1. If the ratio of AB to BC is 4:9, what is the area of Parallelogram ABCD?​

[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:

71.4%

Step-by-step explanation:

7+3+8+3=21 total fish

7+8=15 healthy fish

15÷21=0.7142=71.4%

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:

a

Step-by-step explanation:

y = 3x - 7 → (1)

4x - 5y = - 20 → (2)

substitute y = 3x - 7 into (2)

4x - 5(3x - 7) = - 20

4x - 15x + 35 = - 20

- 11x + 35 = - 20 ( subtract 35 from both sides )

- 11x = - 55 ( divide both sides by - 11 )

x = 5

substitute x = 5 into (1)

y = 3(5) - 7 = 15 - 7 = 8

solution is (5, 8 )

Answer:

It's a linear function.

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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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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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:

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 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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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.  <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

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

Using it's concept, the percentile rank for a score of 85 on this test is the 50th percentile.

When a measure is in the xth percentile of a data-set, it is greater or equal than x% of the measures and lesser than (100 - x)%.

In this problem, there are 20 scores, and 85 corresponds to the 10th highest score, hence the percentile is given by:

p = 10/20 = 0.5 x 100% = 50th percentile.

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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 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

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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The x and y-intercepts are (-3/4, 0) and (0, 7/3) respectively

The y-intercept is the point where the value of x is zero while the x-intercept is the point where the value of y is zero

Given the function below;

-4x + 7y = 3

For the x-intercept

-4x = 3

x = -3/4

The x-intercept is (-3/4, 0)

For the y-intercept

7y = 3

y = 3/7

The y-intercept is (0, 7/3)

Hence the x and y-intercepts are (-3/4, 0) and (0, 7/3) respectively

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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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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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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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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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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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Answer:

About 56%

Step-by-step explanation:

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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Let's see

For line A

Slope

For line B

Slope

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].

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