jayla bought the ingredients to make chicken soup, and wanted to make a double batch, which would be 12 cups of soup. a quick search told her that this was 173.3 cubic inches. she hoped the soup pot below would be big enough. the soup pot is 8 inches tall with a radius of 3 inches. what is the volume of the soup pot?

The option that provides the best description of the relationship between a quadratic parent function and a square root parent function is A. The square root function is the quadratic function reflected across the line y = x, with a limited domain.

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.

The square root function is the quadratic function reflected across the line y = x, with a limited domain. The graph y=x² and y=√x and y=x. The graph is attached.

In conclusion, the correct option is A.

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Answer: x=9, excluded value x≠5

Step-by-step explanation:

1. add 3 to both sides -> 16/x-5 = 4

2. then multiply both sides by x-5 -> 16=4(x-5) -> 16=4x-20

3. add 20 to both sides -> 36=4x

4. divide both sides by 4 to solve for x -> 9=x

the excluded value is whatever would make the denominator of the fraction equal to 0. You can't divide by 0. Therefore in this case, x can't equal 5 because 5-5=0

Answer: (x - 6)(x + 6)

Step-by-step explanation:

To factor this, recall the difference of squares

[tex]a^{2} - b^{2} = (a-b)(a+b)[/tex]

And because 36 is [tex]6^{2}[/tex], that means

[tex]x^{2} - 36 = x^{2} - 6^{2} = (x-6)(x+6)[/tex]

[tex] \bold{(x-6)(x+6)}[/tex]

To simplify this equation, quadratic factoring patterns should be used. These patterns are the following:

[tex] \bold{a^2-b^2=(a-b)(a+b)}[/tex]

This pattern works because if one distributes the terms in the parentheses by multiplying each term in one of the parentheses by each term in the other, the result is the original equation:

[tex] \bold{36=6^2}[/tex]

So it can be applied to the given equation:

[tex] \bold{x^2-36}[/tex]

[tex] \bold{ \bold{\boxed{(x-6)(x+6)}}}[/tex]

The factored form of the expression is [tex]\bold{(x-6)(x+6)}[/tex]

Answer:

B. Same-side interior angles

Step-by-step explanation:

Same Side interior angles are angles that are on the same side and add up to 180 degrees. So, the answer is B

Given A = rolling a number lower than 2

A six- sided bones has possible issues and 6. We also note that the only outgrowth lower than 2. probability of both issues is equal i.e. 50 or 1/2.

So, the probability of an event is Favorable issues Total number of issues. It's denoted with the gap i.e. P( Event) The possibility of the result of any arbitrary event is known as probability. This expression refers to determining the liability that any given circumstance will do. What are the chances of entering a head, for case, when we toss a coin in the air? The number of issues that could do is the base for the response to this question. The outgrowth in this case might be either head or tail. thus, there's a 50 chance that the result will be a head. The probability serves as a hand for how probably an event is to do. It gauges how likely an event is. The probability formula is as follows P( E) is equal to the rate of favourable issues to overall issues.

P( E) = n( E)/ n( S)

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The probability that an 11-bit string is a palindrome is 1 in 2048, or 0.00048828125%.

A group of characters known as a palindrome read the same both forward and backward

For an 11-bit string, there are 2048 possible combinations of 0s and 1s. Of those, only one combination is a palindrome. Therefore, the probability of randomly selecting an 11-bit string that is a palindrome is 1 in 2048, or 0.00048828125%.

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Answer:Yes,

There is a direct proportional relationship

between the cost of items before tax and the

cost of items after tax.

5.0

Step-by-step explanation:

Given - A city has a 5% sales tax.

To find - Is there a proportional relationship

between the cost of items

before tax and the cost of items after

tax?

Proof

Yes, cost of items before tax is directly

proportional to cost of items after tax.

Reason

With the increase in the sales tax, there is

increase in the cost of items after tax, therefore,

there is a direct relation between cost of items

before tax and cost of items after tax.

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

60 hours in 7 days   =   60/7     hours per day

Answer:

A is correct

Step-by-step explanation:

I got it right on my test

The elevation of this mountain in feet is 28,169 feet. This gives us the original number of 9,417 yards, confirming that our answer is correct.

To convert yards to feet, we simply need to multiply the number of yards by 3. There are 3 feet in a yard, so to convert 9,417 yards to feet, we multiply 9,417 by 3.

This gives us the total of 28,169 feet as the elevation of this mountain. To check our answer, we can also convert 28,169 feet back to yards by dividing 28,169 by 3.

This gives us the original number of 9,417 yards, confirming that our answer is correct.

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The value of x we get from the equation is [tex]\frac{- 10 ±\sqrt{208}}{18}\\[/tex]

The given equation is [tex]9x^{2} + 10x -3=0[/tex]

We know, the quadratic formula is [tex]x=\frac{-b ± \sqrt{b^{2}-4ac}}{2a}[/tex] where [tex]a\neq 0[/tex]

Using the Quadratic Formula where

a = 9, b = 10, and c = -3

We get,

[tex]x=\frac{-b ± \sqrt{b^{2}-4ac}}{2a}[/tex]

[tex]x=\frac{- 10± \sqrt{10^{2}-4(9)(-3) }}{2(9)}\\[/tex]

[tex]x=\frac{- 10± \sqrt{100--108 }}{18}\\[/tex]

[tex]x=\frac{- 10± \sqrt{208}}{18}\\[/tex]

The discriminant [tex]b^{2} -4ac[/tex]>0 so, there are two real roots

From this, we get 2 values of x

[tex]x=0.245678[/tex]

[tex]x= -1.35679[/tex]

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Answer:-10±√208÷18

Step-by-step explanation

1) so, there is a formula that is  x= -b±√b²-4ac÷2a, we can use this to solve this equation.

2) put these value in the formula, then we will get

  here, a=9

            b=10

            c=-3

  x=-10±√100-4*9*-3÷2*9

  x=-10±√208÷18

Answer:

(3, 9)

Step-by-step explanation:

You start on (0, 0), and try and remember the term, "you run before you can jump(x before y, (x, y)) when working with coordinates.

X axis: so you "run" 3 units to the right, as it's not a negative number. so now your on (3, 0) (dark blue arrows)

Y axis: now you do the "jumping" portion of this, so you jump up six units as it's a negative, so now your on (3, 6) (red arrows)

Y: axis: but now you have to move down 1 unit, so you essentially "fall" 1 unit down, (3, 5) (pink arrow)

Y axis:  you have to "jump" 4 units up now, so now your at (3, 9) (green arrows)

you haven't moved along the X axis so you keep the 3, you only moved the Y axis.

So your asnwer is (3, 9)!

Hope this helped!! (picture help as well!)

Answer: 17

Step-by-step explanation: 2 is an even number and 17 is an odd number, therefore it can't be divisible by 2. 17 does not have a 5 or a 0 in it therefore it is not divisible by 5. Any multiple of 5 will always have a 5 or 0 in it. If it doesn't have a zero in it anywhere it is not divisible by 10. A multiple of 10 will always have a zero in it.

The required equation of the line is y = 4x + 1.

The Slope-intercept form of a line is given by

Where m is the slope of the line and c is the y-intercept

Note:

The product of slopes of perpendicular lines = -1

Here we have

y = -1/4x + 6 Line (1)  

Here slope of the line m₁ = -1/4

Let y = m₂x + c Line (2)

Assume that Line (2) is the perpendicular line to Line

As we know The product of slope of two perpendicular lines is -1  

=> m₁m₂ = -1        [∵ Line (1) and Line (2) perpendicular lines ]

=> -1/4(m₂) = -1     [ ∵ m₁ = -1/4  ]

=>  m₂ = 4

The line (2) => y = 4x + c  

Given that the line passes through (2, 9)

=> 9 = 4(2) + c

=> c = 9 - 8

=> c = 1

Therefore,

The required equation of the line is  y = 4x + 1

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The complete table of values of the proportional relationship is

A= 8, 24, 40

B= 3, 9, 15

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

A= 8, _, 40

B= 3, 9, _

Calculate the constant of proportion using

constant = B/A

Substitute the known values in the above equation, so, we have the following representation

constant = 3/8

Substitute constant = 3/8 in constant = B/A

3/8 = B/A

So, we have

3A = 8B

When B = 9, we have

3A = 8 * 9

This gives

A = 24

When A = 40, we have

3 * 40 = 8B

This gives

B = 15

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Complete question

Complete the table such that a and b represent a proportional relationship

A= 8, _, 40

B= 3, 9, _

the Utopian treat valuable develop the central idea is the Utopians give valuables to children, who treat them as toys.

The central idea of the above passage is that the Utopians give valuables, such as diamonds and carbuncles to children, who treat them as toys. As such, the Utopians are delighted with these valuables, and glory in them during their childhood but lay them aside when they come to years.

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The total amount of interest that Maria will owe on her unsubsidized loan = $113.63

In this question we have been given Maria received a $5,000 subsidized loan and a $4,500 unsubsidized loan with an apr of 5.05%

We need to find the total amount of interest that Maria will owe on her unsubsidized loan.

Using simple interest formula,

I = P * t * r

where P - the principal

r - the interest rate,

and t - time period

Maria  begins making payments 6 months after graduation, this means there are 12 - 6 = 6 months between graduation and the start of payments.

so, t = 6 months

i.e., t = 0.5 year

Here, R = 5.05%, P = $4500

Now we convert R percent to r a decimal

r = R/100

 = 5.05%/100

 = 0.0505 per year,

Using the formula of simple interest,

I = 4500 * 0.0505 * 0.5

I = $113.63

Therefore, the interest amount is $113.625

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The complete question is:

At the beginning of her senior year maria received a $5,000 subsidized loan and a $4,500 unsubsidized loan with an apr of 5.05%. if maria begins making payments on her loans 6 months after graduation, how much interest will she owe to the nearest dollar?

In 84 ways 3 employees can be chosen from the set of 9.

What is combination?

Total 9 employees from that 3 employees can be chosen.

Total number of combination = ⁹C₃

= 9! / (9-3)! 3!

= 9 *8 *7/3*2

=3* 4* 7

= 12 * 7

= 84

Hence, in 84 ways 3 employees can be chosen from the set of 9.

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The value of the discriminant of f is 0.

There is one distinct real number of zeroes.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 3x² + 24x + 48

This is in the form of ax² + bx + c

a = 3

b = 24

c = 48

The discriminant is given by b² - 4ac.

There are two real solutions when it is greater than 0.

There is one real solution when it is equal to 0.

There are two imaginary solutions when it is less than 0.

Now,

= 24² - 4 x 3 x 48

= 576 - 576

= 0

So,

There is one real solution.

Thus,

The value of the discriminant of f is 0.

There is one distinct real number of zeroes since the discriminant is zero.

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Answer:

The lengths of the two pieces are 7 cm and 14 cm.

Step-by-step explanation:

Let x represent the length of the longer piece of the rod. Since the lengths of the two pieces are in the ratio 7:2, the length of the shorter piece is 2x. The total length of the two pieces is therefore 7x + 2x = 9x. Since the total length of the two pieces is 63 cm, we have:

9x = 63

Dividing both sides by 9, we get:

x = 7

Thus, the length of the longer piece is 7 cm, and the length of the shorter piece is 2 * 7 = 14 cm. Therefore, the lengths of the two pieces are 7 cm and 14 cm.

48 is the number does not belong in the following series 1, 2, 5, 10, 13, 26, 29, 48

The series is formed by following the sequence that is:

1, 2, 5, 10, 13, 26, 29, 48

Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers. A recursive pattern rule is a pattern rule that tells you the start number of a pattern and how the pattern continues.

The first number is multiplied by 2 and the next number should be added by 3 to the previous number.

The first number is 1 and it should be multiplied by 2

1 × 2 = 2

Then the next number should be added by 3

2 + 3 = 5

The series will be continued:

5 × 2 = 10

10 + 3 = 13

13 × 2 = 26

26 + 3 = 29

but 29 × 2 = 58 ≠ 48.

Therefore the number 48 does not belongs to the given series.

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The length of the bae of an iocele triangle i x. The length of a leg i 2x-3. The perimeter of the triangle i 44 then x= 10

since the triangle is isosceles then the 2 legs are congruent, that is both 2x - 3

the perimeter is the sum of the 3 sides , that is

x + 2x - 3 + 2x - 3 = 44

5x - 6 = 44 ( add 6 to both sides )

5x = 50 ( divide both sides by 5)

x = 10

hence The length of the bae of an iocele triangle i x. The length of a leg i 2x-3. The perimeter of the triangle i 44 then x= 10

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Answer: -3n + 18

Step-by-step explanation:

When examining the sequence, you can see that every time, it decreases by 3, therefore the first part of your rule should be:

-3n

(Extra note to wow your maths teacher! This is a linear sequence as it decreases/increases by the same amount each time.)

Next, you will need to find the number before the given sequence. As it decreases by 3 every time, to find the number before you need to increase by 3. Therefore, the next part you need is + 18.

Leave a comment if you don't understand anything :)

Answer:

------------------------------------

Given sequence:

This is an AP, with the first term a = 15 and common difference of - 3, as it is decreasing by 3.

Use nth term equation for an AP:

The profit function for this problem is defined as follows:

P(x) = 5x - 260.

The profit function is defined as the subtraction of the revenue function by the cost function, as follows:

P(x) = R(x) - C(x).

In which:

From the image given at the end of the answer, the revenue function and the cost function are given as follows:

Then the profit function is calculated as follows:

P(x) = R(x) - C(x)

P(x) = 3x² + 4x - 60 - (3x² - x + 200).

Combining the like terms, we have that:

P(x) = (3 - 3)x² + (4 + 1)x - 60 - 200

P(x) = 5x - 250.

Meaning that the third option is correct.

The problem is given by the image shown at the end of the answer.

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The area under the curve r²=50sin2Θ is (15.71)unit square

A parabola is defined as a plane curve that is mirror-symmetrical and approximately U-shaped.

Given:

parabola is r²=50sin 2[tex]\theta[/tex],

where r=5

So, 5²=50 sin 2[tex]\theta[/tex],

Simplifying the equation

25=50 sin 2[tex]\theta[/tex],

sin 2[tex]\theta[/tex] = 1/2

2[tex]\theta[/tex] = [tex]sin^{-1[/tex] 0.5

[tex]\theta[/tex] = 15 degree.

Now, the Area = 22/7 × 5

Area = 15.71 unit²

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The equation of a circle with center  (1,-2) and radius 2 is ( x - 1 )² + ( y + 2 )² = 4.

The standard form of the circle is x² + y² = r²

Where r is the radius.

h and k is the horizontal and vertical translation which represent the center of the circle..

Hence, the formula is derived from the distance formula where the distance is between the center and every point on the circle is equal to the length of the radius.

( x - h )² + ( y - k )² = r²

Given that;

Center: (1,-2)

Plug the given values into the equation and simplify.

( x - h )² + ( y - k )² = r²

( x - 1 )² + ( y - (-2) )² = 2²

( x - 1 )² + ( y + 2 )² = 2²

( x - 1 )² + ( y + 2 )² = 4

Therefore, the equation of the circle is ( x - 1 )² + ( y + 2 )² = 4

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Convert the radicals as follows:

The simplification of the expression are;

[tex]\sqrt[6]{25^3}[/tex] = 5

[tex]\dfrac{1}{\sqrt[3]{5^4} } =\dfrac{1}{5^{4/3}} }[/tex]

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.

We are given the expression as;

[tex]\sqrt[6]{25^3}[/tex]

Convert the radicals as follows:

[tex]\sqrt[6]{25^3}\\\\= \sqrt[6]{(5^2)^3}\\\\= \sqrt[6]{5^6}\\\\=5^{6/6}\\=5^1=5[/tex]

Now,

[tex]\dfrac{1}{\sqrt[3]{5^4} } =\dfrac{1}{5^{4/3}} }[/tex]

Here this cannot be further simplified.

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The mixed number between 2 and 10. I am nearer to 8 than 10 is 6 1/9, it  is an entire quantity, and a right fraction represented together.

A mixed fraction is an entire quantity, and a right fraction represented together. It commonly represents a range of among any  complete numbers. Look on the given image, it represents a fragment this is extra than 1 however much less than 2. It is thus, a mixed fraction. A fraction represented with its quotient and the rest is a combined fraction. For example, 2 1/three is a combined fraction, wherein 2 is the quotient, 1 is the the rest. So, a combined fraction is a aggregate of an entire quantity and a right fraction.

Thus, the mixed number if 6 1/9.

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[tex]\stackrel{mixed}{1\frac{2}{3}}\implies \cfrac{1\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{5}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{w}{4}~~ = ~~\cfrac{2}{~~1 \frac{2 }{3 } ~~}\implies \cfrac{w}{4}~~ = ~~\cfrac{2}{~~ \frac{5 }{3 } ~~}\implies \cfrac{w}{4}~~ = ~~\cfrac{\frac{2}{1}}{~~ \frac{5 }{3 } ~~}\implies \cfrac{w}{4}=\cfrac{2}{1}\cdot \cfrac{3}{5} \\\\\\ \cfrac{w}{4}=\cfrac{6}{5}\implies 5w=24\implies w=\cfrac{24}{5}\implies {\Large \begin{array}{llll} w=4\frac{4}{5} \end{array}}[/tex]

The statements that are true are:

π is the area of a circle of radius 1.

π is the circumference of a circle of diameter 1.

π is the constant of proportionality relating the diameter of a circle to its circumference.

A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.

The area of a circle is given as:

We have,

Circumference of a circle = 2πr

Area of a circle = πr²

π is the area of a circle of radius 1.

Area = πr² = π x 1 = π

π is the area of diameter 1.

2r = 1

r = 1/2

Area = πr² = π x 1/4 = π/4

π is the circumference of a circle of radius 1.

Circumference of a circle = 2πr = 2 x π x 1 = 2π.

π is the circumference of a circle of diameter 1.

Circumference of a circle = 2πr = 2 x π x 1/2 = π.

π is the constant of proportionality relating the diameter of a circle to its circumference.

Diameter ∝ Circumference

2r = 2πr

2r = π (2r)

π is the constant of proportionality relating the radius of a circle to its area.

r = (πr)r

Thus,

π is the area of a circle of radius 1 is true.

π is the circumference of a circle of diameter 1 is true.

π is the constant of proportionality relating the diameter of a circle to its circumference is true.

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Answer:

Step-by-step explanation:

in x intercepts y is equals to 0

10x = 8

x = 8/10

x = 4/5

in y intercepts x is equals to 0

y = 8