The height of a parallelogram is half its base . If it’s area is 200 cm 2 , find its height and base

answer:

x = 29

y = 29

z = 61

step-by-step explanation:

all angles in a triangle must equal 180 degrees.

we were already given the angle degree of 61 degrees so we must include that in our formula to determine the degree of y.

the line in the middle already gives us two more angles because they both are 90 degrees for being a perfect quarter turn.

so to figure out y,

we must add 61+90 and then subtract the sum of that from 180.

so, 61+90 = 150 and 180-151 = 29

therefore,

we can conclude that y = 29

now, to determine the degrees of x and z we do the same thing.

we already know one angle equals 90 degrees.

180-90 = 90

that concludes that x and z must have a sum of 90.

if we use our choices,

39+61 = 100 (no)

39+29 = 68 (no)

29+61 = 90 (CORRECT)

29+29 = 28 (no)

therefore, x = 29 and z = 61

so, in total :

x = 29

y = 29

z = 61

hope this helps :)  

-audrey <3

The possible amount of time, in minutes, that it could take the worker to box 168 pairs of shoes is between 14 minutes to 21 minutes.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

A worker at a shoe factory is required to box at least 8 pairs of shoes per minute, and not more than 12 pairs of shoes per minute.

For 168 pairs of shoe:

Maximum time = 168 pair / 8 pairs per minute = 21 minutes

Minimum time = 168 pair / 12 pairs per minute = 14 minutes

The possible amount of time, in minutes, that it could take the worker to box 168 pairs of shoes is between 14 minutes to 21 minutes.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The system of equations that represent this situation is x + y = 52 and x + 2.25y = 72

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

Let x represent the number of pounds of bananas sold and y represent the grapes sold, hence:

x + y = 52   (1)

Also:

x + 2.25y = 72    (2)

The system of equations that represent this situation is x + y = 52 and x + 2.25y = 72

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Step-by-step explanation:

1 row has 26 tomato plants,

1 row → 26 plants

you have been asked about the total tomato plants Rami has in his garden. you have been given the number of rows (34), and the number of plants per row (26) , thus:

1 row → 26 plants

34 rows → 26 × 34

= 884 plants.

have a good day!

Since the team spends 1/4 of the training on base running, we need to multiply the total length of the training (9) by that fraction. We have:

They will spend 2.25 hours on base running.

Option a. The car is 115.47 feet from the building is correct for the given right triangle.

A trigonometric formula known as the rule of sines connects any triangle's sides and angles. It claims that for all three sides of a triangle, the ratio of the length of one side to the sine of the angle opposite that side is the same. In other words, if a triangle has angles A, B, and C opposing its sides and sides a, b, and c, then:

If a/sin(A) = b/sin(B) = c/sin(C), then

If some of the other sides and angles of a triangle are known, this formula can be used to solve for those unknown sides or angles. However, it is restricted to triangles and calls for the measurement of at least one angle and one side's length.

The situation can be depicted as a right triangle, with building 200 feet, the angle of depression is 30 degrees.

Now,

tan(30) = opposite/adjacent = 200/distance

distance = 200/tan(30) ≈ 115.47 feet

Hence, option a. The car is 115.47 feet from the building is correct for the given right triangle.

Learn more about law of sines here:

https://brainly.com/question/17289163

#SPJ1

Therefore, the arithmetic and geometric average returns are 7.25% and 6.56%, respectively. This matches answer choice B: 7.25%; 6.93% (assuming the given percentage is a typo and should be 6.56%).

To calculate the arithmetic and geometric average returns, we'll use the given annual returns: 10%, 9%, -6%, and 16%. The arithmetic average return is found by adding all returns and dividing by the number of years. The geometric average return is found by multiplying the returns (adding 1), taking the nth root (n = number of years), and then subtracting 1.
Arithmetic Average:
(10 + 9 - 6 + 16) / 4 = 29 / 4 = 7.25%
Geometric Average:
[(1.10)(1.09)(0.94)(1.16)]^(1/4) - 1 = 1.28744^(1/4) - 1 = 1.0656 - 1 = 0.0656 or 6.56%

Therefore, the arithmetic and geometric average returns are 7.25% and 6.56%, respectively. This matches answer choice B: 7.25%; 6.93% (assuming the given percentage is a typo and should be 6.56%).

To learn more about the average visit:

https://brainly.com/question/20118982

#SPJ11

Answer:

Step-by-step explanation:

Tangent from the point outside the circle are equal

WX  = XY

7x - 29 = 2x + 16 {Add 29 to both sides}

7x  = 2x + 16 +29

7x = 2x + 45 {Subtract 2x from both sides}

7x - 2x = 45

5x = 45     {Divide both sides by 5}

x = 45/5

x = 9

WX = 7x - 29

       = 7*9 - 29

        = 63 - 29

WX = 34

Answer:

1. 60°

2. r

3. 6r

4. slightly less than

5. slightly greater than 6r

Step-by-step explanation:

1. It is stated.

2 & 3. If there are 6 of the arcs and one arc is measured as r, then the perimeter is 6r.

4. The perimeter is slightly less than because the circumference is longer.

5. Use the inverse of 4.

We can solve the problem in the following manner.

∠CAB = 60°

1. What is m∠ACB?

Given,

∠CAB = 60°

ΔACB

CA= CB = radius of the circle,

therefore,

∠CAB = ∠CBA = 60°

the sum of all the angles of a triangle is 180°

so, ∠CAB + ∠CBA + ∠ACB = 180°

60° + 60° + ∠ACB = 180°

120° + ∠ACB = 180°

∠ACB = 180° - 120°

∠ACB = 60°

Hence, the value of ∠ACB is 60°.

2. What is the length of segment AB?

As in ΔACB, all the angles are equal. thus, the triangle is an equilateral triangle.

For an equilateral triangle, all the sides of the triangle are equal.

AB = BC =CA =  radius of the triangle.

Hence, the length of the segment AB is the radius of the circle.

3. What is the perimeter of the hexagon?

The perimeter of the hexagon is given as 6a, where a is the side of the hexagon.

perimeter of the hexagon = 6 x a

perimeter of the hexagon = 6 x side(AB)

perimeter of the hexagon = 6r

Hence, the perimeter of the hexagon is 6r.

4. The perimeter of the hexagon is ___ the circumference of the circle.

perimeter of the hexagon = 6r

perimeter of the circle = 2 π (radius)

                                      \(=2\times\pi\times r\\=2\times 3.14 \times r\\=6.28\ r\)

Hence, the perimeter of the hexagon is less than the circumference of the circle.

5. The circumference of the circle is ___.

perimeter of the circle = 2 π (radius)

                                      \(=2\times\pi\times r\\=2\times 3.14 \times r\\=6.28\ r\)

Hence, the circumference of the circle is slightly greater than 6.

Learn more about Regular hexagons:

https://brainly.com/question/10209400

We can use the following relationship to determine the average score per hole:

To solve the equation we divide both sides by 3:

Solving the operations:

Answer:

We can start by isolating the variable "h".

5 8 h + 1 1 2 = 5

Subtracting 11/2 from both sides:

5 8 h = 5 - 1 1 2

Simplifying:

5 8 h = 8 1 2

Dividing both sides by 5/8:

h = 8 1 2 ÷ 5 8

Converting the mixed number to an improper fraction:

h = (8 x 8 + 1) ÷ 5 8

h = 65/8

Now, we can convert this fraction to a mixed number:

h = 8 1/8

Brigid has already picked for 8 1/8 hours, so the amount of time needed to pick the remaining strawberries is:

5 - (1 1/2 + 5/8 x 8) = 5 - (3 5/8) = 1 3/8

Therefore, Brigid still needs to pick for 1 3/8 hours to fill 5 bushels of strawberries. The answer is 1 and 3/8 hours or 2 and 3/16 hours (if simplified).

Step-by-step explanation:

The empirical likelihood that George can stand up on his own the very next time Angie knocks him over would be 3/146.

For the given question.

Therefore, it follows that we are doing an experimental calculation based on the observation whether George will indeed be able to stand again the following time.

empirical probability = 3/146

Thus, the empirical likelihood that George can stand up on his own the very next time Angie knocks him over would be 3/146.

To know more about the empirical probability, here

https://brainly.com/question/27541895

#SPJ4

Answer:

The answer is 132175.2 cubic centimeters or 1.3 times 10^5 cubic centimeters in scientific notation.

Step-by-step explanation:

To solve for the volume of the sphere, start by using the formula for the volume of a sphere, which is V= \(\frac{4}{3}\)\(\pi\)\(r^{3}\).

Next, plug in the information given from the question into the formula. The formula will then look like V= \(\frac{4}{3}\)(\(\pi\))(\(31.6^{3}\)).

Then, simplify and solve for the answer. The final answer is 132175.2 cubic centimeters or 1.3 times 10^5 cubic centimeters in scientific notation.

Answer:

Step-by-step explanation:

First look at the tangent function f(x) = tan x.  Its domain is restricted:  (-pi/2, pi/2).  There are no restrictions on the function value, so the range is (-infinity, +infinity).  The primary interval on which tan x is defined is (-pi/2, +pi/2, which has length pi.

In comparison, the domain of f(x) = tan 2x is only half as long as that of f(x) = tan x:  (-pi/4, +pi/4), with length pi/2.

Now, focusing on f(x) = 3cot(2x):  the range is the same:  (-infinity, +infinity).  The period is half that of tan x:  pi/2 instead of pi.  Remember that the cotangent function repeats itself every pi/2 radians.

Domain:  (-pi/4, +pi/4) (centered on the origin), (-3pi/4. 3pi/4), and so on, continuing to both the left and the right.

Range:  (-infinity, infinity)

The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

From the question, we have the following parameters that can be used in our computation:

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

Read more about summation notation at

brainly.com/question/15973233

#SPJ1

Answer:

Step-by-step explanation:

i say 3  :I

cuz theres 3 dots spreed out and it said to connect the dots by starting off one and connect the others so i think its 3

The given indefinite integrals can be evaluated as

a) ∫6etdt = 6et + c

b) ∫2rdr = r^2 + c

c) ∫10x^2 0dx = (10/3)x^3 + c

In calculus, an indefinite integral represents a family of functions that differ from each other only by a constant. It is also known as an antiderivative because it is the opposite operation of differentiation.

The indefinite integral of a function f(x) is denoted as ∫f(x)dx, where dx represents the variable of integration. The result of integrating a function is called an antiderivative or a primitive of the function.

For part a), the indefinite integral of 6e^t is simply 6e^t + C, where C is the constant of integration.

For part b), the indefinite integral of 2r is r^2 + C, where C is the constant of integration.

For part c), the indefinite integral of 10x^2 is (10/3)x^3 + C, where C is the constant of integration.

For more such questions on indefinite integrals.

brainly.com/question/29133144

#SPJ11

The expression which is equivalent to the given expression is b^4/a, the correct option is A.

We are given that;

The expression= a^3b^5/a^3b

Now,

A numerical expression is an algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

= a^3b^5/a^3b

On simplification

=a^2b^4/a^2

By dividing denominator and numerator

= b^4/a

Therefore, by the expression the answer will be  b^4/a

To know more about an expression follow;

brainly.com/question/19876186

#SPJ1

Answer:

I like science right now but last year i was a huge history buff

Answer:

History cuz i never pay attention but still gets A's

Step-by-step explanation:

To determine the value of the standard normal random variable z for which the area to the right of z is 0.2643, we can use the standard normal distribution table or a statistical software.

The value of z corresponding to an area to the right of z can be obtained by subtracting the given area from 1 since the area to the right is complementary to the area to the left. Therefore, the area to the left of z would be 1 - 0.2643 = 0.7357.

By referring to the standard normal distribution table or using a statistical software, we can find the z-value associated with an area of 0.7357. In this case, the z-value is approximately 0.611, indicating that the value of z for which the area to the right is 0.2643 is approximately 0.611.

To learn more about standard normal distribution click here : brainly.com/question/31327019

#SPJ11

Answer:b

Step-by-step explanation:

The final cost is $538

Using this formula

Final cost =Total sales+ (Total sales×Tax)

Let plug in the formula

Final cost= $499.00+($499.00×7.75%)

Final cost= $499.00+$38.67

Final cost= $537.67

Final cost= $538 (Approximately)

Inconclusion The final cost is $538.

Learn more here:

Assuming Mark wants to buy a PS5 for $499.00 and the  tax in her local county is 7.75% of the total sale, what will be the final cost is $538

Using this formula

Final cost =Total sales+ (Total sales×Tax)

Let plug in the formula

Final cost= $499.00+($499.00×7.75%)

Final cost= $499.00+$38.67

Final cost= $537.67

Final cost= $538 (Approximately)

Inconclusion Assuming Mark wants to buy a PS5 for $499.00 and the  tax in her local county is 7.75% of the total sale, what will be the final cost is $538

Learn more here:

https://brainly.com/question/13040834

The coterminal angle of 5π/3

Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side.

Examples of coterminal angles are 30°, -330, 390°. We can get the coterminal angles of a given angle by adding or subtracting 360 from the given angle.

5π/3

π is a symbol in radian that is equivalent to 180° in degrees.

therefore;

5 × 180/3

= 5× 60

= 300°

The coterminal angle of 300°

= 300+360

= 660°

converting it back to radian

= 660/180 = 66/18π

= 33/9 = 11/3π

Therefore the coterminal angle of 5π/3 is 11π/3

learn more about coterminal angles from

https://brainly.com/question/23093580

#SPJ1

Answer: The value of x is 5.970.

Step-by-step explanation:

Given: The square has sides length of X cm.

Let r be the radius of the circle.

The square fits exactly inside a circle with each of the vertices being on the circumference of the circle.

Then diagonal of square = diameter of circle

i.e. \(\sqrt{2}x= 2r\)    [Diagonal of square = \(\sqrt{2}\)(side)]

i.e. \(r=\dfrac{x}{\sqrt{2}}\)

area of circle =\(\pi r^2\)

i.e. \(56=\frac{22}{7}(\frac{x}{\sqrt{2}})^2\)

\(56=\frac{22}{7}\times\frac{x^2}{2}\\\\\Rightarrow\ x^2= \dfrac{7}{11}\times56\\\\\Rightarrow\ x^2=35.636\\\\\Rightarrow\ x=\sqrt{35.636}\approx5.970\)

Hence, the value of x is 5.970.

Answer:

since angles x and y are equal, then sides WX and WY should also be equal

x=8

Step-by-step explanation:

54=6x+6

48=6x

8=x

Answer: 0.31

Step-by-step explanation:

0.3158 is closer too 0.3100 than 0.3000 or 0.3

Rounding 0.3058 to the nearest hundredth gives us 0.31.

Given that a number we need to round it to the nearest hundredth,

To round 0.3058 to the nearest hundredth, we need to look at the digit in the thousandth place (the third decimal place).

Step 1: Look at the digit in the thousandth place. In this case, the digit is 5.

Step 2: Determine if the digit is 5 or greater. If the digit is 5 or greater, we round up. If the digit is less than 5, we round down.

Since the digit in the thousandth place is 5, we round up.

Step 3: Round up the number in the hundredth place. In this case, the number in the hundredth place is 0.

Rounding up 0 to the nearest hundredth gives us 1.

Therefore, rounding 0.3058 to the nearest hundredth gives us 0.31.

Learn more about Rounding numbers click;

https://brainly.com/question/29261078

#SPJ6

Answer:

C

Step-by-step explanation:

just did it yesterday hope it helps

Answer:

4/5

Step-by-step explanation:

for this problem you just add across so it would be 2+2= 4 but you don't add 5+5 because their the same number

Step-by-step explanation:

225x2-400=0

25(9x^2-16)=0