Kala bought 6 CDs that were each the same price. Including sales tax, she paid a total of $97.20. Each CD had a tax of $1.30. What was the price of each CD before tax?

Answer:

B

Step-by-step explanation:

3(3y-1) = 9y-3

3*3y=9y

3*1=3

combine those and you get 9y-3.

Answer:

-14x² - x + 4

Step-by-step explanation:

(-10x² + 5x - 3) - (4x² + 6x - 7)

= (-10x² + 5x - 3) - (+4x²) - (+6x) - (-7)

= (-10x² + 5x - 3) -4x² -6x +7

= -10x²-4x² +5x-6x -3+7

= -14x²  - x + 4

Answer:

27 frames per second

Step-by-step explanation:

108 ÷ 4 = 27

Answer:

108 ÷ 4 = 27

27 frames per second

The table represents an exponential function given by:

\(f(x) = 24*(1/2)^x\)

Here we have the table:

x    f(x)

0    24

1      12

2      6

3       3

First, notice that for each unit that x increases, the value of f(x) decreases by its half.

This is clearly an exponential equation, whose base must be equal to (1/2).

And because when x = 0, f(0) = 24, we know that the initial value of the function is 24.

Then the exponential function is:

\(f(x) = 24*(1/2)^x\)

Such that:

\(f(0) = 24*(1/2)^0 = 24\\\\f(1) = 24*(1/2)^1 = 12\\\\f(2) = 24*(1/2)^2 = 24*(1/4) = 6\\\\f(3) = 24*(1/2)^3 = 24*(1/8) = 3\)

Concluding, the table represents an exponential function.

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For the expression \(x^64 + ax^b + 25\) to be a perfect square for all integer values of x, b must be 64, and a must be a perfect square, written as a = \(y^2.\)

To determine the values of a and b such that the expression\(x^64 + ax^b\) + 25 is a perfect square for all integer values of x, we need to analyze the properties of perfect squares.

A perfect square is an expression that can be written as the square of another expression. In this case, we want the given expression to be in the form of\((x^n)^2,\) where n is an even integer.

Let's examine the given expression: \(x^64 + ax^b\) + 25

For it to be a perfect square, the quadratic term \(ax^b\)must have the same exponent as the leading term\(x^6^4.\) This means b must be equal to 64.

So we have:\(x^64 + ax^64 + 25\)

Now, we can rewrite this as:\((x^32)^2 + 2(x^32) (\sqrt{a}) + (\sqrt{25})^2\)

By comparing this with the standard form of a perfect square, (\(x^n +\sqrt{k} )^2\), we can deduce that √a must be equal to x^32 and \(\sqrt{25}\) must be equal to \(\sqrt{k.}\)

Therefore, we have: \(\sqrt{a} = x^3^2\)and\(\sqrt{25} = \sqrt{k}\)

From the second equation, we know that k = 25.

Now, substituting the value of k back into the first equation, we have: \(\sqrt{a} = x^3^2\)

To satisfy this equation for all integer values of x, a must be a perfect square. Therefore, we can express a as a =\(y^2\), where y is an integer.

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Answer:

There are 6,500,000 possible student IDs

Step-by-step explanation:

Berry, we want to calculate the number of possible student ID’s

The numbers to choose from are;

0 1 2 3 4 5 6 7 8 9 - Ten numbers

and 26 alphabets

For the first digit - there are 10 choices

Second digits - 10 choices

Third digit - 10 choices

Fourth digit - 10 choices

1st Alphabet - 26 choices

2nd Alphabet- we can choose all other alphabets aside the one chosen at first and that leaves us with 25 choices

So, the number of possible student ID will be;

10 * 10 * 10 * 10 * 25 * 26 = 6,500,000

Step-by-step explanation:

we would have needed only one corresponding side length. because for similar triangles all corresponding lines (like sides but also heights and so on) would be related in size by using the same scaling factor.

going from the large to the small triangle : what do I need to multiply the large side length with to get the small one ?

27 × x = 9

x = 9/27 = 1/3

that is the scale factor.

The inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours landscaping, is  

w + l ≥ 17.

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

Given:

Mackenzie is working two summer jobs, washing cars and landscaping. She must work at least 17 hours altogether between both jobs in a given week.

Total number of hours is w + l and it should be at least 17 hours, (equal to 17 or greater).

We can set inequality as:

w + l ≥ 17

Hence, the inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours landscaping, is  w + l ≥ 17.

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The rate of interest is 73%.

What is the annual rate?

The term annual percentage rate of charge refers to the interest rate for an entire year rather than just a monthly fee or rate as applied on a loan, mortgage loan, credit card, etc. It can also be referred to as a nominal APR or an effective APR. It is an annual rate of a finance charge.

Given that 1 dollar to grow to X dollars in 2 years is given by the formula X = (1+r) ².

A dollar to triple in 2 years.

Thus putting X = 3 in X = (1+r) ²

3 = (1+r) ²

Take square root on both sides:

√3 = 1 + r

Subtract 1 from both sides:

r = √3 - 1

r = 0.73

r = 73%

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Answer:

$562.50

Step-by-step explanation:

6% of the first $2,000 is $120

8% of the next $3,000 is $240

9% of the rest of the $2,250 is $202.50

Add all of it together any you have $562.50

Answer:

Inverse

Step-by-step explanation:

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

Question 11 :

the equations are :

now, let's graph the lines ~

As you can see in the attachment, The lines coincides each other, so the equations are :

Answer:

x = 16

Step-by-step explanation:

7(x + 2) = 6(x + 5)

First, to start solving this problem, we have to distribute the "7" to the "x + 2" in the parenthesis and the "6" to the "x + 5" in the parenthesis.

7x + 14 = 6x + 30

Next, let's subtract "6x" from both sides of this equation!

x + 14 = 30

Now, we have to subtract "14" from both sides of the equation.

x = 16

Lastly! Let's make sure our "x=" equation is correct by inputting our value into the "x" values.

7(16 + 2) = 6(16 + 5)

7(18) = 6(21)

126 = 126

Since our equations equal each other we know that our x-value is correct!

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

\(\cos\theta = \pm\frac{2\sqrt{2}}{3}\\\tan\theta=\pm\frac{\sqrt{2}}{4}\)

Step-by-step explanation:

sinθ = 1/3

\(\cos\theta=\pm\sqrt{1-\cos^2\theta} = \pm\sqrt{1-\frac{1}{9}}=\pm\sqrt\frac{8}{9}=\pm\frac{2\sqrt{2}}{3}\)

\(\tan\theta=\frac{\sin\theta}{\cos\theta}=\pm\frac{1}{2 \sqrt{2}}=\pm\frac{\sqrt{2}}{4}\)

The measures of angle 4 (m<4) and angle 7 (m<7) are 42° and 96°, respectively.

To find the measures of angles 4 and 7, we need to apply some geometric principles. Since the top and bottom pieces of the crib are parallel to each other, we can use the property of alternate interior angles.

Angle 4 (m<4) is formed by a transversal (the line connecting the top and bottom pieces of the crib) intersecting two parallel lines. Given that angle m<2 is 42°, we know that angle 4 is congruent to angle 2. Therefore, m<4 = m<2 = 42°.

Angle 7 (m<7) is formed by a transversal intersecting two parallel lines as well. However, in this case, angle 7 is an exterior angle, which is equal to the sum of the two remote interior angles. The remote interior angles are angles 2 and 4. We know that m<2 = 42° (as given) and m<4 = m<2 = 42° (as explained above). Therefore, the sum of angles 2 and 4 is 42° + 42° = 84°. Since angle 7 is an exterior angle, it is equal to 180° minus the sum of the remote interior angles. Thus, m<7 = 180° - 84° = 96°.

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one time i screwed up a test and asked for a retake and they accepted

and then i passed the test the second time

Answer:

C. x + 4 = 15

D. 4=15−x

Step-by-step explanation:

Well, C is the same exact problem but D could be it too because it is easier to solve for X.. I'm pretty sure you can choose 2 answers

Answer:

(0,0)

Step-by-step explanation:

Do the opposite. (2-5+3,0) is (0,0)

The value of the inverse function f-¹ (3) is (e) 11

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

f(x) = x - 8

To calculate the inverse value at f-¹ (3)

We set the value to 3

using the above as a guide, we have the following:

x - 8 = 3

Evaluate the like terms

x = 11

Hence, the value of the inverse function is (e) 11

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Complete question

if f(x) = x - 8, what is the value of f-¹ (3)?

Car 12 of Train B is also 12 cars away from Car 19 on Train B.

Since each train boasts 31 cars, we can ascertain the total amount of vehicles between Car 19 and Car 12 on Train A:

31 - 19 = 12

Thus, Car 12 on Train A is a dozen units distant from Car 19 on Train A.

Nevertheless, Train B is furthermore moving in an inverring direction and has its exclusive set of automobiles between Car 19 and Car 12. We comprehend that the matching figure of cars must be amongst Car 19 and Car 12 on Train B as with Train A.

In essence, Car 12 of Train B is also 12 cars away from Car 19 on Train B.

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Answer:

Step-by-step explanation:

f(1/2)=x2

f(1/2)=1/2^2

f(1/2)=1/4

(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of

\(y^{2} - 9y + 8.\)

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step \("22x + 49(2) = 0,"\) the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step \("y^{2} - 9y + 8 = 0,"\) the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be \((y - 8)(y - 1) = y^{2} - 9y + 8.\)

(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:

Starting with the original equation: \(22x + 4 - 9(2) = 0\)

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the equation is x = 7/11.

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The value of m + n is given as follows:

A. 18.

The exponential expression for this problem is defined as follows:

\((x^5y^6)^{\frac{1}{5}}(x^3y^4}^{\frac{1}{4}}\)

Applying the power of power rule, we have that the exponents are given as follows:

Then the values of m and n are given as follows:

m = 7, n = 11.

Thus the sum is given as follows:

m + n = 7 + 11 = 18.

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To solve this problem, we need to use vector addition to find the resultant velocity of Julia.

Let's assume that the east direction is the positive x-axis and the south direction is the negative y-axis.

The velocity of Julia in still water is 8 km/hr in the positive x-axis direction.

The velocity of the river is 3 km/hr in the negative y-axis direction.

To find the magnitude and direction of Julia's velocity, we need to find the resultant velocity vector, which is the vector sum of her velocity in still water and the velocity of the river.

Using the Pythagorean theorem, the magnitude of the resultant velocity can be calculated as:

|V| = √(Vx² + Vy²)

where Vx is the x-component of the resultant velocity and is equal to Julia's velocity in still water, and Vy is the y-component of the resultant velocity and is equal to the velocity of the river.

Vx = 8 km/hr

Vy = -3 km/hr

|V| = √(8² + (-3)²) = √(64 + 9) = √73 km/hr

The direction of the resultant velocity can be calculated as:

θ = tan⁻¹(Vy / Vx)

θ = tan⁻¹(-3 / 8) = -20.56°

The negative sign indicates that the resultant velocity vector makes an angle of 20.56° below the positive x-axis (east direction).

Therefore, the magnitude of Julia's velocity is approximately 8.54 km/hr, and the direction of her velocity is 20.56° below the positive x-axis (east direction).

Answer:

c is the correct answer

Step-by-step explanation:

Answer:

k = -0.1

Step-by-step explanation:

An ordered pair is in the form (x,y)  We can use the x and y from the point (-30,3) to find k

y = kx  We will replace x with -30 and y with 3

3 = (-30)k  divide both sides by -30

-0.1 = k  or \(\frac{-1}{10}\) in the fraction form

Here, we are required to find the daily mileage for which the Ultimo charge is twice the Primo charge.

The daily mileage for which the Ultimo charge is twice the Primo charge is at 300miles.

For the Primo car rental agency;

For the Ultimo car rental agency;

where x = number of miles covered.

The question requests that we find the daily mileage for which the Ultimo charge is twice the Primo charge,. i.e U(c) = 2P(c)

Therefore,

$0.70x + $30 = 2($0.30x + $30)

$0.70x + $30 = 2($0.30x + $30)$0.70x + $30 = $0.60x + $60

$0.70x + $30 = 2($0.30x + $30)$0.70x + $30 = $0.60x + $60$0.10x = $30

x = 300 miles.

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Answer:

The 32 electricians will take 1 day and 3 hours to complete the wiring.

Step-by-step explanation:

Since it takes electricians 36 days to wire a new housing subdivision, to determine how many days would 32 electricians take to do the same job the following calculation must be performed:

36/32 = X

1.125 = X

1 = 24

0.125 = X

0.125 x 24 = X

3 = X

Therefore, the 32 electricians will take 1 day and 3 hours to complete the wiring.

The number of cups of broccoli that would be needed for a pound of beef is C. 1 1/2 cup of broccoli per beef.

From the information, it was stated that Tyler was making a meal for his family and that for every 3/4 pound of beef, the recipe calls for 9/8 cups of broccoli.

Therefore, the cups of broccoli that would be needed for a pound of beef will be:

3/4/1 = 9/8/x.

where x = cups of broccoli

Cross multiply

3/4x = 9/8

x = 9/8 ÷ 3/4

x = 9/8 × 4/3

x = 3/2

x = 1 1/2cups

Therefore, the correct option is C.

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Answer:

\(\textsf{c) \quad $1 \frac{1}{2}$ cups of broccoli per 1 lb of beef}.\)

Step-by-step explanation:

Given information:

Create a ratio of pounds of beef to cups of broccoli, where x is the number of cups of broccoli to one pound of beef:

\(\implies \dfrac{3}{4}: \dfrac{9}{8}=1:x\)

\(\implies \dfrac{\frac{3}{4}}{\frac{9}{8}}=\dfrac{1}{x}\)

Cross multiply:

\(\implies \dfrac{3}{4}x=\dfrac{9}{8}\)

\(\implies x=\dfrac{9}{8} \div \dfrac{3}{4}\)

To divide fractions, flip the second fraction (make the numerator the denominator, and the denominator the numerator) then multiply it by the first fraction:

\(\implies x=\dfrac{9}{8} \times \dfrac{4}{3}\)

\(\implies x=\dfrac{9 \times 4}{8 \times 3}\)

\(\implies x=\dfrac{36}{24}\)

\(\implies x=\dfrac{3 \cdot \diagup\!\!\!\!\!\!12}{2 \cdot \diagup\!\!\!\!\!\!12}\)

\(\implies x=\dfrac{3}{2}\)

\(\implies x=1 \frac{1}{2}\)

Therefore, 1¹/₂ cups of broccoli would be needed to one pound of beef.