Find a cubic polynomial whose zeros are 1/2,1 and -3.

The coordinate of the point C from the given triangle ABC after translation is C' = (4, -2)

A triangle is a 2D figure with 3 sides and angles. Given the coordinate C points of the triangle;

C = (-2, -3)

If these coordinate point is translated 6 units to the right and 1 units up, the resulting coordinate will be at:

C' = (-2 + 6, -3 + 1)

C' = (4, -2)

Hence the coordinate of the point C from the given triangle ABC after translation is C' = (4, -2)

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Answer: the answer is A         C'(4, -2)

Step-by-step explanation:

The greatest number of adult tickets sold if the box office receipts was not more than $3,190 is 328.

let

number of children tickets = x

number of adult ticket sold = 1 / 3 x

The greatest number of adult tickets sold if the box office receipts was not more than $3,190 can be calculated as follows:

The equations that represent the situation is as follows:

5.50x + 8.50 (1/3 x) = 3190

5.50x + 2.83333333333x = 3190

8.33333333333x = 3190

x = 3190 / 8.33333333333

x = 982.839313573

x ≈ 983

Therefore,

adult ticket = 983/3 = 328

Therefore, the greatest number of adult tickets sold if the box office receipts was not more than $3,190 is 328.

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The equation representing the given case is 2(x - 8) = 3(x + 3), where x is the number.

The number satisfying this equation is -25.

In the question, we are asked to find the number when twice the difference of the number and 8 is equal to thrice the sum of the number and 3.

We assume the number to be x.

The expression representing twice the difference between the number and 8, can be shown as 2(x - 8).

The expression representing thrice the sum of the number and 3, can be shown as 3(x + 3).

We are informed that these two expressions are equal. This can be shown as the equation:

2(x - 8) = 3(x + 3).

Thus, the equation representing the given case is 2(x - 8) = 3(x + 3), where x is the number.

Now, to find the number, we solve the equation as follows:

2(x - 8) = 3(x + 3),

or, 2x - 16 = 3x + 9 {Simplifying},

or, 2x - 16 + (16 - 3x) = 3x + 9 + (16 - 3x) {Adding (16 - 3x) to both sides of the equation},

or, 2x - 16 + 16 - 3x = 3x + 9 + 16 - 3x {Simplifying},

or, -x = 25 {Simplifying},

or, -x(-1) = 25(-1) {Multiplying both sides of the equation with -1},

or, x = -25 {Simplifying}.

Thus, the number satisfying the equation is -25.

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The solution is given below:

An index number expressing the level of a group of commodity prices relative to the level of the prices of the same commodities during an arbitrarily chosen base period and used to indicate changes in the level of prices from one period to another.

Given:

Comm.         p0        q0       p1       q1       p0q0    p1q0       p1q1        p0q1

     A           25      750       30    960    18750      750       28800     24000

    B             30      450       25    550    13500     750       13750      16500

    C             5        250        6     360      1250     30        2160          1800

    D              6        90         7       210      540       42        1470           1260

    E               10        140       10     190     1400      100       1900          1900

     F                 4         48       5     65      192          240        365         260

Now,

[tex]\sum[/tex]p0q0 = 35632

[tex]\sum[/tex]p1q0 = 1912

[tex]\sum[/tex]p1q1 = 48445

[tex]\sum[/tex]p0q1= 45720

1) P01(L) = [tex]\sum[/tex]p1q0/[tex]\sum[/tex]p0q0 * 100

             = 5.36

2) P01(L) = [tex]\sum[/tex]p1q1/[tex]\sum[/tex]p0q1 * 100

            = 105.96

Dorbish- Bowley

= 5.36+ 105.96/2

=55.66

Marshall- Edgeworth

=  1912+  48445/35632 + 45720

= 50357/ 81352

= 0.619 *100= 61.9

Fisher's price index

=( 5.36 * 105.96 )^ 0.5

=23.831

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The confidence interval for the mean usage of water is (18.7,20.5).

Given population standard deviation of 2.4, mean of 19.5 gallons per day and confidence interval of 98%.

We have to find the confidence interval for the mean usage of water.

To find out the confidence interval we have to first find margin of error.

μ=19.5

σ=2.4

α=0.98

α/2=0.49

We have to find the z value for the p value 0.49 which is z=2.33

Margin of error=z*μ/[tex]\sqrt{n}[/tex]

=2.33*19.5/[tex]\sqrt{3034}[/tex]

=0.82

lower level=mean -m

=19.5-0.82

=18.68

after rounding upto 1 decimal

=18.7

upper mean = mean+m

=19.5+0.82

=20.52

Hence the confidence interval for the usage of water is (18.7,20.52).

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Answer:

0.625

Step-by-step explanation:

To find the constant, you do y/x. For the first pair, if we divide 1.25/2, we get 0.625. We can do the same for all the pairs and get 0.625

Hope this helps :)

Answer:

1.6

Step-by-step explanation:

To find the constant of proportionality, we do [tex]\frac{x}{y}[/tex]. We see that 2/1.25=1.6, 4/2.5=1.6, 6/3.75=1.6, and 10/6.25=1.6. This means that the constant of proportionality is equal to 1.6.

The algebraic expression is: x% * 100

The statement is given as:

How much x% of sugar syrup can you make if you have 100 grams of sugar?

The amount of sugar is given as:

100 grams

So, the algebraic expression is:

x% * 100

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The inequality that explains why the three segments cannot be used to construct a triangle is ED + EF < DF

From the question, we are to determine which of the given inequalities explains why the three segments cannot be used to construct a triangle

From the given information,

Line DE is about half the length of line DF

That is,

ED = 1/2 DF

Also,

Line FE is about one-third of the length of line DF

That is,

EF = 1/3 DF

Then, we can write that

ED + EF = 1/2DF + 1/3DF

ED + EF = 5/6 DF

Since,

5/6 DF < DF

Then,

ED + EF < DF

Hence, the inequality that explains why the three segments cannot be used to construct a triangle is ED + EF < DF

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Answer:

The answer is Sh 700

Step-by-step explanation:

Let's set x as the original price

30% * x = 210

0.3 * x = 210

x = 210/0.3

x = 700

Answer: $14708.14

Step-by-step explanation:

Amount = initial balance(1 + annual rate/periods per year)^(periods per year*years)

A = 6000(1+0.03/4)^4*30

A = 6000(1.0075)^120

A = 6000(2.451)

A = 14708.14

Hope this helps!

Answer:

Step-by-step explanation:

Let's start by reading the problem since it maybe is a bit confusing at first.

The product of 8

Now we know that it starts with 8 multiplied by another number. We do not know that number yet, so let's put 8 * () and fill in the parentheses later.

So far, our equation is:

8()

.. And the sum of 4 and a number

So, 4 + n

We can enter that into our equation

8(4+n)

The next line says "..Is 112"

So, the solution to our equation is 112

Our equation becomes:

8(4+n)=112

Answer:

6. x + x + 14 = 90

   2x + 14 = 90

   2x = 76

   x = 38

angle b = 38 + 14 = 52°

7. angles on a straight line add up to 180°

   x + x - 32 = 180

   2x = 212

    x = 106°

angle d = 106 - 32 = 74°

8. vertically opposite angles are equal

   7x - 80 = 3x

    -80 = -4x

     20 = x

angle 1 = 7(20) - 80 = 60°

angle 2 = 3(20) = 60°

Answer:

Step-by-step explanation:

1,500-400=1,100 he has 800 calories left so no if he ate 1,100 more calories he would go over his goal of 1,900  so C is the answer hope this helps

By definition of quotient, the rational number 1/3 represents a periodic infinite decimal number. That is to say, 1/3 is equivalent to the decimal number [tex]0.\overline{333}[/tex]

The quotient of a fraction is found by dividing the fraction. Results in decimal form can be finite and infinite, infinite forms can be periodic or no periodic. This fraction represents a periodic infinite decimal number.

[tex]\frac{1}{3} = 0.\overline{333}[/tex]

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The expression of the fraction 1/3 as a quotient is; 0 remainder 3 or 0 r 3.

Quotient is described as the quantity produced by the division of two numbers.

Now, we want to find the quotient of 1/3. It should be noted that this quotient should not be in decimal form and so it gives us;

0 remainder 3 since 3 as a denominator is bigger than 1 as numerator.

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The area of ​​the trapezoid is x+11 cm.

Given a trapezoid has one side of (x+6) cm, the other side is 5 cm, and the height is 2 cm.

A two-dimensional quadrilateral consisting of the sum of non-adjacent parallel sides and a suitable non-parallel side is denoted as a trapezoid.

Now we will use the formula to find the area of ​​a trapezoid

Area = 1/2 × (base 1 + base 2) × height

Here base 1 = (x+6) cm, base 2 = 5cm and height = 2cm

Substituting the values ​​into the formula,  we get

Area = 1/2 × (x+6+5) × 2

Area = 1/2 × (x+11) × 2

Area = x+11

Thus, the area of ​​the given figure when one side is x+6, the other side is 5 cm and the height is 2 cm is x+11 cm.

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Using the permutation formula, it is found that there are 600 ways to fill the pitcher and catcher positions.

The order is important, as one player is the pitcher and the other is the catcher, hence the permutation formula is used to solve this question.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

2 players are taken from a set of 25, hence the number of ways is given by:

[tex]P_{(25,2)} = \frac{25!}{23!} = 600[/tex].

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Answer:

feet: 7.5

Inches: 90

Step-by-step explanation:

Answer:

amber should graph the second equation

The given expression in simplified form is x - 5

From the question, we are to simplify the given expression

The given expression is

-4x -3 + 5x -2

To simplify the expression, we collect like terms and then simplify

That is,

-4x + 5x -3 -2

= x - 5

Hence, the given expression in simplified form is x - 5

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[tex]y=78^{\circ}[/tex] (alternate interior angles theorem)

[tex]x=78^{\circ}[/tex] (alternate segment theorem)

[tex]z=24^{\circ}[/tex] (angles in a triangle add to 180 degrees)

The algebraic expression that represents the total distance traveled by the car is 10s

The given parameters are:

The distance is calculated using:

Distance = Speed * Time

So, we have:

Distance = s* 10

Evaluate

Distance = 10s

Hence, the algebraic expression that represents the total distance traveled by the car is 10s

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Complete question

Your car travels for 10 hours at an average speed of s miles per hour. Write an algebraic expression that represents the total distance traveled by the car

Answer:

A.

Step-by-step explanation:

6, 11,14,14,19,20

Adding these 6 numbers we get  84.

84 / 6 = 14 = mean.

Median =  middle number(s) = 14

Mode = number occurring most = 14.

Answer:

I'm not sure if B. is incorrectly written but the answer would be

65c + 90s [tex]\geq[/tex]600

Step-by-step explanation:

since he needs AT LEAST 600$ then the sign should look like that. 65 dollars per car, and c represents the amount of cars, and 90 per SUV and s represents how many SUVS

B. 65c + 90s ≥ 600 is the correct option.

Our friend really wants to buy the newest cell phone which will cost him $600. He gets a job detailing cars and SUVs and plans to save all the money he earns.

Inequality can be defined as the relation of the equation contains the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,

If he gets paid $65 to detail a car and $90 to detail an SUV

The inequality form for above condition so he can earn at least $600

= 65c + 90s ≥ 600, where c = cars and s = SUV

Thus, the required inequality is given by 65c + 90s ≥ 600.

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The ratio x:y as required in the task content is; 25:18.

It follows from the information given in the task content that;

The area of rectangle P is; 40x.

The area of rectangle Q is; y × (1.25 × 40) = 50y.

Hence, since the area of Q is 10% less than the area of P, it follows that A(q) = 0.9A(p).

And, A(p)/A(q) = 10/9

Hence, 10/9 = 40x/50y

x/y= 50/36 = 25/18

Hence, the required ratio is; 25: 18.

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Answer:

Baby 4

Step-by-step explanation:

This is because the baby we are finding is thin and red haired.

This takes out Baby 1 because he is heavier. This takes out Baby 2 because he has blonde hair. This takes out Baby 3 who is blonde. This takes out Baby 5 who is heavier.

Answer:

On opening the bracket, we have (x^-28)/(x^56)

This is the same as (x^-28) . 1 / (x^56)

Following the law of indices 1/(x^a) = x^-a, we have 1 / (x^56) = (x^-56)

Hence (x^-28) . (x^-56)

The  value of this expression when =-2 and x=-1 is: 3.

Given equation:

-2 and x=-1

Solving the value of the given equation

-2 and x=-1

Hence:

=-(-1)+2

=1+2

=3

Therefore the value of this expression when =-2 and x=-1 is: 3.

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Answer:

Step-by-step explanation:

60 inches is 5 feet, so just add on the remaining inches to get

5 feet and 4.75 inches