I need to solve this system of equations, how do I do that?
3x-4y=20
y=3/4x-5

Answer:

The area of the corral is 2976 ft²

Step-by-step explanation:

Here, we have the perimeter of the rectangle given as 220 ft

Therefore, since in a rectangle, we have 2 sides of the four sides equal, that is;

Perimeter = 2×One side + 2×Other side

or Perimeter = 2×X + 2×Y

Here perimeter = 220 ft = 2×X + 2×Y

As one of the sides is 48 ft, we have;

220 ft = 2 × 48 + 2×Y

Therefore, 2×Y = 220 ft - 2×48 ft = 124 ft

∴ Y = 124 ft ÷ 2 = 62 ft

The area of the corral = Area of rectangle = Length × Width = 62 ft × 48 ft

Area of the corral = 2976 ft².

A=Player A runs; B=Player B runs=A-16

A+B=242 Substitute for B.

A+A-16=242 Add 16 to each side.

2A=258 Divide each side by 2.

A=129 ANSWER 1: Player A batted in 129 runs.

B=A-16=129-16=113 ANSWER 2: Player B batted in 113 runs

CHECK:

A+B=242

129+113=242

242=242

Final answer:

Player A batted in 118 runs and Player B batted in 104 runs during the 2008 regular season. We found this by setting up two equations based on the given information and solving for the variables representing the number of runs batted in by each player.

Explanation:

To solve this problem, let's use two variables, A for the number of runs batted in by Player A, and B for the number of runs batted in by Player B. We know that Player A led the league, and Player B had 14 fewer runs batted in, so we can write the following equation:

B = A - 14

We also know that together they brought in 222 runs, so we can write another equation:

A + B = 222

Substituting the first equation into the second gives us:

A + (A - 14) = 222

Simplifying this equation, we get:

2A - 14 = 222

2A = 236

A = 118

Using the value of A, we can find B:

B = 118 - 14

B = 104

Therefore, Player A batted in 118 runs and Player B batted in 104 runs during the 2008 regular season.

Answer:

1,3,10

Step-by-step explanation:

I got it wright on the test.

Answer:

1

3

10

Step-by-step explanation:

edu 2020

Answer:

3 m + 4  n = $24.25

9 m +   n = $37.00  are the required set of equations.

The cost of 1 cold drink  = $3.75

The cost of 1 pop corn bag  = $3.25

Step-by-step explanation:

Let us assume the cost of 1 drink = $ m

And the cost of 1 bag of popcorn = $ n

Now, Brianna buys 3 drinks + 4 bag popcorn  for  $24.25

⇒ Cost of 3 drinks +  4 bag popcorn =  $ 24.25

or, 3 ( Cost of 1 drink) + 4 ( Cost of i bag popcorn)  = $ 24.25

⇒ 3 m + 4  n = $24.25  ...  (1)

Also, Chloe buys 9 drinks + 1 bag popcorn  for  $37.00

⇒ Cost of 9 drinks +  1 bag popcorn =  $37.00

or, 9 ( Cost of 1 drink) + 1 ( Cost of 1 bag popcorn)  = $37.00

⇒ 9 m +   n = $37.00 ...  (2)

Now, solving equation (1) and (2) ,we get:

3 m + 4  n = $24.25

9 m +   n = $37.00   ⇒ n  = 37 -  9 m

Substitute the value of n in the equation (1),we get:

3 m + 4  n = $24.25  ⇒ 3  m + 4 ( 37 - 9 m ) = 24.25

or, 3 m + 148 - 36 m = 24.25

or, -33 m = -123.75

or, m = 123.75/33 =  3.75, or m = 3.75

Now, n = 37 - 9 m = 37  - 9(3.75)  =  3.25, or n = 3.25

Hence the cost of 1 cold drink =  m = $3.75

And the cost of 1 pop corn bag  =  n  = $3.25

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Step-by-step explanation:

Answer:

60

Step-by-step explanation:

Final answer:

To solve for x when g(x) = 0 for the function g(x) = 5x + 5, subtract 5 from both sides and then divide by 5, resulting in x = -1.

Explanation:

To solve the equation g(x) = 5x + 5 when g(x) = 0, you need to find the value of x that makes the equation true.

Set up the equation: 5x + 5 = 0.

Subtract 5 from both sides: 5x = -5.

Divide both sides by 5 to solve for x: x = -5 / 5.

Thus, x = -1.

Therefore, the solution for x when g(x) = 0 is x = -1.

Answer: Given:

(r, θ) is equivalent to (x, y) = (7, 5).

By definition,

r = √(7² + 5²) = 8.6023

θ = tan⁻¹ (7/5) = 0.9505 rad

Therefore

2r = 17.2047

θ + π/2 = 0.9505 + π/2 = 2.5213

In rectangular coordinates,

x = 2r cos(θ + π/2) = 17.2047*cos(2.5213) = -14

y = 2r sin(θ + π/2) = 17.2047*sin(2.5213) = 10

Answer: (-14, 10)

The rectangular coordinates of the polar coordinates (2√2, -π/12) are (-14,10).

The polar coordinate system is a two-dimensional coordinate system in mathematics in which points are defined by an angle and a distance from a central point known as the pole (equivalent to the origin in the more familiar Cartesian coordinate system).

We know polar coordinates are in the form (r, θ).

Also, (r, θ) = (x, y) = (7, 5).

So, r = √(7² + 5²)

r = 8.6023

and, θ = tan⁻¹ (7/5)

θ = 0.9505 rad

Now, 2r = 17.2047

and, θ + π/2 = 0.9505 + π/2 = 2.5213

Thus, the rectangular coordinates are

x = 2r cos(θ + π/2)

x = 17.2047 . cos(2.5213)

x = -14

and, y = 2r sin(θ + π/2)

y = 17.2047 . sin(2.5213)

y = 10

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Answer:

A) 330 cd/sq. M per m

Step-by-step explanation:

To find the average rate at which the light intensity decreases as Caleb goes from a depth of 5m to a depth of 14m inside the cave, we need to calculate the change in light intensity and divide it by the change in depth.

To find the average rate at which the light intensity decreases as Caleb goes from a depth of 5m to a depth of 14m, we need to calculate the change in light intensity and divide it by the change in depth.

Let's denote the initial light intensity at 5m as I1 and the final light intensity at 14m as I2. Using the graph, we can estimate the values of I1 and I2.

Then, the average rate of decrease in light intensity is given by:

Average rate = (I2 - I1) / (14m - 5m)

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Answer:

10x^3+16

Step-by-step explanation:

Answer: 918km^2

Step-by-step explanation:

[tex]area(a): 1700km^2\\percentage(p): 5.75 = \frac{5.75}{100}=0.0575\\years(y): 8[/tex]

Let x be the new dimension of the area;

[tex]x=a-(a*p*y)[/tex]

[tex]x=(1700km^2)-(1700km^2*0.0575*8)\\x=1700km^2-782km^2\\x=918km^2[/tex]

The mean of the normal monthly precipitation for August in these 20 U.S. cities is obtained by adding all precipitation values and dividing by the total number of values, which gives a mean of 3.09 inches.

To find the mean of the data, we sum all the values and then divide by the number of values. After adding all the given 20 precipitation values, the total sum comes out to be 61.8 inches. So the mean of the data will be 61.8/20 = 3.09 inches. Therefore, the mean normal monthly precipitation for August in these 20 U.S. cities is 3.09 inches.

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Step-by-step explanation:

Given

Radius (r) = 9 yards

Area of circle

= πr²

= 3.14 * 9²

= 3.14 * 81

= 254.34 yards²

Answer:

D on e2020

Step-by-step explanation:

got it right

Answer:

D. (StartFraction 7 Over 2 EndFraction) squared

Step-by-step explanation:

Answer:

the answer is D

Step-by-step explanation:

D) Westfield's data shows greater variability, since Westfield's MAD is approximately 2.9 times greater than Eastfield's MAD.  

Answer:

D) Westfield's data shows greater variability, since Westfield's MAD is approximately 2.9 times greater than Eastfield's MAD.

Step-by-step explanation:

Westfield's data shows greater variability, since Westfield's MAD is approximately 2.9 times greater than Eastfield's MAD.

Westfield's MAD = 6.56

Eastfield's MAD = 2.28

Therefore,

6.56

2.28

= 2.877

MAD =

∑|x − X|

n

, where x = Data value, X = Mean, and n = Number of values

Answer:

45 Handshakes

Step-by-step explanation:

45 Handshakes have taken place all together

Answer:

45

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

First, you find the mean (((4 + 5 + 6 + 1)/4) = 4)

Find the absolute difference between each data value and the mean: 0, 1, 2, 3

Add the differences (in the previous step) and divide by number of terms: (0+1+2+3)/4 = 6/4 = 3/2

Answer:

The sum of the first 6 terms of the series is 504.

Step-by-step explanation:

Given that,

Common ratio in a geometric series is, r = 0.5

First term of the series, a = 256

We need to find the sum of the first 6 terms in the series. If a and r area the first term and common ratio of a series, then the series becomes:

[tex]a,ar^1,ar^2,ar^3......[/tex]

The sum of n terms of a GP is given by :

[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]

Here, n = 6

[tex]S_n=\dfrac{256\times (1-(0.5)^6)}{1-0.5}\\\\S_n=504[/tex]

So, the sum of the first 6 terms of the series is 504.

Answer: Your sister is not correct. You can determine how far the overhang should extend by dividing 8 by [tex]tan(70\°)[/tex]

Step-by-step explanation:

The complete exercise is attached.

Observe the picture attached. You can identify that the angle A and the angle B are congruent (which means that they have equal measure).

Let be "CB" is the length in feet that the overhang should be in order to keep the Sun out when it is at its highest point in the sky.

You need to use the following Trigonometric Identity:

[tex]tan\alpha =\frac{opposite}{adjacent}[/tex]

You can notice that, in this case:

[tex]\alpha =70\°\\\\opposite=8\ ft\\\\adjacent=CB[/tex]

Knowing these values you can substitute them into  [tex]tan\alpha =\frac{opposite}{adjacent}[/tex] and then solve for "CB" in orde to find its value.

You get:

[tex]tan(70\°)=\frac{8}{CB}\\\\CB*tan(70\°)=8\\\\CB=\frac{8}{tan(70\°)}\\\\CB=2.91[/tex]

Therefore, your sisteter is not correct.

Answer:

Your sister is not correct. You can determine how far the overhang should extend by dividing 8.

Step-by-step explanation:

You can determine how far the overhang should extend by dividing

Observe the picture attached. You can identify that the angle A and the angle B are congruent (which means that they have equal measure).

Let be "CB" is the length in feet that the overhang should be in order to keep the Sun out when it is at its highest point in the sky.

You need to use the following Trigonometric Identity:

You can notice that, in this case:

Knowing these values you can substitute them into   and then solve for "CB" in orde to find its value.

Therefore, your sisteter is not correct.

Answer:

add the third choice, "the average rate of change for the function is 1"

Step-by-step explanation:

Answer:

The value of k is 0.448.

Step-by-step explanation:

Given the exponential growth function is

[tex]A=23e^{kt}[/tex]

A= The population of the country

k= growth rate.

The population of the country increased by 10 million in 13 years after 1982.

Then the population is =(23+13)million = 36 million.

Here,

A= 36 million, t= 13

[tex]A=23e^{kt}[/tex]

[tex]\Rightarrow 36=23e^{13k}[/tex]

[tex]\Rightarrow e^{13k}=\frac{36}{23}[/tex]

Taking ln function both sides

[tex]\Rightarrow ln|e^{13k}|=ln|\frac{36}{23}|[/tex]

[tex]\Rightarrow {13k}=ln|\frac{36}{23}|[/tex]

[tex]\Rightarrow {k}=\frac{ln|\frac{36}{23}|}{13}[/tex]

[tex]\Rightarrow k=0.448[/tex]

The value of k is 0.448.

Answer:

125000 square feet

Step-by-step explanation:

Since there are only three sides of the rectangle, the perimeter of the fence is:

Let x and y be the sides of the rectangle, we are left with:

2 * x + y = 1000

solving for and:

y = 1000 - 2 * x

The area of the corral is:

A = x * y

replacing

A = x * (1000 - 2*x)

A = 1000 * x - 2*x^2

to find the maximum for the parabolic function A = 1000 * x - 2*x^2

The function has a maximum since the quotient before x ^ 2 is negative: -2 <0

Amax = c - b^2 /4*a

where a = -2, b = 1000, c = 0

A max = 0 - 1000^2/(4 * (- 2))

A max = 125000 ft^2

The maximum possible area of the pen is 125000 square feet.

Final answer:

125,000 square feet,

Explanation:

Let us denote the length of the rectangular area parallel to the creek as L and the width of the area as W. Given that the total amount of fencing available is 1000 feet, we can express the perimeter that Jake can fence as 2W + L = 1000 feet, since the creek forms one of the longer sides of the rectangle, and no fencing is required there.

The area A of the rectangle is given by the product of its length and width, i.e., A = L × W. Our goal is to maximize A. From the perimeter equation 2W + L = 1000, we can express L as L = 1000 - 2W.

Substituting this into the area formula, we get A = W * (1000 - 2W). This is a quadratic function and can be written as

A = -2W^2 + 1000W, which is a parabola opening downwards. The maximum value of this function can be found by completing the square or by using the vertex form of a parabola.

The vertex of the parabola, which gives the maximum area, occurs at W = -b/(2a), with 'a' being the coefficient of

W^2 (-2 in this case) and 'b' the coefficient of W (1000 in this case). Plugging these values in, we find that

W = -1000 / (2 * -2) = 250.

Therefore, the width that gives the maximum area is 250 feet. Substituting W back into the perimeter formula, we get

L = 1000 - 2*250 = 500 feet.

So, the dimensions for the maximum area are 500 feet by 250 feet, and the maximum area is A = 500 * 250 = 125,000 square feet.

Answer:

9 fruit baskets.

Step-by-step explanation:

Given:

Steve sold 36 fruit baskets for a school fundraiser.

Evie sold 25% of the number of baskets that Steve sold.

Question asked:

How many fruit baskets did Evie sell?

Solution:

As given that Evie sold 25% of the number of baskets that Steve sold.

Number of baskets sold by Evie = 25% of 36

                                                      [tex]=\frac{25}{100}\times36\\\\ =\frac{900}{100}\\ \\=9[/tex]

Thus, 9 fruit baskets sold by Evie.

Answer:

27

Step-by-step explanation:

StartRoot 27 EndRoot cm

Answer:

I'd say 2/3

Step-by-step explanation:

I play a lot of Monopoly

Answer:

1 in 216

Step-by-step explanation:

the chance of rolling doubles once is 1/6 if you go through all possible outcomes, and six to the power of 3 (the amount of consecutive doubles desired) is 216

Answer:

your expression is (10x+15)+11x

Step-by-step explanation:

let the missing number be X

(10x+15)+11x

Answer:

D

Step-by-step explanation:  

Hope this Helps :D

Answer:

D

Step-by-step explanation:

Answer:

The correct answer is must have a positive slope.

Step-by-step explanation:

The coefficient of determination varies between -1 to 1. It shows the how strong is the relationship between two variables.

Coefficient closer to -1 indicate negative relationship and that y decreases with increase in x and the regression equation has a negative slope.

Coefficient closer to 1 indicate positive relationship and that y increases with increase in x and the regression equation has a positive slope.

Coefficient closer to 0 indicate that there is no possible relationship between the variables under consideration. It is not possible to construct a particular regression equation.

Final answer:

To solve the equation by factoring, we factor out common terms from both sides of the equation and set each factor equal to zero. We consider the factors separately and solve for θ to find the solutions.

Explanation:

To solve the given equation, we need to factorize the trigonometric terms. Let's start by factoring out the common factor of sin(θ) cot(θ) from the left side of the equation:

csc(θ) cot(θ) − sin(θ) tan(θ) = cos(θ)

sin(θ) cot(θ)(csc(θ) − tan(θ)) = cos(θ)

Now we have a product of two factors equal to zero, so we can set each factor equal to zero and solve for θ:

sin(θ) cot(θ) = 0

csc(θ) − tan(θ) = cos(θ)

To find the solutions for sin(θ) cot(θ) = 0, we can consider the factors separately:

sin(θ) = 0 or cot(θ) = 0

For sin(θ) = 0, the solutions are θ = kπ, where k is an integer.

For cot(θ) = 0, we can rewrite it as cos(θ)/sin(θ) = 0, which means cos(θ) = 0 and sin(θ) ≠ 0. The solutions for cos(θ) = 0 are θ = (2k + 1)π/2, where k is an integer.

Now let's solve csc(θ) − tan(θ) = cos(θ):

csc(θ) − (sin(θ)/cos(θ)) = cos(θ)

(1/sin(θ)) − (sin(θ)/cos(θ)) = cos(θ)

Using a common denominator, we can combine the fractions:

(cos(θ) − sin(θ))/sin(θ) = cos(θ)

Now we have a fraction equal to a constant. This can only be true if the numerator is zero:

cos(θ) − sin(θ) = 0

Using the identity cos(θ) − sin(θ) = −√2 sin(θ + π/4), we can rewrite the equation as:

−√2 sin(θ + π/4) = 0

Solving for sin(θ + π/4) = 0, we get θ + π/4 = kπ, where k is an integer.

Therefore, the solutions to the equation csc(θ) cot(θ) − sin(θ) tan(θ) = cos(θ) are:

θ = kπ (for sin(θ) cot(θ) = 0)

θ = (2k + 1)π/2 (for csc(θ) − tan(θ) = cos(θ))

Answer:

16th term = 39.

Step-by-step explanation:

Plug 16 into the formula -6 + 3(n - 1):

A(16) = -6 + 3(16-1)

= - 6 + 3*15

= -6 + 45

= 39.

Answer:

Step-by-step explanation:

Answer: the winnings are reduced

Step-by-step explanation:

Given 10 percent chance to win $1,000 for $100. That is

Gain = $900

Assuming diminishing marginal utility of dollars, when the utility of the gain and the money used for bet are considered, it is discovered that the utility of the $100 used to make the bet is greater than the $900 that you might gain if you win the bet.

this is not a fair bet in terms of utility because the winnings are reduced.

A mathematically fair bet does not account for the diminishing marginal utility of money. The expected utility calculated with a utility function might show a different picture, revealing the bet might not be fair in terms of utility. Samuelson's story illustrates statistical independence and that repeated gambles with positive expectations lead to better outcomes.

A "mathematically fair bet" is one where the expected value of the bet is equal to the cost of making the bet. In other words, if you bet $100 for a 10 percent chance to win $1,000, the mathematically calculated expectation would be $100, or 0.10 times $1,000. However, the concept of diminishing marginal utility suggests that the utility or satisfaction derived from each additional dollar decreases as one has more money. Thus, the utility of the potential win cannot simply be calculated by multiplying the probabilities by the monetary outcome.

Under the concept of expected utility, the expected utility of a bet should also be considered. To calculate this, one might use a utility function, like the von Neumann-Morgenstern utility function, to determine the utility of each possible outcome and then finding the average utility. For example, let's assume that the utility function is represented by the square root of the dollar amount (this is just an example, utility functions can take many forms). Hence, the expected utility of winning $1,000 would be the square root of $1,000, not just $1,000.

Paul Samuelson's story illustrates the idea of statistical independence and the law of large numbers, where repeated play of a gamble with positive expectation can lead to more stable and predictable results, as opposed to a single high-risk gamble. This idea reflects human behavior and the role of hope in encouraging smart risk-taking, even when each individual bet may not be favorable in terms of utility.