Two right triangles are proportional. The shortest leg of the small triangle is 4 in and the hypotenuse is 12 in. The shortest leg of the large triangle 8 in. Find the length of the hypotenuse of the large triangle.

Answer:

B

Step-by-step explanation:

the zeros are the values of x on the x- axis where the graph crosses

the graph crosses the x- axis at 1 and 3

then the zeros are x = 1 , x = 3

The equations of the parabolas are y = x² - 6x - 7 and y = x² - 7

Parabola 1

Given that

The points (-1,0), (7, 0) and (3,-16)

The equation is represented as

y = ax² + bx + c

So, we have

a - b + c = 0

49a + 7b + c = 0

9a + 3b + c = -16

Make c the subject in a - b + c = 0

c = b - a

So, we have

49a + 7b + b - a = 0

9a + 3b + b - a = -16

48a + 8b = 0

8a + 4b = -16

Multiply 8a + 4b = -16 by 2

48a + 8b = 0

16a + 8b = -32

Subtract

32a = 32

So, we have

a = 1

Recall that 48a + 8b = 0

So, we have

48 + 8b = 0

This gives

8b = -48

Divide

b = -6

Also, we have

c = b - a

This gives

c = -6 - 1

c = -7

So, the equation is

y = x² - 6x - 7

Parabola 2

Given that

The points (-4,9), (-3, 2) and (0,-7) and (4,9)

The equation is represented as

y = ax² + bx + c

So, we have

16a - 4b + c = 9

9a - 3b + c = 2

c = -7

16a + 4b + c = 9

The equations become

16a - 4b = 16

9a - 3b = 9

16a + 4b = 16

Add (1) and (3)

32a = 32

So, we have

a = 1

Subtract (1) and (3)

-8b = 0

So, we have

b = 0

So, the equation is

y = x² - 7

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x^2 - 2x + 1 is the required quadratic equation using the completing the square

Given the quadratic expression below

x^2 - 2x

We need to determine the constant that will make the expression a perfect square.

The constant will be the half of the square of coefficient of 'x'

Coefficient of 'x' = -2

Half of the coefficient of 'x' = -2/2 = -1

Square of the coefficient = (-2/2)^2

Square of the coefficient = 1

Hence the complete quadratic expression using the completing the square is x^2 - 2x + 1

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(a) The union set is AUB'={f, k, m, x, y}.

(b) The union set is A'UB'={q,k, x, y}.

The union of two sets is also a set. This set contains all the elements of both two sets.

The universal set is U= {f, k, m, q, x,y} and two subsets are A={f, k, m, y} and B = {f, m,q}.

(a)

B' is the complementary set of B. So, find the elements of B'=U-B.

B'= {f, k, m, q, x,y}-{f, m,q}

={k, x,y}

Now, find the union set AUB'.

AUB' ={f, k, m, y}U{k, x,y}

={f, k, m, x, y}

Therefore, the required answer is AUB'={f, k, m, x, y}.

(b)

Also, A' is the complementary set of A. So, find the elements of A'=A-B.

A'= {f, k, m, q, x,y}-{f, k,m, y}

={q,x}

Now, find the union set A'UB'.

A'UB' ={q,x}U{k, x,y}

={q,k, x, y}

Therefore, the required answer is A'UB'={q,k, x, y}.

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Answer:

Standard form of the equation for the circle

(x + 3)² + (y + 5)² = 40

Step-by-step explanation:

The equation of a circle in standard form is
[tex]\boxed{(x - a)^2 + (y-b)^2= r^2}[/tex]

where (a, b) is the center of the circle and r is the radius

To find center of circle

The end points of the diameter are (-5, -11) and (-1, 1)

The center of the circle is midway between these two points

The x-coordinate of the midpoint = (-5 + -1)/2 = -6/2 = -3

The y-coordinate of the midpoint is (-11 + 1) /2 = -10/2 = -5

So the center of the circle is at (-3, -5)

To find the radius,

Calculate the distance from (-3, -5) to any of of the endpoints.

Let's take the endpoint (-1, 1) and find its distance from (-3, -5)

The distance between any two points (x₁, y₁) and (x₂, y₂) is calculated from the formula

[tex]d^2 = {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2[/tex]

Substituting
(x₁, y₁) = (-1, 1)
(x₂, y₂)  = (-3, -5)

and r for distance

we get

[tex]r^2 = {(-3 - (-1))^2 + (-5 - 1)^2[/tex]

[tex]r^2 = {(-2)^2 + (-6)^2}[/tex]

[tex]r^2 = {{4} + {36}}[/tex]

[tex]r^2 = {40}[/tex]

So the center (a, b) is (-3, -5) and r² =40

Plugging this into the circle equation:
(x - (-3))² + (y - (-5))² = 40

(x + 3)² + (y + 5)² = 40

The two integers are 5 and 10.

What do you mean by Integers?

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Integer is a Latin word which means 'whole' or 'intact'. This means integers do not include fractions or decimals.

A number is positive if it is greater than zero, so it said to be positive integers

A number is negative if it is less than zero, so it said to be negative integers.

A number line is a visual representation of numbers on a straight line. This line is used for the comparison of numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally.

Given:

Let x be the positive number

2x be the other positive number

Find the first integer

[tex]\frac{1}{x} - \frac{1}{2x} = \frac{1}{10}[/tex]

[tex]\frac{2x - x}{2x^2} = \frac{1}{10}[/tex]

[tex]\frac{x}{2x^2} = \frac{1}{10}[/tex]

[tex]\frac{1}{2x} = \frac{1}{10}[/tex]

2x = 10

x = 5

Therefore, the first positive integer is 5.

Find the other integer

2x = 2(5) = 10

Therefore, the other integer is 10.

To check:

[tex]\frac{1}{x} - \frac{1}{2x} = \frac{1}{10}[/tex]

[tex]\frac{1}{5} - \frac{1}{10} = \frac{1}{10}[/tex]

[tex]\frac{2}{10} - \frac{1}{10} = \frac{1}{10}[/tex]

[tex]\frac{1}{10} = \frac{1}{10}[/tex]

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find the length of the x

a^2 + b^2 = c^2

12x^2 + b^2 = 13^2

144 + b^2 = 169

b^2 = 25

b = 25; x = 5

use the formula

a = (1/2)(24)(5)

a = (1/2)(120)

area = 60

Answer:you never asked for like in what minutes or hours?

Step-by-step explanation:

The car, traveling at a speed 5 mph faster than the truck, will take more than 4.6 hours to be more than 23 miles ahead.

This question pertains to relative speed. When the car is traveling at 55 mph and the truck at 50 mph, the car is effectively moving away from the truck at (55 mph - 50 mph) = 5 mph. To calculate the time it will take for the car to be more than 23 miles ahead, we can use the formula: Time = Distance/Speed. So the time it would take is Time = 23 miles / 5 mph = 4.6 hours. Therefore, it will take the car more than 4.6 hours to be more than 23 miles ahead.

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The required value of the given expression which satisfy it is b = 3/5.

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

We have,

3 - 2(b - 2) = 2 - 7b

= 3 - 2b - 4 = 2 - 7b

= 5b = 3

= b = 3/5

Thus, required value of the b for the given function is b = 3/5.

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Answer:

Step-by-step explanation:

Answer: the answer is 5/12

Equivalence means to be same, whether it be value, temperature, size, etc.

Let's make an equation to solve this problem. We first would need to take the total (12 pounds) and divide that total by the amount each slice must weigh (1.5 pounds) to get an equal number of slices.

To check our work, we can take number of slices (8), and multiply that by the weight of each slice (1.5 pounds) to get the original weight of the watermelon.

Now, we know for sure that Mr. Ramirez can make 8 watermelon slices each weighing 1.5 pounds if he has a 12-pound watermelon.

Answer: Let's follow the same steps as in the previous example:

Identify the constants and the variables.

The known constant here is 4. Shailyn read 4 fewer books than Oswaldo. Let's call the number of books Oswaldo read "o".

Identify the operations.

The phrase "four fewer" tells us we need to subtract.

Rewrite the phrase as an expression.

"Four fewer books than Oswaldo" is o - 4.

So, the expression that shows how many books Shailyn read last year is o - 4.

Step-by-step explanation:

The statement regarding the census in this problem is classified as a True statement.

Population: Collection or set of individuals or objects or events whose properties will be studied.

Sample: The sample is a subset of the population, and a well chosen sample, that is, a representative sample will contain most of the information about the population parameter. A representative sample means that all groups of the population are inserted into the sample.

A Census is when a group of the population is chosen, that is, a sample is chosen, hence the statement for this problem is true.

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Answer:

4.4 cubic feet of water weighs approximately 273.5016 pounds or 0.13676 tons.

Step-by-step explanation:

To find the weight of 4.4 cubic feet of water in pounds, we need to find the number of gallons it contains and then multiply it by the weight of one gallon of water.

1 cubic foot = 7.48 gallons

So, 4.4 cubic feet = 4.4 * 7.48 = 32.912 gallons

And the weight of 32.912 gallons of water in pounds is:

32.912 gallons * 8.33 pounds/gallon = 273.5016 pounds

To convert this weight to tons, we divide the weight in pounds by 2000:

273.5016 pounds / 2000 = 0.13676 tons

So, 4.4 cubic feet of water weighs approximately 273.5016 pounds or 0.13676 tons.

well, in 2007 it was 12000, so initially that's what it was, and in 2019 it went to 23000, so that's 12 years later, and in 2040, that'll be 33 years later.

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 23000\\ P=\textit{initial amount}\dotfill &12000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &12\\ \end{cases} \\\\\\ 23000 = 12000(1 + \frac{r}{100})^{12}\implies \cfrac{23000}{12000} =\left(1+ \cfrac{r}{100} \right)^{12} \\\\\\ \cfrac{23}{12}=\left(\cfrac{100+r}{100} \right)^{12}\implies \sqrt[12]{\cfrac{23}{12}}=\cfrac{100+r}{100}[/tex]

[tex]100\sqrt[12]{\cfrac{23}{12}}=100+r\implies 100\sqrt[12]{\cfrac{23}{12}}-100=r\implies \boxed{5.57\approx r} \\\\[-0.35em] ~\dotfill\\\\ \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &12000\\ r=rate\to 5.57\%\to \frac{5.57}{100}\dotfill &0.0557\\ t=years\dotfill &\stackrel{year~2040 }{33}\\ \end{cases} \\\\\\ A \approx 12000(1 + 0.0557)^{33} \implies \boxed{A \approx 71782}[/tex]

The vertices of the image of triangle ABC are A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4) and C''(x, y) = (- 4, 4).

Any triangle can be generated by three points that are not collinear, in this problem we need to determine the image of a triangle, which is the result of two rigid transformations: (i) Reflection over the y-axis, (ii) Dilation centered at the origin with a scale factor of 2, whose definitions are shown below:

Reflection over the y-axis:

(x, y) → (- x, y)

Dilation centered at the origin with a scale factor of 2:

(x, y) → (2 · x, 2 · y)

If we know that A(x, y) = (3, 4), B(x, y) = (4, 2), C(x, y) = (2, 2), then the image of the vertices are determined below:

Reflection over the y-axis

A'(x, y) = (- 3, 4), B'(x, y) = (- 4, 2), C'(x, y) = (- 2, 2)

Dilation centered at the origin with a scale factor of 2

A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4), C''(x, y) = (- 4, 4)

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Using commutative and associative properties of addition, the solution for given expression is -5.

What is commutative and associative property?

The associative and commutative characteristics are universal principles that apply to addition and multiplication. The associative property states that rearranging the numbers will get the same result, while the commutative property states that rearranging the numbers will yield the same result.

These properties tell that one can add in any order, the result will always be the same.

We are given an expression as 8+(-8-5).

So, in this instead of adding from left to right, we can see that the 8 + (-8) will be zero and only -5 will be left as an answer.

Hence, the solution for given expression is -5.

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Answer:

16

Step-by-step explanation:

As the question states, we are counting downwards which means with every interval we are going back -1. Therefore, 17 - 1 = 16

The reasons for (1) and (2) are added below

One reason why it might be reasonable to model the relationship between time and height of the candle with a linear function is that the rate of change of the candle's height appears to be constant over time.

One reason why it might NOT be reasonable to model this relationship with a linear function is that the candle's height cannot continue to decrease indefinitely.

This means that the candle's height is bounded and cannot continue to decrease linearly forever.

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Answer: no

Step-by-step explanation:

The amount that should be invested in order to have $2,290 in 16 years is $929.11.

What is compound interest?

The interest on a deposit calculated using both the initial principle and the accrued interest from prior periods is known as compound interest. In other words, compound interest is interest that is earned on interest.

Here, we have

Given: Xin will invest in an account paying an interest rate of 5.8% compounded annually.

Amount to invest = Future value / (1 + r)ᵗ

Where:

r = interest rate

t = time

X = $2,290 / (1 + 0.058)¹⁶

X = 2,290 / 2.46474

X = $929.11

Hence, the amount that should be invested in order to have $2,290 in 16 years is $929.11.

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Answer:

p = x(y)(z)

Step-by-step explanation:

product is multiplication.

multiplication has no specific order.

The measure of angle ∠ACB is 45 degrees

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

A (-3, 2), B (0, 0), C (2, 3)

The graph is attached

The lines AB and BC are perpendicular lines

This means that

∠B = 90 degrees

Calculate the length AB and BC using

distance = √[(x2 - x1)² + (y2 - y1)²]

So, we have

AB = √[(-3 - 0)² + (2 - 0)²] = √13

BC = √[(0 - 2)² + (0 - 3)²] = √13

The angle C is then calculated as

tan(C) = AB/BC

tan(C) = √13/√13

tan(C) = 1

Take the arctan of both sides

C = 45

Hence, the measure of ∠ACB is 45 degrees

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Answer:

2

Step-by-step explanation:

1 plus 1 due to the characterisation of the number 1 increasing by 1 gives you 2

Answer:

9 trucks/hour

Step-by-step explanation:

If he loaded 9 trucks in one hour, his loading speed is 9 trucks per hour.

The function operation (f/g)(x) in the functions f(x) = √( x² - 1 ) and g(x) = √( x - 1 ) is √( x + 1).

A function is simply a relationship that maps one input to one output.

Given the functions in the question;

To evaluate (f/g), replace the function designators in f/g with the actual functions.

(f/g)(x) = f(x) / g(x)

(f/g)(x) = ( √( x² - 1 ) ) / ( √( x - 1 ) )

Now, rewrite 1 as 1²

(f/g)(x) = ( √( x² - 1² ) ) / ( √( x - 1 ) )

Factor using difference of square

(f/g)(x) = ( √( (x - 1)(x + 1 ) ) / ( √( x - 1 ) )

Combine into a single radical

(f/g)(x) = √( ( (x - 1)(x + 1) ) / ( x - 1 ) )

Now, cancel out the common factors (x-1)

(f/g)(x) = √(  (x + 1) / 1 )

(f/g)(x) = √( x + 1)

Therefore, the function operation (f/g)(x) is √( x + 1).

Option A) √( x + 1) is the correct answer.

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Answer: 44.20-10.68=33.52

He need 33.52$

Step-by-step explanation: