Two cyclists left simultaneously from cities A and B heading towards each other at constant rates and met in 5 hours. The rate of the cyclist from A was 3 mph less than the rate of the other cyclist. If the cyclist from B had started moving 30 minutes later than the other cyclist, then the two cyclists would have met 31.8 miles away from A. What is the distance between A and B, in miles?

Answer:

Area: 4069.44

Circumference: 226.08

Step-by-step explanation:

The equation for the area of a circle is:

pi(r^2)

So they told us to use 3.14 for pi, the r (radius)is found by dividing the diameter (72) by 2 since

r = d/2

r = 72/2 = 36

plug this into the equation for the area of a circle:

3.14(36^2) = 4069.44

——————————————————————————————————

To find the circumference, use the equation for it:

2 x pi x r or pi x d

Let’s use the second equation, since the diameter is already given

2(3.14)(72) = 226.08

Answer:

Area is 4069.44 m². Circumference is 226.08 m.

Step-by-step explanation:

Area:

a = r²π

a = 36²π

a = 4069.44

Circumference:

c = dπ

c = 72 × 3.14

c = 226.08

Answer:

g(- 3) = 23

Step-by-step explanation:

We require to find the value of t so that g(t) = 23

Equate g(t) to 23 and solve for t, that is

- 9t - 4 = 23 ( add 4 to both sides )

- 9t = 27 ( divide both sides by - 9 )

t = - 3

Hence g(- 3) = 23

If the value of the function g(t) = -9t - 4 is 23. Then the value of t will be negative three.

A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.

The function g(t) is given below.

g(t) = - 9t - 4

If the value of the function g(t) is 23. Then the value of t will be given as

23 = - 9t - 4

27 = - 9t

  t = - 3

Then the value of t will be negative 3.

More about the function link is given below.

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Answer:

- The neighbor's fencing project that will cost the most is: Neighbor A.

- The neighbor's fencing project that will cost the least is: Neighbor B.

Step-by-step explanation:

To calculate the amount of fence that Neighbor A has to put up, you need to add the following distances:

[tex]Fence_A=5yards+8yards+25yards+8yards\\Fence_A=46yards[/tex]

Convert yards to feet (Remember that [tex]1yard=3feet[/tex]:

[tex]Fence_A=(46yards)(\frac{3feet}{1yard})=138feet[/tex]

You know that wood fencing is sold in 8 foot sections for $111.50, then, the number of sections for this fence will be:

[tex]sections=\frac{138feet}{8feet}=17.25[/tex]≈18

Then,  the cost for this fencing project will be:

[tex]Cost_A=\frac{(18sections)(\$111.50)}{1section}=\$2,007[/tex]

 To calculate the amount of fence that Neighbor B has to put up, you need to use the formula for calculate the circumference of a circle:

[tex]C=2\pi r[/tex]

Where r is the radius.

In this case, the radius is:

[tex]r=\frac{30feet+10feet}{2}=20feet[/tex]

Substituting, you get:

[tex]C=Fence_B=2\pi (20feet)=125.66feet[/tex]≈126 feet

You know that the Chain link fencing costs $9.75 per linear foot, then, the cost for this fencing project will be:

[tex]Cost_B=(126)(\$9.75)=\$1,228.5[/tex]

To calculate the amount of fence that Neighbor C has to put up, you need to add the following distances:

[tex]Fence_C=16feet+58feet+16feet\\Fence_C=90feet[/tex]

Convert from feet to yards (Remember that [tex]1yard=3feet[/tex]:

[tex]Fence_A=(90feet)(\frac{1yard}{3feet})=30yards[/tex]

You know that the vinyl fencing can be purchased for $53.55 per linear yard , then, the cost for this fencing project will be:

[tex]Cost_C=(30)(\$53.55)=\$1,606.5[/tex]

Therefore, the neighbor's fencing project that will cost the most is: Neighbor A.

The neighbor's fencing project that will cost the least is: Neighbor B.

Answer:

Therefore, the neighbor's fencing project that will cost the most is: Neighbor A.

The neighbor's fencing project that will cost the least is: Neighbor B.

Step-by-step explanation:

By looking at this data, you can see that while most of the data is in between 70 and 73, the only number that isn't in that range is 78. Therefore, the term outlier describes 78in the best.

Answer:

D) Outlier

Step-by-step explanation:

Answer:

Surface area I'm guessing.  1,130.4

Step-by-step explanation:

The formula for the surface area of a cylinder is: 2*pi*r^2 + 2*pi*r*h.

Plug in the values given.

2*pi*10^2 + 2*pi*10*8

628 + 502.4 = 1,130.4

(If you want the most precise value, use a calculator for pi instead of just 3.14.)

ANSWER

[tex]S A = 1130.4[/tex]

square units.

EXPLANATION

The given cylinder has a height of 8 and a radius of 10.

The formula for calculating the surface area of a cylinder is

[tex]S A = 2\pi \: r(r + h)[/tex]

We substitute r=8 and h=10 into the formula to get:

[tex]S A = 2\pi \: 10(10+ 8)[/tex]

[tex]S A = 360\pi [/tex]

Or using π=3.14

[tex]S A = 1130.4[/tex]

units square.

The answer will be B

letter B is the answer

Answer:

Step-by-step explanation:

f(x) - n - shift the graph n units down

f(x) + n - shift the graph n units up

f(x - n) - shift the graph n units to the right

f(x + n) - shift the graph n units to the left

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

From the graph:

G(x) - the graph F(x) has been shifted 3 units to the left (look at the vertex).

Therefore your answer is G(x) = F(x + 3) = (x + 3)²

The answer is D. D is the answer

Answer:

[tex]\large\boxed{x>-\dfrac{11}{24}}[/tex]

Step-by-step explanation:

[tex]-\dfrac{4}{3}x+\dfrac{1}{6}<\dfrac{7}{9}\qquad\text{multiply by common denominator}\to18\\\\18\!\!\!\!\!\diagup^6\left(-\dfrac{4}{3\!\!\!\!\diagup_1}x\right)+18\!\!\!\!\!\diagup^3\left(\dfrac{1}{6\!\!\!\!\diagup_1}\right)<18\!\!\!\!\!\diagup^2\left(\dfrac{7}{9\!\!\!\!\diagup_1}\right)\\\\(6)(-4x)+(3)(1)<(2)(7)\\\\-24x+3<14\qquad\text{subtract 3 from both sides}\\\\-24x<11\qquad\text{change the signs}\\\\24x>-11\qquad\text{divide both sides by 24}\\\\x>-\dfrac{11}{24}[/tex]

I think the answer is in the question itself

x-9

[tex]area = \pi {r}^{2} \\ r = \frac{1}{2} \times 7.5 = 3.75 \\ 3.14 \times 3.75 {}^{2} \\ 3.75 {}^{2} = 14.06 \\ 3.14 \times 14.06 = 44.1484 \: inches {}^{2} [/tex]

hope that helped

[tex]A = \pi {r}^{2} \\ \\ r = \frac{7.5}{2} = 3.75[/tex]

So

[tex]A = (3.14)({3.75}^{2} ) \\ A = (3.14)(14.0625) \\ A = 44.15625 \\ A =44.16[/tex]

The Pythagorean theorem is used in a similar manner to compute the diagonal of a rectangle and a rectangular prism. In both cases, the theorem is utilized to find the length of a line connecting two opposite corners across the shape or space.

In the field of Mathematics, the Pythagorean theorem presents a fundamental relationship within a right triangle which expresses that the square of the hypotenuse (the side opposite the right angle) is equivalent to the sum of the squares of the other two sides. This theorem is represented mathematically as a² + b² = c².

When applying this theorem in a rectangle, consider a diagonal drawn from one corner to the opposite corner, which gives us a right triangle. To find the length of this diagonal (hypotenuse), we use the Pythagorean theorem, considering the two sides of the rectangle as the other two sides of the triangle.

In a rectangular prism, the same principle applies. However, instead of two sides (as in a rectangle), we now have three dimensions (length, width, and height) to consider. When one wishes to find the distance from one corner to the opposite corner (a diagonal cutting through the prism), the Pythagorean theorem can be employed. First, a right triangle is considered in the base of the prism, and the Pythagorean theorem is used to find the length of the diagonal of the base. Next, a second right triangle is constructed using the height of the prism and the diagonal of the base. Once again, the Pythagorean theorem can be implemented to calculate the length of the longest diagonal of the prism.

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The Pythagorean theorem applies similarly in both rectangular prisms and rectangles, using right triangles to calculate distances.

The Pythagorean theorem is fundamentally the same in both a rectangular prism and a rectangle, as it relies on the properties of right triangles. For a rectangle, the theorem states that the sum of the squares of the two shorter sides (a and b) equals the square of the hypotenuse (c), or a² + b² = c².

When applied to a rectangular prism, the theorem is used in three dimensions to find the length of the diagonal (d) stretching between opposite corners. In a rectangular prism, by applying the Pythagorean theorem successively across two-dimensional planes, we first calculate the diagonal of one face of the prism (b² = x² + y²).

Then, we incorporate the third dimension z to find the space diagonal: d² = x² + y² + z². This sequential application of the Pythagorean theorem leverages its two-dimensional principle to solve for three-dimensional distances.

Steps to Apply Pythagorean Theorem in a Rectangular Prism:

This demonstrates how the Pythagorean theorem's consistent application in both two and three dimensions allows calculation of diagonals and distances in various geometric contexts.

Answer: [tex]-2x^{9}[/tex]

Step-by-step explanation:

 To find the quotient, you  need to apply the Quotient of powers property. This is:

[tex]\frac{a^m}{a^n}=a^{(m-n)[/tex]

Then given the expression [tex]\frac{-8x^6}{4x^{-3}}[/tex] you can apply the property mentioned before. Then you get:

[tex]\frac{-8x^{(6-(-3))}}{4}[/tex]

You should remember the multiplication of signs:

[tex](-)(-)=+\\(+)(+)=+\\(-)(+)=-[/tex]

Therefore, simplifying the expression, you get that the quotient of [tex]\frac{-8x^6}{4x^{-3}}[/tex] is:

 [tex]-2x^{9}[/tex]

Answer:

d

Step-by-step explanation:

d

45.2 (for question 1/#19)

To find the angle, you need to use the cosine because you have the adjacent and the hypotenuse.

Cosine 0 = 9.3/13.2

Cosine 0 = 9.3/13.2 = 0.705

Arccos 0.705

Angle 0 = 45.2

Answer:

C = 77°

Step-by-step explanation:

From the intercepted arc theorem, we can say that Angle ABC (angle B) is HALF of the arc intercepted (which is 110).

Hence, angle ABC = 55.

Now, looking at triangle ABC, we know that sum of 3 angles of a triangle is 180. We already know Angle A to be 48 and Angle B to be 55, thus Angle C is:

A + B + C = 180

48 + 55 + C = 180

103 + C = 180

C = 180 - 103

C = 77

answer: $2413.50

y=original amount of money(1+ the percent divided by 100)^the number of years is the power

we do this with the 1+ ... because the original amount plus the extra 8.25%

so the equation would be ...

y=1500(1+0.0825)^6

y=1500(1.60904218428)

y=1500(1.609) (I rounded)

y=$2413.50

Answer:

Start by dividing things up so that you know them. Use the dotted line to make a square a 2 triangles. Base and height for the square is 4 so that total is 16. Then the triangles have a base an height of 4 as well so that ((4•4)/2)= 8. Then add them together = 24

Hope this helps.

Answer:

Step-by-step explanation:

Assuming that said hexagon is regular then triangles formed (split in half by the apothem) are 30-60-90 triangles. The side that you'd get would be 10√3/3. Multiplied by two, you'd get 20√3/3. The perimeter would be 120√3/3, which would be 40√3 as the answer.

The perimeter of the hexagon is 40√3  if the apothem is 10 after applying tan ratio.

A hexagon is a six-sided polygon with six inner angles totalling 720° and six outside angles totalling 360° in geometry. Regular, irregular, concave, convex, and complicated hexagons are two-dimensional shapes.

From the figure, we can calculate the side length of the hexagon:

We know each interior angle of the hexagons = 120 degree

Half of the angle = 120/2 = 60 degree

From the tan ratio:

tan30 = (s/2)/10

1/√3 = s/20

s = 20/√3

Perimeter = 6×(20/√3) = 120/√3 = 40√3

Thus, the perimeter of the hexagon is 40√3  if the apothem is 10 after applying tan ratio.

Learn more about the hexagon here:

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Answer:

f(x) = 3x - 1

Step-by-step explanation:

The line can be represented in the form f(x) = mx + b, where m is the rate of change of the line and b is the value of the function when x = 0.

Looking at the graph, we can tell that when x = 0 the function = -1. (The point on the line and the y-axis).

We can also tell that when x increases by 1, y increases by 3. The points (0,-1) and (1, 2) are both on the line and their difference in x is 1 and their difference in y is 3.

The formula for slope (rate of change) is [tex]\frac{change\ in\ y}{change\ in\ x}[/tex], so m = [tex]\frac{3}{1}[/tex] or 3.

Now we have the equation for the line is f(x) = 3x - 1

-5y = -5 = 1

7x + 6y = 7

=-1.167

your answer is B) no

The given coordinate (5,1) is not a solution to the system of equations -5y = -5 and 7x + 6y = 7. Both equations do not hold true when 5 and 1 are substituted for y and x respectively.

In Mathematics, to confirm if the given set of numbers ((5,1)) are a solution to the system, we substitute these values back into both system equations. In this case, 5 for y and 1 for x. As a result, the equation -5y = -5 becomes -5*5= -25, which is not equal to -5. Therefore, 5 is not a solution for y. Similarly, solving 7x + 6y = 7 after substituting the values becomes 7*1 + 6*5= 37, which is not equal to 7. So, 1 is not a solution for x. Therefore, the provided answer (5,1) is not a solution for the given system of equations. Thus, the answer is B. No.

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Answer:

= 5880 +

                                      = 5880 + (0.10 × 5880)

                                      = 5880 + 588

                                      = 6,468

In 2014 subscriptions would be sold 6,468.

Step-by-step explanation:

Answer:

[tex]\boxed{\bold{One \ Solution}}[/tex]

Step-by-step explanation:

Combine: 6z - 3z = 3z

[tex]\bold{3z-7=-2+3}[/tex]

Add: -2 + 3 = 1

[tex]\bold{3z-7=1}[/tex]

Add 7 to both sides:

[tex]\bold{3z-7+7=1+7}[/tex]

Simplify:

[tex]\bold{3z=8}[/tex]

Divide both sides by 3:

[tex]\bold{\frac{3z}{3}=\frac{8}{3}}[/tex]

Simplify:

[tex]\bold{z=\frac{8}{3}}[/tex]

- M -

11, 11 •11 equals 121 which makes it a factor

Answer:

-5.5

Step-by-step explanation:

Add all numbers and divide by 4 (the total amount of numbers)

10+(-27)+4+(-9)=-22

-22/4 = -5.5

-5.5

In order to find the mean, you add up all numbers and then divide by the amount of numbers

Answer:

25.

Step-by-step explanation:

Use the identity cos 2x = 2 cos^2 x - 1

So cos 50 = 2 cos^2 25 - 1

So the space  = 25.

Answer:

25°

Step-by-step explanation:

Using the double angle trigonometric identity for cosine

• cos2x = 2cos²x - 1

Here 2x = 50° ⇒ x = 25°, thus

cos50° = 2cos²25° - 1

Answer:11%

Step-by-step explanation:

A percent is always a number over 100, so 11/100 = 11%

Answer:

11%

Step-by-step explanation:

Answer:

8/24=1/3

There are 24 balls in total and 8 of them are red. So you get 8/24 but you need to simplify it to its simplest form which is 1/3

Final answer:

The probability of picking a red ball from a container with 5 white, 8 red, 7 yellow, and 4 green balls is 1/3, because you divide the number of red balls (8) by the total number of balls (24).

Explanation:

The subject of this question is probability, a branch of mathematics concerned with the likelihood of an event occurring. To find the probability of picking a red ball, we need to divide the number of red balls by the total number of balls in the container.

In the question, there are 5 white balls, 8 red balls, 7 yellow balls, and 4 green balls, which means there are a total of 24 balls. The probability of picking a red ball is calculated by taking the number of red balls and dividing it by the total number of balls:

Probability of picking a red ball = Number of red balls / Total number of balls = 8 / 24 = 1/3.

Answer:

Step 1

Step-by-step explanation:

When you subtract a polynomial in parentheses, you have to remove them from the parentheses first, which Kenisha did right. The problem is that because the numbers are being subtracted, all of the signs switch, which they forgot to do. Step one should look like: 2b² + 3b + 11 - 7b² + 5b - 1

Answer:

3y+5x=0

Step-by-step explanation:

The question is on equations of parallel lines

Finding the gradient m of line AB

m=change in y coordinates/change in x-co-ordinates

Given points A(-3,0) and B (-6,5)

m=Δy/Δx  Δy=5-0=5      Δx=-6 - -3= -3  ⇒m= - 5/3

Equation

The line will have its gradient equal to - 5/3

m=-5/3  

point is the origin (0,0)

m=Δy/Δx

y-0/x-0 = -5/3

3(y-0)=-5(x-0)

3y-0= -5x+0

3y=-5x

3y+5x=0

Answer:

c is the correct answer

Step-by-step explanation:

Answer:

1 fifteenth, or 1/15

Step-by-step explanation:

If there are 3 sons multiply the fraction by 3 and then you have 12/15 because 12/15 is equal to 4/5, so the remaining is 3 out of 15, so divide that between the 3 sons and boom, 1/15th per son.  

The correct answer is C