In two or more complete sentences, compare the number of x-intercepts in the graph of f(t) = t2 to the number of x-intercepts in the graph of g(t) = (t – 8)2. Be sure to include the transformations that occurred between the parent function f(t) and its image g(t).

Answer:

Addition and Multiplication

Step-by-step explanation:

The keywords more than in this case means "addition", and the keyphrase product of a number and two means "multiplication". Here is what your expression should look like:

2n + 8

I am joyous to assist you anytime.

Answer:

(3g+4) (2g^2-5)

Step-by-step explanation:

6g^3 + 8g^2 - 15g - 20

Lets factor by grouping

Taking a 2 g^2 out of the first two terms and -5 out of the last two terms

2g^2 (3g+4) -5(3g+4)

Factoring out (3g+4)

(3g+4) (2g^2-5)

Answer:

The factors are (3g+4)(2g^2-5)....

Step-by-step explanation:

The expression is:

6g^3 + 8g^2 - 15g - 20

Make a group of the first two terms and last two terms:

(6g^3 + 8g^2) - (15g + 20)

Now factor out the common from each group:

2g^2(3g+4)-5(3g+4)

(3g+4)(2g^2-5)

Therefore the factors are (3g+4)(2g^2-5)....

Answer:

Step-by-step explanation:

[tex]x^m=(x^{13})^5x(x^{-8})^{-5}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\x^m=(x^{(13)(5)})x(x^{(-8)(-5)})\\\\x^m=(x^{65})x^1(x^{40})\qquad\text{use} \ a^na^m=a^{n+m}\\\\x^m=x^{65+1+40}\\\\x^m=x^{106}\Rightarrow m=106[/tex]

Answer:

[tex](f+g)(x)=\sqrt{3x+7}+\sqrt{3x-7}[/tex]

[tex]f(g(x))=x+1[/tex]

[tex]f(x)=x+9 \text{ and } g(x)=\frac{4}{x^2}[/tex]

[tex]f^{-1}(x)=\frax{x+2}{3}[/tex]

Let me know if you have any questions about any of my work.

Step-by-step explanation:

You are given the following:

[tex]f(x)=\sqrt{3x+7} \text{ and } g(x)=\sqrt{3x-7}[/tex]

and asked to find [tex](f+g)(x) \text{ which means } f(x)+g(x)[/tex].

If you add those because we are asked to find f(x)+g(x) you get:

[tex]\sqrt{3x+7}+\sqrt{3x-7}[/tex]

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

You are given the following:

[tex]f(x)=x^2+3 \text{ and } g(x)=\sqrt{x-2}[/tex]

and asked to find [tex]f(g(x))[/tex].

[tex]f(g(x))[/tex]

[tex]f(\sqrt{x-2})[/tex] I replaced g(x) with sqrt(x-2) because that is what it equals.

Now this last thing means to replace old input in x^2+3 with new input sqrt(x-2) giving us:

[tex](\sqrt{x-2})^2+3[/tex]

[tex]x-2+3[/tex]

[tex]x+1[/tex]

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

We are given [tex]y=\frac{4}{x^2}+9[/tex] and asked to find g(x) and f(x) such that y=f(g(x)).

We have choices so let's use the choices:

Choice A:

[tex]f(g(x))[/tex]

[tex]f(\frac{4}{x^2}){/tex]    I replace g(x) with 4/x^2:

[tex]\frac{4}{x^2}+9[/tex]  I replaced the old input x with new input 4/x^2.

This was actually the desired result.

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

To find the inverse of f(x)=3x-2 or y=3x-2, your objective is to swap x and y and then remake y the subject.

y=3x-2

Swap x and y:

x=3y-2

Now solve for y.

Add 2 on both sides:

x+2=3y

Divide both sides by 3:

(x+2)/3=y

y=(x+2)/3

[tex]f^{-1}(x)=\frax{x+2}{3}[/tex]

Answer:

[tex]\boxed{(\frac{3}{2} ,-1)}[/tex]

Step-by-step explanation:

[tex]\left \{ {{2x-3y=6} \atop {4x+2y=4}} \right.[/tex]

It seems this system of equations would be solved easier using the elimination method (the x and y values are lined up).

Multiply everything in the first equation by -2 (we want the 4x to be able to cancel out with a -4x).

[tex]2x-3y=6 \rightarrow -4x+6y=-12[/tex]

Now line up the equations (they are already lined up - convenient) and add them from top to bottom.

[tex]\left \{ {{-4x+6y=-12} \atop {4x+2y=4}} \right.[/tex]

The -4x and 4x are opposites, so they cancel out.

Adding 6y and 2y gives you 8y, and adding -12 and 4 gives you -8.

[tex]8y=-8[/tex]

Divide both sides by 8.

[tex]y=-1[/tex]

Since you have the y-value you can substitute this in to the second (or first equation, it doesn't necessarily matter) equation.

[tex]4x +2(-1)=4[/tex]

Simplify.

[tex]4x -2=4[/tex]

Add 2 to both sides.

[tex]4x=6[/tex]

Divide both sides by 4.

[tex]x=\frac{6}{4} \rightarrow\frac{3}{2}[/tex]

The final answer is [tex]x=\frac{3}{2} ,~y=-1[/tex].

[tex](\frac{3}{2} ,-1)[/tex]

do it

like this

i have done by coordinates of geometry

Answer:

Area = 24 square unit,

Fourth vertex = (-4, -3)

Step-by-step explanation:

Suppose we have a parallelogram ABCD,

Having vertex A(1, -2), B(2, 3), and C(-3, 2),

Let D(x,y) be the fourth vertex of the parallelogram,

∵ The diagonals of a parallelogram bisect each other,

Thus, the midpoint of AC = midpoint of  BD

[tex](\frac{1-3}{2}, \frac{-2+2}{2})=(\frac{2+x}{2}, \frac{3+y}{2})[/tex]

[tex](\frac{-2}{2}, 0)=(\frac{2+x}{2}, \frac{3+y}{2})[/tex]

By comparing,

[tex]-2=2+x\implies x=-4[/tex]

[tex]3+y=0\implies y = -3[/tex]

Thus, the fourth vertex is (-4, -3),

Now, the area of the parallelogram ABCD = 2 × area of triangle ABC (Because both diagonals divide the parallelogram in two equal triangles)

Area of a triangle having vertex [tex](x_1, y_1)[/tex], [tex](x_2, y_2)[/tex] and [tex](x_3, y_3)[/tex] is,

[tex]A=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]

So, the area of triangle ABC

[tex]A=\frac{1}{2}|(1(3-2)+2(2+2)-3(-2-3)}|[/tex]

[tex]=\frac{1}{2}(1+8+15)[/tex]

[tex]=\frac{1}{2}\times 24[/tex]

[tex]=12\text{ square unit}[/tex]

Hence, the area of the parallelogram ABCD = 2 × 12 = 24 square unit.

Answer:

[tex]\large\boxed{m\angle S=78^o}[/tex]

Step-by-step explanation:

[tex]\text{If}\ \triangle MNP\cong\triangle QST,\ \text{then corresponding angles}\\\text{and corresponging sides are congruent.}\\\\\angle M\cong\angle Q\\\angle N\cong\angle S\\\angle P\cong\angle\\\\m\angle N=78^o,\ \text{therefore}\ m\angle S=78^o[/tex]

Answer:

14.4

Step-by-step explanation:

72/5 in decimal form equals 14.4

[tex]\frac{72}{5}[/tex] in decimal form is 14.4

[tex]\frac{72}{5}[/tex] is the same as 72 ÷ 5

72 ÷ 5 = 14.4

All we have to do to turn this fraction into a decimal is divide the fractions numerator by its denominator and we will get our decimal.

Answer:

Tan A = 3/4

Step-by-step explanation:

sin A = y/r

Cos A = x/r

Tan A = y/x

Answer:

3/4

Step-by-step explanation:

sin A = 3/5

cosA =4/5

We know that tan A = sin A / cos A

                                   = 3/5  /   4/5

                                    = 3/5 * 5/4

                                    = 3/4

Answer:

x = 6

Step-by-step explanation:

Using the rules of logarithms

• log x - log y ⇔ log ([tex]\frac{x}{y}[/tex] )

• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Given

log(5x) - log(x - 3) = 1

log ( [tex]\frac{5x}{x-3}[/tex] ) = 1, then

[tex]\frac{5x}{x-3}[/tex] = [tex]10^{1}[/tex] = 10 ( cross- multiply )

10(x - 3) = 5x

10x - 30 = 5x ( subtract 5x from both sides )

5x - 30 = 0 ( add 30 to both sides )

5x = 30 ( divide both sides by 5 )

x = 6

Answer:

x =6

Step-by-step explanation:

log(5x) - log(x - 3) = 1

Recall that  the logarithm of a fraction is the difference of the logarithms,

so, the difference between two logarithms is logarithm  of the fraction. Then,

[tex]\begin{array}{rcll}\\\\\log \dfrac{5x}{x-3} & = & 1 &\\\\\dfrac{5x}{x - 3} & = & 10 & \text{Took the antilogarithm of each side}\\\\5x & = & 10(x - 3) & \text{Multiplied each side by x - 3}\\5x & = & 10x - 30 & \text{Distributed the 10}\\-5x & = & -30 & \text{Subtracted 10 x from each side}\\x & = & \mathbf{6} & \text{Divided each side by -5}\\\end{array}[/tex]

Check:

[tex]\begin{array}{rcl}\log(5\times6) - \log (6 - 3) & = & 1\\\log 30 - \log 3 & = &1\\\\\log \dfrac{30}{3} & = & 1\\\\\log 10 & = & 1\\1 & = & 1\\\end{array}[/tex]

OK.

Answer:

The length of the bold figure ABCDEFGH is 30.8 units

Step-by-step explanation:

* To solve the problem look to the attached figure

- There is a square of area 81 units²

∵ The area of the square = L² , where L is the length of the side of

   the square

∵ The area of the square = 81 units²

∴ L² = 81 ⇒ take √ for both sides

∴ L = 9 units

- Two points are drawn on each side of a square dividing it into 3

  congruent parts

∵ 9 ÷ 3 = 3

∴ The length of each part is 3 units

- Quarter-circle arcs connect the points on adjacent sides to create

 the attached figure

∵ The radius of each quarter circle is 3 units

∵ The length of each side joining the two quarter circle is 3 units

∵ The figure ABCDEFGH consists of 4 quarters circle and 4 lines

- The length of the 4 quarters circle = the length of one circle

∵ The length of the circle is 2πr

∴ The length of the 4 quarters circle = 2 π (3) = 6π units

∵ The length of each line = 3 units

∴ The length of the figure = 6π + 4 × 3 = 30.8 units

* The length of the bold figure ABCDEFGH is 30.8 units

Answer:

30.8

Step-by-step explanation:

Answer:

Option A is correct.

Step-by-step explanation:

We need to find the product of

[tex]\frac{(x^2-16)}{(2x+8)} * \frac{(x^3-2x^2+x)}{(x^2+3x-4)}[/tex]

We know (a^2-b^2) = (a+b)(a-b)

so, (x^2-16) = (x)^2-(4)^2 = (x-4)(x+4)

2x+8 Taking 2 common from this term:

2x+8 = 2(x+4)

(x^3-2x^2+x) Taking x common from this term

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

(x^2+3x-4) factorizing this term

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

= (x-1)(x+4)

Now, Putting these simplified terms in the given equation:

[tex]\frac{(x-4)(x+4)}{2(x+4)}*\frac{x(x-1)(x-1)}{(x-1)(x+4)}[/tex]

Now cancelling the same terms that are in numerator and denominator

[tex]=\frac{(x-4)}{2}*\frac{x(x-1)}{(x+4)}\\=\frac{(x-4)(x)(x-1)}{2(x+4)}\\=\frac{x(x-4)(x-1)}{2(x+4)}[/tex]

So, Option A is correct.

Answer:

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

Step-by-step explanation:

=x^2-4^2/2(x+4) * x^3-2x^2+x/x^2+3x-4

=(x+4)(x-4)/2(x+4) * x(x^2-2x+1)/x^2+3x-4

Factor x^2-2x+1 using the perfect square root

=(x+4)(x-4)/2(x+4) * x(x-1)^2/x^2+3x-4

Factor x^2+3x-4 using AC method.

=(x+4)(x-4)/2(x+4) * x(x-1)^2/(x-1)(x+4)

Cancel the common factor of x+4 and x-1

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

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

Reorder the terms

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

Answer:

A. Tina's favorite shade is more blue than Tyler's

Answer:  The correct option is

(A) Tina's favorite shade is more blue than Tyler's.

Step-by-step explanation:  Given that Tina's favorite shade of teal is made with 7 ounces of blue paint for every 5 ounces of green paint.

Tyler's favorite shade of teal is made with 5 ounces of blue paint for every 7 ounces of green paint.

We are to find how Tina's favorite shade of teal compare to Tyler's shade of teal.

The fraction of blue paint in Tina's  favorite shade of teal is given by

[tex]F_{ti}=\dfrac{7}{7+5}=\dfrac{7}{12}[/tex]

and the fraction of blue paint in Tyler's  favorite shade of teal is given by

[tex]F_{ty}=\dfrac{5}{7+5}=\dfrac{5}{12}[/tex]

We get

[tex]F_{ti}-F_{ty}=\dfrac{7}{12}-\dfrac{5}{12}=\dfrac{2}{12}=\dfrac{1}{6}>0\\\\\\\Rightarrow F_{ti}>F_{ty}.[/tex]

That is, the fraction of blue paint in Tina's  favorite shade is more than the fraction of blue paint in Tyler's favorite shade.

Thus, Tina's  favorite shade is more blue than Tyler's.

(A) is the correct option.

Answer:

This graph is a not a Function because it doesn't pass the vertical line test. The opened and closed circles are not  in relation to the y-value and the x-value. This function also doesn't corresponds to one another, which messes up the domain and range.

Step-by-step explanation:

kinda.

x     = total of movies rented, INPUT

g(x) = total cost for all movies rented, OUTPUT.

the point of ( 6.5 , 17.50) means, that 6.5 movies were rented at a price of 17.50 total, that makes sense since 17.5 is more than 6.5 so the price is more than the quantity, however, whoever rents 6.5 movies?  I mean, unless the movie store clerk gives you 6 movies and then cuts another with a chainsaw and gives you half of another.

so, the input is not too feasible, since no one rents 6.5 movies.

Answer:

B. No the input is not feasible

because you cannot rent 6,5 movies  :p

Answer:

It would be 60.

Answer:

Step-by-step explanation:

(3000×2)/100 = 6000/100 = 60

Answer:

9) The equation that represents our monthly bill is y=20+0.05m.

10) The equation that gives us the cost for the month is y=5+0.1m.

Step-by-step explanation:

9) So if we are trying to find how much our monthly bill is where the monthly fee is 20 and we are charged $.05 per minute, then:

For 0 minutes, we spend 20 dollars in the month.

For 1 minute, we spend 20+.05=20.05 dollars in the month.

For 2 minutes, we spend 20+.05+0.05 or 20+2(.05)=20+.1=20.10 dollars in the month.

For m minutes, we spend 20+.05m.

The equation that represents our monthly bill is y=20+0.05m.

They gave us the y-intercept (the initial amount=20) and the rate (the slope=.05).

Remember: slope-intercept form is y=mx+b.

10) I'm going to shorten number 10.

They give us the rate=$.1/min and the initial cost=5 dollars.

The equation that gives us the cost for the month is y=5+0.1m.

Answer:

ASA

Step-by-step explanation:

There is an included side in between both angles in each triangle.

I hope this helps you out, and as always, I am joyous to assist anyone at any time.

Answer:

70°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

let the equal angles be x then the third angle = x + 15

Sum the 3 angle and equate to 180

x + x + x + 15 = 180

3x + 15 = 180 ( subtract 15 from both sides )

3x  = 165 ( divide both sides by 3 )

x = 55

Hence

The largest angle = x + 15 = 55 + 15 = 70°

Answer:

3000 pounds

Step-by-step explanation:

first sub in info to find k

2000=k/15 ; multiply both sides by 15 ; k=30000. if k is the constant, then to find the safe load (y) with the new beam (x), we input our new info into the equation.

y=30000/10 ; y=3000

Answer:

Safe load of the beam is 3000 pounds.

Step-by-step explanation:

If a horizontal beam of x feet length can hold y pounds safe load, the expression that represents the relation between load and length of the beam is

y = [tex]\frac{k}{x}[/tex]

If y = 2000 pounds and x = 15 feet

then 2000 = [tex]\frac{k}{15}[/tex]

k = 15×2000 = 30000

Now we will calculate the safe load when beam is 10 feet long.

From the formula,

y = [tex]\frac{30000}{10}=3000[/tex] pounds

Therefore, safe load of the beam is 3000 pounds.

[tex]f(3)=2^3=8[/tex]

Answer:

D. 8

Step-by-step explanation:

The value of f(3) in f(x)=2x is 8.

f(3)=2^3=8

To find the proportion of boys in the original class, divide the number of boys by the total number of students in the class.

To find the proportion of boys in the original class, we need to compare the number of boys in the original class to the total number of students in the original class.

The original class had 18 students, and it was joined by 6 boys from another class. This means there are now 18 + 6 = 24 boys on the field trip.

The overall ratio of boys to girls on the field trip is 2:3, which means for every 2 boys, there are 3 girls. If we have 24 boys, we can find the number of girls by dividing 24 by 2 and then multiplying by 3. This gives us (24/2) * 3 = 36 girls.

So, the original class had 24 boys and 36 girls. To find the proportion of boys in the original class, we divide the number of boys (24) by the total number of students (24 + 36 = 60). This gives us 24/60 = 0.4, or 40%.

Answer:

50.5 km

Step-by-step explanation:

If speed=distance/time, then distance=time*speed.

So we have the time and the speed to find the distance.

We just need to multiply 5 hours and 10.1 km/hour.

distance=(5 hours)(10.1 km/hour)

The time unit cancels and you are just left with the distance unit.

distance=50.5 km

Answer:50.5 km

Step-by-step explanation:

Answer:

[tex]g(x)=x+6[/tex] is the answer

given

[tex]h(x)=4\sqrt{x+7}[/tex] and [tex]f(x)=4\sqrt{x+1}[/tex].

Step-by-step explanation:

[tex]h(x)=(f \circ g)(x)[/tex]

[tex]h(x)=f(g(x))[/tex]

Inputting the given function for h(x)  into the above:

[tex]4\sqrt{x+7}=f(g(x))[/tex]

Now we are plugging in g(x) for x in the expression for f which is [tex]4\sqrt{x+1}[/tex] which gives us [tex]4\sqrt{g(x)+1}[/tex]:

[tex]4\sqrt{x+7}=4\sqrt{g(x)+1}[/tex]

We want to solve this for g(x).

If you don't like the looks of g(x) (if you think it is too daunting to look at), replace it with u and solve for u.

[tex]4\sqrt{x+7}=4\sqrt{u+1}[/tex]

Divide both sides by 4:

[tex]\sqrt{x+7}=\sqrt{u+1}[/tex]

Square both sides:

[tex]x+7=u+1[/tex]

Subtract 1 on both sides:

[tex]x+7-1=u[/tex]

Simplify left hand side:

[tex]x+6=u[/tex]

[tex]u=x+6[/tex]

Remember u was g(x) so you just found g(x) so congratulations.

[tex]g(x)=x+6[/tex].

Let's check it:

[tex](f \circ g)(x)[/tex]

[tex]f(g(x))[/tex]

[tex]f(x+6)[/tex] I replace g(x) with x+6 since g(x)=x+6.

[tex]4\sqrt{(x+6)+1}[/tex] I replace x in f with (x+6).

[tex]4\sqrt{x+6+1}[/tex]

[tex]4\sqrt{x+7}[/tex]

[tex]h(x)[/tex]

The check is done. We have that [tex](f \circ g)(x)=h(x)[/tex].

Answer:

(4,0)

Step-by-step explanation:

Plug them into see:

Check (4,0)

In order for the lines to intersect at (4,0) it must be on both lines.

2(4)+0=8 is true because it is saying 8=8

4+0=4 is true because 4=4

So (4,0) is a intersection point.

Check (0,4)

2(0)+4=8 is not true because it is saying 4=8

0+4=4 is true so it's on this line while not on the other line.

So (0,4) is not an interestion point for the mentioned lines.

Well all points can't be on the line since (0,4) is not on both lines but just one of them.  

We could have solve this out instead plugging in but the problem gave us the option here with the choices.

The system of linear equations given intersects at the point (4, 0), and since these equations represent distinct lines, they only intersect at this single point.

The question involves solving a system of linear equations to find the point of intersection. The system given is:

Let's solve the equations step by step:

Therefore, the lines intersect at the point (4, 0).

To determine whether the lines intersect at all points on a line, note that these equations represent distinct lines with different slopes, meaning they only intersect at one point, facing the choice given, (4, 0) is correct.

Answer:

Step-by-step explanation:

2+(-2+23)-/8-9/=

2+ 21- /-1/=

2+21-1=

2+20=

22

Please mark as brianliest! Hope this helps!

Answer:

Solution of the expression is 22.

Step-by-step explanation:

The given expression is 2 + (-2 + 23) – Ӏ 8 - 9 Ӏ

We have to solve this expression

2 + (-2 + 23) - | 8-9 |

= 2 + (21) - |-1 |

= 2 + 21 - 1    [Since absolute value of (-x) is x or |-x | = x ]

= 23 - 1

= 22

Solution of the expression is 22.

Answer:

It can be a rigid or a nonrigid transformation depending on whether the corresponding side lengths have the same measures.

Step-by-step explanation:

Answer:C

Step-by-step explanation:

I know

[tex]\huge{\boxed{36}}[/tex]

Substitute the values. [tex]48 - 18 \div 3 * 2[/tex]

Follow PEMDAS and multiply and divide first. [tex]48 - 6 * 2[/tex]

[tex]48 - 12[/tex]

Continue following PEMDAS and subtract. [tex]\boxed{36}[/tex]

Answer:

92

Step-by-step explanation:

87 + 91 + 92 = 270

270 / 3 = 90

The average ticket price in 2018-2019 by calculating increase and add it to previous year ticket price and rounded it to the nearest penny is $88.93

Given that the average NBA ticket price for the 2018-2019 season is up 14.01% from the average ticket price of $78 during the 2015-2016 season.

To find the average ticket price in 2018-2019 by calculating increase and add it to previous year ticket price and rounded it to the nearest penny.

Step 1:  Find the increase ticket price by multiplying the increase % with the previous ticket price:

Increase ticket price = increase % x previous ticket price

Plugging the given data:

Increase ticket price = 14.01 % x 78

Convert percent into decimal:

Increase ticket price = 0.1401 x 78

On multiplying gives:

Increase ticket price = $10.9278

Step 2: Find the  average ticket price in 2018-2019 by add it to previous year ticket price :

average ticket price= previous ticket price +Increase ticket price

Plugging the given data:

average ticket price=78 + 10.9278

On adding gives:

average ticket price=88.9278

Round to the nearest penny

average ticket price = $88.93

Therefore, the average ticket price in 2018-2019 by calculating increase and add it to previous year ticket price and rounded it to the nearest penny is $88.93

Learn more about average here:

https://brainly.com/question/34397603

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Final answer:

The average NBA ticket price for the 2018-2019 season, based on a 14.01% increase from the 2015-2016 average of $78, is approximately $88.93 after rounding to the nearest penny.

Explanation:

To calculate the average NBA ticket price in the 2018-2019 season, we can use the percentage increase from the 2015-2016 season ticket price. We start with the average ticket price of $78 during the 2015-2016 season. According to the question, the ticket prices have increased by 14.01%. This percentage needs to be converted into a decimal (by dividing by 100) and then multiplied by the original average price to find the increase amount.

The calculation for the increase amount will be:

Convert the percentage increase into a decimal: 14.01% ÷ 100 = 0.1401.

Multiply this decimal by the original average price: 0.1401 × $78 = $10.9278.

Add this increase to the original average price to get the new average price: $78 + $10.9278 = $88.9278.

When we round this to the nearest penny, the new average ticket price for the 2018-2019 season is approximately $88.93.