Segment AC has a length of 60. Find the following values.

Given the distance and average speed, the runner will take approximately 2.76 hours to complete the marathon.

Speed is simply distance traveled per unit time.

Speed = distance / time

Given the data in the question;

First, convert the unit of distance from miles to meter.

Distance = 26.2 miles = ( 26.2 × 1609.34 )m = 42164.708m

Now, plug the values into the equation and solve for time.

Speed = distance / time

4.25m/s = 42164.708m / time

Time = 42164.708m ÷ 4.25m/s

Time = 9921.1077647s

Next, convert to hours,

Time = 9921.1077647 ÷ ( 60 × 60 )

Time = 9921.1077647 ÷ 3600

Time = 2.76 hours

Given the distance and average speed, the runner will take approximately 2.76 hours to complete the marathon.

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∠24°

What is an inscribed angle in a circle?

Inscribed angles are angles whose vertices are on a circle and that intersect an arc on the circle. The measure of an inscribed angle is half of the measure of the intercepted arc and half the measure of the central angle intersecting the same arc.

given that intercepted arc = ∠48°

The intercepted arc is the arc that is inside the inscribed angle and whose endpoints are on the angle.

If the intercepted arc is twice the size of the inscribed angle, then the inscribed angle is half the size of the intercepted arc. So if the intercepted arc is 48 degrees, the inscribed angle is 48 / 2 = 24 degrees.

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The property of real numbers that was applied in the equation, 3.8+(−4.8+(−6.2))=(3.8+(−4.8))+(−6.2), is known as the: distribution property of multiplication.

The distribution property of multiplication is one of the properties of real numbers which states that, given that a(c + d), then we would have:

a(c) + a(d) = ac + ad.

Given the expression, 3.8+(−4.8+(−6.2)), applying the distribution property of multiplication will give us:

(3.8+(−4.8))+(−6.2).

Therefore, the property of real numbers that was applied in the equation, 3.8+(−4.8+(−6.2))=(3.8+(−4.8))+(−6.2), is known as the: distribution property of multiplication.

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Answer: -r(8r^3-2r-3)

Step-by-step explanation:

Step-by-step explanation:

the line equation is in the slope-intercept form.

that looks like

y = ax + b

"a" is the slope (always the factor of x). "b" is the y-intercept (the y value when x = 0).

so, when it says "the same slope", we know we have to use the same factor of x.

and yes, the coordinates of a point are (x, y). so, you really need to use it in the places of x and y to get "b".

9.

y = -4x + b

2 = -4×0 + b = b

so, yes, the equation is

y = -4x + 2

but as you can see : b is NOT y in general.

10.

y = 2/3 x + b

-1 = 2/3 × 4 + b = 8/3 + b

now, let's multiply both sides by 3 to get rid of the fraction :

-3 = 8 + 3b

-11 = 3b

b = -11/3

so, the equation is

y = 2/3 x - 11/3

or

y = 1/3 × (2x - 11)

Answer:

11

Step-by-step explanation:

90=55+3e+2

33=3e

e=11

The measure of angles are

i) Angle ABD = 67°

ii) Angle CBD = 67°

iii) Angle ABC = 134°

We have been given that ray BD bisects angle ABC and also

Angle ABC = (25x+34)°

Angle CBD = (11x + 23)°

Note that angle ABC = angle ABD + angle CBD          (1)

And angle ABD = angle CBD = (11x + 23)° as it is bisected into two equal half.

Therefore putting the required values of angle in equation (1) we get

          (25x+34)° = 2(11x+23)°

           25x+34 = 22x+46

           25x – 22x = 46 – 34

                3x = 12

                  x = 4

Hence,   angle ABD = (11*4 + 23) ° = 44+23 = 67°

               Angle CBD = (11*4 + 23) ° = 44+23 = 67°

               angle ABC = (25*4 + 34)° = 100+34 = 134°

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Answer:

breakeven point,

Step-by-step explanation:

answer is -1 < x < 5

-|x - 2|+ 9 > 6

Rearrange the terms

-|x - 2| > 6 - 9

-|x - 2| > - 3

then divide both sides of the inequality by the co- efficient of variable

|x - 2| < 3

convert the absolute inequality to standard inequality

-3 <x - 2 < 3

separate compound inequalities into system of inequality

{x - 2}> -3

{x - 2 < 3}

Rearrange variable to the left side of the equation

x > -3 + 2                    

calculate the sum or difference

x > -1

x -2 < 3

Rearrange variable to the left side of the equation

x < 3 + 2

calculate the sum or difference

x < 5

x > -1 and x < 5

Find intersection

-1 < x < 5

Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol =. Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

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Answer:

For f (x):

f (x) = (x + 3) ^ 2 - 2

For x = -1

f (-1) = (-1 + 3) ^ 2 - 2

f (-1) = (2) ^ 2 - 2

f (-1) = 4 - 2

f (-1) = 2

For x = 3

f (3) = (3 + 3) ^ 2 - 2

f (3) = (6) ^ 2 - 2

f (3) = 36 - 2

f (3) = 34

AVR = ((34) - (2)) / ((3) - (- 1))

AVR = 8

For g (x):

linear graph with and intercept of negative 3 over 2 and x intercept of 3

y = mx + b

b = -3/2

For me we have:

0 = m (3) - 3/2

3m = 3/2

m = 1/2

The function g (x) is:

g (x) = (1/2) x - 3/2

For x = -1

g (-1) = (1/2) (- 1) - 3/2

g (-1) = -1/2 - 3/2

g (-1) = -4/2

g (-1) = -2

For x = 3

g (3) = (1/2) (3) - 3/2

g (3) = 3/2 - 3/2

g (3) = 0

AVR = ((0) - (- 2)) / ((3) - (- 1))

AVR = 1/2

For h (x):

Using the table we have:

AVR = ((62) - (14)) / ((3) - (- 1))

AVR = 12

Step-by-step explanation:

Answer:

from least to greatest:

1) g (x)

2) f (x)

3) h (x)

Step-by-step explanation:

There will be only 6  cubes with only one side painted red.

Cube : A cube is a 3D shape having 6 equal square sides. it has 6 faces , 8 vertices and 12 edges.

According to the question

A 3 cm cube is divided into one centimeter cube.

Every face will have 9 cube each and from that 9 cube there will be only one 1 cube that will have one side painted red.

Since there are 6 faces,

cubes painted one side red = 6x1=6.

Therefore , There will be only 6  cubes with only one side painted red.

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The product in scientific notation is 1.36 x 10^22

The product expression is given as:

3.2 x 1012 and 4.25 x 109

Express the product, properly

3.2 x 10^12 x 4.25 x 10^9

Regroup the factors

3.2  x 4.25 x 10^12 x 10^9

Evaluate the product

13.6 x 10^21

Rewrite as:

1.36 x 10^22

Hence, the product in scientific notation is 1.36 x 10^22

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Answer:

c 1.36 x 1012

explanation:

Probability are important information when applying descriptive statistics. Probability is the branch of mathematics concerning numerical descriptions. the correct option is (B).

Descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur.

here, we have,

A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).

The probability formula defines the likelihood of the happening of an event. It is the ratio of favorable outcomes to the total favorable outcomes. The probability formula can be expressed as,

Probability formula:

P(A) = Probability(Event) = Favorable Outcomes/Total Outcomes

P(A) =   x/n

where,

P(B) is the probability of an event 'B'.

n(B) is the number of favorable outcomes of an event 'B'.

n(S) is the total number of events occurring in a sample space

Descriptive statistics are brief informational coefficients that summarize a given data set, which can be either a representation of the entire population or a sample of a population. Descriptive statistics are broken down into measures of central tendency and measures of variability (spread). Measures of central tendency include the mean, median, and mode, while measures of variability include standard deviation, variance, minimum and maximum variables, kurtosis, and skewness.

The main purpose of descriptive statistics is to provide information about a data set. In the example above, there are hundreds of baseballs players that engage in thousands of games. Descriptive statistics summarizes the large amount of data into several useful bits of information.

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Answer:

1/3

Step-by-step explanation:

Gradient or slope can be found using the point-slope formula:

[tex]y-y_{1} =m(x-x_{1} )[/tex]

We can rearrange the equation to find slope (m) like so:

[tex]m=\frac{y-y_{1} }{x-x_{1} }[/tex]

To use this formula we need to find two well-defined points and use their coordinates.

Let's use (0,2) and (3,3) because they are clear points on the graph.

(0,2) will represent [tex]x[/tex] and [tex]y[/tex] in the equation respectively, and (3,3) our other point will represent [tex]x_{1}[/tex] and [tex]y_{1}[/tex].

Now we just need to plug the numbers into the equation:

[tex]m=\frac{2-3}{0-3} \\\\m=\frac{-1}{-3} \\m=\frac{1}{3}[/tex]

The gradient of the graph is 1/3.

Hope this helped!

Answer:

91/7=13

so x=11×13

x=143

Step-by-step explanation:

= -7ab² + 9a³b

= -7b × ab + 9a² × ab

= ab × (-7b + 9a²)

Answer: Ok I don’t have the answer but I have an example!

Step-by-step explanation: Solve for x and check: x + 5 = 3. Solution.

I hope this help maybe it might or might not give you the answer for your question I tried. ✨I hope this help!✨

Answer: The value of (1 + sin 8)(1-sin 8) (1 + cos 0) (1 - cos8) =0.2086

and [tex]cot^{1}[/tex]θ=7/8

Step-by-step explanation:

Let base and height of a triangle be 7k and 8k

By applying Pythagoras theorem in Δ ABC, we get

[tex]AC^{2} = AB^{2} +BC^{2}[/tex]

= (7k)2 + (8k)2

= 49k2 + 64k2

= 113k2

AC = √113k2

= √113k

so hypotenuse =[tex]\sqrt{133}k[/tex];

now ;

=(1 + sin θ) (1 - sin θ)(1 + cos θ) (1 - cos θ)[since : (a + b)(a - b) = (a2 - b2)]

=(1 - [tex]sin^{2}[/tex]θ)(1 - [tex]cos^{2}[/tex]θ)

=[1 - (8/√113)2] [1 - (7/√113)2]

= (1 - 64/113) (1 - 49/113)

= (49/113) (64/113)

= 0.2086

hence;

The value of (1 + sin 8)(1-sin 8) (1 + cos 0) (1 - cos8) =0.2086

and [tex]cot^{1}[/tex]θ=7/8

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Answer:

Step-by-step explanation:We will use the basic concepts of trigonometric ratios to solve the problem.

Consider ΔABC as shown below where angle B is a right angle.

If cot θ = 7/8, evaluate: (i) (1 + sin θ)(1 - sin θ) / (1 + cos θ)(1- cos θ), (ii) cot²θ

cot θ = side adjacent to θ / side opposite to θ = AB/BC = 7/8

Let AB = 7k and BC = 8k, where k is a positive integer.

By applying Pythagoras theorem in Δ ABC, we get

AC2 = AB2 + BC2

= (7k)2 + (8k)2

= 49k2 + 64k2

= 113k2

AC = √113k2

= √113k

Therefore, sin θ = side opposite to θ / hypotenuse = BC/AC = 8k/√113k = 8/√113

cos θ = side adjacent to θ / hypotenuse = AB/AC = 7k/√113k = 7/√113

(i) (1 + sin θ) (1 - sin θ) / (1 + cos θ) (1 - cos θ) = 1 - sin2θ / 1 - cos2θ  [Since, (a + b)(a - b) = (a2 - b2)]

= [1 - (8/√113)2] / [1 - (7/√113)2]

= (1 - 64/113) / (1 - 49/113)

= (49/113) / (64/113)

(ii) cotФ≈

= 49/64

Answer:

2

Step-by-step explanation:

Because 2 goes into 24, 36 and 50.

Answer: 19

Step-by-step explanation:

2+1+1+12+3=19

Answer:

2

-

2 - 4 ^ 5

Step-by-step explanation:

Dividing the number 5 by 4 gives a rational number 5/4.

The word 'rational' comes from the word 'ratio.'

For the given expression;

When 5 is divided by the number 4, 4 will not completely divide the number 5 as 5 is not the multiple of 4.

Thus, dividing 5 by 4 gives the rational number 5/4.

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Answer:

B

Step-by-step explanation:

The slope of a line is written as a fraction of the vertical distance to the horizontal distance. The line drops down from (0,1) to (4,-2). This is a vertical distance of -3 and a horizontal distance of 4. The slope if the fraction -3/4.

Answer:

[tex] \sf \: b) \: \frac{ - 3 \: }{ 4} [/tex]

Step-by-step explanation:

The coordinates are,

→ x1 = 4, y1 = -2

→ x2 = -4, y2 = 4

Formula we use,

→ Slope(m) = (y2 - y1)/(x2 - x1)

Now the required slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (4 -(-2))/(-4 - 4)

→ m = (4 + 2)/-8

→ m = 6/-8

→ [ m = -3/4 ]

Hence, the option (b) is correct.

Answer:

The and is –6

Step-by-step explanation:

–2A= –2[0 , –6]

2B= 2[–8 , –1]

–2A= –2 [0 , +12]

2B= 2[–16 , –2]

–2A + 2B=[0 ,12] + [–16 ,–2]

=[0+(–16) + 12+(–2)]

=[0–16+12–2]

= –16+10

= –6.

Hope it was helpful

Answer:

A.

Step-by-step explanation:

In the 2nd Quadrant, the y is POS and the x is NEG. That's what will happen if reflected from the 1st Quadrant over the Y axis.

Answer: A

Step-by-step explanation:

The price of a clematis vine, rose bush, and peony plant is given by a set of three linear equations with three variables: 29, 14, 13.

A linear equation is one that has a degree of 1 as its maximum value .In a linear equation, no variable has an exponent bigger than 1, thus.. A linear equation's graph will always be a straight line.

An algebraic equation known as a linear equation has an exponent of 1 for each term, and when it is graphed, it always yields a straight line.

According to given data;

let c is price of clematis vine

let r is price of rose

P is price of peony plants.

bush

c=2p+3

r=c+5+

=3c + 4r+ 2p = 233

b) putting(1) in 2

a 2p+ 3 + 5 2 p +8 -9 putting(1) and (4)in 3

3(2p+3)+4(2p+8) + 2 p² 233

2

6p+9+8p+16+2p = 233

16p=25=233

16 p= 233-25

16p = 208

p=208÷13

p= 13

putting value of p in (1)and(4)

c= 2 p +3

=2X13+3

C = 29

r= 2p+8

 =2×13+8

 =34

price of clematis vines =29

rose bush = 34.

peony plants = 13.

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Answer:

[tex]e=\frac{-5e-90}{216}[/tex]

Step-by-step explanation:

[tex]\frac{2}{5}d+\frac{4}{9}e=-2d+\frac{7}{18}e-1[/tex]
[tex]\frac{2}{5}d+\frac{4e}{9}=-2d+\frac{7}{18}e-1 < - Muiltiply[/tex]
[tex]\frac{2}{5}d+\frac{4e}{9}=-2d+\frac{7e}{18}- < - Muiltiply Again\\[/tex]
[tex]\frac{2}{5}d+\frac{4e}{9}-\frac{4e}{9}=-2d+\frac{7e}{18}-1-\frac{4e}{9} < - Subtract BothSides[/tex]
[tex]\frac{2}{5}d=-2d-\frac{e}{18}-1 < - Simplify[/tex]
[tex]\frac{2}{5}d+2d=-2d-\frac{e}{18}-1+2d < - AddToBothSides[/tex]
[tex]\frac{12}{5}d=-\frac{e}{18}-1 < - Simplify[/tex][tex]\frac{12d}{12}=-\frac{\frac{5e}{18}}{12}-\frac{5}{12} < - DivideBothSides[/tex]
[tex]e=\frac{-5e-90}{216}[/tex]

Answer:

(-5,3)

Step-by-step explanation:

That's the coordinates of it being reflected over X axis for point P.