How do you find the hypotenuse of an isosceles right triangle when given the area?

Option B is correct. 0.39 goldfish per cubic feet is the density of the tank given that there are 22 goldfishes and volume of the tank is 56 cubic feet. This can be obtained by using the formula of density.

Given that there are 22 goldfishes,

mass of tank = 22 goldfishes

volume of tank = 56 cubic feet

                      = 22/56

                      = 0.39 goldfish per cubic feet

Hence 0.39 goldfish per cubic feet is the density of the tank given that there are 22 goldfishes and volume of the tank is 56 cubic feet.

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Answer: 0.39 goldfish

Step-by-step explanation:

The equation that can be used to find y, the year in which both bodies of water have the same amount of mercury is 0.05 + 0.1y = 0.12 + 0.06y. Hence, the 3rd option is the right choice.

In the question, we have been asked for the equation that can be used to find y, the year in which both bodies of water have the same amount of mercury.

First, we will find the equations showing the level of mercury in each body of water.

For the first water body:

Initial measure of mercury = 0.05 ppb.

Rate of rising = 0.1 ppb each year.

Number of years = y.

Thus, the equation showing level of mercury = 0.05 + 0.1y.

For the second water body:

Initial measure of mercury = 0.12 ppb.

Rate of rising = 0.06 ppb each year.

Number of years = y.

Thus, the equation showing level of mercury = 0.12 + 0.06y.

We are looking for the equation, to find y, the year in which both bodies of water have the same amount of mercury.

As they will have the same amount of mercury, their respective equations showing the level of mercury should be equal, that is:

0.05 + 0.1y = 0.12 + 0.06y, which is the required equation.

Thus, the equation that can be used to find y, the year in which both bodies of water have the same amount of mercury is 0.05 + 0.1y = 0.12 + 0.06y. Hence, the 3rd option is the right choice.

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For the complete question, refer to the attachment.

The value of x when y =2 is 8

The inverse proportion to the square of x represented as:

k = yx^2

Where

k represents the constant of proportion

When y = 2, x = 8.

So, we have:

k =2 * 8^2

k =128

Substitute k = 128 in k = yx^2

So, we have:

yx^2 = 128

When y = 2, we have:

2x^2 = 128

Divide by 2

x^2 = 64

Take the square roots

x = 8

Hence, the value of x when y =2 is 8

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Answer:

(-3, 1)

Step-by-step explanation:

the easiest thing to do is look at the graph and find the point where the two lines intersect

Answer:

6

Step-by-step explanation:

[tex]5(5+3)=4(x+4) \\ \\ 40=4(x+4) \\ \\ 10=x+4 \\ \\ x=6[/tex]

Answer:

3x²y (2x²-3y²+ 4y)

Step-by-step explanation:

Factor the expression 6x^4y-9x²y³+12x²y².

First, check if there is a GCF. The GCF is 3x²y.

3x²y (2x²-3y²+ 4y).

This equation cannot be factored further. Therefore, the answer is
3x²y (2x²-3y²+ 4y).

Hope this helps!

Answer:

3x²y(-3y²+4y+2)

Step-by-step explanation:

6x⁴y-9x²y³+12x²y²

solution:

first common

3x²y(2x²-3y²+4y)

3x²y(-3y²+4y+2)

Answer: [tex]MP=10, PN=6[/tex]

Step-by-step explanation:

Corresponding sides of similar triangles are proportional, so:

[tex]\\\\frac{MP}{5}=\frac{8}{4}\\\\MP=10\\\\\frac{PN}{3}=\frac{8}{4}\\\\PN=6[/tex]

Based on the average monthly rainfall amounts as shown in the graph, the sum of the average monthly rainfall 11/12 inches.

The average can be found by adding up the monthly rainfall and dividing by 12 months.

Solving gives:

= (1/8 + 1/8 + 1/8 + 2/8+ 2/8 + 5/8 + 7/8 + 9/8 + 13/8 + 15/8 + 16/8 + 16/8) / 12

= (88/8) / 12

= 11/12 inches

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Option C. The function that has the table here has  exactly one x-intercept.

As the signs of the functions are changing, we can see that there is a crossing to the x axis.

This tells us that the zero value that we see is the x intercept and there is no other x intercept in the question.

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The value of r in the exponential decay function 7000 = 20000(1-r)^10 is 10%

The equation is given as:

7000 = 20000(1-r)^10

The above equation is an exponential decay function.

So, we have:

7000 = 20000(1-r)^10

Divide both sides of the equation by 20000

0.35 = (1-r)^10

Take the 10th root of both sides

0.35^(1/10) = 1 - r

Evaluate the exponent

0.9 = 1 - r

Add r to both sides

0.9 + r = 1

Subtract 0.9 from both sides

r = 1 - 0.9

Evaluate

r = 0.1

Express as percentage

r = 10%

Hence, the value of r in the exponential decay function 7000 = 20000(1-r)^10 is 10%

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The quotient of 24x2y + 8xy2 + 8xy and -4xy is -6x - 2y - 2

The statement is given as:

Divide 24x2y + 8xy2 + 8xy by -4xy

The quotient is represented as:

Quotient = (24x^2y + 8xy^2 + 8xy)/(-4xy)

Factor out -4xy

Quotient = (-4xy)(-6x - 2y - 2)/(-4xy)

Evaluate the quotient

Quotient = -6x - 2y - 2

Hence, the quotient of 24x2y + 8xy2 + 8xy and -4xy is -6x - 2y - 2

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The correct option is A. m ≤ (8)(20)

The inequality which gives the possible values of 'm' is m ≤ (8)(20).

A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

According to the question;

Terrence's car contains 8 gallons of fuel.

Terrence can drive the car 'm' miles using the fuel currently in the car.

The car can drive 20 miles per gallon of fuel,(which is maximum fuel capacity of the car to drive).

Then,

The total miles 'm' covered by the car is 8×20 which is maximum capacity of the car to travel.

Thus, total miles covered by the car are less than the maximum value which is given by the inequality-

m ≤ (8)(20)

Therefore, the inequality which gives the possible values of 'm' is m ≤ (8)(20).

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The complete question is-

Terrence's car contains 8 gallons of fuel. He plans to drive the car 'm' miles using the fuel currently in the car. If the car can drive 20 miles per gallon of fuel, which inequality gives the possible values of 'm'?

answer choices

A. m ≤ (8)(20)

B. m ≥ (8)(20)

C. 8 ≤ 20m

D. 8 ≥ 20 m

The y-value of the terminal point of the vector is 3.

In this question we must apply a matricial form of rotation, which is a kind of rigid transformation. This transformation is defined by the following formula:

[tex]\vec A' = \vec T\cdot \vec A[/tex], where [tex]\vec A' , \vec A \in \mathbb{R}_{1 \times 2}[/tex], [tex]\vec T \in \mathbb{R}_{2 \times 2}[/tex]

If we knw that [tex]\vec A = \left[\begin{array}{c}- 4\\3\end{array}\right][/tex] and [tex]\vec T = \left[\begin{array}{cc}-1&0\\0&1\end{array}\right][/tex], then the transformed vector column is:

[tex]\left[\begin{array}{cc}x\\y\end{array}\right] = \left[\begin{array}{cc}-1&0\\0&1\end{array}\right] \cdot \left[\begin{array}{cc}-4\\3\end{array}\right][/tex]

[tex]\left[\begin{array}{cc}x\\y\end{array}\right] = \left[\begin{array}{cc}4\\3\end{array}\right][/tex]

The y-value of the terminal point of the vector is 3.

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The equivalent expression of [tex](1 + \frac{1}{y}) \div (1-\frac 1y)[/tex] is [tex]\frac{y + 1}{y-1}[/tex]

The fraction is given as:

[tex](1 + \frac{1}{y}) \div (1-\frac 1y)[/tex]

Take the LCM

[tex]\frac{y + 1}{y} \div \frac{y-1}y[/tex]

Express as products

[tex]\frac{y + 1}{y} \times \frac{y}{y-1}[/tex]

Evaluate the product

[tex]\frac{y + 1}{y-1}[/tex]

Hence, the equivalent expression of [tex](1 + \frac{1}{y}) \div (1-\frac 1y)[/tex] is [tex]\frac{y + 1}{y-1}[/tex]

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Answer:

  A.  The volumes are the same, based on Cavalieri's principle.

Step-by-step explanation:

Cavalieri's principle tells us the volumes of solids will be identical if their cross sectional areas are identical at every height.

A right cylinder and an oblique cylinder of the same height and radius will both have circular cross sections of the given radius at any height. Since the radius is the same, the area of the circle is the same. Hence the requirements of Cavalieri's principle are met, and the cylinders have the same volume.

To calculate accurate vital statistics rates to represent the entire United States, the quotient is multiplied by an appropriate factor such as 1,000 or 100,000 to represent the larger population.

As it is given in the description itself, to compute accurate vital statistics rates for the full United States, multiply the quotient by a suitable factor, such as 1,000 or 100,000 to represent the greater population.

Therefore, to calculate accurate vital statistics rates to represent the entire United States, the quotient is multiplied by an appropriate factor such as 1,000 or 100,000 to represent the larger population.

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Answer:

b.  -x + y = 0

Step-by-step explanation:

Direct variation:

Direct variation means "y varies directly as x”:

[tex]y \propto x \implies y=kx[/tex]

where k is the (non-zero) constant of variation.

To determine which of the given equations represents a direct variation, isolate y for each and compare with the direct variation equation.

Equation a

[tex]y=\dfrac{4}{3}x-2[/tex]

This is not a direct variation equation as there is an addition of -2.

Equation b

[tex]-x+y=0[/tex]

[tex]\implies y=x[/tex]

This is a direct variation equation where the constant of variation is 1.

Equation c

[tex]xy=8[/tex]

[tex]\implies y=\dfrac{8}{x}[/tex]

This is not a direct variation equation as y is inversely proportional to x.

Equation d

[tex]y=14[/tex]

This equation does not include the variable x, and so is therefore not a direct variation equation.

If y varies inversely with x then the line must be linear and increasing

And the y intercept must be 0 in y=mx+c

#1

c=-2

#2

Yes

#3

No

#4

Parallel to x axis no direct variation

The type of transformations that maps triangle ABC onto Triangle prime ABC is a  Reflection across the line y=x ; translation 10 units to the right and 4 units up.

Note that: Triangle ABC has vertices at points  which are:

A(-6,2), B(-2,6) and C(-4,2).

Therefore, the reflection across the line y=x has the rule of"

(x, y) ---(y, x).

Hence:

A(-6,2) -- A''(2,-6);

B(-2,6)--- B''(6,-2);

C(-4,2)----C''(2,-4).

2. The translation 10 units to the right and 4 units up is:

(x, y)----(x+10,y+4).

Hence

A''(2,-6)----A'(12,-2);

B''(6,-2)----B'(16,2);

C''(2,-4)----C'(12,0).

Therefore, Points A'B'C' are said to be exactly of the vertices of that of triangle A'B'C'.

Hence, The type of transformations that maps triangle ABC onto Triangle prime ABC is a  Reflection across the line y=x ; translation 10 units to the right and 4 units up.

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The correct statement comparing the theoretical and experimental probabilities is given as follows:

[tex]\frac{1}{4} < \frac{7}{25}[/tex].

A probability is given by the number of desired outcomes divided by the number of total outcomes.

The theoretical probability is taken before any experiment. Since the four sections are equal, the theoretical probability is:

T(H) = 1/4.

The experimental probability is taken considering previous experiments. Out of 100 tosses, 28 landed on H, hence:

E(H) = 28/100 = 7/25.

Hence the correct statement is:

[tex]\frac{1}{4} < \frac{7}{25}[/tex].

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No directions given here. What exactly do you need to be done with this trigonometric function?

The probability of not drawing a black marble is 4/5

The probability of drawing a red marble is 3/10

Probability determines the odds of the occurrence of a random event. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Probability of not drawing a black marble = total marbles that are not black / total number of marbles

(5 + 3) / (5 + 3 + 2) = 8/10 = 4/5

The probability of drawing a red marble = total number of red marbles / total number of marbles

= 3/10

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Answer:

See image

Step-by-step explanation:

Plato

The number will represent a number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

Inequality are expressions not separated by an equal sign. Given the inequality expression:

3(8 – 4x) < 6(x – 5)

Expand

24 - 12x < 6x - 30

Collect the like terms

-12x-6x < -30 - 24

-18x <-54

x > 3

Hence the number will represent a number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

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Answer:

a) is the correct answer

Answer:

First, use the distributive property and distribute 8 to the [tex](x,2)[/tex] in the first part of the equation to get [tex]8x + 16[/tex].

Next, also use the distributive property to distribute the 4 to the [tex](2x+9)[/tex] in the second part of the equation to get [tex]8x+36[/tex].

The simplified equation looks like this: [tex]8x+16=8x+36[/tex].

The fraction m/n that lies between 0 and 1 is equivalent to the real number m · n⁻¹, where m, n > 0 and m < n.

By algebra, we know that fractions, a kind of rational numbers, are real numbers of the form m/n, where m and n are integers and n ≠ 0.

In addition, the operator "/" means division, an operator derived from the existence of multiplicative inverse and fundamental operation of multiplication in the real field.

Thus, the rational number m/n is equivalent to the number m · n⁻¹. If the rational number is between 0 and 1, then m, n > 0 and m < n.

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Considering the linear functions on the graph, the inequality that matches the situation is:

B.

A linear function is modeled by:

y = mx + b

In which:

The lower bound of the interval is a linear function with y-intercept of b = 2, that also passes through (2,3), hence the slope is:

m = (3 - 2)/(2 - 0) = 1/2.

Hence the inequality is:

[tex]y \geq \frac{1}{2}x + 2[/tex]

The upper bound of the interval is a linear function with y-intercept of b = 1, that also passes through (2,5), hence the slope is:

m = (5 - 1)/(2 - 0) = 2.

Hence the inequality is:

[tex]y \leq 2x + 1[/tex]

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The events are not independent

Say that there are n marbles in the bag

When the first red marble is drawn, the number of marbles in the bags becomes n - 1

This means that the first red marble has changed the probability of drawing the second red marble

This represents a dependent event

Hence, the events are not independent

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This can be proved by using identities of trigonometry.

Given that,  

sin x + sin²x = 1 ⇒ sin x = 1 - sin²x

⇒ sin x = cos²x   (∵sin²x + cos²x = 1)

We have to prove that,

cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x = 1

LHS = cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x

= sin⁶x + 3sin⁵x + 3sin⁴ + sin³x

= (sin²x)³ + 3(sin²x)²sin x + 3(sin²x) (sin x)² + (sin x)³

= (sin²x + sin x)³           (∵(a+b)³ = a³ + 3a²b + 3 ab² + b³)

= 1³ = 1 = RHS

LHS = RHS

Hence the equation is proved since both sides of the equation are equal.

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The value of the function is h(w - 5) = w^2 - 11w +25

The function is given as:

h(y) = y^2 - y - 5

Substitute w - 5 for y

h(w - 5) = (w - 5)^2 - (w - 5) - 5

Expand the equation

h(w - 5) = w^2 - 10w + 25 - w + 5 - 5

Evaluate the like terms

h(w - 5) = w^2 - 11w +25

Hence, the value of the function is h(w - 5) = w^2 - 11w +25

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Answer:

18 students

Step-by-step explanation:

Answer:

the range between 18 and 24 is 6

Step-by-step explanation:

24-18=6