Simplify each expression. Use positive exponents.
(x–2y–4x3) –2,

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 

                     x^2-(16/25)=0 

 2.1   Subtracting a fraction from a whole 

Rewrite the whole as a fraction using  25  as the denominator :

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole 

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

 2.2       Adding up the two equivalent fractions 
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 2.3      Factoring:  25x2 - 16 

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A2 - AB + BA - B2 =
         A2 - AB + AB - B2 = 
         A2 - B2

Note :  AB = BA is the commutative property of multiplication. 

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  25  is the square of  5 
Check : 16 is the square of 4
Check :  x2  is the square of  x1 

Factorization is :       (5x + 4)  •  (5x - 4) 

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

Now, on the left hand side, the  25  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   (5x+4)  •  (5x-4)  = 0

 3.2    A product of several terms equals zero. 

 When a product of two or more terms equals zero, then at least one of the terms must be zero. 

 We shall now solve each term = 0 separately 

 In other words, we are going to solve as many equations as there are terms in the product 

 Any solution of term = 0 solves product = 0 as well.

 3.3      Solve  :    5x+4 = 0 

 Subtract  4  from both sides of the equation : 
                      5x = -4 
Divide both sides of the equation by 5:
                     x = -4/5 = -0.800 

 3.4      Solve  :    5x-4 = 0 

 Add  4  to both sides of the equation : 
                      5x = 4 
Divide both sides of the equation by 5:
                     x = 4/5 = 0.800 

The first step in solving the equation [tex]\rm x^2-\dfrac{16}{25}=0[/tex] is adding and subtracting 4\5x in the equation.

The quadratic formula helps to evaluate the solution of quadratic equations by replacing the factorization method.

The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b and c are real numbers, also called “numeric coefficients”.

The given quadratic equation is;

[tex]\rm x^2-\dfrac{16}{25}=0\\\\x^2-\dfrac{4^2}{5^2}=0\\\\ x^2+ \dfrac{4}{5}x-\dfrac{4}{5}x - \dfrac{4^2}{5^2}=0\\\\\left (x-\dfrac{4}{5} \right ) \left (x+\dfrac{4}{5} \right )=0[/tex]

Hence, the first step in solving the equation [tex]\rm x^2-\dfrac{16}{25}=0[/tex] is adding and subtracting 4\5x in the equation.

Learn more quadratic equations here;

https://brainly.com/question/16932064

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Final answer:

The cross-sectional area of a cylinder is found using the formula πr², and the external surface area is calculated by adding twice the area of the ends (2πr²) with the area of the side (2πrh). For volume, use V = πr²h. It's important to use consistent units throughout the calculations.

Explanation:

Finding the Area of a Cylinder

To find the cross-sectional area of a cylinder, you need to calculate the area of the circular base. The formula for the area of a circle is πr², where π is approximately 3.142 and r is the radius of the cylinder. To find the external surface area of a cylinder, you need to calculate the area of both circular ends and the rectangular side that wraps around the cylinder. The formula for that is 2πr² for the ends, plus 2πrh for the side, where h is the height of the cylinder.

If you want to find the volume of the cylinder, use the formula V = πr²h. This formula tells us that the volume is the area of the base times the height of the cylinder. This exemplifies the idea that understanding geometry can help calculate different geometric quantities such as cross-sectional area, the area of different parts, and volume effectively.

Remember to use consistent units in all calculations to ensure the correct solutions. For instance, if you're working in the metric system, keep all measurements in meters or centimeters.

Final answer:

The exact probability that you win the first prize and your friend wins the second prize in a raffle with 18 participants is 1/306.

Explanation:

To calculate the exact probability that you win the first prize and your friend wins the second prize in a raffle, we need to look at the total number of possible outcomes and the number of favorable outcomes. Assuming that there are 18 tickets in total (yours, your friend's, and 16 others), the chance that you win the first prize is 1 in 18. After you win, there are 17 tickets left, so your friend's chance of winning the second prize is 1 in 17. To find the combined probability, we multiply these individual probabilities:

The probability that you win first prize = 1/18
The probability that your friend wins second prize given you've won first = 1/17

Combined probability = (1/18) x (1/17) = 1/306

The exact probability that you win the first prize and your friend wins the second prize is 1/306.

The exact probability that you win the first prize and your friend wins the second prize is[tex]\( \frac{1}{306} \).[/tex]

To determine the probability that you win the first prize and your friend wins the second prize in the raffle, we need to calculate the total number of possible outcomes and the number of favorable outcomes where this specific event occurs.

Total number of participants: You and your friend are among 18 people who bought raffle tickets.

Total number of outcomes: There are 18 people in total, so there are

( 18 ) possible winners for the first prize and ( 17 ) remaining people eligible for the second prize after the first winner is chosen.

Therefore, the total number of outcomes where one person wins the first prize and another wins the second prize is:

[tex]\[ 18 \times 17 = 306 \][/tex]

This represents all possible ways the first and second prize can be awarded to two different individuals.

Favorable outcomes (desired event): There is exactly ( 1 ) way for you to win the first prize and ( 1 ) way for your friend to win the second prize.

So, the number of favorable outcomes where you win the first prize and your friend wins the second prize is:

[tex]\[ 1 \times 1 = 1 \][/tex]

Probability calculation: The probability ( P ) that you win the first prize and your friend wins the second prize is given by the ratio of the number of favorable outcomes to the total number of outcomes:

[tex]\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{306} \][/tex]

Therefore, the exact probability that you win the first prize and your friend wins the second prize is [tex]\( \frac{1}{306} \).[/tex]

Answer:

Let your monthly income = $ x

As, Mortgage payment does not exceed 28% of the total monthly income.

Monthly mortgage payment = $1,125.98

So, 28% of x=1125.98

[tex]=\frac{28x}{100}=1125.98\\\\x=\frac{112598}{28}\\\\ x=4021.3571[/tex]

So, Your monthly income should be $ 4021.36 (approx) to stay within acceptable housing expense limits.

Final answer:

After increasing and then decreasing a number by 10%, the final result is less than the original number because the decrease is calculated from a higher number, resulting in a net decrease.

Explanation:

When a number, let's call it xx, increases by 10%, this can be represented as xx plus 10% of xx, which is xx + 0.10xx or 1.10xx. Then, if this new number decreases by 10%, we need to take 10% off this new value, so we calculate 10% of 1.10xx which is 0.10 × 1.10xx. The resulting value is 1.10xx - 0.11xx, which simplifies to 0.99xx.

Thus, after an increase and a subsequent decrease of 10%, the final value is less than the original since 0.99xx is 99% of the original value xx.

1. BC/CD = AC/CE 1. Given

2. <BCA is congruent to <ECD 2. Vertical angles are congruent

3. Tr.ACB is congr to Tr.ECD 3. SAS Similarity

Answer:

Hes wrong trust me its C or three more than the quotient of nine and a number cubed, decreased by two; 3 +  9 Over n cubed minus 2 I trusted him and got it wrong

Step-by-step explanation:

The estimated probability of the basketball player making the next free throw is 0.8 or 80%, calculated by dividing the number of successful throws by total attempts (160/200).

The student's question involves estimating the probability of a basketball player making the next free throw based on past performance. Given the player made 160 out of 200 free throws, the estimated probability is calculated by dividing the number of successful throws by the total number of throws attempted. Therefore, the estimated probability is:

   P(successful free throw) = Number of successful free throws / Total free throws attempted
   P(successful free throw) = 160 / 200 = 0.8 or 80%

Probability lessons often use sports examples to explain concepts because they provide clear, real-world instances of chance and outcomes. To further understand the concept, one can look at various situations, such as Helen's basketball free throw practice where P(C) = 0.75 and P(D) = 0.75 for her making each shot, or Carlos's soccer goal shooting with a probability of 0.65 for each shot, and special situations like streak shooting where probabilities may change after a successful event.

To find (g o h)(0), first calculate h(0) which is -4, then apply this result to g(x), leading to a final result of -8.

The student's question asks to find (g o h)(0), which means to find the value of g(h(0)). This involves two functions, g(x) = 2x and h(x) = x2 - 4. First, we need to find h(0), which is 02 - 4 = -4. Then, we use this result as the input for g(x), resulting in g(-4) = 2*(-4) = -8. Therefore, (g o h)(0) = -8.

Answer:

You have to follow the landlord/owner's rules. For example, if you are renting an apartment and want to have a pet, but your landlord says no then you can't get a pet, or you'll be kicked out.

Answer:

D. Mean: 10, Median: 12, Mode: 12, Range: 14

Step-by-step explanation:

3, 6, 7, 12, 12, 13, 17

Mean: 3 + 6 + 7 + 12 + 12 + 13 + 17 = 70/7 = 10

Median: 12

Mode: 12

Range: 17 - 3 = 14

Final answer:

The number of calories burned on a 5 km run are 375 calories burned.

Explanation:

The question involves burning calories relative to the distance run by a runner. To find out how many calories would be burned on a 5 km run, we need to set up a proportion since the relationship is assumed to be linear.

Let's start by examining the given data: a runner burns 120 calories for a 1.6 km distance. If we divide the number of calories burned by the distance, we get the rate of calories burned per kilometer:

120 calories / 1.6 km = 75 calories/km.

Now, we can find the total calories burned for a 5 km run:

75 calories/km x 5 km = 375 calories.

Therefore, the runner would burn 375 calories on a 5 km run.