Mathematics College

The graph below shows where the two functions y = f(x) and y = g(x) intersect. Solve the equation f(x) = g(x).

Answers

Answer 1

Answer: (-2, 2) and (4, 8)

There are two solutions because the two functions cross each other twice.

Answer 2

The solutions of the equation f(x) = g(x) are (4, 8) and (-2, 2).

We have a graphical representation of two functions f(x) and g(x) and where they intersect.

We have to solve the equation f(x) = g(x)

Two functions A(x) and B(x) are plotted on the graph such that these these two functions intersect each other at three different coordinates. The total number of solutions possible for - A(x) = B(x) is ?

The total number of solutions can be calculated by counting the points at which these curves intersect each other. Hence, the total number of possible solutions are 3.

In the question given - We have a straight line and a parabola -

Now, we just have to look at the points at which these two graphs intersect each other. It can be seen that - both the graphs cut each other at coordinates - (4, 8) and (-2, 2).

Hence, the solutions of the equation f(x) = g(x) are (4, 8) and (-2, 2).

Alternative Method -

The general equation of straight line is : y = mx + c and that of parabola is : y = [tex]\sqrt{4ax}[/tex]

The solution can be calculated by equating both of the above expressions and solving them.

mx + c = [tex]\sqrt{4ax}[/tex]

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Related Questions

Union City Bakery uses a chocolate chip muffin recipe that yields 1/2 cup of milk for every batch of 12 chocolate chip muffins. Based on the recipe:

How much milk is needed to make each muffin?

How much milk in needed to make 24 chocolate chip muffins?

Answers

you need 1/24 of a cup to make one muffin you would need one cup of milk to make 24 muffins

PLEASE HELP!!!

John and Chuck are building a new house. When finished, the house will cost $190,750. The price of the house is 9% higher than the price when the original plans were made. What was the price of the house when the original plans were made?

Answers

Answer:

190,750 decreased by 9% is 173,582.5

Step-by-step explanation:

D 2. Which of the following is correctly written in Standard Form?
A 3/7x + 2y =9
B y= 3/7x+6
C 5x – 4y = 9
D -3x + 7y = 12
Pls help me

Answers

The equations that are correctly written in standard form are

A. 3/7x + 2y =9

C. 5x – 4y = 9

D. -3x + 7y = 12

Standard form of a Linear equations

From the question, we are to determine which of the given equations are written in standard form

The standard form of a linear equation is Ax + By = C.

Where A, B, and C are constants,

and

x and y are variables

Hence, the equations that are correctly written in standard form are

A. 3/7x + 2y =9

C. 5x – 4y = 9

D. -3x + 7y = 12

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find the value of x. A. 35 B. 40 C. 45 D. 50

Answers

Answer:

Step-by-step explanation:

Answer:

scalene trangle

Step-by-step explanation:

you pay $2 to play a game in which you roll one fair die. If you roll a 5 on the first roll, you win $5. If you roll a 1 or 2, you win $3 . If not you lose your money. Find the expected value for this game.

Answers

Show the online response please but I say 4

Answer:

the answer is 4

Step-by-step explanation:

You spend $63 on books and movies. You pay $12 per book and $15 per movie. You buy 3 more books than movies. How many of each item do you buy?

Answers

Answer:12B - 12M = 36

12B + 15M = 63

Subtract one from the other:

12B + 15M = 63

-(12B - 12M = 36

-------------------------

0 + 27M = 27

27M = 27

M = 1

B - M = 3 (from the original equations)

B - 1 = 3

B = 4

You bought 4 books and 1 movie.

Step-by-step explanation:

Answer:you buy 4 books and 1 movie

Step-by-step explanation:

12x4=48 + 15(one movie)=63

Can I have some help? What is LCM for 5 and 14

Answers

Answer:

Step-by-step explanation:

Least common multiple (LCM) of 5 and 14 is 70.

The answer for LCM
=70

Round 154,101 to the nearest ten.

Answers

Answer:

154,100

Step-by-step explanation:

the tenth is the 0

5 or more up the score 4 or less let it rest.

Which of the following is an example of a culture maintaining traditional ways?

Answers

Answer:

Amish driving buggies and using horses and mules instead of tractors

Step-by-step explanation:

Which pair of vectors is orthogonal?

u = ⟨–3, 2⟩ and v = ⟨–2, 1⟩
u = ⟨1, 5⟩ and v = ⟨–5, 1⟩
u = ⟨2, 1⟩ and v = ⟨–4, 3⟩
u = ⟨2, 3⟩ and v = ⟨3, 1⟩

Answers

Answer:

B: u = (1,5) and v = (-5,1)

Step-by-step explanation:

edge 2021

The pair of vectors which are orthogonal to each other will be u = ⟨1, 5⟩ and v = ⟨–5, 1⟩. Then the correct option is B.

What is a vector?

The quantity which has magnitude, direction and follows the law of vector addition is called a vector.

For the orthogonal vector, the dot product of two vectors will be zero.

Check first option, we have

u·v = ⟨–3, 2⟩·⟨–2, 1⟩

u·v = 6 + 2 = 8 (incorrect)

Check second option, we have

u·v = ⟨1, 5⟩·⟨–5, 1⟩

u·v = –5 + 5 = 0 (correct)

Check third option, we have

u·v = ⟨2, 1⟩·⟨–4, 3⟩

u·v = –8 + 3 = –5 (incorrect)

Check fourth option, we have

u·v = ⟨2, 3⟩·⟨3, 1⟩

u·v = 6 + 3 = 9 (incorrect)

Then the correct option is B.

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2500 + 110h < 3000 can you pls answer this

Answers

Answer:

4.5454545454545454. . .

Step-by-step explanation:

Original equation:

2500 + 110h < 3000

Subtract 2500 from both sides

110h < 500

Divide both sides by 110

h < 4.5 (rounded to the nearest tenth)

Hope this helps :)

Please consider Brainliest :)

Help! - Answer = Brainliest!

Thanks!

Answers

Answer:

Step-by-step explanation:

i copied the person above me :)

sorryyy not sorry lol

#respectfully

when solving an equation, which is the best first step to begin to simplify the equation? -2(x+3)=-10

Answers

Answer: Following the rules of PEMDAS, you want to divide both sides of the equation by -2. This would change your equation to x+3=5. Then you move your constant to the right-hand side and change its sign. Your equation is now x=5-3. subtract 5-3 and your answer is x=2.

Find an equation for the line below

Answers

y = 6/9x + 1
Rise/run

Which value(s) below ma 6.05x - 12.5 = 48 Show all of your work. Ju box below. HELP ME PLEASE

Explain:

Answer

Answers

Answer:

I got you

Step-by-step explanation:

6.05-12.50=13.55

48 divided by 13.55=3.542

x=3.542

Answer:

X= 1

Step-by-step explanation:

6.05x-12.5=48 Add 12.5 to both side

+12.5 +12.5

6.05x = 60.5 now divide both sides by 6.05

/ 6.05 /60.5

X = 1

In a small private liberal arts college, 40 percent of the students receive financial aid, and 30 percent of the students that receive financial aid also are first generation college students. In addition, 25 percent of the students in the college own a hybrid car. What is the probability that a randomly selected student receives financial aid and is first generation college student

Answers

Answer:

P(A∩B) = 0.12

Step-by-step explanation:

Given:

Students receive financial aid P(A) = 40% = 0.4

Students receive financial aid and first generation P(B/A) = 30% = 0.3

Find:

Probability [Selected student receives financial aid and is first generation college student] P(A∩B)

Computation:

P(A∩B) = P(A) x P(B/A)

P(A∩B) = 0.4 x 0.3

P(A∩B) = 0.12

Gia has 80 tiles each tile is white or blue she arranges the tiles in 8 equal rows each row has an equal number of with and blue tiles. how many blue tiles are in each row?

Answers

Answer:

Step-by-step explanation:

80 divided by 8 = 10 divided by 2 = 5

A triangle has side lengths of 21, 27, and 35 inches. Is it
right triangle?

Answers

Answer: No
In right triangle we have 30:60:90
and the ratios are
x: x root of 3: 2x
so, for example, if we have side of length 3 against 30 degrees, then against 60 degrees the side will be 3 root of 3, and against 90 degrees it will be 6.
Hope it helps!

Help me please *an image is attached*

Answers

Answer:

its C

Step-by-step explanation:

Answer:

C. The graph has y-intercept - 2, not initial value - 2.

Step-by-step explanation:

Hope this helps

George invited 65 students in his school to volunteer at a charity race. 39 of the students signed up to volunteer. What percent of the invited students signed up?

Answers

Answer:

60%

Step-by-step explanation:

39/65 gives you the answer.

Cassie earned $40 in July. She earned $48 in August..
What is the percent increase or decrease in Cassie's monthly earnings?
A. 10% decrease
B. 25% decrease
C. 20% increase
D. 30% increase

Answers

Answer: 20% increase

Step-by-step explanation:

Answer:

C. 20% increase

Step-by-step explanation:

if it was decreasing it would be less and 20% is even and seven is also even

Help meeeeeeeee

Pleaseeee

Answers

Answer:

give them all a common denominator

1/3= 2/6

5/6= 5/6

1/2= 3/6

1/6= 1/6

and then use the "new" fraction to order the other ones. but be sure to use the original values, not the ones you made using the GCF. so the answer would be:

1/6, 1/3, 1/2, 5/6

What is the slope if 2y=x

Answers

Answer:

1/2

Step-by-step explanation:

divide both sides by 2

What is the slope intercept.

Answers

y=mx+b
Slope: 1
y-intercept: (0, -8)
Slope intercept: y=x-8

Which expression is equivalent to 6n - 24?*
8n - 10+14
3/4 (8n - 32)
-2(-3n - 12)
O 10n - 12 - (4n - 12)

Answers

Answer:

-2(-3n - 12)

Step-by-step explanation:

Solve for x. (PLEASE HELP)

Answers

9514 1404 393

Answer:

x = 6

Step-by-step explanation:

The parallel lines divide the sides proportionally. So, we can write the equation ...

x/4 = (x +3)/6

3x = 2(x +3) . . . . . multiply by 12

x = 6 . . . . . . . . . . . subtract 2x

Watch help video
If using the method of completing the square to solve the quadratic equation
X2 – 9x + 38 = 0, which number would have to be added to "complete the
square"?

Answers

Answer:

Step 1 Divide all terms by a (the coefficient of x2).

Step 2 Move the number term (c/a) to the right side of the equation.

Step 3 Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.

hope this help

but this is little info dont worry i will answer your question just in a minute

Step-by-step explanation:

It’s Question 15. I need help!

Answers

Answer: Its b i took that

Step-by-step explanation:

Trust me

Answer:

Step-by-step explanation:

c = 15n

A 6 ounce serving of grapefruit juice contains 171 grams of water. How many grams of water are in 20 ounces of grapefruit juice?

Please help me with this question. I have 2 minutes left to answer it.

Answers

Answer:

570 grams of water

Step-by-step explanation:

171 divided by 6 = 28.5

28.5 grams are in 1 ounce

so Multiply 28.5 by 20 to get the new amout which is 570

The amount of water present in 20 ounces of grapefruit juice will be 570 grams.

What are ratio and proportion?

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

A 6-ounce serving of grapefruit juice contains 171 grams of water.

The ratio of the amount of grapefruit and water present will remain constant.

Let 'x' be the amount of water present. Then the equation is given as,

x / 20 = 171 / 6

x = 20 · 171 / 6

x = 570 grams

The amount of water present in 20 ounces of grapefruit juice will be 570 grams.

More about the ratio and the proportion link is given below.

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Which is the solution to 2^x = 9^x - 9? A. 11.5714 B. 13.1476 C. -6.8417 D.6.5738

Answers

Answer: B

Step-by-step explanation:

13.14760878

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