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An equation of the line in point-slope form is y = 6x + 50.

y = y₁ = m(x -x₁) is the equation of a straight line, where m is the slope and (x₁, y₁) are the coordinates at a given point on the line (see slope-intercept form). When you know the slope and another point on the line, the point-slope form of a linear equation is most helpful for locating a point on a line. When two other points are known, it can also be used to locate a point on a line.

Given,

y₂ = 200

y₁ = 230

x₂ = 30

x₁ = 25

Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Slope = [tex]\frac{230-200}{30-25}[/tex]

Slope = [tex]\frac{30}{5}[/tex]

Slope = 6

Equation:

y - y₁ = m(x - x₁)

y - 200 = 6(x - 25)

y - 200 = 6x - 150

y = 6x + 50

An equation of the line in point-slope form is y = 6x + 50.

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Answer:

3/7

Hope this helps!

Have a good day :).

The equation is of the form y=mx+b, where m = slope and b = y-interset. Therefore, find m and b:

For m

For b

So, the equation is:

Answer: D.

Time can be used to quantify, contrast, or even rank the length of events or the gaps between them. To complete the cooking at 2:00 PM, George needs to start his cooking at  12:30 PM.

Time can be defined in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present and into the future. The duration of events or the gaps between them can be calculated, compared, or even ordered utilizing time.

Given time needed for each meals are;

Turkey = 70 min

Pumpkin pie = 17 min

Rolls = 30 sec

coffee = 45 sec

Total time = 87 min 75 sec

                = 1 hour 27min 75 sec

So in order to complete the cooking at 2:00 PM, George needs to start his cooking at  12:30 PM.

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Lowest degree polynomial with f(0) = 960 with zeros of -4 (multiplicity 3), 3(multiplicity 1). The polynomial is f(x)=-5(x+4)³(x-3).

Given that,

Lowest degree polynomial with f(0) = 960 with zeros of -4 (multiplicity 3), 3(multiplicity 1)

We have to find the polynomial of f(x) which satisfy the conditions.

Here,
We have the zeros of the polynomial are -4 (multiplicity 3), 3(multiplicity 1)

Which we can write as -4,-4,-4,3 are the zeros.

Then we can write the polynomial as

f(x)=ω(x+4)³(x-3)

We have to first find the value of ω.

So,

We have f(0)=960

ω(0+4)³(0-3)=960

ω(4)³(-3)=960

64ω(-3)=960

-192ω=960

ω=960/-192

ω=-5

We got the ω as -5.

The polynomial f(x)=-5(x+4)³(x-3)

Therefore, the polynomial is f(x)=-5(x+4)³(x-3).

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The irrational numbers lying between 1/12 and 1/10 are -

For the given question;

The number are given as  1/12 and 1/10

Write both number in its decimal form.

1/12 = 0.8333333

1/10 = 0.1

Thus, write number which lies between these two.

1/12 = 0.8333333

0.456258824......

0.32547965.......

0.21448663324........

1/10 = 0.1

The dotted parts shows that the number is nether terminating nor repeating.

Thus, the irrational numbers lying between 1/12 and 1/10 are found.

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Answer:

y = 1/3 x + 3

Step-by-step explanation:

1) when finding a perpendicular line, you take the slope and use the reciprocal (you flip it) and change the sign (from negative to positive or positive to negative)

-3 ---> 1/3

2) plug in the slope into a new equation

y=1/3 x + b

3) plug in the points

3= 1/3 (0) + b

b=3

4) rewrite the equation

y=1/3 x + 3

Answer:

  x^8

Step-by-step explanation:

You want to simplify x^10/x^2.

The applicable rule of exponents is ...

  (a^b)/(a^c) = a^(b-c)

Using this rule on the given expression, we find ...

  (x^10)/(x^2) = x^(10-2) = x^8

__

Additional comment

An exponent can be considered to be an indicator of repeated multiplication. That is, it tells how many times the base is a factor in the product. Knowing this, you can use the usual rules of division to cancel common factors:

  [tex]\dfrac{x^{10}}{x^2}=\dfrac{x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x}{x\cdot x}=x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x=x^8[/tex]

Answer:

Bottom left

Step-by-step explanation:

The figure that looks like <-------------------------> is a line

Top left *------------------------* is a segment

Bottom right is a ray *---------------->

Top right is a * point or dot

I hope this helps!

Answer:

  -8

Step-by-step explanation:

You want the value of c(3) when c(x) = (x -5)^3.

The value of a function is found by substituting the argument for the variable and doing the arithmetic.

  c(x) = (x -5)^3

  c(3) = (3 -5)^3 = (-2)^3

  c(3) = -8

The actual fraction of growth-

a) population = 10 million; growth rate = 559/155.

b) population = 30 million; growth rate = 344/155

c) population = 50 million; growth rate = 126/155

The base growth rate = 4.3%.

The current carrying capacity = 62 million.

The actual fractional growth for the given values are-

growth rate = r * (1 - population/carrying capacity)

a) population = 10 million,

Put the values;

growth rate = 4.3 × (1 - 10/62)

growth rate = 559/155 is the actual fraction of growth.

b) population = 30 million,

Put the values;

growth rate = 4.3 × (1 - 30/62)

growth rate = 344/155 is the actual fraction of growth.

c) population = 50 million,

Put the values;

growth rate = 4.3 × (1 - 50/62)

growth rate = 126/155 is the actual fraction of growth.

Thus, the actual fraction of growth is estimated.

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The statement that justifies the triangles' similarity is (c) SSS similarity theorem

The triangles are given as

Triangle ABC and Triangle DBE

From the figure, we can see that the corresponding vertical lines of either triangle are parallel (but not equal)

This means that, the triangles are similar triangles

This is so because the other two sides of the smaller triangle lie completely on the bigger triangle

As a general rule, the corresponding sides of similar triangles are in proportions

So, we can say that the corresponding side lengths of the triangles are similar

The statement that justifies this is the Side-Side-Side similarity theorem

Hence, the true statement is (c) SSS similarity theorem

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Answer:

You cant use the distributive property because it is when the equation is like this: ax(b+c) so if it was 11x(5+0) you would multiply the 5 by 11 by itself and multiply 0 with 11 then you add them and get 55. I hope that helps :)

Step-by-step explanation:

Answer:

P(A|B) =  1/2

Step-by-step explanation:

Sample space for B = {10, 20, 30, 40, 50, 60, 70, 80}

where B is even

Total number of elements in sample space = 8

P(A|B) = Probability of a number being 40 or less from the sample space of 8

Sample space for A|B  = {10, 20, 30, 40}

So out of a possible 8 elements in the sample space for B only 4 elements can be chosen for the sample space of A

So P(A|B) = 4/8 = 1/2

The modal mark is 16.because as we can see there are two 15, two 13,one 14, two 17 and three 16.

The mean = 0.2,  variance = 0.03226 and Standard deviation = 0.1796

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Given:

level            x

1             0.419

2            0.276

3            0.225

4            0.068

5            0.012

So, mean = (0.419+ 0.276 + 0.225+ 0.068 + 0.012)/5

mean = 0.2

level          x        (x- mean)       (x- mean)²        

1             0.419        0.219            0.0479  

2            0.276       0.076            0.0057

3            0.225        0.025         0.000625

4            0.068       -0.268         0 .0718

5            0.012        -0.188          0.0353

So, variance = 0.032265

standard deviation = √(variance)

Standard deviation = √(0.032265)

Standard deviation = 0.1796

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Answer:

Step-by-step explanation:

thanks

Parul ran the fastest.

For Mary,

4/8 = x/1

4/8 or 1/2 laps per minute.

x= 0.5

For Paul,

12/18 = y/1

12/18 or 2/3 laps per minute.

y=0.666

Hence, Parul ran faster.

The SI unit of speed is m/s, and speed is defined as the ratio of distance to time.

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The solution of the equation is x = 5.

The equation is written as follows:

- 94  = -2 (8x + 7)

The variable to be found as variable x.

A variable is a number represented with a letter in an equation.

Hence,

- 94  = -2 (8x + 7)

open the bracket on the right side of the equation

-94 = - 16x - 14

add 14 to both sides of the equation

-94 = - 16x - 14

-94 + 14 = - 16x - 14 + 14

-80 = - 16x

divide both sides by -16

x = -80 / -16

x = 5

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Answer:

4

Step-by-step explanation:

first we go over where 8 is on the x-axis then we move up to the line, and look at the corresponding y value, which is 4

Answer:

224

Step-by-step explanation:

The answer is 224 since 8 x 28 = 224

Answer: Terrence planted 224 flowers in total

Step-by-step explanation:  8x28

The zeros of the function f(x) = x³ + 9x² + 20x  is :

0, 5 ,4

Steps to solve quadratic equation:

Check your answer by plugging it into the original equation.

Given function,

f(x) = x³ + 9x² +20x

take x common from f(x),

=> x(x² + x - 20) = 0

=> x(x² + 5x + 4x + 20) = 0

=> x( x + 5 ) + 4 ( x +5 ) = 0

=> (x + 5)  ( x + 4 ) = 0

=> x -5 = 0 or x -4 = 0

=> x = 5 and x = 4 .

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Given:

5, 9, 96, 3, 2, 8, 79, 1, 4, 16

To determine the mode based on the given data set, we note first that mode is the number in a data set that occurs most frequently. Since each value occurs only once, there is no mode of this data set.

Therefore, the answer is: no mode or none.

Answer:

bottom right

Step-by-step explanation:

bottom right

Based on the fact that the researchers are 96% confident that they are correct, then the probability that they are actually wrong is 4%.

If we are to believe the assertions of the researchers that they are 96% certain of them being correct, then the probability that they are wrong can be found by the formula:

= 1 - Percentage certainty

Solving for that probability of being wrong then gives:

= 1 - 96%

= 4%

It is worthy of note that this probability of being wrong is based on their estimates and so there is a chance that the probability of being wrong is 4%.

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Given that P is a point on the perpendicular bisector, l, of MN, we have proved that PM = PN because By the definition of reflection, point P is the image of itself and point N is the image of N.

We are given :

P is a point on the perpendicular bisector, l, of MN.

Now, we want to prove that PM = PN

A Reflection is a transformation in which the figure is the mirror image of the other. Every point is a mirror reflection of itself .

By the definition of reflection, we can deduce that point P is the image of itself , and point N is the image of M .

The line l acts as a Line of symmetry or axis of reflection.

Now, in transformations, we know that reflections preserve length and as a result, PM = PN.

Therefore, we will conclude that point N is the image of M .

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Answer: Point M

Step-by-step explanation:edge 2023

Answer:

Is this correct??

if yes reply

For the graph of a linear function x=-3 and y=4 is horizontal line , the equation for this linear function is y = 0(x) +4.

As given in the question,

Graph of a required linear function is a horizontal line.

Given :

When x=-3 y=4

Two coordinates of the required linear function are :

(x₁ ,y₁) = (-3, 4)

(x₂, y₂) = ( 0,4)

Equation of the linear function :

(y -y₁) /(x-x₁) = (y₂ -y₁) / (x₂- x₁)

⇒( y-4)/(x+3) =(4-4)/(0+3)

⇒ (y-4)/(x+3) = 0/3

⇒ y = 0(x) +4

Therefore, for the graph of a linear function x=-3 and y=4 is horizontal line , the equation for this linear function is y = 0(x) +4.

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Answer:

  $1258.09

Step-by-step explanation:

You want the monthly annuity payment that will let you withdraw $150,000 per year forever from an account earning 8% after 30 years.

In order to withdraw an amount "forever," the withdrawal amount must be equal to the interest earned by the account.

  I = Prt

  150,000 = P(0.08)(1)

  P = 150,000/0.08 = 1,875,000

The value of an ordinary annuity is given by the formula ...

  A = P(12/r)((1 +r/12)^(12t) -1) . . . . . where P is the monthly payment, and r is the annual interest rate earned over a period of t years.

Using the values we know, we can find P:

  1875000 = P(12/0.08)((1 +0.08/12)^(12·30) -1) = 1490.359449P

  P ≈ 1258.09

You would need to deposit $1258.09 each month.

__

Additional comment

The formulas used here assume that the deposits and withdrawals occur at the end of the month.

Answer:  2,175 divided by 12 will give you 181.25.