1. Todd purchased 2 CDs and 3 cassettes for $75. Paulena went to the same music stores and purchased 1 CD and 5 cassettes for $76. Find the cost of one CD and one cassette

KM, JK, PK, and MJ are shown on the diagram.

Then the correct options are B, C, D, and F.

Since, Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

A line segment in mathematics has two different points on it that define its boundaries.

All the line segments will be

JK, JM, KM, MP, PK, and KL

The triangle KPM.

And the angle will be ∠LKJ, ∠PKM. ∠KMP. and ∠MPK.

Then the correct options are B, C, D, and F.

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Answer:

45

Step-by-step explanation:

answer

729

Step-by-step explanation:

a=l×5w

3×243=729

The value of \(log_35 \times log_{25}9\) is 1.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

\(log_35 \times log_{25}9\)

\(log_ab = \frac{logb}{loga}\)

So,

= log 5 / log 3 x log 9 / log 25

= log 5 / log 3 x log 3² / log 5²

\(logm^n = n~logm\)

So,

= log 5 / log 3 x log 3² / log 5²

= (log 5 / log 3) x (2 log 3 / 2 log 5)

= (log 5 / log 3) x (log 3 / log 5)

= 1

Thus,

1 is the value.

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Answer:

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Step-by-step explanation:

We can use the trigonometric identity:

cos 2a = 1 - 2 sin^2 a

to rewrite 1 + 2cos a as:

1 + 2cos a = 1 + 2(1 - sin^2 a/2)

= 1 + 2 - 2(sin^2 a/2)

= 3 - 2(sin^2 a/2)

Now, using another trigonometric identity:

sin a = 2 sin(a/2) cos(a/2)

we can rewrite sin^2 a/2 as:

sin^2 a/2 = (1 - cos a)/2

Substituting this into the expression for 1 + 2cos a, we get:

1 + 2cos a = 3 - 2((1 - cos a)/2)

= 3 - (1 - cos a)

= 2 + cos a

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Answer:

Step-by-step explanation:

you have to find the mean of the two fractions, adding and then dividing by two

(1/5 + 1/9) : 2 =

14/45 : 2 =

7/45

Answer:

To find the slope use the slope-intercept form y=mx+b.

m = 1/3

Answer:

-x+3y=10

the slope is1/3

m=-1/3

Answer: let me explain!

Step-by-step explanation: So this might seem really confusing at first, but it’s actually suuuuuuper easy :P

So, if you think about it, every five seconds the amount of peanuts…well I don’t know how to explain it but let me show you this with numbers.
(4x2)x2x2x2 and so on. The number multiplies by two every five seconds from there. So figure out how many groups of five second there are in 100 seconds by dividing!

It’s 20!

So since 5 happens 20 times, and every time 5 happens, 2 happens, 2 also happens 20 times! (If that makes any sense)

So that answer would be 8x*twenty twos*

Which is…*drumroll please*

8,388,608
I even double checked!

And for the briefcase skeleton thing

She needs to try it 25 times because there are 5 books and each book can be switched with the other 4 times if the first one doesn’t work, therefore you need to multiply and the equation would be 5^2, or in other words, 25.
Don’t forget ur units!

Hope this helps :P

Answer:

Step-by-step explanation:

Solving by factoring is a strategy used to solve quadratic in form polynomials, which are equations that can be written in the form of ax^2 + bx + c = 0. The goal of this strategy is to factor the equation into two binomials that are equal to zero. Once the equation is factored, we can use the zero product property to set each binomial equal to zero and solve for the roots or solutions of the equation.

The process of factoring begins by finding the greatest common factor of all the terms in the equation. Once the GCF is identified, it can be factored out of the equation. Next, we look for two binomials that multiply to give the remaining terms in the equation and add to give the remaining constant term.

For example, consider the equation: 3x^2 + 6x - 9 = 0.

To factor this equation, we first find the GCF of all the terms, which is 3. We can factor out 3 from all the terms, giving us: 3(x^2 + 2x - 3) = 0.

Now, we look for two binomials that multiply to give x^2 + 2x - 3 and add to give -2. We can see that (x-3)(x+1) satisfies this condition.

By factoring the equation, we have now factored the polynomial into (x-3)(x+1) = 0. We can use the zero product property to set each binomial equal to zero and solve for the roots: x-3 = 0 and x+1 = 0. The solutions are x=3 and x=-1.

By using the factoring strategy, we were able to solve the quadratic in form polynomial 3x^2 + 6x - 9 = 0 and find the roots x=3 and x=-1. This strategy can be applied to any quadratic in form polynomial and is a useful tool in solving equations.

The graph of f(x) is the second one, so the correct option is B.

Here we have f(x), a piecewise function, and we want to see which one of the four graphs is the correct one.

You can see that the first domain of the function is:

x ≤ -4

So we must have a closed circle at x = -4, when the parabola ends.

The second domain is:

-4 < x < 1

So x here is not equal to -4 nor 1, so this part starts and ends with open circles.

finally, the linear part starts with a closed circle.

Also, notice that the line has a negative slope, so it goes down, then we can discard the first option.

Then we can see that the correct option is the second graph.

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9514 1404 393

Answer:

  x = 135

Step-by-step explanation:

The sum of the differences from the mean of the known numbers is

  -15 +8 -7 +0 -7 = -21

The value of x must have a difference from the mean that is the opposite of this sum. (That is, the total of differences from the mean of all the numbers must be zero.)

  x = 114 +21

  x = 135

For the given expression, the addition of coefficients is \(5x^2 + 2x - 7\).

In algebra, a coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression. In other words, it is the number that is being multiplied by the variable.

Addition is a basic mathematical operation that combines two or more numbers or quantities to produce a sum. It is denoted by the plus sign (+). When two or more numbers are added, the result is called the sum or total.

First, we need to combine like terms by adding the coefficients of terms with the same variable(s) raised to the same power.

\((6x^2 + 10x - 7) + (-x^2 - 8x)\)

\(= 6x^2 + (-x^2) + 10x + (-8x) - 7\) (grouping like terms together)

\(= (6x^2 - x^2) + (10x - 8x) - 7\) (rearranging terms)

\(= 5x^2 + 2x - 7\) (combining the coefficients)

Therefore, the final answer for the addition of coefficients is \(5x^2 + 2x - 7.\)

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Answer:

B(6, 5), C(1, -7)

Step-by-step explanation:

A(2, 5)

From A to B, there is translation x, (4, 0).

Add 4 to A's x-coordinate, and add 0 to A's y-coordinate.

B(2 + 4, 5 + 0) = B(6, 5)

From C to B there is the translation y, (5, 12).

Since we are going from B to C, we undo translation y.

The translation from B to C is (-5, -12).

C(6 - 5, 5 - 12) = C(1, -7)

Answer:

$12 per hour

Step-by-step explanation:

You would divide both 72 and 6, by 6. That should get you 12 dollars for 1 hour.

The descending order for the polynomial is \(-x^3y^5 - 2x^2y^3 + 4xy + x^4\). So, option D) None of the other answers are correct is the right answer.

What is a polynomial?

Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

The polynomial expression is -

\(x^4-x^3y^5+4xy-2x^2y^3\)

To get this expression, we arrange the terms based on their degree of y, starting from the highest degree and working our way down.

If two terms have the same degree of y, we arrange them based on their degree of x, starting from the highest degree and working our way down.

In this case, the term with the highest degree of y is \(-x^3y^5\), followed by \(-2x^2y^3\), then 4xy, and finally \(x^4\), which has no y term.

Thus, we write the expression in descending order as -

\(-x^3y^5 - 2x^2y^3 + 4xy + x^4\)

Therefore, the expression is obtained as \(-x^3y^5 - 2x^2y^3 + 4xy + x^4\).

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Answer: They are not parallel, they are coincident

Step-by-step explanation:

If two lines have the same slope but a different y-intercept, the lines are parallel. If two lines have the same slope and the same y-intercept, the lines are coincident.

We can rewrite 5x−y=−5 adding -5x to both sides and multiplying by -1:

5x - y =-5

5x - y -5x = -5 - 5x (adding -5x to both sides)

-y = -5 - 5x

Multiplying by -1

y = 5x + 5

Both equations look the same so they are coincident. They have the same intercept y=5 and the same slope m=5.

Answer:

Parent function:

f(x) = √x

Add a number to the value of the function, such as k:

f(x) = (√x) + k

If k is positive, the function moves up. If k is negative, the function moves down.

The values given in standard form are 8.59 and 7.003

The standard form of a number is a way of writing the number in a form that follows certain rules. Any number that has exponents and decimals is said to be a standard notation.

Given the following statements

eight and fifty-nine hundredths

8 + 59/100

8 + 0.59

8.59

For the expression seven and three thousandths

7 + 3/1000

7 + 0.003

7.003

Hence the values given in standard form are 8.59 and 7.003

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Answer:

First box ⇒ 3.6 x 10^-1

Second box ⇒ 3.1 x 10^6

Third box ⇒ 5.3 x 10^-6

Fourth box ⇒ 4.2 x 10^-1

Step-by-step explanation:

I used a calculator and solved it :)

Answer:

first square = 3.6 x \(10^{-1}\)

Step-by-step explanation:

They are all multiplying so there is no need for parenthesis

(3.8 * 10³) * (9.4 * \(10^{-5}\))

3.8 * 10³ * 9.4 * \(10^{-5}\)
35.72 * \(10^{-2}\)

35.72 =~ 36

Everytime you elevate a number, it's the same as...
3 * 10² = 100 * 3 = 300

0.3 * 10³ = 1000 * 0.3 = 300

so then...

36 *      \(10^{-2}\) = 3.6 * \(10^{-1}\)

The solution for x is x = -2 + sqrt(17) and x = -2 - sqrt(17) will give the brainliest.

What is the quadratic equation?

A quadratic equation is a type of polynomial equation of degree 2, that can be written in the form of ax^2 + bx + c = 0 where x is the variable, a,b,c are constant and a is not equal to zero.

To solve for x in the equation 9/(x+4) = 2x, we can first clear the fractions by multiplying both sides of the equation by (x+4). This gives us:

9 = 2x*(x+4)

Then we can simplify the right side of the equation:

9 = 2x^2 + 8x

Next, we can move all the x terms to one side of the equation and all the constants to the other side:

2x^2 + 8x - 9 = 0

Now we can use the quadratic formula to solve for x:

x = (-b +/- sqrt(b^2 - 4ac)) / 2a

where a = 2, b = 8, and c = -9

So we have:

x = (-8 +/- sqrt(8^2 - 42-9)) / 2*2

x = (-8 +/- sqrt(64 + 72)) / 4

x = (-8 +/- sqrt(136)) / 4

x = (-8 +/- 4*sqrt(17)) / 4

x = (-2 +/- sqrt(17))

So the solutions for x are x = -2 + sqrt(17) and x = -2 - sqrt(17)

The solution for x is x = -2 + sqrt(17) and x = -2 - sqrt(17) will give the brainliest.

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Answer: The answer is b!!

Step-by-step explanation: I just took the test!

Answer:

B

Step-by-step explanation:

Ed2021

Answer:

Step-by-step explanation:

a) Probability-Above 30 min = 5.72% = .0572

b) Probability-Above 15 min =  99.11% = .9911

c) *Probability-Between  1 - 59.49% = .4051

d) 19.136 minutes  z = -1.28

a) The probability that trip will take at least 1/2 hour will be 0.0606.

b) The percentage of time the lawyer is late for work will be 99.18%.

c) The probability that lawyer misses coffee will be 0.3659.

d) The length of time above which we find the slowest 10​% of trips will be 0.5438.

e) The probability that exactly 2 out of 3 trips will take at least one half

1/2 hour is 0.0103.

What do you mean by normal distribution ?

A probability distribution known as a "normal distribution" shows that data are more likely to occur when they are close to the mean than when they are far from the mean.

Let assume the time taken for a one way trip be x .

x ⇒ N( μ , σ ²)

x  ⇒ N( 24 , 3.8 ²)

a)

The probability that trip will take at least 1/2 hour or 30 minutes will be :

P ( x ≥ 30)

= P [ (x - μ) / σ ≥ (30 - μ) / σ ]

We know that , (x - μ) / σ = z.

= P [ z ≥ (30 - 24) / 3.8)]

= P [ z ≥ 1.578 ]

= 1 - P [  z ≤ 1.578 ]

Now , using the standard normal table :

P ( x ≥ 30)

= 1 - 0.9394

= 0.0606

b)

The percentage of the time the lawyer is late for work will be :

P ( x  ≥ 15)

= P [ z ≥ -2.368 ]

= P [  z ≤ 2.368]

= 0.9918

or

99.18%

c)

The probability that lawyer misses coffee :

P ( 15 < x < 25 ) = P ( x < 25 ) - P ( x < 15)

= P [  z < 0.263] - P ( z < -2.368)

or

= 0.3659

d)

The length of time above which we find the slowest 10​% of trips :

P( x ≥ X ) ≤ 0.10

=  0.5438

e)

Let's assume that y represents the number of trips that takes at least half hour.

y ⇒ B ( n , p)

y ⇒ B ( 3 , 0.0606)

So , the probability that exactly 2 out of 3 trips will take at least one half

1/2 hour is :

P ( Y = 2 )

= 3C2 × (0.0606)² × ( 1 - 0.0606)

= 0.0103

Therefore , the answers are :

a) The probability that trip will take at least 1/2 hour will be 0.0606.

b) The percentage of time the lawyer is late for work will be 99.18%.

c) The probability that lawyer misses coffee will be 0.3659.

d) The length of time above which we find the slowest 10​% of trips will be 0.5438.

e) The probability that exactly 2 out of 3 trips will take at least one half

1/2 hour is 0.0103.

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The length of the apothem is 10. 99cm

To determine the apothem of a polygon, we have to use the formula;

a = s/2 tan (180/n)

Such that the parameters are;

Now, substitute the values, we have;

a = 8/2tan(180/9)

divide the values

a = 8/2tan 20

Find the values

a = 8/0. 7279

Divide the values

a = 10. 99cm

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Answer:

Below

Step-by-step explanation:

Losing 1/4 means there is 3/4 left when discharged

3/4 * 160 = 120 #

Answer:

c

Step-by-step explanation:

The y-values of the graph increases as the value of x increases, which

indicates that a characteristic of the base of the logarithm function.

Correct response:

The given points on the graph are;

The point where the graph starts = Quadrant 4

Direction of the graph = From quadrant 4 to quadrant 1

Points on the graph are;

(0.5, -0.4), (1, 0), and (6, 1)

The given options are;

\(y = \mathrm{log_{\frac{1}{6} } x}\)

\(y = \mathrm{log_{0.5} x}\)

\(y = \mathrm{log_1 x}\)

\(y = \mathrm{log_{6} x}\)

From the shape of the graph, in which, log x increases as x increases, therefore;

The base, b, of the logarithm is larger than 1, given that we have;

\(\mathbf{log_bx} = y\)

\(\mathbf{b^y} = x\)

From the given coordinate points, x increases as y increases, therefore;

b > 1

The possibly option is therefore, y = log₆x

Verifying, we have;

At x = -0.4, y = 0.5

\(b^y = x\)

\(6 ^{(-0.4)}\) ≈ 0.488

Therefore, the point (0.5, -0.4) is close to the graph of y = log₆x

At the point (1, 0), we have;

6⁰ = 1

Therefore, the point (1, 0), is on the graph of y = log₆x

At the point (6, 1), we have;

6¹ = 6

Therefore, the point (6, 1) is on the graph of y = log₆x

The function of the graph is therefore;

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The equation of the line is (y - 1/12) = -4/3(x - 7/5).

What is the slope of a line?

A line's slope in mathematics is defined as the ratio of the change in the y coordinates to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are represented by y and x, respectively.

Consequently, the formula for the change in the y-coordinate with respect to the change in the x-coordinate is

m = y/x = y/x = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line can be depicted by

tan θ = Δy/Δx

So, the slope of a line is tan.

The given equation of a line is:

3x-4y=7

-4y = -3x + 7

y = 3/4 x - 7/4

The slope of the line is 3/4.

The slope of the line perpendicular to the given line is - 1/m = - 4/3

The point-slope of a line is y - y₁ = m(x - x₁).

The given point is (7/5,1/12)

The equation of the line is

(y - 1/12) = -4/3(x - 7/5)

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Answer:

A

Step-by-step explanation:

Answer:

Line A

Step-by-step explanation:

Line A is the only one that starts at -2

Answer:

140

Step-by-step explanation:

V=whl=7·4·5=140cm³

Answer:

140cm^3

Step-by-step explanation:

It is 140 because volume is base x length x height so 7 x 5 x 4 = 35 x 4 = 140 cm cubed so 140cm^3

Hope this helps