What is the Area of the Figure?

The value of y in the triangle is 2√10 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

The value of y can be found using the similar triangle ratios as follows:

Hence,

8 / y = y / 5

cross multiply

y² = 8 × 5

y²= 40

square root both sides of the equation

y = √40

Therefore,

y = 2√10 units

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Volume of the cylinder =  6838.92 cubic inches

We have to given that;

Sam needs to fill a cylindrical container with punch.

And, The container has a radius of 11 inches and a height of 18 inches.

Since, To determine the amount of cat litter the cylinder can hold, we need to calculate the volume of the cylinder.

Volume of a cylinder = πr²h

Where,

r=radius

h= height

Then,

π=22/7 or 3.14 (constant value)

r=11 inches

h=18 inches

Volume of a cylinder is,

= 3.14 × (11)² × 18

= 6838.92 cubic inches

Hence, Volume of the cylinder =  6838.92 cubic inches

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Answer:

The answer selected is correct

Step-by-step explanation:

When talking about balance, having -X (being X in the negative) , means owing X.

Dylan owes $19.25

Elise owes $42.75

Francesca owes $23

Jamaal owes $35.50

So naturally, Dylan owes the least.

Answer:

mean see weididjdbd ksksns e

Answer:

Let's take an example.

If you put the value of x as 1, it gives one.

Even if you put 3.997654, it will give 3.997654.

But for any negative real number, it gives the same number but not with it's negative sign. Like if x =-3/7,

It will give 3/7.

The notation used here means it is the modulus function.......

Answer:

42 ratones

Step-by-step explanation:

Los gatos comen 6 ratones cada 5 minutos. Aplicar esto a 7 y 7x6 = 42. Perdón por el mal español

Answer:1.7 x 10 ^ -5

Step-by-step explanation:

Answer:1.7 x 10-5

hope this helps

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

First we need to get the formula for calculating the average of two numbers which is easy because it is (x + y) / 2

So, the equation will be A = (x + y) / 2

Now all we have to do is get 'y' on one side and the rest of the equation on the opposite side and we will have our solution!

A = (x + y) / 2

A * 2 = (x + y) / 2 * 2 # This will get rid of the number 2 on the right hand side

A * 2 = x + y

A * 2 - x = x + y - x # Subtract the variable 'x' from each side.

A * 2 - x = y

And we can flip it around using the reflexive property of equality!

The answer is:

y = A * 2 - x

Hope this helps!

Answer:

3

Step-by-step explanation:

\(4x * x = 9 * 4\)

\(4x^2 = 36\)

\(x^2 = 9\)

\(x = 3\)

The probability of the book picking at random is a novel or a dictionary is 1/8.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Bookshelf:

5 cookbooks, 4 novels, 6 picture books, and 1 dictionary.

Total number of books = 5 + 4 + 6 + 1 = 16

The probability of picking a novel.

= 1/16

The probability of picking a dictionary.

= 1/16

The probability of the book picking at random is a novel or a dictionary.

= 1/16 + 1/16
= 2/16

= 1/8

Thus,

The probability is 1/18.

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Answer:

  (c)  The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).

Step-by-step explanation:

You want to know the relationship between the graphs of function f(x) and its inverse f⁻¹(x).

The inverse of a function maps every y-value of the original function to its corresponding x-value. That is if you have ...

  f(a) = b

then the graph of f(x) contains the ordered pair (a, b).

The inverse function will have the ordered pair (b, a). That is,

  f⁻¹(b) = a

If an ordered pair (x-intercept) of the inverse function is ...

  (P, 0)

Then there will be an ordered pair (0, P) on the graph of the original function. That point is the y-intercept, and its y-coordinate is the same as the x-coordinate of the x-intercept of the inverse function.

The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).

__

Additional comment

The graphs of the two functions are mirror images of each other across the line y=x.

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The joint costs allocated to Product B is $240,000.

We must allocate joint costs based on the relative physical quantities produced by each product.

The total physical quantity produced by both products is:

= Quantity of A + Quantity of B

= 10,000 + 40,000

= 50,000 pounds

We will calculate the proportion of physical quantity produced by product A:

= Quantity of B / Total physical quantity

= 40,000 / 50,000

= 0.8

The amount of joint costs allocated to Product B is will be

= Total joint costs x Proportion of

= $300,000 x 0.8

= $240,000.

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Answer:

Move the decimal place to the right 2 places.

Step-by-step explanation:

If you are multiplying it is right and the opposite for dividing.

Answer:

  B.  129.7°

Step-by-step explanation:

The law of sines tells you ...

  sin(C)/c = sin(A)/a

  sin(C) = (c/a)sin(A)

  C = arcsin((c/a)sin(A)) = arcsin(117/57·sin(22°)) = 50.3°

The value shown is the result of using the arcsin function, but we know that the supplement of this angle has the same sine value. Then, we could have ...

  C = 180° -50.3° = 129.7°

The figure shows C as an obtuse angle, so we choose this latter value as the appropriate answer to this question.

  C = 129.7° . . . . . matches choice B

_____

Comment on the answer

We note that choice C (50.3°) matches the result of straightforward use of the law of sines. This triangle actually has two solutions for angle C, as we have noted above. Often, figures are "not to scale," so the appearance of angle C as an obtuse angle cannot always be taken at face value. Here, because both choices for angle C are offered, we use the appearance of the figure to help decide the right one.

The equation 2 log₅ x = log₅ 4 + log₅ 9 has two solutions: x = 6.

To solve the equation 2 log₅ x = log₅ 4 + log₅ 9, we can use logarithmic properties to simplify and find the value of x.

Using the properties of logarithms, we can rewrite the equation as follows:

2 log₅ x = log₅ (4 * 9)

Next, we simplify the right side:

2 log₅ x = log₅ (36)

Now, we can use the property of logarithms that states logₐ b = c is equivalent to aᶜ = b. Applying this property, we have:

x² = 36

Taking the square root of both sides, we get:

x =  √36

Since the square root of 36 can be either positive or negative, we have two possible solutions:

x = 6

It's important to note that when working with logarithmic equations, we must always check if the obtained solutions satisfy the domain restrictions of the original equation. In this case, since the logarithm has a base of 5, the solution x = 6.

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Answer:

2.5 sec

Step-by-step explanation:

Height of wall = 2.5 m

initial speed of ball = 14 m/s

height from which ball is kicked = 0.4 m

we calculate the speed of the ball at the height that matches the wall first

height that matches wall = 2.5 - 0.4 = 2.1 m

using  =  + 2as

where a = acceleration due to gravity = -9.81 m/s^2 (negative in upwards movement)

=  + 2(-9.81 x 2.1)

= 196 - 41.202

= 154.8

v =  = 12.44 m/s

this is the velocity of the ball at exactly the point where the wall ends.

At the maximum height, the speed of the ball becomes zero

therefore,

u = 12.44 m/s

v = 0 m/s

a = -9.81 m/s^2

t = ?

using V = U + at

0 = 12.44 - 9.81t

-12.44 = -9.81

t = -12.44/-9.81

t = 1.27 s

the maximum height the ball reaches will be gotten with

=  + 2as

a = -9.81 m/s^2

0 =  + 2(-9.81s)

0 = 196 - 19.62s

s = -196/-19.62 = 9.99 m. This the maximum height reached by the ball.

height from maximum height to height of ball = 9.99 - 2.5 = 7.49 m

we calculate for the time taken for the ball to travel down this height

a = 9.81 m/s^2 (positive in downwards movement)

u = 0

s = 7.49 m

using s = ut + a

7.49 = (0 x t) +  (9.81 x  )

7.49 = 0 + 4.9

 = 7.49/4.9 = 1.53

t =  = 1.23 sec

Total time spent above wall = 1.27 s + 1.23 s = 2.5 sec

Answer:

20 becuase thats how many shells are in the table

Step-by-step explanation:

Answer:

1. = (-5 , -1)

2.= (4 , 0.5)

3 = infinite solutions

I dont know if 2 is right but I tried

The transformations of f(x) are (a) a horizontal shrink by a factor of 1/4,

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

f(x) = x²

g(x) = (4x)²

Mathematically, these equations can be represented as

g(x) = f(4x)

The above equations implies that, we have the transformation to be:

The 4x implies that the function f(x) is horizontally shrunk by a factor of 1/4

Hence, the transformed function is (a)

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Answer:

100 people

Step-by-step explanation:

Population Of People=115Percentagencrease=15%

The New Population corresponds to 115%

(That is 100+15)

We want to find the population that corresponds to 100% that is the original population.

Therefore Original Population;

\( \frac{100}{115}\times {115}{} \)

\(100 \: people\)

7 raised to the power of 4 equals 2,401, and the exponent we were looking for is 4.

What is meant by power?

Power is a function that represents the number of times a base number is multiplied by itself. It is the rate at which work is done or energy is transferred, measured in watts.

What is meant by exponent?

An exponent is a mathematical notation used to indicate the number of times a quantity is multiplied by itself. It is written as a superscript and represents the power to which a number or expression is raised.

According to the given information

To find the value of the exponent that satisfies the equation 7ˣ = 2,401, we can take the logarithm of both sides of the equation with respect to base 7. This gives us:

log7(7ˣ) = log7(2,401)

x = log7(2,401)

Using a calculator, we can find that log7(2,401) is approximately 3. Therefore, the value of x that satisfies the equation 7ˣ = 2,401 is 3.

Alternatively, we could also use the fact that 2,401 is equal to 7⁴ - 2, which can be written as:

7⁴ - 2 = (7²)² - 2

= 49² - 2

= 2,401

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Answer:

How to show that they are equal.

Step-by-step explanation:

3/4 times 25 equals 75/100 and then when you turn it into a decimal it is 0.75. That is why they are equal.

Answer:

net amount 143 89 tax 6.25 % which is $8.99 gross amount is $152.88

Answer: Hello, everyone. Today I will talk about linear relationship. Linear relationship can be off two times I have as positive and negative. Was it the relationship? Then we have two variables increase and degrees simultaneously. For example, if you study Morris, you are starting Mourners, then new score more exams. So as much as ours, we will devote to the studies as much You will score. If the number of ours increases, then the school's increases and if number of ours decreases sense were also decreases. This is a perfect example off positive linear relationship between two variables. Uh, we can have negatively near relationship there. One changes opposite together. If one increases the other decreases. For example, if prize price off goes up, then in my force. So if our price off sorting productive increases, then demand will start decreasing on by civil. So if prices will decrease, then our demon will start increasing. So this is an example where you can see the negatively. No relationship between two variables. Hank

Step-by-step explanation:

Step-by-step explanation:

75 cm/s

75/100 m/s

0.75 m/s

(SINCE 100 CM =1M-------75 CM=75/100M)

Answer: A

Step-by-step explanation: x=-2, y=3, z=-3

Answer:

A. -2, 3, -3

Step-by-step explanation:

x = 7 - 2y + z

y = 21 + 6x + 2z = 21 + 6×(7 - 2y + z) + 2z =

= 21 + 42 - 12y + 6z + 2z = 63 - 12y + 8z

13y = 63 + 8z

y = (63 + 8z)/13

2x + 2y - 3z = 11

2×(7 - 2y + z) + 2×(63 + 8z)/13 - 3z = 11

2×(7 - 2×(63 + 8z)/13 + z) + 2×(63 + 8z)/13 - 3z = 11

14 - 4×(63 + 8z)/13 + 2z + 2×(63 + 8z)/13 - 3z = 11

-2×(63 + 8z)/13 - z = -3

-2×(63 + 8z) - 13z = -39

-126 - 16z - 13z = -39

-29z = 87

z = -3

y = (63 + 8×-3)/13 = (63 - 24)/13 = 39/13 = 3

x = 7 - 2×3 + -3 = 7 - 6 - 3 = -2