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2 years ago

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Mathematics

1 answer:

Kryger [21]2 years ago

5 0

Answer:

2nd option

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c

Given

- 3x - 2y = 30 ( add 3x to both sides )

- 2y = 3x + 30 ( divide terms by - 2 )

y = - $\frac{3}{2}$ x - 15 ← in slope- intercept form

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Twelve boxes of pencils cost $16. Which equation could you use to find the cost per box

zheka24 [161]

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Hello!

✧･ﾟ: *✧･ﾟ:* *:･ﾟ✧*:･ﾟ✧

❖ You can use the equation 16 ÷ 12 = 1.33

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3 0

2 years ago

Read 2 more answers

hi, i dont undertand number 20 because i was absent in class today and i rerally need help, i will appraciate with the help, and

Mariulka [41]

Given:

The equation is,

$2\log _3x-\log _3(x-2)=2$

Explanation:

Simplify the equation by using logarthimic property.

$\begin{gathered} 2\log _3x-\log _3(x-2)=2 \\ \log _3x^2-\log _3(x-2)=2_{}\text{ \lbrack{}log(a)-log(b) = log(a/b)\rbrack} \\ \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \end{gathered}$

Simplify further.

$\begin{gathered} \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \\ \frac{x^2}{x-2}=3^2 \\ x^2=9(x-2) \\ x^2-9x+18=0 \end{gathered}$

Solve the quadratic equation for x.

$\begin{gathered} x^2-6x-3x+18=0 \\ x(x-6)-3(x-6)=0 \\ (x-6)(x-3)=0 \end{gathered}$

From the above equation (x - 6) = 0 or (x - 3) = 0.

For (x - 6) = 0,

$\begin{gathered} x-6=0 \\ x=6 \end{gathered}$

For (x - 3) = 0,

$\begin{gathered} x-3=0 \\ x=3 \end{gathered}$

The values of x from solving the equations are x = 3 and x = 6.

Substitute the values of x in the equation to check answers are valid or not.

For x = 3,

$\begin{gathered} 2\log _3(3^{})-\log _3(3-2)=2 \\ 2\log _33-\log _31=2 \\ 2\cdot1-0=2 \\ 2=2 \end{gathered}$

Equation satisfy for x = 3. So x = 3 is valid value of x.

For x = 6,

$\begin{gathered} 2\log _36-\log _3(6-2)=2 \\ 2\log _36-\log _34=2 \\ \log _3(6^2)-\log _34=2 \\ \log _3(\frac{36}{4})=2 \\ \log _39=2 \\ \log _3(3^2)=2 \\ 2\log _33=2 \\ 2=2 \end{gathered}$

Equation satifies for x = 6.

Thus values of x for equation are x = 3 and x = 6.

6 0

11 months ago

A circular garden has a circumference of 130 feet. A gardener would like to install a path going through the middle of the garde

natali 33 [55]

Answer:

The southwest corner of the garden will be 2 feet south and 3 feet west of the tree. A circle has a center at (3,5). What is the area of the circle to the nearest tenth of a square unit? Which of the following could be the vertices of the triangle? A garden that is 5 feet by 6 feet has a walkway that is 2 feet wide around it.

3 0

3 years ago

A square painting painting is surrounded by a frame. the outside edges of the frame are 3 inches in length, and the frame is 3 i

sdas [7]

Answer:

Area = 36 $inches ^ 2$

Step-by-step explanation:

There must be an error with the statement, because it is strange that the length of the frame is equal to its thickness.

Assuming that the data supplied is correct, we can do the following procedure.

Let's call L the length of the frame.

We know how much each side of the square measures.

L = 3 inches

We also know that the thickness (s) is:

s = 3 inches.

Then the area of the frame is equal to:

Area = Perimeter * thickness

Area = 4L*s

Area = 3*4*3

Area = 36 $inches ^ 2$

3 0

2 years ago

PLEASE HELP! 8 POINTS!! Find the value

Pepsi [2]

Answer:

-sqrt(3)/2

Step-by-step explanation:

Use double angle identity for sin(2x)

sin(2x)=2sin(x)cos(x)

We are given sin(x)=-1/2 so we already have so far that:

sin(2x)=2(-1/2)cos(x)

sin(2x)=-1*cos(x)

We just need to find cos(x).

x is in the fourth quadrant so cosine will be positive there

knowing the unit circle we should know that if sin(x)=-1/2 then cos(x)=sqrt(3)/2 while in 4th quadrant.

So the answer is sin(2x)=-1*sqrt(3)/2=-sqrt(3)/2

5 0

2 years ago