Question 4 (Essay Worth 10 points)

(05.06 MC)

The distance, y, in centimeters, of an ant from a hole in the tree for a certain amount of time, x, in seconds, is shown in the graph:

A graph titled Motion of Ant is shown. The graph shows time in seconds on the x-axis and the Distance from Hole in centimeters on the y-axis. The scale on the x-axis is shown from 0 to 7 at increments of 1, and the scale on the y-axis is shown from 0 to 24 at increments of 4. The graph has 3 straight lines. The first line is labeled A and joins ordered pairs 0, 0 and 2, 16. The second line is labeled B and joins ordered pairs 2, 16 and 4, 16. The third line is labeled C and joins ordered pairs 4, 16 and 6, 0.

Part A: Is the graph linear or nonlinear? Explain your answer. (2 points)
Part B: In which segments is the graph increasing, decreasing, and constant? (3 points)
Part C: In your own words, describe the motion of the ant, as shown on the graph. (5 points)

Source
StylesFormat

Answer:

Step-by-step explanation:

Let the number is in the form of aabb.

We can put it as:

The number is a perfect square so it must be divisible by 11.

It is divisible by 11 if (a + b) is divisible by 11..

On the other hand, b = 0, 1, 4, 5, 6, 9 as the last digit of a perfect square.

Also, both a and b must be within (0,9) interval.

Considering the above conditions we have options:

The numbers are:

By testing we confirm only one of them is a perfect square:

9514 1404 393

Answer:

  8

Step-by-step explanation:

The matrix being multiplied is the same in all cases, so we can "collect terms" in the usual way.

  3A +5A = (3+5)A = 8A . . . . . . where A represents the 2×2 matrix

The missing number is 8.

Step-by-step explanation:

[tex]area \: of \: a \: triangle = \frac{1}{2} \times base \times height \\ \\ base = \frac{a}{2} cm \\ {h}^{2} + {( \frac{a}{2} )}^{2} = {a}^{2} \\ \\ h = \sqrt{ {a}^{2} - \frac{ {a}^{2} }{4} } \\ \\ area \: of \: triangle = \frac{1}{2} \times b \times h \\ = \frac{1}{2} \times \frac{a}{2} \times \sqrt{ {a}^{2} - \frac{ {a}^{2} }{4} } \\ \\ = \frac{a}{4} \times \sqrt{ {a}^{2} - \frac{ {a}^{2} }{4} } [/tex]

Answer:

Option a, 13

if you solve it, you get 13 as the answer

³√(5x-1)=4

or, 5x-1=64

or, 5x=65

or, x=13

Answer:

85 minutes

Step-by-step explanation:

425/50=8.5 10 minute increments

8.5*10= 85 minutes

Answer:

∠ ELM = 149°

Step-by-step explanation:

∠ KLM = ∠ KLE + ∠ ELM  , substitute values

17x - 1 = 20 + 15x - 1

17x - 1 = 15x + 19 ( subtract 15x from both sides )

2x - 1 = 19 ( add 1 to both sides  )

2x = 20 ( divide both sides by 2 )

x = 10

Then

∠ ELM = 15x - 1 = 15(10) - 1 = 150 - 1 = 149°

=========================================================

Work Shown:

SA = surface area of the rectangular prism (aka block or box)

SA = 2*(LW + LH + WH)

SA = 2*(8*3 + 8*1 + 3*1)

SA = 2*(24 + 8 + 3)

SA = 2*(35)

SA = 70 square feet

This is the amount of wrapping paper you would need to cover all six sides of the box. This assumes that there are no gaps or overlaps.

Answer:

Its 2.5 percent ladd enjoy

Step-by-step explanation:

Answer:

2 per team and 2 left

Step-by-step explanation:

10 can't split into 4 evenly so, you can only give 2 to each team causing there to be 2 left.

4*2 = 8

10-8 = 2

Answer:

Step-by-step on:ơ

Answer:

b. 8/9

Step-by-step explanation:

step by step explanation

Answer:

A

Step-by-step explanation:

Because if you were to out each fraction into a calculator you see that b,c, and d have a never ending decimal. The only fraction that does end in option A, therefore ur answer is option a

Answer:

f(x +1 ) =14

Step-by-step explanation:

12= f(x +1) -2

f(x +1) = 12 +2

f (x+1 ) = 12

Answer:

D

Step-by-step explanation:

Output = 3*input - 2. Observe the graph again

Answer:

70 feet

Step-by-step explanation:

If the miniature model has size of 1 inch, the real statue will be 10 feet in size. So if the model is 7 inch in size, the real statue will be 70 feet in size.

Answer:

I think option b i.e 7 is right but not sure

Answer:

-14

Step-by-step explanation:

12mn-8mt+9t²-6mt

12mn+9t²-14mt

the coefficient of mt is -14

The coefficient of the given expansion 4m(3n-2t)+3t(3t-2m)​ will be -14.

Expanded form is the term used in mathematics to refer to the process of expanding a number to convey the value of every digit and place value.

When a mathematical object is increased by a multiplier that is bigger in actual values than one, an expansion follows.

In another word, if you solve a factor by opening the bracket then you will go to get on some expanded term called expansion.

In mathematics, all real-life problems can be converted into equations which are sometimes in form of factors and we need to expand them to create solutions.

Given that

⇒ 4m(3n-2t)+3t(3t-2m)​

⇒  12mn -8mt + 9t² - 6mt

⇒  12mn + 9t² + 14 mt

Hence it's clear that the coefficient of mt will be -14.

For more information about the expansion

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Answer:

x = 20

Step-by-step explanation:

[tex]16x+90=2(10x+5)\\\\16x+90=20x+10\\\\90=4x+10\\\\80=4x\\\\20=x[/tex]

Answer: quadrant 1

Step-by-step explanation:

the triangle will make 5 360° rotations and then one 180° rotation. we know this because 1980/360=5.5

Answer:

17

Step-by-step explanation:

Look at Triangle ABC, The rays meet at line BC and they are both from the interior point A. So this means that AB=AC. This makes ABC a isosceles triangle. Using the isosceles triangle theorem, Angle B and Angle C measure is equal to each other so

[tex]50 + x + x = 180[/tex]

[tex]50 + 2x = 180[/tex]

[tex]2x = 130[/tex]

[tex]x = 65[/tex]

This means angle b and C of the triangle ABC measure is 65.

External bisector bisect a figure that it makes the original angle split into half that they are equal to each other.

This means the angle below Angle B and angle C measure is 32.5. We can find the measure of Angle B and C in triangle BOC. This is a isosceles triangle as well so

[tex]32.5 + 65 + x = 180[/tex]

[tex]98.5 + x = 180[/tex]

[tex]x = 81.5[/tex]

Angle C is 81.5 as well so

[tex]81.5 + 81.5 = 163[/tex]

Find angle o

[tex]180 - 163 = 17[/tex]

Answer:

D. 72 [tex]in^2[/tex]

Step-by-step explanation:

The square is 36 in2

The 2 triangles are both 18 in2.

36+18+18=72 in2

I hope this helps!

pls ❤ and give brainliest pls

Answer:

Area is 72 in²

Step-by-step explanation:

= Area of three triangles + area of square.

[tex]{ \bf{ = 3 \times ( \frac{1}{2} b \times h) + (s \times s)}}[/tex]

substitute:

[tex]{ \sf{ = ( \frac{1}{2} \times 6 \times 6) + 2( \frac{1}{2} \times 6 \times 3) + (6 \times 6)}} \\ = { \sf{18 + 18 + 36}} \\ = { \sf{ {72 \: in}^{2} }}[/tex]

Answer:

7

Step-by-step explanation:

Consider the absolute value of the difference , that is

| - 5 - 2 | = | - 7 | = 7

or

| 2 - (- 5) | = | 2 + 5 | = | 7 | = 7

Answer:

7

Step-by-step explanation:

Difference is - sign so the equation is: 2- -5 which is 7. Or

think a number line, -5 is 5 spots to 0, then two more spots to 2 so 5+2=7

Answer:

Applying Heron's Formula

[tex]s=\frac{2.89+4.3+6.81}{2}[/tex]

[tex]s_1=7[/tex]

[tex]A_1=\sqrt{7(7-2.89)(7-4.3)(7-6.81)}[/tex]

[tex]A_1=10.56[/tex]

Now, [tex]s_2=\frac{6.81+8.59+7.58}{2}[/tex]

[tex]s_2=11.49[/tex]

[tex]A_2=\sqrt{11.49(11.49-6.81)(11.49-8.59)(11.49-7.59)}[/tex]

[tex]A_2=24.69[/tex]

Total Area:

[tex]10.56+24.69[/tex]

[tex]=35.25[/tex]

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Answer:

17.02939

Step-by-step explanation:

Answer:

The answer is 7x²+5x

Step-by-step explanation:

[tex]\sf{}[/tex]

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Answer: 4 8/10m

Explanation:

Total Ribbon = 24m

Total children = 5

Ribbon each student gets = 24÷5

= 4.8

Now 4.8 = 48/10

4 8/10m is the mixed fraction

So each child will get 4 8/10m ribbon

Must click thanks and mark brainliest

If five children share 24m of ribbon equally then each children gets [tex]4\frac{4}{5}[/tex] of ribbon.

A division is a process of splitting a specific amount into equal parts.

Given that five children share 24m of ribbon equally.

We have to find the amount of ribbon each children gets.

To find this we have to divide the length of the ribbon with the number of children.

Twenty four divided by five.

24 is the dividend and five will be the divisor

24/5

Now we have to write this in mixed fraction

[tex]4\frac{4}{5}[/tex]

Hence, if five children share 24m of ribbon equally then each children gets [tex]4\frac{4}{5}[/tex] of ribbon.

To learn more on Division click:

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Answer:

The correct choice is option C. 4xy√3y

Step-by-step explanation:

√12x^2y^3 + 2xy√3y

√12x^2y^3 = 2√3 xy√y

2xy√3y = 2√3 xy√y

2√3 xy√y +  2√3 xy√y

= 4√3 xy√y

= 4xy√3y

f(x+1)=3x+4

[tex]\\ \sf\longmapsto f(y)=3(y-1)+4[/tex]

[tex]\\ \sf\longmapsto f(y)=3y-3+4[/tex]

[tex]\\ \sf\longmapsto f(y)=3y+1[/tex]

[tex]\\ \sf\longmapsto f(x)=3x+1\checkmark[/tex]

[tex]\\ \sf\longmapsto f(3)[/tex]

[tex]\\ \sf\longmapsto 3(3)+1[/tex]

[tex]\\ \sf\longmapsto 9+1[/tex]

[tex]\\ \sf\longmapsto 10[/tex]

Answer:

[tex]20^{\circ}[/tex]

Step-by-step explanation:

In any right triangle, the cosine of an angle is equal to its adjacent side divided by the hypotenuse.

Let the angle we want to find be [tex]\theta[/tex]. [tex]\theta[/tex]'s adjacent side is 49 and the hypotenuse of the triangle is 52.

Therefore, we have the equation:

[tex]\cos \theta=\frac{49}{52}[/tex]

Take the inverse cosine of both sides:

[tex]\arccos (\cos \theta)=\arccos(\frac{49}{52})[/tex]

Simplify using [tex]\arccos (\cos \theta)=\theta \text{ for }\theta \in (0, 180^{\circ})[/tex]:

[tex]\theta=\arccos(\frac{49}{52}),\\\theta=19.557214,\\\theta\approx \boxed{20^{\circ}}[/tex]