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Distance between M(6,-7) and a line that contains the points C(-6,-2) and H(-1,10) is 7.846

First we will find the equation of the line containing the points C(-6,-2) and H(-1,10).

Take (x₁, y₁) = (-6,-2) and (x₂, y₂) = (-1,10).

Then the slope of the line, m = y₂-y₁/x₂-x₁

                                           = 10- -2/-1- -6

                                           = -12/7

So the equation of the line is

y-y₁ = m(x-x₁)

⇒ y- -2 = -12/7(x- -6)

⇒ y+2 = -12/7(x+6)

⇒7(y+2) = -12(x+6)

⇒ 7y +14 = -12x -72

⇒ 12x+7y +14+72 = 0

⇒ 12x+7y+86 = 0

This is in the form ax+ by+ c = 0

Also given the point (x, y) = (6, -7).

Distance between a point (x, y) and a line ax+ by+ c = 0 is,

[tex]\frac{|ax+by+c|}{\sqrt{a^2+b^2} }[/tex].

So Distance between M(6,-7)  and the line 12x+7y+86 = 0 is

[tex]\frac{|12.6+7.-7+86|}{\sqrt{12^2+7^2} }[/tex] = |72-49+86|/√(144+49)

                    = 109/√193

                    = 7.846

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According to the given figure, angles GHE and DFH are corresponding angles, which are equal because GH and DF are parallels. So, we can express the following

Replacing the given expressions, we have

Let's solve for x

Then, we find the measure of the angle DFH

Answer:

[tex]x=0, \quad x=3[/tex]

Step-by-step explanation:

Given equation:

[tex]9x^2-27x=0[/tex]

Factor out the common term 9x:

[tex]\implies 9x(x-3)=0[/tex]

Zero Product Property:   If a⋅b = 0 then either a = 0 or b = 0 (or both).

Using the Zero Product Property, set each factor equal to zero and solve for x:

[tex]\begin{aligned}\underline{\sf Case\; 1} & & \underline{\sf Case \;2}\\9x&=0 & x-3&=0\\\dfrac{9x}{9} & =\dfrac{0}{9} & \quad \quad x-3+3 & =0+3\\x&=0 & x&=3\end{aligned}[/tex]

Therefore, the solutions to the given equation are:

[tex]x=0, \quad x=3[/tex]

Answer:

C. $27

Step-by-step explanation:

9.95÷2=4.975

9.95+9.95+4.975=24.875 or 24.88

24.88×7%+24.88=26.62

If we write [tex]k[/tex] where we see [tex]x[/tex] in the equation and set the result equal to [tex]-10[/tex], we get the result.

The length of segment A'E'  under a dilation with a scale factor of 3/4 is; 3/2 units.

From the included graph the coordinates of the points A and E, in the pentagon ABCDE with reference to point A are;

A: (0, 0)

E: (0, 2)

The length of the segment AE = √((2 - 0)² + (0 - 0)²) = √(2²) = 2

When a pentagon ABCDE is dilated to pentagon A'B'C'D'E' with a scale factor of 3/4, we have;

Length of segment A'E' = 3/4 × Length of segment AE

Therefore;

Length of segment A'E' = 3/4 × 2 = 3/2  units.

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Answer:

She will have a total of 17 pounds.

Step-by-step explanation:

You could simply put the question is slop intercept form to figure it out from there.

y = m(x) + b

y = 3(x) + 8

y = 3(3) + 8

y = 9 + 8

y = 17

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Answer: 3x

Step-by-step explanation:

5x-2x=

5*x-2*x=

x(5-2)=

x*3=3x

Answer:3x

Step-by-step explanation:

combine like terms

5x-2x

2x is a negative

so 5-2=3

so in conclusion 3x

The inequalities that are the constraints for the situation are 12x + 8y ≥ 1000 and x + y ≤ 200 options (B) and (D) are correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

It is given that:

A theater manager is planning an upcoming concert. Regular tickets will cost $12 and student tickets will cost $8.

Let x represent the number of regular tickets sold. Let y represent the number of student tickets sold.

Total collection = 12x + 8y

12x + 8y ≥ 1000

x + y ≤ 200

Thus, the inequalities that are the constraints for the situation are 12x + 8y ≥ 1000, and x + y ≤ 200 options (B) and (D) are correct.

The missing options are:

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36.

When you divide powers with the same base (in this case, 6), you subtract the exponents.

See details:

[tex]\frac{6^{8} }{6^{6} } \\8-6=2\\6^{2}=36[/tex]

The account balance is $883.264 after 5 years.

The Principal amount is $800, the time given is 5 years and the rate of interest is 2%.

We have to find the account balance after 5 years.

Formula to find the amount

Amount = Principal × [tex](1 +\frac{rate}{100}) ^{time}[/tex]

Now putting the value we get,

Amount = 800 × [tex](1 + \frac{2}{100} )^{5}[/tex]

             = 800 × [tex]\frac{102}{100 } ^{5}[/tex]

             = 800  ×[tex]1.02^{5}[/tex]

             = 800× 1.104

             = 883.264

Therefore the amount is $883.264 that is the account balance after 5 years.

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Answer:

y = - [tex]\frac{3}{2}[/tex] x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

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

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (2, 0) ← 2 points on the line

m = [tex]\frac{0-3}{2-0}[/tex] = [tex]\frac{-3}{2}[/tex] = - [tex]\frac{3}{2}[/tex]

the line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = - [tex]\frac{3}{2}[/tex] x + 3 ← equation of line

How many  cups of water do you need to make lemonade? 9/4 cups

How is the number of cups calculated?

Given:

8 lemons need =18 cups of water

1 lemon needs= x cups of water

By cross- multiplication method,

[tex]\frac{8}{1} =\frac{18}{x}[/tex]

8x = 18

x = 18/8

 = 9/4 cups of water is needed to make lemonade

What is the cross- multiplication method?

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Answer:

No

Step-by-step explanation:

Without even answering 218*12 it is obvious this is the wrong answer

the last digit of each number determines the last digit in the answer

218 has 8 as the last number and 12 has 2

multiply them together

2*8 is 16

the last digit is 6 and not 1

Answer:

No- 218 * 12 = 2616.

Multiply with an algorithm and add the partial products up to check. You don't get 5,521 when you multiply 218 * 12.

Answer:

-12 is the answer

Step-by-step explanation:

Substitute 1/4 for a and 6 for b in the equation

-8ab

-8(1/4)(6) Multiply

-8(1.5) Multiply

-12

The number of vowels is:

The total number of tiles is:

Therefore, the total number of letters not vowels is given by:

Hence, the probability of picking a letter that is not a vowel:

Therefore the required probability is 4/5

The power can be re written as a product of  (2ax)^3 as (2ax *2ax* 2ax ).

Product can be described as the multiplication operation of two or more terms so that another term can be gotten just like the one that is been given in the question that we were asked to rewrite.

Power serves as the degree that is been found on the terms , the degree that can be on the term is 3, then this can be expressed in three terms which will be done below.

Therefore, the given expression  (2ax)^3   can be rewritten as (2ax *2ax* 2ax )

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Answer:

Step-by-step explanation:

Comment

That's an awful lot of points to give away. Ten or 15 should be enough.

Completing the square.

1. First of all you can find the minimum or maximum immediately.

2. Second it cuts out the need to use the givens (a, b, c) in the quadratic formula which can at times be very cumbersome.

3. It gives you the opportunity to estimate the x and y roots without calculating them. Estimating on a test is a very valuable asset.

The ordered pairs are (0,-7).

Any equation's ordered pair can be calculated by substituting any integer or the rational number for one of the variables, then solving for the remaining variable.

Consequently, we obtain values for both variables that meet the stated equation.

Solution:

5x - y = 7

Lets take, x = 0

Then,

5(0) - y = 7

y = -7

Then,

The ordered pair is (0,-7).

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Prediction of the mean value of the dependent variable y for values of the independent variables x 1, x 2, . . . , x q that are outside the experimental range is called extrapolation of data.

In statistics and mathematics, especially in the branch of data-science it is quite common to use a range of values from a parameter to predict the values of the dependent variable.

One of the most common applications of this is regression equations, when pairs of one of the independent variables with the dependent variable are used to predict the dependent variable.

In the case of this problem, we want to predict the dependent variable, but with values that are outside the experimental range, hence we extrapolate the data inside the experimental range for values that are outside the experimental range.

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Answer: z aprox = 9.2

Step-by-step explanation:

1) Square root 85 to get the answer

sqrt(z^2)=sqrt(85)

z = sqrt(85)

z = 9.2195

z aprox = 9.2

Answer:

(f∘g)(12) = 24

Step-by-step explanation:

We are given the functions f(x)=4x+8 and [tex]g(x)=\sqrt{x+4}[/tex]. We want to find (f∘g)(12).

(f∘g)(12) means that we first find the value of g(12), and then plug that value into f(x).

First, we find g(12). To do this, substitute x as 12.

[tex]g(12) = \sqrt{12 + 4}[/tex]

Add 12 and 4 together under the radical.

[tex]g(12) = \sqrt{16}[/tex]

Take the square root of 16.

g(12) = 4

Now, substitute 4 as x in f(x) = 4x + 8.

f(4) = 4(4) + 8

Multiply.

f(4) = 16 + 8

Add 16 and 8 together.

f(4) = 24

f(4) has the same value as (f∘g)(12), since 4 is the value of (g)(12), and then the value of g(12) was plugged in as x in f(x).

Therefore, (f∘g)(12) is 24.

The percent of pizzas that are less than 12.04 inches is 56.36%

Given the following:

Mean, μ=12

Standard deviation, σ=0.25

Percent of pizzas less than 12.04:

Let P(X<12.04) be percent of pizzas less than 12.04

P(X<12.04)=P(Z<(x-μ)/σ)

               =P(Z<(12.04-12)/0.25)

               =P(Z<0.16)

Z-value of 0.16 from cumulative standardized normal distribution is 0.5636

Given that P(X<12.04)=P(Z<0.16), and P(Z<0.16) from normal distribution table is 0.5636,

P(X<12.04)=P(Z<0.16)=0.5636

P(X<12.04)=0.5636

                 =56.36%

Hence, the correct choice is 56.36%

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Max is designing a hot tub for a local spa, he wants the hot tub to have a diameter of 90 inches, the approximate area required for the installation of the hot tub is [tex]6358.5in^{2}[/tex]

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant. The radius of a circle is  separation between any point on the circle and its center. The radius must typically be a positive integer. A degenerate case is a circle with r=0. Except when otherwise specified, this article discusses circles in Euclidean geometry, namely the Euclidean plane.

A circle, specifically, is a straightforward closed curve that separates the plane into its inner and exterior. In common parlance, the word "circle" can apply to either the figure's boundary or its entirety, including its inside; in rigorous technical parlance, the circle only refers to the boundary and the entire shape is referred to as a disc.

A circle can also be described as a particular type of ellipse where the semi-major and semi-minor axes are equal, the eccentricity is 0, and the two foci are coincident, or as the two-dimensional shape with the greatest area per unit perimeter squared when applying calculus of variations.

if, diameter= 90 inches

radius = 90/2= 45inches

area= [tex]\pi r^{2}[/tex]

       = 3.14* 45* 45

      = 6358.5[tex]in^{2}[/tex]

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Answer:

144

Step-by-step explanation:

12 * 12 = 144

Answer:

It's 144.

..............

Answer:

a

Step-by-step explanation:

The number that makes the mixed fraction equation true is -1.

The number that makes the equation true is calculated by applying the following formula as follows;

The given equation;

-7 ¹/₂ + ? = - 8 ¹/₂

The solution of the equation is calculated as follows;

Convert each mixed fraction into improper fraction;

-7 ¹/₂ = -15/2

-8 ¹/₂ = -17/2

-15/2 + ? = -17/2

Collect the similar terms together as follows;

? = -17/2 + 15/2

? = (-17 + 15) / 2

? = -2/2

? = - 1

Thus, the number that makes the equation true is -1.

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