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Answer:

(fg)(x) = (4x^2 + x^4)(x^2 + 4)^(1/2)

Step-by-step explanation:

Mathematically;

(fg)(x) = f(x) * g(x)

so we have;

4x^2 +x^4 * √(x^2 + 4)

But √(x^2 + 4) = (x^2 + 4)^(1/2)

So we have;

(fg)(x) = (4x^2 + x^4)(x^2 + 4)^(1/2)

Answer:

3 or

C

Step-by-step explanation:

(45 - 3x)^1/2 = x - 9                     Square both sides

45 - 3x = x^2 - 18x + 81               Switch sides

x^2 - 18x + 81 = 45 - 3x               Add 3x to both sides

x^2 - 15x + 81 = 45                      Subtract 45 from both sides

x^2 - 15x + 36 = 0                       Factor

(x - 12)(x - 3) =0

The answers are

x = 12

x = 3

Now the question asks which is extraneous. The answer will be which ever number won't solve the original equation. Looking at it right now, both look OK.

(45 - 3*12)^1/2 = 12 - 9

(45 - 36)^1/2 = 3

(9)^1/2 = 3

So 12 is a proper solution.

What about 3?

(45 - 3*3)^1/2 = 12 - 3

(45 - 9)^1/2 = 9

36^1/2 = 9

6 does not = 9

The extraneous solution is x = 3

Answer:

11. 90

12. 90

13. 90

14. 90

15. 180

16. 135

17. 225

18. 270

Step-by-step explanation:

Answer:

BC=90

AC=90

AE=90

EB=90

ACB=180

AD=135

CBF=225

ADC=270

Step-by-step explanation:

for numbers 11-14 they're all linear pairs which means they're each 90 degrees

and as long as O is the center point, all the arcs are the same value as the degree.

for numbers 16-17 you can assume that line FO and DO bisects the right angles which makes them 45 degrees

and for 18, you just multiply 3 and 90 degrees

Answer:

2.02

Step-by-step explanation:

Hello, I took the quiz. The correct answer is 2.02

Answer:

(A) y = (x - 2)^2 + 1

Step-by-step explanation:

All the answer choices are in vertex form. Here's the formula for vertex form:

y = a(x - h)^2 + k

h = x coordinate of vertex

k = y coordinate of vertex

We already know that a = 1 because all of the answer choices have a = 1, so to find the right answer, you have to know how to write vertex form when given the vertex.

The vertex is (2, 1). The x coordiante (2) is equal to h, and the y coordinate (1) is equal to k.

Plug these two numbers into the formula and that's your answer!

y = (x - 2)^2 + 1

Hope it helps (●'◡'●)

Step-by-step explanation:

We can start by writing an equation to describe the data set. For 2D data, one equation form we can use is y=m*x + b, where x is the input and y is the output. Since yuan are put in and dollars are put out, x represents yuan and y represents dollars in this instance.

To find the equation, we can start by plugging in two points, such as (50, 1.25) and (100, 7.5). The slope, or m, is equal to the change in y/change in x, or

(7.5-1.25)/(100-50) = 6.25/50

= 0.125. This means that for each yuan put in, 0.125 dollars come out, according to the formula.

Next, we must find b. Plugging 0.125 in for m and taking a set of points, such as (50, 1.25), we get

1.25 = 50(0.125) + b

1.25 = 6.25 + b

subtract both sides by 6.25 to isolate the b

-5 = b

Therefore, we can write our equation as

y = 0.125 * x - 5

In this equation, there is an exchange rate of 0.125, meaning that for each yuan put in, 0.125 dollars are coming out. The -5 symbolizes that for each transaction, 5 yuan are being lost, which is the fee for exchanging money.

To check if the equation works, we can try it for options such as (200, 20) and (250, 26.25). This does work, so we can move forward with our equation.

For (c), our equation is y = 0.125 * x - 5, with the y representing dollars, x representing yuan, 0.125 representing the exchange rate, and -5 representing the fee for exchaning mone

For (b), because 5 yuan are subtracted from the exchange rate for each transaction, it is fair to assume that there is a fee for exchanging money. There is a fee of 5 yuan per transaction. In dollars, using the exchange rate of 0.125 dollars per yuan, this is equal to 0.625 dollars

For  (a), the exchange rate is 0.125 dollars per yuan. We know this because for each yuan put in, 0.125 dollars are coming out after taking into account the fee

Hello!

0.4x + 3 = 0.2(3x + 1) - x

0.4x + 3 = 0.6x + 0.2 - x

0.4x + 3 = -0.4x + 0.2

0.4x + 0.4x = 0,2 - 3

0.8x = -2.8

x = -2.8 : 0.8

x = -7/2

Good luck! :)

Answer:

26.31

Step-by-step explanation:

Use distance formula

d = [tex]\sqrt{(x_{2}-x_{1)^{2} + (y_{2}-y_ ^{1)^2} } }[/tex]

substitute in points and solve

d =  [tex]\sqrt{(7-3)^2 + (23-(-3))^{2} }[/tex]

d = [tex]\sqrt{4^{2}+26^{2} }[/tex]

d = [tex]\sqrt{16 + 676}[/tex]

d = [tex]\sqrt{692}[/tex]

d = 26.30589288

d = 26.31 rounded

Answer:

-1

Step-by-step explanation:

Replace x with -2

f(-2)=-(-2)^2+3

Solve.

f(-2)=-4+3

      =-1

I hope this helps!

Answer:

-1

Step-by-step explanation:

When you have f(x) =- x^2 +3 and want to find f(-2), it is basically asking you to calculate the function where x is -2. So if you plug in -2 for x you get:

-(-2)^2 + 3= f(-2)

-4+3= f(-2)

-1=f(-2)

Answer:

A rhino runs at a speed of about 28 miles per hour.

We need to determine the speed in feet per second.

Converting miles to feet:

The miles can be converted to feet by multiplying 5280 with 28 miles per hour.

Thus, we have;

28 x 5280 = 14784028 × 5280 = 147840

Thus, the speed of the rhino in feet per hour is 147840

Converting hours to seconds:

The hours can be converted into seconds by dividing 147840 by 3600 (Because an hour has 60 seconds in a minute and 60 minutes in an hour)

Thus, we get;

Speed=\frac{147840}{3600}Speed=

3600

147840

Speed = 41.066667Speed=41.066667

Rounding off to the nearest whole number, we get;

Speed = 41

Therefore, the speed of the rhino is 41 feet per second.

p(0)=2

p(1)=2+1+2-1=4

p(2)=2+2+8-8=4

[tex]a = 28.[/tex]

Step-by-step explanation:

[tex] {a}n = a + (n - 1)d[/tex]

[tex]4 = a + (7 - 1)( - 4)[/tex]

[tex]4 = a + 6( - 4)[/tex]

[tex]4 = a + ( - 24)[/tex]

[tex]4 = a - 24[/tex]

[tex]4 + 24 = a[/tex]

[tex]28 = a[/tex]

(OR)

[tex]a = 28.[/tex]

Answer:

(1,5),(2,7),(3,9)

Step-by-step explanation:

x= 1

=> y=2*1+3 = 5

x=2

=> y=2*2+3 = 7

x=3

=> y=2*3+3 = 9

Answer:

25.5

Step-by-step explanation:

first find angle E.

remember, all angles in a triangle always add up to 180 degrees.

E = 180 - 90 - 20 = 70 degrees

now we use the law of sines.

ED/sin(20) = DC/sin(70) = EC/sin(D)

EC = x

sin(D) = sin(90) = 1

24/sin(70) = x/1 = x

x = 25.5

Answer:

the above answer help you guy.

Answer:

b

Step-by-step explanation:

Answer:

The one that looks like a letter U

Answer:

C

Step-by-step explanation:

Cause C met the rules of scientific notation which is:

Answer:

y=2x+5

Step-by-step explanation:

y=2x+4 means that the slope is m1=2

A parallel line shall have the same slope so

m2=m1=2

Therefore, the equation of the new line will be

y=2x+q

where q is the y-intercept, that is 5 because the line must pass in (0,5), so

q=5

and

y=2x+5

Answer: Amy is incorrect. The answer is -5 points.

Step-by-step explanation:

From the question, we are informed that Amanda earned 20 points for winning a sprint in the first race but got -25 points in the second race.

Based on the information above, Amanda's total score now will be:

= 20 + (-25)

= 20 - 25

= -5

The answer is -5 points.

Amy is wrong because (+) × (-) = (-)

Answer:

19

Step-by-step explanation:

19 is the answer I think so

Answer:

Hey, could you please add the number line to the question too

The equation of the new path would be y=1/3x+4.

Explanation

If two lines are perpendicular, their slopes are negative reciprocals of each other.  The original equation is written in slope-intercept form, y=mx+b, where m is the slope.  In this equation, m=-3=-3/1.

In the new equation, the slope would be the opposite sign and flipped; this means it would be 1/3.

We can use the point given, the slope and slope-intercept form to write the equation of the new line:

y=mx+b

3=1/3(-3)+b

3=1/3(-3/1)+b

3=(-3/3)+b

3=-1+b

Add 1 to both sides:

3+1=-1+b+1

4=b

This makes the equation y=1/3x+4.

Answer:

B

Step-by-step explanation:

> if the lines are perpendicular then their slopes are negative reciprocal so

y=mx+b , is the general form where is m = slope

y= -3x -4, old path has slope m= -3

y= (1/3)x +b , is the new path with slope m=(1/3)

>if the paths intersect at (-3,3) then this point is on the new path as well

y= (1/3)x +b, now substitute x= -3, and y=3 to find b

3 = (1/3)(-3)+b , divide -3/3

3= -1 +b, add 1 to both sides

4 = b

>the equation of the new path is

y= (1/3)x +4

The angle based on the diameter is always right

Then <ABC=90 and ∠BAC=∠ACB=45° ;  and ∠BCD=180-45=135 then                x=(180-135):2=22,5°

Answer:

143

Step-by-step explanation:

A = [tex]\frac{Base1 + Base2}{2}[/tex] x h

A = [tex]\frac{8 + 18}{2}[/tex] x 11

A = [tex]\frac{26}{2}[/tex] x 11

A = 13 x 11

A = 143

Answer:

none of the multiple choice are right, it's 143

Step-by-step explanation:

use trapezoid formula

a+b

------- h

2

26

----- h

2

13×11= 143

Answer:

20 units

Step-by-step explanation:

Let the length be x. According to the question,

➝ Width = 15% of the length

➝ Width = 15/100x

➝ Width = 3/20x

We have the perimeter of the rectangle that is 46 units.

[tex]\longrightarrow \sf {Perimeter_{(Rec.)} = 2(L + W) } \\ [/tex]

[tex]\longrightarrow \sf {46= 2\Bigg \lgroup x + \dfrac{3}{20}x \Bigg \rgroup } \\ [/tex]

[tex]\longrightarrow \sf {46= 2\Bigg \lgroup x + \dfrac{3}{20}x \Bigg \rgroup } \\ [/tex]

[tex]\longrightarrow \sf {46= 2\Bigg \lgroup \dfrac{20x + 3x}{20} \Bigg \rgroup } \\ [/tex]

[tex]\longrightarrow \sf {46= 2\Bigg \lgroup \dfrac{23x}{20} \Bigg \rgroup } \\ [/tex]

[tex]\longrightarrow \sf {\dfrac{46}{2}= \dfrac{23x}{20}} \\ [/tex]

[tex]\longrightarrow \sf {23= \dfrac{23x}{20}} \\ [/tex]

[tex]\longrightarrow \sf {23 \times 20 = 23x} \\ [/tex]

[tex]\longrightarrow \sf {460= 23x} \\ [/tex]

[tex]\longrightarrow \sf {\cancel{\dfrac{460}{23}} = x} \\ [/tex]

[tex]\longrightarrow \underline{\boxed{ \bf {20\; units = x}}} \\ [/tex]

Therefore, length of the rectangle is 20 units.

Answer:

1 = Input G

2 = Input F

3 = Input H

Step-by-step explanation:

4 x minus four-fifths = 2 and one-fifth; x = three-fourths of a pound

Answer:

11.3

Step-by-step explanation:

first we find angle F.

remember, all angles in a triangle always sum up to 180 degrees.

so,

F = 180 - 90 - 61 = 29 degrees

now we use the law of sines.

EF/sin(D) = ED/sin(F) = DF/sin(E)

DF = x

sin(E) = sin(90) = 1

5.5/sin(29) = x/1 = x

x = 11.3