31. There are two gears that are connected to each other. One gear has 20 teeth and the other gear has 10 teeth. If the bigger gear turns around 5 times, how many times will the smaller gear turn?

Equation that represents the total number of miles he runs after weeks is n * (n + 2).

The equation that represents the total number of miles Tripp runs after "n" weeks can be written as:

Total miles = 3 + 5 + 7 + ... + (2n + 1)

We can see that the first week Tripp runs 3 miles, and every week after that, he adds 2 more miles to the previous week's total. So, for the second week, he runs 3 + 2 = 5 miles, and for the third week, he runs 5 + 2 = 7 miles, and so on.

To simplify the equation, we can use the formula for the sum of an arithmetic series:

S = (n/2) * (a + l)

where S is the sum of the series, n is the number of terms in the series, a is the first term, and l is the last term.

In this case, the first term is 3, and the last term is (2n + 1), since Tripp is adding 2 miles each week. So, we have:

Total miles = (n/2) * (3 + 2n + 1)

Simplifying this equation, we get:

Total miles = (n/2) * (2n + 4)

Total miles = n * (n + 2)

Therefore, the equation that represents the total number of miles Tripp runs after "n" weeks is:

Total miles = n * (n + 2)

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Answer:

13 years

Step-by-step explanation:

Answer: The slope of the ramp is defined as the rise over the run, where the rise is the height of the step (2 feet) and the run is the horizontal distance from the bottom of the ramp to the step (7.0 feet). However, since the ramp is not straight but inclined, we need to use the length of the ramp (7.3 feet) to calculate the actual horizontal distance it covers.

Therefore, the run of the ramp is the square root of the difference between the length of the ramp squared and the height of the step squared:

run = sqrt(7.3^2 - 2^2) = sqrt(52.29 - 4) = sqrt(48.29) ≈ 6.95 feet

Now we can calculate the slope of the ramp:

slope = rise / run = 2 / 6.95 = 0.2885 ≈ 2/7

Therefore, the slope of the ramp is approximately 2/7.

In the given equation, We can start by isolating the square root term on one side of the equation. The answer is {-2, 10}.

x + 6 - 9 = [tex]\sqrt{2x+29}[/tex]

Simplifying the left-hand side:

x - 3 = root(2x + 29)

Squaring both sides of the equation to eliminate the square root:

(x - 3)^2 = 2x + 29

Expanding the left-hand side:

[tex]x^2[/tex] - 6x + 9 = 2x + 29

Moving all the terms to one side of the equation:

[tex]x^2[/tex] - 8x - 20 = 0

We can now use the quadratic formula to solve for x:

x = (-b ± sqrt([tex]b^2[/tex] - 4ac)) / 2a

where a = 1, b = -8, and c = -20.

Substituting these values into the formula, we get:

x = (-(-8) ± sqrt([tex](-8)^2[/tex] - 4(1)(-20))) / 2(1)

Simplifying the equation:

x = (8 ± sqrt(144)) / 2

x = (8 ± 12) / 2

So, we have two possible solutions:

x1 = 10

x2 = -2

Thus, the answer is {-2, 10}.

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The graph of the inequality is on the image at the end.

To graph this, we need to do a solid graph of the linear equation:

y = -(7/2)x + 4

And because the symbol ≥  (and that is why we will use a solid line instead of a dashed line) is used, we need to shade all the region above that line graph.

Then the graph of the inequality will be something like the one of the graph at the end.

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The coordinates that represents a point that is collinear with the given points: (4, -10) and (-2, 0) is (0, 10/3). So the correct answer is option C.

We must check to see if a point is on the straight line that connects two other points in order to determine if they are collinear.

Using the point-slope form of a line we can find the equation of the straight line passing through the points (4,-10) and (-2,0):

(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)

where (x1, y1) = (4, -10) and (x2, y2) = (-2, 0).

Substituting the values, we get:

(y + 10)/(x - 4) = (0 + 10)/(-2 - 4)

Simplifying, we get:

(y + 10)/(x - 4) = -5/3

Multiplying both sides by (x - 4), we get:

y + 10 = (-5/3)(x - 4)

Simplifying, we get:

y = (-5/3)x + (10 + 20/3)

y = (-5/3)x + (50/3)

So, any point that satisfies this equation is collinear with the given points.

Now checking all the three points whether they satisfy the equation:

(a) (2, -6)

Substituting the values in the equation, we get:

-6 = (-5/3)(2) + (50/3)

-6 = -10/3 + 50/3

-6 = 40/3, which is not true.

Therefore, the point (2, -6) is not collinear with the given points.

(b) (3, -3)

Substituting the values in the equation, we get:

-3 = (-5/3)(3) + (50/3)

-3 = -15/3 + 50/3

-3 = 35/3, which is not true.

Therefore, the point (3, -3) is not collinear with the given points.

(c) (0, 10/3)

Substituting the values in the equation, we get:

10/3 = (-5/3)(0) + (50/3)

10/3 = 50/3, which is true.

Therefore, the point (0, 10/3) is collinear with the given points.

Hence, the answer is (c) (0, 10/3).

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Correct Question

Which of the following coordinates represents a point that is collinear with the given points.

(4, -10) and (-2, 0)
(a) (2, -6)

(b) (3, -3)

(c) (0, 10/3)

The line equations according to its features are, respectively:

Case C: y = - 2

Case D: x = - 7

Case E: y = - x + 1 / 2

Case F: y = - (1 / 3) · x + 20 / 3

Case G: y = 4 · x + 17

In this question we must determine five line equations based on its features. The equation of the line can be found by understanding the following features:

There are two forms of the equation of the line:

Slope-intercept

y = m · x + k

Standard

a · x + b · y + c = 0

Where:

Now we proceed to determine the equation of each line:

Case C: m = 0, (x, y) = (- 7, - 2)

- 2 = 0 · (- 7) + k

k = - 2

y = - 2

Case D: m = 0, (x, y) = (- 7, - 2)

x = - 7

Case E: k = 1 / 2, m = - 1

y = - x + 1 / 2

Case F: Parallel to x - 3 · y = 9, (x, y) = (2, 6)

x - 3 · y = 9

3 · y = 9 - x

y = 3 - (1 / 3) · x

m = - 1 / 3

6 = - (1 / 3) · 2 + k

6 = - 2 / 3 + k

k = 20 / 3

y = - (1 / 3) · x + 20 / 3

Case G: Perpendicular to y + (1 / 4) · x - 5 = 0, (x, y) = (- 3, 5)

y + (1 / 4) · x - 5 = 0

y = - (1 / 4) · x + 5

m = - 1 / 4

m' = 4

5 = 4 · (- 3) + k

5 = - 12 + k

k =  17

y = 4 · x + 17

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The lateral area of the triangular prism is 288 square inches and the surface area is 336 square inches

The lateral area of a right triangular prism is given by:

LA = perimeter of base triangle * height

LA = (a + b + c) * h    (check attached image for labeling)

where a, b and c are the bases of the rectangular faces and h is the total height of the prism.

a = 10 in, c = 8 in and h = 12 in

b = √(10² - 8²)      (Pythagoras)

b = 6 in

LA = (10 + 6 + 8) * 12

LA =  288 square inches

The surface area of a right triangular prism is sum of the areas of the faces that make the prism.

The surface area of a right triangular prism is given by:

SA = (a + b + c)h + bc

SA = [(10 + 6 + 8)*12] + [6 * 8]

SA = 288 + 48

SA = 338 square inches

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Complete Question

Check image

Answer:

False. The product of two negative integers is a positive integer.

The implementing of subtraction as a money lesson need a starting with concrete examples and building students' understanding of the concept in scenarios.

As a mathematical concept, subtraction is useful in real-life scenarios including managing money. To implement it, we must note that it important to start with concrete examples that students can relate to like making purchases or earning an allowance.

We can provide the students with a set amount of money and ask them to subtract the cost of various items from it to determine how much they have left. For example, if a student has $10 and wants to buy a $3 toy, they would need to subtract $3 from $10 to determine that they have $7 remaining.

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It will take Boris approximately 4.02 years to have enough money for his project if he invests $6000 now at an annual rate of 7%, compounded quarterly.

The formula for compound interest is:

[tex]A = P(1 + \dfrac{r}{n})^{(nt)}[/tex]

where A is the future value of the investment, P is the principal amount invested, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, Boris has invested $6000 at an annual interest rate of 7%, compounded quarterly. Therefore, we have:

P = 6000

r = 0.07 (since 7% is the annual interest rate)

n = 4 (since the interest is compounded quarterly)

A = 8058

We can solve for t by rearranging the formula:

[tex]t =\dfrac{ ln(\dfrac{A}{P})} { n ln(1 + \dfrac{r}{n})}[/tex]

Substituting the values we have:

[tex]t = \dfrac{ln(\dfrac{8058}{6000}) }{ [4 ln(1 + \dfrac{0.07}{4})]}[/tex]

t ≈ 4.02 years

Therefore, it will take Boris approximately 4.02 years to have enough money for his project if he invests $6000 now at an annual rate of 7%, compounded quarterly.

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The volume of C.a .cylinder is twice the volume of a cone.

The formula fro the cylinder is πr²h and that of the cone is ⅓ the volume It should be noted that the volume of a cone can be equated to theone-third of the volume of a cylinder , this can be established when they are having same base radius and height.

The cylinder's volume  can be expressed as π r² h,  along with the surface area  which can be expressed as 2π r h + 2π r² and this can be used to get the values.

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Answer:

p≥35

Step-by-step explanation:

because you have done 15 so you subtract 15 from 50 giving you 35 and then you would say p is greater than or equal to 35 cause 50 pages is your minimum

Answer: h(-8) = 21

Step-by-step explanation:

Answer: 21

Step-by-step explanation:

You equation is h(y)  but you need to find h(-8) which means substitute y for -8 into equation

h(-8)= 4|(-8)+2| -3             do what's inside absolute value first

=4|-6| -3                           for absolute value, take positive of number

=4(6)-3                             multiply

=24-3                               subtract

=21

The polar coordinates in rectangular coordinates are (3√2, 2√6)

Given are polar coordinates (6√2, 7π/3), we need to convert it into, rectangular coordinates.

so, (r, θ) = (6√2, 7π/3)

x = rcosθ

y = rsinθ

r = 6√2, θ = 7π/3

x = 6√2 cos 7π/3 = 3√2

y = 6√2 sin 7π/3 = 2√6

Hence, the polar coordinates in rectangular coordinates are (3√2, 2√6)

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The transformation sequence of the function is:

The function is first shifted to the left, then vertically stretched, and finally vertically shifted up and down to get the final graph.

We have,

The transformations of f(x) = 2^x to get to g(x) = -5 + 2^{x + 6} + 3 are as follows:

Translation:

f(x) is translated 6 units to the left, which gives 2^{x+6}.

Vertical stretch/compression:

The entire function is multiplied by 2, which makes it taller.

Vertical shift:

The entire function is shifted up 3 units and down 5 units, which raises the entire graph 3 units and then lowers it 5 units from its original position.

Thus,

The function is first shifted to the left, then vertically stretched, and finally vertically shifted up and down to get the final graph.

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The new mean annual wage is; $ 43,149.82.

Given that the initial mean weekly wage is $ 2.117.

The growth rate is 4.75%.

We need to find a new annual wage.

Consider the equation, A be the new annual wage.

Here R is the growth rate and P is the initial mean weekly wage and T is the number of weeks in a year.

The number of weeks in a year = 52 weeks.

Substitute P= 2,117, R =4.75% = 0.0475and T =52 in the equation.

A = 2.117 x 52(1 + 0.0475)

A = 43,149.82

The new mean annual wage is; $ 43,149.82.

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The probability that Bashir chooses a card that is either a face card or a spade is 11/26.

To find the probability that the card Bashir chooses is either a face card or a spade, we need to add the probabilities of the two events occurring and then subtract the probability of their intersection (choosing a face card that is also a spade).

First, we need to find the probability of choosing a face card. There are 12 face cards in a deck (4 jacks, 4 queens, and 4 kings), and a total of 52 cards, so the probability of choosing a face card is

P(F) = 12/52 = 3/13

Next, we need to find the probability of choosing a spade. There are 13 spades in a deck (from 2 to ace), and a total of 52 cards, so the probability of choosing a spade is

P(S) = 13/52 = 1/4

To find the probability of choosing either a face card or a spade, we can use the formula

P(F or S) = P(F) + P(S) - P(F and S)

We need to find the probability of choosing a face card that is also a spade (their intersection). There are only 3 face cards that are spades (jack of spades, queen of spades, king of spades), so the probability of choosing a face card that is also a spade is

P(F and S) = 3/52

Now we can plug in the values to get

P(F or S) = P(F) + P(S) - P(F and S)

P(F or S) = 3/13 + 1/4 - 3/52

P(F or S) = 12/52 + 13/52 - 3/52

P(F or S) = 22/52

P(F or S) = 11/26

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The equation will have the solution in the form of an imaginary number "i" as: x = (3 ± 2i)/2

In a quadratic equation, an imaginary number is a complex number that can arise when trying to take the square root of a negative number.

We shall solve for x in the equation as follows:

(2x + 3)² - 2 = -6

add 2 to both sides

(2x + 3)² = 2 - 6

(2x + 3)² = -4

2x + 3 = √(-4) {taking square root of both sides}

subtract 3 from both sides

2x = 3 ± √(-4)

divide through by 2

x = [3 ± √(-4)]/2

note that: √(-4) = √(1-) × √4 where √(-1) = I, so;

x = (3 ± 2i)/2.

Therefore, the equation will have the solution in the form of an imaginary number "i" as: x = (3 ± 2i)/2

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Answer:

(2,2), (4,8), (3,4)

Step-by-step explanation:

Plug in the x-coodinate and it should equal your desired y value

If the radius of Jasmine's swimming pool is 4.2 meter, then it's circumference is 26.4 meters.

The "Circumference" of a circle is known as the distance around the boundary of a circle.

The circumference of a circle is given by the formula : 2 × π × radius,

where π (pi) is a mathematical constant approximately equal to 3.14,

We are given that Jasmine's swimming pool has a radius of 4.2 meters.
So, we can calculate the circumference of the pool as :

⇒ Circumference = 2 × 3.14 × 4.2 meters,

⇒ Circumference ≈ 26.4 meters,

Therefore, the circumference of Jasmine's swimming pool is 26.4 meters.

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Answer:

no not satisacl

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

24 divided by X(3) is equal to 8, then 8+8 equals 16 (EASY)

The volume of the resulting solid revolved around the x-axis is equal to  28.274 cubic units (round to the nearest thousandth).

Vertices of the right triangle are,

(0, 0), (0, 3) and (-4, 0)

To obtain the solid formed by revolving the given right triangle about the x-axis, use the disk method.

The cross-sectional area of the solid at a given height is a circle with radius = distance between the x-axis and the upper edge of the triangle at that height.

The height of the triangle is 3 units,

and the base of the triangle is 4 units.

So, the equation of the hypotenuse of the right triangle can be found as follows,

y = (3/4)x + 3

Now, let us consider a horizontal slice of the solid at a distance y units above the x-axis.

The radius of the circle at this height is ,

r = y - 3

The area of the circle at this height is ,

A = πr²

   = π(y - 3)²

The limits of integration are y = 0 the x-axis to y = 3 the height of the triangle.

Using the disk method, the volume of the solid is,

V = [tex]\int_{0}^{3}[/tex] π(y - 3)²dy

Evaluating the integral, we get,

⇒ V = π /3 ( y - 3 )³[tex]|_{0}^{3}[/tex]

⇒ V = π/3 [( 3- 3 )³ - ( 0 -3)³ ]

⇒ V = (π /3) ( 27)

⇒V  = 9π

⇒V  = 9 (3.1415)

Rounding to the nearest thousandth gives,

V ≈ 28.274

Therefore, the volume of the solid formed by revolving the given right triangle about the x-axis is approximately 28.274 cubic units.

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The input value that corresponds to an output value of 15 is x = -1/3.

To find the input value (x) that corresponds to an output value of 15, we need to derive an equation:

15 = 60 / (3x + 5)

Multiplying both sides by (3x + 5), we get:

15(3x + 5) = 60

Expanding the left side, we get:

45x + 75 = 60

Subtracting 75 from both sides, we get:

45x = -15

Dividing both sides by 45, we get:

x = -1/3

Therefore, the input value that corresponds to an output value of 15 is x = -1/3.

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The time it will take the bird to travel 1.4 m is 0.5738 seconds.

In Science and Mathematics, velocity can be defined as the distance covered by an object per unit of time in a specific direction. This ultimately implies that, velocity is a vector quantity because it has both magnitude and direction.

In Mathematics and Science, the velocity of any a physical object can be calculated by using this formula;

Velocity = distance/time

244 cm/s to m = 244/100 = 2.44 cm/s

By making time the subject of formula, we have:

Time = distance/velocity

Time = 1.4/2.44

Time = 0.5738 seconds.

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Answer:

180 cmStep-by-step explanation:

Answer:

(2, -5)

(4, -3)

(3, -1)

Step-by-step explanation:

When reflected across the X-axis, the sign of the y will change to the opposite.

(x, y) → (x, -y)

Let's solve

(2,5) → (2, -5)

(4,3) → (4, -3)

(3,1) → (3, -1)

So, the missing coordinates are: (2, -5)

                                                       (4, -3)

                                                       (3, -1)

t < 8 is the inequality to solve the variable "t" as per the given data.

The cost C (in dollars) of renting the room for t hours can be expressed as:

C(t) = 4t + 18

To spend less than $50, we can set up an inequality:

C(t) < 50

Substituting the expression for C(t), we have:

4t + 18 < 50

Subtracting 18 from both sides, we get:

4t < 32

Dividing both sides by 4, we obtain:

t < 8

Therefore, the chemistry club could rent the meeting room for any number of hours less than 8 in order to spend less than $50.

The inequality solved for t is:

t < 8

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