Factor this expression completely 9a4 - b2

Answer:

Step-by-step explanation:

Using algebra, the dimensions of the rectangular sheet metal with an area of 216 sq ft and width being 6 ft less than the length are found to be 18 ft by 12 ft.

The area of a rectangular piece of sheet metal is given as 216 square feet, and the width is stated to be 6 feet less than the length. Use algebra to find the length (l) and the width (w) of the sheet. Since the width is 6 ft less than the length, we can express this relationship as: w=l- 6.

The area of a rectangle is calculated by the formula Area = length  imes width, so we can set up the equation 216 = l  imes (l - 6). Solving the quadratic equation l^2 - 6l - 216 = 0 we find that the possible values for l are 18 ft (acceptable since length is positive) and -12 ft (which is not physically meaningful for this context), leaving us with the length of the piece of metal being 18 feet. Consequently, the width would be l - 6, which is 18 - 6 = 12 ft.

Therefore, the dimensions of the piece of metal are 18 feet in length and 12 feet in width.

To calculate dl/da when a=12, find the derivative of the cubic polynomial and substitute a=12. The rate of change of the length is approximately 1.682 inches per year.

To calculate dl/da when a=12, we need to find the derivative of the given cubic polynomial with respect to a. The derivative of l with respect to a can be found by taking the derivative of each term separately and then simplifying:

Now substitute a=12 into the derivatives we found:

So, dl/da when a=12 is approximately 0.0465(12)^2 - 0.744(12) + 3.95 = 6.66 - 8.928 + 3.95 = 1.682.

Interpretation: The value dl/da represents the rate of change of the length of the alaskan rockfish with respect to its age. In this case, when the rockfish is 12 years old, its length is changing at a rate of approximately 1.682 inches per year.

https://brainly.com/question/25324584

#SPJ11

Bill's investment increased by $1666 over the year, which is 24.5% of the original $6800. At the end of the year, the total amount of money in the account was $8466.

To determine the increase in dollars due to the investment growth of 24.5%, we would calculate 24.5% of $6800. We can use the formula increase = principal × (rate/100), where principal is the starting amount and rate is the percentage increase.

So, increase = $6800 × (24.5/100) = $6800 × 0.245 = $1666. This means that the increase in dollars is $1666.

Next, to find out how much money was in his account at the end of last year, we add this increase to the original investment: total amount = original amount + increase = $6800 + $1666 = $8466. Therefore, the total amount in the account at the end of the year was $8466.

Answer:

[tex]y=4x+5[/tex]

Step-by-step explanation:

Mathematically, the slope m of a line is:

[tex]m=\frac{\Delta y}{\Delta x} = \frac{y-y_o}{x-x_o}[/tex]

Therefore, if we know the slope m of the line and a point [tex](x_o , y_o)[/tex] we will be able to find its equation simply solving for y:

[tex]y-y_o=m(x-x_o)[/tex]

Replacing the data provided by the problem:

[tex]y-5=4(x-0)\\\\y-5=4x\\\\y=4x+5[/tex]

Hence, the multiplicative Rate of change is:

5

The multiplicative Rate of change refers to the fixed constant which when multiplied to the output will lead to increase/decrease in the next output value.

We have the table of values as:

    x                y

  -1                1/10

   0                1/2

    1                5/2

    2               25/2

    3                125/2

Hence, we see that when 5 is multiplied to the output value we obtain the next output value.

i.e.

1/10×5=1/2

1/2×5=5/2

5/2×5=25/2

25/2×5=125/2

Hence, the multiplicative Rate of change is:

5

When x equals -4, the value of y is 6 by substituting -4 into the equation x + 3y = 14 and solving for y.

To complete the solution of the equation and find the value of y when x equals -4, simply substitute -4 for x into the equation x + 3y = 14. The steps are as follows:

Therefore, when x equals -4, the value of y is 6.

The rectangle with maximum area does not exist as the curve y = 74 + x^2 does not intersect the x-axis.

To find the vertices of the rectangle with maximum area, we need to find the points of intersection between the curve y = 74 + x^2 and the x-axis.

Setting y = 0, we can solve the equation 74 + x^2 = 0 to find the x-coordinates of the vertices.

Since the curve is a parabola facing upwards, there are no points of intersection with the x-axis.

Therefore, the rectangle does not exist.

https://brainly.com/question/29055011

#SPJ11

To double the area of the rectangular vegetable garden, we need to add the same distance, x, to the length and width. The value of x is 10 feet, and the new dimensions of the garden are 25 feet by 20 feet.

To double the area of the garden, we need to add the same distance, x, to both the length and width of the garden. The original dimensions of the garden are 15 feet by 10 feet, with an area of 150 square feet. To double the area, we set up the equation 2(15+x)(10+x) = 2(15)(10). Solving this equation gives us the value of x and the new dimensions of the garden.

Expanding the equation, we have 30x + x² + 300 = 300. This simplifies to x² + 30x - 300 = 0. Factoring this quadratic equation, we get (x - 10)(x + 30) = 0. So x = -30 or x = 10. We discard the negative value since distance cannot be negative, so x = 10 feet.

The new dimensions of the garden are 15+10 = 25 feet and 10+10 = 20 feet.

https://brainly.com/question/9550655

#SPJ12

The correct answer is option C g > 5.

To solve the inequality, we need to isolate the variable g. Here are the steps:

Add 6 to both sides of the inequality to isolate g.

The inequality now becomes: g - 6 + 6 > -1 + 6

Simplify both sides: g > 5

The solution to the inequality is g > 5.

Therefore, the correct answer is option C.

This question is based on the concept of logical reasoning.Therefore,they both have the same amounts of coins, the one with 100 quarters has more money.Thus, Anna has more money than Jasmine.

Given:

Anna has 10 to the 2nd power quarters. Jazmin has 10 to the second power dimes.

We need to calculate the who has more money, Anna or Jasmine.

According to the question,

Anna has 10 to the 2nd power quarters.

In mathematically expressed as,

[tex]\bold{10^2 = 100}[/tex] quarters

Now, Jazmin has 10 to the second power dimes.

In mathematically expressed as,

[tex]\bold{10^2 = 100}[/tex] dimes

So,they both have 100 coins. But, we know that quarter is 25 cents, while a dime is only 10 cents.

Anna has 100 quarters =  [tex]\bold{100 \times 25 = 2500}[/tex]. That is 25 dollars.

Jasmine has 100 dimes =    [tex]\bold{100 \times 10 = 1000}[/tex]. This is 10 dollars.

Therefore,they both have the same amounts of coins, the one with 100 quarters has more money.Thus, Anna has more money than Jasmine.

For more details, prefer this link:

https://brainly.com/question/15169469

a. let us say that:

a = cost of phones with camera

b = cost of phones with camera and mp3

c = cost of phones without any features

b = 2 a – 35

c = a – 100

a + b + c = 525

b > a > c

b. We are given three equations with three unknowns. So we can solve the problem.

a + (2 a – 35) + (a – 100) = 525

a + 2 a – 35 + a – 100 = 525

4 a – 135 = 525

4 a = 660

a = $165

a) According to the problem, purchasing all three phones would cost at least $525, which leads us to the inequality:
[tex]4x - 135 \geq 525[/tex]

b) The cost of the phone with just a camera is at least $165.

a) Setting Up the Inequality

Let’s define the variables based on the information given:

Now, the total cost of buying all three types of phones can be expressed as:
[tex]x + y + z[/tex]

Substituting the expressions for [tex]y[/tex] and [tex]z[/tex], we get:
[tex]x + (2x - 35) + (x - 100)[/tex]

This simplifies to:
[tex]4x - 135[/tex]

b) Finding the Cost of the Phone with Just the Camera

To find out the value of [tex]x[/tex], we can solve the inequality:
[tex]4x - 135 \geq 525[/tex]

Adding 135 to both sides gives:
[tex]4x \geq 660[/tex]

Now, dividing both sides by 4:
[tex]x \geq 165[/tex]

Answer:

The answer is D)$372

Step-by-step explanation:

The answer is B :)

I hope this helped

It’s B and D for Plato users

Answer:

4.125 hope this helps!

Step-by-step explanation:

I know u meant 3/4 of an hour

Answer:

D. [tex](-\infty,-3]\text{U}(-1,\infty)[/tex]

Step-by-step explanation:

We have been given solution of an inequality on number line. We are asked to write the solution to the given inequality in interval notation.

We can see that all values of x less than or equal [tex]-3[/tex] and greater than  [tex]-1[/tex] are solution for our given inequality.

We have a solid dot at [tex]-3[/tex], so [tex]-3[/tex] is a solution of inequality.

We have a open dot at [tex]-1[/tex], so [tex]-1[/tex] is not a solution of inequality.

Upon combining both solutions, we will get:

[tex](-\infty,-3]\text{U}(-1,\infty)[/tex]

Therefore, the solution for the inequality is [tex](-\infty,-3]\text{U}(-1,\infty)[/tex].