Write the equation of the line described below in slope-intercept form.
Find the equation of the line that is perpendicular to the line y=2 x and passes through the point (10,2).

Step-by-step explanation:

It is not possible to determine the congruent angles in the given statement, as it is incomplete and does not provide enough information. In order to determine congruent angles, we need to know the shape and the specific angles being compared. For example, if the statement was "In a triangle ABC, angles A and C are congruent," then we would know that angles A and C are congruent.

The four tables available in choices, table option D is not a function. This is because there is the same x value, x = 2 i.e : ( 2, 3 ) , ( 2, 5 ) , ( 2, 7 ).

What is Function?

Function is a relation which each member of the domain is mapped onto exactly one member of the codomain.

There are many types of functions in mathematics such as :

Linear Function → f(x) = ax + b

Quadratic Function → f(x) = ax² + bx + c

Trigonometric Function → f(x) = sin x or f(x) = cos x or f(x) = tan x

Logarithmic function → f(x) = ln x

Polynomial function → f(x) = axⁿ + bxⁿ⁻¹ + ...

If function f : x → y , then inverse function f⁻¹ : y → x

Let us now tackle the problem!

According to the definition above, it can be concluded that a function cannot have the same x value.

Of the four tables available in choices, table option D is not a function. This is because there is the same x value, x = 2 i.e :

( 2, 3 ) , ( 2, 5 ) , ( 2, 7 ).

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Answer:

write the given equation in a standard form of y = mx + c

7x + 2y = 0

2y = -7x

y = -7/2x

parallel lines have equal gradient

m = -7/2

y - y1 = m(x - x1)

y - 2 = -7/2(x - (-7) )

y - 2 = -7/2( x + 7 )

y - 2 = -7/2x - 49/2

y = -7/2x - 49/2 + 2

y = -7/2 - 45/2

The number of people were 200 in the theater when it was full.

What is a theater?

In architecture, a theatre, usually spelled theatre, is a structure or area where a play can be conducted in front of spectators. The term comes from the Greek theatron, which means "a place of seeing." The actual performance usually takes place on a stage in a theatre.

Given that, the theater was full when the movie began.

76 people leave the theater before end the movie. At the end of the movie, there is 124 people left.

Apply algebraical operation that is addition to find the required answer.

Therefore, the number of people that was present at the beginning of the movie is (76 + 124) = 200.

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The number of cannonballs in illustration is 506.

Math Illustrations enables you to produce more useful geometry figures for your students in less time by fusing the constraint-based design of Geometry Expressions with simple-to-use sketching and graphing features.

The number of cannonballs in the first layer = 1² = 1

Number of cannonballs in the second layer = 2² = 4

Number of cannonballs in the third layer = 3² = 9

So, the generalized formula to count the balls is given as

= n(n + 1) (2n + 1)/ 6

Here, n= the total number of layers

Put n =11

11(11 + 1)(2(11) + 1) / 6

= 11(12)(23)/6

= 3036/6
= 506

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The composition function for the given situation is (c·r·b)(x) or (r·c·b)(x). Therefore, options B and F are the correct answers.

The given functions are c(x)=2x, b(x)=x+5 and r(x)=0.75x.

When the result of one function is used as the input for another, this is known as a composite function.

The most common kind of critical hit simply deals additional damage, most commonly dealing double the normal damage that would have been dealt, but many other formulas exist as well (such as ignoring defense of the target or always awarding the maximum possible damage).

A critical hit has the base damage x multiplied, next the damage reduction is applied to the critical hit. Bonus damage is not subject to damage reduction or critical hits, so this is applied last.

Here, Critical hit × Bonus × Damage reduction

That is, (c·r·b)(x) or (r·c·b)(x)

The composition function for the given situation is (c·r·b)(x) or (r·c·b)(x). Therefore, options B and F are the correct answers.

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Answer:

11

Step-by-step explanation:

The value of f(-3) if f(x) = 5x - 10 and g(x) = -x + 4 is -25.

Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.

Given:

f(x) = 5x - 10 and g(x) = -x+4

Calculate the  f(-3) by putting the value of x = -3 as shown below,

f(x) = 5(-3) - 10

f(x) = - 15 - 10

f(x) = -25

Therefore, the value of f(-3) if f(x) = 5x-10 and g(x) = -x+4 is -25.

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Answer:

look it up

Step-by-step explanation:

The equation of a hyperbola with a=7 and c=9 is (x-0)²/a²-(y-0)²/b²=1, x²/49-y²/32=1.

A hyperbola is a kind of smooth curve that appears to lie in a plane. It is made up of two connected components or branches that are mirror reflections of one another and look like two infinite bows. A hyperbola is a collection of points whose difference in distance between two foci is a fixed amount. This discrepancy is calculated by subtracting the distance from the farther focus from the distance from the closest focus.

As we know the standard equation of the hyperbola with a horizontal transverse axis is:

(x-h)²/a²-(y-k)²/b²

Now, put the given values a=7 and c=9 in the Pythagorean theorem to get the value of b.

c²=a²+b²

(9)²=(7)²+b²

81=49+b²

81-49=b²

32=b²

Now square root both sides:√

32=√b²

√32=b

Assuming that the center of a hyperbola is (0,0):

(x-0)²/a²-(y-0)²/b²=1

x²/a²-y²/b²=1

x²/(7)²-y²/(√32)²=1

x²/49-y²/32 = 1

Therefore, the equation of a hyperbola with a=7 and c=9 (x-0)²/a²-(y-0)²/b²=1, x²/49-y²/32=1.

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After solving the equation for x, the resultant answer is (3, -2).

The definition of an equation in algebra is a mathematical statement that shows the equivalence of two mathematical expressions.

For example, the equation 3x + 5 = 14 comprises the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

So, we have the equation:

y = -2x +4

Now, get value of x for y = -2 as follows:

Fill in the equation with the value of y and find x:

-2 = -2x +4 . . . . use -2 for y

-6 = -2x . . . . . . . subtract 4

3 = x . . . . . . . . . .divide by -2

Therefore, after solving the equation for x, the resultant answer is (3, -2).

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Complete question:
y=−2x+4y, equals, minus, 2, x, plus, 4

Complete the missing value in the solution to the equation.

Answer:

Welcome to Brainly! I saw that this was your very first question. I will gladly assist you with your problem. (see explanation)

Step-by-step explanation:

We must create equations from the provided data and relationships in order to determine the length of the rectangular flower garden. The area and the relationship between the width and length are the measurements that are provided. We create the necessary equations from these. What we do is:

Area = Length x Width

where length = x ft

width = x - 3 ft

area = [tex]54 ft^2[/tex]

[tex]54 ft^2 = x ft (x -3) ft\\\54 ft^2 = x^2 - 3x ft^2[/tex]

When we solve for x, we will get two answers, one of which is x = -6 ft (NOTE: This number cannot be the solution because the length cannot have a negative value).

Which means the correct answer is:

length(x)=9ft

(Hope this helped you

use y = mx + b

this is slope and y intercept

m is slope       b is y intercept

y = 1/4x -2

Two-column proof

See missing statements and reasons below.

    Statement                                      Reason                                          

Answer:

Hope the picture will help you........

The speed that the train travels is given as follows:

45 miles per hour.

The train travels at a constant speed, hence the distance traveled by the train over time is modeled by the proportional relationship defined as follows:

d = vt.

In which the variables of the equation are defined as follows:

Since the velocity is constant, it's equation is defined as follows:

v = d/t.

One point on the table is given as follows:

(1,45).

Hence the constant velocity of the train is calculated as follows:

v = 45/1 = 45 miles per hour.

The problem is given by the image shown at the end of the answer.

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The value of x is 13 units and the value of y is 13 units

The given triangle is right triangle

The ratio of the given triangle angles = 45-45-90 degrees

To find the length of the sides we have to use the trigonometric functions

sin θ = Opposite side / hypotenuse

cos θ = Adjacent side / hypotenuse

tan θ = Opposite side / adjacent side

Find the value of x

sin 45 = Opposite side / 13[tex]\sqrt{2}[/tex]

Opposite side = 13[tex]\sqrt{2}[/tex] × sin 45

= 13 units

Similarly

cos 45 = Adjacent side / 13[tex]\sqrt{2}[/tex]

Adjacent side =  13[tex]\sqrt{2}[/tex] × cos 45

= 13 units

Therefore, the length of the side x and y is 13 units

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Answer:

36.9 degrees

Step-by-step explanation:

distance that the plane travels (hypotenuse) = 1000m

horizontal distance (adjacent) = 800m

cos(angle) = adjacent/hypotenuse

cos(angle) = 800/1000

angle = cos-1(800/1000)

angle = 36.9 degrees

The ordered pair (1, 12) lies on the graph of the exponential function f(x) = 3(2)2x. which is the correct answer would be option (A).

The graph of an exponential function of the form f(x) = abˣ is a curve that passes through the point (0, a), where a is the initial value of the function.

In the given equation, the initial value is 3, so the graph of f(x) passes through the point (0, 3).

To find other points on the graph of f(x), we can plug different values of x into the equation and solve for the corresponding value of y.

For example, if we plug x = 3 into the equation, we get:

f(3) = 3(2)² × 3

= 3(16)

= 48

Therefore, point (3, 48) does not lie on the graph of f(x).

Similarly, if we plug x = 1 into the equation, we get:

f(1) = 3(2)² × 1

= 3(4)

= 12

Thus, point (1, 12) lies on the graph of f(x).

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Answer:

Step-by-step explanation:

You want the solutions to the rational equation ...

  [tex]\dfrac{2}{2x-6}-\dfrac{x}{x^2-9}=\dfrac{3}{x-3}[/tex]

We choose to rewrite the equation in the form f(x) = 0. We can start by subtracting the term on the right side (from both sides).

  [tex]\dfrac{2}{2x-6}-\dfrac{x}{x^2-9}-\dfrac{3}{x-3}=0\\\\\dfrac{2}{2(x-3)}-\dfrac{x}{(x-3)(x+3)}-\dfrac{3}{x-3}=0\\\\\\\dfrac{(x+3)-x-3(x+3)}{(x-3)(x+3)}=0\qquad\text{cancel 2 in first term; common denominator}\\\\\\\dfrac{-3x-6}{(x-3)(x+3)}=0\qquad\text{collect terms}[/tex]

The "not-possible values" will be values of x that make the denominator zero: x = ±3. The solution is ...

  [tex]-3(x+2)=0\qquad\text{numerator must be zero}\\\\\boxed{x=-2}\qquad\text{divide by -3, subtract 2}[/tex]

In the original equation, we have ...

  [tex]\dfrac{2}{2(-2)-6}-\dfrac{-2}{(-2)^2-9}=\dfrac{3}{(-2)-3}\\\\\dfrac{2}{-10}-\dfrac{-2}{-5}=\dfrac{3}{-5}\\\\-\dfrac{1}{5}-\dfrac{2}{5}=-\dfrac{3}{5}\qquad\text{TRUE}[/tex]

__

Additional comment

We like to write the equation as a single fraction compared to zero so that any common factors can be cancelled from numerator and denominator. This helps prevent extraneous solutions. Here, there are none.

Any fraction whose numerator is the same number as its denominator will equal 1, which is 100%. Hence, fraction [tex]\frac{5}{5}[/tex] is a fraction that equals 100%.

Answer:

[tex]\frac{5}{5}[/tex]

Step-by-step explanation:

To get a percentage out of a fraction, you divide the fraction and then move the decimal point two places to the right. [tex]\frac{5}{5} =1[/tex]  is also equal to 1.0

Move the decimal two places to the right and you get 100%

Answer:

[tex]4(x^4+7)[/tex]

Step-by-step explanation:

Taking out the greatest common factor,[tex]16x^4+28=4(x^4+7)[/tex].

Answer:

p=106

Step-by-step explanation:

p and 106 are corresponding so they are =

Answer:

54% are females

Step-by-step explanation:

In total there would be 225 participants -

104 + 121 = 225

Next, Divide 121 and 225. After, multiply by 100.

225/121(100)=53.78

53.78 rounded to the nearest percent is 54.

I hope this helped your question!

Then translons the resulting image  units to the right is   y=0 5  units.

What is  line?

A line segment in geometry is a section of a straight line that is enclosed by two clearly defined end points and contains all of the points on the line that are inside those endpoints. The Euclidean distance between two ends of a line segment determines its length.

Reflect [tex]$\triangle P Q R$[/tex] across the line [tex]$y=0$[/tex]. we can get [tex]$\Delta P^{\prime} Q^{\prime} R^{\prime}$[/tex]. then translate [tex]$\Delta P^{\prime} Q^{\prime} R^{\prime}$[/tex] 5 units to the right. we can get s STU. So the answer is A. y=0 5  units.

A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.

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Answer:

B

Step-by-step explanation:

This is the only pair of functions where [tex]f(g(x))=g(f(x))=x[/tex].

The net pay of Billy after 8% taxes and 10% retirement policy is $1600.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, From Billy's salary of $2000 8% of his paycheck goes to income taxes, and 10% automatically goes into retirement.

So, To obtain a net salary of Billy we'll subtract the percentage amount of 8% and 10% from the base of $2000.

Therefore, Net pay of Billy is {2000 - (8/100)×2000 - (10/100)×2000}.

= {2000 - 160 - 200}.

= (2000 - 360).

= $1640

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Answer:

The answer is p = -6/3. This is the value of p that makes the original equation true.

Step-by-step explanation:

To solve this equation, we must first isolate the variable p on one side of the equation. To do this, we can use the properties of equality to add or subtract the same value from both sides of the equation.

First, we can subtract 2p from both sides of the equation to get rid of the 2p term on the left side. This gives us 0 = -3p - 6/4.

Next, we can add 6/4 to both sides of the equation to get rid of the constant term on the right side. This gives us 6/4 = -3p.

Finally, we can multiply both sides of the equation by -4/3 to get rid of the coefficient -3 on the right side. This gives us -6/3 = p.

Therefore, the value of p that makes the equation true is p = -6/3.