Charles factors the expression 4/3xy+1/3x using a factor of 1/3x. He writes the factored expression 1/3x(4y+1). Which best describes the accuracy of Charles solution?

A. His solution is accurate

B. His solution is inaccurate. The factor does not divide evenly into both terms.

C. His solution is inaccurate. The factoring of 4/3xy using the given GCF is incorrect.

D. His solution is inaccurate. The factoring of 1/3x using the given GCF is incorrect.

Answer:

x=2

Step-by-step explanation:

Find the total of male students:

4 + 6 + 2 + 2 = 14 total males.

There are 2 male juniors.

The probability of a male being a junior is 2/14 = 1/7 = 0.143 = 14.3 = 14%

Find the total of male students:

4 + 6 + 2 + 2 = 14 total males.

There are 2 male juniors.

The probability of a male being a junior is 2/14 = 1/7 = 0.143 = 14.3 = 14%

ANSWER

The volume of the dilated cone is

[tex]40 {m}^{3}[/tex]

EXPLANATION

The volume of the given cone is

[tex]5000 {m}^{3} [/tex]

When this cone is dilated with a scale factor of 1/5, the volume of the dilated cone becomes,

[tex] ({ \frac{1}{5} })^{3} \times 5000 {m}^{3} [/tex]

We simplify to obtain:

[tex] { \frac{1}{125} }\times 5000 {m}^{3} [/tex]

This gives us:

[tex]40 {m}^{3} [/tex]

Final answer:

When a cone is scaled down by a factor of 1/5, its new volume is 40 m³, calculated by cubing the scale factor and multiplying it by the original volume.

Explanation:

When a cone is dilated by a scale factor, its volume changes according to the cube of that scale factor.

Since the original volume of the cone is 5000 m³ and the scale factor is 1/5, we use the proportionality principle which states that the volume of a shape is proportional to the cube of its linear dimensions (V ∝ L3).

Therefore, if we dilate the cone by a scale factor of 1/5, the new volume (V1) would be:

V1 = V-original × (scale factor)³
= 5000 m³ × (1/5)³
= 5000 m³ × 1/125
= 40 m³

This calculation shows that, as a result of applying the scale factor, the volume of the cone has been reduced significantly.

ANSWER

[tex]y = 2x -4[/tex]

EXPLANATION

Part a)

Eliminating the parameter:

The parametric equation is

[tex]x = 5 + ln(t) [/tex]

[tex]y = {t}^{2} + 5[/tex]

From the first equation we make t the subject to get;

[tex]x - 5 = ln(t) [/tex]

[tex]t = {e}^{x - 5} [/tex]

We put it into the second equation.

[tex]y = { ({e}^{x - 5}) }^{2} + 5[/tex]

[tex]y = { ({e}^{2(x - 5)}) } + 5[/tex]

We differentiate to get;

[tex] \frac{dy}{dx} = 2 {e}^{2(x - 5)} [/tex]

At x=5,

[tex] \frac{dy}{dx} = 2 {e}^{2(5 - 5)} [/tex]

[tex]\frac{dy}{dx} = 2 {e}^{0} = 2[/tex]

The slope of the tangent is 2.

The equation of the tangent through

(5,6) is given by

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y - 6 = 2(x - 5)[/tex]

[tex]y = 2x - 10 + 6[/tex]

[tex]y = 2x -4[/tex]

Without eliminating the parameter,

[tex] \frac{dy}{dx} = \frac{ \frac{dy}{dt} }{ \frac{dx}{dt} } [/tex]

[tex]\frac{dy}{dx} = \frac{ 2t}{ \frac{1}{t} } [/tex]

[tex]\frac{dy}{dx} = 2 {t}^{2} [/tex]

At x=5,

[tex]5 = 5 + ln(t) [/tex]

[tex] ln(t) = 0[/tex]

[tex]t = {e}^{0} = 1[/tex]

This implies that,

[tex]\frac{dy}{dx} = 2 {(1)}^{2} = 2[/tex]

The slope of the tangent is 2.

The equation of the tangent through

(5,6) is given by

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y - 6 = 2(x - 5) =[/tex]

[tex]y = 2x -4[/tex]

The equation of the tangent to the curve at the point (5,6) is [tex]\(y = 2x - 4\)[/tex].

To find the equation of the tangent to the curve given by the parametric equations [tex]\(x = 5 + \ln(t)\)[/tex] and [tex]\(y = t^2 + 5\)[/tex] at the point (5,6), we can approach this problem in two ways: by eliminating the parameter \(t\) and without eliminating the parameter.

Method 1: Eliminating the Parameter

Step 1: Express (t) in terms of (x)

[tex]\[ x = 5 + \ln(t) \implies \ln(t) = x - 5 \implies t = e^{x-5} \][/tex]

Step 2: Substitute (t) into (y)

[tex]\[ y = t^2 + 5 \implies y = (e^{x-5})^2 + 5 \implies y = e^{2(x-5)} + 5 \][/tex]

Step 3: Find [tex]\(\frac{dy}{dx}\)[/tex]

[tex]\[ y = e^{2(x-5)} + 5 \][/tex]

[tex]\[ \frac{dy}{dx} = 2e^{2(x-5)} \][/tex]

Step 4: Evaluate [tex]\(\frac{dy}{dx}\)[/tex] at (x = 5)

[tex]\[ \frac{dy}{dx}\bigg|_{x=5} = 2e^{2(5-5)} = 2e^0 = 2 \][/tex]

Step 5: Equation of the tangent line

The slope (m = 2). The tangent line at (5,6) is:

[tex]\[ y - 6 = 2(x - 5) \][/tex]

[tex]\[ y = 2x - 10 + 6 \][/tex]

[tex]\[ y = 2x - 4 \][/tex]

Method 2: Without Eliminating the Parameter

Step 1: Find [tex]\(\frac{dx}{dt}\)[/tex] and [tex]\(\frac{dy}{dt}\)[/tex]

[tex]\[ x = 5 + \ln(t) \implies \frac{dx}{dt} = \frac{1}{t} \][/tex]

[tex]\[ y = t^2 + 5 \implies \frac{dy}{dt} = 2t \][/tex]

Step 2: Find [tex]\(\frac{dy}{dx}\)[/tex]

[tex]\[ \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{2t}{\frac{1}{t}} = 2t^2 \][/tex]

Step 3: Find (t) at the point (5,6)

From [tex]\(x = 5 + \ln(t)\)[/tex]:

[tex]\[ 5 = 5 + \ln(t) \implies \ln(t) = 0 \implies t = e^0 = 1 \][/tex]

Step 4: Evaluate [tex]\(\frac{dy}{dx}\)[/tex] at (t = 1)

[tex]\[ \frac{dy}{dx}\bigg|_{t=1} = 2(1)^2 = 2 \][/tex]

Step 5: Equation of the tangent line

The slope (m = 2). The tangent line at (5,6) is:

[tex]\[ y - 6 = 2(x - 5) \][/tex]

[tex]\[ y = 2x - 10 + 6 \][/tex]

[tex]\[ y = 2x - 4 \][/tex]

Thus, using both methods, the equation of the tangent to the curve at the point (5,6) is [tex]\(y = 2x - 4\)[/tex].

Answer:

Step-by-step explanation:

The total sold is the sum of the individual numbers sold, hence c+h.

We assume "3 times more" means "3 times as many", so the number of hotdogs sold (h) is 3 times the number of cheeseburgers sold (c), hence 3c.

  c + h = 220

  h = 3c

_____

55 cheeseburgers and 165 hotdogs were sold.

Answer:

x = 0

Step-by-step explanation:

Since the product is not equal zero, we need to multiply both parenthesis first:

[tex](x-3)(x+9) =-27[/tex]

[tex]x*x+x*9+(-3)*x+(-3)*9=27[/tex]

[tex]x^2+9x-3x-27=27[/tex]

[tex]x^2+6x-27=27[/tex]

Add 27 from both sides:

[tex]x^2+6x-27+27=-27+27[/tex]

[tex]x^2-6x=0[/tex]

Factor [tex]x[/tex] out:

[tex]x(x+6)=0[/tex]

Apply the zero product:

[tex]x=0,x+6=0[/tex]

[tex]x=0,x=-6[/tex]

The solutions of the equation are [tex]x=0[/tex] and [tex]x=-6[/tex].

We can conclude that the correct answer is x = 0.

Answer:

C: x = 0

There is no solution.

Answer:

Option C and D are correct.

Step-by-step explanation:

Area of rectangle = 144 cm^2

Width of rectangle = 9 cm

Length of rectangle = ?

We know,

Area of rectangle = Length * Width

144 = Length * 9

144/9 = Length

=> length = 16 cm

Option A is incorrect as 3 times width = 3* 9 = 27 but our length = 16 cm

Option B is incorrect as length = 16 cm and not 63 cm

Option C is correct as Length < 2(Width)

=> 16 < 2(9) => 16 < 18 which is true.

Option D is correct.

Perimeter = 2(Length + Width)

Perimeter = 2(16+9)

Perimeter = 50 cm

Option E is incorrect as Length ≠ Width

Answer:

C. The length is less than 2 times the width.

D. The perimeter is 50 centimeters.

Step-by-step explanation:

The area of the rectangle is given as 144 square centimeters and its width is 9 centimeters. The formula for the area of a rectangle is given as;

Area = length*width

144 = length*9

length = 144/9

length = 16 centimeters

A. The length is 3 times the width.

3 times the width; 3*9 = 27 cm which is not equal to 16. Hence this statement is false.

B.The length is 63 centimeters.

This statement is also false since the length is 16 cm

C.The length is less than 2 times the width.

Answer:

B) 34.1 cm

Step-by-step explanation:

The longer diagonal is longer than either side, but shorter than their sum. The only answer choice in the range of 24–39 cm is choice B.

_____

You are given sufficient information to use the Law of Cosines to find the diagonal length. If we call it "c", then the angle opposite that diagonal is the larger of the angles in the parallelogram: 120°. The law of cosines tells you ...

c^2 = a^2 +b^2 -2ab·cos(C)

Here, we have a=24, b=15, C=120°, so ...

c^2 = 24^2 +15^2 -2·24·15·cos(120°) = 576 +225 +360 = 1161

c = √1161 ≈ 34.073 . . . . cm

Rounded to tenths, the diagonal length is 34.1 cm.

Answer:

  3y - 5 + 2y = 7

Step-by-step explanation:

Subtracting 5 from the second equation gives ...

  x = 3y -5

Using the expression on the right for x in the first equation gives ...

  x + 2y = 7 . . . . . . . . first equation

  (3y -5) +2y = 7 . . . . with expression substituted for x

  3y - 5 + 2y = 7 . . . . with parentheses removed

Answer:

Sally; Sally

Step-by-step explanation:

For the free throws... let's see the stats:

Sally: 10 free throws

Jesse: 8 free throws.

Advantage?: Sally

For the three-points baskets:

Sally: 3

Jesse: 1

Advantage: Sally

Sally dominates in both categories, sorry Jesse.

Answer:

sally sally

Step-by-step explanation:

the numbers are just greater for both stats for her

Answer: Third Option

[tex]f(x) +3[/tex]

Step-by-step explanation:

The function [tex]y=log_2(x)[/tex] passes through point (2, 1) because the exponential function [tex]2 ^ x = 2[/tex] when [tex]x = 1[/tex].

Then, if the transformed function passes through point (2, 4) then this means that the graph of [tex]y=log_2(x)[/tex] was moved vertically 3 units up.

The transformation that vertically displaces the graph of a function k units upwards is:

[tex]y = f (x) + k[/tex]

Where k is a positive number. In this case [tex]k = 3[/tex]

Then the transformation is:

[tex]f(x) +3[/tex]

and the transformed function is:

[tex]y = log_2 (x) +3[/tex]

Answer:

5/12 or 41.66%

Step-by-step explanation:

When throwing two six-sided dice, you have 36 possible outcomes:

{1,1} {1,2} {1,3} {1,4} {1,5} {1,6} {2,1} {2,2} {2,3} {2,4} {2,5} {2,6} {3,1} {3,2} {3,3} {3,4} {3,5} {3,6} {4,1} {4,2} {4,3} {4,4} {4,5} {4,6} {5,1} {5,2} {5,3} {5,4} {5,5} {5,6} {6,1} {6,2} {6,3} {6,4} {6,5} {6,6}

To find what is the probability the second player will win, we need to see how many of those 36 possibilities have a combined total of 8 or more (to beat the 7 of the first player):

These 15 combinations have a total of 8 or more:

{2,6} {3,5} {3,6} {4,4} {4,5} {4,6} {5,3} {5,4} {5,5} {5,6} {6,2} {6,3} {6,4} {6,5} {6,6}

So, the probability the second player gets 8 or more and wins is:

15/36 or 5/12 or 41.66%

Find the points of Midtown and Downtown then use the midpoint formula.

Midtown = (6,12)

Downtown = (12,4)

Midpoint = X2+X1 /2 , Y2+Y1 /2

Midpoint = 12+6 /2 , 4+12 /2

Midpoint = 18/2 , 16,2

Midpoint = (9,8)

Answer:

3.5 seconds, B

Step-by-step explanation:

This is an upside down parabola, a function that is extremetly useful in helping us to understand position and velocity and time and how they are all related.  Her upwards velocity is 16 ft/sec and she starts from a height of 140 feet, according to the problem.  The h is the height she ends up at after a certain amount of time has gone by.  You want to know how long it will take her to hit the water.  When she hits the water, she has no more height.  Therefore, her height above the water when she hits the water is 0.  Plug in a 0 for h and factor the quadratic to get t = -2.5 seconds and t = 3.5 seconds.  The only two things in math that will never ever be negative is a distance measure and time, so we can disregard the -2.5 and go with 3.5 seconds as our answer.

Answer:

B

Step-by-step explanation:

Answer:

No. Anna is incorrect.

Step-by-step explanation:

In order to find if the answer is right, just find the diagonals using the pythogorean theorem.

a² + b² = c²

For the rectangle, the base is 14 and the height is 7. We will have to find the hypotenuse.

14² + 7² = c²

196 + 49 = c²

245 = c²

c = √245

c = √49 × √5

c = 7√5

For the square, the base is 7 and the height is 7. We will have to find the hypotenuse.

7² + 7² = c²

49 + 49 = c²

98 = c²

c = √98

c = √49 × √2

c = 7√2

Now compare :

7√5 and 7√2

Clearly, 7√5 is not the double of 7√2

Expand:

[tex]n(n-1)-(n+3)(n+2)=(n^2-n)-(n^2+5n+6)=-6n-6[/tex]

Then we can write

[tex]n(n-1)-(n+3)(n+2)=6\boxed{(-n-1)}[/tex]

which means [tex]6\mid n(n-1)-(n+3)(n+2)[/tex] as required.

Answer:

P(cream and sugar) = 0.4

Step-by-step explanation:

* Lets study the meaning of or , and on probability

- The use of the word or means that you are calculating the probability

 that either event A or event B happened

-  Both events do not have to happen

- The use the word and, means that both event A and B have to happen

* The addition rules are:

# P(A or B) = P(A) + P(B) ⇒ mutually exclusive (events cannot happen

 at the same time)

# P(A or B) = P(A) + P(B) - P(A and B) ⇒ non-mutually exclusive (if they

 have at least one outcome in common)

- The union is written as A∪B or “A or B”.

- The intersection is written as A∩B or “A and B”

* Lets solve the question

∵ P(cream) = 0.5

∵ P(sugar) = 0.6

∵ P(cream or sugar) = 0.7

- To find P(cream and sugar) lets use the rule of non-mutually exclusive

∵ P(A or B) = P(A) + P(B) - P(A and B)

∴ P(cream or sugar) = P(cream) + P(sugar) - P(cream and sugar)

- Lets substitute the values of P(cream) , P(sugar) , P(cream or sugar)

 in the rule

∵ 0.7 = 0.5 + 0.6 - P(cream and sugar) ⇒ add the like terms

∴ 0.7 = 1.1 - P(cream and sugar) ⇒ subtract 1.1 from both sides

∴ 0.7 - 1.1 = - P(cream and sugar)

∴ - 0.4 = - P(cream and sugar) ⇒ multiply both sides by -1

∴ 0.4 = P(cream and sugar)

* P(cream and sugar) = 0.4

Answer:

0.4

Step-by-step explanation:

Answer:

Last option

−1 • f(x)

Step-by-step explanation:

The function [tex]f(x) = (0.5) ^ x[/tex] passes through point (-1, 2) because:

[tex]f(-1) = (0.5) ^ {-1}= \frac{1}{(0.5)} = 2[/tex]

and also goes through the point (0, 1)

Because:

[tex]f(0) = (0.5)^0 = 1[/tex]

Then, if the transformed function passes through the point (0, -1) and passes through the point (-1, -2) then this means that the graph of [tex]f(x) = (0.5) ^ x[/tex] reflected on the axis x. This means that if the point [tex](x_0, y_0)[/tex] belongs to f(x), then the point [tex](x_0, -y_0)[/tex] belongs to the transformed function

The transformation that reflects the graph of a function on the x-axis is.

[tex]y = cf(x)[/tex]

Where c is a negative number. In this case [tex]c = -1[/tex]

Then the transformation is:

[tex]y = -1*f(x)[/tex]

and the transformed function is:

[tex]f (x) = - (0.5) ^ x[/tex]

Answer:

f(x) -2 is the correct answer.

Step-by-step explanation:

Just took the test!

The area of shaded regions can be found using geometric principles or methods of integration depending on the actual shape and context. In most cases, area is proportional to the square of the distances. Integration techniques would be used if the shaded region is under a curve on a graph.

To find the area of the shaded regions, depending upon the shape and complexity of the region, you'd typically use geometric principles and calculations, potentially including those related to rectangles, triangles, circles, and/or other shapes. In some cases, these calculations might include figuring out the area of a larger shape and then subtracting the area of a smaller, non-shaded shape. For example, the area of a disc could be found by using the equation А = лr², and placing limits of integration from r = 0 to r = R in case the shaded area is comprised of thin rings of different radii. In other cases, you might be using principles of integration if the shaded region is under a curve on a graph, integrating the function f(x) from a certain lower limit x₁ to upper limit x₂. Also, keep in mind that the area is usually proportional to the square of the distances in a certain set-up.

https://brainly.com/question/34380164

#SPJ12

Answer:

x = 52/9

Step-by-step explanation:

The exterior angle is half the difference of the intercepted arcs, so we have ...

9x -5 = (158 -64)/2

9x = 52 . . . . . . . . . . . add 5

x = 52/9 = 5 7/9

The domain of all three functions is all real numbers. The range of f(x) and h(x) is all real numbers, but the range of g(x) is all real numbers except 0.

The statements that accurately compare the domain and range of the functions are:

For the functions f(x) = 3x^2, g(x) = 1/3x, and h(x) = 3x:

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#SPJ3

Answer:c and d

Step-by-step explanation:

i got it right

Answer:

D.

Step-by-step explanation:

I also haven't learned this yet but i could tell that in the second image if A.F = 1/2AC and DE = A.F, therefore DE = 1/2AC. The problem is that i don't know if it is B or D.

Sorry .-.

1 Simplify \frac{14}{30}

​30

​

​14

​​  to \frac{7}{15}

​15

​

​7

​​ .

\frac{7}{15}\div 14.00

​15

​

​7

​​ ÷14.00

2 Use this rule: a\div \frac{b}{c}=a\times \frac{c}{b}a÷

​c

​

​b

​​ =a×

​b

​

​c

​​ .

\frac{7}{15}\times \frac{1}{14.00}

​15

​

​7

​​ ×

​14.00

​

​1

​​  

3 Use this rule: \frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd}

​b

​

​a

​​ ×

​d

​

​c

​​ =

​bd

​

​ac

​​ .

\frac{7\times 1}{15\times 14.00}

​15×14.00

​

​7×1

​​  

4 Simplify 7\times 17×1 to 77.

\frac{7}{15\times 14.00}

​15×14.00

​

​7

​​  

5 Simplify 15\times 14.0015×14.00 to 210210.

\frac{7}{210}

​210

​

​7

​​  

6 Simplify.

1/30

Answer:

68

Step-by-step explanation:

∠DPG and ∠EPF are vertical angles, so they are equal.

7x = 4x + 48

3x = 48

x = 16

So ∠DPG is:

∠DPG = 7x

∠DPG = 112

∠DPE and ∠DPG are supplementary, so they add up to 180:

∠DPE + ∠DPG = 180

∠DPE + 112 = 180

∠DPE = 68

Answer:

Nickola swam for 4 hours and ran for 5.5 hours

Step-by-step explanation:

To solve this, we can use a system of equations.

First we can set up a system of equations like this

[tex]2s+15r=90.5[/tex] and

[tex]s+r=9.5[/tex]

Next we will use substitution to solve for one of the values. We can solve the second equation such that

[tex]s=9.5-r[/tex]

Now we can substitute this into the first equation for s

[tex]2(9.5-r)+15r=90.5[/tex]

Now we can solve for r

[tex]19-2r+15r=90.5[/tex]

[tex]19+13r=90.5[/tex]

[tex]13r=71.5[/tex]

[tex]r=5.5[/tex]

Now we can plug this value into the second equation to get the value for s

[tex]s+5.5=9.5[/tex]

[tex]s=4[/tex]

Now we can plug these values into the first equation to make sure we have the right values

[tex]2(4)+15(5.5)=90.5[/tex]

[tex]90.5=90.5[/tex]

1. C. -512√3+512i

2. B. 16(cos240°+i sin240°)

3. D. 3√2+3√6i, -3√2-3√6i

4. A. cos60°+i sin60°, cos180°+i sin180°, cos300°+i sin300°

5. D. 2√3(cos π/6+i sin π/6), 2√3(cos 7π/6+i sin 7π/6)

We will see that the equivalent expression is:

[tex]8*(cos(240\°) + i*sin(240\°))[/tex]

So the correct option is the first one.

We have the expression:

[2*(cos(240°) + i*sin(240°))]^4

Remember that Euler's formula says that:

[tex]e^{ix} = cos(x) + i*sin(x)[/tex]

Then we can rewrite our expression as:

[tex][2*(cos(240\°) + i*sin(240\°)]^4 = [2*e^{i*240\°}]^4[/tex]

Now we distribute the exponent:

[tex]2^4*e^{4*i*240\°} = 8*e^{i*960\°}[/tex]

Now, we need to find an angle equivalent to 960°.

Remember that the period of the trigonometric functions is 360°, then we can rewrite:

960° - 2*360° = 240°

This means that 960° is equivalent to 240°. Then we can write:

[tex]8*e^{i*960\°} = 8*e^{i*240\°} = 8*(cos(240\°) + i*sin(240\°))[/tex]

So the correct option is the first one.

If you want to learn more about complex numbers, you can read:

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Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

The absolute value function prevents the expression from being a polynomial. The degree of 3 in y^3 is an odd number so that polynomial function will not be even.

Answer:

The equation [tex]y=x^3[/tex] is not an equation of a simple , even polynomial function.

Step-by-step explanation:

Even  function : A function  is even when its graph is symmetric with respect to y-axis.

Algebrically , the function f is even if and only if

f(-x)=f(x) for all x in the domain of f.

When the function does not satisfied the above condition then the function is called non even function.

f(x)[tex]\neq[/tex] f(-x)

Now , we check given function is even or not

A. y= [tex]\mid x\mid[/tex]

If x is replaced by -x

Then we get the function

f(-x)=[tex]\mid -x \mid[/tex]

f(-x)=[tex]\mid x \mid[/tex]

Hence, f(-x)=f(x)

Therefore , it is even  polynomial function.

B. [tex]y=x^2[/tex]

If x is replace by -x

Then we get

f(-x)=[tex](-x)^2[/tex]

f(-x)=[tex]x^2[/tex]

Hence, f(-x)=f(x)

Therefore, it is even polynomial function.

C. [tex]y=x^3[/tex]

If x is replace by -x

Then we get

f(-x)=[tex](-x)^3[/tex]

f(-x)=[tex]-x^3[/tex]

Hence, f(-x)[tex]\neq[/tex] f(x)

Therefore, it is not even polynomial function.

D.[tex]y= -x^2[/tex]

If x is replace by -x

Then we get

f(-x)= - [tex](-x)^2[/tex]

f(-x)=-[tex]x^2[/tex]

Hence, f(-x)=f(x)

Therefore, it is even polynomial function.

Answer: C. [tex]y=x^3[/tex] is not simple , even polynomial function.

The answer is:

The number of teeth of Gear 2 is 90 teeth.

[tex]N_{2}=90teeth[/tex]

To calculate the number of teeth for the Gear 2, we need to use the following formula that establishes a relation between the number of RPM and the number of teeth of two or more gears.

[tex]N_{1}Z_{1}=N_{2}Z_{2}[/tex]

Where,

N, are the rpm of the gears

Z, are the teeth of the gears.

We are given the following information:

[tex]Z_{1}=30teeth\\N_{1}=150RPM\\N_{2}=50RPM[/tex]

Then, substituting and calculating we have:

[tex]N_{1}Z_{1}=N_{2}Z_{2}[/tex]

[tex]150RPM*30teeth=N_{2}50RPM[/tex]

[tex]N_{2}=\frac{150RPM*30teeth}{50RPM}=90teeth[/tex]

[tex]N_{2}=90teeth[/tex]

Hence, we have that the number of teeth of Gear 2 is 90 teeth.

Have a nice day!

Answer:

y = 2x+3

Step-by-step explanation:

The slope is "what happens to the graph when you move one unit to the right in x-direction". As you can check, if you move 1 to the right, the y value increases by 2. Therefore the slope is 2.

The intercept is the graph's y value when x=0, ie., when it passes the y axis. This is at y=3.

Now we have our two ingredients, so y = slope * x + intercept, so 2x+3