Find the equation of the line passing through the given point and parallel to the given line.
( 1 , 9), y = 4
(-1 ,-3), y= 2
(4, -6), y = -5

Answer:

Step-by-step explanation:

Answer: 5x^3 + 4x^2 – (6x^2 – 2x – 9) =

5x^3 + 4x^2 – 6x^2 + 2x + 9 =

5x^3 – 2x^2 + 2x + 9

Step-by-step explanation: We have to find the difference (5x^3 + 4x^2) - (6x^2 - 2x - 9)

On distributing the minus over the parenthesis, we get

5x^3 + 4x^2 - 6x^2 + 2x + 9

Now, we group the like terms and combine them

5x^3 + (4x^2 - 6x^2) + 2x + 9

=5x^3-2x^2 + 2x +9

Therefore, the last expression is the correct option.

The difference of the polynomial is 5x^3-2x^2 + 2x +9

Answer:

Step-by-step explanation:

The height of a building is 7 m that casts a shadow of 11.3 m

The ratio between height to shadow length of man will be equal to the ratio of building. So, equating these two to find the height of building.

Height : Shadow length (man) = Height : shadow length (Building)

Keep the values as fraction

1.8/2.9 = Height/11.3

Height of building = (1.8 × 11.3) ÷ 2.9

Performing multiplication in numerator on Right Hand Side of the equation

Height of building = 20.34 ÷ 2.9

Performing division on Right Hand Side of the equation

Height of building = 7 m

Thus, the height of building is 7 m.

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[tex]\frac{1}{2} -\frac{3}{7} =\frac{7}{14} -\frac{6}{14} =\frac{1}{14}[/tex]

Answer:

[tex] \frac{1}{14} [/tex]

Step-by-step explanation:

[tex] \frac{1}{2} - \frac{3}{7} = \frac{7}{14} - \frac{6}{14} [/tex]

[tex] = \frac{1}{14} [/tex]

The simplification of the given expression would be = 9^-¹⁶

Simplification is defined as editing of a given mathematical expression in a more easy to under form or less complex form.

To simplify the given expression such as 9^-53·9^37 the law of exponents should be observed.

According to the law of exponents, a^m * a^n = a^m + n

9^-53·9^37

= 9^ -53+37

= 9^-16

Therefore, the simplification of the expression above would be = 9^-¹⁶.

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The solution of the equation [tex]e^{6x}[/tex] - 11 = 104 is x = 0.79

The given equation is

[tex]e^{6x}[/tex] - 11 = 104

The equation is the mathematical statement that shows the relationship between two expression. The equation is consist of different variable, numbers and mathematical operators with the equal sign. The mathematical operators are addition, subtraction, division and multiplication. The inequality will not be the part of equation

The given equation is

[tex]e^{6x}[/tex] - 11 = 104

[tex]e^{6x}[/tex]  = 104 + 11

Add the terms

[tex]e^{6x}[/tex] = 115

6x = ln (115)

x  = ln (115) / 6

x = 0.79

Hence, the solution of the equation [tex]e^{6x}[/tex] - 11 = 104 is x = 0.79

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The probability of x being equal o 19.62 is d) 0.

It is given that x is normally distributed with a mean of 12 and a standard deviation of 3.

Now, Normal distribution is a continuous distribution.

This implies that the probability is measured over an interval, taking an infinite number of points in between.

If we plot a continuous distribution, the probability here at a point is not the value of the y coordinate at that point. Instead, it is seen as an area under the curve of the distribution, between the two intervals, say a and b.

Therefore, if we take up a single point say c, then the probability will be the area under the curve from c to c, which will obviously be 0.

Hence, the probability that x = 19.62 will be 0.

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Answer:

Step-by-step explanation:

Answer:

2.5

Step-by-step explanation:

The Elevator’s rate of change is found to be 3 floors per second using the given data.

Speed (or rate, r) is a scalar number that represents the distance traveled (d) divided by the change in time (t) by the equation r = d/t.

Given: In 40 seconds, an elevator travels from the 124 floor to the 8 floor of a skyscraper. The elevator maintains a constant speed.

We know that,

Rate = Distance/Time

Elevator’s rate of change = (124-8)/40

                                          = 116/40

                                           = 2.9 ≈ 3 floors per second

Therefore, the Elevator’s rate of change  is found to be 3 floors per second using the given data.

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Answer:

B

Step-by-step explanation:

plug in 1 for x and 4 for y

4 + 4 = 4(1+1)

8 = 8

Plug in 2 for x and 8 for y

8+ 4 = 4(2+1)

12 = 12

Answer: [tex]x = 34[/tex]

Step-by-step explanation:

Let x be the original amount of Pokémon cards Tommy had, we know that he sold half of them; this can be express as:

                                                              [tex]\frac{x}{2}[/tex]

After this he changed his mind and bought 17 cards, then he has:

                                                         [tex]\frac{x}{2} + 17\\[/tex]

We know that he has 34, then we have the equation:

                                                       [tex]\frac{x}{2} + 17 = 34[/tex]

Solving for x we have:

                                                        [tex]\frac{x}{2} + 17 = 34[/tex]

                                                        [tex]\frac{x}{2} = 34 - 17[/tex]

                                                            [tex]\frac{x}{2} = 17[/tex]

                                                         [tex]x = (2)(17)[/tex]

                                                            [tex]x = 34[/tex]

Answer:

x=1 y=4.5, x=2 y=4

Step-by-step explanation:

plug in random values of x and solve for y then you get your answer.

The slope of the perpendicular line is 1/5

The equation of the line is given as

5x + y = -4

The equation of a line can be represented as

y = mx + c

Where

Slope = m

So, the first step is to make the variable y the subject in 5x + y = -4

This gives

y = -5x - 4

By comparing the equations, we have the following

m = -5

This means that the slope of 5x + y = -4 is -5

So, we have

Slope 1 = -5

The slopes of perpendicular lines are opposite reciprocals

i.e.

Slope 2 = -1/Slope 1

This gives

Slope 2 = -1/-5

Evaluate

Slope 2 = 1/5

Hence, the perpendicular line has a slope of 1/5

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Answer:

x = -0.8

Step-by-step explanation:

2.35+0.25x = 1.75+0.4

To find x, we must first isolate the value.

This is done by subtracting any values on the same side as the x.

Thus, we subtract 2.35 from both sides.

We are now left with the following:

0.25x=1.75+0.4-2.35

Now you should simplify the right side by finding the sum, which is -0.2, so:

0.25x=-0.2

Finally, solve by dividing each side by 0.25.

x = -0.8

Answer:

[tex]x = -\dfrac{4}{5} \ \ \textrm{or} \ \ x = -0.8[/tex]

Step-by-step explanation:

First, multiply both sides by 100 to make the numbers nicer to work with.

[tex](100)(2.35 + 0.25x) = (1.75 + 0.40)(100)[/tex]

[tex]235+25x=175+40[/tex]

Next, isolate x by moving all the constant terms to one side and then dividing by x's coefficient.

[tex]25x=175+40-235[/tex]

[tex]25x = -20\\\overline{\, \, 25 \, \,} \: \, \, \, \, \, \, \, \overline{ \,\, 25 \, \,}[/tex]

[tex]x = -\dfrac{20}{25}[/tex]

[tex]x = -\dfrac{4}{5}[/tex]

So, the value of x is -4/5 or 0.8.

The image of the point (0, -4) after the transformation T3,3 R270 is (3, 1).

The image of the given point after transformation considers the given point is P(0, -4)

Rules of transformation R(27°,0)° T<3, 3> representing translation T<3, 3> after that rotate 270 degrees counter-clockwise If a figure translated by T<3, 3>

( x,y)= (( x + 3), ( y + 3))

p (0, -4) = p' (( 0 + 3), ( -4 + 3))  

p (0, -4) = p'(3, -1)

When rotating a point 270 degrees counter-clockwise about the origin our point

p'(x,y) becomes p''(y,-x)

p'(3, -1) = p''(3, -(-1))

p'(-10,2) =p"(3, 1)

Therefore, the image of the point (0, -4) after the transformation T3,3 R270 is (3, 1).

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Answer:

m=2

Step-by-step explanation:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex](x_1,y_1) = (-3,-3)\\(x_2,y_2) = (3,9)\\[/tex]

[tex]m=\frac{[9-(-3)]}{[3-(-3)]}\\m=\frac{9+3}{3+3}\\m=\frac{12}{6}\\m=2[/tex]

Answer:

523

Step-by-step explanation:

the game

x=14 in is the smaller part of lumber

55-x=55-14=41 in is the larger  part of lumber

Linear equations are described for strains withinside the coordinate system. If an equation has  homogeneous variables of diploma 1 (that is, best one variable), the equation is stated to be a linear equation in a single variable. A linear equation may have more than one variables. When linear equations have  variables, they may be known as bivariate linear equations.

Examples of linear equations are 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x - y + z = 3. This article gives definitions of linear equations, preferred types of linear equations in a single, , and 3 variables,  and  examples of them with complete explanations.

Let x=the smaller part

Then 55-x=the larger part

Now we are told the following:

2(55-x)=5x+12 simplify

110-2x=5x+12 add 2x to and subtract 12 from each side

110-2x+2x-12=5x+2x+12-12 collect like terms

98=7x

x=14 in--------------------smaller part

55-x=55-14=41 in-----------larger part

CK

2 times larger part=2*41=82 in

5 times smaller part=5*14=70 in

70+12=82

82=82

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The number of miles when they'll cost the same for Ann is 137.5 miles.

Ann can choose one of two plans. The first plan has an initial fee of 55$ and costs $0.4 an additional per mile driven and the second plan has no initial fee but costs 0.8$ per mile driven.

This will be illustrated as:

55 + 0.4m = 0.8m

Collect like terms

0.8m - 0.4m = 55

0.4m = 55

Divide

m = 55/0.4

m = 137.5m

The miles is 137.5 miles.

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Complete question

Ann will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of 55$ and costs $0.4 an additional per mile driven. The second plan has no initial fee but costs 0.8$ per mile driven. How many miles will they cost the same?

Answer: A and D

Step-by-step explanation:

Option (D) is the correct one and the number -(-2) is 2 units to the right of 0.

Given, a number -(-2),

we have to describe the location of the number -(-2) on a number line.

On simplifying, we get

-(-2) = +2

So, the number we have to plot is 2.

As, we know that the positive numbers are on the right side of the origin.

So, the number will be 2 units to the right of 0.

Hence, Option (D) is the correct one and the number is 2 units to the right of 0.

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The quadrilateral VWXY that has an equal length of  diagonals and equal length of sides is the quadrilateral is a square

Since the information given to us about the quadrilateral  VWXY is :

VW = 15, WX = 15, XY = 15, YV = 15

Since the side lengths of the quadrilateral VWXY  and the diagonal lengths are equal. So, VX = WY = VX = WY. As we know The properties of a square are that their interior angles are congruent and are  90°, plus The four sides are of  equal length, the Opposite sides  are congruent and The length of the diagonals is equal.So it can be concluded that the  equal length of the diagonals  of a quadrilateral indicates   that it can be a  square

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The fourth term a₄ of the sequence aₙ is 15

The definition of the function is given as

a(1)=-11

a(n)=a(n-1)x10

When this definition is rewritten properly, we have the following representation

a₁= 11

aₙ = aₙ₋₁ * 10

The above definitions imply that we simply multiply 10 and the previous term to get the current term

Using the above as a guide,

So, we have the following representation

a₂ = 11 * 10

Evaluate the products

So, we have

a₂ = 110

Also, we have

a₃ = 110 * 10

Evaluate the products

So, we have

a₃ = 1100

Lastly, we have

a₄ = 1100 * 10

Evaluate the products

So, we have

a₄ = 11000

This represents the 4th term of the sequence

Hence, the value of a₄ is 11000

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By simplifying the expression (-4-√7)² we get the value as 23+8√7 in decimals we get 44.12.

Given that,

The expression is (-4-√7)²

We need to find the value and simplify the expression.

Take the expression.

(-4-√7)²

We know that (a+b)²=a²+2ab+b²

The expression is in the form of (a+b)² substitute the formula.

(-4)²+2(-4)(-√7)+(-√7)²

Now do the square

16+2(-4)(-√7)+7

Now do the multiplication.

16+8√7+7

Now do the addition.

23+8√7

We can write the √7 value

23+8(2.64)

Multiply 8 and 2.64

23+ 21.12

Now adding

44.12

Therefore, By simplifying the expression (-4-√7)² we get the value as 23+8√7 in decimals we get 44.12.

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Answer:

Step-by-step explanation:

Median is the line drawn from the midpoint of one the sides of the triangle to the opposite vertex is called Center of Mass of Triangle.
So, Q is center of mass of triangle.

The perpendicular of a triangle is perpendicular to the sides drawn from the opposite vertices and divides the sides into two equal parts.
so, P is perpendicular point of the triangle.