Three gears are arranged as shown in the figure. Find angle θ.

Hello!

It is given information that this triangle is a right triangle, meaning that the Pythagorean Theorem can apply here.

[tex]a^2+b^2=c^2[/tex]

We can set the length of a leg as an unknown variable [tex]x[/tex].

[tex]x^2+4^2=(3x)^2[/tex]

Remember that it is the whole [tex]3x[/tex] term being squared, meaning that it'll simplify to [tex]9x^2[/tex], not [tex]3x^2[/tex].

[tex]x^2+16=9x^2[/tex]

[tex]8x^2=16[/tex]

[tex]x^2=2[/tex]

[tex]x=\sqrt{2}[/tex]

This means we can plug back in to find the sides.

The hypotenuse would be [tex]3\sqrt{2}[/tex], or 4.2.

And the legs would be 1.4 and 4, respectively.

Hope this helps!

Answer:

Step-by-step explanation:

From the given information;

We will realize that in the 2nd & 3rd equation, the integer "x" is missing.

So, the correct equation should be:

4x - 2 + 6z = 0

x - y - z = 0

2x - y + 3z = 0

By rearrangement; if we switch equation (1) and (2)

x - y - z = 0      ----- (1)

4x - 2 + 6z = 0 ------ (2)

2x - y + 3z = 0  ------ (3)

If we multiply equation (1) and add that to  equation (2);

Then, we have:

x - y - z = 0

2y + 10z = 0

2x - y + 3z = 0

Also, if we multiply equation (1) by -2 and add that to equation (3), we have:

x - y - z = 0

2y + 10z = 0

y + 5z = 0

From above recent equation, if we swap equation (2) and (3);

x - y - z = 0

y + 5z = 0

2y + 10z = 0

Then, multiply equation (2) with -2, followed by adding it to equation(3);

Then:

x - y - z = 0

y + 5z = 0

0 = 0

Now, there exists no equation (3). Thus, let assume z = t to solve for x & y

y + 5z = 0

y = -5t

Similarly;

x - y - z = 0

x = -5t + t

x = -4t

Hence;

x = -4t; y = -5t; &  z = t

Answer:

Step-by-step explanation:

Total number of rolls = 50

Number of times rolling a 6 = 8 times

Number of times not rolling a 6 = 50 -8 = 42

P(~6) = 42/50 = 0.84

Answer:

t = 9 s

Step-by-step explanation:

A stone is thrown downward with an intitial velocity of 29.5 m/sec will travel a distance of a meters, where

[tex]s(t) = -4.9t^2 + 29.4+132.3[/tex]

We need to find when the stone will hit the ground. It means when s(t) = 0. So,

[tex]-4.9t^2 + 29.4t+132.3=0\\\\t=-3\ and\ t=9[/tex]

So, the stone will take 9 seconds to hit the ground. Hence, this is the required solution.

Answer:64 Meters

Step-by-step explanation:

Answer:

Imaoo

Step-by-step explanation:

answer: C

Answer: Letsssss goooooo

the answer is 4y

dababy letssssssssssss gooooooooooooooooo

Step-by-step explanation:

Answer:

x^12

Step-by-step explanation:

when multiplying with exponents, keep base and add exponents

when dividing with exponents, keep base and subtract exponents

Answer:

the value of x is acb 133°

Answer:

69

because you put them in order least to greatest (or greatest to least)

55, 58, 62, 63, 68, 70, 71, 79, 81, 82

there are 10 numbers total

the two middle numbers are

68 and 70

the number in between is 69

Step-by-step explanation:

median= middle number.

where there is an even amount of numbers, you find the number in between the middle two numbers when in order.

(this can be found by adding the two numbers together and then dividing by 2)

Answer:

1 1/8 cups of flour are required to bake 1 1/2 batches of cookies.

Step-by-step explanation:

Given that a recipe for 1 batch of cookies calls for 3/4 cup of flour, to determine how much flour is required to bake 1 1/2 batches of cookies, the following calculation must be performed:

3/4 = 0.75

1/2 = 0.5

1 = 0.75

1.5 = X

1.5 x 0.75 / 1 = X

1.125 = X

0.125 = 1/8

Thus, 1 1/8 cups of flour are required to bake 1 1/2 batches of cookies.

Answer:

(-1)(247.43)(-1)(5) = (-1)(-1)(247.43)(5)

Step-by-step explanation:

key answer

From the image we can see that; Lines r and s and lines t and u must be parallel.

The term parallel lines refers to those lines that can not meet. We know parallel lines by the arrows that show us where they are pointing to.

Thus, from the image we can see that; Lines r and s and lines t and u must be parallel.

Learn more about parallel lines:https://brainly.com/question/16701300

#SPJ1

Answer:

$240

Step-by-step explanation:

Answer:

29 day) $15.00

30 day $15.00

31 day $15.00

The cost was the same for all three days

Step-by-step explanation:

Rover = 3/4 can

Bobo = 1/2 can

29(3/4) + 29(1/2) = 21.75 + 14.5 = 36.25 cans

36.25/3 = 12.08

must buy 4 packs of 3 at $5.00 each = $15.00

30(3/4) + 30(1/2) = 22.5 + 15 = 37.5 cans

37.5/3 = 12.5

must buy 4 packs of 3 at $5.00 each = $15.00

31(3/4) + 31(1/2) = 23.25 + 15.5 = 38.75 cans

38.75/3 = 12.92

must buy 4 packs of 3 at $5.00 each = $15.00

Answer:

This is actually easy.

You need to multiply the term outside the bracket with the ones in the bracket (I hope I make sense lol)

Answer is 50 + 10n

Answer:

Step-by-step explanation:

Answer: y times y 8 times

Apply Exponent Rule

Simplified Form y^8

To write without exponents is basically just writing out y times itself 8 times.

9514 1404 393

Answer:

Step-by-step explanation:

EG and IF are assumed to be diameters of the circle. The measures of the two arcs created by a diameter are 180°.

1. There is no M

__

2. arc EF = arc EG -arc FG = 180° -35°

  arc EF = 145°

__

3. Angle EDI is a vertical angle to angle FDG, so has the same measure: 35°. Long arc EGI will be 360° minus the measure arc EI

  arc EGI = 360° -arc EI = 360° -35°

  arc EGI = 325°

__

4. Arc Gi is double the measure of arc GH, so is 38°×2 = 76°. Arc EI is the supplement to this:

  arc EI = 180° -arc GI = 180° -76°

  arc EI = 104°

Answer:

a) 100

b) 7

Step-by-step explanation:

Remember that angle measurements correspond to side lengths. This also means that if two sides or angles are congruent, then the angle or side opposite of them will also be congruent. For example, in part a two sides are both 6. This means that the angles opposite of them are also both 40. Finally, to find <K subtract 80 (because that is 40+40) from 180. Therefore, the answer is 100 degrees.

Next, remember that the markings on the angles in part b mean that the angles are congruent. Since all the angles are congruent, the sides must be as well. So HI=7.

Answer:

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

If A is an event that will never happen, then P(A)=​0

Answer:

36°

Step-by-step explanation:

From the question,

The sum of the exterior angle of a polygon = 360

From the diagram. the polygon is Decagon

Note: A Decagon is a polygon with 10 sides.

number of sides = 10 .

The exterior angle of a regular polygon = sum of the exterior angle/number of sides.

Exterior angle = 360/10

Exterior angle = 36°

Hence the measure the single extrior angle = 36°

Answer:

24 ft²

Step-by-step explanation:

1/2x12x4=24 ft²

Answer:

It would be D.

Step-by-step explanation:

This formula, A=1/2 bh, 1/2 base multiplied by height, is used to find the area of a triangle, therefore, D is the only viable answer.  

Answer:

A

Step-by-step explanation:

2.34 divided by 6 so then that gives you o.39

Answer:

third option

Step-by-step explanation:

subtract 125/4 from each side to get:

x² + 11x -1

use quadratic formula to get:

-11 ± √121 - 4(-1)/2

= -11 ± ([tex]\sqrt{125}[/tex]) / 2

* [tex]\sqrt{125}[/tex] = [tex]\sqrt{25}[/tex] · [tex]\sqrt{5}[/tex] = 5[tex]\sqrt{5}[/tex]

= -11 ± (5[tex]\sqrt{5}[/tex]) / 2

Answer:

24 blue cars

Step-by-step explanation:

In this problem, one is given the ratio of red to blue cars in the parking lot. One is given the actual number of red cars, and one is asked to find the number of blue cars. One can set up a proportion; ratio to actual, then solve to find the number of actual blue cars using the method of cross-products. One can set up the proportion using the ratios, but it is easier to express the proportion as the equality of two fractions. Thus, the following equation can be formed, let the parameter (x) represent the actual amount of blue cars;

[tex]\frac{red}{blue}= \frac{5}{3} = \frac{40}{x}[/tex]

Cross products,

[tex]5x = 120[/tex]

Inverse operations,

[tex]x = 24[/tex]