What are the 3 formulas for slope?

The equation of the line passing through (3,4) and having slope m = 3/2 is y = 3/2x + 4.

Given points : (3,4)

The equation of a line with slope 3/2 and passing through point (3,4) is y = 3/2x + 4. This equation can be used to calculate the y-coordinate of any point on the line, given its x-coordinate. For example, if the x-coordinate of a point is 6, then its corresponding y-coordinate is 11. In general, for any x-coordinate, the corresponding y-coordinate is given by 3/2 times the x-coordinate plus 4.

Given slope : m = 3/2

We know that the equation of a line with slope m and passing through point (x1, y1)is given by :

y - y1 = m(x - x1)

Substituting the given values, we get

y - 4 = 3/2(x - 3)

Simplifying equation, we get

y = 3/2x + 4

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The Average speed of a world class sprinter, is he runs 100 yards in 10 sec is 36 km/h.

If an athlete can run 100 meters in 10 seconds,  It is said that he cannot run 10 meters in one second. That may also apply to the physical world we live in. But you clearly state that you want to say mathematically whether he ran 10 meters in his 1 second.

If a sprinter runs 100 meters in 10 seconds, then, First, we need to convert meters to kilometers and seconds to hours. 1 meter = 1/1000 kilometers 100 meters = 100/1000 kilometers = 1/10 = 0.1 kilometers 1 second = 1/3600 hours 10 seconds = 10/3600 = 1/360 hours.

Now,
According to the question:

Given that,

Distance covered by sprinkler = 100m

Time taken by sprinkler = 10 seconds

Using the equation of velocity

Distance/ Time = velocity

Now, substituting the values -

= 100/10

= 10

Thus, the velocity is 10m/s

To convert it into m/s in to km/h -

= (10/1000) x 3600

= 36000/1000

= 36

Therefore, The average velocity of sprinkler is 36 km/h

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Answer:

it will be 4.60

Step-by-step explanation:

Answer:

You have to pay $9.60 for 24 ounces of the sandwich spread.

Given:

Unit cost of sandwich spread = $6.40 per pound

Weight of sandwich spread = 24 ounces

We need to convert the ounces into pound before we can compute the cost of the sandwich spread.

1 pound is equivalent to 16 ounces.

24 ounces x 1 pound/16 ounces = 24 pound/16 = 1.5 pounds

total cost of 24 ounces sandwich spread

1.5 pounds x $6.40 per pound = $9.60

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The probability that the scores differ by 5 or more points in either direction is 0.0764.

According to the Question,

the mean and standard deviation of are

μₓ = 24

σₓ = 2

We have to find the probability of the scores differ by or more points on either direction.

Considering the X₁ and X₂ as the random variable,  the scores of Leon and Fred.

Define the variable:

D = X₁ - X₂

We have to find : P(IDI ≥ 5)

According to the Question,  the two scores are independent

The mean of :

D : μₐ = 0

The standard deviation of :

D : σₐ = 2.828

Standardizing the mean and standard deviation:

D = -5

Z = X - μₐ / σₐ

  = -5 -0 / 2.828

  = -1.77

Now,  we standardize

D = 5

Z = X - μₐ / σₐ

  = 5 -0/ 2.828

  = 1.77

Now,

Calculating the probability:

Using a table of typical normal probabilities as a guide,

P(D ≤ -5) or P(D ≥ 5)

= P ( z ≤ - 1.77) + P( z ≥ 1.77)

= P(z ≥ 1.77) + P(Z ≥ 1.77)

= 2P( z ≥ 1.77)

= 2[ 1 - p(z≤ 1.77)]

= 2[ 1 - 0.9618]

= 0.0764

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When the scale factor is greater than one, then the size of the object will enlarge

The scale factor is defined as the ratio of the new measurements of the object to the original measurements of the object

We can enlarge or shrink the size of the object by keeping the shape of the object same
The enlarge or shrink of he object can be determined by the value of scale factor

If the value of scale factor is between 0 and 1, then the object shirks and if the value of scale factor is greater than 1, then the object enlarge

Therefore, the size of the object will enlarge when the scale factor is greater than one

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The features of the function are given as follows:

The horizontal asymptote is the limit of f(x) as x goes to infinity. To obtain this limit, we consider only the terms with the highest exponent of the numerator and of the denominator, hence:

g(x) = -5x/x -> y = 5 is the horizontal asymptote.

The vertical asymptote is the value of x for which the function is not defined, hence it is the zero of the denominator, thus:

x - 2 = 0 -> x = 2.

The x-intercept is the point (x,0), in which x is found when y = 0, hence:

-5x + 10 = 0

-5x = -10

5x = 10

x = 2.

However, the function is not defined at x = 2, meaning that it has no x-intercept.

The y-intercept is the value of y when x = 0, hence:

y = 10/-2 = -5.

The coordinates are (0,-5).

The entire function can be simplified as follows:

(-5x + 10)/(x - 2) = [-5(x - 2)]/(x - 2) = -5.

Meaning that the function has no holes.

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The equation of a line passing through (x1, y1) is y - y1 = m(x - x1).

The equation of a line:

The equation of a line means an equation in x and y whose solution set is a line in the (x,y) plane. The most popular form in algebra is the "slope-intercept" form. y = mx + b. This in effect uses x as a parameter and writes y as a function of x: y = f(x) = mx+b.

Here we have to find the equation of a line passing through (x1, y1) and the slope.

Data given:

Point on the line = (x1, y1)

Slope = m

By this we get the equation of a line as:

y - y1 = m(x - x1)

Therefore the equation of a line is y - y1 = m(x-x1).

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Answer:

-18

Step-by-step explanation:

[tex]\frac{2}{3}n=-12 \\ \\ \frac{3}{2} \cdot \frac{2}{3}n=\frac{3}{2}(-12) \\ \\ n=-18[/tex]

60 bowlers participated in the spring.

The local bowling league had 48 bowlers during the fall league. In the Spring there was a 25%increase in the number of bowlers.

Formulate: based on the circumstances stated.

48 * ( 25% + 1 )

Determine the total or difference:

48 * 1.25

Determine the quotient or product:

60.

60 bowlers participated in the spring.

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The minutes that is used by Jaci to run 240 miles is 40 minutes.

Expression simply refers to the mathematical statements which have at least two terms that are related by an operator and contain either numbers, variables, or both. An average is one number chosen to represent a group of numbers; it is typically the sum of the numbers divided by the number of numbers in the group. By adding a group of numbers and then dividing by their count, the average, or arithmetic mean, is determined.

In this case, Jaci runs cross country for her high school. on average she runs 6 minutes per mile.

The minutes used to run 240 miles will be Total minutes divided by Speed:

= Total minutes / Speed

= 240 / 6

= 40 minutes

40 minutes is the amount of time Jaci spent running 240 miles.

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Complete question

jaci runs cross country for her high school. on average she runs 6 minutes per mile. What is the minutes used to ran 240 miles?

Answer:

C

Step-by-step explanation:

Everything else doesn't really make sense

Answer:

C. headquarters

Step-by-step explanation:

is the correct answer. A headquarters is the main office or center of operations for a business, particularly a large multinational corporation. A subsidiary, on the other hand, is a company that is owned or controlled by another company, often referred to as the parent company or holding company. A home locale is not a commonly used term in business, but it could refer to the location where a company is based or originated.

As the time increases, the angular velocity i.e. omega also increases quadratically with time.

Given,

From the figure,

Radius of wheel = 0.2 m

Acceleration, a = 4t m/s^2

then the angular acceleration of wheel can be determined by formula,

[tex]a=\alpha * r[/tex]

Where, r=radius of wheel =0.2 m

[tex]4t=\alpha * 0.2\\20t=\alpha[/tex]

We know that the angular acceleration is the change in angular velocity over time.

[tex]\alpha=\frac{d\omega}{dt}\\\\20t=\frac{d\omega}{dt}\\\\d\omega=20tdt\\\\\omega=\int\limits^t_0 {20t} \, dt \\\\\omega=\frac{20t^2}{2}-0\\\\\omega=10t^2[/tex]

From the above equation it is clear that omega i.e. angular velocity is dependent of time

omega is directly proportional to square of time

For

t=1 then ω=10

t=2 then ω=10(4)=40

t=3 then ω=10(9)=90.....and so on.

It means as time increases, then angular velocity also increases quadratically with time.

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Your question is incomplete, here is the complete question.

When a body rotates about fixed axis , any point located in the body travels along the circular path. the angular acceleration α measures the rate of change of angular velocity. A cord is wrapped around a wheel, which is initially at rest when θ=0. The force F gives the cord an acceleration [tex]a= 4t\ m/s^2.[/tex]

How does omega change over time?

1. To multiply two powers with the same base, we add their exponents.

2. An expression that you could simplify using the quotient of powers property is of: 3³/3² = 3.

The results of the expressions are given as follows:

3. 4^11.

4. 5^11.

5. 6^8.

6. 7^9.

When two or more terms have the same base and different exponents and then are multiplied, the base is kept while the exponents are added.

When two terms have the same base and different exponents and then are divided, the base is kept while the exponents are subtracted.

The multiplication rule is used for each of the items from 3 to 6, as:

3. 4^11, as 2 + 9 = 11.

4. 5^11, as 3 + 8 = 11.

5. 6^8, as 7 + 1 = 8.

6. 7^9, as 3 + 4 + 2 = 9.

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The unit rate for the ratio 6 deliveries in 2 hours is 3 deliveries per hours

From the question, we have the following parameters that can be used in our computation:

Ratio = 6 deliveries in 2 hours

The unit rate is simply the value of the above ratio

However, with a denominator of 1

This means that we evaluate the quotient in the above expression

So, we have the following representation

Ratio = 6 deliveries/2 hours

Express as unit rate

Unit rate = 3 deliveries per hours

Hence, the unit rate is 3 deliveries per hours

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Break up the problem into 26,000 pounds and 9 pounds.

To find total boxes needed, divide by weight per box.

26,000 / 20 = 1300

Last box has 9/20 pounds of material

Hope this helps :)

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- Jeron

The length of the Yangtze River is 5530 kilometers.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Given that,

The length of the Nile river = 6,690 kilometers.

Also, The Nile river is 1,160 kilometers longer than the Yangtze River.

Let the length of Yangtze River is x kilometers,

Use equation format,

x + 1160 = 6690

x = 6690 - 1160

x = 5530

The length of the Yangtze River is 5530 kilometers.

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Answer: the answer is 1

Step-by-step explanation: if you divide 12 by 12

15 gallons of 30% butterfat cream must be mixed with milk.

How to solve word problems?

It's actually fairly easy to solve word problems using a tried-and-true step-by-step approach.

If m is the gallons of 30% butterfat cream, and c is the gallons of 3% butterfat milk, then:

Let m be the milk and c be the cream:

m + c = 45 ⇒ (i)

0.03m + 0.3c = 0.12 * 45 ⇒ (ii)

Solve the system of equations with substitution or elimination.  Using substitution:

0.30 m + 0.03 (45 − c) = 0.12 * 45

0.30 m + 1.35 − 0.03 c = 5.4

0.27 m = 4.05

m = 15

Hence, 15 gallons of 30% butterfat cream must be mixed with milk.

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With a p-value of 0.000, the test statistic is 2.834.

A statistical test's calculation of a number is known as a test statistic. It explains the distance between your observed data and the null hypothesis, which states that there is no correlation between the variables or difference between the sample groups,

given

                sample size            sample mean            sample sd

 City 1           12                                 66000                   1100

 City 2          12                                 68000                  2200

mean is 71121 point ,41 standard deviation is sample size, the test hypothesis greater than 69110 point.

find dust statistics which are there , equation t, which equals x, bar minus mu, and sigma by rho type, is used to determine the test statistic.

The square root of 41 points equals minus 69110. Is it accurate that our test numbers come out to 1.719? Next, we need to determine the p value. P value is derived from x. Since our alpha in this instance is.05, our significance is more relevant than the p value.

Accordingly, there is little to no pay disparity between registered nurses in the two locations.

With a p-value of 0.000, the test statistic is 2.834.

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The initial speed of the ball traveling when it leaves the bat is  95.9 mph and the angle at it initially forms with the horizon is  39.49°.

A parallelogram is a four-sided shape having two sets of parallel sides, with the opposite sides being equal in length and the angles opposite each other being equal. A triangle is a three-sided shape with three angles, the sum of which adds up to 180 degrees.

∠x + ∠y + ∠z = 180°

The baseball was hit by the batter with a starting speed of 74 miles per hour horizontally and a lift of 61 miles per hour. The initial speed

v = √(v(h)² + v(c)²)

v = √((74)² + (61)²)

v = 95.9 mph

The angle made will be -

Ф = tan⁻¹(61/74) = 39.49°

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Answer:

0.25

Step-by-step explanation:

:)

Answer: the absolute value of 1/4 is 1

Step-by-step explanation:

Answer:the answer is 16 feet

Step-by-step explanation:

The value of a₀ is 5 and value of k is 12 if the exponential model of 5 ˣ 12x is written with the base e.

Exponential models portray circumstances where the pace of progress of something is straightforwardly corresponding to the amount of that thing there is. In number related terms: dy dt = ky where dy dt is the pace of progress in a moment, y is how much what we're discussing right then and there, and k is the consistent of proportionality. We need to use logarithmic functions to evaluate the values.

We are given function in form of x which is f(x) = 5×12ˣ,it is equivalent to

=>f(x)=5 × expo(ln(12ˣ)

=>f(x) =5 ˣ  [tex]e(^1^2)^x[/tex]

On comparing with the given equation - a₀[tex]e^(k)^x[/tex] ,we get

=>a₀=5 and k=12.

Hence, required values are 5 and 12,

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Answer:

[tex]\boxed{\underline{\bf v=16}}[/tex]

Step-by-step explanation:

[tex]\tt 3.8\left(v-12.3\right)-6.34=7.72[/tex]

Simplify both sides of the equation:-

[tex]\tt 3.8(v-12.3)-6.34=7.72[/tex]

Distribute:-

[tex]\tt (3.8)(v)+(3.8)(-12.3)+-6.34=7.72[/tex]

[tex]\tt 3.8v+-46.74+-6.34=7.72[/tex]

Combine Like Terms:-

[tex]\tt (3.8v)+(-46.74+-6.34)=7.72[/tex]

[tex]\tt 3.8v+-53.08=7.72[/tex]

[tex]\tt 3.8v-53.08=7.72[/tex]

Add 53.08 to both sides:-

[tex]\tt 3.8v-53.08+53.08=7.72+53.08[/tex]

[tex]\tt 3.8v=60.8[/tex]

Divide both sides by 3.8:-

[tex]\tt \cfrac{3.8v}{3.8}=\cfrac{60.8}{3.8}[/tex]

[tex]\tt v=16[/tex]

______________________

Hope this helps!

Have a great day!

The hourly pay before the increase for Marta and for Khalid is $18 and $15 respectively.

Given that, the ratio of Marta’s hourly pay to Khalid’s hourly pay is 6:5.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Now, Marta’s hourly pay is 6x and Khalid’s hourly pay is 5x

Both Marta and Khalid get an increase of £1.50 in their hourly pay.

So, Marta’s hourly pay will be 6x+1.50 and Khalid’s hourly pay will be 5x+1.50

The ratio of Marta’s hourly pay to Khalid’s hourly pay after this increase is 13:11

Here, (6x+1.50)/(5x+1.50) =13/11

11(6x+1.50)=13(5x+1.50)

⇒ 66x+16.5=65x+19.5

⇒ x=3

So, Marta’s hourly pay is $18 and Khalid’s hourly pay is $15

Therefore, the hourly pay before the increase for Marta and for Khalid is $18 and $15 respectively.

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Answer:

  y ≈ 60.6 units

Step-by-step explanation:

Given a triangle with angles 18° and 117°, and sides 21 opposite 18° and y opposite 117°, you want to know the value of y.

The law of sines tells you the ratios of side length to the sine of the opposite angle are the same for all side/angle pairs in the triangle.

  y/sin(117°) = 21/sin(18°)

  y = 21·sin(117°)/sin(18°) ≈ 60.55

The value of y is about 60.6 units.

Answer:

453.75

Step-by-step explanation:

To find the volume of a pyramid, we can use the formula V = (1/3)Bh, where V is the volume of the pyramid, B is the area of the base, and h is the height of the pyramid.

Since the base of the pyramid is a square, we can use the formula for the area of a square to find the area of the base. The formula for the area of a square is A = s^2, where A is the area of the square and s is the length of one side of the square. In this case, each side of the square base is 11 inches, so the area of the base is 11^2 = 121 square inches.

Now that we know the area of the base, we can use the volume formula to find the volume of the pyramid. The height of the pyramid is 15 inches, so the volume of the pyramid is V = (1/3) * 121 * 15 = 605 cubic inches.

Since Lucinda plans to fill the pyramid three fourths full with sand, the volume of the pyramid that will be filled with sand is 3/4 * 605 = <<3/4*605=453.75>>453.75 cubic inches.

Answer:

The graph should look something like this

Step-by-step explanation:

The  simplified expression for  the  given problem  will be :6x² and -10y²

Since the expression given to us is  :

3 x² + 5 y²[]  + 3 [] + 4 y²+ 6

= 3 x² + 5 y² + 4 y²[][]+6+3

=>3 x² + 9 y² [][]+9

The above equation is equal to   9 x²-  y² + 9

=> 3 x² + 9 y² [][]+9 =9 x^2-  y^2 + 9

now  Equating the coefficients of x²and y²  in LHS and RHS:

One box has = 9 x²-   y²= +6x²

and the other will have = -y²- 9 = -10y²

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Answer:

y = -0.5x + 1

Step-by-step explanation:

The slope intercept form of a line is given by:

y = mx + b

where m is the slope of the line and b is the y-intercept (i.e. the point at which the line crosses the y-axis). To find the equation of a line using two points, we can use the slope formula to calculate the slope, then use one of the points to find the y-intercept.

The slope of a line is given by:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates of the two given points into this formula, we get:

m = (-1 - 1) / (4 - 0) = -2 / 4 = -1/2

Now that we know the slope of the line, we can use one of the points to find the y-intercept. Let's use the point (4,-1):

y = mx + b

-1 = (-1/2) * 4 + b

-1 = -2 + b

b = 1

Therefore, the equation of the line that passes through the points (4,-1) and (0,1) in slope intercept form is:

y = (-1/2)x + 1

Note that the equation can also be written as:

y = -0.5x + 1