Brayden starts out riding his bike for 5 kilometers. He stops and takes a turn and rides his bike
14 more kilometers. After resting, he takes another road that will lead him back toward his starting
point. He is only on that road for 8 kilometers. Is it possible that he made it back to his starting point
Explain your answer and include a sketch to support your argument.
Part I: Sketch the route that represents Brayden's route. Label the distance traveled for each
portion of his ride.
Part ll: Is it possible that he made it back to his starting point?

[tex]\huge{\boxed{\sqrt{65}}}\ \ \boxed{\text{approx. 8.06225775}}[/tex]

The distance formula is [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are the points.

Substitute in the values. [tex]\sqrt{(3-(-1))^2 + (-5-2)^2}[/tex]

Simplify the negative subtraction. [tex]\sqrt{(3+1)^2 + (-5-2)^2}[/tex]

Add and subtract. [tex]\sqrt{4^2 + (-7)^2}[/tex]

Solve the exponents. [tex]\sqrt{16 + 49}[/tex]

Add. [tex]\sqrt{65}[/tex]

[tex]65[/tex] has no square factors, so this is as simple as the answer can get. You can use a calculator to find that [tex]\sqrt{65}[/tex] is approximately [tex]8.06225775[/tex].

The formula for distance between two points is:

[tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2}}[/tex]

In this case:

[tex]x_{2} =3\\x_{1} =-1\\y_{2} =-5\\y_{1} =2[/tex]

^^^Plug these numbers into the formula for distance like so...

[tex]\sqrt{(3 -(-1))^{2} + (-5-2)^{2}}[/tex]

To solve this you must use the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)

First we have parentheses. Remember that when solving you must go from left to right

[tex]\sqrt{(3 -(-1))^{2} + (-5-2)^{2}}[/tex]

3 - (-1) = 4

[tex]\sqrt{(4)^{2} + (-5-2)^{2}}[/tex]

-5 - 2 = -7

[tex]\sqrt{(4)^{2} + (-7)^{2}}[/tex]

Next solve the exponent. Again, you must do this from left to right

[tex]\sqrt{(4)^{2} + (-7)^{2}}[/tex]

4² = 16

[tex]\sqrt{16 + (-7)^{2}}[/tex]

(-7)² = 49

[tex]\sqrt{(16 + 49)}[/tex]

Now for the addition

[tex]\sqrt{(16 + 49)}[/tex]

16 + 49 = 65

√65 <<<This can not be further simplified so this is your exact answer

Your approximate answer would be about 8.06

***Remember that the above answers are in terms of units

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The length of the pool is 400 feet.

The width of the pool is 120 feet.

Step-by-step explanation:

We are given the width (W) is 30% of the length (L).

We are also given the perimeter of the pool is 1040.

So in equation form this is what we have:

W=.3L   (of means multiply)

2L+2W=1040

We are going to plug the first equation into the second like so:

2L+2(.3L)=1040

2L+.6L=1040

2.6L=1040

Divide both sides by 2.6

L=1040/2.6

L=400

The length of the pool is 400 feet.

W=.3L

W=.3(400)

W=120

The width of the pool is 120 feet.

We get two equations that we can use for this equation.

2w + 2L = 1040

and

w = 0.3L

We can input w into the first equation:

0.6L + 2L = 1040

2.6L = 1040

L= 400

W = 120

Answer:

y = [tex]\frac{1}{3}[/tex] x

Step-by-step explanation:

Compare the values of y with the values of x for each ordered pair

x  y

3  1 → y = 3 ÷ 3

6  2 → y = 6 ÷ 3

9  3 → y = 9 ÷ 3 = 3

12 4 → y = 12 ÷ 3 = 4

15 5 → y = 15 ÷ 3 = 5

The y value in each case is the x value divided by 3

Hence rule is

y = [tex]\frac{1}{3}[/tex] x

The cross-section of a cylinder is in the shape of a Circle

Cross section for a cylinder is circle in shape.

" Cross section is defined as the intersection of the solid body with a plane along it particular axis."

According to the question,

Given shape,

Cylinder

Cylinder is having a circular base.

Intersection of a plane with the cylinder is circular.

Cross section of cylinder is circle.

Hence, Option(C) is the correct answer.

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[tex]\huge{\boxed{y+8=-4(x-2)}}[/tex]

Point slope form is [tex]y-y_1=m(x-x_1)[/tex], where [tex]m[/tex] is the slope and [tex](x_1, y_1)[/tex] is any point on the line.

We can simply plug in the values. [tex]y-(-8)=-4(x-2)[/tex]

Then, just simplify the negative subtraction. [tex]y+8=-4(x-2)[/tex]

Answer:

B.

Step-by-step explanation:

B.

Answer:

22

Step-by-step explanation:

law cosines

a^2=b^2+c^2 - 2bc cos A

plug in numbers

21.7 ish

round

22

Answer:

363

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

d = - 85 - (- 92) = - 85 + 92 = 7 and a₁ = - 92, hence

[tex]a_{66}[/tex] = - 92 + (65 × 7 ) = - 92 + 455 = 363

Answer: 150°

Step-by-step explanation:

In the given triangle ABC ∠A=70°, ∠C=80°

therefore ∠B=180-(∠A+∠C)=180-(70+80)  [sum angle property of triangle]

⇒∠B=30°

Now, heights(altitude) are drawn from vertices A and C on respective bases

they intersect at a point M. Also, we know that heights are perpendicular on the bases.

Also, point of intersection of altitudes is called orthocenter.

Now since M is orthocenter,    ∠ABC+∠AMC=180° (property of orthocenter in a triangle)

⇒30°+∠AMC=180°

⇒∠AMC=180°-30°=150°

Hence in the triangle ABC, ∠AMC=150°

Answer:

Step-by-step explanation:

(f · g)(x) = f(x) · g(x)

We have f(x) = 3x² and g(x) = x + 2. Substitute:

(f · g)(x) = (3x²) · (x + 2)              use the distributive property

(f · g)(x) = (3x²)(x) + (3x²)(2)

(f · g)(x) = 3x³ + 6x²

Answer:

A) 1

Step-by-step explanation:

|4| - |-3|

4 - 3

1

1) Divide the numbers

6/22= 0.27 (27 is repeating)

2) Multiply the decimal by 100

0.2727(100)= 27.27

3) Round

27.27 is closer to 27

Therefore, 6/22 to the nearest whole number is 27%.

Hopefully this helps!

Answer: 27%

Step-by-step explanation:

Given the fraction [tex]\frac{6}{22}[/tex], you need to divide the numerator by the denominator in order to rewrite it as a decimal number.

 [tex]\frac{6}{22}=0.27[/tex]

Now, to express it in percentage, the final step is to multiply the decimal number by 100.

Therefore, you get that [tex]\frac{6}{22}[/tex] to the nearest whole percent is:

[tex](0.27)(100)=27\%[/tex]

Answer:

The answer is 6 cups of flour.

To find the amount of flour needed for 3 sticks of butter, a proportion based on the original recipe ratio is used, resulting in 6 cups of flour.

Jermiah's recipe calls for 1 1/2 cups of flour for every 3/4 stick of butter. Therefore, if he uses 3 sticks of butter, we need to find out how many cups of flour that corresponds to.

To determine the amount of flour needed, we set up a proportion, where the original amount of butter and flour are proportional to the new amount of butter and flour.

Since 3/4 stick of butter corresponds to 1 1/2 cups of flour, 3 sticks of butter would be 4 times as much, because 3 divided by 3/4 equals 4. Therefore, he will need 4 times the original amount of flour.

Here is the math: 1 1/2 cups of flour x 4 = 6 cups of flour.

Answer:

D

Step-by-step explanation:

Since GH and JK  are congruent then the central angles are congruent, that is

∠KOJ = ∠HOG = 68° → D

The  measure of KOJ = 68 degree.

A sector is formed by two radii and the intercepted arc on the circle.

The angle subtended by the sector at the center is called Central Angle.

It is given that the

sector , GH and JK are congruent.

As they are congruent the angle subtended by them at the center will be equal.

The measure of ∠GOH = 68 degree

∠KOJ = ∠GOH = 68 degree

Therefore , The  measure of KOJ = 68 degree.

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Answer:

a) [tex]\frac{14}{285}[/tex]

b) [tex]\frac{11}{57}[/tex]

Step-by-step explanation:

We are given that a committee of three people is selected at random from a set of eight teachers, seven parents of students, and five alumni.

We are to find:

a) the probability the committee consists of all teachers is:

Number of ways to select three that are all teachers = [tex]8C3[/tex]

Number of ways to select three randomly = [tex]20C3[/tex]

P (3 all teachers) = [tex]\frac{8C3}{20C3}[/tex] = [tex]\frac{14}{285}[/tex]

b) the probability the committee has no teachers is:

Number of ways to select three that it has no teachers = [tex]12C3[/tex]

Number of ways to select three randomly = [tex]20C3[/tex]

P (no teachers) = [tex]\frac{12C3}{20C3}[/tex] = [tex]\frac{11}{57}[/tex]

Answer:

The mode is 10.

Step-by-step explanation:

A mode is basically the number that occurs most in a data set, so first to make it easier you can list the number least to greatest. After that look at the data set and see what number occurs the most. In this situation it is 10 because it occurs 3 times.

In a data set, the mode is the value that appears the most frequently. A set of data can have just one mode, multiple modes, or none at all.

To solve mode given series is

[tex]10\\16\\15\\14\\8\\21\\10\\5\\19\\18\\4\\5\\16\\12\\10\\9\\[/tex]

Rearranging series we get

[tex]4\\5\\5\\8\\9\\10\\10\\10\\12\\14\\15\\16\\16\\18\\19\\21\\[/tex]

hence, mode is number with highest frequency which is 10 in this series

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Answer:

[tex]MN=18\ units[/tex]

Step-by-step explanation:

we know that

The Intersecting Chord Theorem, states that When two chords intersect each other inside a circle, the products of their segments are equal.

so

In this problem

[tex]AB*BD=MB*BN[/tex]

substitute

[tex](9)(x+1)=(x-1)(15)\\ \\9x+9=15x-15\\ \\15x-9x=9+15\\ \\ 6x=24\\ \\x=4\ units[/tex]

Find the length of line segment MN

[tex]MN=MB+BN=(x-1)+15=x+14[/tex]

substitute the value of x

[tex]MN=4+14=18\ units[/tex]

Answer:

MN = 18

Step-by-step explanation:

AD and MN are two chords intersecting inside the circle at point B.

As we know from intersecting chords theorem.

AB × BD = BN × BM

So 9(x-1)  = 15 (x-1)

9x + 9  = 15x - 15

15x - 9x = 15 + 9

6x = 24

x = 4

and MN = (x-1) + 15

             = (x + 14)

             = 4 + 14 ( By putting x = 4 )

             = (18)

Therefore, MN = 18 is the answer.

Answer:

The area of the shaded region is [tex]11.6\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of the sector of circle of angle 68.9 degrees minus the area of the isosceles triangle

step 1

Find the area of sector of the circle

The area of circle is equal to

[tex]A=\pi r^{2}[/tex]

assume

[tex]\pi =3.14[/tex]

[tex]r=9.28\ cm[/tex]

substitute

[tex]A=(3.14)(9.28)^{2}[/tex]

[tex]A=270.41\ cm^{2}[/tex]

Remember that the area of a circle subtends a central angle of 360 degrees

so

using proportion Find out the area of a sector with a central angle of 68.90 degrees

Let

x -----> the area of a sector

[tex]270.41/360=x/68.90\\\\x=68.90*270.41/360\\\\x=51.75\ cm^{2}[/tex]

step 2

Find the area of the isosceles triangle

Applying the law of sines

The area is equal to

[tex]A=(1/2)r^{2}sin(68.90)[/tex]

we have

[tex]r=9.28\ cm[/tex]

substitute

[tex]A=(1/2)(9.28)^{2}sin(68.90)=40.17\ cm^{2}[/tex]

step 3

Find the area of the shaded region

[tex]51.75-40.17=11.58\ cm^{2}[/tex]

Round to the nearest tenth

[tex]11.58=11.6\ cm^{2}[/tex]

The calculated area of the shaded region is 11.6 square cm

from the question, we have the following parameters that can be used in our computation:

The circle

The area of the shaded region is calculated as

Area of shaded region = Area of sector - Area of triangle

Using the respective formulas, we have

Area of shaded region = 68.9/360 * 3.14 * 9.28 * 9.28 - 1/2 * 9.28 * 9.28 * sin(68.9)

Evaluate

Area of shaded region = 11.6

Hence, the area of the shaded region is 11.6 square cm

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Answer:

               3

       ______

    4 |       12

              -12            

              -----

                0

Step-by-step explanation:

12/4  

The top number always goes inside (larger or not), and the bottom number always goes on the outside (larger or not).

         ______

    4 |       12

Ask yourself how many 4's are in 12.

Let's see one 4 is just 4.

We can probably do more 4's than that.

Two 4's gives us 4+4=8.

Let's see if we can put one 4 in there.

Three 4's gives us 4+4+4=12.

So we can fit three 4's into 12 and there is nothing left over.

               3

       ______

    4 |       12

              -12                (since 4 times 3 or 4+4+4 is 12)

              -----

                0

[tex]\displaystylea_1=-2\\r=8\\a_n=8a_{n-1}\\\\\left \{ {{a_1=-2} \atop {a_n=8a_{n-1}}} \right.[/tex]

Answer: The sequence is: An = -2*8^(n-1)

Step-by-step explanation:

 geometric sequence is of the form:

An = a*r^(n-1)

where can be any positive integer number.

here the first two numbers are -2 and -16, so we have that:

A1 = a*r^(0) = a = -2

now, we know that our sequence is of the form:

An = -2*r^(n-1)

now, for n= 2 we have that:

A2 = -2*r^(1) = -2*r = -16

r = -16/-2 = 8

now we have determinated our sequence:

An = -2*8^(n-1)

Answer:

Step-by-step explanation:

1) f(x) = |x| has its vertex at (0, 0), so the x-value is 0.

2) Cannot figure out what you meant by  \x{ + 3.

3) f(x) = 5x + 31 has a straight line graph, no vertex.

4)   [x] - 6 does not have a vertex, or at least not a well-defined one like |x|

5)  Unsure of what you meant by 5x + 31 - 6.  Did you mean 5x + 25?  This does not have a vertex.

Answer:

3

Step-by-step explanation:

For this case we must express algebraically the following sentence:

"Nine times five less than twice x"

We have to:

Nine times five represents: [tex]9 * 5 = 45[/tex]

Twice x represents:[tex]2x[/tex]

So we have that "Nine times five less than twice x" is represented as:

[tex]2x-45[/tex]

Answer:

[tex]2x-45[/tex]

Answer:

1500

Step-by-step explanation:

List of multiples of 125 between 800 and 2000: 875,1000,1125,1250,1375,1500,1625,1750,1875,2000

Of those only 1500 is divisible by 30: 1500 / 30 = 50

The john number should be 1,500,

The List of multiples of 125 that lies between 800 and 2000 should be 875,1000,1125,1250,1375,1500,1625,1750,1875,2000

Here we can see that there is only 1500 that should be the multiple of 30

Therefore, the john number should be 1500

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Answer:

3 square root 13

Step-by-step explanation:

I used the distance formula and I got this answer.

Distance is the length of the path linking two sites is the distance between them.

Distance between two points is solved by formula

[tex]=\sqrt{(x1-x2)^2 +(y1-y2)^2}\\=\sqrt{(6-0)^2+(-4-5)^2} \\=\sqrt{36+81} \\=\sqrt{117} \\=10.81[/tex]

Hence distance between points is 10.81

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Answer:

C

Step-by-step explanation:

For it be an arithmetic sequence it must either be going up by the same number each time or down by the same number each time.

Lets look at the choices:

A. From 2 to 3 that went up by 1. But from 3 to 7, that doesn't continue to go up by 1. So this sequence is not arithmetic.

B. From 2 to 4, that went up by 2. But from 4 to 16, that doesn't continue to go up by 2. So this sequence is not arithmetic.

C. From 3 to 0, that goes down by 3. From 0 to -3, that goes down by 3. From -3 to -6, thar goes down by 3. This sequence is arithmetic.

Answer:

12 dollars

Step-by-step explanation:

Mile  3.58  rounds to 4 dollars

cookies 2.97 rounds to 3 dollars

bread 2.17 rounds to 2 dollars

pineapple 2.54 rounds to 3 dollars

Adding the whole dollar amounts

4+3+2+3 = 12 dollars

Solution:

Dan will round the price of each item to the nearest dollar. So, the price of milk is rounded to $4, the price of cookies is rounded to $3, the price of bread is rounded to $2, and the pineapple's price is rounded to $3. Adding these numbers up, we get 4+3+2+3=12.Therefore, Dan estimates that he will spend about 12 dollars at the store.

Answer:

To find the percetage of data points that lie between the points -3.01 and 2.61, on a normal distribution we're going to need the help of a calculator. The result is: 99.42%

Attached you will find the graph that represents the result.

Answer:

4x^2 -8

Step-by-step explanation:

f(x)=3x^2-9

g(x)=x^2+1

(f+g)(x)=3x^2-9 +x^2+1

Combine like terms

           = 4x^2 -8

Answer:

depends

Step-by-step explanation:

The Alternate Interior Angles theorem states, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent

Answer:

Yes they are

Step-by-step explanation:

when a line cuts two parallel lines, the alternate interiors angles are congruent. Hope this helps :)

Answer:

Step-by-step explanation:

Use FOIL: (a + b)(c + d) = ac + ad + bc + bd

and i² = -1

(6 + i)(2 + 9i) = (6)(2) + (6)(9i) + (i)(2) + (i)(9i)

= 12 + 54i + 2i + 9i²

= 12 + 54i + 2i + 9(-1)

= 12 + 54i + 2i - 9               combine like terms

= (12 - 9) + (54i + 2i)

= 3 + 56i

[tex](6+i)(2+9i)=18+54i+2i-9=9+56i[/tex]