Keiko makes 8 dollars for each hour of work. Write an equation to represent her total pay p after working h hours.

Answer:

Difference of cubes polynomial identity prove that 117 =125-8

Step-by-step explanation:

Difference of cubes:- A polynomial in the form of [tex]a^3 -b^3[/tex] is called  the difference of cubes.

The formula for difference of cubes is;

[tex]a^3 -b^3 = (a-b)(a^2+b^2+ab)[/tex]

To prove: 117 = 125 - 8

Take RHS

[tex]125-8 = 5^3 -2^3[/tex]

Apply difference of cubes;

[tex]5^3-2^3 = (5-2)(5^2+2^2+5\cdot 2)[/tex]

                     =[tex]3(25+4+10) = 3(39) = 117[/tex] = LHS       hence proved!

Therefore, difference of cubes polynomial identity will prove that 117 = 125-8

Answer:

9x - 8

Step-by-step explanation:

the perimeter is the sum of the sides, hence

perimeter = 5x - 2 + 3x + 4 + x - 10 ( collect like terms )

                = 9x - 8 ← polynomial of degree 1

Answer:

(6, -3)

Step-by-step explanation:

I will solve this system using elimination.

[tex][tex]\left \{ {{-x+2y=-12} \atop {2x+3y=3}} \right.[/tex][/tex]

I will multiply [tex]-x+2y=-12[/tex] by 2 so that -x becomes -2x.

2(-x + 2y = -12)

Distribute.

-2x + 4y = -24

Now subtract this from the other equation.

2x + 3y = 3

-2x + 4y = -24

        7y  =  -21

Divide both sides by 7.

y = -3

Now that we have the value of y, plug it into the original equation.

-x + 2(-3) = -12

Simplify.

-x - 6 = -12

Add 6 to both sides.

-x = -6

Divide both sides by -1.

x = 6

(6, -3)

Answer:

88 cm

Step-by-step explanation:

The side of the square = 6 cm, so the shorter side of each rectangle = 6 cms.

The area of each rectangle =  36 *  1 1/3

= 36 * 4/3 = 48 cm^2

So the longer side of each rectangle = 48 / 6 =  8 cms

Therefore, the perimeter of the whole figure

=  4( shorter sides ) + 8(longer sides)

= 4*6 + 8*8

= 24 + 64

= 88 cm   (answer)

Answer:

d - 10

Step-by-step explanation:

Because the amount of Leila’s baseball cards was d, subtract 10 from it to get Leila’s amount of baseball cards now.

d - 10

Answer:

d-10

Step-by-step explanation:

I don't know the word after "Using".

"Gave away" means having less, which means that you should subtract.

d-10

Answer:

Solution to system is

x = 6 and y= 4

S.set={6,4}

Step-by-step explanation:

The given equations are

x + 3y = 18                      ................(i)

x + 2y=14                        .................(ii)

Subtracting both equation

(x+3y)-(x+2y)=18-14

x+3y-x-2y = 4

y = 4

put the value of y in equation (i)

the equation becomes

x + 3(4) = 18

x + 12 = 18

subtracting 12 from both sides

x + 12 -12 = 18-12

x =6

Solution to system is

x = 6 and y= 4

S.set={6,4}                            

Answer:

x= 7

Step-by-step explanation:

2x^2=98

\frac{2x^2}{2}=\frac{98}{2}

x^2=49

7^2=49

Final answer:

The solutions to the equation 2x^2 = 98 are x = 7 and x = -7, obtained by isolating the x^2 term and taking the square root of both sides.

Explanation:

To solve the equation 2x^2 = 98, we need to convert it into a standard quadratic equation by bringing the terms to one side of the equals sign, setting it equal to zero:

2x^2 - 98 = 0

Now, we will proceed to solve the quadratic equation. In this simple case, we can find the solutions by factoring or by taking square roots. First, we move the constant to the other side:

2x^2 = 98

Divide both sides by 2 to isolate the x^2 term:

x^2 = 49

To find x, we take the square root of both sides. Do not forget to consider both the positive and negative roots:

x = ±√49

x = ± 7

So the solutions to the equation 2x^2 = 98 are x = 7 and x = -7.

Answer:

60

Step-by-step explanation:

5 ( 9 + d )

Let d=3 and substitute it in

5(9+3)

According to PEMDAS, we do what is in the parentheses first

5(12)

Now we multiply.

60

Answer:

60

Step-by-step explanation:

5 ( 9 + d )

Let d=3 and substitute it in

5(9+3)

According to PEMDAS, we do what is in the parentheses first

5(12)

Now we multiply.

60

The hypotenuse of the ΔBAD is the side BD.

The longest side in a right angled triangle is called hypotenuse, it is the side which is opposite to 90° angle.

Step 1 : In the given cube, we should look at the face ABCD

Step 2 : Let us draw an imaginary line between the point B and D

Step 3 : Now the face ABCD is split into two triangles ΔBAD and ΔBCD respectively

Step 4 : The side opposite to the 90° angle of ΔBAD is BD

Hence the side BD is hypotenuse of ΔBAD.

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Answer:

74.30

Step-by-step explanation:

Let s = entry price for a student

Let t = entry price for a teacher

4s +5t = 95

6s+10t = 173

I will use elimination to solve this problem.

Multiply the first equation by -2

-2(4s +5t) = -2*95

Distribute

-8s - 10t = -190

Add this equation to the second equation to eliminate t

-8s - 10t = -190

6s+10t = 173

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

-2s = -17

Divide by -2

-2s/-2 = -17/-2

s = 8.50

Now we need to find t

4s +5t = 95

Substitute s=8.50

4(8.50) +5(t) = 95

34 +5t = 95

Subtract 34 from each side

34-34 +5t = 95-34

5t = 61

Divide by 5

5t/5 = 61/5

t = 12.20

We want to find the cost for 3 students and 4 teachers

3s+4t

3(8.50) + 4(12.20)

25.50 + 48.80

74.30

Answer:

12

Step-by-step explanation:

Orange juice: $2.20 per bottle.

10 bottles of orange juice cost 10 * $2.20 = $22.00.

We subtract the cost of the 10 bottles of orange juice from the amount of money he has to find out the amount he will have left for bottles of apple juice.

$50.80 - $22.00 = $28.80

After buying the 10 bottles of orange juice, he has $28.80 left.

We divide the money he has left for apple juice bottles by the price of one apple juice bottle to find out the number of apple juice bottles he can buy.

$28.80/$2.40 = 12

He can buy 12 bottles of apple juice.

Answer: [tex]50^{\circ}[/tex]

Step-by-step explanation:

By the definition  of quadrilateral,

A quadrilateral has four interior angles and the sum of all interior angle of a quadrilateral is always equal to [tex]360^{\circ}[/tex]

Here the measurements of three interior angles are [tex]85^{\circ}[/tex], [tex]105^{\circ}[/tex] and [tex]120^{\circ}[/tex]

Let the measurement of fourth angle is x degree.

Thus,  [tex]85^{\circ}+105^{\circ}+120^{\circ}+x=360^{\circ}[/tex]

[tex]310^{\circ}+x=360^{\circ}[/tex]

[tex]x = 360^{\circ}-310^{\circ}=50^{\circ}[/tex]

Thus, the measure of fourth angle is [tex]50^{\circ}[/tex]

The measure of the 4th angle is 50 degrees.

To find the measure of the fourth angle of a quadrilateral, we need to know that the sum of all the interior angles of a quadrilateral is always 360 degrees. Therefore, to find the measure of the fourth angle, we can subtract the sum of the other three angles from 360. In this case, the given angles are 85, 105, and 120 degrees, so the sum of these three angles is 85 + 105 + 120 = 310 degrees. To find the measure of the fourth angle, we subtract 310 from 360: 360 - 310 = 50 degrees.

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Answer:

X=5 (Or (5,0))

Step-by-step explanation:

The Y intercept is when X=0

The X Intercept is when Y=0

Our equation is y=-4200x+21000

So let's rewrite it... First subtract 21,000 (Also, remember Y is 0)

0-21000=-4200x

-21000=-4200x

Now to get X alone, divide -21000 by -4200

This will give us 5=x, which is the same as x=5. There is your answer!

The slope means that the value decreases by -4,200 per year.

Here we have the linear equation:

y = -4,200x + 21,000

We know that this equation relates the value of something, y, after x years.

So a slope will tell us how many units does the value increase or decraeses each year.

Here the slope is -4,200, which means that the price decreases by -4,200 dollars each year.

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Answer:

The outlier slightly affected the median.

Step-by-step explanation:

Answer:

simple terms its A

Step-by-step explanation:

Answer:

Bowl B contains 2 apples more than Bowl A and Bowl A contains 1 mango more than Bowl B.

Step-by-step explanation:

Number of apples in Bowl A = 6

Number of mangoes in Bowl B = 8

Difference in apples = 8 - 6 = 2

So, Bowl B contains 2 apples more than Bowl A.

Number of mangoes in Bowl A = 3

Number of mangoes in Bowl B =2

Difference in mangoes = 3 - 2 = 1

So, Bowl A contains 1 mango more than Bowl B.

Bowl B has 2 more apples and 1 fewer mango compared to Bowl A. Thus, the primary differences are in the quantities of apples and mangoes in each bowl.

Step by Step Solution:

To understand the differences between Bowl A and Bowl B, let's break down the contents of each bowl:

Bowl A contains 6 apples and 3 mangoes.

Bowl B contains 8 apples and 2 mangoes.

Now, let's find the differences in the number of apples and mangoes between the two bowls:

Difference in Apples: Bowl B has 8 apples, and Bowl A has 6 apples. Therefore, the difference is 8 - 6 = 2 apples. Bowl B has 2 more apples than Bowl A.

Difference in Mangoes: Bowl A has 3 mangoes, and Bowl B has 2 mangoes. Therefore, the difference is 3 - 2 = 1 mango. Bowl A has 1 more mango than Bowl B.

In summary, Bowl B has 2 more apples and 1 fewer mango compared to Bowl A.

Answer:

I think this is right but I may be wrong

Step-by-step explanation:

Answer:

Easy! Y=0.5x

Step-by-step explanation:

First, we have to find unit rate.

6/6 = 1

3.00 / 6 = 0.5

Y=0.5x

Answer:

A

Step-by-step explanation:

this is a standard right triangle 30-60-90

with legs 1 and [tex]\sqrt{3}[/tex] and hypotenuse 2, hence

s = [tex]\sqrt{3}[/tex] and h = 2

Answer:

A. [tex]\sqrt{3}[/tex] ; 2

Step-by-step explanation:

Since We have all the angles of the triangle and one side we can use SIN, COS, and TAN to find the missing side lengths. SIN which is [tex]sin(x) = \frac{opposite}{hypotenuse}[/tex] can be used to find the hypotenuse

[tex]sin(30) = \frac{1}{h}[/tex]

[tex]\frac{1}{sin(30)} = \frac{h}{1}[/tex] ..... inverse both sides

[tex]\frac{1}{sin(30)} = h[/tex]

[tex]2 = h[/tex]

Now we can use the Pythagorean theorem to find the missing length. The Pythagorean Theorem is [tex]a^{2} +s^{2} = h^{2}[/tex]. So we just plug in the values we already have and solve for s.

[tex]1^{2} +x^{2} = 2^{2}[/tex]

[tex]1+s^{2} = 4[/tex]

[tex]s^{2} = 3[/tex]

[tex]s = \sqrt{3}[/tex]

In Conclusion, s = [tex]\sqrt{3}[/tex] and h = 2

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It took Stephen 2.5 hours to run the entire 5-mile race.

To find out how long it took Stephen to run the entire race, we need to know how many 1/4 mile segments are present in a 5 mile race. We can do this by dividing the total distance by the distance ran in each segment. Since 1/4 mile is ran in 1/8 hour, we can divide 5 miles by 1/4 mile to find the total number of segments, which is 20. Multiplying 20 by 1/8 hour, we get the total time it took Stephen to run the race, which is 2.5 hours.

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Answer:

Divided by 3.

They are all divided by 3.

Answer:

b(1)= 27

b(n)=b(n-1)* (-1/3)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Under a rotation about the origin of 180°

a point (x, y ) → (- x, - y) → D

Note this only happens if the rotation is about the origin

The largest decimal is :

0.68

Because: In the tenths place, 6 is the biggest number.  Now we go to the hundredths to see which one is the biggest.  8 Is the largest one out of them.  But what about the 0's?  The 0's at the end don't really matter.  They are there to confuze you or to add more extra 0's.  The 0 at the front of the decimal is also smaller then the 6.  For example:  0.0175  < 0.68

Hope helps!-Aparri

The largest decimal among 0.0688, 0.667, 0.68, and 0.6 is 0.68. This can be determined by comparing each digit from left to right in the numbers. Hence, 0.68 is the highest.

To determine which is the largest decimal among 0.0688, 0.667, 0.68, and 0.6, we compare each decimal value:

We start from the leftmost digit and compare:

Therefore, the largest decimal among the given numbers is 0.68.

Answer:

x-value is 6.87

Step-by-step explanation:

we are given

Polynomial as

[tex]y=2x^2+7[/tex]

Exponential as

[tex]y=5^{x-4}[/tex]

Firstly, we can draw graph

We can see that intersection point is (6.87,101.392)

so, x=6.87

At (6.97, 101.392) the exponential function surpasses the polynomial function.

Graphical solutions of a system of equations are way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

Given, A system of equation y = 2x² + 7 and y = 5^(x - 4).

Now by graphing these two equations we observe that at 6.87 the exponential function surpasses the polynomial function.

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i always use 3.1415 but just to be safe use the pi symbol  :)

Answer:

The first attached graph showing the plotted point (0, 3) represents Ramon's initial step.

Step-by-step explanation:

We are given that Ramon is graphing the function f(x) = 3(4)x and that he begins by plotting the initial value.

So if we will input 1 for the value of x and then evaluate the plot point.

Therefore, we will get the point (0, 3) as the answer for this initial step.

Also, the first attached graph here showing the plotted point (0, 3) represents Ramon's initial step.

Answer:

The graph that represent the initial step in the attached figure

Step-by-step explanation:

we have

[tex]f(x)=3(4^{x})[/tex]

we know that

The initial value is the value of the function when the value of x is equal to zero

so

For [tex]x=0[/tex]

substitute in the function

[tex]f(x)=3(4^{0})=3(1)=3[/tex]

therefore

The initial value is the point [tex](0,3)[/tex]  

The graph that represent the initial value in the attached figure

Answer:

8.4444...

Step-by-step explanation:

So it's easier if we can write it first in mixed fractions. 9 x 8 is 72 and th is the highest we can go. So it becomes [tex]8\frac{4}{9}[/tex]. Then, if you just long divide 4 by 9 you get .44444.... So it is 8.4 repeating.

8.444 decimal is equivalent to fraction 76/9.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given a fraction of 76/9

Simplifying the above fraction,

=> 76/9

=> (72 + 4)/9

=> 8 + 4/9

=> 8 + 0.444

=> 8.444

Therefore, 8.444 decimal is equivalent to fraction 76/9.

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Answer:

x=3

Step-by-step explanation:

By vertical line test, x=3 fails because more than 2 points have the same x value. Functions must pass the vertical line test.

Answer:54x6432y=7644335

Step-by-step explanation:

tab;e times table

Answer:

[tex]x=3-\sqrt{6},x=3+\sqrt{6}[/tex]

Step-by-step explanation:

we are given equation as

[tex]2x^2-12x=-6[/tex]

Since, we have to solve it by using complete square

so, firstly we will complete square

and then we can solve for x

step-1:

Factor 2 from both sides

[tex]2(x^2-6x)=-3\times 2[/tex]

step-2:

Simplify it

[tex]x^2-6x=-3[/tex]

step-3:

Add both sides 3^2

[tex]x^2-6x+3^2=-3+3^2[/tex]

now, we can complete square

[tex](x-3)^2=6[/tex]

step-4:

Take sqrt both sides

[tex](x-3)=-\sqrt{6},(x-3)=\sqrt{6}[/tex]

step-5:

Add both sides by 3

we get

[tex]x=3-\sqrt{6},x=3+\sqrt{6}[/tex]