Order the steps to solve the equation
Log(x^2-15)=log(2x) form 1 to 5.

A linear graph is most useful when depicting piece rates as it clearly shows the continuous relationship and trend between the number of items produced and the pay received, represented by a positive, negative, or zero slope.

When depicting piece rates, which relate the payment an individual receives to the number of pieces produced or tasks completed, a linear graph or line graph is often most useful. Linear graphs effectively illustrate relationships between two variables, such as the number of items produced (on the x-axis) and the amount of money earned (on the y-axis), highlighting trends and changes over a range of values. A bar graph may be best to illustrate comparisons when showing the relationship of separate and distinct categories. However, in the context of piece rates, where there is a continuous relationship between work done and pay received, the connected data points in a line graph provide a clear visual of the rate of payment as it changes with the number of pieces.

Understanding the appearance of slopes is essential in reading graphs. A positive slope indicates an increase or upward trend in the relationship between the two variables, a negative slope represents a decrease or downward trend, and a zero slope indicates a consistent, flat relationship with no change over time.

Final answer:

The student takes home a check of $25.94 each week after deductions and direct deposit. Of the amount direct-deposited, $38.92 is placed into a savings account weekly, resulting in $155.68 being deposited into the savings account monthly.

Explanation:

To solve the first problem, we must start by calculating the gross income for one week of work:

Next, we calculate each of the deductions from the gross income:

Now we calculate the total deductions:

The net income after deductions is:

We then determine the amount directly deposited:

The remaining paycheck given as a check each week is:

For the second question, we already know from the scenario that $77.84 is directly deposited. We just need to calculate the amount that goes into the savings account:

To find the monthly savings deposit, we assume there are 4 weeks in a month:

a is 2q^2r

b is 3s^2t

the expression factored is...

(2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)

The given expression is a sum of two cubes. The factorization of the given expression is [tex](2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)[/tex].

Given:

The given identity is, [tex]a^3 + b^3 = (a + b)(a^2 - ab + b^2)[/tex].

It is required to factorize [tex]8q^6r^3 + 27s^6t^3[/tex] using the given identity.

The given expression can be written in the form of sum of two cubes as,

[tex]8q^6r^3 + 27s^6t^3=2^3q^6r^3 + 3^3s^6t^3\\=(2q^2r)^3+(3s^2t)^3[/tex]

Here, a and b are [tex]2q^2r[/tex] and [tex]3s^2t[/tex] respectively.

Now, the factorization of the given expression can be one as,

[tex]a^3 + b^3 = (a + b)(a^2 - ab + b^2)\\(2q^2r)^3+(3s^2t)^3=(2q^2r+3s^2t)((2q^2r)^2-(2q^2r)(3s^2t)+(3s^2t)^2)\\=(2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)[/tex]

Therefore, the factorization of the given expression is [tex](2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)[/tex].

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Answer:

the correct answer is B

The answer is

Y=x^4-6x^3 +6x^2 -6x+5

The quartic function with only two real zeroes given as; x=5 and x=1 is; x⁴ -12x³ +46x²-60x +25

With two zeroes given for a quartic equation;

The zeroes must appear twice each such that the factors of the function are;

The quartic function is therefore:

(x² -10x +25) (x² -2x +1)x⁴ -2x³ +x² -10x³ +20x² -10x + 25x² -50x +25= x⁴ -12x³ +46x²-60x +25

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Answer:

101 g of Potassium is equivalent to 2.583 moles of Potassium.

Step-by-step explanation:

As per definition of moles, molecular weight of a substance = 1 mole

So molecular weight of Potassium = 39.0983 g

∵ 39.0983 g weight of Potassium = 1 mole

∴ 1 g weight of Potassium = [tex]\frac{1}{39.0983}[/tex] g

∴ 101 g of Potassium = [tex]\frac{101}{39.0983}[/tex] g

                                  = 2.583 moles

Therefore, 101 g of Potassium is equivalent to 2.583 moles of Potassium.

The numbers arranged from least to greatest will be -0.4, -1.33, 0.8, 1.41, and 3.32.

It is the order of the numbers in which a smaller number comes first and then followed by the next number and then the last number will be the biggest one.

The decimal number is the sum of a whole number and part of the fraction number. The fraction number is greater than zero but less than one.

The numbers are given below.

√11, -0.4, (-4/3), 0.8, √2

Convert all the numbers into decimal form, then we have

√11, -0.4, (-4/3), 0.8, √2

3.32, -0.4, -1.33, 0.8, 1.41

Then the numbers arranged from least to greatest will be -0.4, -1.33, 0.8, 1.41, and 3.32.

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5*1 is the dimension of the original rectangle.

The scale is the proportion that is used to show how the dimensions of a model or scaled figure compare to the equivalent dimensions of the real figure or item. In contrast, a scale factor is a number that is multiplied by each component of an item to create an expanded or reduced figure.

Given With a scale factor of 6, the diagram depicts the expansion of a rectangle.

and the new rectangle is 30*6 in size.

The scaling factor is 6

thus,

the length of the original rectangle = 30/6

the length of the original rectangle = 5

the width of the original rectangle = 6/6

the width of the original rectangle = 1

therefore, the dimension of the original rectangle is 5*1.

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Complete question:

What measurements did the initial rectangle have?

Answer:

Scott's method is linear because the number of minutes increased by an equal number each week.

Arithmetic progressions use the linear method.

The graph proves it, by obtaining a straight line.

Step-by-step explanation:

Scott used an arithmetic progression, with a ratio of 5, that is adding 5 to the value of each previous week.

Let us call the time in minutes of each week, so the arithmetic progression is of the following linear form:

S1 = k0 = 10

S2 = k1 + 5 = 10 + 5 = 15

S3 = k2 + 5 = 15 + 5 = 20

S4 = k3 + 5 = 20 + 5 = 25

See attached chart.

Harry used a geometric progression, with a ratio of 2, that is multiplying by 2 the value of each week.

Let us call time in minutes of each week, so the geometric progression is of the following exponential form:

S1 = k0 = 10

S2 = k1 x 2 = 10 x 2 = 20

S3 = k2 x 2 = 20 x 2 = 40

S4 = k3 x 2 = 40 x 2 = 80

See attached chart.

Let's analyze the four options given:

Scott's method is linear because the number of minutes increased by an equal number each week.

True: The graph proves it, by obtaining a straight line.

Also, Arithmetic progressions use the linear method.

Harry's method is linear because the number of minutes increased by an equal factor each week.

False: The graph shows that it is not linear, a straight line is not obtained.

Both Harry and Scott's method are exponential because the number of minutes increases by an equal factor each week.

False: Scott's method is linear.

Both Harry and Scott's method are exponential because the number of minutes increases by an equal number each week.

False: Scott's method is linear.

Answer:

(B) is correct

Step-by-step explanation:

As the credit reports shows different scores so it will be resolved by credit bureaus and the report only shows different scores in case they have incorrect or different info about our credit history so we should contact the credit bureaus and ask them to correct the information of our credit history.

So, the right answer is (B).

In this problem, to solve for the gross profit, you have to deduct the cost of each knapsack to its selling price.

The gross profit of Jim is $3.50 ($10.50 - $7).

To compute the gross profit rate, you have to divide the gross profit ($3.50) to the cost of each knapsack ($7).

$3.50 / $7 = 0.5 or 50%

Therefore, Jim makes 50% profit on each knapsack.

Answer:

14.03

Step-by-step explanation:

I took a test

There are $14.03 get change do you get back.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

You are buying a $24.50 item that has 6% sales tax.

And, You give the cashier $40 to pay for the item.

Here, You are buying a $24.50 item that has 6% sales tax.

Hence, The amount of sales tax = 6% of $24.50

                                                  = 6/100 × $24.50

                                                  = $1.47

Thus, The amount of charge = $40 - ($24.50 + $1.47)

                                            = $40 - $25.97

                                            = $14.03

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He need $25.85 more to pay.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Charge for week = $170

earnings from leaves raking = 58.35

Earnings from snow shoving = 85.80

Total earnings = 85.80 + 58.35 = $144.15

So, he need more

=170 - 144.15

=$25.85

Hence, He need $25.85 more to pay.

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Answer:

Step-by-step explanation:

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