2. Abby, Chantral, Dougie, Kajan, Minh, and
Zara are all in a race and are considered
to be equally fast. What is the probability
that Abby and Chantral will be the first two
finishers?
1414

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{2}}x-6\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so for a perpendicular line to that one then

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{1}\implies -2}}[/tex]

so we're really looking for the equation of a line whose slope is -2 and that it passes through (2 , -1)

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-1})\hspace{10em} \stackrel{slope}{m} ~=~ - 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{- 2}(x-\stackrel{x_1}{2}) \implies y +1= -2 (x -2) \\\\\\ y+1=-2x+4\implies {\LARGE \begin{array}{llll} y=-2x+3 \end{array}}[/tex]

The interval in which the function has positive average rate of change is x > √3

The function is given as

f(x) = x^3 - 9x

Differentiate the above function to determine the average rate of change

So, we have

f'(x) = 3x^2 - 9

Set the function to greater than 0

So, we have

3x^2 - 9 > 0

Add 9 to both sides

3x^2 > 9

Divide by 3

x^2 > 3

Take the square root of both sides

x > √3

Hence, the interval in which the function has positive average rate of change is x > √3

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Answer:

the numbers are 27,28

Step-by-step explanation:

Let the numbers be x,x+1

The sum is 55

⟹x+x+1=55

2x+1=55

2x+54

x=27

So the numbers are 27,28

It should be noted that the slope shows that the rate of change in elevation rise at first but later reduced.

The total change in elevation is 10500 feet

It should be noted that from the table, the time and the elevation has been given.

Therefore, the total elevation will be the addition of all the values given. This will be 10500 feet.

Also, the slope shows that the rate of change in elevation rise at first but later reduced.

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Answer: ob false

Step-by-step explanation: look at a calculator and it will show 8 is not a 5 is not 8 times five is 40 hope this helps

The required factors of the expression, 4x² - 9 are 4, x, x, -3, 3.

What are the factors of an expression?

Any number or expression that completely divides another number or expression is called as the factor of an expression. These can be positive or negative depending upon the given expression.

Calculating the factor of expression. 4x² - 9

Given an expression, 4x² - 9

Terms of an expression are 4x², - 9

Further breaking the terms to factors, we obtain,

4, x, x, -3, 3

Hence, the required factors of the expression, 4x² - 9 are 4, x, x, -3, 3.

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Answer:

F

Step-by-step explanation:

using the cosine ratio in the right triangle and the exact value

cos45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{s}{6}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )

2s = 6[tex]\sqrt{2}[/tex] ( divide both sides by 2 )

s = 3[tex]\sqrt{2}[/tex]

The length of side s in the given square is 3√2 units. Therefore, option F is the correct answer.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

From the given square, each sides measures s units and the diagonal measures 6 units.

We know that, sinθ=Opposite/Hypotenuse

Now, sin45°=s/6

1/√2 =s/6

s=6/√2

s=3√2

Therefore, option F is the correct answer.

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Answer:

Hello! Here's the correct answer to your question:)

5y+23

7x +2y= -17 is the result of adding these two equations 2x+3y=-5 and 5z-y = -12

What is equation ?

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc.

given equations

2x+3y=-5

5z-y = -12

we have to add these two equations

Add 2x and 5x to get 7x

Add the y's

3y + (-1y)  OR 3y - y      

Which gives you 2y

add the (-5 and -12)

-12 + (-5) or -12 - 5 giving you -15

7x+2y=-17

Hence ,7x +2y= -17 is the result of adding these two equations 2x+3y=-5 and 5z-y = -12

the complete question is

What is the result of adding these two equations?

2x+3y= -5

5x - y = - 12

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Answer:

155 degrees

Step-by-step explanation:

It is halfway in between the 150 and 160 marks.

Answer:

Step-by-step explanation:

Answer: $43.33

Solution:

Sale price = Original Price x 1.20(discount)

Original price = Sales Price divided by discount

Therefore:

Original price = $52 / 1.2 = $43.33 dollars (just round)

Answer:

y = (1/6)x - 11

Step-by-step explanation:

y = (1/6)x + 7; Point: (12, -9)

                                 (x₁, y₁)

y - y₁ = m (x - x₁)

y - (-9) = (1/6) (x - 12)

y + 9 = (1/6)x - 2

    -9              -9

y = (1/6)x - 11

I hope this helps!

The area that can be watered by the pipe of length 500 inches is approximately 18.03 square yards, when the length of the pipe is 800 inches the area watered is approximately 46.16 square yards and when the length of pipe is 1300 inches the area watered is approximately 121.89 square yards as calculated by the given function.

A function is defined as a relation between the dependent variable and the independent variable.

The length of the pipe is given by the function L=117.75√A where A is the area of the lawn that can be watered.

Now to calculate the area that can be watered using a particular length of pipe we have to find the inverse of the given function.

Given L=117.75√A

Squaring both sides we get

L²=13865.0625 × A

or , A=L²÷13865.0625

Now given length L=500 inches

Substituting the values we get:

A=(500)²÷13865.0625

A=18.0309...

A≈18.03 square yards

Hence the area that can be watered is approximately 64.68 square yards.

Similarly for length 800 inches

Area watered= (800)²÷13865.0625=46.159 square yards.

≈46.16 square yards

Similarly for length 1300 inches

Area watered=1300²÷13865.0625=121.889 square yards

≈121.89 square yards

Therefore the area that can be watered by the pipe of length 500 inches is approximately 18.03 square yards, when the length of the pipe is 800 inches the area watered is 46.16 square yards and when the length of pipe is 1300 inches the area watered is 121.89 square yards.

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Answer:

a. -5 b. 23 c. 871 d. -5

Step-by-step explanation:

f(x) = x^2 + 6x and g(x) = x - 4

a). (fog)(3) = (x - 4)^2 + 6(x - 4)

= (3 - 4)^2 + 6(-1)

= 1 -6

= -5

b). (gof)(3) = ( x^2 + 6x) - 4

= (9 + 18) - 4

= 23

c). (fof)(3) = (x^2 + 6x)^2 + 6(x^2 + 6x)

= 27^2 + 27(6)

= 871

d). (gog)(3) = (x - 4) -4

= (3 - 4) - 4

= -5

Answer:

Step-by-step explanation:

a. 4.2-2.8= 1.4

b. 72.1-45.6=26.5

c. 82.2-41.3-29.2=11.7

d.17.1-11.7-0.8=4.6

e.29.2-12.5-0.9=15.8

Answer: A. 1.428, B. 26.41, C. 11.686, D. 4.574, E. 15.77

Step-by-step explanation: These are the answers for all of them

Based on the exterior angle theorem, an expression that can be used to find the measure of angle 4 is:

m∠1 + m∠2 = m∠4.

The exterior angle theorem is a theorem that states that the sum of the measures of two opposite interior angles is equal to the measure of an exterior angle of the triangle.

For example, if c is an exterior angle of a triangle, and a and b are the two interior angles that are opposite to c, the exterior angle theorem states that: a + b = c.

Angle 1 and angle 2 are interior angles of the triangle in the diagram which are opposite to angle 4.

Therefore, based on the exterior angle theorem, an expression that can be used to find the measure of angle 4 is:

m∠1 + m∠2 = m∠4.

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[tex]\textit{since the roots are }-2\pm \sqrt{3}\implies \begin{cases} x=-2 + \sqrt{3}\implies&x+2-\sqrt{3}=0\\\\ x=-2 - \sqrt{3}\implies&x+2+\sqrt{3}=0 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]( ~~ x+2-\sqrt{3} ~~ )( ~~ x+2+\sqrt{3} ~~ )=\stackrel{y}{0} \\\\\\ \underset{\textit{difference of squares}}{( ~~ \underline{(x+2)}-\sqrt{3} ~~ )( ~~ \underline{(x+2)}+\sqrt{3} ~~ )}=y\implies (x+2)^2~~ - ~~(\sqrt{3})^2~~ = ~~y \\\\\\ (\stackrel{F~O~I~L}{x^2+4x+4})~~ - ~~(3)~~ = ~~y\implies {\LARGE \begin{array}{llll} x^2+4x+1=y \end{array}}[/tex]

Answer: 27

Step-by-step explanation:

An expression which is represented by the diagram (see attachment) is: A. -6 - (-1).

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

By critically observing the diagram (see attachment), we can logically deduce the following information:

In this context, we can the diagram (see attachment) by using the following expression:

-6 - (-1)

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the real roots are

y=0

x=3

x=4

therefore two rational roots (A)

The results of the composition of two functions are listed below:

Let f and g be functions, with which we are asked to find the expressions of composite functions, where the input of one of the functions is substituted by the other function. The operation of composition is defined below:

f ° g (x) = f [g (x)]    

If we know that f(x) = x + 1 and g(x) = 2 · x + 5, then the resulting expression are shown below:

a) f ° g (x) = f [g (x)]

f ° g (x) = (2 · x + 5) + 1

f ° g (x) = 2 · x + 6

b) g ° f (x) = g [h (x)]

g ° f(x) = 2 · (x + 1) + 5

g ° f (x) = 2 · x + 7

c) f ° g (- 1) = f [g (- 1)]

f ° g (- 1) = 2 · (- 1) + 6

f ° g (- 1) = 4

d) g ° f (- 1) = g [f (- 1)]

g ° f (- 1) = 2 · (- 1) + 7

g ° f(- 1) = 5

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The linear equation that we want to graph is:

y = (2/3)*x - 9

And its graph can be sen at the end of the answer.

First, we need to find the linear equation. We know that it passes through the point (6, - 5) and it has a slope of (2/3), then we can write:

y = (2/3)*x + b

To find the value of b, the y-intercept, we replace the values of the point:

-5 = (2/3)*6 + b

-5 = 4 + b

-5 - 4= b = -9

The linear equation is:

y = (2/3)*x - 9

And its graph can be seen in the image below:

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Answer:

63 3/4

Step-by-step explanation:

First:

convert any mixed numbers to fractions.

Then your initial equation becomes:

17/2 ÷ 2/15

Applying the fractions formula for divison,

= 17/2×15/2

= 255/4

Simplifying 255/4, the answer is = 63 3/4.

Hope this helps :)

Answer:

63.9

Step-by-Step Expectation:

8.5/0.133=63.9

Answer:

C

Step-by-step explanation:

Speed is distance/time. We can solve for the highest speed by looking at each spot on the graph.

In a, the highest speed is 7/1, or 7. In b, it's 30/4, or 7.5. In c, it's 60/7, or about 8.57. In D, it's about the same, but since it's decreasing drastically, it will go to C.

Answer:

the person was moving the highest at C

since speed=gradient in distance time graphs so if you find each gradient c will be the highest being 30m/h while point A was 7.5m/h, b was stationery and point d was -20m/h, negative means it's decelerating. you could also guess that C has the highest speed since its the steepest line out of them all.

The number of cycles of the periodic function is 3.75 cycles if the period of a periodic function is 8 s option (G) 3.75 is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The period of a periodic function is 8 s

From the question:

8n = 30

n = 30/8

n = 3.75 cycles

Thus, the number of cycles of the periodic function is 3.75 cycles if the  period of a periodic function is 8 s option (G) 3.75 is correct.

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The inverse of [tex]f(x) = \sqrt{x - 4}[/tex] is [tex]f^{-1}(x) = x^{2} +4[/tex] that is option G) is correct

According to the question we have been given the function which is :

                  [tex]f(x) = \sqrt{x - 4}[/tex]

To find the inverse of this function we will solve this step by step

First we will convert it into equation form

    [tex]y = \sqrt{x - 4}[/tex]

Then we will interchange the variables x and y

 [tex]x = \sqrt{y - 4}[/tex]

Then we will solve for y, we get

Taking square on both sides of the equation, we get

[tex]x^{2} = y - 4[/tex]

[tex]y = x^{2} + 4[/tex]

Now replacing variable y with [tex]f^{-1} (x)[/tex] , we get

[tex]f^{-1}(x)[/tex] = [tex]x^{2} +4[/tex]

Thus the inverse of [tex]f(x) = \sqrt{x -4}[/tex] is [tex]f^{-1} = x^{2} +4[/tex] that is option G) is correct

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Answer:

y=2x+25

Step-by-step explanation:

please if you like the answer rate it 5 stars and mark as brainliest

The area of a rectangular flower garden is 25/16

the area of the rectangular garden is =length x width

 given,

length=5/8

width=2 1/2

area = l x b

       =5/8 x 2 1/2

        = 25/16

To find the area of a rectangle, multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area. This is the same as saying length2 or length squared.

Area is the amount of space that a flat, 2D object takes up. Area is measured in square units, like square feet or square meters.

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The area of a rectangular flower garden is 25/16 .

Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

To find the area of a rectangle, multiply its height by its width.

The area of the rectangular garden is =length x width

Given that: length=5/8

width=2 1/2

Area = l x b

        =5/8 x 2 1/2

        = 25/16

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Answer:

-2x2 - 50

Step-by-step explanation:

First, you collect the like terms:

x2 - 3x2 + 5 x -8 -10

Do multiplication first:

x2 - 3x2 + (-40) - 10

Combine the terms:

-2x2 - 50

Answer:

5 star of you

Step-by-step explanation:

you are cool dictator