Find a ⋅ b.

a = 7i - 4j, b = 4i + 3j

A) <28, -12>
B) 16
C) -40
D) <11, -1>

To find the tax revenue in 1995 and 2006 for a city with an annual increase of 3.5%, we use the formula for exponential growth. The revenue in 1995 is calculated to be $296,923, and for 2006, it is calculated to be $438,995.

The tax revenue that a small city receives increases by 3.5% per year. To calculate the tax revenue for the years 1995 and 2006, we can use the formula for exponential growth: Final Amount = Initial Amount * (1 + Growth Rate)Number of Years.

For 1995, which is 5 years after 1990, the calculation would be:
Revenue in 1995 = $250,000 * (1 + 0.035)5
Revenue in 1995 = $250,000 * (1.035)5
Revenue in 1995 = $250,000 * 1.18769
Revenue in 1995 = $296,923

Similarly, for 2006, which is 16 years after 1990, the calculation would be:
Revenue in 2006 = $250,000 * (1 + 0.035)16
Revenue in 2006 = $250,000 * (1.035)16
Revenue in 2006 = $250,000 * 1.75598
Revenue in 2006 = $438,995

Answer:

What is the question?yea

Step-by-step explanation:

To calculate the sales tax on the second item, we determined the sales tax rate from the first item and applied it to the second item's cost, resulting in $7.99 sales tax on the second item.

To find the sales tax on the second item, we use the information provided about the first item to determine the rate of sales tax and then apply this rate to the second item. If the first item costs $147 with a sales tax of $14, we can find the sales tax rate by dividing the sales tax by the cost of the item before tax:

Sales tax rate = Sales tax / Price before tax

= $14 / $147

= 0.0952 or 9.52%

Once we have the sales tax rate, we can calculate the sales tax on the second item, which costs $84 before tax:

Amount of sales tax = Price × Rate of sales tax

= $84 × 0.0952

= $7.99 (rounded to the nearest cent)

Therefore, the sales tax on the second item is $7.99.

Answer:

.56 (C)

Step-by-step explanation:

Answer:

s=3

Step-by-step explanation:

Answer:

it's c

Step-by-step explanation:

because for .087  you move the decimal 3 times

                  so the decimal is going to end up 08.7

                                                                                here

We can write 0.87 as 87 / 100.

Option D is the correct answer

Given,

0.087

We have to see the other form it can be written.

The numbers which have a decimal point.

Example: 23.4

It can be written in fractions aswell.

23.4 = 234/10

We have,

0.87

Since there are two numbers after the decimal point we can write it as:

= 0.87
= 087 / 100

= 87 / 100

Thus we can write 0.87 as 87 / 100.

Option D is the correct answer.

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The first factor with the value of the product is compared as below.

Factors of a number or an algebraic expression are the numbers or expressions which divides the given number evenly.

For example, 10 = 2 × 5

So we can say that 2 and 5 are factors of 10.

Here there are 3 products.

(a) [tex]\frac{1}{3}[/tex] × 1

Here the first factor is [tex]\frac{1}{3}[/tex].

And the product of the two factors is [tex]\frac{3}{9}[/tex].

[tex]\frac{3}{9}[/tex] = [tex]\frac{1}{3}[/tex] × [tex]\frac{3}{3}[/tex]

Numerator and denominator when take three times gives the product.

(b) First factor is [tex]\frac{2}{3}[/tex] and the product is [tex]\frac{14}{21}[/tex].

[tex]\frac{14}{21}[/tex] = [tex]\frac{2}{3}[/tex] × [tex]\frac{7}{7}[/tex]

Numerator and denominator when multiplied by 7 times gives the [tex]\frac{14}{21}[/tex].

(c) First factor is [tex]\frac{5}{2}[/tex] and the product is [tex]\frac{25}{10}[/tex].

[tex]\frac{25}{10}[/tex] = [tex]\frac{5}{2}[/tex] × [tex]\frac{5}{5}[/tex]

Numerator and denominator when multiplied by 5 gives [tex]\frac{25}{10}[/tex].

Hence the first factor and products are compared.

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Answer: THE 3RDDDDDDDDDDDDDDDDDDDDD

Answer: The graph is represented by the inequality y>3x+2

Step-by-step explanation:

Linear inequality is like linear equation just we have inequality signs (<,>,≤,≥) instead of equal sign(=).

In the given question we have the linear inequality represented by graph

We can see the line in the graph passing through the point (-3,-7)

Let's check which option satisfy the point

1) y<3x+2 for this the line should be y=3x+2

⇒ -7=3(-3)+2

⇒-7= -9+2⇒-7=-7,which is true.

2) y>3x+2 which similar as first.

3) y<x+2 for this the line should be y=x+2

⇒ -7= -3+2

⇒-7=-1 which is not true.

4) y > x + 2 is similar to third.

Option 3) and 4) cannot be the required linear inequality.

Now from 1) and 2) , 2) should be the required linear inequality as the graph is shaded above the line and that must be for y (>) greater than inequality. [ for y (<) less than inequality the graph must be shaded below the line]

Therefore, 2)  y > 3x + 2 is the required linear inequality which is represented by the graph.

The linear equality represented by the graph is [tex]\boxed{{\mathbf{y>3x+2}}}[/tex] and it matches with [tex]\boxed{{\mathbf{OPTION B}}}[/tex] .

Further explanation:

It is given that a line passes through points [tex]\left({0,2}\right)[/tex] and [tex]\left({-3,-7}\right)[/tex]  as shown below in Figure 1.

The slope of a line passes through points [tex]\left({{x_1},{y_1}}\right)[/tex] and [tex]\left( {{x_2},{y_2}}\right)[/tex]is calculated as follows:

[tex]m=\frac{{{y_2}-{y_1}}}{{{x_2}-{x_1}}}[/tex]                    ........(1)

Here, the slope of a line is denoted as [tex]m[/tex] and points are [tex]\left({{x_1},{y_1}}\right)[/tex] and [tex]\left({{x_2},{y_2}}\right)[/tex].

Substitute [tex]0[/tex]  for [tex]{x_1}[/tex] , [tex]2[/tex]  for [tex]{y_1}[/tex] , [tex]-3[/tex]  for [tex]{x_2}[/tex]  and [tex]-7[/tex]  for [tex]{y_2}[/tex]  in equation (1) to obtain the slope of a line that passes through points [tex]\left({0,2}\right)[/tex] and [tex]\left({-3,-7}\right)[/tex] .

[tex]\begin{aligned}m&=\frac{{-7-2}}{{-3-0}}\\&=\frac{{-9}}{{-3}}\\&=3\\\end{aligned}[/tex]

Therefore, the slope is [tex]3[/tex] .

The point-slope form of the equation of a line with slope [tex]m[/tex]  passes through point [tex]\left({{x_1},{y_1}}\right)[/tex] is represented as follows:

[tex]y-{y_1}=m\left({x-{x_1}}\right)[/tex]                                 .......(2)

Substitute [tex]0[/tex]  for [tex]{x_1}[/tex] ,  [tex]2[/tex] for [tex]{y_1}[/tex]  and [tex]3[/tex]  for [tex]m[/tex]  in equation (2) to obtain the equation of line.

[tex]\begin{aligned}y-2&=3\left({x-0}\right)\\y-2&=3x\\y&=3x+2\\\end{aligned}[/tex]

Therefore, the value of [tex]y[/tex]  is [tex]3x+2[/tex] .

Since the shaded part in Figure 1 is above the equation of line [tex]y=3x+2[/tex], therefore, greater than sign is used instead of is equal to.

Thus, the linear inequality is [tex]y>3x+2[/tex]  as shown below in Figure 2.

Now, the four options are given below.

[tex]\begin{aligned}{\text{OPTION A}}\to &y<3x+2\hfill\\{\text{OPTION B}}\to &y>3x+2\hfill\\{\text{OPTION C}}\to &y<x+2\hfill\\{\text{OPTION D}}\to &y>x+2\hfill\\\end{aligned}[/tex]

Since OPTION B matches the obtained equation that is [tex]y>3x+2[/tex] .

Thus, the linear equality represented by the graph is [tex]\boxed{{\mathbf{y>3x+2}}}[/tex]  and it matches with [tex]\boxed{{\mathbf{OPTION B}}}[/tex].

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Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Coordinate Geometry

Keywords: Coordinate Geometry, linear equation, system of linear equations in two variables, variables, mathematics, inequality

Part A:

As given,

Base of the triangle = 8x + 2 units

Height of the triangle = 4x − 5 units

Formula to find area of a triangle = [tex]\frac{base * height}{2}[/tex]

= 0.5bh

we have been given base and height, so the area becomes,

area = [tex]\frac{(8x+2)(4x-5)}{2}[/tex]

area = 0.5(8x+2)(4x-5)

= 0.5(32x²-32x-10)

= 16x²-16-5

after factoring it, we get

area = (4x-5)(4x+1) units.

Part B:

It is a degree 2 polynomial as the polynomial has one variable that is x, and the largest exponent of that variable is 2.

Part C:

Part A demonstrates the closure property of polynomials because after multiplying two polynomials we get another polynomial.

Answer:

Please see the attachment for graph.

Step-by-step explanation:

We are a given a equation and need to graph it.

It is square root function. We make table of x and y and then plot the points on graph and join the points.

We will take some random values of x and then find the value of y corresponding to the value of x.

For x=1, Put x=1 into equation

[tex]y=-4\sqrt{1}=-4[/tex]

For x=4, Put x=4 into equation

[tex]y=-4\sqrt{4}=-8[/tex]

For x=9, Put x=9 into equation

[tex]y=-4\sqrt{9}=-12[/tex]

Table of x and y

     x          y

     1         -4

    4         -8

    9         -12

Now we plot the points on graph and join the points.

Please see the attachment for graph.

If 30 cents out of every 1 dollar go to taxes, the remaining 70 cents is the net income. Therefore, the ratio of taxes to net income is 3:7.

The question asks for the ratio of taxes to net income if 30 cents out of every 1 dollar go to taxes. This question is asking for a mathematical comparison between the amount of money that goes to taxes and the remaining amount of money, which is the net income.

If 30 cents go to taxes out of 1 dollar, that means 70 cents (or $0.70) is the net income because 1 dollar minus 30 cents equals 70 cents. To arrive at the ratio, we compare the amount that goes into taxes to the net income. This would be 0.30 (taxes) to 0.70 (net income).

When we express this as a ratio in simplest form, we do not usually use decimals. Instead, we can convert the decimal into a whole number. Think of the 0.30 and the 0.70 as 30 and 70. The greatest common divisor of 30 and 70 is 10. If we divide both numbers by 10, we get 3 and 7. So, the ratio of taxes to net income is 3:7. Thus, the correct option is C. 3 : 7.

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Answer:

3/2

Step-by-step explanation:

To find the slope of the line that contains the points A(3, 2) and B(7, 8), we can use the formula for slope:

slope = (change in y) / (change in x)

Let's calculate the values:

Change in y = 8 - 2 = 6

Change in x = 7 - 3 = 4

Now, we can find the slope:

slope = 6 / 4 = 3/2

Therefore, the slope of the line that contains the points A(3, 2) and B(7, 8) is 3/2.