Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each expression to the scenario it represents. Expressions Scenario the price of a game that’s been discounted 18% off its list price (x) arrowRight the price of a toy that sells for 18% more than the amount (x) needed to build the toy arrowRight the volume of water remaining in a tank after of its original volume (x) is drained out arrowRight the total amount of flour in a bakery after receiving new stock equal to of its current stock (x) arrowRight

Answer:

The table represents a nonlinear function because the rate is not constant.

Step-by-step explanation:

As shown in the picture below, the x side of the table has the same rate of change of +1. However, due to the fact that the y side does not have the same rate of change, +6 and +3, the table represents a non linear function. If the rate on the y side of the table were all the same, then this would be a Linear function.

Answer:

\(y=\frac{1}{3} x-1.\)

Step-by-step explanation:

if A(9;2), B(-3;-2) then it is possible to make up the required equation according to the form:

\(1. \ \frac{x-X_B}{X_A-X_B} =\frac{y-Y_B}{Y_A-Y_B}\)

2. after the substitutuion X(A)=9; X(B)=-3; Y(A)=2 and Y(B)=-2 into the form:

\(\frac{x+3}{9+3} =\frac{y+2}{2+2}; \ => \frac{x+3}{12} =\frac{y+2}{4}; \ => \frac{x+3}{3} =y+2.\)

or in slope-interception form:

\(y=\frac{1}{3} x-1.\)

Answer:    The ratio value of oil to popcorn kernels for theatre C is 6 / 32 = 3 / 16.

Step-by-step explanation: Given that the manager of Theatre A says that they usually go through about 15 cups of popcorn kernels and about 5 cups of oil each weeknight.

Then, the ratio value of oil to popcorn kernels for theatre A is 5 / 15 = 1 / 5.

Given that the manager of Theatre B says that they order 18 cups of oil and 72 cups of popcorn kernels each week.

Then, the ratio value of oil to popcorn kernels for theatre B is 18 / 72 = 1 / 4.

Given that the manager of Theatre C says that their concessions use 6 cups of oil and 32 cups of popcorn kernels on a busy Saturday.

Then, the ratio value of oil to popcorn kernels for theatre C is 6 / 32 = 3 / 16.

=======================================================

Explanation:

Let c < 0 be a test root of f(x). The key here is that c must be negative.

If we use this value of c in the synthetic division table, and we get the third row alternating in signs, then we have proven c is a lower bound of the roots of f(x). This is what the lower bound theorem tells us.

In this case, c = -7 fits the description of c < 0.

Refer to the diagram below to see the synthetic division. The third row of values is: 5, -37, 254, and -1780

The terms alternate in sign which is sufficient evidence to conclude -7 is a lower bound for the real zeros of f(x).

What this means is that we don't need to look lower than -7 since we know -7 is like a "floor" of sorts. It's not the highest lower bound as there may be higher floor values.

-----------

For more information, search out \(\text{``lower bound theorem'' algebra}\) where the quotes are needed. One of the results is from the West Texas A&M University (WTAMU) Virtual Math Lab, which may be handy.

Answer:

x-3 and y=2

Step-by-step explanation:

The function is an exponential growth function

The function is given as

y=2(1.06)^9

We can begin by rewriting the given equation as:

y = 2 * 1.06t

So, we have

y = 2 * (1 + 0.06)^t

Now we can see that the equation is in the form y = a*b^t,

where a = 2 and b = 1.06^9

This equation represents exponential growth because the base of the exponent, b = 1.06, is greater than 1.

We can re-write it in the form y = a(1+r)t,

we can find the value of r by subtracting 1 from 1.06 which is 0.06 and the value of a is 2.

so we have y = 2(1+0.06)^t

So, the equation represents exponential growth with a = 2 and r = 0.06

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There is no real Value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

(i) Zeroes of the polynomial:

In the graph, we have two points where the curve intersects the x-axis: one is at (-1,0), and the other is at (2,0).The corresponding values of x are -1 and 2, and they are the zeros of the polynomial. Therefore, the zeros of the polynomial are -1 and 2.(ii) Forming the quadratic polynomial:

From the graph, we can observe that the curve intersects the y-axis at the point (0,5), implying that the constant term of the polynomial is 5.

We can use the formula to find the quadratic polynomial if we have two zeros and one constant term. Thus, the quadratic polynomial is given by:(x + 1)(x - 2) = x² - x - 2x + 2 = x² - 3x + 2. Therefore, the quadratic polynomial is x² - 3x + 2.(iii) Value of k if a, 1/a are the zeroes of the polynomial 2x² - x + 8k:

We know that a and 1/a are the zeroes of the polynomial 2x² - x + 8k. Therefore, we can find the sum and product of the roots and use them to determine the value of k.

The sum of the roots is a + 1/a, and their product is a(1/a) = 1. Using the sum and product of the roots, we can write: a + 1/a = 1/2 (1/2 is the coefficient of x)Substituting a with 1/a in the above equation, we get: 1/a + a = 1/2Multiplying both sides of the equation by 2a, we get: 2 + 2a² = a

Simplifying the equation, we get: 2a² - a + 2 = 0Multiplying both sides by 2,

we get: 4a² - 2a + 4 = 0Dividing both sides by 2, we get: 2a² - a + 2 = 0

Using the quadratic formula, we get: a = [1 ± √(1 - 4(2)(2))]/(2(2))

Simplifying, we get: a = [1 ± √(-31)]/4Since the discriminant of the quadratic formula is negative, the roots are imaginary. Therefore, there is no real value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

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Answer:

\(Scale\ Factor = 1.5\)

Step-by-step explanation:

See attachment for proper presentation of question.

From the attachment, we have:

\(A = 7\)

\(A' = 10.5\)

Required

Determine the scale factor

To solve this, simply divide the circumference of A' by that of A.

This gives the scale factor used

i.e.

\(Scale\ Factor = \frac{A'}{A}\)

Substitute values for A and A'

\(Scale\ Factor = \frac{10.5}{7}\)

\(Scale\ Factor = 1.5\)

Hence, the scale factor used is 1.5

Additional Note:

If the given parameters had been the area of A and A', you'll need to first solve for the radius of both circles.

Then determine the scale factor by A'/A

Answer:

24-n

Step-by-step explanation: hope this helps if it does pls give brainliest tysm!

Answer:

24-n

Step-by-step explanation: we taking away so that is substraction.

The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.

To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.

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the slope for this line is 2

The slope or gradient of a line is a number  that describe both the direction and the steepness of the line. the steepness of a line is defined as the slope (or gradient). The slope is the ratio of vertical distance to the horizontal distance between any two points on a line. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).The greater the value of the slope, the "steeper" the slope is, and vice versa. So the smallest value of the absolute value of these slopes is 1/2.

So, A.T.Q:-

  The formula of slopet intercept is  Y2 -Y1 /X2-X1

  From the question:

              slope = -1-1/0-1

              slope = 2

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The traveler will need (y / x) dollars to purchase y yen.

To determine the number of dollars the traveler will need to purchase a certain amount of yen, we need to divide the desired amount of yen by the exchange rate.

Let's assume the traveler wants to purchase y yen.

and, the exchange rate is 1 dollar = x yen.

To find the number of dollars, we can set up the following equation:

y yen × (1 dollar / x yen) = (y / x) dollars

Therefore, the traveler will need (y / x) dollars to purchase y yen.

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To calculate the number of dollars needed to purchase a specific amount of Japanese yen, we'll need the exchange rate between the two currencies. However, the exchange rate provided in your question is missing. Please provide the exchange rate between the US dollar (USD) and the Japanese yen (JPY) so that I can help you calculate accurately.

Answer:

the bigger pack is better

The Polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

The quotient and remainder when the polynomial x⁵ + x³ - 5 is divided by x - 2, we can use polynomial long division. Here's the step-by-step process:

1. Write the dividend (x⁵ + x³ - 5) and the divisor (x - 2).

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

2. Divide the first term of the dividend (x⁵) by the first term of the divisor (x) to get x⁴. Write x⁴ above the line. x⁴

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

3. Multiply the divisor (x - 2) by the quotient term (x⁴) to get x⁵ - 2x⁴. Write this under the dividend and subtract it.  x⁴

  x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

4. Bring down the next term (-5) from the dividend.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

5. Divide the first term of the new dividend (3x⁴) by the first term of the divisor (x) to get 3x³. Write 3x³ above the line.

 x⁴ + 3x³

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

6. Multiply the divisor (x - 2) by the new quotient term (3x³) to get 3x⁴ - 6x³. Write this under the new dividend and subtract it.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

7. Repeat steps 4-6 until you have subtracted all terms.

x⁴ + 3x³ + 6x² + 12x + 24

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

- (6x³ - 12x²)

12x² + 0x + 0

 - (12x² - 24x)

 24x + 0

- (24x - 48)

 48

8. The quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

Therefore, when the polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

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Answer:

isnt 9?

Step-by-step explanation:

i asked google lololol

Answer:

9.

Step-by-step explanation:

Factors of 27: 1, 3, 9, 27

Factors of 45: 1, 3, 5, 9, 15, 45.

The GCF (Greatest Common Factor) of 27 and 45 is NOT 1, 3, or 27 because 27 is not a factor of 45, and since we are trying to figure out the GREATEST common factor, one and three do not work either. If you need more help, feel free to ask! I am on Brainly from 1 - 2 pm. EST, so if you have any further questions about this subject or my answer, feel free to ask me!

Answer: 1134.11

A=3.14*r^2

Step-by-step explanation:

Answer:

a ≈ 1134.11 cm2

Step-by-step explanation:

The formula:

\(a=\pi r^{2}\)

\(a=\pi (19)^{2} =361\pi\)

\(a=1134.11cm^{2}\)

Hope this helps

Answer:

The second one

Step-by-step explanation:

The area of a parallelogram = base length times height

If the parallelogram has a height of 4 and a base length of 9 then the area = 4 * 9

Answer:

The answer is: A= 4 x 9

Step-by-step explanation:

Answer:

The Inverse Tangent Function (arctan)

Graph of y = tan x.

The graph of arctan(x) is second graph.

We have inverse function \(y=tan^{-1} x\)

Creating the table

x     0   π/4    π/2     -π/2     -π/3      π/3

y     0   1         ∞        -∞       -√3       √3

From the given graphs we see that the second graph satisfies the values.

So, the correct graph for arctan(x) is second graph.

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The number in cell A14 is 2744

The pattern is given as

1, 8, 27, 64, 125

When the above number in the pattern is represented as exponents, we have

1^3, 2^3, 3^3, 4^3, 5^3

So, the nth term is

Tn = n^3

In cell A14, the value of n is 14

So, we have

T14 = 14^3

Evaluate

T14 = 2744

Hence, the number in cell A14 is 2744

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Answer:

Seven isn't part of the set of irrational numbers.

Step-by-step explanation:

Start with the smallest set among the choices. The set of all natural numbers, \(\mathbb{N}\), starts with \(0\) (or \(1\), for some people.) A number \(n\) is in \(\mathbb{N}\!\!\!\) (write \(n \in \mathbb{N}\)) if and only if \((n - 1)\) is in \(\mathbb{N}\!\). Conversely, if \(n\!\) is indeed in \(\mathbb{N}\!\!\!\!\!\), then \((n + 1)\) would also be in \(\mathbb{N}\!\!\!\!\!\!\!\). For \(7\):

\(1 \in \mathbb{N} \implies 2 \in \mathbb{N}\).

\(\vdots\).

\(6 \in \mathbb{N} \implies 7 \in \mathbb{N}\).

Therefore, \(7\) is indeed in the set of all natural numbers.

Similarly, a number \(n\) is in the set of integers, \(\mathbb{Z}\), if and only if either \((n - 1)\) or \((n + 1)\) is (or both are) in \(\mathbb{Z}\!\!\).

Conversely, if a number \(n\) is in \(\mathbb{Z}\), then both \((n - 1)\) and \((n + 1)\) will be in \(\mathbb{Z}\!\).

It can be shown in a similar iterative way that \(7 \in \mathbb{Z}\).

Alternatively, consider the fact that the set of all natural numbers, \(\mathbb{N}\), is a subset of the set of all integers, \(\mathbb{Z}\). Therefore, \(7 \in \mathbb{N}\) implies that \(7 \in \mathbb{Z}\).

A number \(m\) is a member of the set of all rational numbers \(\mathbb{Q}\) if and only if there exists two integers \(p\) and \(q\) such that:

\(\displaystyle m = \frac{p}{q}\).

\(1\) and \(7\) are both integers. If \(p = 7\) and \(q = 1\), then \(\displaystyle 7 = \frac{7}{1} = \frac{p}{q}\). Hence,

Alternatively, note that the set of all integers, \(\mathbb{Z}\), is a subset of the set of all rational numbers, \(\mathbb{Q}\). Therefore, the fact that \(7 \in \mathbb{Z}\) would imply that \(7 \in \mathbb{Q}\).

A number is in the set of all irrational numbers if and only if:

Therefore, the fact that \(7\) is a rational number implies that it is not an irrational number.

Answer:

irrational numbers

Step-by-step explanation:

To achieve a comparable rate of return, Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly on his ordinary annuity.

To find the interest rate, compounded monthly, that Hank would need to earn on an ordinary annuity for a comparable rate of return, we can use the present value formula for an ordinary annuity.

First, let's calculate the present value of Hank's payments. He made payments of $219 per month for 30 years, so the total payments amount to $219 * 12 * 30 = $78840.

Now, we need to find the interest rate that would make this present value equal to the selling price of the property, which is $195,258.

Using the formula for the present value of an ordinary annuity, we have:

PV = P * (1 - (1+r)\(^{(-n)})\)/r,
where PV is the present value, P is the payment per period, r is the interest rate per period, and n is the number of periods.

Plugging in the values we have, we get:
$78840 = $219 * (1 - (1+r)\({(-360)}\))/r.

Solving this equation for r, we find that Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly, in order to have a comparable rate of return.

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C = pi x d

C = 3,14 x 18 = 56,52 m

Answer:

The answer is 56.57

thank you

Answer:

Step-by-step explanation:To calculate the savings percentage, we first need to find out the cost of the cardboard required for each box.

For the larger box:

Total Surface Area = 2 * (1926 + 1934.5 + 26*34.5) = 2 * (494 + 655.5 + 897) = 4093 cm²

Cost of cardboard for larger box = 0.502 * 4093 = 2055.986 cents = 20.55986 dollars (rounded to 5 decimal places)

For the smaller box:

Total Surface Area = 2 * (2517 + 2526 + 1726) + 6 * (25-21)* (17-2*1) = 3034 cm²

Note that the additional term in the equation is the surface area of the six sides of the lid and base of the box.

Cost of cardboard for smaller box = 0.502 * 3034 = 1522.268 cents = 15.22268 dollars (rounded to 5 decimal places)

The difference in cost between the larger and smaller boxes is:

20.55986 - 15.22268 = 5.33718 dollars (rounded to 5 decimal places)

The percentage savings can be calculated as follows:

Percentage savings = (difference in cost / cost of larger box) * 100%

= (5.33718 / 20.55986) * 100%

= 25.98%

Therefore, using the smaller box will result in a savings of approximately 26% on cardboard costs for Bathu Sneakers compared to using the normal larger box.

Answer: Read the solution

Step-by-step explanation:

A. For diagram A, triangles ANC and BDE are similar. Thus, we can use similarity ratios to find the length of AC. (x+1)/12 = (x+5)/15. 15x+15=12x+60. Thus 3x=45, and x=15. Since we need to find AC, AC = 15+1 = 16.

B. For diagram B, triangles SRT and VUT are similar. Again, using similarity ratios, (4x-1)/14=(x+2)/6 or 14x+28=24x-6. 10x=34, x=3.4.

The difference in volume between the two boxes would be = 156in³

To calculate the difference in volume between the boxes is the find the individual volume of the boxes using the formula ;

Volume = length×width×height.

For box 1 = length = 12in, width = 7¾in, height= 2in

Vol = 12×7¾×2 = 186in³

For box 2; length = 3⅔in, width = 3½in, height= 2⅓in

Volume = 3⅔×3½×2⅓ = 30

The difference = 186-30 = 156in³

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Answer:

Step-by-step explanation:

10 feet............................6 seconds

?......................................45 seconds

? feet=10*45/6=75 feet

75 feet in 45 seconds

Answer:

B. y = (x + 3)^2 - 17

Step-by-step explanation:

Answer:34,000

Step-by-step explanation:

Answer:

its 34,000 because it below 5

Step-by-step explanation:

brainliest please

Answer:

see explanation

Step-by-step explanation:

using the tangent ratio in the right triangle

tan A = \(\frac{opposite}{adjacent}\) = \(\frac{BC}{AB}\) = \(\frac{5}{11}\) , then

∠ A = \(tan^{-1}\) ( \(\frac{5}{11}\) ) ≈ 24.4° ( to 1 decimal place )

tan C = \(\frac{opposite}{adjacent}\) = \(\frac{AB}{BC}\) = \(\frac{11}{5}\) , then

∠ C = \(tan^{-1}\) ( \(\frac{11}{5}\) ) ≈ 65.6° ( to 1 decimal place )

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

AC² = AB² + BC² = 11² + 5² = 121 + 25 = 146 ( take square root of both sides )

AC = \(\sqrt{146}\) ≈ 12.08 ( to 2 decimal places )