The table shows ordered pairs of the function y = 16 + 0.5x .

A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 2, 0

Answer:

A.  <T=17, RS= 10

Step-by-step explanation:

These triangles are congruent by AAS congruency. This means that RS and UV will have the same measure and so will <Q and <T. Simply use that info with the measurements given.

Solving for <T:

8y-44 = 5y+7

3y = 51

y = 17

Solving for RS:

7x-2 = 5x+18

2x = 20

x = 10

Answer:

Step-by-step explanation:

6. The rate of change is essentially the slope. But in other words, it's how much the y changes as x increases by 1. If this rate of change is 0, that means the y-value is constant, while the x can be any real number. It can be generally given in the formula: y=b, which comes from simplifying the slope-intercept form: y=(0)x+b = b. You can also derive the same thing for a point-slope form: y-a = 0(x-b)=0 so y=a. In both cases, y is equal to some constant value. So graphing this makes a horizontal line.

7. To define a parallel line, you need the same slope, and a different y-intercept, which is under the assumption that the line has a slope that is definable. If the slope is definable, you'll have the equation: y=mx+b, where m is the same as the other line. Then you plug in the known values as x and y, to solve for b, which is the y-intercept. Now if the line is a vertical line, a parallel line can be defined as: x=a, where a doesn't equal the constant, the other vertical line is equal to. To make it pass through some point (c, d). Then you would simply set x=c, since the x is the only thing that matters, since the y-value is all real numbers, so it will eventually have the y-value d somewhere on the line.

8. To define a perpendicular line, you get the reciprocal of the slope and change the sign. So if the slope is: [tex]\frac{a}{b}[/tex] then it becomes [tex]-\frac{b}{a}[/tex] and vice versa depending on the sign. In this example, let's just say m=a/b, then the perpendicular slope would be -b/a. You can then plug this into the slope-intercept formula: [tex]y=-\frac{b}{a}+c[/tex] where c is the y-intercept. Then you plug in the known point as (x, y) and solve for c, the y-intercept. Now let's say for example that you have a vertical line: x=a. In this case you can see the slope as: [tex]\frac{1}{0}[/tex][tex]\frac{y_2-y_1}{a-a}[/tex]. Of course this isn't definable, but if you take the reciprocal you get something that is: [tex]-\frac{0}{y_2-y_1}[/tex] which will always evaluate to 0. This means you get a horizontal line, since the slope is 0. This means if you have a vertical line, any horizontal line should be perpendicular, which makes sense, since it should form a 90 degree angle when they intersect, because they're straight lines. To make sure that horizontal line passes through the point (b, c), you simply set the y equal to c. So y=c, will pass through (b, c), since the c is constant, and the x can equal anything so somewhere on the line it will intersect (b, c). But let's say we had a horizontal line, the reciprocal can be defined as: [tex]\frac{a-a}{x_2-x_1}[/tex] where a is the y constant. If you take the reciprocal, then you have a-a in the denominator, which gives you an undefined slope, because the perpendicular line to a horizontal line, is a vertical line. To ensure this perpendicular line passes through the point (b, c). You simply set x equal to b. so that x=b.

#6

if m is 0

Hence line is parallel to x axis

#7

parallel lines have equal slopes

so we can use the point slope form of line to find the equation

#2

Same process like no 7 but

slope of perpendicular line is negative reciprocal of given line's slope

By applying definition of limits, the end behavior of the rational function f(x) = 10/(x² - 7 · x - 30) is represented for the horizontal asymptote x = 0.

The end behavior of a rational functions is the horizontal asymptote of the rational function when x tends to ± ∞. Then, we find the end behavior by applying limits:

[tex]\lim_{x \to \pm \infty} \frac{10}{x^{2}-7\cdot x - 30}[/tex]

[tex]\lim_{n \to \infty} \frac{10}{x^{2}-7\cdot x - 30}\cdot \frac{x^{2}}{x^{2}}[/tex]

[tex]\lim_{x \to \pm \infty} \frac{\frac{10}{x^{2}} }{1 - \frac{7}{x}-\frac{30}{x^{2}}}[/tex]

[tex]\lim_{x \to \pm \infty} 0[/tex]

0

By applying definition of limits, the end behavior of the rational function f(x) = 10/(x² - 7 · x - 30) is represented for the horizontal asymptote x = 0.

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The formula for x in terms of other terms in the equation is; x = (cz-yw)/(y-c).

According to the task content, it follows that the variable X is to be made the subject of the formula;

Hence, it follows that;

y ( x + w ) = c ( x + z )

yx +yw = cx +cz

x(y-c) = (cz-yw)

x = (cz-yw)/(y-c)

Remarks: The complete question requires that x be made the subject of the formula.

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Answer:

It's a linear function.

The probability of winning the game is 0.065

The game involves throwing two darts at two targets.

To win the game, the darts must hit anywhere in the following shapes

The area of the paper is:

Area = 8.5 inches * 11 inches

Area = 93.5 square inches

The area of the rectangle on the paper is:

Area = 5 inches * 4 inches

Area = 20 square inches

The area of the circle on the paper is:

Area = π * (3 inches)²

Area = 28.3 square inches

The probability of landing on both shapes is

P(Both) = 20/93.5 * 28.3/93.5

Evaluate

P(Both) = 0.065

Hence, the probability of winning the game is 0.065

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The relationship between the y-axis and the line connecting F to F′ is (c) They are perpendicular to each other.

When a triangle FIT is reflected over the y-axis, the image and the pre-image of the triangle would be at either sides of the y-axis.

This means that the points on the image and the pre-image of the triangle are perpendicular to each other

Hence, the relationship between the y-axis and the line connecting F to F′ is (c) They are perpendicular to each other.

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Answer:

23.3 mpg

Step-by-step explanation:

For the unit rate of miles per gallon (mpg)

140 miles / 6 gallons = 23 1/3   mpg  = 23.3 mpg

The required ratio as a unit rate is 23.3 mi/gal, which is determined by dividing the number of miles by the number of gallons.. The correct answer is option (a).

To express each ratio as a unit rate (mi/gal), we need to divide the number of miles by the number of gallons.

The units rate can be calculated as:

Units rate = number of miles / the number of gallons.

Unit rate = 140 miles / 6 gallons

Apply the division operation to get:

Unit rate = 23.3 mi/gal

Thus, the required ratio as a unit rate is 23.3 mi/gal.

Hence, the correct answer is option (a).

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David paid $22 for the beanie baby.

Profit and loss formulas are used to calculate the profit or loss that has been incurred by selling a particular product. They are mainly used in business and financial transactions to depict how much profit or loss a trader has incurred from any particular deal.

Let the cost which  David pay for the beanie baby be x and y be the price at which Jessica bought the beanie baby

Profit formula :

Profit = Selling price (S.P.) - Cost price (C.P.)

So using the profit formula

$6 = $25 - y

$19 = y

Now using the same equation for David

-$3 = $19 - x

$22 = x.

Thus David paid $22 for the beanie baby.

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Answer:

14 in^2

Step-by-step explanation:

Break the figure up into two rectangles (vertical line down the middle). Use the formula area = length x width for the Rectangle A (2 in x 4 in = 8 in^2) and Rectangle B (3 in x 2 in = 6 in^2) Add 8 in^2 and 6 in^2 for a total area of 14 in^2

Answer:

15,746,400

Step-by-step explanation:

This is an example of an exponential function.

1. The function is: [tex]800 * 3^{x}[/tex]

2. We can plug the number of hours into the equation.

3. population = 800 * [tex]3^{9}[/tex]

4. population = 15,746,400

Answer:

3.4

Step-by-step explanation:

[tex]Interval=\frac{4-2.2}{9}\\Interval=0.2\\therefore :\\ 6 intervals =6(0.2)\\ 6 intervals =1.2\\x=2.2+1.2\\x=3.4[/tex]

Answer:

A)

Step-by-step explanation:

The cube root parent function is [tex]y=x^3[/tex]

When y=0, x=0, hence (0,0) is the x and y-intercept of the function.

Hope I helped!

The attached graph represents the graph of [tex]\frac{(x - 2)^2}{16} - \frac{(y + 1)^2}{9} \le 1[/tex]

The inequality is given as:

[tex]\frac{(x - 2)^2}{16} - \frac{(y + 1)^2}{9} \le 1[/tex]

The above inequality represents a conic section.

The inequality symbol <= implies that, we make use of a closed line on the graph.

Next, we plot the graph using a graphing tool

See attachment for the graph of [tex]\frac{(x - 2)^2}{16} - \frac{(y + 1)^2}{9} \le 1[/tex]

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Complete question

Which graph represents [tex]\frac{(x - 2)^2}{16} = \frac{(y + 1)^2}{9}[/tex]?

Answer:

C

Step-by-step explanation:

Got it right on Edge

Answer:

The solution set in interval form is [tex]$\left[\frac{-4}{3}, 4\right]$[/tex].

Step-by-step explanation:

It is given in the question an inequality as [tex]$|3 x-4| \leq 8$[/tex].

It is required to determine the solution of the inequality.

To determine the solution of the inequality, solve the inequality [tex]$3 x-4 \leq 8$[/tex] and, [tex]$-8 \leq 3 x-4$[/tex].

Step 1 of 2

Solve the inequality [tex]$3 x-4 \leq 8$[/tex]

[tex]$$\begin{aligned}&3 x-4 \leq 8 \\&3 x-4+4 \leq 8+4 \\&3 x \leq 12 \\&x \leq 4\end{aligned}$$[/tex]

Solve the inequality [tex]$-8 \leq 3 x-4$[/tex].

[tex]$$\begin{aligned}&-8+4 \leq 3 x-4+4 \\&-4 \leq 3 x \\&-\frac{4}{3} \leq x \\&x \geq-\frac{4}{3}\end{aligned}$$[/tex]

Step 2 of 2

The common solution from the above two solutions is x less than 4 and [tex]$x \geq-\frac{4}{3}$[/tex]. The solution set in terms of interval is [tex]$\left[\frac{-4}{3}, 4\right]$[/tex].

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Which ordered pairs make the equation [tex]\bf{3x+2y=-7}[/tex] true? Select all that apply. 3 options are given

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

We can tell which ordered pairs make equations true by plugging in the coordinates.

[tex]\mathbb{ORDERED\;PAIR\;NUMBER\;ONE}[/tex]

[tex]\bf{3(3)+2(-8)=-7}[/tex] | simplify

[tex]\bf{9-16=-7}[/tex] |simplify

[tex]\bf{-7\equiv-7}[/tex] | this one checks

[tex]\mathbb{ORDERED\;PAIR\;NUMBER\;TWO}[/tex]

[tex]\bf{3(-2)+2(-1)=-7}[/tex] | simplify

[tex]\bf{-6-2=-7}[/tex] | simplify

[tex]\bf{-8\neq-7}[/tex] | this one does not check

[tex]\mathbb{ORDERED\;PAIR\;NUMBER\;THREE}[/tex]

[tex]\bf{3(1)+2(-4)=-7}[/tex] | simplify

[tex]\bf{3-8=-7}[/tex] | simplify

[tex]\bf{-5\ne-7}[/tex] | this one does not check

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

              [tex]\bf{=The\;First\;Option[/tex]

[tex]\boxed{\bf{aesthetic \not101}}[/tex]

By knowing the length of the three sides of the triangle and applying the law of the cosine, we find that the measure of the three angles are 33.544°, 114.998° and 31.458°.

In this question we know the length of the three sides of a triangle, we can find the measure of all angles by using the law of the cosine. So, we know that:

a = 270, b = 442.85, c = 255

Then, by the law of the cosine:

[tex]\cos A = \frac{270^{2}-255^{2}-442.85^{2}}{-2\cdot (442.85)\cdot (255)}[/tex]

A ≈ 33.544°

[tex]\cos B = \frac{442.85^{2}-270^{2}-255^{2}}{-2\cdot (270)\cdot (255)}[/tex]

B ≈ 114.998°

[tex]\cos C = \frac{255^{2}-270^{2}-442.85^{2}}{-2\cdot (270)\cdot (442.85)}[/tex]

C ≈ 31.458°

By knowing the length of the three sides of the triangle and applying the law of the cosine, we find that the measure of the three angles are 33.544°, 114.998° and 31.458°.

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The angle z is equal to 110° by vertically opposite angles. Hence, the correct option will be C. z = 110°.

The vertically opposite angles are those angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.

Given;

The one angle is given as 110°.

So, angle z will be equal to 110° by vertically opposite angles.

Hence, the correct option will be C. z = 110°.

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[tex]\huge\boxed{192\ \text{in}^2}[/tex]

There are three parts to this figure: a rectangle and two triangles that are congruent.

We'll add together the area for each to get the total area.

We'll start by finding the area of the rectangle. We don't know its length, so we need to find the bases of the triangles and add them together.

We know that [tex]a^2+b^2=c^2[/tex]. Substitute and solve for [tex]a[/tex]:

[tex]\begin{aligned}a^2+6^2&=10^2\\a^2+36&=100\\a^2+36-36&=100-36\\a^2&=64\\\sqrt{a^2}&=\sqrt{64}\\a&=8\end{aligned}[/tex]

Now, double this to get the total length of the rectangle, which is [tex]16[/tex] inches.

The area of the rectangle is equal to its length times its height:

[tex]16\cdot9=\underline{144}[/tex]

Now, we'll find the area of one of the triangles and double it since they're congruent.

The area of a triangle is one-half of its base times its height, which we then double.

[tex]2\left(\frac{1}{2}\cdot b\cdot h\right)[/tex]

The [tex]2[/tex] and the [tex]\frac{1}{2}[/tex] cancel each other out.

[tex]b\cdot h[/tex]

Substitute and solve:

[tex]8\cdot6=\underline{48}[/tex]

Finally, add the rectangle's area to the two triangles' area.

[tex]144+48=\boxed{192}[/tex]

Answer:

1.19x = 12

Step-by-step explanation:

To write an equation, we multiply the cost of each song by the number of songs, x

1.19 * x

This is equal to the total amount he is allowed to spend

1.19x = 12

Answer:

D

Step-by-step explanation:

If Doug can download new songs for $1.19 each, then he will be able to download 12 songs.

The napkin covered approximately 56 square centimeters of the plate. The third option is correct.

The area of an isosceles triangle can be estimated by using the trigonometric function:

[tex]\mathbf{=\dfrac{1}{2} \times a \times b\times sin (C)}[/tex]

From the given information:

The perimeter of the triangle:

P = a + b + c

38 = a + 8 + c

where;

So;

38 = 8 + 2a

38 - 8 = 2a

2a = 30

a = c = 15

Similarly, ∠ABC = 30

∠A + ∠B + ∠C = 180   (sum of angles in a triangle)

∠A + 30 + ∠C = 180

∠A = ∠C = x

2x = 180 - 30

2x = 150

x = 150/2

∠A = ∠C = x  = 75°

Using the trigonometric function:

[tex]\mathbf{=\dfrac{1}{2} \times (15) \times (8) \times sin (75)}[/tex]

= 56 square centimeters.

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Answer: Option C

Step-by-step explanation:

Edge 2020

Answer:

9

Step-by-step explanation:

So first step is to subtract [tex]3x^2+4x[/tex] from [tex]7x^2+x+9[/tex]. In setting this up you get the following expression

[tex](7x^2+x+9)-(3x^2+4x)[/tex]

Distribute the negative

[tex]7x^2+x+9-3x^2-4x[/tex]

Group like terms

[tex](7x^2-3x^2)+(x-4x)+9[/tex]

Simplify:

[tex]4x^2-3x+9[/tex]

Now subtract [tex]4x^2-3x[/tex]. In setting this up you get the following expression

[tex](4x^2-3x+9)-(4x^2-3x)[/tex]

Distribute the negative:

[tex]4x^2-3x+9-4x^2+3x[/tex]

Group like terms

[tex](4x^2-4x^2) + (-3x+3x) + 9[/tex]

Simplify:

[tex]9[/tex]

Let's see

For line A

Slope

For line B

Slope

The answer choice which shows y+2x<4x-3, rewritten to isolate y is; y < 2x -3.

From the task content, it follows that the inequality given in the task content is; y+2x<4x-3.

Hence, the variable y can be isolated from the inequality as follows;

y+2x<4x-3

y < 4x -2x -3

y < 2x -3.

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The equation of the straight line is y = -1/6(x - 10) + 4

The equation is given as:

y = 2x + 6

Linear equations are represented as:

y = mx + c

Where:

Slope = m

So, we have:

m = 6

The slopes of perpendicular lines are represented as:

n = -1/m

So, we have:

n = -1/6

The equation is then represented as:

y = n(x - x1) + y1

This gives

y = -1/6(x - 10) + 4

Hence, the equation of the straight line is y = -1/6(x - 10) + 4

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I think the answered is ×=20

The inverse operations used after the distributive property is B. subtraction then division.

The equation given goes thus:

5(x + 6) = 50.

5x + 30 = 50

5x = 20.

x = 4

Therefore, the inverse operations used after the distributive property is subtraction then division.

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The logarithmic expression of 4^(1/2) = 2 is [tex]\log_4(2) = \frac 12[/tex]

The expression is given as:

4^(1/2) = 2

Take the logarithm of both sides

log(4^(1/2)) = log(2)

Apply the change of base rule

1/2log(4) = log(2)

Divide both sides by log(4)

1/2 = log(2)/log(4)

Change the base

[tex]\frac 12 =\log_4(2)[/tex]

Rewrite as:

[tex]\log_4(2) = \frac 12[/tex]

Hence, the logarithmic expression of 4^(1/2) = 2 is [tex]\log_4(2) = \frac 12[/tex]

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Without having to raise funds externally sales could increase by $84,507.04.

Given that $4 million sales in 2021 and in end of the year total assets are $3.2, current liabilities are $500,000, payable notes are $200,000, accounts payable is $200,000 and accrued liabilities are $100,000 and in 2022 assets must increase by $.80 for every $1.00 increase in sales.

The amount of sales increase that the company can achieve without having to raise funds externally is calculated by multiplying the current year sales with the self-supporting growth rate.

Current Year Sales = $4,000,000

Profit Margin = 3.00%

Dividend Payout Ratio = 50%

Therefore, the Retention Ratio = 50%

Total Spontaneous Liabilities is, $200,000 + $100,000=$300,000

Last Year Total Assets = $3,200,000

Therefore, the Self-supporting Growth Rate=Addition to Retained Earnings÷[Total Assets–Total Spontaneous Liabilities-Addition to Retained Earnings]

= [Last year sales×Profit Margin×(1-Dividend Payout Ratio)]÷[Total Assets-Total Spontaneous Liabilities-Addition to Retained Earnings]

= [$4,000,000×0.03×(1–0.50)]÷[$3,200,000-$300,000–{[$4,000,000×0.04×(1–0.050)}]

= $60,000÷[$3,200,000-$300,000-$60,000]

= $80,000÷$2,840,000

= 0.02112676 or 2.112676%

Therefore, the increase in sales that the company can achieve without having to raise funds externally = Last Year Sales×Self-supporting Growth Rate

= $4,000,000×2.112676%

= $84,507.04

Hence, the Increase in Sales so the company achieve without having to raise funds externally $84,507.04”

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