What is a dependent variable in algebra

Answer:

1/2

Step-by-step explanation:

The y-intercept is [tex]\frac{1}{2}[/tex].

Given that f(x) = 4x-2.

To find the inverse function:

1) Write f(x) = y

2) Switch x and y.

3) Solve for y.

4) Write [tex]y=f^{-1}\left(x\right)[/tex].

So,

[tex]f(x) = 4x - 2\\y=4x-2\\x=4y-2\\4y=x+2\\y=\frac{\left(x+2\right)}{4}\\y=\frac{1}{4}x+\frac{2}{4}\\y=\frac{1}{4}x+\frac{1}{2}\\f^{-1}\left(x\right)=\frac{1}{4}x+\frac{1}{2}[/tex]

Comparing this with y=mx+b,

b = y-intercept = [tex]\frac{1}{2}[/tex]

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Answer:

It is NOT possible for a solution to be both x<9 and x>9

It IS possible for a solution to be both x≤9 and x≥9

Step-by-step explanation:

Because for x<9 and x>9 the GREATER than symbol means it less than 9 and cannot be 9 or it is greater than 9 but cannot be 9.

With x≤9 and x≥9 the greater than or EQUAL sign makes a big difference. Because x≥9 may be the actual solution but since it is possible to be  equal to 9 so can x≤9.

(Sorry if this seemed very confusing to explain).

Answer:

-4

Step-by-step explanation:

6 times 4 equals 24

24 minus 12 equals 12

12 divided by 3 equals 4

4 minus 8 equals -4

(btw i did this in the order from the question and not BIDMAS )

Answer:

π = a/(r²) = a÷(r²)

Answer:

pie is equal to the square root of A divided by r

Step-by-step explanation:

Set the equation first...a=pie times r squared. Then u need to get rid of everything to make pie by itself. U square both sides or all the equation. the square cancels out and on the other side, it will be the square root of a. Next, divide by r on each sides. The r cancels out. Then it's gonna be pie =the square root of a all over r. It can't be a/r square because in the original...pie is being multiplied by r which is squared so that means both variables are squared. U cant find pie if the square is stopping it so u square for the very first step

Answer:

The answer to your question is  (4/3, -1)

Step-by-step explanation:

Convert both equations to the same base

                                    [tex]27^{x - 2} = 9^{y}[/tex]

        27 = 3 x 3 x 3 = 3³  

          9 = 3 x 3 = 3²

Substitution

                                   [tex]3^{3(x - 2)} = 3^{2y}[/tex]

Simplify

                                      3x - 6 = 2y                         Equation l

                                   [tex]32^{y - 3/5} = \frac{1}{8^{2x}}[/tex]

            32 = 2 x 2 x 2 x 2 x 2 = 2⁵

             8 = 2 x 2 x 2 = 2³          

                                   2[tex]^{5(y - 3/5)} = 2^{-3(2x)}[/tex]

Simplify

                                  5y - 3 = -6x                            Equation ll

Equal to zero both equations

                                3x - 2y - 6 = 0                         Equation l

                                6x + 5y - 3 = 0                          Equation ll

Solve by elimination

Multiply equation l by 5 and equation ll by 2

                               15x - 10y - 30 = 0

                               12x + 10y - 6 = 0

                                27x        -36 = 0

Solve for x

                                 27x = 36

                                     x = 36 / 27

Simplify                        x = 4/3

Find the y value

                                6(4/3) + 5y - 3 = 0

                                8 + 5y - 3 = 0

                                      5y = -8 + 3

                                      5y = -5

                                        y = -5/5

                                        y = -1

Solution

                                  (4/3, -1)

Option B

The factored form by grouping is:

[tex]xy+2y^2+3x+6y = (x+2y)(y+3)[/tex]

Solution:

Given that we have to factor the given polynomial by grouping

Given polynomial is:

[tex]xy+2y^2+3x+6y[/tex]

Factoring by grouping means that you will group terms with common factors before factoring.

This is done by grouping a pair of terms. Then factor each pair of two terms

In the given polynomial, group the terms that has "x" as common and group the terms that has "y" as common

[tex](xy+3x)+(2y^2+6y)[/tex]

Factor out "x" from first group and factor out "2y" from second group

[tex]x(3+y)+2y(y+3)[/tex]

Factor out y + 3

[tex]x(3+y)+2y(y+3) = (x+2y)(y+3)[/tex]

Thus the factored form by grouping is:

[tex]xy+2y^2+3x+6y = (x+2y)(y+3)[/tex]

Answer:

5/12

Step-by-step explanation:

1/4×3/3=3/12

1/3×4/4=4/12

4/12+3/12=7/12

12/12-7/12=5/12

Answer:

if you're solving for inequality its y>2

The complete question is:

A geometric sequence is defined recursively by

    [tex]a_{(1)}=40\text{ and }a_n=(-1/2)a_{(n-1)}[/tex]

(a) Write out the first four terms of this sequence.

(b) Is the 9th term of this sequence larger or smaller than 1/10? Show the calculation that you use to determine your answer.

Answer:

Explanation:

You are given the first term,    [tex]a_(1)=40[/tex] , and the recursive formula

   [tex]a_{(n)}=(-1/2)a_{(n-1}[/tex]

Thus, you can find the sequence of terms by multiplying each term by the constant ratio, (-1/2).

(a) First four terms of the sequence

[tex]a_{(1)}=40\\ \\ a_{(2)}=40\times (-1/2)=-20\\ \\ a_{(3)}=-20\times (-1/2)=10\\\\ a_{(4)}=10\times (-1/2)=-5[/tex]

Those are the first four terms.

(b) 9th term

You can write the explicit formula of the sequence as:

[tex]a_{(n)}=a_{(1)}\times r^{(n-1)}\\ \\ a_{(n)}=40(-1/2)^{(n-1)}[/tex]

Thus, for the 9th term, n = 9, and the term is:

[tex]a_{(9)}=40\times (-1/2)^{(9-1)}\\ \\ a_{(9)}=40\times(-1/2)^8\\ \\ a_{(9)}=40\times(1/256)=0.1526[/tex]

Since 1/10 = 0.1, and 0.1 < 0.1526, the 9th term is larger than 1/10.

The factors of given expression are: -5 and 3/4

Step-by-step explanation:

Given equation is:

[tex]4x^2+17x-15[/tex]

Making pairs for the mid-term 17x by factoring the product of co-efficient of 4x^2 and 15

[tex]4x^2+20x-3x-15[/tex]

[tex]= 4x(x+5) - 3(x+5)[/tex]

[tex]=(4x-3)(x+5)[/tex]

Now

[tex]4x-3 = 0\\4x = 3\\x = \frac{3}{4}[/tex]

[tex]x+5 = 0\\x = -5[/tex]

Hence,

The factors of given expression are: -5 and 3/4

Keywords: Quadratic equation, factors

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Answer:

[tex]z=12[/tex]

Step-by-step explanation:

The lines a and b intersect at point D. Angles with measures [tex](5z+8)^{\circ}[/tex] and [tex](4z+20)^{\circ}[/tex] are vertical angles.

Vertical angles theorem states that vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent.

Congruent angles have equal measures.

Hence,

[tex]5z+8=4z+20\\ \\5z-4z=20-8\\ \\z=12[/tex]

Answer:

12

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

If you see this kind of problem do this two steps:

1. Multiply the numerator and the multiplier.

2. Divide the result with the denominator.

[tex]\frac{3}{10}[/tex] × 120

3 × 120 = 360 (STEP 1)

360 ÷ 10 = 36 (STEP 2)

Answer:

36

Step-by-step explanation:

Answer:

  480

Step-by-step explanation:

Let h represent the number of high-quality downloads. Then the total download size is ...

  4.1h +2.7(1130-h) = 3723

  1.4h = 672 . . . . . . . . . . . . . . subtract 2.7·1130 = 3051

  h = 480 . . . . . . . divide by 1.4

There were 480 downloads of the high-quality version.

Answer:

8 3/5

Step-by-step explanation:

subtract the whole numbers first and then the fractions. you have 10 4/5-2 1/5. subtract the whole numbers and you have 8(put that off to the side). then do 4/5-1/5. 4-1=3 and the denominators stay the same so you have 3/5. you don’t need to simplify so your final answer is 8 3/5.

Answer:

43 / 5 or 8 3/5

Step-by-step explanation:

Answer: 8/5 or 1 ⅗ acres

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

50*2= b  b/2=40 40+10=50

Answer: 20 pencils and 80 cards

Step-by-step explanation:

See the graph below

We need to remember the following rules:

[tex]For \ any \ function \ f(x) \ we have: \\ \\ \\ \bullet \ g(x)=f(x-k) \ Translation \ k \ units \ to \ the \ right \\ \\ \bullet \ g(x)=f(x+k) \ Translation \ k \ units \ to \ the \ left \\ \\ \bullet \ g(x)=f(x)+c \ Translation \ c \ units \ up \\ \\ \bullet \ g(x)=f(x)-c \ Translation \ c \ units \ down \\ \\ With \ c>0 \ and \ k>0[/tex]

Here we know that The function y = log (x) is translated 1 unit right and 2 units down, so:

[tex]k=1 \\ \\ c=2 \\ \\ \\ Finally: \\ \\ g(x)=log(x-1)-2[/tex]

Below you can see the graph. The red one is the original function while the blue one is the translated one.

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Answer:

B

Step-by-step explanation:

Took test on edge

Answer:

B. right

Step-by-step explanation:

In the bottom left corner there is a square. The square represents a 90 degree angle. A 90 degree angle is named a right angle.

Since you know the value of n = 3, plug in 3 for n in the equation

4(n + 1)

4(3 + 1)      

4(4)

= 16

Answer:

-1/3

Step-by-step explanation:

it goes down one and over three

Answer: your slope would be -[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Answer:

53/50

Step-by-step explanation:

The ratio of males to females is 53:50.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

Number of baby boys = 106

Number of baby girls = 100

So, the ratio of males to females

= 106/100

= 53/50

Hence, the ratio of males to females is 53:50.

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The solution of given inequality is: [tex]x>-3[/tex]

Solution:

Given inequality is:

[tex]7(x+1)>-14[/tex]

We have to find the value of "x"

Let us solve the given inequality

Divide both sides of inequality by 7

[tex]\frac{7\left(x+1\right)}{7}>\frac{-14}{7}\\[/tex]

Simplify the above expression

[tex](x+1)>-2[/tex]

[tex]x+1>-2[/tex]

[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides\: of\: inequality}[/tex]

[tex]x+1-1>-2-1\\\\x>-3[/tex]

Thus the value of x is [tex]x>-3[/tex]

Answer:

infinite solution

Step-by-step explanation:

no matter what you have for x, 3x still equals 3x, so it is infinite

Answer:

Step-by-step explanation:

A = 3/4B

A = 72.75

3/4B = 72.75

B = 72.75 * 4/3

B = 291/3 = 97

you would save (97 - 72.75) = $ 24.25 when buying them at store A

By calculating the original price of the headphones at Store B and subtracting the price at Store A, we find that you would save $24.25 by purchasing the headphones at Store A.

To find out how much you save by buying the headphones at Store A, we need to determine the original price of the headphones at Store B.

Let's denote the price at Store B as P. According to the information given, the price at Store A is 3/4 of the price at Store B. We can write the following equation:

P × (3/4) = $72.75

Solving for P, we get:

P = $72.75 ÷ (3/4)
  P = $72.75 ÷ 0.75
  P = $97.00

Therefore, the price of the headphones at Store B is $97.00. To find the savings, subtract the price at Store A from the price at Store B:

Savings = Price at Store B - Price at Store A
  Savings = $97.00 - $72.75
  Savings = $24.25

By buying the headphones at Store A, you save $24.25.

The calculated coordinates of the point F is (-1, 5)

How to determine the coordinates of F

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

D(2,3),E(-5,2),G(6,6)

We have that

The quadrilateral DEFG is a parallelogram

This means that the opposite sides have equal slopes

i.e.

Slope of DE = Slope of FG

Using slope formula, we have

(3 - 2)/(2 + 5) = (y - 6)/(x - 6)

This gives

1/7 = (y - 6)/(x - 6)

Cross multiply

x - 6 = 7y - 42

x = 7y - 36

Set y = 5

So, we have

x = 7 * 5 - 36

x = -1

So, we have

(x, y) = (-1, 5)

Hence, the coordinates of the point F is (-1, 5)

Question

Consider the parallogram DEFG with three vertices D(2,3),E(-5,2),G(6,6). Find the coordinates of F.

Final answer:

To find the coordinates of vertex F in the parallelogram DEFG with given vertices D(2,3), E(-5,2), and G(6,6), we can use vector subtraction to deduce that the coordinates of F are (-1, 5).

Explanation:

The question requires us to find the coordinates of vertex F of the quadrilateral DEFG given that we have the coordinates of vertices D(2,3), E(-5,2), and G(6,6). Assuming that DEFG is a parallelogram (as the question implies a symmetry-based approach though it doesn't specify), we can find F using the properties of parallelograms, which dictate that opposite sides are equal and parallel. The vector from D to E is ∂D = (-5 - 2, 2 - 3) = (-7, -1), and the vector from G to F (let's call it F's coordinates (x, y)) would be equivalent, as they are opposite sides. So, G + ∂D = F. Substituting G's values, we get (6 - 7, 6 -1), which simplifies to (-1, 5). Thus, the coordinates of F are (-1, 5).

Answer:

2.339×10^3

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10

If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

2.339×10^3

Answer:

(0, 0)

Step-by-step explanation:

You can see immediately that the line AB passes through (0, 0) (the origin) and that points A and B are equidistant from the origin.  In other words, (0, 0) is the midpoint of line AB.

Answer:

Step-by-step explanation:

Answer:

[tex]AB=\sqrt{3}\ in[/tex]

Step-by-step explanation:

The correct question is

The diagonal of rectangle ABCD measures 2 inches in length.

What is the length of line segment AB?

The picture of the question in the attached figure

we know that

In the right triangle ABD

[tex]cos(30^o)=\frac{AB}{BD}[/tex] ----> by CAH (adjacent side divided by the hypotenuse)

substitute the given values

[tex]cos(30^o)=\frac{AB}{2}[/tex]

Remember that

[tex]cos(30^o)=\frac{\sqrt{3}}{2}[/tex]

so

[tex]\frac{AB}{2}=\frac{\sqrt{3}}{2}[/tex]

[tex]AB=\sqrt{3}\ in[/tex]

Answer:

B

Step-by-step explanation:

the answer is B on edge.