Find the value of each variable in the parallelogram.

Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

a. 5x7 = 35 days

b. 12 x 7 = 84 days

c. not sure, its missing the number

Answer: A is not equivalent to the other 2

Step-by-step explanation:

A. 15j+30

B. 5(3j-6) = 15j-30

C 3(5j-10) = 15j-30

multiply the stuff inside paranthesis for the last 2

So a is the outsider

Answer:

A: y = -2/5x - 1

B: 2x + 5y = -5

E: y - 1 = -2/5(x+5)

Step-by-step explanation:

I only got 2 out of 3 answers, but the ones listed above should be correct :) Hope this helps! :D

The equation of the line is 2x + 5y = -5.

The equation of a line is given by:

y = mx + c

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

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of a line that is parallel to the line 2x + 5y = 10 will have the same slope as the given line, which is -2/5.

Using the point-slope form of the equation of a line, we can find the equation of the line passing through the point (-5, 1) with slope -2/5:

y - 1 = (-2/5)(x + 5)

Multiplying both sides by 5.

5y - 5 = -2x - 10

Adding 10 to both sides.

2x + 5y = -5

Now,

2x + 5y = -5

This can be written as,

5y = -2x -5

y = (-2/5)x - 1

Thus,

The equation of the line is 2x + 5y = -5.

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95% confidence that the population mean is less than 6 minutes since the upper limit of the confidence interval is below 6 minutes.

95% confidence that the population mean is within the range of 4.897 to 5.763 minutes.

The t-based 95 percent confidence interval for the population mean:

CI =\(\bar x\pm t\alpha/2 \times (s/\sqrt n)\)

\(\bar x\)  is the sample mean, s is the sample standard deviation, n is the sample size, tα=/2 is the t-value corresponding to the desired level of confidence and (s/√n) is the standard error of the mean.

The sample size is 100, the sample mean is 5.33, and the sample standard deviation is 2.207, the standard error of the mean is:

s/√n

= 2.207/√100

= 0.221

The t-value corresponding to a 95% confidence level with 99 degrees of freedom (100 - 1), look it up in a t-distribution table or use a calculator.

The t-value is approximately 1.984.

The 95% confidence interval for the population mean is:

CI = 5.33 ± 1.984 × 0.221

= [4.897, 5.763]

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To find the derivative dy/dx of the given equation 3\(x^{2}\) - 4\(x^{2}\)y + 5\(y^2\) = \(cscx\) using implicit differentiation, we start by differentiating each term with respect to x and then solve for dy/dx.

To find dy/dx using implicit differentiation, we'll differentiate both sides of the equation with respect to x, treating y as a function of x.

Let's start by differentiating each term separately:

Differentiating 3\(x^{2}\) with respect to x gives us: d/dx (3\(x^{2}\)) = 6x.

To differentiate -4\(x^{2}\)y with respect to x, we'll use the product rule. Let u = -4\(x^{2}\) and v = y. Applying the product rule:

d/dx (-4\(x^{2}\)y) = u * (dv/dx) + v * (du/dx)

= -4\(x^{2}\) * (dy/dx) + y * (-8x).

Differentiating 5\(y^2\) with respect to x requires the chain rule. Let u = 5\(y^2\) and v = csc(x). We'll use the chain rule to differentiate this term:

d/dx (5\(y^2\)) = (du/dy) * (dy/dx) = 10y * (dy/dx).

For differentiating csc(x) with respect to x, we can rewrite it as 1/sin(x). Applying the chain rule:

d/dx (csc(x)) = d/dx (1/sin(x)) = (-1/\(sin^2(x)\)) * cos(x) = -cos(x)/\(sin^2(x)\).

Putting it all together, our differentiated equation becomes:

6x - 4\(x^{2}\) * (dy/dx) + y * (-8x) + 10y * (dy/dx) = -cos(x)/\(sin^2(x)\).

Now we can isolate dy/dx by moving the terms involving dy/dx to one side and the remaining terms to the other side:

-4\(x^{2}\) * (dy/dx) + 10y * (dy/dx) = -6x + y * 8x - cos(x)/\(sin^2(x)\).

Factoring out dy/dx as a common factor:

(10y - 4\(x^{2}\)) * (dy/dx) = -6x + y * 8x - cos(x)/\(sin^2(x)\).

Finally, we can solve for dy/dx by dividing both sides by (10y - 4\(x^{2}\)):

dy/dx = (-6x + y * 8x - cos(x)/\(sin^2(x)\)) / (10y - 4\(x^{2}\)).

This is the expression for dy/dx obtained through implicit differentiation of the given equation.

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Answer:

y = 1/3x - 2

General Formulas and Concepts:

Pre-Algebra

Algebra I

Standard Form: Ax + By = C

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

Standard Form:   x - 3y = 6

Step 2: Rewrite

Find Slope-Intercept Form

Answer:

1/3x-2

Step-by-step explanation:

Slope intercept form is y=mx+b

So change this to that form x-3y=6

-3y=-x+6 now divide both sides by -3

y=1/3x-2

It will need 10 cupcakes for the 100 percent of order.

Percentage is defined as the parts of a number per fraction of 100.

We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

Percentage is usually denoted by the symbol '%'.

Given that,

6 cupcakes comprises 60 percent of my order.

Let x be the 100 percent of the order.

60% of x = 6

60% × x = 6

0.6x = 6

x = 6 / 0.6 = 10

Hence the total number of cupcakes of order is 10.

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Your question is incomplete. Probably the complete question is as follows.

I'm  gonna give 6 cupcakes to my friends that is 60 percent of my order how many more cupcakes do I need to get my order to 100 percent?

Answer:

Step-by-step explanation:

The values of x for which f(x) = g(x) are x = -4 and x = 3. To find the values of x for which f(x) = g(x), we can set the two functions equal to each other and solve for x.

f(x) = g(x) can be written as:

\(x^2 + 6x - 24 = 4x - x^2\)

Let's simplify the equation:

\(x^2 + 6x - 24 = -x^2 + 4x\)

Rearranging the terms:

\(2x^2 + 2x - 24 = 0\)

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's solve it by factoring:

\(2x^2 + 2x - 24 = 0\)

Divide through by 2 to simplify the equation:

\(x^2 + x - 12 = 0\)

Now, we factor the quadratic equation:

(x + 4)(x - 3) = 0

Setting each factor equal to zero:

x + 4 = 0   or   x - 3 = 0

Solving for x:

x = -4   or   x = 3

Therefore, the values of x for which f(x) = g(x) are x = -4 and x = 3.

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Answer:

Breadth= 4.5cm

Step-by-step explanation:

Area= length x breadth

54cm²=12× b

b=54cm²÷12

b=4.5cm

Answer:

5

Step-by-step explanation:

The amount of money in Lucia's account after 5 years will be $1,105.5.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Lucia opened a savings account and deposited $600.00 as principal. The account earns 13% interest, compounded annually. Then the amount of money after 5 years will be given as,

A = $600 × (1 + 0.13)⁵

A = $600 × (1.13)⁵

A = $600 × 1.84

A = $1,105.5

The amount of money in Lucia's account after 5 years will be $1,105.5.

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If the two firms do not cooperate, the payoff that North Springs and South Springs receive in the dominant-strategy equilibrium and the Nash equilibrium would depend on the specific game or scenario being played. Without more information about the specific game being played and the strategies of the two firms, it is impossible to provide a definitive answer.

However, in general, the dominant-strategy equilibrium refers to the situation where each player chooses their best strategy, regardless of what the other player does. The Nash equilibrium refers to the situation where each player chooses their best strategy given what the other player is doing. In some cases, the dominant-strategy equilibrium and the Nash equilibrium may be the same, but in other cases, they may differ.

So, in order to determine the payoff that North Springs and South Springs receive in these equilibria, more information about the game being played and the strategies of the two firms would be needed.
Based on the information given, we can analyze the payoff for both North Springs and South Springs firms in the dominant-strategy equilibrium and the Nash equilibrium.

Dominant-Strategy Equilibrium:
1. Identify each firm's dominant strategy (the best response regardless of the other firm's action).
2. Combine the dominant strategies for both firms to find the outcome.

Nash Equilibrium:
1. Identify each firm's best response given the other firm's action.
2. Find the outcome where both firms are simultaneously choosing their best responses.

Without specific numerical payoffs, I cannot provide the exact payoff amounts. However, once you have the payoff matrix, you can follow the steps mentioned above to find the payoffs for North Springs and South Springs in the dominant-strategy equilibrium and the Nash equilibrium.

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The inverse of the function in slope-intercept form is f⁻(x) = -x/2 - 2

What is the inverse function?

A function that can change into another function is referred to as inverse. In other words, the inverse of any function "f" will take y to x if it takes x to y in the first place. If a function is written as "f" or "F," the inverse function is written as "f⁻" or "F⁻."

What is slope-intercept form?

The slope-intercept form of a straight line is used to find the equation of a line.

Here,

A function is given to us and we need to find the inverse of the function in slope-intercept form. The given function is,

f(x)= −2x−4

Let assume that y = f(x), then

y = -2x - 4

Now interchange the positions of x and y, and we get

x = -2y - 4

Solve this equation for y in terms of x,

Adding 4 on both sides, we get

x + 4 = -2y

After, dividing both sides by 2, we get

x/2 + 2 = -y

-x/2 - 2 = y

Now replace y with f⁻(x)

f⁻(x) = -x/2 - 2

Hence, the inverse of the function in slope-intercept form is f⁻(x) = -x/2 - 2

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Answer:

436.25 I think

Step-by-step explanation:

Answer:

answer is 1st one

Step-by-step explanation:

because I think so it is the additive inverse

Answer:

(5r + 6)(5r² + 4)

Step-by-step explanation:

Given

25r³ + 30r² + 20r + 24 ( factor the first/second and third/fourth terms )

= 5r²(5r + 6) + 4(5r + 6) ← factor out (5r + 6) from each term

= (5r + 6)(5r² + 4)

Answer:

3 and 5

Step-by-step explanation:

Answer:

300,000

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

\(using \: pythagoras \: theorem \\ let \: the \: unknown \: side = x \\ 25 {}^{2} = x {}^{2} + 20 {}^{2} \\ 625 = x {}^{2} + 400 \\ x {}^{2} = 625 - 400 \\ x {}^{2} { = 225} \\ x = \sqrt{225} \\ x = 15 \\ lenght \: of \: the \: third \: side = 15\)

Ryosuke drove his friend 24 miles, which used 1.14 gallons of gas. The total cost of the gas was $4.64, calculated by multiplying 1.14 gallons by the price of one gallon which was $4.05.

1. Calculate the number of miles driven: Subtract the odometer reading when Ryosuke picked his friend up (74,568) from the odometer reading when he dropped his friend off (74,592). This gives us the total number of miles driven (24).

2. Calculate the number of gallons used: Divide the total number of miles driven (24) by the car's gas mileage (28). This gives us the number of gallons used (1.14).

3. Calculate the cost of the gas: Multiply the number of gallons used (1.14) by the price of one gallon of gas ($4.05). This gives us the cost of the gas used ($4.64).

28 miles

= \($\frac{74,592-74,568}{28}$\)

= 1.14 gallons

Cost of gas

= 1.14 gallons x\($\$4.05$\)

= \($\$4.64$\)

1. 74,592 - 74,568 = 24

2. 24 / 28 = 1.14

3. 1.14 x $4.05 = $4.64

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Answer:

Driving 275 miles would take Elsa 5 hrs.

Step-by-step explanation:

Write and solve an equation of ratios:

 715 mi         13 hrs

------------- = --------------

 275 mi              x

This leads to:  715x = 13(275), or x = 5 (hrs)

Driving 275 miles would take Elsa 5 hrs.

Answer:

7

Step-by-step explanation:

According to the Question,

Given, There is a 2-digit number, the unit digit is 3 & The sum of its tens digit, and the unit digit is 10.

Suppose The Number is XY .

Now, We Know X+Y=10 & Y=3 .

So, X+3=10 ⇔ 7 is the number on Tens Place.

And, the Number is 73 .

The algebraic expression of the given phrases is,

1)k-7

2) m+10

3) 2n-18

4) n+4=12

5) n-9=11

6) 2n+6=n-10.

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

The algebraic expression of the given phrases is,

1) seven subtracted from k

 k-7

2)  m increased by ten

  m+10

3. eighteen less than half a number

   let number is n.

   2n-18

4. A number increased by four is twelve.

 n+4=12,

5. A number decreased by nine is equal to eleven.

n-9=11

6, A number increase by six is half the number decrease by ten

2n+6=n-10.

The complete question is-

Translate the following word phrases into algebraic expressions/equations.

1. seven subtracted from k

_______________________

2. m increased by ten

_______________________

3. eighteen less than half a number

_______________________

4. A number increased by four is twelve.

_______________________

5. A number decreased by nine is equal to eleven.

6, A number increase by six is half the number decrease by ten

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1) The property of equality that justifies the statement "If AB=CD, then CD=AB" is the symmetric property.

2) The correct pair of corresponding angles is <1 and <8.

3) The slope of the line passing through (2,3) and (-2,-5) is 4/(-4) = -1.

4) The value of x cannot be determined without additional information or context.

5) The scale factor of AABC to ALMN is 1/3.

6) In circle C, m = 180 - 2(72) = 36 degrees.

7) The sum of the measures of the interior angles of an 18-gon is (18-2) x 180 = 2880 degrees.

8) The height of the tree is approximately 86.4 ft.

9) m = 180 - (31+88) = 61 degrees.

10) The polygon has 5 sides (a pentagon).

Procedure Part . Explaining
1) The symmetric property of equality states that if a=b, then b=a. In the given statement, AB=CD and CD=AB are equivalent statements and can be interchanged using the symmetric property.
2) Corresponding angles are pairs of angles that are in the same position relative to the parallel lines and the transversal. In the given figure, angles 1 and 8 are on the same side of the transversal and in the same position relative to the parallel lines, making them corresponding angles.
3) The slope of a line passing through two points (x1,y1) and (x2,y2) is given by (y2-y1)/(x2-x1). Applying this formula to the given points, we get the slope as (3-(-5))/(2-(-2)) = 8/4 = 2. However, the given answer choices do not include 2 as an option.
4) Without additional information or context, it is impossible to determine the value of x.
5) The scale factor of two similar figures is the ratio of their corresponding side lengths. In the given problem, AABC and ALMN are similar triangles, and the scale factor is given by AB/LN = 18/9 = 2 and BC/LM = 12/6 = 2. Since both ratios are equal, the scale factor is 1/3.
6) In a circle, the measure of an inscribed angle is half the measure of the intercepted arc. In this case, the intercepted arc is 72 degrees, so the inscribed angle is 36 degrees.
7) The sum of the measures of the interior angles of a polygon with n sides is given by (n-2) x 180 degrees. Substituting n=18, we get (18-2) x 180 = 2880 degrees.
8) The height of the tree can be determined using similar triangles. The ratio of the height of the tree to its shadow is equal to the ratio of Nancy's height to her shadow, which is 5/9. Thus, the height of the tree is (5/9) x 48 = 26.67 ft. However, the given answer choices are not close to this value, so it is unclear how the problem is meant to be solved.
9) The sum of the measures of the angles in a triangle is 180 degrees. In the given triangle, angles m and n are given, so we can find angle A using A+m+n=180.
10) The measure of each interior angle in a regular polygon with n sides is given by (n-2) x 180 / n degrees. Setting this expression equal to 108 and solving for n, we get n=5. Thus, the polygon has 5 sides, which is a pentagon.

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Elsa can correct her mistake by informing that Carson's pumpkin weighs 1/2 pounds instead of 3/4 pounds.

Weight is a measure of the force exerted on an object due to gravity. It is the gravitational force acting on an object's mass. The weight of an object depends on its mass and the strength of the gravitational field it is in.

Weight plays a significant role in various fields such as physics, engineering, sports, and everyday life. It determines the force exerted by objects on surfaces, affects the performance of structures and vehicles, and is relevant in areas like weightlifting, aviation, and space exploration.

Given that Elsa pumpkin weighs 2/4 pounds and is 1/4 pound heavier than Carson's pumpkin.

Elsa thinks that Carson's pumpkin must weight 3/4 pound.

To find out how Elsa can correct her mistake, let's assume the weight of Carson's pumpkin to be x pounds.

It is given that Elsa's pumpkin weighs 1/4 pound heavier than Carson's pumpkin.

Therefore, Elsa's pumpkin weighs (x + 1/4) pounds. As per the question, Elsa thinks that Carson's pumpkin weighs 3/4 pounds.

But according to the information provided in the question, Elsa's pumpkin weighs (x + 1/4) pounds.

So, it can be inferred that: (x + 1/4) = 3/4⇒ x + 1/4 - 1/4 = 3/4 - 1/4⇒ x = 1/2

Therefore, Carson's pumpkin weighs 1/2 pounds which is different from what Elsa thought.

Therefore, Elsa can correct her mistake by informing that Carson's pumpkin weighs 1/2 pounds instead of 3/4 pounds.

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Answer:

\(n = 500e^{-4.1589x}\)

Step-by-step explanation:

Using the exponential growth equation \(N(t) = N_0e^{-kt}\) where;

N₀ is the initial population of the bacteria

N(t) is the population of the bacteria during time t

If a biologist puts an initial population of 500 bacteria into a growth plate, this means that N₀ = 500 at t = 0

\(N(t) = N_0e^{-kt}\\N(t) = 500e^{-k(0)}\\N(t) = 500e^0\\N(t) = 500\)

If the population is expected to double every 4 hours, this means when t = 4, N₀  = 2(500) = 1000

\(N(t) = N_0e^{-kt}\\500 = 1000e^{-4k}\\\frac{500}{1000} = e^{-4k}\\0.5 = e^{-4k}\\ln(0.5) = lne^{-4k}\\ln(0.5) = -4k\\k = \frac{ln0.5}{-4} \\k = 0.1733\)

The equation that will give the expected number of bacteria, n, after x days, can be gotten by substituting N(t) = n and t = x days = 24x hours

\(N(t) = N_0e^{-kt}\\n = N_0e^{-0.1733(24x)}\\n = 500e^{-4.1589x}\)

Hence the equation that will give the expected number of bacteria, n, after x days is \(n = 500e^{-4.1589x}\)

Answer:

function - is a relation for which each value from the set the first components of the ordered pairs