examples of exponents product rule​

Answer:

A. -5/4, 9

Step-by-step explanation:

The solution is in the picture

Answer:

A

Step-by-step explanation:

Given

4m² - 31m - 45 = 0

Consider the factors of the product of the coefficient of the m² term and the constant term which sum to give the coefficient of the m- term

product = 4 × - 45 = - 180 and sum = - 31

The factors are - 36 and + 5

Use these factors to split the m- term

4m² - 36m + 5m - 45 = 0 ( factor the first/second and third/fourth terms )

4m(m - 9) + 5(m - 9) = 0 ← factor out (m - 9) from each term

(m - 9)(4m + 5) = 0

Equate each factor to zero and solve for m

m - 9 = 0 ⇒ m = 9

4m + 5 = 0 ⇒ 4m = - 5 ⇒ m = - [tex]\frac{5}{4}[/tex]

Answer:

Option B R(2,4) is correct

Step-by-step explanation:

The equation of the circle is:

[tex](x-a)^2 + (y-b)^2 = r^2[/tex]

Where r = radius

a and b are coordinates of the center of circle.

To check which point lies on a circle, we need to verify the equation

[tex](x-6)^2 + (y-1)^2 = (5)^2[/tex]

We will check for each option.

Option A Q(1,11)

x=1 and y =11

[tex](1-6)^2 + (11-1)^2 = 25\\(-5)^2 + (10)^2 = 25\\25 + 100 = 25\\125 \neq 25[/tex]

So, Option A is incorrect

Option B R(2,4)

x =2 and y = 4

[tex](2-6)^2 + (4-1)^2 = 25\\(-4)^2 + (3)^2 = 25\\16 + 9 = 25\\25 = 25[/tex]

Option B is correct.

Option C S(4,-4)

x =4 and y =-4

[tex](4-6)^2 + (-4-1)^2 = 25\\(-2)^2 + (-5)^2 = 25\\4 + 25 = 25\\29 \neq 25[/tex]

Option C is incorrect

Option D T(9,-2)

x =9 and y =-2

[tex](9-6)^2 + (-2-1)^2 = 25\\(3)^2 + (-3)^2 = 25\\9 + 9 = 25\\18 \neq 25[/tex]

Option D is incorrect.

Answer:

B.

Step-by-step explanation:

The general equation of a circle is [tex](x-h)^{2}+(y-k)^{2} = r^{2}[/tex] where (h,k) is the center and r the radius. In this case, the general equation of the circle with radius 5 and center at (6,1) is [tex](x-6)^{2}+(y-1)^{2} = 5^{2}[/tex], so the point that satisfies the equation will be in the circle.

A.  [tex](1-6)^{2}+(11-1)^{2} = 25+100 = 125[/tex] this option is not correct.

B.   [tex](2-6)^{2}+(4-1)^{2} = 16+9= 25[/tex] this option is correct so is the answer.

let x = a number

difference means that its subtraction

twice a number is 2x

so the equation should be

2x-5=3

add 5 to both sides

2x=8

divide both sides by 2

x=4

Answer:

x^3 +8x^2 +13

Step-by-step explanation:

(6x^2 - 3 + 5x^3) - (4x^3 - 2x^2 - 16​)

Distribute the minus sign

6x^2 - 3 + 5x^3 -4x^3 + 2x^2 + 16​

Combine like terms

x^3 +8x^2 +13

Answer:

Simplify (6x2 − 3 + 5x3) − (4x3 − 2x2 − 16).

its (C) -------> x^3 + 8x2 + 13

Step-by-step explanation:

Answer:

9.5 inches

Step-by-step explanation:

We are given that in a right angled triangle, one leg is 3 inches long while the hypotenuse is 10 inches long. We are to find the length of the other leg.

For this, we will use the Pythagoras Theorem.

Assuming x to be the length of the other leg.

[tex] 1 0 ^ 2 = 3 ^ 2 + x ^ 2 [/tex]

[tex]100=9+x^2[/tex]

[tex]x^2=91[/tex]

[tex]\sqrt{x^2} =\sqrt{91}[/tex]

x = 9.5

Answer:

9.53 inches

Step-by-step explanation:

In a right  angles triangle, the sum of the squares of the two legs (a and b) equals the square of the the hypotenuse.

a²+b²=c²

Substituting for the values provided in the question we get the following:

3²+b²=10²

b²=10²-3²

b²=91

b=9.53 inches.

Answer:

Option (B) 4 = 2x - 3

Step-by-step explanation:

Let distance travel by Marcus be "x" miles

Then, according to question

Distanced travelled by Jenney will be

twice of "x" minus 3.

Distance travelled by Jenny = 2x - 3.

Also, it is given that Jenny has travelled 4 miles.

then, 4 = 2x - 3. So, here option (B) is the correct option.

Answer:

B

Step-by-step explanation:

Answer:

86

Step-by-step explanation:

To evaluate f(- 9) substitute x = - 9 into f(x)

f(- 9) = (- 9)² + 5 = 81 + 5 = 86

The correct answer is not listed in the provided options. f(-9) is found by substituting -9 into the function f(x) = x² + 5, giving us (-9)² + 5, which results in 86. The provided options do not include the correct answer, suggesting there may be a mistake.

To find f(-9) when f(x) = x² + 5, we simply substitute -9 for x in the function and calculate the result.

Step-by-Step Solution:

Replace every x in the function with -9: f(-9) = (-9)² + 5.

Calculate the square of -9: (-9)² = 81.

Add 5 to the result: 81 + 5 = 86.

Thus, f(-9) = 86.

The correct answer is not listed in the provided options, so there might be a typo in the original function or the options given.

Answer:

+- square root of x+36

Step-by-step explanation:

f(x) = x^2 -36

y = x^2 -36

Exchange x and y

x = y^2 -36

Solve for y

Add 36 to each side

x+36 = y^2 -36+36

x+36 = y^2

Take the square root of each side

±sqrt(x+36) = y

±sqrt(x+36) = f^-1(x)

Apollo Spas would require approximately 17.325 liters of muriatic acid to service all 105 hot tubs.

The student is looking to find out the total amount of muriatic acid, noted in liters, required to service all hot tubs. The problem states Apollo Spas needs to service 105 hot tubs, with each one requiring 165 mL of acid.

Firstly, we need to multiply the number of hot tubs by the amount of acid each one needs: 105 hot tubs * 165 mL/hot tub = 17325 mL.

However, the student needs the amount in liters, not milliliters. To convert mL to L, we need to divide the total mL by 1000 because there are 1000 mL in a liter.  Therefore, 17325 mL / 1000 =  17.325 L.

So, Apollo Spas will need 17.325 liters of muriatic acid to service all 105 hot tubs.

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Answer:

c = 6.1 in

Option B.

Step-by-step explanation:

Your full question can be found in the image below

Since we are dealing with a right triangle, we can use a great number of properties,

We know that

cos(35°)  = Adj cathetus / Hypotenuse

cos(35°)  = 5 in / c

c = 5 in / cos(35°)

Option B.

c = 5 in / 0.82

c = 6.1 in

Answer:

D. c=5/sin(35°)

Step-by-step explanation:

got it right on edge

I would think 168

Because 84×2= 168

The measure of an arc is twice the measure of the angle that intercepted it.

Answer:

Equidistant is your answer.

Step-by-step explanation:

Hope i have helped you!

Answer:

y intercept = 5

Step-by-step explanation:

f(x)=5•(1/6)^x

The y intercept is when x =0

Let x =0

f(0)=5•(1/6)^0      

= 5* 1     = 5

The y intercept is 5

If the question is

f(x)=5•(1/6)x

although I have never seen the question written this way

The y intercept is when x =0

Let x =0

f(0)=5•(1/6)0      

= 5* 0     = 0

The y intercept is 0

Answer:

20 pts

Step-by-step explanation:

50 points corresponds to a 100% grade.  How many points (x) correspond to a 40% grade?

     x            40%

------------ = ---------

50 pts       100%

Then 100x = 2000, and so x = 20.

A score of 20 points would correspond with a test score of 40%.  

Answer:

A score of 20 points would correspond with a test score of 40%.  

Step-by-step explanation:

    x            40%           How many points (x) correspond to a 40% grade?

------------ = ---------

50 pts       100%          50 points corresponds to a 100% grade.  

100x = 2000                divide both sides by 100

x = 20

Answer:

sqrt(2-sqrt(3))/2

Step-by-step explanation:

sin(15)=sin(30/2)=sqrt(1-cos(x))/sqrt(2)=(1-sqrt(3)/2)/sqrt(2)

Again we don't like compound fractions so multiply top and bottom inside sqrt( ) by 2.

sin(15)=sqrt(2-sqrt(3))/sqrt(4)

simplify

sin(15)=sqrt(2-sqrt(3))/2

Answer:

[tex]\frac{\sqrt{2-\sqrt{3} } }{2}[/tex]

Step-by-step explanation:

[tex]sin(\frac{u}{2} =\sqrt[+]{\frac{1-cosu}{2} }                              =\sqrt{\frac{1-cos30^0}{2} } \\=\sqrt{(\frac{1-\frac{\sqrt{3} }{2)} }{2}  } \\=\sqrt{\frac{2-\sqrt{3} }{4} } \\=\sqrt{\frac{2-\sqrt{3} }{\sqrt{4} } } \\=\sqrt{\frac{2-\sqrt{3} }{2} } \\[/tex]

Answer:

x = {4, 4}

Step-by-step explanation:

(x - 4)(x - 4) = 0 has two real, equal roots:  x = 4 and x = 4.  Notice that subbing 4 for x in this equation results in a TRUE equation.

The value of x in  (x - 4)(x - 4) = 0 is x = (4, 4) repeated roots.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given (x - 4)(x - 4) = 0.

∴ Either (x - 4) = 0 or (x - 4) = 0.

x - 4 = 0 ⇒ x = 4 or x - 4 = 0 ⇒ x = 4.

So, x = (4, 4).

This is a case when a quadratic equation has real repeated roots.

The vertex of this graph of this quadratic equation just touches the x-axis.

learn more about quadratic equations here :

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Answer:

A

Step-by-step explanation:

The answer is A as the height starts at 36 and decreases by 9 inches vertically every 12 inches it goes down horizontally.

If you turn this into an equation, you get y = -(9/12)x+36.

Then, you simplify this to y = -(3/4)x+36, which is A.

The function that models the height y railing in inches according to the horizontal distance in inches x, from the top of the stairs is [tex]y = -\frac{3}{4} x \ + \ 36[/tex]. (Option A).

The function that models the height y railing in inches according to the horizontal distance in inches x, from the top of the stairs is calculated as follows;

The general equation of a line;

y = mx + c

where;

If the stairs decreases by 9 inches vertically every 12 inches it goes down horizontally, then the slope becomes;

m = (0 - 9)/(12 - 0)

m = - 3/4

The y - intercept becomes the initial vertical height = 36

The equation that models the problem becomes;

[tex]y = -\frac{3}{4} x \ + \ 36[/tex]

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Answer:

$44,800

Step-by-step explanation:

Original salary : $40,000

12% of original salary = 12% x 40,000 = 0.12 x 40,000 = $4,800

New salary = $40,000 + $4,800 = $44,800

Answer:

  b.  (x, y, z) = (-8, 10, -6)

Step-by-step explanation:

The easiest way to do this one is to try the answers to see which works.

  2(-8) +4(10) +3(-6) = -16 +40 -18 = 6

  5(-8) +8(10) +6(-6) = -40 +80 -36 = 4

  4(-8) +5(10) +2(-6) = -32 +50 -12 = 6

The answers of choice B work in the given equations.

___

In case you don't have answers to select from, you generally solve this sort of problem using elimination. You can also use Cramer's rule, a graphing calculator, an on-line equation solving tool, or any of a variety of other methods.

Here, we can find the variable x by subtracting twice the first equation from the second:

  (5x +8y +6z) -2(2x +4y +3z) = (4) -2(6)

  x = -8

This is sufficient to identify the correct answer choice.

We can substitute this into the last two equations to get ...

  -40 +8y +6z = 4 . . . . 8y +6z = 44

  -32 +5y +2z = 6 . . . . 5y +2z = 38

Subtracting the first of these from 3 times the second gives ...

  3(5y +2z) -(8y +6z) = 3(38) -(44)

  7y = 70 . . . . . . . simplify

  y = 10 . . . . . . . . divide by 7

Substituting this into the second of the above equations, we have ...

  5(10) +2z = 38

  25 +z = 19 . . . . . . divide by 2

  z = -6 . . . . . . . . . . subtract 25

_____

The choice of the combinations to use to eliminate variables can be ad hoc (as here), or it can be made according to some rules (as in Gaussian elimination).

My personal choice for solving systems like this is to use the matrix functions of a graphing calculator.

Answer:

B.4

Step-by-step explanation:

1.5(x+4) - 3 = 4.5( x-2)-----------------------open brackets on both sides

1.5 x +6 -3= 4.5x- 9.................................collect like terms

3+9 = 4.5 x- 1.5x

12=3x..................................divide by 3 both sides to get x

12/3=x

x=4

ANSWER

x=4

EXPLANATION

The given equation is

[tex]1.5(x + 4) - 3= 4.5(x - 2)[/tex]

Multiply through by 10

[tex]15(x + 4) - 30= 45(x - 2)[/tex]

We expand to get:

[tex]15x + 60 - 30= 45x - 90[/tex]

Group similar terms to get;

[tex]15x - 45x = - 90 - 60+ 30[/tex]

[tex] - 30x = - 120[/tex]

[tex] x= 4[/tex]

Answer:

Option D.

Step-by-step explanation:

We will solve the given equation and compare it with the solution of Amit's solution.

[tex]\frac{5}{12}=-\frac{x}{420}[/tex]

We will multiply by (-420) on both the sides of the equation.

[tex]\frac{5}{12}(-420)=-\frac{x}{420}(-420)[/tex]

-175 = x

By comparing the solutions we find that the product of [tex]\frac{5}{12}[/tex] and (-420) should have been the value of x, while Amit multiplied the equation by (420).

Therefore, Option D. is the correct option.

Answer:

if cone is on there then it'd be cone but it may also be a cylinder

Step-by-step explanation:

i dont know the list of objects so i cant guarantee this

[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{3})~\hspace{10em} slope = m\implies -4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-3=-4[x-(-2)]\implies y-3=-4(x+2)[/tex]

Answer:  [tex](y-3)=(-4)(x+2)[/tex]

Step-by-step explanation:

We know that the equation of a line in point-slope form that is passing through a point (a,b) and has slope m is given by :-

[tex](y-b)=m(x-a)[/tex]

Then, the point-slope form of a line with slope -4 that contains the point (-2,3) :-

[tex](y-3)=(-4)(x-(-2))\\\\\Rightarrow\ (y-3)=(-4)(x+2)[/tex]

Hence, the point-slope form of a line with slope -4 that contains the point (-2,3) is [tex](y-3)=(-4)(x+2)[/tex]

Answer:

12.54 square miles

Step-by-step explanation:

Area of Parallelogram = Base x Height

In this case, Base = 3.3 mi and Height = 3.8 mi

Hence,

Area = 3.3 x 3.8 = 12.54 square miles

Answer:

the product of [tex]7\sqrt{x^5} * 7\sqrt{x^5}[/tex] is [tex]49\,x^5[/tex]

Step-by-step explanation:

We need to find the simplifies form of

[tex]7\sqrt{x^5} * 7\sqrt{x^5}[/tex]

We need to find product of above terms

We can write as

[tex](7*7)(\sqrt{x^5}*\sqrt{x^5})\\(7^2)((\sqrt{x^5})^2)\\49\,x^5[/tex]

So, the product of [tex]7\sqrt{x^5} * 7\sqrt{x^5}[/tex] is [tex]49\,x^5[/tex]

Answer:

40 MPH (Miles Per Hour)

Step-by-step explanation:

Well i will put it in simple terms. Put 2/3 into a decimal point, which for this fraction is 0.66666666667 (the 6 is infinite basically). Then you multiply it by 60, because you know it goes in that distance in one minute and 60 minutes makes a hour, which equals 40. So the answer is 40 MPH.

40 miles per hour.

To determine how many miles per hour a bird is flying when it covers 2/3 of a mile per minute, we can follow a simple conversion. Since there are 60 minutes in an hour, we need to multiply 2/3 by 60.

Let's do the calculation:

(2/3 mile/minute) times 60 minutes/hour = 40 miles/hour

This means that when a bird flies 2/3 of a mile per minute, it is equivalent to flying at a speed of 40 miles per hour.

Answer:

(x-6)^2

Step-by-step explanation:

x^2-12x+36

What two numbers multiply to 36 and add to -12

-6 * -6 = 36

-6 + -6 = -12

(x-6) (x-6)

(x-6)^2

Answer:

C. two thirds x + 10 = 21

Step-by-step explanation:

Given

Price of adult ticket = $21.00

Let x be the price of student ticket

Then

two third of the student ticket will be:

[tex]\frac{2}{3} x[/tex]

The statement $10.00 more than two third of student ticket:

[tex]\frac{2}{3} x+10[/tex]

As we are given in the question that the adult ticket price is $21.00 and the second explanation is th equation formed by the given statement

So, both will be equivalent

[tex]\frac{2}{3} x+10 = 21[/tex]

Solving this equation for x will give us the price for the student ticket.

Hence,

C. two thirdsx + 10 = 21 is the correct answer ..

Answer:

C

Step-by-step explanation:

Answer:

x = 5; the slope is undefined

Step-by-step explanation:

A line perpendicular to the x-axis is a vertical line.

In a vertical line, every point has a different y-coordinate and the same x-coordinate. Since you want a line that is vertical and passes through the point (5, -3), then every point on the line must have x-coordinate 5 no matter what its y-coordinate is. The slope of a vertical line is undefined.

Answer: The equation is x = 5; the slope is undefined

Answer:

A and B

Step-by-step explanation:

We can add 48 to both sides of the equation to get

3x^2 = 48

Dividing by 3 on both sides,

x^2 = 16

Taking the square root of both sides,

x = +/- 4

So A and B are our answers.

Answer: Option A and Option B

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

Step-by-step explanation:

We must find the solutions of the following equation

[tex]3x^2-48=0[/tex]

Add 48 on both sides of the equality

[tex]3x^2-48+48=48[/tex]

[tex]3x^2=48[/tex]

Divide both sides of equality by 3

[tex]\frac{3}{3}x^2=\frac{48}{3}[/tex]

[tex]x^2=16[/tex]

Apply the square root on both sides of the equation

[tex]x=\±\sqrt{16}[/tex]

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