There are 5 gears connected in a row, the first one is connected to the second one, the second one is connected to the third one, and so on.If the first gear is rotating clockwise, what direction is the fifth gear turning?

Answers

Answer 1

Answer:

Answer:

fifth gear is also rotating clockwise

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Solve the system of equations using cramer's rule -x+y-3z=-4 3x-2y+8z=14 2x-2y+5z=7
Please help me solve this question.
Simplify the expression. q+12qa. -13qb. -11qc. 11qd. 13q

Given: Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8.

Simplify Q + S - T.

Answers

$Q+S-T=7m+3n+n+5-(-m-3n+8)\nQ+S-T=7m+4n+5+m+3n-8\nQ+S-T=8m+7n-3$

An equation in the system is y = x + 1. What is the other equation in the system if the solution is only at (0, 1)?x − y = 1

2x + 2y = 4

x + y = 1

x + 2y = 2

Answers

Answer:

The correct options are 3 and 4.

Step-by-step explanation:

An equation in the system is

$y=x+1$

The only one solution of the system of equation is (0,1). It means the equation must be satisfied by the point (0,1) and the equation is not equivalent to the given equation.

Two equations $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$ are equivalent if

$(a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2)$

All the given equations are not equivalent equations because for all equation s

$(a_1)/(a_2)\neq (b_1)/(b_2)\neq (c_1)/(c_2)$

Check each equation by (0,1).

For equation 1,

$x-y=1$

$0-1=1$

$-1=1$

This statement is false, therefore the option 1 is incorrect.

For equation 2,

$2x+2y=4$

$2(0)+2(1)=4$

$2=4$

This statement is false, therefore the option 2 is incorrect.

For equation 3,

$x+y=1$

$0+1=1$

$1=1$

This statement is true, therefore the option 3 is correct.

For equation 4,

$x+2y=2$

$0+2(1)=2$

$2=2$

This statement is true, therefore the option 4 is correct.

A)
x − y = 1
0 - 1 = 1
-1 = 1

Not true.

B)
2x + 2y = 4
2(0) + 2(1) = 4
0 + 2 = 4
2 = 4
Not true

C)
x + y = 1
0 + 1 = 1
1 = 1
True

D)
x + 2y = 2
0 + 2(1) = 2
2 = 2
True

The answer is C and D.

The formula for converting degrees Celsius to Fahrenheit is F= $(9)/(5)$ F+32. Which expression is correctly written to convert Fahrenheit temperatures into degrees Celsius?1) C= $(9)/(5)$ F+32
2) C= $(5)/(9)$ F-160
3) C= $(5F-160)/(9)$
4) C=32F+160

Answers

$F= (9)/(5) C+32\ /\cdot5\n \n5F=9C+160\ \ \ \Rightarrow\ \ \ 9C=5F-160\ /:9\n \nC= (5F-160)/(9) \ \ \ \Rightarrow\ \ \ Ans.\ 3)$

the answer to your question is number 3

A rectangle has an area of 4x2 +19x + 12 and a length of (x + 4). What is the width?

Answers

The width of the rectangle with an area x² = 19x + 12 is (4x + 3).

What are the area and perimeter of a rectangle?

The area of a rectangle is the product of its length and width.

The perimeter of a rectangle is the sum of the lengths of all the sides.

We know the area of a rectangle is (length×widh).

Given, A rectangle has an area of 4x² + 19x + 12 and a length of (x + 4).

∴ width of the rectangle is = (4x² + 19x + 12)/(x + 4).

Or, we know that the product of two linear equations is a quadratic so,

4x² + 19x + 12.

4x² + 16x + 3x + 12.

4x(x + 4) + 3(x + 4).

(x + 4)(4x + 3).

So, the width of the rectangle is (4x + 3).

learn more about quadratic equations here :

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The answer is (4x + 3) (x + 4)

Solve 2cos2x + cosx − 1 = 0 for x over the interval [0, 2pi ).

Answers

The solution of 2cos2x + cosx − 1 = 0 is $x=\pi.$

What is a Trigonometric equation?

A Trigonometric equation is an equation involving one or more trigonometric ratios of unknown angles.

How to solve?

2cos2x + cosx − 1 = 0

$-3+\cos \left(x\right)+4\cos ^2\left(x\right)=0$

$\cos \left(x\right)=(3)/(4),\:\cos \left(x\right)=-1$

And now,

$x=\pi +2\pi n$

Which is only $x=\pi$ .

Learn more about Trigonometric equations:

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Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 17. What percentage of people has an in score between 83 and 117

Answers

To find the percentage of people with an IQ score between 83 and 117, we need to find the area under the bell-shaped curve between these two scores.

First, we need to standardize the scores by subtracting the mean from each score and dividing by the standard deviation.

For a score of 83:

Standardized score = (83 - 100) / 17 = -1

For a score of 117:Standardized score = (117 - 100) / 17 = 1

Now, we can find the area under the curve between these standardized scores using a standard normal distribution table or calculator.

Using a standard normal distribution table, we can find the area for a standardized score of -1 as 0.1587. This represents the percentage of people below a score of 83.

Similarly, the area for a standardized score of 1 is 0.8413, representing the percentage of people below a score of 117.

To find the area between these two scores, we subtract the area below 83 from the area below 117:

0.8413 - 0.1587 = 0.6826

So approximately 68.26% of people have an IQ score between 83 and 117.

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