You are remodeling your kitchen. You've contacted two tiling companies who gladly told you how long it took their workers to tile a floor of a similar size. Jim completed half the floor in 7 hours. Pete completed the other half of the floor in 6 hours. If Pete can lay 15 more tiles per hour than Jim, what equation would you use to find the rate that Jim can lay tiles? Let x represent Jim's rate.

explain why the answer is correct

Final answer:

To find the coefficient of 1/x in the expansion of (2x - 1/x)^5, we use the binomial theorem, specifically the term where the exponent of x is -1. We find that the coefficient of 1/x is -80.

Explanation:

To find the coefficient of 1/x in the expansion of (2x - 1/x)^5, we can use the binomial theorem. The binomial theorem states that:

(a + b)^n = Σ (n choose k) a^(n-k) b^k

where 'n choose k' is the binomial coefficient, computed as:

n! / [(n-k)!k!]

In our case, a = 2x and b = -1/x, and we want the term where the power of x is -1, which occurs when k = 4:

(5 choose 4) (2x)^(5-4) (-1/x)^4 = 5 * 2 * 1 * 1/x^4 = 10/x^4

However, to get the term with 1/x, we need a positive power of 1 for x. We achieve this when k = 1:

(5 choose 1) (2x)^(5-1) (-1/x)^1 = 5 * 16x^4 * (-1/x) = -80

Therefore, the coefficient of 1/x in the expansion is -80.

Answer:

The correct option is 2.

Step-by-step explanation:

It is given that triangle ABC is similar to triangle PQR.

In triangle ABC, AB=c, BC=a, and AC=b.

In triangle PQR, PQ=r, QR=p, PR=q.

The corresponding sides of similar triangles are proportional.

Since [tex]\triangle ABC\sim \triangle PQR[/tex], therefore their corresponding sides are proportional.

[tex]\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}[/tex]

[tex]\frac{c}{r}=\frac{a}{p}=\frac{b}{q}[/tex]

It meas the ratio c:r = a:p = b:q.

Therefore the correct option is 2.

Answer:

Since, a 45°-45°-90° triangle is a special type of isosceles right triangle, where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.

In 45°−45°−90° triangle

Sides are in the proportion [tex]1:1:\sqrt{2}[/tex]

then,

the measures of the sides are [tex]x , x ,\sqrt{2}x[/tex]

The length of hypotenuse= [tex]\sqrt{2}[/tex] times the length of the leg.   ....[1]

Given: length of hypotenuse = 128 cm.

then,

from [1] we have;

128 = [tex]\sqrt{2}\cdot x[/tex]

or

[tex]x=\frac{128}{\sqrt{2}}[/tex] = [tex]\frac{128}{\sqrt{2} } \times  \frac{\sqrt{2}}{\sqrt{2}}  = \frac{128\sqrt{2}}{\sqrt{2}\cdot \sqrt{2}}[/tex]

Simplify:

[tex]x =\frac{128 \cdot \sqrt{2}}{2} =64\sqrt{2}[/tex] cm.

Therefore, the length of one leg of the triangle is; [tex]64\sqrt{2}[/tex] cm.

Answer:

In FLVS it is the third option

Step-by-step explanation:

Hope this helps :)

To calculate the probability of getting a blackjack from a single well-shuffled deck, you must consider the probability of drawing an Ace and then a 10-value card or vice versa, and add those probabilities together. The same process applies to two decks with adjusted numbers. You will then round the final probabilities to four decimal places.

To answer the question of the probability of getting a blackjack in a single deck, consider that there are 4 aces in a deck and 16 cards that are either a face card or a 10 (each suit has 4 such cards - Jacks, Queens, Kings, and 10s). When one card is drawn, the remaining cards are one fewer, so we need to adjust our probability for the second card.

For the probability of a blackjack from two decks, follow the same steps, but adjust the numbers for a 104-card deck.

After doing the calculations, we round the probabilities to four decimal places as instructed.

Given that two numbers sum to 's', and one of the numbers is 'n', the other number can be expressed as 's - n'. In essence, if you subtract 'n' from the sum 's', you obtain the second number.

The student's question relates to expressing one number in terms of another when their sum is given. Given that the sum of the two numbers is s and one of the numbers is n, the second number can be expressed as s - n. This is because when two numbers add to give 's', subtracting one of the numbers (n, in this case) from 's' would give the other number.

For instance, if s = 10 and n = 3, then the second number would be 10 - 3 = 7. Hence, the correct answer from the options provided would be 3. s - n.

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To find the youngest age for a lawyer to have an average income of $450,000, you solve the income function equation and round to the nearest year.

The youngest age for which the average income of a lawyer is $450,000 can be found by solving the given function:

I(x) = 10000 + 2000x

Given I(x) = $450,000, the equation becomes:

Rounded to the nearest year, the youngest age would be 220 years old.

Answer:

yea, most likely it´s 3/4 y + 1/5 ≥ 7/8

Step-by-step explanation:

Answer:

B. be solved

Step-by-step explanation:

Answer:

a) The answer is: (x + a, y + b)

b) The answer is: (-1, -2)

The initial coordinates are:

(x, y) = (-2, -5)

should be the answer.

Let's find a and b.

a is a distance in x direction: a = 1

b is a distance in y direction: b = 3

The final position is:

(x + a, y + b) = (-2 + 1, -5 + 3) = (-1, -2)

Step-by-step explanation:

Answer: X= 55

Step-by-step explanation:

The sum of exterior angles of any polygon will always equal to 360 degrees. which means, we can write:

360 = (x+10)  +  (2x+20) + 3x  

x = 55

The exterior angles have values of 65, 130 and 165. The exterior that will have the largest value will correspond to the smallest interior angle and therefore  have a value of 15 degree!.  ;)

Final answer:

By calculating the value of x and using the relationship that each exterior angle and its corresponding interior angle are supplementary, we find that the measure of the smallest interior angle of the triangle is 115 degrees.

Explanation:

To find the measure of the smallest interior angle of the triangle, we first need to use the fact that the sum of the exterior angles of a triangle is always 360 degrees. So, we set up the equation (x+10) + (2x+20) + 3x = 360 and solve for x. This gives us:

x + 10

2x + 20

3x

Combining like terms, we get 6x + 30 = 360. Subtracting 30 from both sides, we get 6x = 330. Dividing both sides by 6, we find that x = 55 degrees. Therefore, the exterior angles are 65 degrees, 130 degrees, and 165 degrees. To find the smallest interior angle, we take the smallest exterior angle, 65 degrees and subtract it from 180 degrees (since the exterior angle and interior angle at the same vertex are supplementary). Thus, the smallest interior angle is 180 degrees - 65 degrees = 115 degrees.

Answer:

The population of foxville is 12000.

Step-by-step explanation:

It is given that the population of foxville is about 12 times 10 to the power of 3.

Population of foxville = [tex]12\times 10^3[/tex]

[tex]12\times 10^3[/tex] is a scientific notation of a number.

We need to write this number in another way.

[tex]12\times 10^3=12\times 1000[/tex]

[tex]12\times 10^3=12000[/tex]

Therefore, the population of foxville is 12000.

PEMDAS- [Parenthese, Exponents, Multiplication, Division, Addition, Subtraction.]

Since there is no Parentheses, nor Exponents, you have to go straight to multiplication. Then to addition

30+30×0+1

30×0=0

30+0+1=31.

I hope my answer has come to your help. God bless and have a nice day ahead!

To find the average number of vehicles waiting at a traffic intensity of 0.92, we substitute 0.92 into the function w(x) = x² / (2(1-x)) to arrive at the answer 5.29.

The average number of vehicles waiting in line is modeled by the function w(x) = x^2 / (2(1-x)) where x represents traffic intensity. The question is asking us to calculate the average number of vehicles waiting when the traffic intensity is 0.92. By plugging this value into the function, we get w(0.92) = 0.92^2 / (2(1-0.92)), which simplifies to w(0.92) = 0.8464 / 0.16. The result is 5.29, so the average number of vehicles waiting would be 5.29 when the traffic intensity is 0.92. To find the average number of vehicles waiting when the traffic intensity is 0.92, we substitute the value of x into the given function w(x)=x^2/2(1-x). In this case, x=0.92. So, the average number of vehicles waiting can be found by evaluating w(0.92).

w(0.92) = (0.92)^2 / 2(1 - 0.92)

w(0.92) = 0.8464 / (2 * 0.08)

w(0.92) = 10.58

Therefore, when the traffic intensity is 0.92, the average number of vehicles waiting is approximately 10.58.

The theorem that proves x is parallel to y is the Converse of the Alternate Interior Angles Theorem, which states that if alternate interior angles are congruent, the lines are parallel. The correct answer to the question of which postulate or theorem proves that x is parallel to y is B. Converse of the Alternate Interior Angles Theorem.

According to this theorem, if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel. The other options, such as the converse of the corresponding angles postulate or the converse of the consecutive interior angles theorem, are related but specifically address different sets of angles formed when two lines are cut by a transversal.

In geometry, it is crucial to apply the correct postulates or theorems to prove specific properties, like parallel lines. The reliability of these mathematical proofs, like those in trigonometry or physics, comes from the logical sequence of applying these fundamental principles accurately.

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