Evaluate 4(b + 1)² if b = 4.

Answer:

The price of a senior citizen ticket to the fall musical is $6

The price of a student citizen ticket to the fall musical is $4

Step-by-step explanation:

C = the price of a senior citizen ticket to the fall musical

S = the price of a student citizen ticket to the fall musical

Day 1:

6C + 5S = 50

Day 2:

8C + 1S = 44

Manipulate the equations so that they have a common coefficient.

Multiple Day 2's equation by 5.

8C + 1S = 44

40C + 5S = 220

Subtract Day 2's equation from Day 1's

(40C + 5S = 220) - (6C + 5S = 50)

(40C + 5S) - (6C + 5S) = 220 - 50

(40C - 6C) + (5S - 5S) = 220 - 50

34C = 170

C = 5

Substitute C into either equation to solve for S.

Day 1:

6C + 5S = 50

6(5) + 5S = 50

30 + 5S = 50

5S = 50 - 30

5S = 20

S = 4

Day 2:

8C + 1S = 44

8(5) + 1S = 44

40 + 1S = 44

1S = 44 - 40

S = 4

Answer:

-9

Step-by-step explanation:

[tex]z^{-1}(-2)=k \implies z(k)=-2 \\ \\ k=-9 \implies z^{-1}(-2)=-9[/tex]

Answer:

20

Step-by-step explanation:

Answer:

Step-by-step explanation:

Compound Interest Formula

The Amount A after t years due to a principle P invested at an annual interest rate r compounded n times per year

Compounded Quartely means 4 times per year

A = P(1 + r/n)^nt

A= 13000(1 + 0.04/4)^4(7)

A = 13000(1 + 0.01)^28

A = 13000(1.01)^28

A = 13000(1.321290967)

A = 17176.78|257

A ≈ 17,176.78

[tex]p(x-1)[/tex] is a quadratic in the form

[tex]a(x-1)^2 + b(x-1) + c[/tex]

We want to write [tex]p(x-1)[/tex] instead in the form

[tex]a' x^2 + b' x + c[/tex]

To do this, simply expand the first form completely.

[tex]a(x-1)^2 + b(x-1) + c = a(x^2 - 2x + 1) + b(x-1) + c \\\\ ~~~~~~~~ = ax^2 + (-2a + b)x + (a - b + c)[/tex]

Then [tex]a'=a[/tex], [tex]b'=-2a+b[/tex], and [tex]c'=a-b+c[/tex].

Given

[tex]p(x-1) = 2(x-1)^2 + 3(x-1) + 4[/tex]

(so [tex]a=2[/tex], [tex]b=3[/tex], and [tex]c=4[/tex]) it follows that

[tex]a' = a = 2[/tex]

[tex]b' = -2a + b = -2^2 + 3 = -1[/tex]

[tex]c' = a - b + c = 2 - 3 + 4 = 3[/tex]

[tex]\implies p(x-1) = \boxed{2}\,x^2 - \boxed{1}\,x + \boxed{3}[/tex]

The value of machine after 3 years which costs $25000 will be $17500.

What is the depreciation in value ?

An asset loses value over time as a result of use, damage, or obsolescence. This decline in value is known as depreciation.

The value of a machine is $25000.

The value of the machine after 3 years must be found.

Let y be the machine's price and x be its production time.

We are aware that the line's equation is y = mx + c.

Machine costs $25,000, therefore the point is (0,25000), and when it costs nothing after 10 years, the point becomes (10,0).

Regarding the first point (0 , 25000)

25000 = 0(x) + c

c = 25000

For a second point which is (10,0)

0 = 10(m) + 25000

m = -2500

As a result, y = -2500x + 25000 is the equation.

We know that , we have to find the value of machine after 3 years i.e., x = 3.

So ,

y = - 2500 × 3 + 25000

y = -7500 + 25000

y = $ 17500

Therefore , the value of machine after 3 years which costs $25000 will be $17500.

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The machine after 3 years when depreciates linearly to 0 over a 10 year period is 17500.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given:

A $25,000 machine depreciates linearly to 0 over a 10 year period.

According to given question we have

At the time of launch, its cost is $25,000 so the point becomes (0,25000) and after 10 years its cost becomes zero then the point becomes (10,0).

For the first point (0, 25000)

25000 = 0(x) + c

c = 25000

For second point (10,0)

0 = 10(m) + 25000

m = -2500

Thus the equation become y = -2500x + 25000.

When x=3

y = -2500x + 25000

y=-2500*3+25000

y=17500

Therefore, the machine after 3 years when depreciates linearly to 0 over a 10 year period is 17500.

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States from least population density (top) to greatest population density (bottom) are Colorado Arizona Minnesota Kentucky.

In the problem we are given with some datas

State      Population                 Land Area        

Arizona    6 . 83 × [tex]10^{6}[/tex]               113 , 594              

Colorado  5 . 46 × [tex]10^{6}[/tex]               103 , 642

Kentucky   4 . 43 × [tex]10^{6}[/tex]               39 , 486

Minnesota   5 . 45 × [tex]10^{6}[/tex]            79 , 627

population density are for

Arizona  (6 . 83 × [tex]10^{6}[/tex] )/113594=60.12

Colorado 52.68

Kentucky  112.19  

Minnesota   68.44

States from least population density (top) to greatest population density (bottom) are Colorado Arizona Minnesota Kentucky.

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Answer: Equation for the line that passes through the points (6,-5) and (-4,1) is equal to 3x+5y+7 = 0.

Step-by-step explanation:

The equation of a line can be written in slope intercept form:  

y = mx + b   where m is the slope and b is the y-intercept

You can use the two points to find the slope m:

m = (y2 - y1 ) / ( x2 - x1 )

Given that points (6,-5) and (-4,1)

It represents the values are,

x1 = 6

y1 = -5

x2 = -4

y2 = 1

so,

Replace with x1, x2, y1, y2 values in this equation,

we can write,

m=(1-(-5)) / (-4-(6))

m = (1+5) / (-4-6)

m= 6/-10

m = 3/-5

Now you can select either point and substitute the coordinates in the equation to determine b, the y intercept.  Let's us (-4, 1):

y= mx + b

so, x = -4 and y = 1 and m = 3/-5

Replace with the values in this equation,

y= mx +b

1 = (-3/5)(-4) + b

1 = (0.6)(4) +b

1 = 2.4 +b

1-2.4 = b

-1.4 = b

b = -1.4

The equation will be:

y = mx +b

substitute m and b values,

Then,

y = (-3/5)x + (-1.4)

y = (-3/5)x -1.4

In standard form, the equation would be transformed as:

y = (-3x-7) / 5

5y = -3x-7

3x+5y = -7

3x+5y+7 = 0

In standard form, the equation would be transformed as: 3x+5y+7 = 0

Therefore,

Equation for the line that passes through the points (6,-5) and (-4,1) is equal to 3x+5y+7 = 0.

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Answer:

c) S : {30}

Step-by-step explanation:

a) S : {17}

→ 17 - 3 > 15

→ 14 < 15

So, it is not suitable.

b) S : {18}

→ 18 - 3 > 15

→ 15 = 15

So, it is not suitable.

c) S : {30}

→ 30 - 3 > 15

→ 27 > 15

So, it is correct answer.

d) S : {15}

→ 15 - 3 > 15

→ 12 < 15

So, it is not suitable.

Answer:

x equals plus or minus square root of 5 minus 2

Step-by-step explanation:

Let's solve your equation step-by-step.

x²+4x=1

Step 1: Subtract 1 from both sides.

x²+4x−1=1−1

x²+4x−1=0

For this equation: a=1, b=4, c=-1

1x²+4x+−1=0

Step 2: Use quadratic formula with a=1, b=4, c=-1.

[tex] \sf \: x = \frac{−b± \sqrt{ b {}^{2} −4ac}}{2a}[/tex]

[tex]\sf \: x = \frac{−(4)± \sqrt{4 {}^{2} −4(1)( - 1)}}{2(1)}[/tex]

[tex] \sf \: x = \frac{−4±√20}{2} [/tex]

x=−2+√5 or x=−2−√5

Correct answer is B. Fred Korematsu was arrested for Refusing to move to the detention center.

Fred Korematsu is detained on May 30, 1942, in San Leandro, California, for defying President Franklin Roosevelt's contentious Executive Order 9066, which called for the internment of almost all Japanese Americans in the US following Japan's assault on Pearl Harbor.

Korematsu, who was 23 at the time, sued in federal court after being found guilty and being imprisoned in a Utah camp. The U.S. Supreme Court ultimately heard his case, and in 1944 it affirmed the government's argument that the detention was necessary due to "military necessity."

However, a federal court overturned Korematsu's sentence for escape internment in 1983, declaring that he had been the victim of a "grave injustice."

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Answer:

0.5b + 4 = 2(b + 2)

0.5b + 4 = 2b + 4

0.5b - 2b = 4 - 4

-1.5b = 0

b = 0/-1.5

b = 0

a) There is 2.54 quarts in the resulting mixture (b) The percentage of the resulting mixture is  50.8% antifreeze.

Percentage is defined as parts per hundred. Percentage is calculated by dividing the given amount by the total amount and multiplying by 100.

a) 18% of 3 quarts antifreeze contains (18/100) × 3 quarts of antifreeze.

amount of antifreeze = 0 .18 × 3 = 0.54 quarts

Now to this solution 2 quarts of antifreeze is added.

Therefore total amount of antifreeze in the resulting mixture = 2 + 0.54 = 2.54 quarts.

b) Total amount of the resulting mixture = 2 + 3 = 5 quarts

amount of antifreeze in the mixture = 2.54 quarts

Percentage antifreeze in the mixture = (2.54 / 5) × 100 % = 50.8 % .

Therefore there is 2.54 quarts of antifreeze in the mixture and its percentage is  50.8% of the total mixture.

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Answer: 8 – (2 + 1) × (5 – 3) = 2

Step-by-step explanation:

8 – 2 + 1 × 5 – 3 = 2

8 – 2 + 1 × 5 – 3 = 2      ==> notice there is an '8-' in the equation, Let's solve for the difference between 8 and 2.

8 – (2 + 1 × 5 – 3)+(2 + 1 × 5 – 3) = 2 + (2 + 1 × 5 – 3)

8=2 + (2 + 1 × 5 – 3)

8-2=2-2+(2 + 1 × 5 – 3)

6=2 + 1 × 5 – 3   ==> 6 is a multiple of 2 and 3. Let's see how we can convert 2 + 1 × 5 – 3 into the product of 2 and 3

6=(2 + 1) × (5 – 3)

6=3 × 2

6=6√  ==> since this is right, let's substitute the parentheses to the original equation

8 – 2 + 1 × 5 – 3 = 2    ==> 8 – (2 + 1) × (5 – 3) = 2

The value of c from the equation is 2

The absolute value of a number can be defined as the non -negative value of a number irrespective of its sign.

It is known as the distance of a number from zero without consideration of its sign.

It is also known as the modulus of a number.

It is denoted with the symbol, " | | "

Given the expression;

∣−c+12∣= 14

find the absolute value

c + 12 = 14

collect like terms

c = 14 - 12

c = 2

Thus, the value of c from the equation is 2

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The total cost based on the equation illustrated as y= 10x is $230.

It should be noted that from the information, the equation y= 10x models the cost to attend the aquarium, where x is the number of students in the class and y is the total cost.

Therefore, it should be noted that the total cost when x is 23 will be illustrated thus:

y = 10x

y = 10 (23)

y = 230

Therefore, the total cost based on the equation illustrated as y= 10x is $230.

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The equation y= 10x models the cost to attend the aquarium, where x is the number of students in the class and y is the total cost. Calculate the total cost when x is 23.

Boys: 2, Girls: 5

There are 6 boys and 15 girls.

If there were 5 boys and 15 girls, the ratio would go to 1 to 3

But this is 6 boys to 15 girls

Final answer: 2:5

Answer:

i want orange juice

Answer:

−5 > x > 10

Step-by-step explanation:

Starting from the x-value (A column) for -7 and going down the y-values values (B column) are 5, 4, 3, 2, 1, 0, 1, 2

The function is given to us in the B column. We can use this to find the y-values without having to plug them in each time.

Finding the Vertex

In absolute value functions, there is a vertex. The vertex, in this case, is the minimum where the y-values change from decreasing to increasing. The absolute value formula is y = a|x - h| + k.

The vertex is equal to (h,k). The h-value in the function above is -2 and the k-value is 0. Thus, the vertex is at (-2,0).

Finding Slope

The slope of an absolute value function is written before the x. Since there isn't anything before the x in this function, the slope must be 1. So, the values either increase or decrease by 1.

Like all positive absolute value functions, the graph will decrease, reach 0, then begin to increase. The graph will reach 0 at the vertex.

Writing Out the Values

The table shows us that the y-values begin at 6. Then, we decrease by one until we get to 0.

Each of these x-values matches up with one of the y-values. Then, the graph begins to increase once again.

So together the y-values for the x-values -8 through 0 are 6, 5, 4, 3, 2, 1, 0, 1, 2.

The probability that the next spin will land on blue or green or purple as a fraction in simplest form is 44/71.

Given that, a spinner is divided into five coloured sections that are not of equal size: red, blue, green, yellow, and purple.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favourable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

The spinner results are as follows:

Colour        Frequency

Red                  19

Blue                 20

Green               14

Yellow               8

Purple               10

Total number of outcomes = 19+20+14+8+10=71

The probability of getting blue =20/71

The probability of getting green =14/71

The probability of getting purple =10/71

So, the probability of getting blue or green or purple = 20/71 + 14/71 + 10/71

=44/71

Therefore, the probability that the next spin will land on blue or green or purple as a fraction in simplest form is 44/71.

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It should be noted that the multiplication of 2.102 × 12.62 is 25.39144.

It should be noted that multiplication simply means the product of a number. It should be noted that this contains the number a specified number of times.

Therefore, it should be noted that the value of 2.012 multiplied by 12.62 will be illustrated thus:

= 2.102 × 12.62

= 25.39144

In conclusion, it should be noted that the multiplication of 2.102 × 12.62 is 25.39144.

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If she contracts to pay the loan in 18 months, Catherine would pay 209.66 in each month

The simple interest on purchase finance is determined as the cost of the items purchased multiplied by the annual interest of 20% and the period the month payments would last:

I=PRT

Where:

So we have:

I=2903*20%*1.5

I= 870.90

total payments=2903+ 870.90

total payments= 3,773.90

monthly payment=3,773.90/18

monthly payment= 209.66

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Answer:

3.39x=y

Step-by-step explanation:

This is because the 'y' part is supposed to be the answer for how much the gallons of gasoline would be.

The 'x' part of the equation represents how much gallons of gasoline you got and you can treat it as a normal number.

Pretend that x is 2 and so you are to find out how much 2 gallons of gasoline costs and to work this out you would do this: 3.39 x 2.

You just basically treat x as a normal number like so and it would look like:

3.39 x x=3.39x

Answer: 62 + |−4| = 66°, 62° is the farthest from 0°

I believe this is the correct answer.

The one that shows how much warmer this location is in April than in December, and which temperature is the farthest away from 0°. will be B Option 62 - |−4| = 566°, 62° is the farthest from 0°

We have got an equation that can relate these three units of measurement of temperature, as given below:

[tex]\dfrac{C}{5} = \dfrac{F - 32}{9} = \dfrac{K - 273}{5}[/tex]

where C represents the measurement of a fixed temperature in celsius, F represents the measurement of that same intensity temperature in fahrenheit, and K represents the measurement of equally intense temperature in kelvin.

Based on the information given, the value of warmer will be;

= 62 - (-4)

= 62 + 4.

= 66

Therefore, the correct option will be option  B. 62 - |−4| = 566°, 62° is the farthest from 0°

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The pages that will be favored for the search terms Chevrolet AND Corvette are Pages that include Chevrolet Corvette. Option B

This is further explained below.

Generally, We may think about AND as the intersection of two sets by applying the concept of the set union to it.

The intersection of two sets is a representation of the components that are included in or shared by both.

In conclusion,  For the sake of this discussion, the sites that contain both Chevrolet and Corvette will be regarded as the most reliable resources.

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what pages will be favored for the following search terms:

Chevrolet AND Corvette

A. Pages about Chevrolet and pages about corvette

B. Pages that include Chevrolet Corvette

C. pages that include Chevrolet and pages that include Corvette plus pages about both.

D. Pages about chevrolet, pages about OR plus pages about corvette

Step-by-step explanation:

1. 10.58

2. 15.87

3. 20.37

4 25.88

5. 8.89

6. 2.24

7. 9.95

8. 4.80