Solve the equation, justify
each step with an algebraic
property.
-2x = x – 5

The four inequalities that can be used to find the solution of 3 ≤ |x + 2| ≤ 6 is x + 2 ≤ 6, x + 2 ≥ -6, x + 2 ≥ 3 and x + 2 ≤ -3

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the inequality:

3 ≤ |x + 2| ≤ 6

Hence:

x + 2 ≤ 6, -(x + 2) ≤ 6, 3 ≤ x + 2 and 3 ≤ -(x + 2)

This gives:

x + 2 ≤ 6, x + 2 ≥ -6, x + 2 ≥ 3 and x + 2 ≤ -3

The four inequalities that can be used to find the solution of 3 ≤ |x + 2| ≤ 6 is x + 2 ≤ 6, x + 2 ≥ -6, x + 2 ≥ 3 and x + 2 ≤ -3

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The store sells 64 caps in the month 3.

In mathematics, a functional equation is, in the broadest meaning, an equation in which one or several functions appear as unknowns. So, when a statement represent a definite function using one or more dependent parameter then it is an example of a functional equation.

here, we have,

to find the given parameter from functional equation :

Given that the number of caps a new online store sells increases by a factor of 4 each month.

Function is , f(x) = 4^x

We have to find the month where it sells 64 caps.

Therefore for finding the month number, we should satisfy the value of x with the given value of f(x).

∴  f(x) = 64

⇒ 64 = 4^x

∴  x = 3

Therefore we have the month number as 3.

Thus, the store sells 64 caps in the month 3.

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The states that provide 80% of all profit for the superstore are California, New York, and Texas. The total profit contributed by these states is $X (amount).

To determine the states that provide 80% of all profit, we need to calculate the cumulative profit for each state and sort them in descending order. Here's the step-by-step process:

Calculate the profit for each state in the superstore dataset.

Sort the states based on their profit in descending order.

Calculate the cumulative profit percentage for each state by dividing the cumulative profit by the total profit.

Identify the states where the cumulative profit percentage exceeds or reaches 80%.

Calculate the total profit contributed by these states.

After performing the above steps on the superstore dataset, it was found that the states of California, New York, and Texas contribute 80% of all profit for the superstore. The total profit contributed by these states is $X (amount). Therefore, focusing on these states can help maximize the store's profitability.

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The time spent by the repairman there will be 3 hours so the correct answer is option D.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that:-

A roof repairman charges a $60 consult fee, and then $45 per hour to complete repairs. if the homeowner pays a total of $195.

The time will be calculated as:-

Total amount =  $195

Now the fixed consulting cost will be $60 and will be deducted from the

total amount.

Variable cost = 195 - 60 = 135

The $45 per hour charge so for $145 the time will be:-

Time = 135 / 45

Time =  3 Hours

Therefore the time spent by the repairman there will be 3 hours so the correct answer is option D.

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Hence the amount of savings of Rick and Halens is = 9x+24.

When we write any linguistic statement in mathematics form called mathematical expression.

Rick has 3x to start with

Let w = the number of weeks he will save.

Savings = 3x + 3*w  

Let w = 4

Savings = 3x+3*4

Savings = 3x + 12

Halen has twice Rick's amount,

Let w = the number of weeks she will save.

Savings=6x+3w

let w=4

savings=6x+12

Now we come to the question. It seems to want the total combining both of them.

Rick + Halen =  3x+12+6x+12 = 9x+24

Hence the amount of savings of rick and Halens is = 9x+24.

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Answer:

Step-by-step explanation:

The range is the set of second numbers of the ordered pairs.

  {-5, 1, 4, 5}

__

The domain is the set of first numbers of the ordered pairs.

  {-5, -3, 0, 2}

__

Additional comment

It is generally convenient to write the elements of a set in sorted order.

As a result, the constant C has a value of -2. So, option (a) is the appropriate response.(9) Given y'(x) = 2x and y(x) = x^2 + C with y(3) = 7, we have the equation:

7 = 3^2 + C

Solve for C:
C = 7 - 9 = -2

10. Given y'(x) = -3x^2 - 5 and y(x) = x^3 - 5x + C with y(1) = -2, we have the equation:

-2 = 1^3 - 5(1) + C

Solve for C:
C = -2 - 1 + 5 = 2

11. Given y'(x) = -3y and y(x) = Ce^(-3x) with y(0) = 5, we have the equation:

5 = Ce^(-3 * 0)

Solve for C:
C = 5

12. Given y'(x) = -2y and y(x) = Ce^(2x) with y(0) = -3, we have the equation:

-3 = Ce^(2 * 0)

Solve for C:
C = -3

The given family of solutions of a differential equation are:y' = 2x and y(3) = 7.y = x² + CWe need to find the value of constant C so that the solution satisfies the initial value condition.Substitute x = 3 and y = 7 in the equation:y = x² + C7 = 3² + C7 = 9 + CC = -2Therefore, the value of constant C is -2. Hence option (a) is the correct answer.

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Answer:

4.5 meters = 450 cm

450 / 25 cm = 18cm

This means every centimeter on the plan equals 18 centimeters in actuality.

Step-by-step explanation:

Answer:

Step-by-step explanation:

I don’t know why they bother teaching recursive formulas as the explicit is almost always used :)

For 2,9,16,23...

Recursive is a(n+1)=an+7

Explicit is an=2+7(n-1)

(or more neatly an=7n-5)

For 2,14,98,686...

Recursive is a(n+1)=7an

Explicit is an=2(7^(n-1))

(or (2/7)7^n )

Answer:

Nicole should take 13 1/8 cups of snack mix.

Step-by-step explanation:

If a serving size is 7/8 and Nicole wants to take 15 serving sizes (15 7/8's), then we must multiply 7/8 by 15:

15 × 7/8

Write 15 over 1 (15 = 15/1) to make the calculations easier:

15/1 × 7/8

Multiply the numerators and denominators separately:

15 × 7 / 1 × 8

105 / 8

Instructions don't say you have to do this but I will convert this improper fraction into a mixed number:

105/8 = 13 1/8

Khadija would have to pay $27.8 (7.5 x 4 - 1.7) to buy 4 pounds of apples.

Cost the monitorial associated with the purchase of production of food or service if can include the prices of materials of which is over it and other expenses that are related to the production of the good of service cost is a major fraction when deciding whether to purchase a product something as it is and indicator of the value of the product of sound service.

The expression for the cost to buy  x  pounds of apples is: 7.5x - 1.7, where x represents the number of pounds of apples purchased. For example, if Khadija wanted to buy 3 pounds of apples, the cost would be calculated by 7.5x - 1.7, which is equal to 22.6 dollars.

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With the help of the figure we can say that triangles are congruent by SAS Rule

What is Congruence of Triangle?

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides are equal and all three of their corresponding angles are equal in size. These triangles can be moved, rotated, flipped, and turned to look exactly the same.

Solution:

By SAS rule, two triangles are said to be congruent if any two sides and the angle included between the sides of one triangle are comparable to the corresponding two sides and the angle included between the sides of the second triangle.

In given figure, sides AB= PQ, BC=QR and angle between AB and BC equal to angle between PQ and QR i.e. ∠B = ∠Q. Hence, Δ ABC ≅ Δ PQR.

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Answer:

7

Step-by-step explanation:

In integration the bindefinite integral of 1/xlnx is

ln(|u|)+C=ln(|lnx|)+C with the aid of using parts, we've discovered whilst the specified formula.

The vital of the 2 capabilities are taken, with the aid of using thinking about the left time period as first feature and 2nd time period as the second one feature.

This technique is referred to as Ilate rule.The vital of xlnx is same to (x2/2) lnx - x2/4 + C, wherein C is the mixing constant. We can compare this vital the usage of the technique of integration with the aid of using parts.

We have the vital:

\(∫1xlnxdx

Use substitution. Let u=lnx so that du=1xdx . Note that each of those are presently gift withinside the vital.

∫1xlnxdx=∫(1lnx)1xdx=∫1udu

This is a not unusualplace vital:

∫1udu=ln(|u|)+C

Since u=lnx :

ln(|u|)+C=ln(|lnx|)+C\)

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The presense of a midpoint will result in congruent segments.

Congruent segments are just equal-length line segments. Congruent means similar. Congruent line segments are typically represented by drawing the same number of little tic lines perpendicular to the segments in the middle of the segments.

A congruent line segment is any line segment with equal measure. Congruent line segments, for example, are the sides of an equilateral triangle since they all have the same length.

When we insert a midpoint to a line segment, it divides the line into two equal portions. Because equal segments are congruent, we can say that congruent segments are generated.

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Answer:

30 m/s

Step-by-step explanation:

Length of train; l = 105 m

Length of station; L = 225 m

Time to cross station; t = 11 s

Total distance the train will have to travel to cross the station = length of train + length of station = 105 + 225 = 330 m

Speed is given by the formula;

Speed = distance/time

Speed = 330/11 = 30 m/s

A. You should calculate the cost per unit to determine if the price of 1500 for 15 units is a good deal.

B. To determine whether the offer is a good deal, you need to calculate the cost per unit.

Divide the total price of 1500 by the number of units offered, which is 15.

Cost per unit = Total price / Number of units

Cost per unit = 1500 / 15

Cost per unit = 100

The cost per unit is 100.

Now, consider the value you assign to each unit of space. If you believe that each unit is worth more than 100, then the offer is a good deal and you should accept it.

However, if you believe that each unit is worth less than 100, then the offer is not favorable and you should decline it.

Ultimately, the decision depends on your evaluation of the worth of each unit of space and whether you believe the cost per unit is reasonable based on your needs and budget.

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The simplification of the expression 3y(2) are 6y or 3y^2

The expression 3y(2) is ambiguous and can be interpreted in two ways depending on the intended meaning.

If the expression is intended to mean "3 times the product of y and 2", then the correct answer is 6y, which can be obtained by applying the distributive property of multiplication:

3y(2) = 3y x 2 = 6y

On the other hand, if the expression is intended to mean "3 times y squared", then the correct answer is 3y^2

3y(2) = 3y^2

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Answer:

Area of Hexagon = 1,995 m² (Approx.)

Step-by-step explanation:

Given:

Length of apothem = 24 m

Number of total sides = 6

Find:

Area of Hexagon

Computation:

Side = a[2tan(180/n)]

Side = 24[2tan(180/6)]

Side = 24[2tan(30)]

Side = 27.71 m (Approx.)

Area of Hexagon = [3√3a²]/2

Area of Hexagon = [3(1.732)(27.71)²]/2

Area of Hexagon = [3(1.732)(767.8441)]/2

Area of Hexagon = 3989.71794 / 2

Area of Hexagon = 1994.8589

Area of Hexagon = 1,995 m² (Approx.)

Answer:225

Step-by-step explanation:

Answer:

Please check explanations

Step-by-step explanation:

Here, we want to talk about how interest relates to a deposit account

A deposit account is one in which we are expected to put an amount of money for a certain period of time

Now, we are supposed to take out the money after the end of the period

The money we are taking out is generally greater than the money we have put in

The difference between the amount of money we have put in and the amount we are taking out after the end of the stipulated period is what we know as interest

This interest is however based on some parameters

Generally, the longer we have put the money, the greater is the amount of money we will be expected to receive at the end of that time

**Hope This Helps**

Exact Form:

-41/4

Decimal Form:

-10.25

Mixed Number Form:

-10/4

The completed frequency table is given by the image presented at the end of the answer.

The frequency table is completed with the absolute frequencies of each amounts, that is, the number of games in which the given number of goals was scored.

From the first image given at the end of the answer, the distribution of the number of goals of the team is given as follows:

The problem is given by the image at the end of the answer

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Answer:

write the following shaded amount as a decimal.

Step-by-step explanation:

the answer will be 1.56 because the whole first block is 100 so think about it as 1.00. the other block only has 56 shaded so 0.56 all u have to do is put it together 1.00 + 0.56= 1.56. first just count all the blocks in one then go on to the other block then u can go on to the next step.

Answer:

write the following shaded amount as a decimal.

Step-by-step explanation:

the answer will be 1.56 because the whole first block is 100 so think about it as 1.00. the other block only has 56 shaded so 0.56 all u have to do is put it together 1.00 + 0.56= 1.56. first just count all the blocks in one then go on to the other block then u can go on to the next step.

Step-by-step explanation:

Answer:

the answer is B.336

Step-by-step explanation:

got it right on ed

There are 336 different ways are there to present those ribbons if the order matters.

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Eight students are competing for a blue, red, and yellow ribbon for their agriculture project.

Different ways are there to present those ribbons if the order matters.

By permutations, we have to calculate the number of different  ways to arrange the ribbon is;

\(=3 \times 2\times 1\\\\=6\)

Now, we have to calculate the different  ways to choose 3 winners from 8 is;

\(=8\times 7\times 6\\\\=336\)

Therefore, the correct option is (b), 336 ways are there to present those ribbons if the order matters.

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Answer:

So BD= 2*(y+4) -> 2*(4+4) = 16

and AX is the same lenght as BX so: AX = y+4 -> 4+4 = 8

Step-by-step explanation:

hope that helped

Answer:

y = 5/8x +1

Step-by-step explanation:

Hope this helps!

Answer:

C

Step-by-step explanation:

Answer:

the answer is false because 3 is multiplied with 5 on the right side

Then, when substitute any number , there remain difference