MATHEMATICS COLLEGE

Solve for the given variable: 4. 24 - 9x = -3x

5. 4(5x + 2) + 11 = 18x + 3

6. 3x - 8x = -27 – 13

Show Your Work

Answers

Answer 1

Answer:

4. x=4

5. x=-8

6. x=8

Step-by-step explanation:

It may take one extra step to get to the solution, but this method always works.

1. find the variable term that is smallest or most negative. Subtract all the terms on that side of the equation from both sides of the equation.

2. collect terms

3. divide the equation by the coefficient of the variable

4. add the opposite of the constant

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4. The most negative variable term is -9x, which is on the left side. Subtracting (24-9x) from both sides of the equation, we have ...

0 = -3x -24 +9x

0 = -24 +6x

0 = -4 +x . . . . . divide by 6

4 = x . . . . . . . . add the opposite of -4

5. The smallest variable term is 18x, on the right. (The variable term on the left is 20x.)

4(5x +2) +11 -18x -3 = 0 . . . subtract the right side

2x +16 = 0 . . . collect terms

x +8 = 0 . . . . . . divide by 2

x = -8 . . . . . . . . add -8

6. All variables are on the left side, so we can just collect terms and divide by the coefficient of the variable.

-5x = -40 . . . collect terms

x = 8 . . . . . divide by -5

If you were to literally follow the steps above, you would recognize that -5x is less than 0x (the x-term on the right side of the equation), so you would subtract the left side, giving ...

0 = 5x -40

0 = x -8 . . . . . divide by 5

8 = x . . . . . . . . add 8

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Comment on this solution technique

You will often be told to solve these equations by separating the variable terms from the constant terms. This method actually puts the variable terms and constant terms together (and zero on the other side of the equal sign). The constant is separated from the variable as the last step of this solution process, rather than as one of the first steps. By doing this, we don't have to worry about which variable term or which constant term we're going to mess with.

The only reason for choosing the variable term with the smallest (least) coefficient in the first step is to ensure that the resulting variable coefficient is positive. This tends to reduce errors later on. You can also use that same strategy when solving the equation following the "separate constant terms and variable terms" approach.

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The orange shape is a dilation of the black shape. What is the scale factor of the dilation?1/10 1/2 10 2

Answers

Answer:

Scale = ¼

Step-by-step explanation:

See attachment for complete question.

In the attached, we have.

Width = 4 units. ----- Orange

Width = 16 units ------- Black

Required

Determine the scale of dilation

The scale of dilation can be calculated as:

Scale = Width(orange)/Width (black)

Scale = 4/16

Scale = ¼

Hence, the scale of dilation is ¼

The ordered pairs in the table below represent a linear function. x y 6 2 9 8 What is the slope of the function? One-fourth One-half 2 4

Answers

Answer:

The answer is C) 2

Step-by-step explanation: I hope you get this right also.

Answer:

Step-by-step explanation:

The taxes on a house assessed at $78,000 are $1950 a year. If the assessment is raised to $93,000 and the tax rate did not change, how much would the taxesbe now?

Answers

Answer:

i dont do taxes

Step-by-step explanation:

Find the perimeter of WXYZ. Round to the nearest tenth if necessary.

Answers

Answer:

C. 15.6

Step-by-step explanation:

Perimeter of WXYZ = WX + XY + YZ + ZW

Use the distance formula, $d = √((x_2 - x_1)^2 + (y_2 - y_1)^2)$ to calculate the length of each segment.

✔️Distance between W(-1, 1) and X(1, 2):

Let,

$W(-1, 1) = (x_1, y_1)$

$X(1, 2) = (x_2, y_2)$

Plug in the values

$WX = √((1 - (-1))^2 + (2 - 1)^2)$

$WX = √((2)^2 + (1)^2)$

$WX = √(4 + 1)$

$WX = √(5)$

$WX = 2.24$

✔️Distance between X(1, 2) and Y(2, -4)

Let,

$X(1, 2) = (x_1, y_1)$

$Y(2, -4) = (x_2, y_2)$

Plug in the values

$XY = √((2 - 1)^2 + (-4 - 2)^2)$

$XY = √((1)^2 + (-6)^2)$

$XY = √(1 + 36)$

$XY = √(37)$

$XY = 6.08$

✔️Distance between Y(2, -4) and Z(-2, -1)

Let,

$Y(2, -4) = (x_1, y_1)$

$Z(-2, -1) = (x_2, y_2)$

Plug in the values

$YZ = √((-2 - 2)^2 + (-1 -(-4))^2)$

$YZ = √((-4)^2 + (3)^2)$

$YZ = √(16 + 9)$

$YZ = √(25)$

$YZ = 5$

✔️Distance between Z(-2, -1) and W(-1, 1)

Let,

$Z(-2, -1) = (x_1, y_1)$

$W(-1, 1) = (x_2, y_2)$

Plug in the values

$ZW = √((-1 -(-2))^2 + (1 - (-1))^2)$

$ZW = √((1)^2 + (2)^2)$

$ZW = √(1 + 4)$

$ZW = √(5)$

$ZW = 2.24$

✅Perimeter = 2.24 + 6.08 + 5 + 2.24 = 15.56

≈ 15.6

Answer:CCCCCCCCCCCCCCCCC

Step-by-step explanation:

A bicycle is traveling at 20 miles per hour. How many feet will it cover in 30 seconds? Round your answer to the nearest tenth of a foot.

Answers

Answer:

$Distance = 880ft$

Step-by-step explanation:

Given

$Speed = 20(miles)/(hour)$

$Time = 30\ seconds$

Required

Determine the distance

To answer this question, we make use of speed-distance relationship

$Speed = (Distance)/(Time)$

Make Distance the subject

$Distance = Speed * Time$

$Distance = 20 miles/hour * 30 seconds$

Convert seconds to hour

$Distance = 20 miles/hour * (30)/(3600) hour$

$Distance = 20 miles * (30)/(3600)$

$Distance = (20 miles * 30)/(3600)$

$Distance = (600\ miles)/(3600)$

$Distance = (1)/(6) miles$

Convert to foot

$Distance = (1)/(6) * 5280\ ft$

$Distance = (1* 5280\ ft)/(6)$

$Distance = (5280\ ft)/(6)$

$Distance = 880ft$

How many outer atoms and lone pairs are present in a molecule with a square pyramidal shape?

Answers

Answer:

5 Outer and 1 lone pair

Step-by-step explanation:

A square pyramidal shape results when one of the bonds of an octahedron structure is occupied by a lone pair.

Hence there are 5 bonded atoms and one lone pair. The hybridization about the central atom is $sp^(3) d^2$ .

One of the most common example is Xenon tetraflouride. $XeF_4$ . Looking at its structure we can see that it has 5 pairs of outer atoms and one lone pair. With its coordination number 5. The shape of the orbitals is octahedral.

Final answer:

In a molecule with a square pyramidal shape, there are two lone pairs and four outer atoms.

Explanation:

When a central atom has two lone electron pairs and four bonding regions, we have an octahedral electron-pair geometry. The two lone pairs are on opposite sides of the octahedron (180° apart), giving a square planar molecular structure that minimizes lone pair-lone pair repulsions.