What steps should be followed to solve the following equation for x: -3x - 8 1 point= 4*Add 8 to both sides, then divide by 3Divide by -3, then add 8 to both sidesAdd 8 to both sides, then divide by -3Add 8 to both sides, then add 3 to both sides

The opposite of a number is the same distance from 0 on a number line as the original number, but on the other side of 0, then we have to invert the sign of the original number, if we have a positive one and we are told to find its opposite we just put it a negative sign, if the original number is negative then we rewrite it as a positive number.

In this case, we have 18/19, then the opposite number of it is -18/19

The equation given is a one variable equation, "p".

The question asks to find the value of "p", which is the pounds of peanuts.

So, we need to solve the euqation for "p".

First, we need to put all the terms that have "p" in one side. For this, we will have to use the distributive property in the parenthesys first:

Now, we can substract 4.05p in both sides to get the "p" term of the left to the right:

Now, we do the same for the 13.50, substract it in both sides:

Now, we can divide both sides by 0.45:

So, the answer is p = 2, thus, you need 2 pounds of peanuts for the trail mix.

The given expression in the form of (a + ib) can be written as -

-2/3 + i(4/3).

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted [i], called the imaginary unit and satisfying the equation -

[tex]{\displaystyle i^{2}=-1}[/tex]

Every complex number can be expressed in the form a + bi, where [a] and [b] are real numbers

We have the following expression -

(4 - 2i)/3i

We have -

(4 - 2i)/3i

4/3i - 2i/3i

- 2/3 + i(4/3)

Therefore, the given expression in the form of (a + ib) can be written as -

-2/3 + i(4/3).

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Answer:

1/3

Step-by-step explanation:

[tex]\frac{5}{6}*\frac{2}{5} = \frac{5*2}{6*5} =\frac{10}{30} = \frac{1}{3}[/tex]

5 and 5 cancel out, 2 becomes 1, and 6 simplifies to 3.

GIVEN:

We are told that the original price of a sofa is $500 and rthen it has been reduced by 20%, leaving the new price at $400.

The company cant sell the sofa after 3 weeks so they reduce the price to $320.

Required;

To find the percentage decrease.

Step-by-step solution;

At the point of reducing the price further, the original price has now been put at $400 and the new price has been set at $320. We take note that in terms of percentage, the original price is 100% while the new price will be represented by x (that is, yet unknown).

With this information we can set up an equation based on the ratio of the two prices as compared to the two percentages.

This means;

Therefore;

Now we cross multiply;

The new price is now given as 80% which simply means 20% was deducted from the original price. In other words, there was a 20% price reduction.

ANSWER:

There was a 20% decrease.

Sarah wants to buy a blouse that costs $28. Her mom said she can buy this when it goes on sale for 2/7 of the original price.

2/7 part of 28 is

So, the selling price will be $8.

Given:

point (2,-3) and (-3,7)

First, solve for the slope of the line

Now that we have solved for the slope, substitute it to the slope-intercept form y = mx + b to find the y-intercept. Use the point (2,-3) but using (-3,7) works just as well.

The slope intercept form of the line is

Rearrange it to follow the standard form Ax + By = C, and we have

Question:

Solution:

Consider the following function:

this is equivalent to:

solving for x, we get:

exchanging the notation we get:

The same procedure is applied analogously for the function f(x) = x-6.

We can conclude that the correct answer is:

YES

Note that the area of a square is the square of its side.

If the area is 12 square inches, the side is approximately :

And the area will be :

The answers are :

3.46 inches

and

11.9716 square inches

The only incorrect choice in the options is B.

A number line with a closed circle on 9 and shading to the left

The given inequality is expressed as:

This means that x is includes 9 and all the numbers above 9.

From the number line drawn above. A number line with a close circle on 9 and shading to the right is drawn.

Answer:

Step-by-step explanation:

The solution for the given inequality is x≥3. Therefore, option C is the correct answer.

The given inequality is (7x-3)/9 ≥ 8-2x.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Inequality can be solved as follows:

(7x-3)/9 ≥ 8-2x

Multiply 9 on both the sides of an inequality, we get

7x-3 ≥ 9(8-2x)

⇒ 7x-3≥72-18x

Add 3 on both the sides of an inequality, we get

7x≥75-18x

Add 18x on both the sides of an inequality, we get

25x≥75

⇒ x≥3

The solution for the given inequality is x≥3. Therefore, option C is the correct answer.

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13/4 m or 3.25 meters

1) Given the width is 10/8 meter

The length is 3/8 meter

2) To wrap the rectangular desk let's use this formula, for the Perimeter (2p):

2p= 2(w+l) Plug into w and l the measures

2p = 2(3/8 +10/8) Proceed with the sum within the parentheses

2p = 2(13/8) Distribute the factor

2p =13/4

3) Hence, the perimeter is 13/4 or 3.25 meters

MAtine:

each ticket = $6

Each popcorn = $3

Evening:

Each ticket = $9

Each popcorn = $4

Number of tickets = t

Number of popcorns = p

Fun club attends at matinee, spends less than $60

6t + 3p < 60

Then attends an evening show and spends more than $36

9t + 4p > 36

The system of inequations:

6t + 3p < 60

9t + 4p > 36

Graph each and find the solution

6x + 3y < 60

9x + 4y > 36

Where both areas overlap is the solution:

Answer: 7 tickets and 5 popcorns

From Phyllis's graph:

At the start of training, Phyllis runs more miles per week than Nigel because Phyllis runs 6 miles per week, while Nigel runs 4 miles per week

In functions, for any value of x, there's a unique value for y.

On the table, in the x column, having 6 yielding two different values of y in rows 2 and 3 will mean that it's not a function because the y values must be unique.

Therefore, the answer is 6

INFORMATION:

We know that:

- Rhombus STAR has vertices S(-1,2), T(2,3), A(3,0), and R(0,-1)

And we must calculate the perimeter of the rhombus

STEP BY STEP EXPLANATION:

To calculate it, we must find first the measure of one of the sides.

We can find one of the sides calculating the distance between two consecutive vertices.

So, calculating the distance between vertices S and T

Finally, to find the perimeter, we need to use that the rhombus has 4 equal sides. So, we the perimeter would be

ANSWER:

D. 4√10

Solution:

Given:

Since both events are independent, then;

Hence,

The number of students taking an online course and prefer basketball to football is;

Therefore, the number of students taking an online course and prefer basketball to football is 408

We have to prove that triangles ABC and ADC are congruents.

We can draw a driagram of the triangles as:

As AB and AD are radius of the same circle, we have:

The same can be said for CB and CD, so:

Then, we have a shared side between the two triangle. Then, given the reflexive property we have:

Then, as we have 3 pair of congruent sides, by the SSS postulate, we can conclude that the triangles ABC and ADC are congruent. Then, all three pair of angles are also congruent.

NOTE:

If we just want to prove that the angles Then, we four right triangles (or a rhombus). Then, each angle of the erhombus is bisected.

The left angle at vertex D is complementary to the lower angle at A. The left angle at vertex B is complementary to the upper angle at A. As both angles at A are equal, The left angle at D and the left angle at B are complementary to the same angle.

Then, they have the same measure.

The same analysis can be done for the right angles.

Then, as both halves of the angles are equal, then the total angle

In order to solve this problem, we need to use proportions.

We have:

cost in dollars number of bags of ice

8.16 6

x 7

We are assuming that the cost is proportional to the number of bags of ice. So, to find the value x that represents the cost for 7 bags of ice, we can cross multiply the proportions above:

x * 6 = 8.16 * 7

Now if we divide both sides by 6, we isolate the variable x on the left side of the equation, and find its value:

x * 6 = 8.16 * 7

x * 6/6 = 8.16 * 7/6

x = (8.16/6) * 7

x = 1.36 * 7

x = 9.52

Therefore, it would have cost them $9.52.

Initial investment = $100

The balance increases annually at a rate = 4%

The increased amount = 4% of $100

This gives

Hence the investment increase annually by $4 yearly

In the second year the investment will increase by 2 x $4 = $8

In the third year the investment will increase by 3 x $4 = $$12

This implies that

In n years

The investment will increase by n × $4 = $4n

The balance at n years is given as

Balance = Investment + year increment

This is as shown below

When you have a function written in explicit form with two variables(let's call them 'x' and 'y'), it is written as a combination of 'x' and 'y' equal to some constant.

To "solve for x in terms of y", is the same as rewritting this function as an equality in the following form:

Let's try an example to show how this works.

Given the following function:

Now, solving for x in terms of y, is the same as rewriting x as a function of y.

Option-D is correct, m∠3 + m∠5 = 180°. This is accurate because according to the transversal theorem, the angles from the same side must sum up to 180°.

Given that,

This is about angle theorems.

Option A: m∠1 = m∠2. This is untrue since the sum of all angles on a straight line is 180° and the line that separates these two angles is not parallel to the horizontal straight line to evenly divide it.

Option B: m∠4 = m∠6; This statement is not true because though their sum is 180° but again they are transverse angles which are not equal from the line that forms them.

Option C: m∠1 + m∠5 = 90°; This is incorrect since the line that forms each of them is not at a 45° angle and m∠1 = m∠5

Option D; m∠3 + m∠5 = 180°. This is accurate because according to the transversal theorem, the angles from the same side must sum up to 180°.

Option E; m∠7 = m∠8. The assertion is false for the same reason as in option A.

That means only option D is true.

Therefore, Option-D is correct, m∠3 + m∠5 = 180°. This is accurate because according to the transversal theorem, the angles from the same side must sum up to 180°.

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Here are the steps in multiplying binomials using the distributive property:

1. Multiply the first 2w and first 7 by the terms inside the second parenthesis/binomial. Add the products.

2. Simplify.

3. Combine similar terms like -14w and 14w and the result is 0.

Hence, the product of the two binomials is 4w² - 49.

Given:

The sequence is 8, 16, 32, 64.

The first term is 8.

Answer:

Step-by-step explanation:

Find out the  area of the running track that goes around the field .

To proof

Formula

Area of rectangle = length× breadth

area of running track = outside area - inside area

First case ( outside )

length = 73 + 2 × 9.76

         = 92.52m

Breadth = 84.39 m

radius of outside semi circle

=46.26m

outside area = area of rectangle + 2× area of the semi- circle

                    =  92.52× 84.39  + 3.14× 46.26 ×46.26

                    =  7807.76+ 6719.56

                    = 14527.32 m² ( approx)

Second case

radius of the semi- circle

=36.5m

inside area =  area of rectangle + 2× area of the semi- circle

                 = 73× 84.39 +  3.14×  36.5 ×36.5

                 = 6160.47 + 4183.27

                 = 10343.74m²

area of running track=   14527.32 m² - 10343.74m²

                    = 4183.58m²

Hence proved

Answer:

Find out the  area of the running track that goes around the field .

Step-by-step explanation:

Answer

Explanation

We want to convert 300 fluid ounces per minute into fluid ounces per second.

Note that

1 minute = 60 seconds

We then do the conversion thus

First let's find the perimeter of the scale drawing. The perimeter is the sum of all sides of the figure.

Looking at the figure, there are two sides without the length. The length of the vertical missing side can be calculated as 8 - 2 = 6 cm, and the length of the horizontal missing side can be calculated as 20 - 9 = 11 cm.

So the perimeter of the scale drawing is:

Now, to find the perimeter of the garden, we can use a rule of three:

So the perimeter of the garden is 280 ft.

Given the equation :

The first step is to add 5 to both sides

so,