Find the value of x.

Given:

The function is:

[tex]f(x)=x^2[/tex]

The graphs of functions [tex]f(x)[/tex] and [tex]g(x)[/tex].

To find:

The function [tex]g(x)[/tex].

Solution:

We have,

[tex]f(x)=x^2[/tex]

The function [tex]f(x)[/tex] is vertically compresses to get the graph of the function [tex]g(x)[/tex]. So, the function [tex]g(x)[/tex] is:

[tex]g(x)=kf(x)[/tex]

[tex]g(x)=kx^2[/tex]               ...(i)

From the given graph it is clear that the graph of the function [tex]g(x)[/tex] passes through the point (3,3). So, putting [tex]x=3[/tex] and [tex]g(x)=3[/tex] in the above function, we get

[tex]3=k(3)^2[/tex]

[tex]3=9k[/tex]

[tex]\dfrac{3}{9}=k[/tex]

[tex]\dfrac{1}{3}=k[/tex]

Putting [tex]k=\dfrac{1}{3}[/tex] in (i), we get

[tex]g(x)=\dfrac{1}{3}x^2[/tex]

Therefore, the correct option is D.

Answer:

60.8 mm^2

D

Step-by-step explanation:

Remark

You have to assume that the left and right sides are both 9.3. The question is undoable without that assumption.

Next, you have to assume that The top is 7.8 mm across and both ends meet 9.3 at right angles. Again if that is not true, the problem can't be done. Sometimes people making these questions make errors which you are asked to correct.

Solution

So let's assume that everything I've assumed is correct.

Find the area of the rectangle.

Area = L*W

L = 9.3

W = 7.8

Area = 7.8 * 9.3

Area = 72.54        Do your rounding at the end.

Now find the are of the triangle that has been cut out.

The height = 3

The base = 7.8

Area = 1/2 b * h

Area = 1/2 7.8 * 3

Area = 11.7

The area of the figure = area of the rectangle - the triangle's area

Figure Area = 72.54 - 11.7

Figure Area = 60.84

Answer:

y< -2x + 3

Step-by-step explanation:

Good luck with your questions :)

Answer:

[tex]6n \div 4[/tex]

Step-by-step explanation:

n is a variable and multiplied by 6, so it is attached to 6. (6 is known as the coefficient.) Then it is divided by 4. (4 is known as the constant because there is no variable attached to it.)

[tex]6n \div 4[/tex]

Answer:

80 toy cars were left in the shop.

Step-by-step explanation:

Since there were toy cars, dolls and teddy bears in a shop, and 30% of the toys were toy cars, and the ratio of the number of dolls to the number of teddy bears were 4: 1, and there were 156 more dolls than toy cars, and after some toy cars were sold, 16% of the remaining toys in the shop were toy cars, to determine how many toy cars were left in the shop the following calculation must be performed:

Toy cars = 30%

Dolls and teddy bears = 70%

70/5 = 14 x 4 = 56

Dolls = 56%

Teddy bears = 14%

56 - 30 = 26

156/26 = 6 (1%)

Toy cars = 30 x 6 = 180

Dolls = 56 x 6 = 336

Teddy bears = 84

100 - 16 = 84

84 = 336 + 84 = 420

16 = X

84 = 420

16 = X

16 x 420/84 = X

80 = X

Therefore, 80 toy cars were left in the shop.

Answer:

1539.4

Step-by-step explanation:

Steps:

Volume of a cylinder= πr²h

radius= diameter/2

         = 14/2

         = 7 cm

Volume= π x 7² x 10

            = 1539.38

            = 1539.4 cm³

Answer:

1539.4

Step-by-step explanation:

to find the area of a cylinder, you solve pi x radius²

3.14 x 7² = 153.94

then you multiply times the height

153.94 x 10 = 1549.4

Answer:

5/247

Step-by-step explanation:

Slope is rise over run

10/494

Simplifying  by dividing top and bottom by 2

5/247

Answer:

.101501615

.84982392

.901244701

Step-by-step explanation:

For this question use a binomial distribtuion

a.

12C3*.44³*(1-.44)⁹= .101501615

b.

to find at least 4 find the probability of less than 4 and take its compliment

12C0*(1-.44)¹²+12C1*.44*(1-.44)¹¹+12C2*.44²*(1-.44)¹⁰+12C3*.44³*(1-.44)⁹= .15017608

1-.15017608=.84982392

c.

To find less than eight's probability find the proability of at least 8 and take its compliment

12C8*.44⁸(1-.44)⁴+12C9*.44⁹(1-.44)³+12C10*.44¹⁰(1-.44)²+12C11*.44¹¹*(1-.44)+12C12*.44¹²= .098755299

1-.098755299= .901244701

Answer:

See Below.

Step-by-step explanation:

We want to use the Squeeze Theorem to show that:

[tex]\displaystyle \lim_{x \to 0}\left(x^2\sin\left(\frac{2}{x}\right)\right)=0[/tex]

Recall that according to the Squeeze Theorem, if:

[tex]\displaystyle g(x)\leq f(x) \leq h(x)[/tex]

And:

[tex]\displaystyle \lim_{x\to c}g(x) =\lim_{x\to c}h(x) = L[/tex]

Then:

[tex]\displaystyle \lim_{x\to c}f(x)=L[/tex]

Recall that the value of sine is always ≥ -1 and ≤ 1. Hence:

[tex]\displaystyle -1 \leq \sin\left(\frac{2}{x}\right) \leq 1[/tex]

We can multiply both sides by x². Since this value is always positive, we do not need to change the signs. Hence:

[tex]\displaystyle -x^2\leq x^2\sin\left(\frac{2}{x}\right)\leq x^2[/tex]

Let g = -x², h = x², and f = x²sin(2 / x). We can see that:

[tex]\displaystyle \lim_{x \to 0}g(x) = \lim_{ x \to 0}h(x) = 0[/tex]

And since g(x) ≤ f(x) ≤ h(x), we can conclude using the Squeeze Theorem that:

[tex]\displaystyle \lim_{x \to 0}f(x) = \lim_{x \to 0}x^2\sin\left(\frac{2}{x}\right)=0[/tex]

Answer:

Step-by-step explanation:

A line perpendicular to the y-axis, which is vertical, is a line that is horizontal. Perfectly horizontal lines always have a slope of 0. Thus, the equation of the line perpendicular to the one given and passing through the given point (5, 1) is

y - 1 = 0(x - 5) and

y - 1 = 0x - 0 and

y - 1 = 0 so

y = 1 is the equation you're looking for.

Answer:

3x-26=2x(because they are vertical angle)

or,3x-2x=26

therefore x=26

Answer:

Step-by-step explanation:

2x + (3x-26) = 90

5x = 90+26

5x = 116

x = 116/5

x = 23.2

Answer:

3486784401/7  

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

djdjdjdjdjdjkkkdkjrr

Answer:

a -> 3

b -> 4

c -> 1

d -> 5

e -> 2

Step-by-step explanation:

We apply the properties to solve this question.

a. √4x^2y^4

[tex]\sqrt{4x^2y^4} = \sqrt{4}\sqrt{x^2}\sqrt{y^4} = 2xy^2[/tex]

So a -> 3

b. √8x^2y

[tex]\sqrt{8x^2y} = \sqrt{8}\sqrt{x^2}\sqrt{y} = \sqrt{4*2}x\sqrt{y} = \sqrt{4}\sqrt{2}x\sqrt{y} = 2x\sqrt{2}\sqrt{y} = 2x\sqrt{2y}[/tex]

So b -> 4

c. √4x^2y

[tex]\sqrt{4x^2y} = \sqrt{4}\sqrt{x^2}\sqrt{y} = 2x\sqrt{y}[/tex]

So c -> 1

d. √16xy^2

[tex]\sqrt{16xy^2} = \sqrt{16}\sqrt{x}\sqrt{y^2} = 4\sqrt{x}y = 4y\sqrt{x}[/tex]

So d -> 5

e. √8xy^2

[tex]\sqrt{8xy^2} = \sqrt{8}\sqrt{x}\sqrt{y^2} = \sqrt{4*2}\sqrt{x}y = \sqrt{4}\sqrt{2}\sqrt{x}y = 2y\sqrt{2}\sqrt{x} = 2y\sqrt{2x}[/tex]

So e -> 2

Answer:

There are 54 in total because if you add them all it gets you 54

Answer:

a. invalid

b. invalid

c. valid

d. valid

Answer:

the answer would be b I'm pretty sure

Answer:

I think the answer is 1,032 pounds

Step-by-step explanation:

You would have to multiply the dimensions of the table first:

8*3*1=24.

Then you would multiply that by 43.

24*43=1,032.

I THINK this is the answer.

The sum of the measures of angle LMN and angle NMP is 180 degrees. The measure of ∠LMN is 153°.

In Euclidean geometry, an angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively.

L, m n is a straight angle, and we want to find the measure of angle, l, m, p, and m p, and since we are told that l m n is a straight angle.

∠LMN + ∠NMP = 180°

The straight line is 180°

180 - 18 = 162

162 = 18g

g = 9

Hence, ∠LMN = (15 x 9 + 18)° = 153°

Therefore, the measure of ∠LMN is 153°.

To learn more about angles, refer to the link:

https://brainly.com/question/14684647

#SPJ1

Answer:

okay, we need to add up for all k=1 till k=22

we could do it like this

(-4*1 -13) + (-4*2 -13) + (-4*3 -13) + ...

but this is long and boring, so we need another valid, yet vastly faster method to calculate this sum

we know that the "-13" part will occur 22 times, so let's write this component as "-13*22"

the -4k gents bigger with each step, k will take all the natural numbers from 1 to 22

so we could write

"-4 * (1+2+3+4+5+6+7...+21+22l

alot simpler and faster, but not fast enough

let's add up all numbers from 1 to 22 into one number

1 + 22 = 23

2 + 21 = 23

3 + 20 = 23

...

this works eleven times (bc we use up 2 numbers in each step), so the numbers from 1 to 22 added up are just

23*11= 230+23 = 252

now let's construct the final calculation

-4 * 252 -13*22 = -1294

there's your sum.

hope it helps you overall.

brainliest would be very kind ic some else leaves an answer, may it be just a greeting

Answer:

1.76x10^4 gallons

Step-by-step explanation:

total amount in the pool = gallon from first hose +  gallon from second hose

(8.2 + 9.4) 10^3

(17.6)10^3

(1.76 x 10^1)10^3

1.76 x 10^3+ 1 = 1.76x10^4 gallons

Answer: 5.5 minutes

Step-by-step explanation:

Your question is not complete but I guess they you want to calculate the number of minutes that Jenne was on the trampoline.

Let the number of minutes be represented by m.

Therefore, based in the information, we can form an equation which will be:

7.25 + (1.45 × m) = 15.23

7.25 + 1.45m = 15.23

1.45m = 15.23 - 7.25

1.45m = 7.98

m = 7.98/1.45

m = 5.50

Therefore, Jenna used 5.5 minutes

Step-by-step explanation:

1) 6s^2

(s mean the length of each side, s=7)

= 6x7^2

= 294

2) 2(3)(2)+2(1)(2)+2(3)(1)

（l=length, w=wide, h=height)

= 12+4+6

= 22

3) 4(π)12^2

(r=radius)

= 576

Answer:

y=(8/3)x

Step-by-step explanation:

First, we make 8x-3y=3 into the form y=mx+b

3y=8x-3

y=(8/3)x-1

For an equation to be parallel to this equation, the slope must be the same, so the new equation will be:

y=(8/3)x+b

We know that (0,0) is a point in this line. We plug (0,0) into the equation to find b:

0=(8/3)*0+b

b=0

y=(8/3)x

9514 1404 393

Answer:

  24.3 ft

Step-by-step explanation:

If h is the height of the ladder up the tree, the geometry can be modeled as a right triangle with legs h and 6, and hypotenuse 25. The Pythagorean theorem gives you the relation ...

  h² +6² = 25²

  h² = 625 -36 = 589

  h = √589 ≈ 24.3

The ladder reaches about 24.3 feet up the tree.

Answer:

Step-by-step explanation:

Answer:

wait ill work this out for you

Step-by-step explanation: