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In a 45-45-90 triangle, what is the length of the hypotenuse when the length of one of the legs is 5 in.?




√5 in.

5√5 in.

2√5 in.

5√2 in.

The mean weight of five complete computer stations is 167.2 pounds.

The weights of four of the computer stations are 158.4 pounds, 162.8 pounds, 165 pounds, and 178.2 pounds.

We have to determine the weight of fifth computer station.

Let the weight of fifth computer station be 'x' pounds.

Mean is calculated by sum of all the observations divided by the total number of observations.

So, [tex] \frac{158.4+162.8+165+178.2+x}{5}=167.2 [/tex]

[tex] \frac{664.4+x}{5}=167.2 [/tex]

[tex] {664.4+x}=167.2 \times 5 [/tex]

[tex] {664.4+x}=836 [/tex]

x= 171.6 pounds

The weight of fifth computer station is 171.6 pounds.

To find the weight of the fifth computer station, subtract the sum of the weights of the four given stations from the mean weight.

The mean weight of five complete computer stations is 167.2 pounds. To find the weight of the fifth computer station, we can calculate the sum of the weights of all five stations and then subtract the sum of the weights of the four given stations. The weight of the fifth station can be found by subtracting the sum of the weights of the four given stations from the mean weight.

Sum of the weights of all five stations = 5 * 167.2 pounds

Sum of the weights of the four given stations = 158.4 pounds + 162.8 pounds + 165 pounds + 178.2 pounds

Weight of the fifth station = Sum of the weights of all five stations - Sum of the weights of the four given stations

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Answer:

3.9 and -3.3

Step-by-step explanation:

1) cot 70=x/12

Cot 70=[opposite side]/[adyacent side]=x/12

The option 1 is correct

2) cot 70=12/x

Cot 70=[opposite side]/[adyacent side]=x/12

The option 2 is not correct

3)sec 20=x/12

Sec 20 =1/cos20

Cos 20==[opposite side]/[hypotenuse]=12/z

1/(1/cos20)-------> 1/(12/z)------> z/12

The option 3 is not correct

 
4) sec 20=12/x

Sec 20 =1/cos20

Cos 20==[opposite side]/[hypotenuse]=12/z

1/(1/cos20)-------> 1/(12/z)------> z/12

The option 4 is not correct

Answer:

A:  cot 70 degrees = x/12

Step-by-step explanation:

on edg... Good Luck!!!

Answer:  The correct options are

(A) ML ∥ NO,

(C) LO ≅ MN.

Step-by-step explanation:  Given that in quadrilateral LMNO, LO ∥ MN.

We are to select the correct additional information that would be sufficient along with the given information to conclude that LMNO is a parallelogram.

PARALLELOGRAM:  A parallelogram is a quadrilateral if ine of the following conditions are satisfied:

(i) Two pairs of opposite sides parallel

or

(ii) one pair of opposite sides parallel and congruent.

The given condition is

LO ∥ MN.

So, the other additional sufficient condition will be

either the other pair of opposite sides parallel, i.e., ML ∥ NO,

or

the same pair of parallel sides are congruent, i.e,  LO ≅ MN.

Thus, the correct statements are ML ∥ NO and  LO ≅ MN.

Option (A) and (C) are correct.

Answer:

a and c

Step-by-step explanation:

The GCF of the given expression is:

                          [tex]5x^2y[/tex]

The GCF ( greatest common factor ) is the greatest divisor which divides all the terms completely.

Here we have the expression as:

[tex]10x^4y^3-5x^3y^2+20x^2y[/tex]

Here we see that the factors of the first term are:

[tex]10x^4y^3=2\times 5\times x\times x\times x\times x\times y\times y\times y[/tex]

The factor of the second term is:

[tex]-5x^3y^2=-1\times 5\times x\times x\times x\times y\times y[/tex]

and the factor of the third term is:

[tex]20x^2y=2\times 2\times 5\times x\times x\times y[/tex]

i.e. the factor which is common to all the three terms are:

[tex]5\times x\times x\times y=5x^2y[/tex]

Hence, the GCF is:   [tex]5x^2y[/tex]

The value of the given expression is 24.

The given expression is 4x-yz.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Put, x=12, y=8 and z=3 in the given expression, we get

4x-yz = 4×12 - 8×3

= 48 - 24

= 24

Therefore, the value of the given expression is 24.

To learn more about an expression visit;

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The first step to solve this problem is to compute for the area of the rectangular backyard. The formula in computing the area of a rectangle is:

A = LW

Substituting the given measurement to the formula:

A = 31 (24)

A = 744 square feet

The area of the backyard is 744 square feet.

Since each pack of seed covers 12 square feet, you need to divide this to the total area of the backyard.

Therefore, you need 62 (744 / 12) packs of seed to cover the backyard.

Trey will need 62 packs of seed to cover his backyard.

To find the number of packs of seed Trey will need to cover his backyard, we need to calculate the total area of the backyard and then divide it by the area covered by each pack of seed.

The formula to find the area of a rectangle is length x width. For Trey's backyard, the length is 31 feet and the width is 24 feet, so the area is 31 x 24 = 744 square feet.

Each pack of seed covers 12 square feet, so we divide the total area of the backyard by the area covered by each pack of seed: 744 / 12 = 62 packs of seed.

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Answer:

Option A. (0, -2)

Step-by-step explanation:

In the given graph coordinates of point A are (2, 0).

Now this point is rotated by -90° about the origin, that means rotation has been done clockwise by 90°.

Now after rotation this point A will lie on the negative side of the y-axis and the new coordinates become (0, -2).

Therefore, option A. (0, -2) is the correct option.

Answer:

y=cos x

Step-by-step explanation:

A P E X

Answer:

$1381.79 withheld from his pay last year.

Step-by-step explanation:

A student working as a pizza delivery man and earned = $6324.00

first we calculate all the taxes at the given tax rates

Federal Tax Rate = 10% of 6324.00

= 0.10 × 6324 = $632.40

State Tax Rate = 4.2% of 6324.00

= 0.042 × 6324 = $265.608

FICA is comprised of taxes for social security and medicare. For social security tax rate is 6.2% and for medicare tax rate is 1.45% which add up to 7.65%.

FICA combined Tax Rate = 7.65% of 6324.00

= 0.0765 × 6324 = $483.786

Now we add all the taxes to get what amount withheld from his pay

= 632.40 + 265.608 + 483.786 = $1381.79

$1381.79 withheld from his pay last year.

Final answer:

To find the equation of a circle, use the formula (x - h)² + (y - k)² = r², where (h,k) is the center of the circle and r is its radius. You apply this knowledge to other circular calculations, such as the angular velocity or the position and velocity of a moving point on the perimeter of the circle.

Explanation:

Finding the Equation of a Circle

To find the equation of a circle, you need to know the circle's radius (r) and the coordinates of its center (h,k). The general form of the equation is (x - h)² + (y - k)² = r². The values of h and k are the x and y coordinates of the center of the circle, respectively. If you recall the formula for the circumference of a circle, which is 2πr, and the area, which is πr², you can see that these both incorporate the radius of the circle in their calculations, similar to how the radius is used in the equation of the circle. When given certain dimensions or related motion problems, you can substitute known values into the equation to solve for the unknowns.

For example, if a circle has a radius of 5 units and its center is at the point (3,4), the equation would be (x - 3)² + (y - 4)² = 25. To find equations related to circular motion, like in the scenario of a student on a merry-go-round, knowing the radius also allows for determining the angular velocity and the velocity of a shadow or any point moving in circular motion.

Answer:

x + 3 + x

Step-by-step explanation:

3x :

This is a product of two terms, where x is any variable.

3 + x :

This is sum of two terms,where x is any variable.

x^3 :

This expresses x to the power of three. It can also be written as  (x times x times x ). Thus it is the product of three terms, where x is any variable.

x + 3 + x :

This is the sum of three terms, where x is any variable.

Thus answer is x + 3 + x

Answer: 58.1

Step-by-step explanation:

98 - 62 / 62 = rounds to 58.1 Thank me Later..