisms, too.)

Note that the cone, a pointed version of a cylinder, has 1/3 the volume. This is true also of any pointed objects in which the horizontal dimensions are proportional to the vertical dimensions*. (That is, this formula (1/3Bh), works for any right- or oblique pyramid-like object.)

__

* in this discussion, we have assumed the base is in a horizontal plane, and the height is measured vertically from that plane. Of course, any orientation is possible.

4 0

3 years ago

Claire has a hot tub with a diameter of 7 feet. She wants to purchase a cover to protect the hot tub. What is the area

harkovskaia [24]

Answer:

The area of the cover for the hot tub must be:

38 square feet.

Step-by-step explanation:

First, you must understand that since a hydromassage tub is mentioned and the diameter, it is assimilated that it is round in its upper part, which is why the formula is used to find the area of a circle:

Area of a circle = pi * radius ^ 2 (you must know that the radius is half the diameter)

Since the diameter is mentioned, it can be replaced in the formula:

Area of a circle = 3.14 * (3.5 feet) ^ 2
Area of a circle = 38,465 square feet. Approximately 38 square feet.

7 0

3 years ago

Read 2 more answers

Hannah și Cassie au împreuna 24 ani Ce varst ATE fiecare dacă Hannah este mai mare cu 6 ani decât sora ei?

satela [25.4K]

Answer:

please speak English

Step-by-step explanation:

just speak English

8 0

3 years ago

Read 2 more answers

If the difference (3x2 - 2x + 5) – (x2 + 3x - 2) is multiplied by 1/2x^2,