David drew a scaled down model of a racquetball court he played on last week what is the actual perimeter of the court david played on last week

\(\\ \sf\longmapsto \dfrac{5}{4x-6}=\dfrac{2}{x-9}\)

\(\\ \sf\longmapsto 5(x-9)=2(4x-6)\)

\(\\ \sf\longmapsto 5x-45=8x-12\)

\(\\ \sf\longmapsto 5x-8x=-12+45\)

\(\\ \sf\longmapsto -3x=33\)

\(\\ \sf\longmapsto x=\dfrac{33}{-3}\)

\(\\ \sf\longmapsto x=-11\)

\( \huge \boxed{\mathfrak{Question} \downarrow}\)

\( \large \sf \: \frac { 5 } { 4 x - 6 } = \frac { 2 } { x - 9}, \: Solve \: for \: x\\ \)

\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)

\( \large \sf\frac { 5 } { 4 x - 6} = \frac { 2 } { x - 9} \\ \)

Variable x cannot be equal to any of the values \(\sf\frac{3}{2}\),9 as division by zero is not defined. Multiply both sides of the equation by \(\sf2\left(x-9\right)\left(2x-3\right)\), the least common multiple of 4x-6 ,x-9.

\( \large \sf\left(x-9\right)\times 5=\left(4x-6\right)\times 2 \)

Use the distributive property to multiply x-9 by 5.

\( \large \sf5x-45=8x-12 \)

Subtract 8x from both sides.

\( \large \sf5x-45-8x=-12 \)

Combine 5x and -8x to get -3x.

\( \large \sf-3x-45=-12 \)

Add 45 to both sides.

\( \large \sf \: -3x=-12+45 \)

Add -12 and 45 to get 33.

\( \large \sf-3x=33 \)

Divide both sides by -3.

\( \large \sf x=\frac{33}{-3} \\ \)

Divide 33 by -3 to get -11.

\(\large\boxed{\boxed{ \boxed{ \mathfrak{x= - 11}}}}\)

Answer:

26 sq units.......

The largest area you can enclose with 20 meters of fencing against a long, straight wall is 50 square meters. Itcan be found using optimization methods.

Step 1: Define the variables
Let x be the length of the fencing parallel to the wall and y be the length of the fencing perpendicular to the wall.
Step 2: Set up the constraint equation
Since you have 20 meters of fencing, the sum of x and 2y (both sides perpendicular to the wall) should equal 20. The constraint equation is:x + 2y = 20
Step 3: Express one variable in terms of the other
Solve the constraint equation for one variable. In this case, solve for x: x = 20 - 2y

Step 4: Write the area function
The area of the rectangle can be expressed as A = xy. Substitute x from the previous step into this equation: A(y) = (20 - 2y)y.

Step 5: Find the critical points
Differentiate the area function with respect to y and set it to zero to find the critical points: dA/dy = 20 - 4y = 0, Solve for y:4y = 20, y = 5
Step 6: Find the corresponding value for x
Plug the value of y back into the equation for x: x = 20 - 2(5), x = 10

Step 7: Check for maximum area
The critical point we found (x=10, y=5) is indeed a maximum since the second derivative of the area function is negative.Step 8: State the largest area
The largest area you can enclose with 20 meters of fencing against a long, straight wall is A = xy = 10 * 5 = 50 square meters.

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Answer:

After 2/5ths of a pizza is eaten, we have 3/5ths left.

Then, 3/4ths of the remaining (3/5) is eaten, so 3/5 multiplied by 1/4 = 3/20 slices left. If you're wondering why we multiplied it by 1/4th, there is one-fourth left after Sam eats it, so we might as well figure out what is 1/4th of 3/5.

Hari then eats his share, which is 3/4ths, so 3/20 times 1/4 = 3/80.

So, there is 3/80th of a pizza left.

The environment changed in such a way that, "guppies with small spots had a better chance of survival and reproduction, leading to an increase in their population and a decrease in the population of guppies with large spots".

Over many generations, guppies with small spots had a survival advantage in the river because the rocks on the river bottom became smaller. This made guppies with small spots harder for larger fish to see and catch, increasing their chances of survival and reproduction.

As a result, more guppies with the small spot gene passed it on to their offspring, leading to an increase in the population of guppies with small spots. At the same time, the population of guppies with large spots decreased as they were more visible to predators and had a lower chance of survival. This process of natural selection led to a change in the frequency of different traits within the population of guppies.

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a) The size of each payment = $8718.4

b) The the total amount paid for the purchase = $204620.8

c) The total interest paid over the life of the loan = $104620.8

In this question we have been given that a man buys a house for $175,000. He makes a $75,000 down payment and amortizes the rest of the debt with semiannual payment sover the next 10 years. The interest rate on the debt is 12%, compounded semiannually.

We need to find the size of each payment, the total amount paid for the purchase and the total interest paid over the life of the loan.

From given data we get 175,000 - 75,000 = $100,000 amount to finance.

We know that the formula for semiannual payment of a loan,

C = PV/[1 - (1 + r)^-t / r]

Here, PV = $100,000

t = 20 (10 years times 2 payment per year)

r = 0.06 (12% annual. so, we divide by 2 to get semiannual)

So, C = 100,000/[1 - (1 + 0.06)^-20 / 0.06]

C =  100,000/[0.6882 / 0.06]

C = 100,000/11.47

C = $8718.4

The total interest paid will be the cuota times the time of the loan:

Total interest paid:

8718.4 x 12 = 104620.8

And the total amount paid over the life of the loan = 104620.8 + 100,000

                                                                                    = $204620.8

The interest will be the difference between the total amount paid and the principal of the loan

Therefore, Interest paid = $8718.4

total payment   = $204620.8

principal = $100,000

Interest expense = $104620.8

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Answer:

The opposite of an integer and negative number is a positive integer number. In this case, the opposite of -4 is +4.

Answer:

Y=3x-1

Step-by-step explanation:

Let x =1 then ,Y=(3×1)-1=2

Let x=2 then, Y=(3×2)-1=5

Let x=3 then Y=(3×3)-1=8

Let x=0 then Y=(3×0)-1=-1

The optimal strategies for Player 1 and Player 2 in this game are A2 and B1, respectively.Player 1 should play A2 to maximize their payoff, while Player 2 should play B1 to maximize their payoff.

To determine the optimal strategies, we need to find the best responses for each player. Player 1's best response is the strategy that maximizes their payoff given Player 2's strategy, and Player 2's best response is the strategy that maximizes their payoff given Player 1's strategy.

For Player 1:

- If Player 2 plays B1, Player 1's payoffs are 4 (A1), 3 (A2), 4 (A3), and 3 (A4).

- If Player 2 plays B2, Player 1's payoffs are -2 (B1), 2 (B2), -2 (B3), and 2 (B4).

Player 1's best response is A2, as it yields the highest payoff of 3, regardless of Player 2's strategy.

For Player 2:

- If Player 1 plays A1, Player 2's payoffs are 4 (B1), -2 (B2), 4 (B3), and 3 (B4).

- If Player 1 plays A2, Player 2's payoffs are 3 (B1), 2 (B2), -2 (B3), and 2 (B4).

- If Player 1 plays A3, Player 2's payoffs are 2 (B1), 2 (B2), 1 (B3), and -3 (B4).

- If Player 1 plays A4, Player 2's payoffs are 1 (B1), -3 (B2), -3 (B3), and 2 (B4).

Player 2's best response is B1, as it yields the highest payoff of 4, regardless of Player 1's strategy.

The optimal strategies for Player 1 and Player 2 are A2 and B1, respectively. Player 1 should play A2 to maximize their payoff, while Player 2 should play B1 to maximize their payoff.

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The results also suggest that television advertising may be slightly more effective than newspaper advertising in generating revenue.

(a)The estimated regression equation with the amount of television advertising as the independent variable is as follows: ŷ = 20.2650 + 22.1250x1(b)The proportion of variation in the sample values of weekly gross revenue that the model in part

(a) explains is given by the coefficient of determination. It is equal to the square of the correlation coefficient, r, and is calculated as follows: r² = 0.5145Thus, the model explains 51.45% of the variation in the sample values of weekly gross revenue. When converted to a percentage, the answer is 51%. Therefore, the answer is 51%.

(c)The estimated regression equation with both television advertising and newspaper advertising as the independent variables is given by:ŷ = -0.2154 + 19.4649x1 + 30.2941x2We will test whether the regression parameter β0 is equal to zero at a 0.05 level of significance using the t-test. The null and alternative hypotheses are as follows:H0: β0 = 0 (the y-intercept is zero)Ha: β0 ≠ 0We use a t-test to calculate the p-value. t = -0.2286 and the p-value is 0.8292. Since the p-value is greater than 0.05, we fail to reject H0. Hence, we cannot conclude that the y-intercept is not equal to zero.

The next step is to test whether the regression parameter β1 is equal to zero at a 0.05 level of significance. The null and alternative hypotheses are as follows:H0: β1 = 0 (there is no relationship between the amount spent on television advertising and weekly gross revenue)Ha: β1 ≠ 0We will use a t-test to calculate the p-value. t = 2.5494 and the p-value is 0.0382.

Since the p-value is less than 0.05, we reject H0. Hence, we can conclude that there is a relationship between the amount spent on television advertising and weekly gross revenue. We will also test whether the regression parameter β2 is equal to zero at a 0.05 level of significance. The null and alternative hypotheses are as follows:H0: β2 = 0 (there is no relationship between the amount spent on newspaper advertising and weekly gross revenue)Ha: β2 ≠ 0

We will use a t-test to calculate the p-value. t = 3.2487 and the p-value is 0.0128. Since the p-value is less than 0.05, we reject H0. Hence, we can conclude that there is a relationship between the amount spent on newspaper advertising and weekly gross revenue.

(e)The next step should be to use the model with both independent variables to make predictions and test the model's accuracy.

(f)The managerial implications of these results are that management can feel confident that increased spending on both television and newspaper advertising coincides with increased weekly gross revenue. The results also suggest that television advertising may be slightly more effective than newspaper advertising in generating revenue.

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Answer:

The answer to the equation is C

Answer:

Surface area of square pyramid = 380 m²

Step-by-step explanation:

Given:

Side of square base =10 m

Height of Square pyramid = 14 m

Find:

Surface area of square pyramid

Computation:

Surface area of square pyramid = Surface area of Base + 4[Surface area of triangle]

Surface area of square pyramid = [side x side] + 4[(1/2)(b)(h)]

Surface area of square pyramid = [10 x 10] + 4[(1/2)(10)(14)]

Surface area of square pyramid = 100 + 4[70]

Surface area of square pyramid = 100 + 280

Surface area of square pyramid = 380 m²

Answer:\(-10, -10, -10\)

Step-by-step explanation:

\(h(x)\) is not dependent on x.

Answer:

4 packs of juice

3 packs of granola bars

Step-by-step explanation:

if you have 4 packs of juice with 6 in them, you will have 24 juice boxes, one per player (4 x 6).

If you have 3 packs of granola bars with 8 in them, you will have 24 granola bars, one per player ( 3 x 8).

Answer:

10,603 cu in

Step-by-step explanation:

For a pipe use its length instead of height: pipe volume = π * radius² * length , where radius = inner diameter/2 . The volume of a pipe is equal to the volume of a liquid inside.

Therefore,

radius = 1 inch ÷ 17 = 5 inch

length = 15 × 5 inches = 75 inches

volume = π (pi) × radius squared × length

volume = 15× (.5 x .5) × 75

volume = 15 × 5 × 2

volume = 10,603 in³

The volume of fluid in a pipe can be found given the inner diameter of the pipe and the length. To estimate pipe volume, use the following formula:

volume = π ×  

d2

4

× h

Thus, the volume of a pipe is equal to pi times the pipe diameter d squared over 4, times the length of the pipe h.

This formula is derived from the cylinder volume formula, which can also be used if you know the radius of the pipe.

volume = π × r2 × h

Answer:

I cant give you an answer but hints:

First you gotta know the angles of the triangle

then how many are there

then those lines in the middle is dividing lines so

right angles are 90 degrees

I would go for B then.

if not I'm sorry

Answer:

y = mx + c

since m = 0

c = 9

Answer: 60

suppose: the width of a rectangle is x (x > 0)

⇒ The length of a rectangle is 4x

because  the area of the rectangle is 144 ft

=> 4x.x = 144

⇔ x² = 144/4 = 36

⇒ x = 6

with x = 6 ⇒ The length of a rectangle is 4.6 = 24

the perimeter of the rectangle is (6 + 24).2 = 60

Step-by-step explanation:

Answer:

For real???

Step-by-step explanation:

Tysm!! <3 you deserve so much!

Answer:thanks

Step-by-step explanation:

This series is an arithmetic series, as the difference between consecutive terms is a constant, the series goes to infinity, meaning it has an infinite number of terms. Since the arithmetic series has an infinite number of terms, it is divergent. Therefore, the answer is DIVERGES.

To determine whether the series ∑n=1∞(4n+1)/(5−n) is convergent or divergent, we can use the ratio test:

lim┬(n→∞)⁡|((4(n+1)+1)/(5-(n+1)))/((4n+1)/(5-n))|

= lim┬(n→∞)⁡|(4n+5)(5-n)/(4n+1)(6-n)|

= 4/6 = 2/3

Since the limit is less than 1, the series is convergent by the ratio test.

To find the sum of the series, we can use the formula for the sum of a convergent geometric series:

S = a/(1-r)

where a is the first term and r is the common ratio. In this case, we have:

a = (4(1)+1)/(5-1) = 5/4

r = (4(2)+1)/(5-2) / (4(1)+1)/(5-1) = 13/6

Therefore, the sum of the series is:

S = (5/4) / (1-(13/6)) = 15/23
The given series is:

∑(4n + 15 - n) from n=1 to infinity.

First, simplify the series:

∑(3n + 15) from n=1 to infinity.

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The equations that represent the given situation, where four times a number added to 3 times a larger number is 31 and seven subtracted from the larger number is equal to twice the smaller number, are y + 3x = 31 and y - 7 = 2x.

Given:

The result of multiplying an integer by itself three times is 31.

When seven is removed from a greater number, the smaller number is multiplied by two.

Let x stand for the lower value and y for the higher number.

To solve:

Equations that represent this situation

Solution:

The equations that represent this situation are y + 3x = 31 and y - 7 = 2x.

We can see that the first equation states that the larger number (y) plus three times the smaller number (3x) equals 31. The second equation states that the larger number (y) minus seven (7) equals twice the smaller number (2x). Therefore, these equations represent the given situation.

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As of the most recent data available (Fall 2019), male undergraduate enrollment in degree-granting post-secondary institutions in the United States was 44 percent, while female enrollment was 56 percent.

This trend of female enrollment outpacing male enrollment has been consistent over the past several years.

                It's important to note that these figures represent the overall trend and may not accurately reflect the gender composition of undergraduate enrollment at every co-ed college and university in the United States. The gender composition can vary greatly depending on the type of institution (e.g. public vs. private, urban vs. rural), the level of selectivity, and other factors.

                    Additionally, it's important to consider that the gender composition of undergraduate enrollment can change over time and that the COVID-19 pandemic may have also impacted enrollment patterns. The NCES website is a good resource for staying up to date on the most recent and accurate data on undergraduate enrollment by gender in co-ed colleges and universities in the United States.

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When solving proportions, we set the cross products equal, and then we solve for the unknown variable.

When solving proportions, we set the cross products equal to each other and then proceed to solve for the unknown variable. A proportion is an equation that states that two ratios or fractions are equal. To solve a proportion, we first identify the two ratios involved and set their cross-products equal.

For example, consider the proportion: a/b = c/d

To solve for the unknown variable, we set the cross products (a * d) and (b * c) equal:

a * d = b * c

This equation allows us to find the value of the unknown variable by manipulating the equation through multiplication or division to isolate the variable on one side of the equation.

By setting the cross products equal, we essentially establish an equality between the two ratios, indicating that the fractions on either side of the proportion are equivalent. Solving for the unknown variable allows us to determine its value based on the relationship between the given ratios.

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me is the big text guy! lol!

Answer:

$28.50

Step-by-step explanation:

21 chicken wings= $39.90

1 chicken wing= 39.90÷21= $1.90

15 chicken wings= 15×1.90= $28.50

:)

Answer:

$28.50

Step-by-step explanation:

Knowing that :
Brandon brought 21 chicken wings for $39.90

Asking:

How much would it cost for 15 Wings?

Solve:

We first need to know how much is 1 Wings.

To find that Divide Cost by chicken

Thus, 39.90 divide by 21..

=1.90

Hence, 1 Wings ⇒ 1.90

Then Multiply by 15 wings to find the cost of 15 wings.

1.90 * 15 = 28.50

Therefore, 15 Wings Cost $28.50

[RevyBreeze]

The statement that  describes how the graph of h is different from the graph of g is: B. The graph of h is the graph of g vertically shifted up 1 unit.

The function h(x) = g(x) + 1 is obtained by adding a constant (1) to the output of the function g(x) = x^2. This means that the graph of h(x) will be the same as the graph of g(x), except that every point on the graph of h(x) will be shifted vertically upward by 1 unit.

Therefore, the correct statement is: B. The graph of h is the graph of g vertically shifted up 1 unit.

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The dimensions of the rectangular pen that maximize the area are a shorter side of 100 ft and a longer side of 200 ft along the river.

To maximize the area of the rectangular pen using 400 ft of fencing, with a river on one side of the property, we need to determine the optimal dimensions. Let's denote the length of the pen along the river as 'x' and the width perpendicular to the river as 'y'.

Since the river is on one side, we only need to use the fencing for the other three sides. The total fencing length is 400 ft, so the equation representing the fencing is:

x + 2y = 400

We need to find the maximum area of the pen, which is given by the product of its length and width, i.e., A = xy.

First, we need to express 'x' in terms of 'y' using the fencing equation. From the equation, we get:

x = 400 - 2y

Now, substitute this expression for 'x' in the area equation:

A(y) = (400 - 2y)y = 400y - 2y²

To find the maximum area, we need to find the critical points of this equation by taking the derivative with respect to 'y' and setting it to zero:

dA/dy = 400 - 4y = 0

Solve for 'y':

4y = 400
y = 100 ft

Now, find 'x' using the expression we derived earlier:

x = 400 - 2y
x = 400 - 2(100)
x = 400 - 200
x = 200 ft

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Answer:

x=35

Step-by-step explanation:

These two angles are supplementary (or a linear pair) meaning that they add up to 180°.

We can use this information to set up an equation:

3x+75=180

Subtract 75 from both sides

3x=105

Divide both sides by 3

x=35

There are several resources where you can find free SAT practice tests, including:

1.Official SAT Practice Tests:

2.Khan Academy:

3.Ivy Global:

4.PrepScholar

5.CrackSAT

6.Peterson's

There are several resources where you can find free SAT practice tests, including:

1.Official SAT Practice Tests: The College Board, the organization that creates and administers the SAT, offers eight official practice tests for free on their website. These tests are the most accurate representation of the real exam.

2.Khan Academy: The College Board has partnered with Khan Academy to provide free SAT practice materials, including full-length practice tests and personalized study plans based on your performance.

3.Ivy Global: Ivy Global offers a free SAT practice test with answer explanations that mimic the actual test.

4.PrepScholar: Prep Scholar offers a free online SAT practice test that closely resembles the real exam.

5.CrackSAT :  CrackSAT offers a wide range of free practice tests, including SAT Subject Tests.

6.Peterson's: Peterson's offers a free online practice test that includes a score report with detailed feedback.

Remember, the more practice you have, the more prepared you'll be for the SAT. So take advantage of these free resources and practice as much as you can.

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Answer:

True the product of a number and its reciprocal is equal to one.

Step-by-step explanation:

let the number be X

Now the reciprocal will be 1/X

And when we multiply them

X ×1 /X = 1