Let a(−9, 4) and b(3, −12) be points in the plane. (a) find the slope of the line that contains a and
b.

ITS 10

Then 1.5% thank this

Answer:

the answer is y=4x+7

Step-by-step explanation:

Answer:

The graph shows the given straight line.    

Step-by-step explanation:

We are given an equation:

[tex]y = \displaystyle\frac{1}{3}x + 3[/tex]

The attached image shows the graphical plot for the given equation.

If we compare the given equation to the

[tex]y = mx+c[/tex]

where m is the slope and c is the y-intercept of the straight line.

Comparing, we get:

[tex]m = \displaystyle\frac{1}{3}\\\\c = 3[/tex]

The line will pass by the points (-3, 2), (0, 3), and (3, 4)

Given is an equation y = x/3+3 we need to graph it,

Let's pick a few x-values and determine the y-values that go with them:

Y equals (1/3) when x = -3(-3) + 3 = -1 + 3 = 2

Y = (1/3)(0) + 3 = 0 + 3 = 3 when x = 0.

Y = (1/3)(3) + 3 = 1 + 3 = 4 for x = 3.

The points (-3, 2), (0, 3), and (3, 4) can now be plotted on the coordinate plane.

A straight line running across these locations will form the graph.

The line will have a positive slope because the value of x is positive (1/3).

Given that the y-intercept is 3, the line will cross the y-axis at (0, 3).

The plotted points (-3, 2), (0, 3), and (3, 4) lie on the line, and the line continues indefinitely in both directions.

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By using the quadratic formula, the roots of the equation are,

⇒ x = 2 ± (√3/2) i

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The quadratic equation is,

⇒ x² - 4x + 13 = 0

Now, By using the quadratic formula, the roots of the equation are,

⇒ x² - 4x + 13 = 0

⇒ x = - (- 4) ± √ (- 4)² - 4×1×13 / 2

⇒ x = 4 ± √16 - 52 / 2

⇒ x = 4 ± √- 36 / 2

⇒ x = 4 ± √6 i / 2

⇒ x = 2 ± (√3/2) i

Thus, We get;

⇒ x = 2 ± (√3/2) i

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Final answer:

The roots of the quadratic equation x² - 4x + 13 = 0 are complex numbers, specifically 2 + 3i and 2 - 3i, obtained through applying the quadratic formula.

Explanation:

To solve the quadratic equation x² – 4x + 13 = 0 using the quadratic formula, we first identify a, b, and c from the equation. Here, a=1, b=-4, and c=13. The quadratic formula is ‘x' equals minus ‘b’, plus-or-minus the square root of ‘b’ squared minus four ‘a’ ‘c', all over two 'a'. Applying these values, we get:

x = – (-4) ± √((-4)² – 4(1)(13)) / (2)(1)

This simplifies to:

x = 4 ± √(16 – 52) / 2

x = 4 ± √(-36) / 2

Since the square root of -36 is 6i (where i is the imaginary unit √(-1)), the solutions are:

x = (4 ± 6i) / 2

x = 2 ± 3i

Therefore, the roots of the equation are 2 + 3i and 2 - 3i, which are complex numbers.

The smallest possible set that contains the given sets as subsets is,

⇒ {jill, john, jack, Susan, sharon}

What is mean by Subsets?

A set 'A' is a subset of another set 'B' , if all the element of the set A are element of set of 'B'.

Given that;

The subsets are;

⇒ {jill, john, jack} , {Susan, sharon}

Now,

Clearly, A subsets of a set is contain all the elements of subsets.

So, We get the set;

Set = {jill, john, jack, Susan, sharon}

Thus, The smallest possible set that contains the given sets as subsets is,

⇒ {jill, john, jack, Susan, sharon}

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Answer:

The correct option is D.

Step-by-step explanation:

From the given number line it is clear that A=0, B=2, C=8, D=14, F=20 and G=22.

The length of line segment AC is

[tex]AC=C-A=8-0=8[/tex]

The length of line segment CF is

[tex]CF=F-C=20-8=12[/tex]

The ratio of line segment AC to CF is

[tex]\frac{AC}{CF}=\frac{8}{12}[/tex]

Cancel out the common factors.

[tex]\frac{AC}{CF}=\frac{2}{3}[/tex]

The simplified ratio of [tex]\frac{AC}{CF}[/tex] is 2/3.

Therefore the correct option is D.

Answer:

3602

Step-by-step explanation:

The population of the town after 15 years will be approximately 3495.

To find the population of the town after 15 years, we need to use the formula for compound interest: A = P(1 + r)^t, where A is the final amount, P is the initial amount, r is the growth rate expressed as a decimal, and t is the number of time periods. In this case, P = 2000, r = 0.04, and t = 15.

Using this formula, we can calculate the population after 15 years:

A = 2000(1 + 0.04)^15

A = 2000(1.04)^15

A ≈ 2000(1.747422)

A ≈ 3494.84

Rounding to the nearest whole number, the population after 15 years will be approximately 3495.

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Answer:

The given expression “ seven more than half of a number” can be written mathematically as [tex]7+\frac{1}{2}N[/tex]

Step-by-step explanation:

Given phrase “ seven more than half of a number”

We have to write the algebraic expression for the given phase.

Algebraic expression is the  way of writing an expression in mathematical form using mathematical operations and variables.

Consider the given phrase “ seven more than half of a number”

Let the number be N,

Then half of number is [tex]\frac{1}{2}N[/tex]

and seven more means seven is added to this, the expresion becomes [tex]7+\frac{1}{2}N[/tex]

Thus, the given expression “ seven more than half of a number” can be written mathematically as [tex]7+\frac{1}{2}N[/tex]

The calculated measure of the angle x is 76 degrees

From the question, we have the following parameters that can be used in our computation:

The figure

Also, we have

Angle with a measure of 76 degrees

By the theorem of corresponding angles, we have

x = 76

Hence, the measure of the angle x is 76 degrees

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To find the cost of tiling the room, you have to calculate the area in square feet, convert tile size to the same units, calculate how many boxes needed and round up, then multiply by the cost per box. The correct answer is D).

The correct answer is D). The process to determine the cost of the tiles needed to cover the room starts with calculating the area of the room in square feet. This is done by multiplying the room's length and width, so 15.5 feet * 18 feet which equals 279 square feet.

The tiles are 12 inches in size on each side, but the dimensions of the room are in feet. Therefore, we need to convert the tile size to square feet. Since 1 foot = 12 inches, 1 square foot = 144 square inches. Our tile is 12 inches * 12 inches = 144 square inches, which equals 1 square foot.

However, the tiles are sold in boxes that cover 25 square feet. So, we will divide the total room area by the area covered by one box of tiles. 279 square feet / 25 = 11.16 boxes needed, approximately.

It's important to round up at this stage, as you can't buy a fraction of a box. So, you'd need 12 boxes.

The last step is to calculate the total cost, which is done by multiplying the number of boxes by the cost of each box. So, 12 * $30 equals $360.

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Answer:

6 and 11

Step-by-step explanation:

Answer:

She will burn 960 calories if she runs 8 miles

Answer:

What is the measure of ∠A?

72°

What is the measure of ∠B?

108°

Step-by-step explanation:

I literally copied and pasted from edge

It's C.

Trust me, I had trouble figuring out this answer...