Khalid is 56 years old. Cathleen is 6 years older than Brody. The sum of Cathleen's and Brody's ages is half of Khalid's age. How old is Cathleen?

The mistakes that Cindy made include:

The answer for Cindy's monthly car payments would be $609.63

To find the monthly payment. first convert the APR to a monthly rate and the number of years to months.

Monthly rate:

= 4% / 12

= 1 / 3%

Number of months:

= 4 x 12 months

= 48 months

The monthly payments is an annuity as it is constant and periodic. The monthly payment for Cindy's car can be found as:

= Cost of car / Present value of annuity factor, 1/3%, 48 months

= 27, 000 / 44.288833874953

= $609.63

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Answer:

-4

Step-by-step explanation:

m = y2-y1 / x2-x1

m = -11-(-7) / 3-2

m = -11+7 / 3-2

m = -4 / 1

m = -4

m = -39-(-27) / 10-7

m = -39+27 / 10-7

m = -12 / 3

if you simplify if further,

m = -4 / 1

m = -4

Answer:

-4.

Step-by-step explanation:

The slope formula is y2-y1/x2-x1. if we plug in the numbers we can get the formula -11 - (-7)/ 3-2. This gets us -4/1 which equals -4. Therefore the slope of the equation is -4.

Question 1

Since the x-coordinates are the same, the line is vertical. Therefore, the slope is undefined.

Question 2

Since the y-coordinates are the same, the line is horizontal. Therefore, the slope is zero.

The inverse function of the given function f(x) = 12x + 10 is

h(x) = (x - 10)/12

Given, a function f(x)

f(x) = 12x + 10

we have to find the inverse of the function f(x) i.e. h(x).

let f(x) = y

y = 12x + 10

12x = y - 10

x = (y - 10)/12

inverse function of f(x) = h(x)

h(x) = (x - 10)/12

So, the inverse function of the given function f(x) is

h(x) = (x - 10)/12

Hence, the inverse function of the given function f(x) is

h(x) = (x - 10)/12

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Answer:

B = 24% - t(3%)

Step-by-step explanation:

You have you battery at 24% represented by B. you have your 3% which is your difference (d). and your hour which is t. For every hour you are subtracting 3%. So your equation would be B = 24% - t(3%)

Answer:

Equation: B = 23 - 3(t)

Step-by-step explanation:

24 is the percent after it was charged, the 3% is the difference, and your time, which is (t). You deduct 3% for each hour. As a result, your equation would be B = 24 - 3(t).

Answer:

30 tadpoles

Step-by-step explanation:

the 3 part of the ratio relates to the number of swans, that is 18 , then

18 ÷ 3 = 6 ← value of 1 part of the ratio

Then

number of tadpoles = 5 × 6 = 30

Answer: 4/3

Step-by-step explanation:

The reciprocal of a/b is b/a.

Answer:

$23.55

Step-by-step explanation:

First we will need to determine the total amount of sales Ryan and Carlos made. To do that we will multiply the amount of products sold by the product cost.

$2.75 x 12 = $33

Now we need to deduct the cost of supplies they need to pay back from their profits.

$33- $9.45= $23.55

Now we are left with Ryan and Carlos' total profit, which is $23.55

The coordinates of the point after the two reflections are (0.3,-7/10).

A reflection is a mapping from an isometric hyperplane with a set of fixed points acting as the reflection's axis or plane from a Euclidean space to itself. A figure's reflection creates its mirror image of that figure in the plane or axis of the reflection.

Given that, the point (-0.3, 7/10) is reflected over the y-axis and then over the x-axis respectively.

The coordinates of the point after the reflection in the y-axis are:
(0.3, 7/10)

Now, the coordinates of the point after the reflection in the x-axis are:
(0.3, -7/10)

Hence, the coordinates of the point after the two reflections are (0.3,-7/10).

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Answer: It indicates that the quadratic has a repeated real number solution.

Step-by-step explanation:

Using the rate, the number of book Mason reads per month is 2 books.

Mason read 4 books in 2 months. Mason reads at a constant rate. The number of books he reads each month can be calculated as follows;

The number of books he reads is at a constant rate. The rate formula can be used to find the number of book Mason read each month.

rate = number of books read / number of month

Therefore,

number of books read = 4 books

number of month = 2 month

Hence,

rate  = 4 / 2

rate = 2 books per month

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An open circle at 5 and a bold line starting at 5 and pointing to the right (>) is the correct representation of the inequality

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.

Given: the inequality –3(2x – 5) < 5(2 – x)

First, we have to solve for x in the inequality

–3(2x – 5) < 5(2 – x)

Clear the parenthesis:

-6x + 15 < 10 - 5x      (Note: This is one of the options to be selected)

Collect like terms:

-6x + 5x < 10 - 15

-x < -5

Divide both sides by -1:

x > 5              ( Note:  Dividing both sides by -1 will change the < to > )

This is what will determine our answer

Since our answer is x > 5.  An open circle will be at 5 and a bold line starts at 5 and is pointing to the right (>)

Therefore,  the correct representation of the inequality is "an open circle is at 5 and a bold line starts at 5 and is pointing to the right". Select 3rd and 4th option is the answer

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Charmaine sends 34 message, Jose send 75 texts and Shen send 25 messages.

What is linear equation?

An equation is a mathematical statement, which has an equal sign (=) between the algebraic expression. Linear equations are the equations of degree 1. It is the equation for the straight line.

Let C be charmaine text, S be shen text, J be jose text.

C +J+ S=134

Shen send 9 messages fewer than charmine .

S = C -9

C = S+9

And Jose sent 3 times more then shen

J =3S

We get,

S+9+3S+S=134

5S +9 = 134

5S = 134 -9

5S = 125

S = 25

C = 25 +9

= 34

J= 75

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Answer:

[tex]f(h(x)) = ( \sqrt{x} - 3)^{2} + 4[/tex]

[tex]f(h(x)) = (x - 9) + 4[/tex]

[tex]f(h(x)) = x - 5[/tex]

Step-by-step explanation:

h(x) became x for function of f(x)

Part a

There are [tex]\frac{\pi}{180}[/tex] radians in a degree, so the angle of rotation in radians is [tex]\frac{930\pi}{180}=\frac{31\pi}{6}[/tex].

Part b

Using the arc length formula, the distance is [tex](31\pi/6)(3.5)=\frac{217\pi}{12}[/tex] inches.

The heights of both trees at the time when they have an equal height are equal to 4 inches and 48 inches respectively.

In order to graphically solve the system of equations, we would first of all write a system of equations that models the situation. Additionally, we would assign variables to the height of Tree A t years after being planted and height of Tree B t years after being planted, and then translate the word problem into algebraic equation as follows:

Therefore, translating the word problem into algebraic equation, we have the following:

A = 32 + 4t

B = 16 + 8t

On a graph, we would plot the height of Tree A on the x-axis while height of Tree B would be plotted on the y-axis of the cartesian coordinate.

By critically observing the graph, the point of intersection which gives a solution to the system of equations include the following:

Height of Tree A, A = 4 inches.

Height of Tree B, B = 48 inches.

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Prime numbers are numbers greater than 1. They only have two factors, 1 and the number itself. This means 1 is a multiple of a prime number except prime number itself.

What are Prime Numbers?

Prime numbers are numbers greater than 1. They only have two factors, 1 and the number itself. This means these numbers cannot be divided by any number other than 1 and the number itself without leaving a remainder.

Numbers that have more than 2 factors are known as composite numbers.

A prime number is a natural number with exactly 2 divisors / factors: 1 and the number itself. Primes are always greater than 1 and they're only divisible by 1 and themselves. They cannot be made by multiplying two other whole numbers that are not 1 or the number itself.

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The function has the end behavior f(x) → -∞  as , x → -∞ as f(x) → +∞ , x → +∞

Since,  The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.  And, if the function has  positive leading coefficient with odd degree then its end behavior is    f(x) → -∞  as , x → -∞ as f(x) → +∞ , x → +∞

Here, The given function has positive leading coefficient with odd degree.

Therefore,  by the definition of end behavior of a function,

The function has the end behavior f(x) → -∞  as , x → -∞ and, f(x) → +∞ , x → +∞

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Answer:

Separating the variables , using equality symbol , drawing boundary line in XY plane , shading the area are the four steps in graphing linear inequalities

Step-by-step explanation:

Mathematical expressions known as linear inequalities compare two expressions using the inequality symbol. The expression may be either a numerical or an algebraic expression, or it may be both.

Step 1: Always start by separating the variable y from the left side of the inequality.

Step 2: The equality symbol should be used in place of the inequality symbol

Step 3: Draw the boundary line from step 2 in the XY plane.

Step 4: The last step is to partially or completely shade the border line.

Separating the variables , using equality symbol , drawing boundary line in XY plane , shading the area are the four steps in graphing linear inequalities

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The area of the trapezoid is equal to 7 square units.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the trapezoid in a two-dimensional plane is called the area of the trapezoid.

Given that the area of a trapezoid is given by the formula A = 1/2

h(b₁ + b₂). The given values are h = 2, b₁=3, and b₂=4.

The area of the trapezoid is calculated as,

Area = (1 / 2) x h(b₁ + b₂)

Area = (1 / 2 ) x 2 x ( 3 + 4 )

Area = 7

Area = 7 square units

Therefore, the area of the trapezoid is equal to 14 square units.

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The reasons put into the correct order to justify solving the inequality:

-2(x + 6) < 3(x + 1) - Given

-2x - 12 < 3x + 3 - Distributive Property

-2x < 3x + 15 - Addition Property of Order

-5x < 15 - Subtraction Property of Order

x > 3 - Division Property of Order

Check how to solve:

-2(x + 6) < 3(x + 1)

Open the parenthesis

-2x - 12 < 3x + 3

Add 12 to both sides

-2x - 12 + 12 < 3x + 3 + 12

-2x < 3x + 15

Subtract 3x from both sides

-2x - 3x < 3x + 15 - 3x

- 5x < 15

divide both sides by -5

x > 3

Therefore, the solution to the given inequality -2(x + 6) < 3(x + 1) is x > 3.

The properties mentioned above are properties of inequalities and hold for all situations of inequalities as given.

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Answer:

43x+3x+17y

Step-by-step explanation:

because 43x+17y+3x=43x+17y+3x

Answer:

[tex]2 \sqrt[3]{3} [/tex]

Step-by-step explanation:

[tex]24 {}^{ \frac{1}{3} } [/tex]

[tex] \sqrt[3]{24} [/tex]

[tex] \sqrt[3]{8 \times 3} [/tex]

[tex] \sqrt[3]{8} \times \sqrt[3]{3} [/tex]

[tex] \sqrt[3]{2 {}^{3} } \times \sqrt[3]{3} [/tex]

[tex]2 \times \sqrt[3]{3} [/tex]

[tex]2 \sqrt[3]{3} [/tex]

Answer:

Answer:

[tex]8\sqrt{11}[/tex]

Step-by-step explanation:

Given:

[tex]x+\dfrac{1}{x}=\sqrt{11}[/tex]

Sum of two squares

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

[tex]\textsf{Let}\; a = x[/tex]

[tex]\textsf{Let}\; b = \dfrac{1}{x}[/tex]

Therefore:

[tex]\begin{aligned}x^2+\dfrac{1}{x^2}&=\left(x+\dfrac{1}{x}\right)^2-2x\left(\dfrac{1}{x}\right)\\\\&=\left(\sqrt{11}\right)^2-2\\\\&=11-2\\\\&=9\end{aligned}[/tex]

Sum of two cubes

[tex]\boxed{a^3+b^3=(a+b)(a^2-ab+b^2)}[/tex]

[tex]\textsf{Let}\; a = x[/tex]

[tex]\textsf{Let}\; b = \dfrac{1}{x}[/tex]

Therefore:

[tex]\begin{aligned}x^3+\dfrac{1}{x^3}&=\left(x+\dfrac{1}{x}\right)\left(x^2-x\left(\dfrac{1}{x}\right)+\left(\dfrac{1}{x}\right)^2\right)\\\\ &=\left(x+\dfrac{1}{x}\right)\left(x^2-1+\dfrac{1}{x^2}\right)\\\\&=\left(x+\dfrac{1}{x}\right)\left(x^2+\dfrac{1}{x^2}-1\right)\\\\&=\sqrt{11}\left(9-1\right)\\\\&=8\sqrt{11}\end{aligned}[/tex]

The domain and range of this square root function are: D: [–4, ∞) and R: [0, ∞).

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function or relation is defined. This ultimately implies that, a domain is the set of all possible input values (x-values) for a function while a range is the set of all possible output values (y-values) of a function.

Based on the information provided, the function is represented as follows:

g(x) = √(x + 4)

Since a square root function doesn't exist for all negative values, the domain of this function is given by:

x + 4 ≥ 0

x ≥ -4

Domain = [-4, ∞]

Since we do not have a vertical translation, the range of this square root function is given by:

x ≥ 0

Range = [0, ∞]

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Answer:

[–4, ∞) and R: [0, ∞)

Step-by-step explanation:

I got it right on the test.

You can occasionally start by isolating and replacing a variable that is squared in both equations if you're required to solve a system of equations without a starting linear equation.

If there isn't a linear equation to begin with, you can pick out and use a squared variable in both equations.

Start by dividing both sides of the supplied nonlinear equation by the variable's coefficient, for instance.

After you've done that and isolated a variable, carry on with the problem-solving by adding that variable to the other equation.

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The common denominator of the complex fraction is (1/a - 1/b)/(1/a + 1/b) is a²b² which is option D.

The provided complex fraction is  (1/a - 1/b)/(1/a + 1/b).

Now, to find the common denominator,

Solving this complex fraction.

First multiplying each component of every bracket to every component of the other bracket,

= 1/a² + 1/ab - 1/ab - 1/b²

Now, simplifying the equation,

= 1/a² + 1/b²

= (a²+b²)/a²b²

The denominator is the lower part of the fraction.

Hence, the common denominator of the complex fraction is a²b².

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Complete question - What is the common denominator of 1/a + 1/b in the complex fraction (1/a - 1/b)/(1/a + 1/b)?

A)a2 b2

B)a – b

C)a + b

D)ab

Factor the expression using the GCF 24y+88x

24y+88x

GCF is 8:

8(3y + 11x)

Answer:

find p (A or ),given that A and B are independent