1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
valkas [14]
3 years ago
13

Solve the following system of equations. Label the solution 4x-2y=8 y=1/2x+2

Mathematics
1 answer:
Zielflug [23.3K]3 years ago
5 0

Answer:

(4,4)

Step-by-step explanation:

4x-2y=8

y=1/2x+2

Since the second equation is solved for y, I will use substitution

4x - 2(1/2x +2) = 8

Distribute

4x - x -4 = 8

Combine like terms

3x -4 = 8

Add 4 to each side

3x-4+4 = 8+4

3x = 12

Divide each side by 3

3x/3 = 12/3

x = 4

Now we need to find y

y=1/2x+2

y = 1/2(4) +2

y = 2+2

y =4

The solution is (4,4)

You might be interested in
Mason says that (12x + 4) - (-3x + 5) and 15x - 1 are equivalent. Is he correct? Explain
julia-pushkina [17]

Answer:

Yes

Step-by-step explanation:

12x minus -3x is the same as adding two positives. That gives us 15x. 4 - 5 is -1. Putting the two simplified parts of the expression together, we get 15x - 1. Mason is correct.

6 0
3 years ago
Read 2 more answers
Tariq designed the pool shown . The owner of the pool has one square to use . Find the area of the space that needs to be covere
Alenkinab [10]

Answer:

Heres the anwser my man 128

Step-by-step explanation:

hope you got it right.

8 0
3 years ago
Read 2 more answers
What happens to the area of a circle when the radius is tripled?
patriot [66]
The circle would triple because the radius is equal to its area
6 0
3 years ago
Read 2 more answers
(2x-1)(x+4)=0 need this question
eduard

Answer:

x = 1/2 or x = -4

Step-by-step explanation:

Since the product equals zero, use the zero product rule.

(2x - 1)(x + 4) = 0

2x - 1 = 0 or x + 4 = 0

2x = 1   or   x = -4

x = 1/2 or x = -4

6 0
3 years ago
Read 2 more answers
The portion of the parabola y²=4ax above the x-axis, where is form 0 to h is revolved about the x-axis. Show that the surface ar
castortr0y [4]

Answer:

See below for Part A.

Part B)

\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614

Step-by-step explanation:

Part A)

The parabola given by the equation:

y^2=4ax

From 0 to <em>h</em> is revolved about the x-axis.

We can take the principal square root of both sides to acquire our function:

y=f(x)=\sqrt{4ax}

Please refer to the attachment below for the sketch.

The area of a surface of revolution is given by:

\displaystyle S=2\pi\int_{a}^{b}r(x)\sqrt{1+\big[f^\prime(x)]^2} \,dx

Where <em>r(x)</em> is the distance between <em>f</em> and the axis of revolution.

From the sketch, we can see that the distance between <em>f</em> and the AoR is simply our equation <em>y</em>. Hence:

r(x)=y(x)=\sqrt{4ax}

Now, we will need to find f’(x). We know that:

f(x)=\sqrt{4ax}

Then by the chain rule, f’(x) is:

\displaystyle f^\prime(x)=\frac{1}{2\sqrt{4ax}}\cdot4a=\frac{2a}{\sqrt{4ax}}

For our limits of integration, we are going from 0 to <em>h</em>.

Hence, our integral becomes:

\displaystyle S=2\pi\int_{0}^{h}(\sqrt{4ax})\sqrt{1+\Big(\frac{2a}{\sqrt{4ax}}\Big)^2}\, dx

Simplify:

\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax}\Big(\sqrt{1+\frac{4a^2}{4ax}}\Big)\,dx

Combine roots;

\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax\Big(1+\frac{4a^2}{4ax}\Big)}\,dx

Simplify:

\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax+4a^2}\, dx

Integrate. We can consider using u-substitution. We will let:

u=4ax+4a^2\text{ then } du=4a\, dx

We also need to change our limits of integration. So:

u=4a(0)+4a^2=4a^2\text{ and } \\ u=4a(h)+4a^2=4ah+4a^2

Hence, our new integral is:

\displaystyle S=2\pi\int_{4a^2}^{4ah+4a^2}\sqrt{u}\, \Big(\frac{1}{4a}\Big)du

Simplify and integrate:

\displaystyle S=\frac{\pi}{2a}\Big[\,\frac{2}{3}u^{\frac{3}{2}}\Big|^{4ah+4a^2}_{4a^2}\Big]

Simplify:

\displaystyle S=\frac{\pi}{3a}\Big[\, u^\frac{3}{2}\Big|^{4ah+4a^2}_{4a^2}\Big]

FTC:

\displaystyle S=\frac{\pi}{3a}\Big[(4ah+4a^2)^\frac{3}{2}-(4a^2)^\frac{3}{2}\Big]

Simplify each term. For the first term, we have:

\displaystyle (4ah+4a^2)^\frac{3}{2}

We can factor out the 4a:

\displaystyle =(4a)^\frac{3}{2}(h+a)^\frac{3}{2}

Simplify:

\displaystyle =8a^\frac{3}{2}(h+a)^\frac{3}{2}

For the second term, we have:

\displaystyle (4a^2)^\frac{3}{2}

Simplify:

\displaystyle =(2a)^3

Hence:

\displaystyle =8a^3

Thus, our equation becomes:

\displaystyle S=\frac{\pi}{3a}\Big[8a^\frac{3}{2}(h+a)^\frac{3}{2}-8a^3\Big]

We can factor out an 8a^(3/2). Hence:

\displaystyle S=\frac{\pi}{3a}(8a^\frac{3}{2})\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big]

Simplify:

\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big]

Hence, we have verified the surface area generated by the function.

Part B)

We have:

y^2=36x

We can rewrite this as:

y^2=4(9)x

Hence, a=9.

The surface area is 1000. So, S=1000.

Therefore, with our equation:

\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big]

We can write:

\displaystyle 1000=\frac{8\pi}{3}\sqrt{9}\Big[(h+9)^\frac{3}{2}-9^\frac{3}{2}\Big]

Solve for h. Simplify:

\displaystyle 1000=8\pi\Big[(h+9)^\frac{3}{2}-27\Big]

Divide both sides by 8π:

\displaystyle \frac{125}{\pi}=(h+9)^\frac{3}{2}-27

Isolate term:

\displaystyle \frac{125}{\pi}+27=(h+9)^\frac{3}{2}

Raise both sides to 2/3:

\displaystyle \Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}=h+9

Hence, the value of h is:

\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614

8 0
2 years ago
Read 2 more answers
Other questions:
  • Factor the trinomial: x^2-x-12 x 2 − x − 12
    7·2 answers
  • 5.28 rounded to the nearest tenth
    11·2 answers
  • ) A __________ is a spot where digits can be placed to the left and right to make numbers that are greater than or less than one
    5·1 answer
  • Lin and Jen each thought of a number. Lin thought of a 2-digit number. Jen’s number is 7 times as big as Lin’s. But, if Lin writ
    5·2 answers
  • Which of the following equations is equivalent to y = 2x + 1?
    11·2 answers
  • The length of each segment.
    11·1 answer
  • If the ratio of boys to girls on the team is 2:3and there are 12 girls how many boys are there?
    10·1 answer
  • 1. Find the next three in the sequence. 2,7,12,17
    8·2 answers
  • If 7% of a number equals 9, find 70% of that number.<br> i need it rn
    13·2 answers
  • Can someone Please help me if you’re correct I’ll give Brainlist!
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!