Question 4 (Essay Worth 10 points)
(04.05 MC)
The graph represents the journey of a bus from the bus stop to different locations:
Bus Journey
Distance
(miles)
Time (hours)
Part A: Use complete sentences to describe the motion of the bus in parts 1, 2, 3, 4, and 5 of the journey. (4 points)
Part B: In which parts of the graph is the function increasing, decreasing, and constant? (4 points)
Part C: Is the graph linear or non-linear? Explain your answer. (2 points)
5

Answer:

acute triangle

Step-by-step explanation:

because (12)^2 = 144 while [tex]8^{2}[/tex] + [tex]10^{2}[/tex] = 164 which means the sum of it's smaller angles are greater than it's greatest angle so it's an acute triangle

Answer:

take the two smaller sides, call them a and b. call the longest side c.

if a^2 + b2 = c^2 you have a right triangle

if < c^2 it's acute

if > c^2 it's obtuse

in addition, if you can find a,b,c such that

a=b=c it's equilateral

a=b≠c it's isosceles

a≠b≠c it's scalene

plug in your numbers and make your choice.

Step-by-step explanation:

Using it's concept, it is found that the probability that the customer also likes pie is of [tex]\frac{2}{7}[/tex]

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Researching the problem on the internet, it is found that of the 14 students that like cake, 4 also like pie, hence the probability is given by:

p = 4/14 = 2/7.

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Answer:

it's a i think

Step-by-step explanation:

Answer:

Zero

Step-by-step explanation:

Work done in the vertical direction is 0 because no displacement can be taken. Hence, the correct answer to this problem is zero

change (x,y) -> (-y,-x)

Answer:

6 meters × 4 meters = 24 square meters

Step-by-step explanation:

to find the area of a rectangle you do the length times the width

the length is 6m and the width is 4m so you times them together which gives you 24m²

Answer:

infinite number of solutions

Step-by-step explanation:

Given equations:

Rearrange the second equation to make y the subject:

⇒ -12x - 2y = -4

⇒ -12x - 2y + 2y = -4 + 2y

⇒ -12x = -4 + 2y

⇒ -12x + 4 = -4 + 2y + 4

⇒ -12x + 4 = 2y

⇒ (-12x + 4) ÷ 2 = 2y ÷ 2

⇒ y = -6x + 2

Comparing the rearranged equation with the first equation, we can see that both equations are the same.  

Therefore, as there is only one line, there are an infinite number of solutions.

Answer:

19/20

Step-by-step explanation:

380÷ 20= 19

400÷20= 20

Answer:

It's -3.125

Step-by-step explanation:

1/8 in decimal is 0.125

the 3 is a whole number so just put it in front.

Remember it's a negative, so you get:

-3.125

Answer:

-3.125

Step-by-step explanation:

- Multiply 3 and 8 to get 24. [tex]-\frac{24+1}{8}[/tex]

- Add 24 and 1 to get 25. [tex]-\frac{25}{8}[/tex]

- Turn [tex]-\frac{25}{8}[/tex] into a decimal to get -3.125

Using the tangent theorem and the inscribed angle theorem, the measure of angle YAC in the figure is: 70°.

The angle formed at the point of tangency of the radius and the tangent equals 90 degrees based on the tangent theorem.

According to the inscribed angle theorem, an inscribed angle equals the measure of the arc intercepted.

m∠BAY = 1/2(40) [inscribed angle theorem]

m∠BAY = 20°

m∠BAC = 90° [tangent theorem]

m∠YAC = 90 - 20

m∠YAC = 70°

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The time taken by the two men will be equal to 26 hours

The speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.

here two men are walking at different speeds like

v₁=6 miles per hour

v₂=10 miles per hour

The time taken by them to separated by the distance of 100 miles each so that both of them separated by the distance of 200 miles.

t₁= {100}/{6}=16.66 hours

t₂= {100}/{10}=10 hours

total time taken will be

t₁+t₂=16.66+10=26.66 hours

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14 and 15

which number multiplies to 14 and add up to 15.

[tex]1 + 14 = 15[/tex]

[tex]1 \times 14 = 14[/tex]

[tex] = 1[/tex]

therefore, the number which multiplies to 14 and add up to 15 is 1

= 1

because,

14×1 = 14

14+1= 15

The answer is B i hopes this helps

Answer:

F = 53.1°

Step-by-step explanation:

When you consider F as your angle

cos F = adjacent / hypotaneous

or, cos F = EF/DF

We do not have DF right now,

so DF² = DE² + EF²

DF = √ (12² + 9²)

DF = 15

cos F = adjacent / hypotaneous

or, cos F = EF/DF

cos F = 9 / 15

F = cos ⁻¹ (9/15)

F = 53.1°

The equation that can be solved when the given quadratic formula is used is c. 3x² + 8x − 10 = -8.

The given quadratic equation is:

x = (-8 ± √(8² - 4(3)(-2))) / 2 (3)

Rewriting the quadratic equation in option C gives:
3x² + 8x − 2 = 0

Seeing as a quadratic equation takes the form:

x = (-b ± √(b² - 4(a)(c))) / 2 (a)

The formula becomes:

x = (-8 ± √(8² - 4(3)(-2))) / 2 (3) which is the given quadratic formula.

In conclusion, option C is correct.

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Answer: D) 80 degrees

Step-by-step explanation:

Answer:

[tex]x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}[/tex]

Step-by-step explanation:

1) Move all terms to one side.

[tex]2x^{3} -x^{2} -3x-210=0[/tex]

2) Factor [tex]2{x}^{3}-{x}^{2}-3x-210[/tex] using Polynomial Division.

1 -  Factor the following.

[tex]2x^{3} -x^{2} -3x-210[/tex]

2 -  First, find all factors of the constant term 210.

[tex]1,2,3,4,5,6,7,10,14,15,21,30,35,42,70,105,210[/tex]

3) Try each factor above using the Remainder Theorem.

Substitute 1 into x. Since the result is not 0, x-1 is not a factor..

[tex]2*1^{3} -1^{2} -3*1-210=-212[/tex]

Substitute -1 into x. Since the result is not 0, x+1 is not a factor..

[tex]2(-1)^{3} -(-1)^{2} -3*-1-210=-210[/tex]

Substitute 2 into x. Since the result is not 0, x-2 is not a factor..

[tex]2*2^{3} -2^{2} -3*2-210=-204[/tex]

Substitute -2 into x. Since the result is not 0, x+2 is not a factor..

[tex]2{(-2)}^{3}-{(-2)}^{2}-3\times -2-210 = -224[/tex]

Substitute 3 into x. Since the result is not 0, x-3 is not a factor..

[tex]2\times {3}^{3}-{3}^{2}-3\times 3-210 = -174[/tex]

Substitute -3 into x. Since the result is not 0, x+3 is not a factor..

[tex]2{(-3)}^{3}-{(-3)}^{2}-3\times -3-210 = -264[/tex]

Substitute 5 into x. Since the result is 0, x-5 is a factor..

[tex]2\times {5}^{3}-{5}^{2}-3\times 5-210 =0[/tex]

------------------------------------------------------------------------------------------

⇒ [tex]x-5[/tex]

4)  Polynomial Division: Divide [tex]2{x}^{3}-{x}^{2}-3x-210[/tex]  by [tex]x-5[/tex].

                                               [tex]2x^{2}[/tex]                       [tex]9x[/tex]                      [tex]42[/tex]

                                      -------------------------------------------------------------------------

[tex]x-5[/tex]                               |    [tex]2x^{3}[/tex]                          [tex]-x^{2}[/tex]                     [tex]-3x[/tex]     [tex]-210[/tex]

                                           [tex]2x^{3}[/tex]                             [tex]-10x^{2}[/tex]

                                        -----------------------------------------------------------------------

                                                                             [tex]9x^{2}[/tex]                [tex]-3x[/tex]       [tex]-210[/tex]

                                     --------------------------------------------------------------------------

                                                                          [tex]42x[/tex]                              [tex]-210[/tex]

                                                                         [tex]42x[/tex]                               [tex]-210[/tex]

                                      -------------------------------------------------------------------------

5)  Rewrite the expression using the above.

[tex]2x^2+9x+42[/tex]

[tex](2x^2+9x+42)(x-5)=0[/tex]

3) Solve for [tex]x.[/tex]

[tex]x=5[/tex]

4)  Use the Quadratic Formula.

1 - In general, given [tex]a{x}^{2}+bx+c=0[/tex] , there exists two solutions where:

[tex]x=\frac{-b+\sqrt{b^{2} -4ac} }{2a} ,\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]

2 -  In this case, [tex]a=2,b=9[/tex] and [tex]c = 42.[/tex]

[tex]x=\frac{-9+\sqrt{9^2*-4*2*42} }{2*2} ,\frac{-9-\sqrt{9^2-4*2*42} }{2*2}[/tex]

3 - Simplify.

[tex]x=\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}[/tex]

5) Collect all solutions from the previous steps.

[tex]x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}[/tex]

Answer:

f(x) = -1/2x + 8

or

The first one

Step-by-step explanation:

hope this helps

have a good day

Answer:

slope = - 4

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, - 9 ) and (x₂, y₂ ) = 1, 3 )

m = [tex]\frac{3-(-9)}{1-4}[/tex] = [tex]\frac{3+9}{-3}[/tex] = [tex]\frac{12}{-3}[/tex] = - 4

Answer:

[tex]m=-4[/tex]; the slope is -4

Step-by-step explanation:

[tex]slope=\frac{rise}{run} =\frac{y^2-y^1}{x^2-x^1}[/tex]

coordinates: (4,-9) (1,3)

[tex]\frac{3-(-9)}{1-4}=\frac{-12}{-3} =-4[/tex]

= -4 is your answer

hope this helped

~rere

Answer: Heyaa! ~

772 divided by 9 is... 80.2

Step-by-step explanation:

Lets solve! ~

Hopefully this helps you! ^^

Check the picture below.

The expressions that are differences of perfect cubes from the options given are:

c. 216a⁶ - 27y³

d. 8a¹⁵ - 27

A perfect cube can be described as a number that is gotten when an integer is multiplied by itself three times.

216a⁶ - 27y³ is a difference of perfect cubes because: (6a²)³ - (3y)³.

So also is the expression, 8a¹⁵ - 27.

The difference of perfect cubes are:

c. 216a⁶ - 27y³

d. 8a¹⁵ - 27

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Answer:

C 216a6 - 27y3

D 216a6 - 27y3

Step-by-step explanation:

I took the test on edge. :)

Answer:

your answer is 10 Goodluck

Answer:

2/9

Step-by-step explanation:

i just took a test with this exact question, and the answer was 2/9

youre welcome future learners ;)

Answer:

y²+x-7=-x+37

Step-by-step explanation:

im a pickle morty its the funniest thing ive ever experienced

Answer:

A

Step-by-step explanation:

The right angle triangle has an angle that is 90° while the other angles makes up 90° too.

Your information is incomplete. Therefore, an overview of right angle triangle will be given. It should be noted that a right angle triangle simply means a triangle that has aright angle which is 90°.

The hypothenuse is the longest side in a right angle triangle which is the side facing the 90°.

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