If m = 4 and n = -7, what is the value of m + n?

Answers

Answer 1

The answer is -3.

If m = 4 and n = -7, we can evaluate the expression by substitution.

m + n

4 + (-7)

-3

Answer 2

❄ H there,

evaluate this expression by substituting the provided parameters –

[tex]\sf{m+n} \ | \ m=4 \ \& \ n=-7 \ | 4+(-7)=4-7=-3}[/tex]

That's it!


Related Questions

A psychologist wants to estimate the proportion of people in a population with IQ scores between 80 and 140. The IQ scores of this population are normally distributed with a mean of 110 and a standard deviation of 15. Use the standard normal table to estimate the proportion.

Answers

Using the Empirical Rule, it is found that the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.

What does the Empirical Rule state?

It states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of  the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Considering the mean of 110 and the standard deviation of 15, we have that:

80 = 110 - 2 x 15.140 = 110 + 2 x 15.

These values are both the most extreme within 2 standard deviations of the mean, hence the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.

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three times the difference between t and y"

Answers

Answer: 3(t-y)

Step-by-step explanation:

The term difference refers to subtraction, so that means t-y in parenthesis since you would have to solve that first.

Then after you'd solve that, then you would multiply it by 3

Hope I helped :)

Determine if the series converges or diverges. If the series converges, find its sum.
9
Σ n(n+3)
n=1


OA. The series diverges.
OB. The series converges to
11
2
7
OC. The series converges to
2
D. The series converges
15
-
2

Answers

The true statement about the series [tex]\sum\limits^{\infty}_{n=1} \frac{9}{n(n +3)}[/tex] is that (a) the series diverges

How to determine if the series diverges or converges?

The series is given as:

[tex]\sum\limits^{\infty}_{n=1} \frac{9}{n(n +3)}[/tex]

Take the limit of the function to infinity

[tex]\lim_{n \to \infty} \frac{9}{n(n +3)}[/tex]

This gives

[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = \frac{9}{\infty * (\infty +3)}[/tex]

Evaluate the sum

[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = \frac{9}{\infty * \infty}[/tex]

Evaluate the product

[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = \frac{9}{\infty}[/tex]

Evaluate the quotient

[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = 0[/tex]

Since the limit is 0, then it means that the series diverges

Hence, the true statement about the series [tex]\sum\limits^{\infty}_{n=1} \frac{9}{n(n +3)}[/tex] is that (a) the series diverges

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Answer:

B. The series converges to [tex]\displaystyle{\frac{11}{2}}[/tex].

Step-by-step explanation:

Before evaluating the infinite series, the expression can be decomposed as the sum of two fractions (partial fraction decomposition) as follows.

Let [tex]\textit{A}[/tex] and [tex]\textit{B}[/tex] be constants such that

                                       [tex]{\displaystyle{\frac{9}{n\left(n+3\right)}}}} \ \ = \ \ \displaystyle{\frac{A}{n} \ \ \ + \ \ \frac{B}{n+3}}[/tex]

Multiply both sides of the equation by the denominator of the left fraction,

[tex]n\left(n+3\right)[/tex], yielding

                                              [tex]9 \ \ = \ \ A\left(n+3\right) \ \ + \ \ B \-\hspace{0.045cm} n[/tex]

Now, let [tex]n \ = \ 0[/tex], thus

                                             [tex]\-\hspace{0.2cm} 9 \ \ = \ \ A\left(0 + 3\right) \ + \ B\left(0\right) \\ \\ 3 \-\hspace{0.035cm} A \ = \ \ 9 \\ \\ \-\hspace{0.11cm} A \ \ = \ \ 3[/tex].

Likewise, let [tex]n \ = \ -3[/tex], then

                                            [tex]\-\hspace{0.5cm} 9 \ \ = \ \ A\left(-3 + 3\right) \ + \ B\left(-3\right) \\ \\ -3 \-\hspace{0.035cm} B \ = \ \ 9 \\ \\ \-\hspace{0.44cm} B \ \ = \ \ -3[/tex]

Hence,

                                       [tex]\displaystyle{\sum_{n=1}^{\infty} {\frac{9}{n\left(n+3\right)}}} \ = \ \displaystyle\sum_{n=1}^{\infty} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right)[/tex].

First and foremost, write the nth partial sum (first nth terms) of the series,

          [tex]\displaystyle\sum_{n=1}^{n} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right) \ \ = \ \-\hspace{0.33cm} \displaytstyle{\frac{3}{1} \ - \frac{3}{4} + \ \frac{3}{2} \ - \frac{3}{5} \ + \frac{3}{3} \ - \frac{3}{6} \ + \frac{3}{4} \ - \frac{3}{7}} \\ \\ \\ \-\hspace{3.58cm} + \ \displaystyle{\frac{3}{5} \ - \ \frac{3}{8} \ + \ \frac{3}{6} \ - \ \frac{3}{9} \ + \ \frac{3}{7} \ - \ \frac{3}{10}} \\ \\ \\ \-\hspace{3.58cm} + \ \ \dots[/tex]

                                                [tex]+ \ \ \displaystyle{\frac{3}{n-3} \ - \ \frac{3}{n} \ + \ \frac{3}{n-2} \ - \ \frac{3}{n+1}} \\ \\ \\ \ + \ \frac{3}{n-1} \ - \ \frac{3}{n+2} \ + \ \frac{3}{n} - \ \frac{3}{n+3}}[/tex].

Notice that the expression forms a telescoping sum where subsequent terms cancel each other, leaving only

        [tex]\displaystyle\sum_{n=1}^{n} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right) \ \ = \ \-\hspace{0.33cm} \displaytstyle{\frac{3}{1} \ + \ \frac{3}{2} \ + \frac{3}{3} \ - \ \frac{3}{n+1}} - \ \frac{3}{n+2} \ - \ \frac{3}{n+3}}}[/tex].

To determine if this infinite series converges or diverges, evaluate the limit of the nth partial sum as [tex]n \ \rightarrow \ \infty[/tex],

         [tex]\displaystyle\sum_{n=1}^{\infty} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right) \ \ = \ \-\hspace{0.33cm} \lim_{n \to \infty} \left(\displaytstyle{\frac{11}{2} \ - \ \frac{3}{n+1} \ - \ \frac{3}{n+2} \ + \ - \ \frac{3}{n+3}\right) \\ \\ \\ \-\hspace{3.25cm} = \ \ \ \displaystyle{\frac{11}{2} \ - \ 0 \ - \ 0 \ - \ 0} \\ \\ \\ \-\hspace{3.25cm} = \ \ \ \displaystyle{\frac{11}{2}[/tex]


(pls help)
5. Write the rule for the linear function. Remember a function rule is written using using f(x).

Answers

The linear function whose points are given is f(x)=[tex]x/5 +1[/tex]

Given the points of the function f(-10)=-1,f(0)=1,f(10)=3.

We are required to find the function whose points are given.

Function is relationship between two or more variables that are expressed in equal to form. In function each value of x must have a corresponding y value.

x value is known as domain and y value if known as codomain of the function.

Take two points (-10,-1) and (0,1) and we can form one equation as under:

y+1=(1+1/0+10) * (x+10)

y+1=2/10 (x+10)

y+1=x/5 +10/5

y+1=x/5+2

y=x/5+2-1

y=x/5+1

Hence the linear function whose points are given is [tex]f(x) = x/5 +1[/tex]

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Land is decreasing at a rate o 17.3 annually. In 2016 there was 3,400 acres. If t represents the number of years since 2016.

Answers

The equation that can be used to determine after how many years the town will have of 900 acres of undeveloped land is 900 = 3400 * (0.827)^t

Estimate the equation that can be used to determine after how many years the town will have of 900 acres of undeveloped land

From the question, the given parameters are:

Initial value = 3400 acres

Rate, r = 17.3%

Final value = 900

An exponential function is represented using the following equation

y = a(1 - r)^t

Substitute the known values in the above equation

y = 3400 * (1 -17.3%)^t

Express 17.3% as decimal

y = 3400 * (1 -0.173)^t

Evaluate the difference

y = 3400 * (0.827)^t

Recall that:

Final value = 900

So, we have

900 = 3400 * (0.827)^t

Hence, the equation that can be used to determine after how many years the town will have of 900 acres of undeveloped land is 900 = 3400 * (0.827)^t

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Armando tiene 25 chocolates en una caja y caja y cada chocolate tiene un relleno de 4 posibles fresa, mora y piña. De los 25 chocolates de la caja de armando sabes que tiene 8 tienen relleno de mora y 5 de piña si una persona torna al azar un chocolate de la caja

cuales de la posibles posibilidades se puede calcular

Answers

La probabilidad que se pueden calcular es:

c: Probabilidad de que el chocolate no tenga relleno de piña.

¿Como encontrar las probabilidades?

Sabemos que hay 25 chocolates en total en la caja, tal que:

8 son de mora.5 son de piñalos 12 restantes son de fresa o cereza.

La probabilidad de obtener un tipo particular de sabor se obtiene como el cociente entre el número de chocolates de ese sabor y el total de chocolates.

La probabilidad que se pueden calcular es:

c: Probabilidad de que el chocolate no tenga relleno de piña.

Sabemos que 5 chocolates tienen relleno de piña, entonces 20 no tienen relleno de piña. es decir, la probabilidad es:

P = 20/25 = 4/5

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The walls of a square room with side length s are being torn down and rebuilt. The area of the new room can be represented by 1.75s(2s + 3).

Which expression represents the area of the new room?

3.75s + 4.75
3.75s2 + 4.75s
3.5s2 + 5.25s
3.5s + 5.25

Answers

The expression that represents the area of the new room is (c) 3.5s^2 + 5.25s

How to determine the area of the new room?

The given parameters are:

Wall =Square

Length = s

When the wall of the square room is torn down and rebuilt, the area of the new room is represented by 1.75s(2s + 3).

This means that

Area= 1.75s(2s + 3)

Expand the expression

Area= 1.75s * 2s + 1.75s * 3

Evaluate the products

Area= 3.5s^2 + 5.25s

This means that the expression that represents the area of the new room is (c) 3.5s^2 + 5.25s

Hence, the expression that represents the area of the new room is (c) 3.5s^2 + 5.25s

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Landon Wallin is an auto mechanic who wishes to start his own business. He will need ​$4200 to purchase tools and equipment. Landon decides to finance the purchase with a 36​-month fixed installment loan with an APR of 5.5​% ​a) Determine​ Landon's finance charge. ​b) Determine​ Landon's monthly payment.

Answers

Landon's finance charge is $613.2

Landon's monthly payment is; $80.22

How to find the finance charge?

It is convenient to compute the monthly payment first, then figure the total amount repaid and the finance charge.

The amortization formula is:

 A = Pr/(1 - (1 + r)⁻ⁿ)

where;

A is the monthly payment

P is the loan amount

r is the monthly interest rate

n is the number of months

b) Using the above formula, we can get the monthly payment as;

A = $4200(0.055/12)/(1 - (1 +0.055/12)⁻⁶⁰) = $19.708333/0.23995049

A = $80.22

The monthly payment amount is $80.22

a) 60 monthly payments add up to;

$80.22 × 60 = $4813.2

Since $4200 of that amount is principal, the finance charge is;

$4813.2 - $4200.00 = $613.2

Landon's finance charge is $613.2

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HELP PLEASE WITH THIS ASAP ASAP

Answers

Answer:

52

Step-by-step explanation:

62 - 42 = 20

20 / 2 = 10

42 + 10 = 52

52... i think :\

I need help
Please help ASAP

Answers

Answer:

The volume of the solid is  [tex]1,021m^3[/tex]

Step-by-step explanation:

1. Cylinder

For find the volume of a cylinder we use the next formula:

[tex]V_{cylinder} = \pi h r^2 = \pi \cdot 9m\cdot (5m)^2 \approx 706.86m^3[/tex]

Then the volume of the cylinder is equal to [tex]706.86m^3[/tex]

2. Cones

For find the volume of a cone we use the next formula:

[tex]V_{cone} = \pi \frac{h}{3} r^2 = \pi \cdot \frac{6m}{3} \cdot (5m)^2 \approx 157.08m^3[/tex]

However there are two cones so we have to multiply the volume of one cone for two and we get the total volume for the cones which is [tex]314.16m^3[/tex]

3. Sum of the volumes

Finally we sum the volumes of the cylinder and the cones for get the final result

[tex]V_{cylinder} + V_{cones} = 706.86m^3 + 314.16m^3 \approx 1021m^3[/tex]

So approximating the result is [tex]1021m^3[/tex]

what the difference between graphing lines and graphing inequalities?

what the difference between arithmetic and geometric ?

how do you explain using sigma notation ?


how to simplify into logarithmic?

Answers

Answer:

Step-by-step explanation:

graphing lines is just what it sounds like, you are taking the equation of the line and putting it on the graph. graphing inequalities shows the area of the coordinate plane that satisfies the inequality, it almost always splits the graph.

arithmetic: -6 , 1 , 8 , 15 , 22

geometric: 2 , 4 , 8 , 16, 32

Find the distance of PQ
P(0,4) and Q(10,-6)

Answers

Answer:

PQ ≈ 14.14 units

Step-by-step explanation:

calculate the distance d using the distance formula

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

with (x₁, y₁ ) = P (0, 4 ) and (x₂, y₂ ) = Q (10, - 6 )

PQ = [tex]\sqrt{(10-0)^2+(-6-4)^2}[/tex]

     = [tex]\sqrt{10^2+(-10)^2}[/tex]

     = [tex]\sqrt{100+100}[/tex]

     = [tex]\sqrt{200}[/tex]

     ≈ 14.14 units ( to 2 dec. places )

Answer:

[tex]PQ=10\sqrt{2}\:\: \sf units[/tex]

Step-by-step explanation:

Distance between two points formula

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}[/tex]

Define the variables:

Let (x₁, y₁) = (0, 4)Let (x₂, y₂) = (10, -6)d = PQ

Substitute the defined variables into the distance formula and solve for PQ:

[tex]\implies PQ=\sqrt{(10-0)^2+(-6-4)^2}[/tex]

[tex]\implies PQ=\sqrt{10^2+(-10)^2}[/tex]

[tex]\implies PQ=\sqrt{100+100}[/tex]

[tex]\implies PQ=\sqrt{200}[/tex]

[tex]\implies PQ=\sqrt{100 \cdot 2}[/tex]

[tex]\implies PQ=\sqrt{100}\sqrt{2}[/tex]

[tex]\implies PQ=10\sqrt{2}\: \sf units[/tex]

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The coordinates of point A on a coordinate grid are (−2, −3). Point A is reflected across the y-axis to obtain point B and point A is reflected across the x-axis to obtain point C. What are the coordinates of points B and C?

B(2, 3) and, C(−2, −3)
B(−2, −3) and C(2, 3)
B(2, −3) and C(−2, 3)
B(−2, 3) and C(2, −3)

Answers

Answer:  B(2, -3) and C(-2, 3) which is choice 3

Further Explanation:

The rule for a y-axis reflection is [tex](\text{x}, \text{y}) \to (-\text{x}, \text{y})[/tex] meaning the x coordinate flips from positive to negative, or vice versa. The y coordinate stays the same.

Therefore, point A(-2,-3) moves to B(2, -3) when reflecting over the y-axis.

A similar rule is [tex](\text{x}, \text{y}) \to (\text{x}, -\text{y})[/tex] to describe an x-axis reflection. This time the y coordinate flips in sign, and the x coordinate stays the same.

In this case, we move from A(-2,-3) to C(-2, 3)

The graph of all three points is shown below. I used GeoGebra to make the graph, but Desmos is another option. I also recommend graphing by hand on graph paper to get practice that way if possible.

Find the area for the shaded polygon

Answers

Taking the distance between dots as 1 unit, we have;

Area of the blue shaded region = square 10 units

Area of the yellow polygon = 6 square units

Which method can be used to find the area of the shaded figures?

Taking the figures as comprising of triangles and trapezoids, we have;

In the blue polygon, we have;

Trapezoid area = ((4 + 3)/2) × 2 = 7

Area of the unshaded triangles = 0.5 × 2 × 1 + 0.5 × 2 × 2 + 0.5 × 2 × 1 = 4

Square area = 3 × 2 = 6

Shaded triangle area = 0.5 × 2 × 1 = 1

Sum of the areas is therefore;

A = 7 - 4 + 6 + 1 = 10

Which gives;

Area of the blue shaded region = 10

Area of the lower yellow trapezoid is found as follows;

Trapezoid area = ((2 + 3)/2) × 4 = 10

Unshaded triangle area = 0.5 × 2 × 1 + 0.5 × 3 × 3 = 5.5

Area of the top triangle = 0.5 × 3 × 1 = 1.5

Area of the shaded yellow polygon is therefore;

A = 10 - 5.5 + 1.5 = 6

Area of the yellow polygon = 6 square units

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Mr. and Mrs. Chan want to buy new furniture that has a cash price of $6230. On the installment plan, they must pay %25 of the cash price as a down payment and make twelve monthly payments of $415. How much interest did they pay due to financing?

Answers

The interest due on financing option is $307.50

What is interest on financing?

Interest on financing is the extra amount paid by the couple when their total payments are compared to the cash price of $6,230.

The total payments would be the 25% down payment plus the sum of the twelve monthly payments of $415 each

Down payment=cash price*25%

Down payment=$6230*25%

Down payment=$1,557.50

Total monthly payments=amount of each monthly payment*number of monthly payments

monthly payment=$415

number of monthly payments=12

Total monthly payments=$415*12

Total monthly payments=$4,980

Total payment under financing=Down payment +Total monthly payments

Total payment under financing=$1,557.50+$4,980

Total payment under financing=$6,537.50

Interest=$6,537.50-$6,230

Interest on financing=$307.50

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u0ukj787y8fr7hjhy7 which one

Answers

If ABC and DEF are complementary, then the value of x will be,

90 - ABC = x

90 - 53 = x

x = 37°

Answer:

x=37

Step-by-step explanation:

complementary means when added up they bring 90
so, 53+x=90

x=90-53

x=37

mark me brainliest if it helped pls :)

PLEASEEEEEEEEEE HELPPPP. which of the following system of inequalities would produce the region indicated on the graph below?

Answers

Answer: C

Step-by-step explanation:

The line [tex]y=x+2[/tex] is shaded below and is solid.

This eliminates all the options except for C.

Select all the correct graphs.
Choose the graphs that indicate equations with no solution.

Answers

The graph first, and the graph fifth have no solution because there are no intersection options (A) and (E) are correct.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The graph of equations is shown in the graph.

As we know, if two equations of a function intersect on the coordinate plane that means they have a solution.

If there will be no intersection then the equations have no solution.

Thus, the graph first, and the graph fifth have no solution because there are no intersection options (A) and (E) are correct.

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m..................................find the value of x ...y and z..​

Answers

angle BCA = 180 - 100
angle BCA = 80

Isosceles triangle ABC has two congruent angles, A and B
2x + 80 = 180
2x = 100
Angles A and B = 50 or y and z = 50

I think lines AB and DE are supposed to be parallel, so angles y and x are consecutive interior angles (supplementary)

x = 180 - 50 = 130

Step-by-step explanation:

x =130.......................

Using the quote, "Those of us on the margins wonder if our stories matter" what is the significance of the quoted text?

Answers

The significance of the quoted text is to illustrate the less privileged in an overwhelmingly crowded and disordered chronological reality.

What is a quote?

Quote means to cite something as a form of proof. It has several other senses as a verb and a noun. It should be noted that to quote something or someone is to repeat the exact words they said or to recite the exact words written in a book.

Great speakers often quote other inspiring people when making speeches. When you quote, you include the words and ideas of others in your text exactly as they have expressed them.

You signal this inclusion by placing quotation marks (“ ”) around the source author's words and providing an in-text citation after the quotation.

In this case, the significance of the quoted text is to illustrate the less privileged in an overwhelmingly crowded and disordered chronological reality. A quotation is the repetition of a sentence, phrase, or passage from speech or text that someone has said or written.

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The lateral edges of a prism are

Answers

Step-by-step explanation:

in a survey of 100 people ,65 read Kantipur ,45 read Gorkhapatra, 40 read himalayan times dream,25 read Kantipur as well as Gorkhapatra ,20 read kantipur as well as himalaya times,15 read gorkhapatra,as well as himalaya times and 5 read all three news papers.

1)draw a Venn diagram to illustrate the above information.

2find how many people do not read all three news paper ?

The lateral edges are congruent and parallel. The correct option is D.

A prism is a 3-dimensional object that has two bases that are similar and congruent to each other and are connected to each other with straight lines. A few examples of the prism are given in the image below.

Lateral edges are the edges that connect the two bases of the prism.

Since the lateral edges are straight lines and connect the similar vertices of the bases. Therefore, the lateral edges are always congruent and parallel.

Hence, the correct option is D.

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The given question is incomplete. Probably the complete question is:

The lateral edges of a prism are

A. congruent, only

B. congruent and perpendicular

C. perpendicular, only

D. congruent and parallel

Julio wants to calculate 200,000 × 300,000. When he used his calculator to multiply, it showed the result below:
6E+10

Write the number shown on the calculator display in standard form.

Answers

The number shown on the calculator display can be written in standard form as 6 x 10¹⁰.

Product of 200,000 and 300,000

The product of 200,000 and 300,000 is calculated as follows;

200,000 × 300,000 = 6E+10

What is standard form?

Standard form is a mathematical way or a standard way of presenting numbers as a mathematical expression.

It presents numbers in the simplest form.

Product of 200,000 and 300,000 in standard form

200,000 × 300,000 = 6 x 10¹⁰

Thus, the number shown on the calculator display can be written in standard form as 6 x 10¹⁰.

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What is the slope of the line that passes through the points (8, 0) and (-4, -8)?
Write your answer in simplest form.

Answers

Answer:

Step-by-step explanation:

(-8 - 0)/(-4 - 8)= -8/-12 = 2/3

The slope of the line that passes through the points (8, 0) and (-4, -8) exists at 0.66667.

How to estimate the slope of the line?

The slope or gradient between two points in the Cartesian coordinate system. The slope exists the amount of slant a line retains and can maintain a positive, negative, zero, or undefined value.

Using the slope formula [tex](y_2 - y_1)/(x_2 - x_1)[/tex]

[tex]x_1 = 8, y_1 = 0[/tex] and [tex]x_2 = -4 , y_2= -8[/tex]

slope [tex]= (y_2 - y_1)/(x_2 - x_1)[/tex]

= ((-8) - 0) / ((-4) - (8))

= (-8) / (-12) = (-2) / (-3)

= 0.66667

Therefore, the slope of the line that passes through the points (8, 0) and (-4, -8) exists at 0.66667.

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What is the answer I need help!

Answers

No

A regular polygon has interior angles that are all equivalent. Because the interior angles of a polygon must add up to 360 degrees and since 55 cannot evenly go into 360, it is not possible for all the interior angles to be 55 degrees.

For the function f(x)=3x²-7, find the value of f(x) when x=3.

Answers

Answer:

Step-by-step explanation:

Simply plug in a 3 where you see an x in the function:

[tex]f(3)=3(3)^2-7[/tex] so

f(3) = 3(9) - 7 and

f(3) = 27 - 7 so

f(3) = 20

urgent need of assistance ​

Answers

Answer:i got 329

Step-by-step explanation:

SV is angle bisector of

Answers

Answer:

Sv is angle bisector of rst.

Express tan α using x?

Answers

Answer:

This questions seems to be incomplete but generally tan with x is expressed as

tan(x) =

irections: Simplify each expressio
25-(√16-1)-(3-9)²

Answers

Answer:

-14

Step-by-step explanation:

[tex]\sqrt{16} = 4\\\\(\sqrt{16} - 1) = (4 -1) =3\\\\(3-9) = (-6)\\\\(3-9) ^2 = (-6)^2 = 36\\\\25 - 3 - 36 = 25 - 39 = -14\\[/tex]

The following formula models the number of automobiles, A,in thousands, that Washington residents purchased
x years after 1980.
A=2x2+24x+300

A) Write an equation that you can use to determine the first year in which residents purchased approximately 566 thousand cars.


B) Now solve your equation and specify the first year (for example, enter 2019 and not 39) in which residents purchased approximately 566 thousand cars.

Answers

Considering the given quadratic equation for the number of automobiles, we have that:

A) The equation to be solved is: x² + 12x - 133 = 0

B) The first year was of 1987.

What is a quadratic function?

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]

In which:

[tex]\Delta = b^2 - 4ac[/tex]

The number of automobiles, in x years after 1980, is modeled by:

A(x) = 2x² + 24x + 300.

The amount is of 566,000 when A(x) = 566, hence the equation is:

2x² + 24x + 300 = 566

2x² + 24x - 266 = 0

x² + 12x - 133 = 0

The coefficients are a = 1, b = 12, c = -133, hence:

[tex]\Delta = 12^2 - 4(1)(-133) = 676[/tex][tex]x_1 = \frac{-12 + \sqrt{676}}{2} = 7[/tex][tex]x_2 = \frac{-12 - \sqrt{676}}{2} = -19[/tex]

Time is a positive measure, hence we take the solution of 7, 1980 + 7 = 1987, which is the year.

More can be learned about quadratic functions at https://brainly.com/question/24737967

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