Use the number line to find the coordinate of the midpoint of
¯¯¯¯¯¯¯
M
P
.

The equation of the quadratic with a directrix of y= -5 and vertex of (-2, -3) is: y = 1/8 (x + 2)² - 3

Quadratic equation when the directrix is at y direction is of the form:

(x - h)² =  4P (y - k)

OR

standard vertex form, y = a(x - h)² + k     where a = 1/4p

The vertex

v (h, k) = (-2,-3)

h = -2

k = -3

P in this problem, is the distance between the vertex and the directrix

P = -3 - -5 = -3 + 5 = 2

p = 2

substitution of the values into the equation gives

(x - h)² =  4P (y - k)

(x - -2)² =  4 * 2 (y - -3)

(x + 2)² =  8 (y + 3)

rearranging the equation

8 (y + 3) = (x + 2)²

y + 3 = 1/8 (x + 2)²

y = 1/8 (x + 2)² - 3 (standard vertex form)

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Answer:

[tex]x=\frac{-1}{7}[/tex]

Step-by-step explanation:

[tex]8=x/7+9\\[/tex]

Subtract 9 from both sides

[tex]-1=x/7[/tex]

Multiply both sides by 7

[tex]\frac{-1}{7} =x[/tex]

Swap the order because you're a smart person

[tex]x=\frac{-1}{7}[/tex]

Answer:

Step-by-step explanation:

A crucial step in null hypothesis testing is finding the likelihood of the sample result if the null hypothesis were true. This probability is called the p value. A low p value means that the sample result would be unlikely if the null hypothesis were true and leads to the rejection of the null hypothesis.

The easiest expression to simplify by using the associative property is expression "b", since there is an addition already set (120 + 80 =200) to be performed.

'The other expressions involve more steps.

Given the function

Then, the function is shifted down 3 units means you subtract 3 to f(x).

And the function is shifted to the right 1 unit means you subtract 1 from the argument of f(x), this is "x". Therefore, the new function is:

Answer:

The given equation is

The y-intercept of the new line is -10.

We have to find a new parallel line to the given equation, which means they must have the same slope.

Remember that the coefficient of x is the slope, so the slope of the given line is -1/4. This means the new line has a slope fo -1/4 because it's parallel.

So, we know that the new line has a slope of -1/4 and its y-intercept is -10. We use the slope-intercept form to write the equation.

Okay, here we have this:

Considering the provided information, we are going to calculate the expected value for the game, so we obtain the following:

We will substitute in the following formula:

Expected Value=(Black Gain)*Black Chance (Gold Gain)*Gold Chance+(Silver Gain)*Silver Chance

Expected Value=(-1)*(25/33)+(3)*(1/33)+(2)*(7/33)

Expected Value≈-0.24

Finally we obtain that the expected value is approximately $-0.24.

A rational number between the two given ones is -0.455, such that:

-0.45 > -0.455 > -0.46

A rational number is any number that can be written as a quotient between two integer numbers.

Particularly, any number with a finite number of digits after the decimal point is also a rational number.

So to find a rational number between -0.45  and -0.46 we could se:

-0.455, such that:

-0.45 > -0.455 > -0.46

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The Three Fractions are :-

10/8, 15/12, 20/16

To convert 81 degrees to radian, we will apply the conversion:

1 π rad = 180°

let the 81° in rad = y

1 π rad = 180°

y = 81°

cross multiply:

1π rad (81) = 180 y

To get y, we divide both sides by 180:

The independent variable is the cost of riding the subway.

The dependent variable is the number of times she can ride the subway.

The independent variable is the variable whose value is given. It is the value of the independent variable that determines the dependent variable.  The dependent variable is the variable whose value is determined by changes in the independent variable.

In this question, the cost of each ride is given. There is little or nothing Nina can do to change the price of the subway ride. Thus, it is the independent variable. The total amount of rides Nina can go on is dependent on the cost per ride and the total amount she has. Thus, it is the dependent variable.

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SOLUTION

(a) The first plan cost $55 and an additional $0.13 per mile driven,

while the second plan cost $48 and an additional $0.17 per mile driven

Let the amount of driving be x

Then, this means that for the first plan we have

And the second plan becomes

So, for the plans to cost the same for a particular amount of driving x, it means that

Collecting like terms we have

Hence the two plans cost the same at 175 miles

(b) The cost when the two plans cost the same is

Hence the answer is $77.75

The measure of this angle is 65°

The measure of this angle is 60°

Explanation:

1) From the diagram the angle is between 10° and 75°

One of the arrows is on 10°

the other arrow is on 75°

the measure of the angle is between the two angles, so we subtract the smaller one from the bigger one

The angle in degrees is the difference between the 75° and 10°

= 75 - 10

= 65°

The measure of this angle is 65°

2) The second diagram is from 0° to 60°

Difference between them = 60° - 0°= 60°

The measure of this angle is 60°

Explanation

Step 1

let x represents the number of minutes.

hence:

Plan A costs $19 plus an additional $0.07 for each minute of calls

Plan B costs $12 plus an additional $0.11 for each minute of calls

Step 2

there is a number of minutes x, such both plnas cost the same,so

The mean height is given as 64.1 . We want to obtain the probability that he mean height for the sample is greater than 65 inches ​if the standard deviation is 2.52.

To proceed we, find the z-score of 65 in the distribution, we make use of the formula;

x = 65, mu = population mean = 64.1, sigma = standard deviation = 2.52, n = sample size = 70.

inserting these values, we have;

The problem now boils down to finding the probability of the z-score greater than 0.043

From z-score tables. the probability of the z-score greater than 0.043;

Therefore, the probability that the mean height for the sample is greater than 65 inches is 0.48285

Answer:

3nd one

Step-by-step explanation:

Hope I helped!

If I got it incorrect, please tell me, so I can at least try and see what I did wrong.

12x^3

Name: Monomial , because it has only 1 term

Degree: 3, exponent of the monomial

this is

Explanation:

The equation of a line in the slope-intercept form is:

Where m is the slope and b is the y-intercept.

We have that the line has a slope of 1/3:

To find the y-intercept b we have to use the point. Replace x = -2 and y=1 and solve for b:

Answer:

The equation is:

The equation of line is y = [tex]\frac{-1}{3}[/tex][tex]x[/tex]+6 .

The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis. Key Point. The equation of a straight line with gradient m and intercept c on the y-axis is y = mx + c.

Given that,

equation of given line with a slope of m = 3

y=3x-5​

A line perpendicular to that line will have a slope that is the negative reciprocal of 3.

The reciprocal of 3 is 1/3. So the negative reciprocal of 3 is -1/3.

Therefore, we want to write the equation of a line with slope, m = -1/3, and passes through the point (6, 4) = (x, y).

y = mx + b

4 = (-1/3)(6) + b      

(we've set up the equation with only one unknown, b, that we can now solve for)

4 = -2 + b

b = 6

With a slope, m = -1/3, and a y-intercept, b = 6, the equation of our line relating x and y is:

y = (-1/3)x + 6

Hence, The equation of line is y = [tex]\frac{-1}{3}[/tex][tex]x[/tex]+6 .

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y = 2x - 5 Eq(1)

6x - 2y= 20 Eq(2)

We are going to use the elimination method to solve the system.

y-2x = -5 Transpose x to the othe side in Eq(1)

2y - 4x = -10 Multiply all terms of Eq(1) by 2. Then add Eq(1) to Eq(2)

2y - 4x = -10

+ -2y +6x= 20

----------------------

2x = 10 Operating like terms

x= 10/2 Isolating x

x = 5

Replacing x in Eq(1)

y = 2*(5) -5

y= 10 - 5 = 5

The answer is the point with coordinates ( 5 (x-coordinate) , 5(y-coordinate)).

Solution

We have the following data:

0, 0, 0, 0, 1, 1, 1, 2, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5

And the mean would be:

Mean = 2.958

And the median

Median = 4

Then if we add a 5 then the median would be the same 4

And the mean = 3.04

then the solution is:

The mean would increase

And for the other part of the question

we have:´

4+3+1+2 = 10 people made 3 or less trips to the movie

We have a deck of 52 cards.

We have to calculate the probability that when a card is randomly drawn from the deck, this cart is a red four.

There is only one red four in the deck. Then, if we calculate the probability of an event as the quotient between the number success events (getting a red four, in this case) and the total possible events (getting any card), we will get:

As there is only one card in the deck that gives a success event within the 52 cards, the probability is 1 in 52.

Answer: the probability is 1/52.

To determine the price for each board game on the stores, we need to divide the total price by the number of board games bought.

The price online is higher, because it is $5.79 per board game.

Answer: The Answer is the addition symbol

Step-by-step explanation:

8 x 50 = 400

8 x 7 = 56

400 + 56 = 456

8 x 57 = 456

Given:

The expression is ___-(-5) = -7.

The objective is to find the missing value using number line.

Consider the missing value as x.

Now, the expression can be rearranged as,

So, we have to solve -7-5 on number line, which means starting from -7 subtract 5 in the number line.

Hence, the missing value is -12.

Number of students qualify for a karate tournament if they train and compete at Blue Bear High School is equal to 60.

As given in the question,

Total number of students enrolled in Blue Bear High School =175

Number of students train in karate = 25

Number of students compete with other school in karate =35

Number of students practice martial arts but not karate=100

Number of students qualify for a karate tournament if they train and compete at Blue Bear High School

= 25 + 35

= 60

Therefore, number of students qualify for a karate tournament if they train and compete at Blue Bear High School is equal to 60.

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k=12

1) Gathering the data, and setting this table:

Blocks | Pounds

5 60

6 72

7 84

8 96

2) Since we have this table, and a proportional relationship means a linear function without linear coefficient, i.e. y =mx

Then we can write:

y =12x

3) So, as we can write it y=kx, then the constant of proportionality k =12 because the weight in pounds is 12 times the number of blocks.

5 x 12 = 60

6 x 12 =

The slope of two perpendicular lines is the negative reciprocal of each other.

Given a line y = -2x + 5, the slope of this line is -2. Therefore, the slope of the line perpendicular to this line is 1/2.

Given a slope of 1/2 and a point at (0, -13), let's use the point-slope form of the equation to be able to identify the equation of this line.

where m = slope.

Therefore, the equation of the line that passes through (0, -13) and is perpendicular to the line y = -2x + 5 is y = 1/2x - 13.

Step-by-step explanation:

The slope of two perpendicular lines is the negative reciprocal of each other.

Given a line y = -2x + 5, the slope of this line is -2. Therefore, the slope of the line perpendicular to this line is 1/2.

Given a slope of 1/2 and a point at (0, -13), let's use the point-slope form of the equation to be able to identify the equation of this line.

y-y_1=m(x-x_1)y−y

1

=m(x−x

1

)

where m = slope.

\begin{gathered}\begin{gathered} y-(-13)=\frac{1}{2}(x-0) \\ y+13=\frac{1}{2}(x) \\ y=\frac{1}{2}x-13 \end{gathered}\end{gathered}

y−(−13)=

2

1

(x−0)

y+13=

2

1

(x)

y=

2

1

x−13

Therefore, the equation of the line that passes through (0, -13) and is perpendicular to the line y = -2x + 5 is y = 1/2x - 13.

The three equations that have the same value of x as 3/5(30 x minus 15) = 72 are:

Equations are mathematical statements that show the equality of mathematical expressions.

These statements claim that two or more expressions are equal or equivalent.

To show this equality, the expressions are joined with the equal sign (=).

3/5(30x - 15) = 72

= 18x - 9 = 72

18x = 81

x = 4.5 (81/18)

Thus, the three correct equations, sharing the same value of x as 3/5(30 x minus 15) = 72 are Options C, D, and E.

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A) 18x - 5 = 72

B) 50x - 25 = 72

C) 18x - 9 = 72

D) x = 4.5

E) 18x = 81