Suppose that you work for a company that offers $25 and $60 gift certificates. Determine the money denominations that you can create using these denominations. Then use strong induction to prove your conjecture.

Answer:

The zeros are:

[tex]x =4, x=2, x = 5[/tex]

Hence, option (B) is true.

Step-by-step explanation:

Given the expression

[tex]h\left(x\right)=\left(x-4\right)^2\left(x^2-7x+\:10\right)[/tex]

Let us determine the zeros of the function by putting h(x) = 0 and solving the expression

[tex]0=\left(x-4\right)^2\left(x^2-7x+10\right)[/tex]

switch sides

[tex]\left(x-4\right)^2\left(x^2-7x+10\right)=0[/tex]

as

[tex]x^2-7x+\:10=\left(x-2\right)\left(x-5\right)[/tex]

so

[tex]\left(x-4\right)^2\left(x-2\right)\left(x-5\right)=0[/tex]

Using the zero factor principle

so

[tex]x-4=0\quad \mathrm{or}\quad \:x-2=0\quad \mathrm{or}\quad \:x-5=0[/tex]

[tex]x =4, x=2, x = 5[/tex]

Thus, the zeros are:

[tex]x =4, x=2, x = 5[/tex]

It is clear that there are three zeros and all the zeros are distinct real numbers.

Therefore,

Hence, option (B) is true.

Answer:

1. False

2. False

3. True

Step-by-step explanation:

1. It fails the 'Vertical Line Test.' Draw a line through the center of the relation and see if the line passes through the graph more than once. It does, therefore it fails the test. Meaning it is not a function.

2. Domain (x) is all the x-values in the equation, the relation only contains the x-values x>0 and x<7 (0 - 7). Meaning it does not contain all real numbers.

3. The range (y) contains negative numbers because the relation is partially in the 4th quadrant, meaning it MUST contain a negative y-value.

Answer:

1.7 everyday

Step-by-step explanation:

Answer:

The width is 18

Step-by-step explanation:

6x3 and get 18 as the width

Answer:

y = x - 5

Step-by-step explanation:

Comparing the given y = x - 7 to y = mx + b, we see that the slope is +1.

In y = x + b we replace y with -11 and x with -6 to determine the y-intercept, b:

-11 = -6  + b

Then b must be -5, and so the desired new equation is

y = x - 5

Answer:

[tex]\frac{612}{999}[/tex]

Step-by-step explanation:

To convert repeating decimals to fractions, you take the numbers that are repeating, in this case 612, and you see how many numbers are repeating. Here we have 3 numbers repeating and so you would divide 612 by 3 9's meaning 999. So 0.612 repeating is equal to [tex]\frac{612}{999}[/tex]. To make sure the answer is right, you can divide the numbers in a calculator to make sure you get the correct decimal.

Answer:

We conclude that the location of A' is: A'(6, 1)

Step-by-step explanation:

Given

To determine:

The location of A'

Translation Rule:

As we have to translate 1 unit left, meaning we need to subtract 1 unit from the x-coordinate of point A(7, 1) to determine the location of A'.

In other words, the translation rule is:

A(x, y) → A'(x-1, y)

as

A(7, 1)

so

A(7, 1) → A'(7-1, 1) = A'(6, 1)

Therefore, we conclude that the location of A' is: A'(6, 1)

Answer:

0.35m + 25 = 42.50

Step-by-step explanation:

If you were to rent a truck for one day you will first have to pay a $25 fee for one day. This is represented by + 25 in the equation above.

Then for every mile you go you must pay $0.35, represented as 0.35m.

As an example to make it easier if you had to pay 1 dollar per mile and you went 10 miles it would cost $10. This can be proved by 1m (m being the variable for number of miles) Plug in 10 for m and you can asee 1(10)=10, because obviously 1 times 10 is 10.

Same premise with $0.35

Then both of those fees added up are equal to a total of $42.50.

To prove it can find the exact number of miles that need to be driven to cost a total of $42.50 just follow steps bellow.

1. 0.35m + 25 - 25 = 42.50 - 25

Subtracting the inital fee since it is part of the total, and if you add/subtract/multiply/divide on one side you must do to the other.

2. 0.35m/0.35 = 17.50/0.35

You divide because m is being multiplied with 0.35 and to undo the multiplication you divide. Doing the same to both sides.

3. m = 50

Plug in 50 to "m" in the equation above and if both sides are equal the answer is valid.

Answer:

C. [tex] 2x^3 + 8x^2 - 28x + 8 [/tex]

Step-by-step explanation:

Product of [tex] 2x - 4 [/tex] and [tex] x^2 + 6x - 2 [/tex]

[tex] (2x - 4)(x^2 + 6x - 2) [/tex]

[tex] 2x(x^2 + 6x - 2) -4(x^2 + 6x - 2) [/tex] (distributive property)

[tex] 2x^3 + 12x^2 - 4x -4x^2 - 24x + 8 [/tex]

Collect like terms

[tex] 2x^3 + 12x^2 - 4x^2 - 4x - 24x + 8 [/tex]

[tex] 2x^3 + 8x^2 - 28x + 8 [/tex]

Answer:

Step-by-step explanation:

4 : 2

8 : 4

12 : 6

16:8

The ratio in the form of n: 1 will be 2: 1.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The ratio is given below.

⇒ 4: 2

Simplify the ratio in the form of n: 1, then we have

⇒ 4: 2

⇒ 2: 1

The ratio in the form of n: 1 will be 2: 1.

More about the ratio and the proportion link is given below.

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Answer:

238 B

Step-by-step explanation:

8.5*28    

Answer:

vertex = (- 10, - 10 )

Step-by-step explanation:

The equation of a quadratic in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square.

Given

h(x) = x² + 20x + 90

add/subtract ( half the coefficient of the x- term )²

h(x) = x² + 2(10)x + 100 - 100 + 90

      = (x + 10)² - 10 ← in vertex form

with (h, k ) = (- 10, - 10 )

Answer:

D:6

Step-by-step explanation:

3/5 = 6/10

6/10 divided by 1/10 equals 6

so 6 is your answer.

Answer:

d

Step-by-step explanation:

Answer: Where is the question?

Step-by-step explanation:

Answer:

60%

Step-by-step explanation:

18 out of 30 movies are adventure so we can vizualize this as

18/30 this giving us the decimal 0.60

Now to convert from a decimal to a percent just multiply by 100 or move the decimal to the right 2 decimal point.

0.60 x 100 = 60%

Answer:

hi

Step-by-step explanation:

because

Answer: 36 cm^3

Step-by-step explanation:

To solve this you multiply the length by the width by height (so 6x2x3) this is the same formula you use to solve volume for similar equations. 6x2x3 is 36 but you need to remember to add the unit of measurement and to cube it (^3). I hope this helps!!!!

Answer:

it Eeeeeeeeeeeeeeeeeeeee

Answer:

I think it roughly 66.67%

Step-by-step explanation:

sorry if I'm no help

The percent of questions she answered correctly is 80%.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Given;

Lana correctly answered 48 of 60 questions on a math exam

Now,

=48*100/60

=480/60

=80

Therefore, the percentage will be 80%.

Learn more about percent here:

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Answer:

4:18 6:27 8:36

Step-by-step explanation:

Answer:12

Step-by-step explanation:

;)88):4?8’kifssvjimdargyjkk

Answer:

60mph

Step-by-step explanation:

330 divided by 5.5 is 60

Answer:

c

Step-by-step explanation:

with the knowledge that we are comparing the x position we can get the equation |x_1-x_2|=4, then just do the maths

(4,2) (8,2) points are separated by a distance of 4 units.

The 2D distance formula gives the shortest distance between two points in a two-dimensional plane.

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

Given

Distance of 4 units

Option A:

[tex](x_{1} ,y_{1})=(7,7)[/tex]

[tex](x_{2} ,y_{2})=(1,7)[/tex]

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

= [tex]\sqrt{(1-7)^{2}+(7-7)^{2} } =6[/tex]

Option B:

[tex](x_{1} ,y_{1})=(3,3)[/tex]

[tex](x_{2} ,y_{2})=(1,3)[/tex]

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

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

Option C:

[tex](x_{1} ,y_{1})=(4,2)[/tex]

[tex](x_{2} ,y_{2})=(8,2)[/tex]

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

= [tex]\sqrt{(8-4)^{2}+(2-2)^{2} } =4[/tex]

Option C is correct.

Option D:

[tex](x_{1} ,y_{1})=(2,4)[/tex]

[tex](x_{2} ,y_{2})=(5,4)[/tex]

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

= [tex]\sqrt{(5-2)^{2}+(4-4)^{2} } =3[/tex]

Hence, (4,2) (8,2) points are separated by a distance of 4 units.

Find out more information about distance formula here

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Step-by-step explanation:

Given

f(x) = 2x - 4

Then

f(2) = 2 * 2 - 4

= 4 - 4

= 0

Therefore f(2) = 0 .

Hope this helps :)

Answer:b

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

hope this helps ")