61= -9c +7
its asking to solve c please help :)

Answer:

a=4 and b = 0

Step-by-step explanation:

Given : \(\dfrac{\sqrt 3 -1}{\sqrt 3+1}+\dfrac{\sqrt 3+1}{\sqrt 3-1}=a+\sqrt 3 b\)

To find, The value of a and b

Solution,

Solving LHS of the given equation,

\(\dfrac{(\sqrt 3-1)^2+(\sqrt3+1)^2}{(\sqrt 3+1)(\sqrt 3-1)}=a+\sqrt 3 b\)

Since,

\((a-b)^2=a^2+b^2-2ab\\\\(a+b)^2=a^2+b^2+2ab\\\\(a-b)(a+b)=a^2+b^2\)

So,

\(\dfrac{3+1-2\sqrt 3+3+1+2\sqrt 3}{3-1}=a+\sqrt 3 b\\\\4=a+\sqrt 3 b\)

or

\(4+0=a+\sqrt 3 b\)

On comparing we get :

a = 4 and b = 0

Hence, according to the question given, we have Jenny got 21 large buttons.

A ratio is a mathematical relationship between two values that are usually expressed as the quotient of one value divided by the other. In order to compare or explain the relative sizes of two or more quantities, ratios can be used.

A particular kind of ratio called a proportional relationship is one in which the ratio between the two quantities is constant. To put it another way, if you increase one amount by a specific factor, the other amount will also be multiplied by that same factor.

Jenny purchased a bag of mixed buttons containing 30 total buttons,70% were large.

We can use the following method to determine how many large buttons she received:

number of large buttons = percentage of large buttons x total number of buttons

By substituting the provided values, we get the following:

number of large buttons = 70% x 30 buttons

                                         = 0.7 x 30 buttons

                                         = 21 buttons

Therefore, Jenny got 21 large buttons in the bag of mixed buttons.

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Answer:

x= 4

Step-by-step explanation:

3x + 7 = 5x - 1

combine the like numbers: add 1 to the other side, isolating 5x

3x + 8 = 5x

Subtract 3x from 5x, isolating 8

8 = 2x

divide

4 = x

Check if it works

3(4) + 7 = 5(4) - 1

19 = 19

Yes, it is correct

Answer:

2

Step-by-step explanation:

the slope is always 1/2 so 5-3

Answer:

a = 4

Step-by-step explanation:

a = ?

b = 5

c = 3

a = √ (c^2 - b^2)

a = √ (3^2 - 5^2)

a = √ 25 - 9

a = √ 16

a = 4

Answer:

1. a. 544%

b. 84%

2. 175

3. $867.18

Step-by-step explanation:

1. a.2.32-0.36=1.96

1.96/0.36=5.44

5.44*100=544

b. 1.96/2.32=0.84

0.84*100=84

2. let x = # of 7th graders

let y = # of 8th graders

y is 125% of x

y=1.25x

x=140

y=1.25*140

y=175

3. A=P(1+r)^t

A=700(1+0.055)^4

A=867.18

Answer: B

Step-by-step explanation:

x -9 will get you 27 (36 is the answer), but you can try every answer and see which one makes sense, as B is the only one that makes sense (D would have been the answer if it was the absolute value which is B)

Answer:

8 feet.

Step-by-step explanation:

     Before remodeling:

                   width = 9 ft

                 Area   = 108 ft²

                 \(\boxed{length = \dfrac{Area}{width}}\)

                              \(=\dfrac{108}{9}\\\\= 12 \ ft\)

After remodeling:

               width = 9 ft

               Area = 180 ft²

             \(length = \dfrac{180}{9}\\\)

                        = 20 ft

length after remodeling = 20 ft

To find the length of the added portion, subtract the length of the living room before modeling from the length after remodeling.

    length of the added portion = 20 - 12

                                                   = 8 ft

The probability directly from the cumulative distributive function:

P(X = 2) = 0.17 , P(X > 3) =  0.31 , P(2 ≤ X ≤ 5) = 0.76, P(2 < X < 5)  = 0.42 ,

These calculations are essential in many areas of probability theory and statistics, including hypothesis testing, confidence intervals, and estimation.

(a) To find P(X = 2), we subtract the probability of the previous value from the probability of X being less than or equal to 2:

P(X = 2) = F(2) - F(1) = 0.33 - 0.16 = 0.17.

(b) To find P(X > 3), we subtract the probability of X being less than or equal to 3 from 1:

P(X > 3) = 1 - F(3) = 1 - 0.69 = 0.31.

(c) To find P(2 ≤ X ≤ 5), we subtract the probability of X being less than 2 from the probability of X being less than or equal to 5:

P(2 ≤ X ≤ 5) = F(5) - F(1) = 0.92 - 0.16 = 0.76.

(d) To find P(2 < X < 5), we subtract the probability of X being less than or equal to 2 from the probability of X being less than or equal to 5, and then subtract the probability of X being equal to 2:

P(2 < X < 5) = F(5) - F(2) - P(X = 2) = 0.92 - 0.33 - 0.17 = 0.42.

In summary, to calculate probabilities from a given cdf, we use the formula P(X = x) = F(x) - F(x-1) for discrete random variables, and P(a < X ≤ b) = F(b) - F(a) for continuous random variables. We can also use complement probabilities to find the probability of events such as P(X > a) or P(a < X < b). These calculations are essential in many areas of probability theory and statistics, including hypothesis testing, confidence intervals, and estimation.

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What is the present value of $25,000 to be received in 5 years if your discount rate is 4% .The formula to calculate the present value of a future sum of money is: P = F / (1 + r)n

Where P is the present value of the future sum of money, F is the future sum of money, r is the discount rate, and n is the number of years.Here,

F = $25,000,

r = 4%, and

n = 5 years.

The present value of $25,000 is: P = $25,000 / (1 + 0.04)5 = $20,102. Type your numeric answer and submit.

What annual rate of return would you need to earn on your investment if you have savings of $8,000 and your goal is to have $10,000 after 3 years he formula to calculate the future value of a present sum of money is:F = P x (1 + r)nwhere F is the future sum of money, P is the present sum of money, r is the annual rate of return, and n is the number of years.Here, P = $8,000, F = $10,000, and n = 3 years. Type your numeric answer and submit.

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There is no point of intersection and no solution to the system of equations.

To determine the number of solutions to the system of equations, we can use any method of solving linear equations, such as substitution or elimination. Here, we will use elimination.

Multiplying the second equation by 125 to eliminate the decimals, we get:

-10x + 12.5y = 12.5

Now, we can add this equation to the first equation to eliminate x:

(-4x - 5y) + (-10x + 12.5y) = 5 + 12.5

Simplifying, we get:

-14x + 7.5y = 17.5

To solve for y, we can isolate y on one side:

7.5y = 14x + 17.5

y = (14/7.5)x + (17.5/7.5)

y = (28/15)x + (7/3)

Now, we can see that the two equations have the same slope, 28/15, which means they are parallel and do not intersect.

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Complete question:

How many solutions are there to the system of equations? {-4x - 5y = 5 -0. 08x + 0. 10y = 0. 10}

A) no solutions

B) one solution

C) two solutions

D) an infinite number of solutions

To plot a point at the approximate location of √15 on a 2D coordinate system, we first need to determine the values for the x and y coordinates.

Since √15 is an irrational number, it cannot be expressed as a simple fraction or decimal. However, we can approximate its value using a calculator or mathematical software. The approximate value of √15 is around 3.87298.

Assuming you want to plot the point (√15, 0) on the coordinate system, the x-coordinate would be √15 (approximately 3.87298), and the y-coordinate would be 0 (since it lies on the x-axis).

So, on the coordinate system, you would plot a point at approximately (3.87298, 0).

The point with the ordered pair on the graph are X(3, 1), U(5, -3), N(0, 2), L(-4, -1) and B(-5, 3).

The given coordinates are (0,2) (3,1) (5,-3) (-5,3) (-4,-1)​.

From the given graph, we have

X(3, 1), U(5, -3), N(0, 2), L(-4, -1) and B(-5, 3)

Therefore, the point with the ordered pair on the graph are X(3, 1), U(5, -3), N(0, 2), L(-4, -1) and B(-5, 3).

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If committee of 16 students must select a president, a vice-president, a secretary, and a treasurer then there is 3360 possible ways can this be accomplished.

In the given question,

If you have 16 students, and wishes to pick a president, secretary, and treasurer, then we have to find how many ways can we choose the officers, if individual members may hold more than one office.

We have total 16 students.

Their have total 3 position president, secretary, and treasurer.

When the one position of president filled then their was left 15 students for the secretary position.

When the one position of secretary filled then their was left 14 students for the  treasurer position.

So the possible ways to fill the position is find by multiplying the 16,15 and 14. So

Possible ways=16*15*14

Possible ways=3,360

Hence, if committee of 16 students must select a president, a vice-president, a secretary, and a treasurer then there is 3360 possible ways can this be accomplished.

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We can rewrite the rational expression (3x² + 5x - 2) / (x - 1) in the form q(x) + r(x) / b(x) as: 3x + 8 + 6 / (x - 1).

To rewrite the rational expression a(x) / b(x) in the form q(x) + r(x) / b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), we can use polynomial long division.

Let's assume a(x) has a degree lower than b(x) or equal to it. If a(x) has a higher degree than b(x), we would need to perform polynomial long division to obtain the quotient q(x) and remainder r(x).

we have the rational expression: (3x² + 5x - 2) / (x - 1).

Divide the leading term of a(x) by the leading term of b(x) to get the first term of the quotient:

3x² / x = 3x.

Multiply the entire divisor (x - 1) by the first term of the quotient (3x):

(3x)(x - 1) = 3x² - 3x.

Subtract the result from step 2 from the original dividend:

(3x² + 5x - 2) - (3x² - 3x) = 8x - 2.

Repeat the process with the remainder (8x - 2) and the divisor (x - 1).

Dividing 8x by x gives 8, so the next term of the quotient is 8.

(8)(x - 1) = 8x - 8.

Subtracting the result from step 4 from the current remainder:

(8x - 2) - (8x - 8) = 6.

At this point, we have a remainder of 6. Since the degree of the remainder (0) is less than the degree of the divisor (1), we can stop the division.

Therefore, we can rewrite the rational expression (3x² + 5x - 2) / (x - 1) in the form q(x) + r(x) / b(x) as:

3x + 8 + 6 / (x - 1).

The quotient q(x) is 3x + 8, and the remainder r(x) is 6, both divided by the divisor b(x) which is (x - 1).

This is the desired form where the degree of r(x) (0) is less than the degree of b(x) (1).

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The question is incomplete the complete question is :

Rewrite simple rational expressions in different forms; write a(x) / b(x) in the form q(x)+r(x) / b(x) , where a(x), b(x), q(x) , and r(x) are polynomials with the degree of r(x) less than the degree of b(x) , using inspection, long division, or, for the more complicated examples, a computer algebra system.

(3x² + 5x - 2) / (x - 1).

Answer:

\(\huge\boxed{\sf (x*4) + (x*5) = 54}\)

Step-by-step explanation:

\(\sf x(4+5) = 54\\\\Applying \ distributive \ property\\\\(x*4) + (x*5) = 54\\\\Distributive\ Property\ is:\\\\A(B+C) = (A*B)+(A*C)\\\\\rule[225]{225}{2}\)

Hope this helped!

Fluid coupling is a hydrodynamic device that transfers rotating mechanical power from a prime mover, such as an internal combustion engine or an electric motor, to a rotating driven load.

Multi-speed gearboxes come in several configurations, including simple two-speed manual transmissions, three-speed automatics, and eight-speed dual-clutch transmissions.

11. Six different types of actuators are:

Linear actuators

Rotary actuators

Pneumatic actuators

Hydraulic actuators

Piezoelectric actuators

Solenoid actuators

12. The four types of directional control valves are:

2/2 Directional Control Valve (2 port and 2-way valve)

3/2 Directional Control Valve (3 port and 2-way valve)

4/2 Directional Control Valve (4 port and 2-way valve)

4/3 Directional Control Valve (4 port and 3-way valve)

Two examples of each type of directional control valve:

2/2 Directional Control Valve: Solenoid valve, spring return valve

3/2 Directional Control Valve: Spring-centered valve, detent-centered valve

4/2 Directional Control Valve: Air-operated, manually operated

4/3 Directional Control Valve: Detent-centered valve, spring-centered valve

13. The principle of operation of fluid coupling:

Fluid coupling is a hydrodynamic device that transfers rotating mechanical power from a prime mover, such as an internal combustion engine or an electric motor, to a rotating driven load.

The most common application of fluid couplings is in automotive transmission systems, where they are used as torque converters to keep the engine idling while the vehicle is at a stop, as well as to multiply torque from the engine to the transmission and drivetrain.

The primary principle behind the operation of a fluid coupling is the conversion of kinetic energy from the prime mover to hydraulic energy within the coupling.

14. Multi-speed gearboxes come in several configurations, including simple two-speed manual transmissions, three-speed automatics, and eight-speed dual-clutch transmissions.

Multi-speed transmissions allow the engine to operate at a range of speeds while maintaining the same output shaft speed to provide the best combination of performance, fuel economy, and noise control.

A diagram of multi-speed gearbox:

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Answer:

the answer to your question is above

Answer:

607,420

Step-by-step explanation:

hope it is correct and helps

Option A is the correct answer. Ellora wants to accumulate 150,000 in an RRSP by making annual contributions of 5,000 at the beginning of each year. If interest is 5.5% compounded quarterly, calculate how long she has to make contributions.

First, we have to find the interest rate per quarter, which will be
\(5.5% / 4\)= 1.375%.
The formula for the future value of an annuity is: 
\(FV = (C * [(1 + r)^n - 1] / r)\),

For Ellora, \(FV = $150,000, C = $5,000, and r = 1.375%.\)
Substituting these values into the formula gives:
\(150,000 = 5,000 * [(1 + 0.01375)^n - 1] / 0.01375\)
Simplifying this equation gives:
\(30 = [(1.01375)^n - 1]\)

We can solve this using logarithms:
\(ln 30 = ln [(1.01375)^n - 1]\)
\(ln 30 = n * ln 1.01375 - ln 1.01375e^(ln 30) / e^(-ln 1.01375) = n18.202125 = n\)

Therefore, it will take Ellora 18.202125 years to accumulate 150,000 in her RRSP through \($5,000\)annual contributions made at the beginning of each year with interest of \(5.5%\) compounded quarterly.

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Answer:

18

Step-by-step explanation:

The centroid divides the median into 2 parts from the vertex to one point to the opposite side of the vertex where the median starts.

Put into simpler language. HB is twice as long as HF

If Hf is 6 then HB is 12. BF is the total length of both or 6 + 12 = 18

Answer:

2.25

Step-by-step explanation:

32 divided by 14 2/9

can I please have brainiest

The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

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The correct statement is the percent increase of her salary is 20% every year. Hence, the answer is option E. Given that a company's vice president's salary n years after becoming vice president is defined by the formula S(n) = 70000(1.2)". We have to determine which of the following statements is true:

Given that a company's vice president's salary n years after becoming vice president is defined by the formula S(n) = 70000(1.2)". We have to determine which of the following statements is true:

She will be receiving a 2% raise per year. Her salary will increase $14,000 every year. The percent increase of her salary is 120% every year. Her salary is always 0.2 times the previous year's salary. The percent increase of her salary is 20% every year.

To calculate the salary of the vice president after n years of becoming a vice president, we use the given formula:

S(n) = 70000(1.2)

S(n) = 84000

The salary of the vice president after one year of becoming a vice president: S(1) = 70000(1.2)

S(1) = 84000

The percent increase of her salary is: S(n) = 70000(1.2)n

S(n) - S(n-1) / S(n-1) × 100%

S(n) - S(n-1) / S(n-1) × 100% = (70000(1.2)n) - (70000(1.2)n-1) / (70000(1.2)n-1) × 100%

S(n) - S(n-1) / S(n-1) × 100% = 20%

Therefore, the correct statement is the percent increase of her salary is 20% every year. Hence, the answer is option E.

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The probability of Roger selling a zucchini bread as the next loaf is 4/21.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

The probability of Roger selling a zucchini bread as the next loaf can be found by dividing the number of zucchini breads sold by the total number of breads sold so far.

The total number of breads sold so far is:

11 (banana) + 8 (zucchini) + 9 (cranberry) + 14 (blueberry) = 42

The number of zucchini breads sold is 8.

So the probability that the next loaf Roger sells will be zucchini bread is:

8/42 = 4/21

Therefore, the probability of Roger selling a zucchini bread as the next loaf is 4/21.

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The maximum number of items that could be purchased together for a total price that is less than the given amount T would be the integer part of (T - $3).

Let's analyze the pricing structure to determine the maximum number of items that can be purchased together for a total price that is less than a given amount.

The first item is priced at $3, and each additional item is priced at $1. This implies that the price increases by $1 for each additional item.

To find the maximum number of items, we need to consider the total price and the number of additional items beyond the first item. Let's denote the total price as P and the number of additional items as n.

The total price can be expressed as follows:

P = $3 + $1 * n

To determine the maximum number of items, we need to find the highest value of n that satisfies the condition P < T, where T is the given amount that the total price should be less than.

Substituting the expression for P, we have:

$3 + $1 * n < T

Simplifying the inequality:

$1 * n < T - $3

n < T - $3

Since the number of items must be a whole number, the maximum value of n would be the largest integer that satisfies the inequality n < T - $3.

Therefore, the maximum number of items that could be purchased together for a total price that is less than the given amount T would be the integer part of (T - $3).

For example, if T is $10, the maximum number of items would be the integer part of (10 - 3) = 7.

It's important to note that the maximum number of items calculated using this pricing structure assumes that customers can purchase fractional amounts of items. In practice, stores may have policies that limit the number of items to whole numbers or impose other restrictions.

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Answer:

∠WXY = 107°

Step-by-step explanation:

In a trapezoid, adjacent angles are supplementary, meaning they add up to 180°. ∠W and ∠WXY are adjacent, so they are supplementary. 180° - 73° = 107°.

Another way to do this is to know that there are 360° in a trapezoid. This is a right trapezoid, so two of the angles are 90°. One angle is 73°. 90° + 90° + 73° = 253°. 360° - 253° = 107°.

I hope this helps :))

The measure of angle WXY is,

= 107°

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

Sides XY and WZ are parallel.

And, Angle W is 73 degrees and angles Y and Z are right angles.

Now, In a trapezoid, adjacent angles are supplementary, meaning they add up to 180°.

Here, ∠W and ∠WXY are adjacent, so they are supplementary.

Hence, We get;

The measure of angle WXY is,

= 180° - 73°

= 107°.

Thus, The measure of angle WXY is,

= 107°

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Answer:

1. p = -9

2. 4y + 16.

Step-by-step explanation:

1.

First, let's simplify the right-hand side of the equation:

11 + 1/4 (12p+4) = 11 + 3p + 1

= 3p + 12

Next, let's simplify the left-hand side of the equation:

1/4p + 3/4 (p-8) = 1/4p + 3/4p - 6

= 1p - 6

Now we can set the left-hand side equal to the right-hand side:

3p + 12 = 1p - 6

Subtract 1p from both sides:

2p + 12 = -6

Subtract 12 from both sides:

2p = -18

Divide by 2:

p = -9

Therefore, the solution to the equation is p = -9.

2.

First, let's simplify the terms inside each of the parentheses:

5 + 1/3 (9y - 12) = 5 + 3y - 4

= 3y + 1

5/6 (y+ 18) = 5/6y + 15

Now we can combine the simplified terms:

3y + 1 + 5/6y + 15 + 1/6y

= 4y + 16

Therefore, the solution to the equation is 4y + 16.