What is an equation of the line that passes through the point (-4,8)(−4,8) and is parallel to the line x+y=6x+y=6?

1) the equation is:

So we can rewrite the equation as a slope intercept so:

So the slope is -1/2

2) the equation is:

Now we evaluete the coordinates to see which one is not on the line so for (1,-1)

So is on the line

for (-1,-4)

So it is on the line

for (3,2)

So it is on the line

Finally for (1,2)

So (1,2) is not on the line

3) if the slope is -2 and goes to the point (3,-1) we can use the equation of a line to find the intercept so:

So the intercept is 5 so the equation is:

Answer:

yes that is the correct answers

4.372 × [tex]10^{13}[/tex] more kilograms the mass of the Antarctic iceberg than the mass of the Rock of Gibraltar.

Mass of the Antarctic iceberg = 4.55 × [tex]10^{13}[/tex]  

Mass of the rock of Gibraltar  = 1.78 × [tex]10^{12}[/tex]  

Excessive mass of Antarctic Icebergs than the rock of Gibraltar,

4.55 × [tex]10^{13}[/tex]  - 1.78 × [tex]10^{12}[/tex]  

Subtract easily both should be in the same power of ten,

= 4.55 × [tex]10^{13}[/tex]  - 1.78 × [tex]10^{12}[/tex]  

= 43.72  × [tex]10^{12}[/tex]  

= 4.372 × [tex]10^{13}[/tex]

Scientific notation is used to express quantities that are either too large or too little to be represented by decimals. Scientific format, standard index format, and standard format are other terms for the same thing.

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The behaviors of the function in the intervals is given as follows:

a) Increasing: (-∞, -4) and (-3, -2).

b) Decreasing: (-4, -3) and (-2, ∞).

c) Constant: No interval.

Considering the graph of the function, we get that a function f(x) is increasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when x increases, y increases.

Hence, in the context of this problem, considering the given graph the function is increasing on these following intervals:

Considering the graph of the function, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down on the graph, meaning that when x increases, y decreases.

Hence, in the context of this problem, considering the given graph the function is decreasing on these following intervals:

A function is constant when the graph is an horizontal line, that is, when changing the value of x causes no effect to the value of y, it remains constant.

Hence, there are no intervals in which the graph of the function is constant.

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The test statistic for this hypothesis test is; t = 1.5

The formula for test statistic is;

t = (x' - μ)/(σ/√n)

where;

x' is sample mean

μ is population mean

σ is standard deviation

n is sample size

We are given;

Sample mean; x' = 8.12 hours

Population mean; μ = 8 hours

Standard deviation; σ = 0.72 hours

sample size ; n = 81 pilots

Thus;

t = (8.12 - 8)/(0.72/√81)

t = 0.12/0.08

t = 1.5

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If grace and jack are playing a game with a gigantic bucket of markers. The probability are  yellow 0.24,  blue 0.74,  red 0.02.

Given data:

Yellow markers = 12

Blue markers =37

Red marker =1

Total number of markers = 12 + 37 + 1

Total number of markers = 50

Probability of an event occuring= Favorable number of outcomes / Total number of outcomes

Probability of getting an yellow marker = 12/50

Probability of getting an yellow marker = 0.24

Probability of getting an blue marker = 37/50

Probability of getting an blue marker = 0.74

Probability of getting an red marker = 1/50

Probability of getting an red marker = 0.02

Probability model

Type of maker  Frequency Probability

Yellow                     12             0.24

Blue                         37              0.74

Red                           1              0.02

Therefore the probability are  0.24, 0.74, 0.02.

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The values of x are x = 13 and x = 1 when we have [tex](x-7)^{2} = 36[/tex].

According to the question,

We have the following information:

[tex](x-7)^{2} = 36[/tex]

Now, we will solve the expression on the left hand side using an identity.

The identity that will be used here is [tex](a-b)^{2}= a^{2}+ b^{2} -2ab[/tex].

In this case, we have a = x and b = 7.

[tex]x^{2}+ 7^{2} -2x*7[/tex] = 36

[tex]x^{2} +49-14x = 36[/tex]

Moving 36 from the right hand side to the left hand side:

[tex]x^{2} +49-14x-36 = 0\\x^{2} -14x+13 = 0[/tex]

Now, to find the values of x, we will factorize this expression by splitting the middle term such that the sum of two terms is -14x and their multiplication is 13[tex]x^{2}[/tex].

The two terms will be -13x and -x.

[tex]x^{2} -13x-x+13 = 0\\[/tex]

Taking x common from the first two terms and -1 common from the last two terms:

x (x-13) -1(x-13) = 0

Taking (x-13) as common:

(x-13) (x-1) = 0

x-13 = 0 and x-1 = 0

x = 13 and x = 1

Hence, the values of x are 13 and 1.

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Using proportions, the coordinates of the point that divides directed line segment YX so that the ratio of YP to PX is 5 to 3 are given by:

[tex](x,y) = \left(\frac{3}{8}(x_y - x_x) + x_x, \frac{3}{8}(y_y - y_x) + y_x\right)[/tex]

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations such as multiplication or division from the given ratios.

Division of line segments is one application of proportions. The entire length of the line segment with endpoints XY is given by:

Y - X.

Now we have point P, dividing the line segment YX so that the ratio of YP to PX is 5 to 3, meaning that XP is 3/8 of XY, that is:

[tex]P - X = \frac{3}{8}(y - x)[/tex]

Then the x-coordinate of P is found as follows:

[tex]x - x_x = \frac{3}{8}(x_y - x_x)[/tex]

[tex]x = \frac{3}{8}(x_y - x_x) + x_x[/tex]

The y-coordinate is found applying the same rule with the y-coordinates of points X and Y, as follows:

[tex]y - y_x = \frac{3}{8}(y_y - y_x)[/tex]

[tex]y = \frac{3}{8}(y_y - y_x) + y_x[/tex]

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ANSWER

EXPLANATION

We want to write the number given in scientific notation. The number is 80,023

Putting a number in scientific notation involves writing that number as a product of a number between 1 and 10 and a power of 10.

We do this by moving the decimal point from behind the last digit of the number (3) to just after the first digit (8).

We move the decimal point 4 times to the left, that is why the power of 10 is +4.

So, we have that 80,023 becomes:

The quadratic function of h (x) in vertex form will be;

⇒ h(x) = (x + 2)² − 3

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The values of x and h (x) for the quadratic function is given as;

x = -3, -2, -1, 0, 1, 2, 3,

h (x) = -2, -3, -2, 1, 6, 13, 22

Now,

Let the quadratic function is,

h (x) = ax² + bx + c

Substitute x = -3 and h (x) = -2 in above quadratic function we get;

h (x) = ax² + bx + c

- 2 = a × (-3)² + b × -3 + c

- 2 = 9a - 3b + c

And, Substitute x = -2 and h (x) = -3 in above quadratic function we get;

h (x) = ax² + bx + c

- 3 = a × (-2)² + b × -2 + c

- 3 = 4a - 2b + c

And, Substitute x = -1 and h (x) = -2 in above quadratic function we get;

h (x) = ax² + bx + c

- 2 = a × (-1)² + b × -1 + c

- 2 = a - b + c

After solving we get;

a = 1 , b = 4 and c = 1

Substitute all the values in above quadratic equation, we get;

h (x) = ax² + bx + c

h (x) = 1 × x² + 4x + 1

h (x) = x² + 4x + 1

h (x) = x² + 4x + 4 - 4 + 1

h (x) = (x + 2)² - 3

Thus, The quadratic function of h (x) in vertex form will be;

⇒ h(x) = (x + 2)² − 3

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A graph of the image of triangle V'W'X' after a rotation of 90° counterclockwise about the origin is: graph A.

A rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

In Geometry, rotating a point 90° about the origin in a counterclockwise (anticlockwise) would produce a point that has the coordinates (-y, x).

Note: Each interval on this graph represents 1 unit.

By applying a rotation of 90° counterclockwise to triangle VWX, the coordinates of the vertices of the image triangle V'W'X' include the following:

(x, y)                    →            (-y, x)

Point V = (-2, -4)   →     Point V' = (-(-4), -2) = (4, -2)

Point W = (-2, -2)   →    Point W' = (-(-2), -2) = (2, -2)

Point X = (-5, -4)   →  Point X' = (-(-4), -5) = (4, -5)

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Answer

x=10.

Step-by-step explanation:

-2.3x-4.2x=-66.3

-2.3+-4.2=-6.5x

-6.5x÷-6.5

-66.3÷-6.5

x=10.

Using inequality, we can conclude that maximum of 14 people can visit the amusement park.

So, (p) a maximum number of people who can visit the park:

Now, calculate as follows:

Therefore, using inequality, we can conclude that maximum of 14 people can visit the amusement park.

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Step-by-step explanation:

Another music store rents trombones for $30 per month plus a yearly fee of $48. Which deal is better? Should Maria change her rental plan?

Part A: Maria needs a trombone for only 12 months. Renting the trombone costs $34 per month. She can buy the trombone for $495. Should she buy or rent the trombone? Explain.

Option 1, SHOP 1: [at $30 a month] When Maria rents for a year, or x = 12 months

This can be described by the equation:

30x + 48

where x = number of months rented

30(12) + 48

= $408

___________

Option 2, SHOP 2:  [at $34 a month] When Maria rents for a year, or x = 12 months

This can be described by the equation:

34x + 48

where x = number of months rented

34(12) + 48

= $456

___________

Option 2, buy: for $495

ANALYSIS:

Because Maria only needs the instrument for a year (12 months), Maria would do best to rent her instrument from option 1, shop 1 (renting at $30 a month + $48 yearly fee). Purchasing the instrument is the most costly.

Should Maria need the instrument longer than a year, then the option preference would change.

Answer:

180

Step-by-step explanation:

9x20

The volume of the cone has a value of 410.67 cubic meters

From the question. the height and the radius of the cone are given as

Height = 7 feet

Radius = 8 feet

The volume of the cone can be calculated using the following volume formula

Volume = 1/3πr^2h

Substitute the known values in the above equation

So, we have

Volume = 1/3 * 22/7 * 8 * 7^2

Evaluate the products

Volume = 410.67

Hence, the volume is 410.67 cubic meters

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Answer:

The radius is from the middle to the edge, in this case it looks the radius is 4

1) Since the equation is y= -3x+3, let's fill in that table by plugging into them the given values for x

x | y= -3x +3 | y

-1 | y=-3(-1)+3 | 6

0 | | 3

1 | | 0

2| | -3

2) Let's plot that equation for points (-1,6) (0,3), (1,0) and (2,-3)

Answer:

Yes

Step-by-step explanation:

Parallel lines are 2 lines that go in the same direction that will never touch each other.

Hope that helps

Step-by-step explanation:

x^3 =64

x^2+x=64( you can write x^3 like this .there is not problem with it )

x+x= root 64

2x= 8 ( 8×8=64)

x=8÷2

x = 4

Answer:

A,) 20

Step-by-step explanation:

First, I am assuming that the problem is 5k = 100, not "5k = 100k =" as it was written.

We need to end up with "k equals some number."  This is called solving for k.  In order to do this we need to have k by itself.  We look at the problem and ask, "what is preventing k from being by itself?"  In this case k has a "times 5" with it.  How can we get rid of that?  Well we can do the opposite of "times 5,"  and that is to divide the left side by 5.  That leaves k by itself which is exactly what we need.  But if do something to one side of an equation, we need to do it to the other side for the equation to still be true.  So in this case we also have to divide the right side by 5 also, which gives us 20 on the right side.  So in our original problem:

5k = 100

Divide both sides by 5 and we have the answer:

k = 20

The power as a product of powers can be rewritten  (2ax)³ as  (2ax )(2ax)(2ax )

Multiplication is the mathematical operation that is used to determine the product of two or more numbers.

The product can be defined as the multiplication operation of two or more terms so that another term can be gotten the same as the one that is been given that we were asked to rewrite.

Power is defined as the degree that is been found on the terms, the degree that can be on the term is 3, then it can be expressed in three terms

Therefore, the given expression is (2ax)³ can be rewritten as;

(2ax)³ =  (2ax )(2ax)(2ax )

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Answer:576 minutes

Step-by-step explanation:

a)P(all seniors) =(25C3)/(30C3) =0.5665

b)P(All Juniors)=(5C3)/(30C3) =0.0025

c)P(2 senior and 1 Junior) =(25C2)(5C1)/(30C3) =0.3695

d)P(1 senior and 2 Junior) =(25C1)(5C2)/(30C3) =0.0616

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Answer:

AC=8

Step-by-step explanation:

2x=2(8)

2x=16

x=16÷2

x=8

Answer:

Answer:The area of the triangle is 60 in.

explanation:

Because we have 6inches in the weigth and 5inches in the height .

The sandwich's price is represented by the variable s , 2 is the coefficient of s and 2.97 represents both the cost of a big drink and a constant

What is  Algebraic Expression?

An algebraic expression is one that has been constructed using integer constants, variables, and algebraic operations. For instance, the algebraic formula 3x2 2xy + c

The cost of Andrew's lunch is written as the algebraic expression

2s + 2.79 as a given. He bought a huge drink and two sandwiches.

In the algebraic expression given;

2s + 2.79

Here, 2 stand in for the coefficients of s, which stands for the quantity of sandwiches he purchased.

The sandwich's price is represented by the variable s, which is a function of the coefficient.

And 2.97 represents both the cost of a big drink and a constant since no further letters have been added.

Hence, sandwich's price is represented by the variable s , 2 is the coefficient of s and 2.97 represents both the cost of a big drink and a constant

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Answer: 333 Cookies

Step-by-step explanation:
Let E = Cookies by Esther
Let L = Cookies by Lee
The equation for amount of cookies: E+L

L=141
E=L+51
Substitute L
E=141+51=192
E+L=141+192=333

Answer:

[tex]10 \div x - 10 \div (x - 1) = 30[/tex]

We will see that the largest number is 9/12, and Russ ate 9/12 of his pizza, so he is the one that ate most of his pizza.

Here we know that:

So we just need to see which of the given numbers is the largest one.

We can rewrite the fractions as:

2/3 = 0.66

3/5 = 0.6

9/12 = 3/4 = 0.75

The largest number is 0.75, in this way we conclude that Russ is the one that ate more pizza.

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