Consider the line 3x+5y=-1 What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line?

Answer:

$38.70

Step-by-step explanation:

21.5% = 0.215

$180.00 times 0.215 = $38.70

So, Sally's Commission is $38.70

The function f(8)=4 defines that it will take x/2 hrs to complete the work and "x being No of workers".

The given data is as follows:

There are x people working in the crew at the racetrack, it takes f(x) hrs to get the track ready.

Let us assume that there is x worker at the racetrack,

f(x) is the function that is going to define the working hours required to get the track ready,

The function will depend on workers as it is mentioned as "f(x)".

Now,

function f(x)=?

But given that f(8)=4

It means when  x=8 that means when are there 8 workers working at the racetrack and it took  4 hours to complete the work.

Now,

we have written a function that gives the relation between a given worker as 8 and time as 4 hrs.

so 8 workers complete work in 4 hrs,

then x worker will complete in y hrs i.e.f(x).

=4x=8*f(x)

=4x/8

=x/2.

Hence the function will be f(x)=x/2

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The complete question is -

max works as a groundskeeper at a racetrack, where he is part of a bigger crew. when x people are working on the crew, it takes them f(x) hours to get the track ready for a day of racing. what does f(8)=4 tells us?

When the parabola y = -1/20(x-3)2 + 6 has a focus of (3,1), the directrix equation is x=3.

Any points on a parabola is situated at a equal distance from both focus, a fixed point, and the hardware platform, a fixed vertical line. A parabola is a U-shaped plane curve.  Three different parabolas exist. Vertex form, leading to the formation, and intercept form seem to be the three forms. You can access a unique major element for the graph on each submission. There are two different methods to write a parabola's calculation: Form 1: y=a(x-h)2 + k. Form 2 is as wants to follow: x = a(y - k)2 + h.

given

( x-3)^2 > 0 , so -1/20(x-3)^2 < 0

when x>3 , it is decrease , when x<3 it is increase so the equation of the directrix is x =3

When the parabola y = -1/20(x-3)2 + 6 has a focus of (3,1), the directrix equation is x=3.

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Answer: 12

Step-by-step explanation: by the end of 12 weeks shell have 200 dollars left

The sum of ages of P & Q before 4 years is 42 years.

Let present age of P is 4x years and the present age of Q is 6x years.

According to the problem, the sum of the present ages of P and Q is 50 years, so we have:

4x + 6x = 50

10x = 50

then, x = 5

So the present age of P is 4 * 5 = 20 years and the present age of Q is 6 * 5 = 30 years.

To find the sum of their ages before 4 years, we subtract 4 from each of their present ages:

20 - 4 = 16 years (for P)

30 - 4 = 26 years (for Q)

hence, sum of their ages before 4 years is 16 + 26 = 42 years.

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Answer:

m= -1 1/2

Step-by-step explanation:

1st point : (-3,15)

2nd point : (1,9)

m=rise/run

= 15-9/-3-1

= 6/-4

=-1 1/2

An old book was bought for Rs 1520 and sold for Rs 1444. The loss percent is 5.263%

Given,

Cost price = 1520

Selling price = 1444

Loss = C.P - S.P

        = 1520 - 1444

        = 76

Now, percentage of loss = [tex]\frac{Loss}{C.P}[/tex] × 100

                                         = [tex]\frac{76}{1444}[/tex] × 100

                                         = 5.263

Hence, the loss percent is 5.263%  

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Converting the value from meters/second to kilometers/hour is 105 m/s =378 km/h

A conversion factor is a number used to change one set of units to another, by multiplying or dividing. When a conversion is necessary, the appropriate conversion factor to an equal value must be used

We have to convert the meters per second into kilometers per hour.

1m /sec = (1/1000)/ (1/3600) km/h = 3600/1000 km /h

So, we have to divide 105 by 1000, and multiply it by 3600.

Mathematically speaking

Hence, converting One kilometer is equal to 1,000 meters, and 1 hour is equal to 3,600 seconds is 378 km/h

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Answer:

a) The measure of the angle created by the car's turning would be 75°. This is because 4th Street is parallel to 3rd Street, thus the angle formed when the car turns onto King Avenue heading northeast would be a 90° angle, which is the same as the angle between 4th Street and 3rd Street.

b) The measure of the angle created by the car's turning would be 180°. This is because when the car is traveling southwest on King Avenue and turns left onto 3rd Street, it is essentially making a full turn to face the opposite direction.

c) The measure of the angle created by the car's turning would be 90°. This is because when the car is traveling northeast on King Avenue and turns right onto 3rd Street, it is essentially making a right angle turn as it transitions from one street to the other.

The number of cakes (x) and cookies (y) are 15 and 60 respectively.

Given the system of equation in the question;

To solve for x and y, plug y = 4x into the first equation and solve for x.

x + y = 75

Plug in y = 4x

x + 4x = 75

5x = 75

Divide both sides by 5

5x/5 = 75/5

x = 75/5

x = 15

Now, plug x = 15 into the second equation and solve for y.

y = 4x

Plug in x = 15

y = 4( 15 )

y = 60.

Therefore, the value of x and y are 15 and 60 respectively.

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Answer:

69.

im not kidding, haha, good luck!

Answer:0.625

Step-by-step explanation:

Answer: 5<x

Step-by-step explanation:

Answer: x>5

Isolate the variable

Answer:

1) -11/180

2) 52/15

3) -43/72

4) 347/70

5) 11/12

6) 75/8

Step-by-step explanation:

1) -11/180

2) 52/15

3) -43/72

4) 347/70

5) 11/12

6) 75/8

Explanation: You can simplify the numbers to smaller numbers and make the denominator the same, or else just use a calculator.

Answer:

see below

Step-by-step explanation:

enter the values of -1 & -2 into the equation

so you'll get 2 equations for 2 variables: m & n

when x = -1

1-(m-2)*(-1)-3+n=0 ==> 1+m-2-3+n =0 so m+n=5

when x = -2

4-(m-2)*(-2)-3+n=0 ==> 4+2m-4-3+n =0 so 2m+n=3

use equation 2 subtract equation 1

2m=-2, so m = -1

n= 6

Answer:

Step-by-step explanation:

Given roots of x² -(m -2)x -(3 -n) = 0 are -1 and -2, you want the values of m and n.

Given roots -1 and -2 for a quadratic equation, we know its factored form is ...

  (x -(-1))(x -(-2)) = 0

  (x +1)(x +2) = 0

Then the standard form is ...

  x² +3x +2 = 0

Comparing this to the given equation, we find ...

  -(m-2) = 3   ⇒   m = -1

  -(3 -n) = 2   ⇒   n = 5

Answer:

Step-by-step explanation:

To solve for x in the equation 3x + 2 = 11, we'll start by subtracting 2 from both sides:

3x + 2 - 2 = 11 - 2

Simplifying the left-hand side:

3x = 9

Finally, divide both sides of the equation by 3 to find x:

(3x) / 3 = 9 / 3

x = 3

The value of 'd' in the expression 2-16 = 12d is 168.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression 2016 = 12d.

Now, To solve for 'd' we have to move the coefficient of 'd' to the other side also it will sit on the denominator now.

Therefore, 2016 = 12d.

2016/12= d.

d = 168.

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The probability of a female student studying abroad is 9.5%. 60% of those who study abroad are female, while 49% of those who do not study abroad are female.

P(Female studying abroad) = P(Female and Studying Abroad) / P(Female)

P(Female and Studying Abroad) = 0.095 × 0.60 = 0.057

P(Female) = 0.095 × 0.60 + 0.905 × 0.49 = 0.902

P(Female studying abroad) = 0.057 / 0.902 = 0.063

Therefore, the probability of a female student studying abroad is 0.063.

The probability of a female student studying abroad is 9.5%. This means that out of all the undergraduate students, 9.5% of them are female and are studying abroad. It is also important to note that out of those who study abroad, 60% are female, while 49% of those who do not study abroad are female. This means that more female students are likely to study abroad than male students, as the percentage of female students studying abroad is higher than the percentage of male students studying abroad. It is also important to note that the overall percentage of female students studying abroad is lower than the overall percentage of male students studying abroad, as the number of female students who study abroad is lower than the number of male students who study abroad. Therefore, the probability of a female student studying abroad is 9.5%.

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Answer:

(m,n) is (-2,2)

Step-by-step explanation:

Elimination means that we should rewrite one of the two equations as an expression of one of the variables isolated, and then use that definition isn the other equation.  It is also called "substitution."

Lets use the first equation and rewrite it so that the variable m is isolated:

3m-4n=-14

-4n = -3m-14

n = (3/4)m +(7/2)

Now use this definition of n in the second equation:

3m+2n=-2

3m+2((3/4)m +(7/2)) = -2

3m + (3/2)m + 7 = -2

4.5m = -9

m = -2

Now use m= -2 in either equation to find n.

3m-4n=-14

3(-2)-4n=-14

-6 -4n = -14

-4n = -8

n = 2

The solution of this system of equations is (-2,2).

See the attached graph, with x and y used in place of m and n.

sjdffdghddffffdbdbbfbdhdbdbfbd

The graph of the given quadratic function, y = -0.5(x + 5)(x - 3), is shown below

From the question, we are to draw the graph of the given quadratic function.

The given quadratic function is

y = -0.5(x + 5)(x - 3)

To plot the graph of the given quadratic function, we will determine the value pairs that satisfy the equation

When x = -5

y = -0.5(-5 + 5)(-5 - 3)

y = -0.5(0)(-8)

y = 0

When x = -2

y = -0.5(-2 + 5)(-2 - 3)

y = -0.5(3)(-5)

y = 7.5

When x = 0

y = -0.5(0 + 5)(0 - 3)

y = -0.5(5)(-3)

y = 7.5

When x = 2

y = -0.5(2 + 5)(2 - 3)

y = -0.5(7)(-1)

y = 3.5

When x = 3

y = -0.5(3 + 5)(3 - 3)

y = -0.5(8)(0)

y = 0

When x = -5

y = -0.5(5 + 5)(5 - 3)

y = -0.5(10)(2)

y = -10

Using the value pairs above, the graph of the given function is shown below

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Step-by-step explanation:

To find the velocity of the particle, we need to take the derivative of the position vector with respect to time.

r(θ) = (a + b * cos(θ)) * i + (b * sin(θ)) * j

d/dt[r(θ)] = d/dt[(a + b * cos(θ)) * i + (b * sin(θ)) * j]

d/dt[r(θ)] = (-b * sin(θ)) * i + (b * cos(θ)) * j

So, the velocity of the particle at a given value of θ is:

v(θ) = (-b * sin(θ)) * i + (b * cos(θ)) * j.

Answer:

Step-by-step explanation:

the velocity of the particle at a given value of θ is:

v(θ) = (-b * sin(θ)) * i + (b * cos(θ)) * j.

Volume= l*b*h

=7*5*3

=105 cubic inches

The perimeter of this rectangle is 94, which is the smallest possible perimeter for a non-square rectangle with integer dimensions that has an area that is triple its perimeter.

Let's call the length of the rectangle "L" and the width of the rectangle "W". The area of the rectangle is then L * W, and the perimeter is 2 * (L + W).

According to the problem, the number of square units in the rectangle's area is triple the number of units in its perimeter:

L * W = 3 * (2 * (L + W))

Expanding the right side and solving for L:

L * W = 6L + 6W

L * W - 6L = 6W

L * (W - 6) = 6W

L = 6W / (W - 6)

Since L and W are both positive integers and L can't be equal to W (because the rectangle can't be a square), we know that W must be greater than 6. Let's try W = 7:

L = 6 * 7 / (7 - 6) = 6 * 7 = 42

This gives us a rectangle with dimensions 42 x 7, which satisfies the conditions of the problem.

The perimeter of this rectangle is 2 * (42 + 7) = 94, which is the smallest possible perimeter for a non-square rectangle with integer dimensions that has an area that is triple its perimeter.

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The boy can wear 720 different outfits to school if he must wear one of each item, we need to find the number of combinations of one pair of pants, one shirt, one tie, and one jacket. The number of different combinations of pants he can wear is 8.

The number of different combinations of shirts he can wear is 5.

The number of different combinations of ties he can wear is 3.

The number of different combinations of jackets he can wear is 6.

To find the total number of different outfits, we multiply the number of combinations of each item:

8 * 5 * 3 * 6 = 8 * 90 = 720

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The situations when you might want to estimate the answer to a division problem are listed below.

There are several situations when you might want to estimate the answer to a division problem:

Large numbers: When dividing large numbers, estimation can be quicker and provide a close enough answer.

Complex decimals: Estimating can help when the answer is a complex decimal and you only need a rough idea.

Time constraints: When you're short on time and need a quick answer, estimation can be useful.

Cost calculations: In budgeting or finance, you may need to estimate the cost of an item, which can be done by dividing the total cost by the number of items.

Determining proportions: In many real-world scenarios, you may need to determine the proportion of a certain characteristic, which involves dividing the number of occurrences of that characteristic by the total number of observations.

Quick analysis: In some cases, you might want a quick and rough estimate of the answer to a division problem to see if it falls within a certain range.

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Use the rules of exponents to divide variables with the same base when dividing monomials. According to this rule, the base should remain in the position (numerator or denominator) where the greater exponent was when dividing variables with the same base after the exponents have been subtracted.

In order to divide a polynomial by a monomial, let's first divide a monomial by another monomial. The monomial should be divided into numerical and variable factors. By deducting the exponents of each y term, divide the coefficients and variables.

Let's go over the three steps that must be completed in order to divide a polynomial by a monomial. Rewrite the issue and divide each polynomial term by the monomial as a first step. Dividing the numbers is the next step. Divide the variables is the third and last stage.

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