While standing on a roof, you drop a hamner. The function y=16-64t^2 represents the height y (in feet) of the hammer t seconds after it is dropped. After how many seconds does the hammer land on the ground?

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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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:

11___________________________

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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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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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.

The angle sum property of a triangle states that:

Sum of three angles of a triangle is 180 degrees.

Now we are given a right angled triangle here.

The question can be described as shows in figure.

Here ABC is a triangle right angles at B.

The other angle is 58 degrees.

Using angle sum property:

∠A + ∠B +∠C =180

let ∠A = 58° and ∠B =90°

So we have ,

58° + 90° +∠C =180

148°+∠C=180°

∠C = 32°

Answer : Angle C is 32 degrees.

Option A is correct choice

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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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:

A, C, C

Step-by-step explanation:

Some other dude answered it. I just simplified his answer.

Answer:

Step-by-step explanation:

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.