Directions: Determine whether each relation is a function. Explain your answer.

The value of x is 27°, m∠=PQY=101° and m∠RQY=79°.

Given that, m∠PQY= 4x-7 and m∠RQY = 2x+25 are linear pairs of angles.

Linear pairs of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.

Now, m∠PQY+m∠RQY=180°

⇒4x-7+2x+25=180°

⇒6x+18=180°

⇒6x=162

⇒x=27°

So, m∠=PQY=4x-7

=101°

and m∠RQY=2x+25

=79°

Therefore, the value of x is 27°, m∠=PQY=101° and m∠RQY=79°.

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Answer:

27

Step-by-step explanation:

The answer choice which represents a point of the circle with r² = 89 is; Choice B; (5, -8).

It follows from the task content that the circle in discuss has a center at the origin, (0,0).

Hence, the since the square of the radius is; = 89.

It follows that the point which fits into the equation of the circle; x² + y² = r² is;

Choice C; (5)² + (-8)² = 25 + 64 = 89.

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The answer choice which represents a point of the circle with r² = 89 is; Choice B; (5, -8).

It follows from the task content that the circle in discuss has a center at the origin, (0,0).

Hence, the since the square of the radius is; = 89.

It follows that the point which fits into the equation of the circle; x² + y² = r² is;

Choice C; (5)² + (-8)² = 25 + 64 = 89.

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Answer:

See below

Step-by-step explanation:

g (h(6))   :

   h (6) =  3 ( 6^2) + 2 = 110

   then g (110) =   sqrt (110)

h (g(5))

    g(5) = sqrt 5

        then h( sqrt5) = 3 ( sqrt5)^2 + 2 = 17

The number of the sheets in a ream of paper is a 500 sheets.

According to the statement

We have to find that the number pf paper sheets in a one ream.

So, For this purpose, we know that the

The standard form of a number is a way of writing the number in a form that follows certain rules.

From the given information:

A standard ream of paper plus another half ream of paper contains 750 sheets of paper.

It means

total number of sheets = 750 sheets

Then

one full ream + half ream = 750 sheets

Let x be a number of sheets

then

x + x/2 = 750

2x+x /2 = 750

3x/2 = 750

3x = 1500

x = 1500/3

x = 500.

So, The number of the sheets in a ream of paper is a 500 sheets.

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Answer:6,299,406

Step-by-step explanation:

Refer to the image for the graph of the lines.

The common form of the equation of a line is y = mx + c, where m is the slope of the line and c is a constant.

We need to draw any line with a slope m = 2, and

another line with a slope m = -2.

Disclaimer: Let us assume that the constant c = 0.

Then the equation to the line with a slope of "positive" 2 is given by

y = 2x

Then the equation to the line with a slope of "negative" 2 is given by

y = -2x

Refer to the attached image for the graph of the lines with the slope of "positive" 2 and "negative" 2.

f: green line indicates a line with a slope of "positive" 2.

g: blue line indicates a line with a slope of "negative" 2.

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Using Chebyshev's Theorem, the minimum proportion of scores that fall within 1.8 standard deviations on both sides of the mean is 69.14%.

When the distribution is unknown, Chebyshev's Theorem is used. It states that:

For this problem, we have that k = 1.8, hence the percentage is:

[tex]P = 100\left(1 - \frac{1}{1.8^{2}}\right) = 69.14[/tex]

The minimum proportion of scores that fall within 1.8 standard deviations on both sides of the mean is 69.14%.

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Mr. Price deposited a $10 bill for $50, a $5 bill for $75, and a $1 bill for $45.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

We have been given that the number of $5 bills was 3 times the number of $10 bills

Let the number of $10 bills would be x

As per the given condition,

$10 = x

$5 = 3x

$1 = 3x+30

Since he deposited $170 in his bank.

So 10x + 5(3x) + 1(3x+30) = 170

⇒ 25x+3x+30=170

⇒ 28x=140

⇒ x = 5

Therefore, $10 for $50

So 3x = 15, $5 for $75

So 3x+30 = 45, $1 for $45

Hence, he deposited a $10 bill for $50, a $5 bill for $75, and a $1 bill for $45.

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The value of x in the figure is 5

From the figure, we have the following parameters are:

NM = 9

ML = 2x - 7

NL = x + 7

This means that

NL = NM + ML

So, we have:

x + 7 = 9 + 2x - 7

Collect the like terns

x - 2x = 9 - 7 - 7

Evaluate

-x = -5

This gives

x = 5

Hence, the value of x in the figure is 5

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Answer:

B

Step-by-step explanation:

(48x-50y)-(35x-5y)

48x-50y-35x+5y

13x-45y

The equation of the line through (3,-5) and perpendicular to -3x + 2y = 12 in slope-intercept form is y =  -2/3x + 1

The equation of a line is expressed as;

y = mx + b

m is the slope

b is the y-intercept

Given the equation -3x + 2y = 12

2y = 3x + 12

y = 3/2x + 6

From the equation, the slope that is perpendicular to the slope is -2/3

Determine the equation

y-(-5) = -2/3(x-3)

y+5 = -2/3x + 6

y =  -2/3x + 6 - 5

y =  -2/3x + 1

Hence the equation of the line through (3,-5) and perpendicular to -3x + 2y = 12 in slope-intercept form is y =  -2/3x + 1

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The mean of the data given 4, 8,5, 13, 3, 4, 1, 10 shows number of shark attacks over 8 different states is 6.

As given,

Number of different states 'n'= 8

Number of sharks attacks for 8 different states

[tex]x_{i}[/tex] = 4, 8,5, 13, 3, 4, 1, 10

Mean = [tex]\frac{\sum x_{i} }{n}[/tex]

         = (4+ 8+ 5 + 13 + 3 + 4 + 1 + 10) /8

         =48 /8

         =6

Therefore, the mean of the data given 4, 8,5, 13, 3, 4, 1, 10 shows number of shark attacks over 8 different states is 6.

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Answer: 16.0 is the correct answer

Step-by-step explanation:

[tex]2(x-3)\geqslant -3(-3+x)\implies 2x-6\geqslant 9-3x\implies 2x\geqslant 15-3x \\\\\\ 5x\geqslant 15\implies x\geqslant \cfrac{15}{5}\implies x\geqslant 3[/tex]

Answer: Determine the mid-point.

Determine the slope between the two points.

The slope of perpendicular is negative reciprocal

Use slope and mid-point is point slope form.

Step-by-step explanation:

The simple interest for R 7,500 is R 1, 800, and she will get it at 3 years with interest of 8%.

Simple interest:

Simple interest means the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

The formula used to calculate the simple interest is

SI = P × R × T

P = The principal is the amount that initially borrowed from the bank or invested.

R = Rate is the rate of interest at which the principal amount is given to someone for a certain time.

T= Time is the duration for which the principal amount is given to someone.

Given,

Cynthia receives a gift of r 7, 500 she decides to invest it for 3 years, she is offered two saving at 8% interest.

Here we need to find the simple interest.

We know that,

P = 7, 500

R = 8/100 = 0.08

T = 3

So, the simple interest is,

SI = 7,500 x 0.08 x 3

SI = 1800

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Answer:

Part 1) The fractions in the list are not equal to the decimal number indicated

Part 2) The fractions 401/99 and 802/198 are equal to the decimal number indicated.

Part 1)

we have the decimal number

4.05 -----> is a terminating decimal ( t's a decimal with a finite number of digits)

Convert to fraction number

Multiply and divide by 100

Simplify

Divide by 5 both numerator and denominator

therefore

The fractions in the list are not equal to the decimal number indicated.

Part 2) we have

4.050505... ------> is a repeating decimal (is a decimal that has a digit, or a block of digits, that repeat without ever ending)

Let

x=4.050505...

we have that

Multiply by 2 both numerator and denominator

therefore

The fractions 401/99 and 802/198 are equal to the decimal number indicated.

Step-by-step explanation:

An angle is denoted by the angle symbol ∠ and the three letters representing the name of the angle.

An angle is denoted by the angle symbol ∠ which is then being followed by three letters that will represent the points that form an angle.

Lets say for example, the expression ∠ABC will mean that “the angle is formed by the points A, B and C”

where the vertex of the angle is at the point B as it is in the middle.

Angles can also be of different types like:

An Acute Angle which means an angle is less than 90 degrees.

A Right Angle which means an angle which is exactly 90 degrees.

An Obtuse Angle which is an angle more than 90 degrees and less than 180 degrees.

A Straight Angle which is an angle that is exactly 180 degrees.

And a Reflex Angle which is an angle greater than 180 degrees and less than 360 degrees.

Therefore, an angle is denoted by the angle symbol ∠ and the three letters representing the name of the angle.

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The value of z = 2.25

Given that z is a standard normal random variable.

Now the area under a standard normal curve between two z -values gives the probability of z lying between these two z-values.

Given that the area to the right of z = 0.0122

That is probability that the standard normal random variable lies after z = 0.0122

Total probability = 1

Therefore half the area under the standard normal curve = 0.5

Therefore, 0.5 - 0.0122 = 0.4878

We will find the corresponding z-value for this probability value from the normal tables. This is because normal tables gives area between two standard normal variables.

The table value corresponding to 0.4878 = 2.25

Therefore, z -value = 2.25

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Answer:

quadrant I

Step-by-step explanation:

because both numbers are positive and quadrant I is the only one that has positive numbers on the y and x axis.

Answer:

C. Quadrant 1

Step-by-step explanation:

if both X and Y are positive, then the point lies in the Quadrant I.

Answer:

11.2 or 11 1/5

Step-by-step explanation:

multiply it ez

Answer: Use a=wl, 13.3

Step-by-step explanation:

a=wl

4.75*2.8=13.

The equation can be summarized as; p = $50 + 3($100 ). Hence William was paid $350.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

Let p represents the paycheck.

William  paid her parents $50 for rent. After paying the rent he evenly divided the rest of the amount into three parts.

He puts $ 100 into her savings account. It means that he also puts $100 into checking account and $ 100 into retirement fund

If we put the parts together, the equation we get is;

p = $50 +$100 +$100 +$100

The equation can be summarized as;

p = $50 + 3($100 )

Now we can easily find how much was William  paid;

p = $50 + 3($100)

p = $50 +$300

p = $350

Hence William was paid $350.

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Answer:

5729627829263#wyyeiwyuwityeioe

Answer: x = -5

Step-by-step explanation:

3x + 4 = 2x - 1

3x = 2x -5

x = -5

Answer:

3

Step-by-step explanation:

9/3 = 3

b is 3 times more than a

Answer:

72

Step-by-step explanation:

7(10) + 2

70 + 2

72

Answer:

10,877

Step-by-step explanation:

The six trigonometric functions of theta for the point (-4, -4) is

sin Θ = -1/√2

cos Θ = -1/√2

tan Θ = 1

cosec Θ = -√2

sec Θ = -√2

cot Θ = 1

Trigonometric Functions:

Trigonometric functions are defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle.

The six trigonometric functions are,

Sin Θ =Opposite/Hypotenuse

Cos Θ = Adjacent/Hypotenuse

Tan Θ = Opposite/Adjacent

Sec Θ =  Hypotenuse/Adjacent

Cosec Θ  = Hypotenuse/Opposite

cot Θ  = Adjacent/Opposite

Given,

Let (-4,-4) be a point on the terminal side of theta in standard position.

Here we need to find the exact values of six trigonometric functions.

Here the give point (-4,-4) represents the values of (opposite, adjacent).

So, the opposite = -4

and adjacent = -4

Now we have to find the hypotenuse of the point,

For that, we have to use the Pythagoras theorem,

hypotenuse = √oppostie² + adjacent²

Therefore,

=> hypotenuse = √(-4)² + (-4)²

=> hypotenuse = √16 + 16

=> hypotenuse = √32

it can be written as,

=> hypotenuse = √2 x 16

=> hypotenuse = 4√2

Now the six trigonometric functions are based on the formula,

sin Θ = -4/4√2 => sin Θ = -1/√2

cos Θ = -4/4√2 => cos Θ = -1/√2

tan Θ = -4/-4 => tan Θ = 1

cosec Θ = 4√2/-4 => cosec Θ  = -√2

sec Θ = 4√2/-4 =>  sec Θ  = -√2

cot Θ = -4/-4 => cot Θ = 1

So, all the six trigonometric values are identified.

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Answer:

2/9

Step-by-step explanation:

To multiply fractions you just multiply the numerators with the numerators and the denominators with the denominators

1/4 * 2/3 = 2/12 which simplifies to 1/6

1/6 * 4/3 = 4/18 which simplifies to 2/9

:D