The sum of the roots of x² + 6x - 55 = 0 is:
A. 6
B. -6
C. -55

Answer:

Step-by-step explanation:

Hi!

To find the inverse, first we express your function as:

y = 3x - 8

Then, we interchange x and y variables:

x = 3y - 8

From there, we isolate y:

x + 8 = 3y

x/3 + 8/3 = y

Then, the inverse, g(x) = (x+8)/3.

We can check this by getting g(f(x)):

(f(x) + 8)/3 = (3x - 8 + 8)/3 = 3x /3 = x.

This is correct by the definition of the inverse function.

You can also think about the inverse as a "reverse function", so for example, in f(x) = 3x-8, x is multiplied by 3, then 8 is subtracted from it.

If we are to go from f(x) to x, we first add 8 (to reverse the subtraction), then divide by 3 (to reverse the multiplication).

This means g(y) = (y+8)/3, the same answer.

Hope this helps!

[tex] \sf :\implies \quad {\pmb{x = - 4}}[/tex]

Let's solve the given equation step by step ;

[tex] \sf :\implies \quad 6(x + 4) + 1 = x + 5[/tex]

The first step is to distribute the equation:

[tex] \sf :\implies \quad (6 \times x ) + (6 \times 4) + 1 = x + 5[/tex]

[tex] \sf :\implies \quad 6x + 24 + 1 = x + 5[/tex]

[tex] \sf :\implies \quad 6x + 25 = x + 5[/tex]

Second step is to combine the like terms:

[tex] \sf :\implies \quad 6x + 25 - x = 5[/tex]

[tex] \sf :\implies \quad( 6x - x) + 25 = 5[/tex]

[tex] \sf :\implies \quad 5x + 25 = 5[/tex]

Now, subtract 25 from both sides :

[tex] \sf :\implies \quad 5x + 25 - 25 = 5 - 25[/tex]

[tex] \sf :\implies \quad 5x = - 20[/tex]

Divide both sides by 5:

[tex] \sf :\implies \quad \dfrac{5x}{5} = - \dfrac{20}{5} [/tex]

[tex] \sf :\implies \quad \boxed{ \pmb{\sf x = - 4}}[/tex]

Hence, your answer is ; x = -4

Answer:

4x+8 =5

Step-by-step explanation:

sum = +

times = Multiply

is = =

4*x +8 = 5

Answer:

4x+8=5

Step-by-step explanation:

Let's assume the number is x

Four times x plus 8 is 5

4x+8=5

***Optional

If you need to solve it...

4x+8=5

4x=-3

x= - [tex]\frac{3}{4}[/tex]

Hope this helps! :D

Answer:

5280 ft/1 mi, 1848 ft

Step-by-step explanation:

Whatever unit is given on the top (miles), you will write it on the bottom of the second fraction. Since we are solving for length in feet, we know that the numerator will be in feet. The only answer choice that has this option is 5280 ft/ 1 mi. You can check this math by taking 0.35 of 5280 feet, or 1 mile = 1848 ft.

[tex]\frac{0.35 mi}{1} *\frac{?ft}{?mi}[/tex]

[tex]\frac{0.35 mi}{1} *\frac{5280 ft}{1mi}[/tex]        (miles cancels out, left with feet)

[tex]\frac{1848ft}{1}[/tex]

1848 feet

I hope this helps!

When the window is expanded to be 4 feet high by 4 feet wide, the volume of the wall quadruples or increases by factor of 4.

The volume of the wall is determined as follows;

V = h x w x t

where;

Initial volume of the wall when some blocks are removed to make a window is 2 feet high by 2 feet wide.

V1 = (6 - 2) x (6 - 2) x (t)

V1 = 16t  ft³

Second volume of the wall when some blocks are removed to make a window is 4 feet high by 4 feet wide.

V2 = (12 - 4) x (12 - 4) x (t)

V2 = 64t  ft³

V2 = 4(16t  ft³)

V2 = 4(V1)

Thus, when the window is expanded to be 4 feet high by 4 feet wide, the volume of the wall quadruples or increases by factor of 4.

Learn more about volume of cuboid here: https://brainly.com/question/22694657

Answer:

(0,0)

(1,3)

(2,6)

(3,9)

(-1,-3)

(-2,-6)

(-3,-9)

Step-by-step explanation:

The equation of the graph is y=3x

Answer:

G: 770 yards

A: diameter

O: multiplication/division

N: 770 = 2πr

S: D = 2r = 770/π

A: 770/π or ≈ 245.0986 yards

Step-by-step explanation:

Hope this helps!

Answer:

Given: circumference = 770 yards

Asked: Diameter of the circle

Solution:

pi x d = 770

      d = 770/ pi

Check the picture below, so let's check the equations below hmmm

[tex]\boxed{A}\\\\ y=\cfrac{16-3x}{4}\implies y=\cfrac{-3x+16}{4}\implies y = \cfrac{-3x}{4}+\cfrac{16}{4}\implies y=-\cfrac{3}{4}x\stackrel{\stackrel{b}{\downarrow }}{+4}~\hfill \bigotimes \\\\[-0.35em] ~\dotfill[/tex]

[tex]\boxed{D}\\\\ y+4=2x\implies y=2x\underset{\stackrel{\uparrow }{b}}{-4}\qquad \textit{\Large \checkmark}\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Step-by-step explanation:

It is a 5th degree binomial. The highest exponetial power of the polynomial is 5, therefore we are dealing with a 5th degree polynomial. "Polynomial" is a general term. Trinomial and binomial categorize it even more by the number of terms the polynomial has. There are two terms, so we are dealing with a binomial. The prefix bi means "two"

Answer:

Binomial with degree 5

Step-by-step explanation:

The polynomial 3x⁵ + 3 is a binomial with degree 5.

Why?

This option is correct because:

[tex]\rule{150pt}{2pt}[/tex]

Step-by-step explanation:

[tex] \tan(2x) = 1.5[/tex]

Take the arc tangent,

[tex] \tan {}^{ - 1} ( \tan(2x) ) = \tan {}^{ - 1} (1.5) [/tex]

[tex]2x = 56.3[/tex]

[tex]x = 28.15[/tex]

b.

[tex](3 \cos(x) + 1)(2 \cos(x) + 3) = - 2[/tex]

[tex]6 \cos {}^{2} (x) + 11 \cos(x) + 3 = - 2[/tex]

[tex]6 \cos {}^{2} (x) + 11 \cos(x) + 5 = 0[/tex]

[tex]6 \cos {}^{2} (x) + 6 \cos(x) + 5 \cos(x) + 5 = 0[/tex]

[tex]6 \cos(x) ( \cos(x) + 1) + 5( \cos(x) + 1) = 0[/tex]

[tex](6 \cos(x) + 5)( \cos(x) + 1) = 0[/tex]

Set each factor equal to zero.

[tex]6 \cos(x) + 5 = 0[/tex]

[tex]6 \cos(x) = - 5[/tex]

[tex] \cos(x) = - \frac{5}{6} [/tex]

[tex]x = \cos {}^{ - 1} ( \frac{5}{6} ) [/tex]

[tex]x = 146.4[/tex]

For the second factor,

[tex] \cos(x) + 1 = 0[/tex]

[tex] \cos(x) = - 1[/tex]

[tex]x = 180[/tex]

So the answer for the second one is

146.4 and 180.

Answer:

Variables

Let m = number of movies rented

Let g = number of video games rented

Given:

System of equations

m + g = 5

2m + 3g = 13

Solution

Rewrite  m + g = 5  to make m the subject:

⇒ m = 5 - g

Substitute this equation into  2m + 3g = 13 and solve for g:

⇒ 2(5 - g) + 3g = 13

⇒ 10 - 2g + 3g = 13

⇒ 10 + g = 13

⇒ g = 3

Substitute found value of g into  m = 5 - g  and solve for m:

⇒ m = 5 - 3

⇒ m = 2

Therefore, 2 movies and 3 video games were rented.

Answer:

How much money did Amy wager on her games?

Step-by-step explanation:

Is she in debt?

Answer:

49

Step-by-step explanation:

So, you can just do 245x1/5.

I got 1/5 from "how many did she LOSE?"

5/5-4/5=1/5.

She lost 49 games.

Answer:

A

Step-by-step explanation:

We do the opposite.

Answer: A. c = nv

Step-by-step explanation: This is simple algebra, despite the complicated variables involved. Just think of it as a normal equation.

First, we multiply both sides by v to get rid of c/v. Thus, nv = c. We can switch sides since c also equals nv. So, the answer of c = nv, or A in the multiple choice.

Answer:

1 1/8 cups of vanilla for a cup of milk.

Step-by-step explanation:

v-3/8  m-1/3

v-6/8  m-2/3

v-1 1/8 m-1

Answer:

Less Likely

Step-by-step explanation:

A 2/7 probability means that it will happen less than half the time.

The eliminates equally likely, more likely, and certain as those are 50% or greater.

The probability is also greater than 0%, so it's not "impossible"

Therefore, the answer must be B, Less Likely.

It happens less than half the time, but can at times happen.

Hope this helps!

The solution is, Less Likely, best describe the likelihood of this event.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

given that,

An event has a probability of 2/7.

now, we get,

A 2/7 probability means that it will happen less than half the time.

The eliminates equally likely, more likely, and certain as those are 50% or greater.

The probability is also greater than 0%, so it's not "impossible"

It happens less than half the time, but can at times happen.

Therefore, the answer must be B, Less Likely.

To learn more on probability click:

brainly.com/question/11234923

#SPJ7

Answer: x=4. PS=QR=15

Step-by-step explanation:

Answer:

35 : 28

Step-by-step explanation:

Check the attachment.

Answer:

400

Step-by-step explanation:

so its actually really easy, take 10x10 and then multiply that by 12 and then divide by the exponent so in this case 10x10x12 then divide by 3

Answer: 400

Step-by-step explanation: 10*10*12/3

The function [tex]y=0.3^x[/tex] represents exponential growth with the initial value equal to 1, the decay factor equal to 0.3, and the rate equal to 0.7.

The formula for the Population Growth Equation is:

[tex]P_f=P_o*(1+\frac{R}{100}) ^t[/tex]

Pf= future population

Po=initial population

r=growth rate

t= time (years)

growth or decay factor =  (1 ±r)

When 1+R  > 1, the equation represents growth, while 1+R < 1 the equation represents decay.

The question gives:

[tex]y=0.3^x[/tex], then

Pf=y

Po= 1  

[tex](1+\frac{R}{100}) =0.3[/tex] , thus

[tex](100+R}) =30\\ \\ R=-100+30\\ \\ R=-70[/tex]

r= -70%= -0.7

decay factor= (1-0.7)=0.3

Therefore,

1+R will be = 1+(-0.7)=1 - 0.7 =0.3

When 1+R >1, the function represents exponential growth.

Read more about the exponential function here:

brainly.com/question/8935549

Answer:

Step-by-step explanation:

The maximum is achieved at vertex of parabola.

The x- coordinate of the vertex is determined by x = - b/(2a).

The maximum height is the corresponding y- coordinate

Find vertex

x coordinate

Y coordinate (Max height)

Answer:

You can memorize formulas like (a+b)^2 but that's about it, I will write down some formulas that might be useful.

(a+b)^2 = a^2+2ab+b^2

(a-b)^2 = a^2-2ab+b^2

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

calculate the zeros: x1,x2 = (-b +/- sqrt(b^2-4ac))/2a

Answer:

Step-by-step explanation:

The required area is between 9+3 = 12 feet and 9 feet radius circles.

Find the area:

Answer:

There's enough soil to plant 8 herbs.

Step-by-step explanation:

24 ÷ 2 7/8 = 8.3

This shows that there's enough soil to plant 8 herbs.

Answer:

345 [tex]cm^{3}[/tex]

Step-by-step explanation:

The volume of 2 rectangular boxes :
7 × 5 × 3 + 5 × 7 × 3 = 210 [tex]cm^{3}[/tex]
The volume of given prism
210 + [(10 - 7 ) × 3 × (5 × 3) ]= 345 [tex]cm^{3}[/tex]

Answer:

70 degrees

Step-by-step explanation:

rectange angle total = 360

1 corner = 90

90-20 = 70