An arithmetic sequence with a thrid term of 8 and constant difference of 5

The equation represents the line that passes through the points (–3, 7) and (9, –1) will be A) y = - 2/3 x + 5.

Its slope would be:

[tex]m = \dfrac{y-q}{x-p}[/tex]

The slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.

The slope = (7 + 1)/(-3 - 9)

                = 8 / -12

                = -2/3

The equation of a line

[tex]y = mx + b\\7 = -2/3(-3) + b\\7 = 2 + b\\b = 5[/tex]

y = -2/3x + 5

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We can solve this problem by setting up a system of equations using the given information and using algebraic methods to solve for each variable, which represent the cost of the individual items.

This question can be solved by using the method of linear equations. Let's denote the cost of a small pizza as P, a liter of soda as S, and a salad as A. From the given information, we can create three equations:

By solving these equations, we can determine the prices of the individual items. The details of solving these equations may vary based on your level of comfort with algebra and systems of equations, but the general method involves isolating one variable in one equation and then substituting it into the other equations to eventually solve for each variable.

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The length of the rectangle is 33.5 feet.

To find the length of the rectangle, we can use the formula for the area of a rectangle:

Area = length * width

Given:

Area = 402 ft^2

Width = 12 ft

Let's solve for the length:

402 ft^2 = length * 12 ft

To find the length, divide both sides by 12 ft:

length = 402 ft^2 / 12 ft

length = 33.5 ft

So, the length of the rectangle is 33.5 feet.

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Answer:  The correct option is

(D) Moved down and to the right.

Step-by-step explanation:  We are given to select the statement that best describes the translation of the following function from the standard position.

[tex]y=-\dfrac{1}{2}(x-2)^2~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

This is an equation of a parabola.

The standard position of a parabola of this type is

[tex]y=x^2,[/tex]

where the vertex is at (0, 0). Since the coefficient of x² is positive, so the parabola opens upwards.

Now, from equation (i), we have

the vertex of the parabola is at (2, 0) and since the coefficient of x² is negative, so the parabola opens downwards.

Also, the vertex (0, 0) has been shifted to (2, 0), so the parabola is moved 2 units to the right.

Therefore, the given parabola is moved down and 2 units to the right as compared to the standard position.

The images of the given parabola (i) and the standard parabola are shown in the attached figure below.

Thus, (d) is the correct option.

Final answer:

The student's question involves determining the present value of annuity payments from a lottery winning, which increase over time and are discounted by a particular rate. The present value is calculated using a formula for a growing annuity, taking into account factors like the growth rate of the payments, the discount rate, and the number of periods. An example with a simple bond issue is provided to illustrate the process of calculating present value at different discount rates.

Explanation:

The student's question pertains to calculating the present value of annuity payments that increase at a fixed percentage rate over time, using a specified discount rate. This is a common exercise in finance and economics, especially related to determining the value of future cash flows given a particular rate of return (or discount rate). To solve the problem, we use the present value formula for a growing annuity.

For the lottery winnings scenario, we would calculate the present value of each individual payment and then sum them up. The first payment of $1,000,000 is received in one year, and it increases by 3 percent each year for 30 years. The discount rate is 7 percent. To analyze this, we must consider the effects of inflation and the time value of money, which is why the payments are 'discounted' back to their present value at the prevailing discount rate.

The general formula for the present value of a growing annuity is:

PV = P * [(1 - ((1 + g)/(1 + r))^n) / (r - g)]

where PV is the present value, P is the first payment, g is the growth rate of the payments, r is the discount rate, and n is the number of periods.

Using the simple two-year bond example provided, the present value calculations at an 8% discount rate are:

$240/(1+0.08) = $222.22

$3,240/(1+0.08)^2 = $2,777.78

Total present value = $222.22 + $2,777.78 = $3,000

If the discount rate increases to 11%, the new present values would be calculated using the higher rate, resulting in a lower total present value for the bond. The calculations reflect the principle that if the cost of borrowing money increases (higher discount rate), the present value of future payments decreases.

By evaluating each function in -x, we will see that the only odd one is:

f(x) = -x

We say that a function is odd if:

f(-x) = f(x)

Then we just need to check that for the given functions, let's see what we get:

1) f(-x) = (-x)^3 + 5*(-x)^2 + (-x) = -x^3 + 5x^2 - x ≠ -f(x)

2) f(-x) = (-x)^2 - x= x^2 - x ≠ -f(x)

3) f(-x) = -(-x) = x = -f(x)

So the only odd function is the third one, one useful thing that you may need to know is that usually when you see even exponents, that function will not be odd.

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Answer:

$2280

Step-by-step explanation:

The solution for y of the given equation is y = (d - 5x)/ 5.

Arithmetic operations can also be specified by the addition, subtract, divide, and multiply built-in functions.

The operator that performs the arithmetic operations are called arithmetic operators.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

Given that the equation as

⇒ d = 5x + 5y

Rearrange the terms in the above equation

⇒ 5y = d - 5x

Divided by 5 both sides of the equation

⇒  y = (d - 5x)/ 5

Hence, the solution for y of the given equation is y = (d - 5x)/ 5.

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Answer:

9600 square inches.

Step-by-step explanation:

We have been given that a puzzle contains a triangular piece with a base of 3 in. and a height of 4 in.

The would used for each triangular piece would be equal to area of triangle.

[tex]\frac{1}{2}\times 3\text{ in}\times 4\text{ in}=3\text{ in}\times 2\text{ in}=6\text{ in}^2[/tex]

Each puzzle contains 20 triangular pieces, so wood used for each piece of puzzle would be 20 times 6 square inches.

[tex]\text{Wood used for each puzzle}=20\times 6\text{ in}^2[/tex]

[tex]\text{Wood used for each puzzle}=120\text{ in}^2[/tex]

[tex]\text{Wood used for 80 puzzles}=80\times 120\text{ in}^2[/tex]

[tex]\text{Wood used for 80 puzzles}=9600\text{ in}^2[/tex]

Therefore, 9600 square inches of wood is needed to make 80 puzzles.

Answer:

option (1) is correct.

the product of the binomial by the trinomial is [tex]y^3+27[/tex].

Step-by-step explanation:

Binomial is the term having two different term and trinomial  having three different terms.

Here, Binomial is [tex]y+3[/tex] and trinomial is [tex]y^2-3y+9[/tex]

We have find the product of the binomial by the trinomial.

[tex](y+3)(y^2-3y+9)[/tex]

Multiply each term of binomial with trinomial,

[tex]\Rightarrow y(y^2-3y+9)+3(y^2-3y+9)[/tex]

[tex]\Rightarrow y^3-3y^2+9y+3y^2-9y+27[/tex]

Combining like term, we get,

[tex]\Rightarrow y^3+(3-3)y^2+(9-9)y+27[/tex]

[tex]\Rightarrow y^3+27[/tex]

Thus, the product of the binomial by the trinomial is [tex]y^3+27[/tex].

Hence, option (1) is correct.

Answer:

A right cone. If an equilateral triangle were to be cut in half then it would form a right triangle then if this right triangle were rotated 360 degrees it would form a right cone

Step-by-step explanation:

The given four consecutive even integers are 2, 4, 6, 8

Even numbers are numbers which are divisible by two.

Any even number can be written as 2n , where n is any integer

If we increase n by 1 then next even number will be obtained. Then the consecutive even numbers be 2n , 2 (n+1), 2(n +2) , 2 (n+3), ....... so on.

Given that the sum of four consecutive even integers is 20

Let the four consecutive even integers are :

2n , 2(n+1) , 2(n+2), 2( n+3)

Then

⇒2n + 2(n+1) + 2(n+2) + 2( n+3) = 20

⇒ 2n + 2n +2 +2n +4 + 2n +6  =20

⇒ 8n + 12 =20

⇒ 8n = 20-12

⇒ 8n = 8

⇒ n =8/8 = 1

Therefore, the given four consecutive even integers are 2, 4, 6, 8

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The answer in the given statement above is sample bias, this is considered to be a sampling error because this type of technique uses a sample in which they don’t represent the population, causing error in which could be eliminated with the use of methods.