Find the measure of each arc. For each arc, write two or more complete sentences explaining which theorem or postulate you used to find your answer. Include your equations and calculations in your final answer.
m arcRPQ

Part a

Let [tex]a=2[/tex]. Then, we have that

[tex]7+2=\sqrt{7b+c}\\\\81=7b+c[/tex]

We can let [tex]b=11[/tex] and [tex]c=4[/tex], meaning the equation is [tex]x+2=\sqrt{11x+4}[/tex].

Part b

[tex]x+2=\sqrt{11x+4}\\\\x^2 +4x+4=11x+4\\\\x^2 -7x=0\\\\x(x-7)=0\\ \\ x=0, 7[/tex]

Substituting both of these values into the equation, we see they are both solutions.

Part c

[tex]x+10=\sqrt{10x+219}[/tex]

The unknown measures of the right angle triangle are m∠V = 69° , RV = 12.85 and m∠R = 21°

A right triangle is a triangle that has one of its angles as 90 degrees.

Therefore, the side and angles of a right triangle can be found using trigonometric ratios.

Hence,

tan v = opposite / adjacent

opposite side = 12

adjacent side = 4.6

Therefore,

tan V = 12 / 4.6

v = tan⁻¹ 2.60869565217

v = 69.0265065627

m∠V = 69°

Let's find  m∠R

m∠R = 180 - 69 - 90

m∠R = 21°

Let's find RV

sin 69° = opposite / hypotenuse

sin 69 = 12 / h

cross multiply

h = 12 / sin 69

h = 12 / 0.93358042649

h = 12.8537402885

RV = 12.85 units

Therefore, the unknown side and angles of the triangle are as follows:

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Recall that the diagonals of a rectangle are congruent. Therefore, we can set the following equation:

Solving the above equation for z, we get:

Answer:

66%

Step-by-step explanation:

99 of 150 is 66%

and 150 of 99 is 151%

The measure of m∠DBC in the semicircle is 90°

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

From the image:

∠BAC = ∠BDC = 45° (angle in same segment are equal)

∠BCD = 90° (angle subtended at circumference by semicircle)

In triangle BDC:

∠BDC + ∠BCD + ∠DBC = 180° (angle in a triangle)

45 + 90 + ∠DBC = 180°

∠DBC = 90°

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The point P is ( -2.2 , -1.4) on the line segment NM, which represents the fractional distance from N to M.

Given:

Fractional Distance from n to m is 1/5 and

points are N (-3, -2),  M (1, 1).

From the graph we can see that the distance from M to R is 4,

And the distance between N to R is 3.

So, 1/5 MR = 1/5 (4)

                    =4/5

And, 1/5 NR=1/5 (3)

                     =3/5

By substituting these values in N (-3, -2),

We get a point p on MN.

-3 + 4/5 = -2.2

and -2 + 3/5 = -1.4

Hence p(-2.2, -1.4) is the point on line segment NM.

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The percent of Thompson's Scores that are greater than 73.8 is 95%

The percent of Thompson's Scores that are between 64.2 and 67.4 is 69% to 94%

given data

a mean of about 70.6 strokes

a standard deviation of about 3.2 strokes

Applying the 68%, 95%, and 99.7% Rule. This rule says that standard deviations is changed to percentages when:

Hence we calculate how many standard Deviations that gives 73.8 as follows

since the73.8 is greater than the mean we add the SD to the mean

70.6 + 3.2 = 73.8

73.8 is 1 SD but we are looking for value greater than 73.8. This should be just above 73.8, hence from 2 SD which is 95%

What percent of Thompson's scores are between 64.2 and 67.4

Applying the 68%, 95%, and 99.7% Rule

The numbers asked is less than the mean hence we subtract

70.6 - 3.2 = 67.4    ( 1 SD = 68% )

70.6 - 3.2 - 3.2 = 64.2    ( 2 SD = 95% )

The question asks the percent of Thompson's scores between 68% and 95%. This is 69% to 94%.

The question said between hence the end values are not inclusive

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The stages of the race ordered from shortest to longest are:

Stage 21 : 4%

Stage 4: 0.044 x 100 = 4.4%

Stage 8: (6 / 125) x 100 = 4.8%

Stage 1 : (11 / 200) x 100 = 5.5%

Stage 17 : 0.06 x 100 = 6%

The first step is to convert the given decimals, percentages and fractions to the same measure to aid comparison. All would be converted to percentages.

Percentage is the fraction of an amount expressed as number out of 100. In order to convert a number to a percentage, multiply by 100. The sign that represents percentage is %.

Stage 1 : (11 / 200) x 100 = 5.5%

Stage 4: 0.044 x 100 = 4.4%

Stage 8: (6 / 125) x 100 = 4.8%

Stage 17 : 0.06 x 100 = 6%

Stage 21 : 4%

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Answer:

y + 10 =2( x +1)

or

y -2 + 2( x -5)

These both name the same line.

Step-by-step explanation:

First we need to find the slope.  The slope is the change in y over the change in x.  In the point (-1,-10)

-1 is the x and -10 is the y.

In the point (5,2)  

5 is the x and 2 is the y.

[tex]\frac{2- -10)}{5 - -1)}[/tex]  Subtracting a negative is the same as adding a positive.

[tex]\frac{2+ 10}{5+1}[/tex] = [tex]\frac{12}{6}[/tex] = 2

We know know the slope.  We will use the form

y - [tex]y_{1}[/tex] = m (x-[tex]x_{1}[/tex])  we will plug in the numbers that we know.  

If we use point (-1, -10)

y -- -10 = 2(x - -1)

y + 10 = 2( x+1)

If we use the point (5,2)

y -2 = 2(x -5)

Both equations mean the same thing.

Answer:

-3

Step-by-step explanation:

your x-axis has to be 0 then the point on the y-axis is the y-intercept

IT MEANS THE GRADIENT OF THE NEW EQUATION IS GOING TO BE

[tex] \frac{2}{5} [/tex]

TOO

[tex]2 = \frac{2}{5} ( - 7) + c \\ 2 = \frac{ - 14}{5} + c \\ c = 2 + \frac{14}{5} \\ c = \frac{24}{5} [/tex]

THE EQUATION PARALLEL TO THE ONE GIVEN NOW IS

[tex]y = \frac{2}{5} x + \frac{24}{5} [/tex]

Answer:

-14 is the correct answer

Y is 2.25 when x is 9.

The relationship between two values where their ratio equals a constant number is known as a direct proportion or direct variation. It is symbolized by the proportional sign (). According to the direct proportion formula, if y is directly proportional to x, we can state that y = kx, where k is a constant. The generic form of the direct proportion equation is also y = kx. where k is the proportionality constant.

Given Data

If x and y vary directly and y is 24 when x is 6, find y when x is 9.​

It is direct proportional

So,

y = kx

To find constant,

k = [tex]\frac{y}{x}[/tex]

x = 6 and y = 24

k = [tex]\frac{6}{24}[/tex]

k = [tex]\frac{1}{4}[/tex]

When x = 9,

k = [tex]\frac{1}{4}[/tex]

y = kx

y = [tex]\frac{1}{4}[/tex](9)

y = [tex]\frac{9}{4}[/tex]

y = 2.25

Y is 2.25 when x is 9.

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Answer:

The equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept.

Answer:

y = x + 6

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, 6) and (x₂, y₂ ) = (4, 10) ← 2 points on the line

m = [tex]\frac{10-6}{4-0}[/tex] = [tex]\frac{4}{4}[/tex] = 1

the line crosses the y- axis at (0, 6 ) ⇒ c = 6

y = x + 6 ← equation of line

Answer: -14

Step-by-step explanation:

-21 - (-7)

-21 + 7

-14

The expression will be (2.99c + 20 = Total cost) and the total cost of Sam's consumption will be $30.465.

So, the expression for the total cost of the person using c pounds of clay:

Total cost when Sam uses 3.5 pounds of clay:

Therefore, the expression will be (2.99c + 20 = Total cost) and the total cost of Sam's consumption will be $30.465.

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Answer:



m < 1 = 146

m < 3 = 146

m < 4 = 34

Step-by-step explanation:

Angles 2 and 3 are suplementary angles that equal 180

angle 2 + angle 3 = 180

34 + angle 3 = 180

angle 3 = 180 - 34

angle 3 = 146

angles 2 (34 degrees) and 4 and angles 1 (146 degrees) and 3 are congruent so...

m < 1 = 146

m < 2 = 34

m < 3 = 146

m < 4 = 34

Hope this helps! :)

Answer:

[tex]m \angle 1= \boxed{146}\;^{\circ}\\\\m \angle 3= \boxed{146}\;^{\circ}\\\\m \angle 4= \boxed{34}\;^{\circ}[/tex]

Step-by-step explanation:

Angles on a straight line sum to 180°.

⇒ m∠1 + m∠2 = 180°

⇒ m∠1 + 34° = 180°

⇒ m∠1 = 146°

Vertical Angle Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Applying the Vertical Angle Theorem:

y = -x equation does not represent a direct variation.

y = 3x + 2

y=-3x

y = 0.5x

equations are represent a direct variation

How can you tell if there is a direct variation?

Simply build ratios from a table of values if you have one and wish to determine whether the data indicate a direct variation. You have a straight variation if all the ratios are the same.

The constant of variation is k = = 3, for instance, if y varies straight as x and y = 6 when x = 2. So, y = 3x serves as the equation to describe this direct variation.

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If you have 15 quarters, 10 dimes, 10 nickels and 10 pennies, then the probabilities of getting quarter, dimes, nickels and pennies are 0.33, 0.22, 0.22 and 0.22 respectively.

Total number of quarters = 15 quarters

Total number of dimes = 10 dimes

Total number of nickels = 10 nickels

Total number of pennies = 10 pennies

Total number of coins = 15+10+10+10 = 45

The probability of getting a quarters = 15/45

= 0.33

The probability of getting a dimes = 10/45

= 0.22

The probability of getting a nickel = 10/45

= 0.22

The probability of getting penny = 10/45

= 0.22

Hence, if you have 15 quarters, 10 dimes, 10 nickels and 10 pennies, then the probabilities of getting quarter, dimes, nickels and pennies are 0.33, 0.22, 0.22 and 0.22 respectively.

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The diagonal of the rectangular solid that has l = 8, w = 4, h = 2, is calculated as: d = 2√21 units.

A rectangular solid has a length (l), height (h), and width (w). The diagonal of the rectangular solid, d, can be calculated using the given formula below:

Diagonal of rectangular solid (d) = √(l² + w² + h²).

Given the following dimensions of the rectangular box:

Substitute l = 8, w = 4,a nd h = 2 into the equation d = √(l² + w² + h²):

Diagonal of rectangular solid (d) = √(8² + 4² + 2²)

Diagonal of rectangular solid (d) = √(64 + 16 + 4)

Diagonal of rectangular solid (d) = √84

Simplify √84 further

Diagonal of rectangular solid (d) = √(4 × 21)

Diagonal of rectangular solid (d) = 2√21 units

Therefore, the rectangular solid has a diagonal that is: 2√21

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I need help on it too. Can any one help me find the answer

Answer: 3 seconds

Step-by-step explanation:  

t = √h / 4

t = (√125) / 4

t = (5√5) / 4

t = 2.795 seconds

Because integer numbers can't be decimals so we round it to 3.

The probabilities from this problem are given as follows:

a) The probability that a student participates in exactly three activities is 0.23.

b) The probability that a student participates in less than three activities is 0.68.

c) The probability that a student participates in at least two activities is 0.82.

The event associated with exactly three activities is given by:

X = 3.

Hence, from the table on the image at the end of the answer, the probability is:

P(X = 3) = 0.23.

The events associated with less than three activities are given by:

X = 0, X = 1 and X = 2.

Hence, from the table on the image at the end of the answer, the probability is:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.05 + 0.13 + 0.45 = 0.68.

The events associated with at least two activities are given by:

X = 2, X = 3, X = 4.

P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.45 + 0.23 + 0.14 = 0.82.

The problem is missing, and is given by the image at the end of the answer.

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When the radius of the snowball is 4 and shrinks at a rate of 2 inches per hour then the rate of change of the surface area s is equal to 64π in²/hr

As the radius r is shrinking at the rate of two inches per hour, it can be represented as;

dr/dt = -2 in / hr

Here, the negative sign represents the shrinking of the snowball with time t.

The surface area of a sphere can be represented by the formula;

S = 4πr²

Now we differentiate S with respect to t by keeping radius (r) as a variable as follows;

dS/dt = d/dt (4πr²)

dS/dt = 4π (d/dt) (r²)

dS/dt = 4π × 2r (dr/dt)

Putting the value of r = 4 and calculated value of dr/dt = -2 in the equation as follows;

dS/dt = 4π × 2(4)(-2)

dS/dt = -64π

Therefore, the rate of change of surface area s is calculated to be 64π in²/hr.

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The second conditional statement is the converse of the first.

A conditional statement has two phrases and each phrase starts with an 'if' and the other with a 'then'.

Symbolically, it is also expressed as 'p ⇒ q'.

The converse of such a statement is expressed as 'q ⇒ p'.

The first conditional statement given is 'If Vivian is eating pizza, then she is at Big Slice Pizza.'

The second conditional statement given is 'If Vivian is at Big Slice Pizza, then she is eating pizza.'

From the definition of the converse of a conditional statement, the second statement is clearly the converse of the first statement.

Contrapositive of the conditional statement 'p ⇒ q ' is 'not q ⇒ not p'.

Inverse of the conditional statement  'p ⇒ q ' is 'not p ⇒ not q'

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She should try to stop the car.

We will discuss the possibilities of trying to stop and trying to speed up in 2s and find the distance she travels to get into a conclusion.

If she try to stop, then the acceleration, a = -5.8 m/s²

Initial velocity, v₀ = 12.5 m/s

Final velocity, v₁ = 0 m/s   [Since the car is stopped]

Let d be the distance the car travels before stopping.

Then, we have, v₁² = v₀² + 2ad

Therefore, d = v₁²-v₀²/2a

                     =  0-(12.5)²/2 x (-5.8)

                     = 156.25/11.6

                     = 13.47 m

So she can stop in time as she is 28m far from the beginning of the intersection.

If she try to speed up, then the acceleration of the car, a = 3.5 m/s²

Initial velocity of the car, v₀ = 12.5 m/s

Time she have, t = 2 s

Let d be the distance the car travels in 2 s.

Then, d = v₀t +(1/2)at²

            = 12.5 x 2 + (1/2) x 3.5 x 2²

            = 25 + 7

            = 32 m

She is 28 m before the beginning of the intersection which is 15 m wide. So if she speed up she will be in the middle of the intersection when the light turns red and may have to stop.

Hence as a legal driver, she should try to stop the car.

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Answer: ≈37.8 m

Step-by-step explanation:

The sum of the angles of a triangle is equal to 180°.

⇒ х+32°+83°=180°

х+115°=180°

x+115°-115°=180°-115°

x=65°

The sine theorem goes like this: the sides of a triangle are proportional to the sines of the opposing angles.

[tex]\displaystyle\\\frac{22}{sin32^0} =\frac{S}{sin65^0} \\\\Multiply\ both \ parts\ of \ the \ equation\ by\ sin65^0:\\\\S=\frac{22(sin65^0)}{sin32^0} \\\\S\approx\frac{22(0.91)}{0.53}\\\\ S\approx37.8 \ m[/tex]

Using the remainder theorem, the remainder of the divisions of p(x) = 4x³ + 6x² - 8x - 2 by the polynomials are given as follows:

Suppose that we have a polynomial p(x), that is divided by a linear term x - a, the remainder is given by the numeric value of p(x) at x = a, that is, p(a).

For this problem, the polynomial is given as follows:

p(x) = 4x³ + 6x² - 8x - 2.

Then the remainder for each division is given as follows:

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The value of m is 104/13

What is Fraction?

A fraction, which also symbolizes a piece of a whole, is a mathematical symbol for any number of equal parts. When expressed in common English, a fraction, such as 1/2, 8/5, or 3/4, represents the number of components of a specific size.

The value of m must be determined.

As can be seen in light of the query

The formula is m/4 = 26 / 13

The equation will now be solved for m m/4 = 26 / 13

The result of multiplying 4 on both sides is

(m/4) x 4 = (26/13) x 4

m = (26 x 4)/13

m = 104/13.

Consequently, m has a value of 104/13.

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