How do I prove this so that angle 3 and angle 4 are complimentary?

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:A. \:\: 10[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } = 102[/tex]

[ subtract 2 from both sides ]

[tex]\qquad \tt \rightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } - 2 = 102 - 2[/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } - \bigg( 2 \sdot x \sdot \cfrac{1}{x} \bigg)= 100[/tex]

[ 2 can written like that, as they cancel out each other ]

Apply Identity [ a² + b² -2ab = (a - b)² ]

[tex]\qquad \tt \rightarrow \: \bigg (x - \cfrac{1}{x} \bigg) {}^{2} = 100[/tex]

[tex]\qquad \tt \rightarrow \: x - \cfrac{1}{x} {}^{} = \sqrt{100}[/tex]

[tex]\qquad \tt \rightarrow \: x - \cfrac{1}{x} {}^{} = 10[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

The independent variable (x) is the amount of time John fixes a computer. The dependent variable (y) is the amount, in dollars, John earns for a computer.

y-intercept: (0,50)

Slope: 45

If Five hundred ten of 650 high school students said that pizza was their favorite food. The margin of error is 0.0322.

Given:

Sample proportion=Five hundred ten=510

Sample size=650

Hence:

Margin of error=z×√p×(1-p)/n

Margin of error=2√510/650× (1-510/650)÷650

Margin of error=2√0.78461538×(1-0.78461538)÷650

Margin of error=2√0.78461538×0.21538462÷650

Margin of error=2√0.168994085÷650

Margin of error=2√0.0002599909

Margin of error=0.0322

Therefore the correct option is D.

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The intervals of the function in which it is increasing, decreasing and constant are given as follows:

a) Increasing: [tex]x \in \left[-4.5, 2\right][/tex].

b) Decreasing: [tex]x \in \left[4,6\right][/tex].

c) Constant: [tex]x \in \left[2,4\right][/tex].

A function is increasing when the graph of the function is pointing upwards, hence this function is increasing on the interval [tex]x \in \left[-4.5, 2\right][/tex].

A function is increasing when the graph of the function is pointing downwards, hence this function is decreasing on the interval [tex]x \in \left[4, 6\right][/tex].

A function is constant when it is graph is a line without inclination, hence this function is constant n the interval [tex]x \in \left[2, 4\right][/tex].

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Answer:

x = 6

Step-by-step explanation:

.16x + 2 * .02 = (x + 2) * .17
.16x + .4 = .17x + .34
.06 = .01x
6 = x

Answer:

D

Step-by-step explanation:

x = 5y²

x = 3y²

Here x is a function of y and so the parabola is open either to right or left.

The coefficient of y² is positive. So the parabola is open to right.

Both parabolas are open to right and  x = 5y² is wider than x = 3y².

Answer:

26,28

Step-by-step explanation:

We can make a system of equations based on the information given

first we can make one for the perimeter

and one for the area using herons formula

(x and y are the two unknown sides)

[tex]84=30+x+y[/tex]

[tex]336=\sqrt{42(12)(42-x)(42-y)}[/tex]

Now solve for x and y or you can find it by graphing

x and y = 26 and 28, the order does not matter since they are both unkown

so the two sides are 26 and 28

The graph of the equation is shown in the attached picture which is a straight line.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

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

We have a graph of a equation:

y + 2 = (x+2)

or

y = x

The above equation is a linear equation or straight line equation the slope of the equation is 1.

m = 1

The y-intercept of the equation is 0.

We can plot the equation y = x by using the slope and y-intercept.

Thus, the graph of the equation is shown in the attached picture which is a straight line.

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The simplified form of the expression has a numerator (x + 9)(2x + 1) and the denominator (x + 7) and the expression doesn't exist at (x = 9).

The given expression is:

= [(3x² - 27x)/(2x² + 13x - 7)]/(3x/4x² - 1)

Firstly, factorize the expression 4x² - 1.

4x² - 1 = (2x - 1)(2x + 1)

Then, factorize 2x² + 13x - 7.

2x² + 13x - 7 = 2x² + 14x - x - 7

2x(x + 7) - 1(x + 7)

= (2x - 1)(x + 7)

Then, factorize the equation 3x² - 27x.

3x² - 27x = 3x(x - 9)

The factorized terms will be substituted into the equation. This will be:

= [3x(x - 9)/(2x - 1)(x + 7)] / 3x[(2x - 1)(2x + 1)]

= (x + 9)(2x + 1)/(x + 7)

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A function assigns the values. The function g(x) can be written as g(x) = -3x + 12.

A function assigns the value of each element of one set to the other specific element of another set.

Given the function f(x)=-x, now since a transformed function g(x) is produced by shifting the function 4 units upwards and vertical stretch by a factor of 3. Therefore, g(x) can be written as,

Vertical Shift by 4 units,

f(x)+4

Vertical stretch by a factor of 3

g(x) = 3(f(x) + 4)

g(x) = -3x + 12

Hence, the function g(x) can be written as g(x) = -3x + 12.

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Their speed in terms of square feet per minute is 3/10 square feet per minute.

We know that the speed formula is the rate at which an object travels a given distance. Speed is defined as the distance traveled by a body in a given amount of time. Speed in the SI is measured in m/s.

Given that the distance = 1/5 square feet.

The time = 2/3 minute.

Speed = distance/time = (1/5)/(2/3) = (1/5)*(3/2) = 3/10

Therefore, we can conclude that their speed in terms of square feet per minute is 3/10 square feet per minute.

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[tex] \frac{ - 3}{5} \\ [/tex]

because , in the third quadrant , the value of cos is negative. Moreover , we can find the third side of the triangle using Pythagoras theorem.

then ,

[tex] \cos(\theta) = \frac{base}{hypotenuse} \\ \\ \dashrightarrow \: \cos(\theta) = \frac{ - 3}{5} [/tex]

hope helpful.

The answer is cos 0 = -3/5

Given :

tan 0 = 4/3 and is in the 3rd quadrant

this implies that both the perpendicular and base are negative.

Perpendicular = -4

Base = -3

Hypotenuse = [tex]\sqrt{(perpendicular)^{2} + (base)^{2} }[/tex]

Hypotenuse = [tex]\sqrt{(-4)^{2} + (-3)^{2} }[/tex]

Hypotenuse = [tex]\sqrt{25} = 5[/tex]

cos 0 = [tex]\frac{Base}{Hypotenuse}[/tex]

cos 0 = -3/5

Therefore, cos 0 = -3/5

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We write the equation in the form of directional.

y -1 = 6x               ⇔    y = 6x + 1

y - 1 = 3x              ⇔    y = 3x + 1

y - 7 = 2x - 6         ⇔    y = 2x - 6 + 7

                                    y = 2x + 1

y - 7 = x - 2           ⇔    y = x - 2 + 7

                                    y = x + 5

Equations cleverly arranged .

Point Q = (0,1)  

b factor , not only fits the last equation

In the drawing have engraved points Q and R are tangent linear function appropriate to that point . This graphics solution . y = 3x + 1

Answer b

We check choice by the system of equations , where substitute wartoćsi points Q and R to the model equations linear function

The result of equations confirmed our choice Answer b

Answer:

6

Step-by-step explanation:

Mean no. of runs per game =

= Total no. of runs/ total no. of games

= 9+8+4+0+7+6+4+5+9+8 / 10

= 60 / 10

= 6

Answer:

sin C = cos A

Step-by-step explanation:

sinC = opp/hyp

=12/13

cosA = adj/hyp

12/13

Answer:

A function is when each input has exactly one output

Step-by-step explanation:

Each input can only have one output, but an output can have multiple inputs.

Answer:

Part A:

A pair of linear equations can only have one solution or infinitely many solutions. In this case, there would only be one solution as they intersection at only one point.

Part B:

The solution would be (3, 4) because it is the point of intersection between the two linear lines.

The formula which used to describe the sequence is f(x)=1.2(2.5)ˣ⁻¹.

The given sequence is 1.2,3,7.5,18.75.

In geometric series, the ratio of two consecutive terms remains the same and this ratio is known as common ratio. a₁ is the first term of a geometric sequence and r is the common ratio, then the general term of the geometric sequence is of the form:

f(x)=a₁⋅rˣ⁻¹.

In the given sequence, a₁=1.2, a₂=3, a₃=7.5 and a₄=18.75.

Find the common ratio by

r=(aₙ₊₁)÷aₙ

r=a₂÷a₁

r=3÷1.2

r=2.5

Substitute the values in the general formula of geometric sequence.

f(x)=(1.2)(2.5)ˣ⁻¹

Hence, the formula which used to describe the sequence 1.2,3,7.5,18.75 is f(x)=(1.2)(2.5)ˣ⁻¹.

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Answer: none

Step-by-step explanation:

The range of the function at domain {-2, -1, and 0} will be { 12 , 3 and 0}.

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given that:-

The range for the given domain: {-2, -1, and 0} and the function is y = 3x².

The range will be the value of y at each given value of the domain.

Domain: { -2, -1, 0 }

y  =  3x²

At x = -2  →  y = 3 ( -2)² = 12

At x = -1   →  y = 3 (-1)²   = 3

At x = 0   →  y = 3 (0)    = 0

Therefore range of the function at domain {-2, -1, and 0} will be { 12 , 3 and 0}.

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If we put a=0 and b=-4.05 then the expression 4a+4b becomes -16.2 and when we put a=-4.05 and b=0 then the expression becomes -16.2.

Given  2 (a + b) = -8.1

Because no relationship between a and b is given so we can put any value of one variable to determine the value of another variable.

If we put a=0 in 2(a+b) =-8.1 then b=-4.05

If we put b=0 then a =-4.05.

We need to put these values in 4a+4b

when a=0 b=-4.05

4a+4b=4*0+4*-4.5

=-16.2

when b=0 and a=-4.05

4a+4b=4*-4.05+4*0

=-16.2

Hence for a=0,b=-4.5 the value of 4a+4b equals -16.2 and for a=-4.05 and b=0 the function equals -16.2.

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Step-by-step explanation:

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Based on the calculations, Celine would earn a total of $65.00 assuming she delivered 10 packages.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variable.

Given the following function:

y = 20.00 + 0.45(x)

In this exercise, you're required to determine Celine's weekly earnings based on the number of packages she delivered. However, the number of packages delivered by Celine wasn't shown, thus, we would assume a value for the purpose of an explanation:

Assuming x = 10 packages.

Substituting the value of x into the function, we have:

y = 20.00 + 0.45(10)

y = 20.00 + 45

y = $65.00.

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Answer:

Step-by-step explanation:

To calculate a+1/a, we first need to calculate for a.

a = 7 - 4 * [tex]\sqrt[2]{3}[/tex]

square root of 3 = 1.73

a = 7 - 4 * 1.73

a = 7 - 6.9

a = 0.1

0.1 + 1 / 0.1 = 0.1 + 10 = 10.1

Now, in case 4 wasn't being multiplied with the square root of 3, and instead, it was four root of 3, I am gonna do the calculations again:

a = 7 - [tex]\sqrt[4]{3}[/tex]

a = 7 - 1.31

a = 5.69

5.69 + 1 / 5.69 = 5.69 + 0.17 = 5.86

Hope I Helped!

Answer:

2.4 hours

Step-by-step explanation:

Because 1 hour Randy clean 1/4 of the room and Trey is 1/6. So we add both together and get that they clean 5/12 of the office in one hour. So 2.4 hours is the greatest amount of time it would take them to clean offices together

Using the continuity concept, as the value of the function has to be equal to the limit, it is found that the value of k is of k = -4.

A function is said to be continuous at x = a if, and only if:

[tex]\lim_{x \rightarrow a} f(x) = f(a)[/tex]

In this problem, we have to check at x = -2, hence:

[tex]\lim_{x \rightarrow -2} f(x) = f(-2)[/tex]

[tex]k = \lim_{x \rightarrow -2} f(x)[/tex]

For the limit, we have to check the lateral conditions, hence:

[tex]\lim_{x \rightarrow -2} f(x) = \lim_{x \rightarrow -2} \frac{x^2 - 4}{x + 2} = \lim_{x \rightarrow -2} \frac{(x - 2)(x + 2)}{x + 2} = \lim_{x \rightarrow -2} x - 2 = -2 -2 = -4[/tex]

Hence, from the continuity condition, k = -4.

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Step-by-step explanation:

since the two angles from a straight line, they make a linear pair and linear pairs are supplementery. by the angle addition postulate, you can determine that the two angles sum to 180. substituting the one angle mearsure that you are guven and using a bit of simple arithmetic and the subtraction property of equality, you can determine that the other angle,angle YXZ, is 45 degrees. I hope this is helpful

Answer: two units to the left, four units down and reflected across the y axis

Answer:

y = x/2 -3

Step-by-step explanation:

x - 2y = 6

Slope intercept form is y = mx+b  where m is the slope and b is the y intercept

We need to solve for y

Subtract x from each side

x-2y-x = -x+6

-2y = -x+6

Divide each side by -2

-2y/-2 = -x/-2 +6/-2

y = x/2 -3

The slope intercept form is

y = x/2 -3

Answer: slope intercept form is

y = x/2 -3

Step-by-step explanation:

hope this helps ; )