MATHEMATICS HIGH SCHOOL

Three times a number increases by 15 is equal to 30

Answers

Answer 1
Answer:

Answer:       The number is 5.

Step-by-step explanation:

First, let d be our number.

Since we know that d is our number, we rewrite the expression this way:

3 times d incresed by 15 is 30.

3 times d is 3d; 3d increased by 15 => 3d + 15. This equals 30:

3d + 15 = 30

To solve for d, subtract 15 from both sides:

3d = 15

Next, divide both sides by 3:

d = 5
Answer 2
Answer: Using the equation 3x+15=30 x being the number we are trying to find out we replace x with 5 as 3*5 is 15+15 = 30

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Find four consecutive integers such that twice the sum of the two greater integers exceeds three times the first by 91

Answers

Answer:

81, 82, 83, 84.

Step-by-step explanation:

Let x represent 1st integer. Then the next three consecutive integers would be x+1,x+2\text{ and }x+3.

We have been given that twice the sum of the two greater integers exceeds three times the first by 91. We can represent our given information in an equation as:

2(x+2+x+3)=3x+91

Let us solve for x.

2(2x+5)=3x+91

4x+10=3x+91

4x-3x+10=3x-3x+91

x+10=91

x+10-10=91-10

x=81

Therefore, the 1st integer would be 81.

The next three consecutive integers would be:

81+1=82\n81+2=83\n81+3=84

Therefore, our required four consecutive integers are 81, 82, 83, 84.

Final answer:

To find four consecutive integers, set up an equation using the given information and solve for x. The four consecutive integers are -86, -85, -84, and -83.

Explanation:

To find four consecutive integers, we can let the first integer be x. The next three consecutive integers would then be x+1, x+2, and x+3. According to the given condition, twice the sum of the two greater integers (x+2 + x+3 = 2x+5) exceeds three times the first integer (3x) by 91. So, we can set up the equation 2x+5 = 3x + 91 and solve for x.

Subtracting 2x from both sides yields 5 = x + 91. Subtracting 91 from both sides gives -86 = x. Therefore, the four consecutive integers are -86, -85, -84, and -83.

Learn more about Consecutive Integers here:

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Harry is building a house with a sloping roof. If the roof is 44 feet long and 10 feet high, what is the angle that the roof makes with the horizontal?

Answers

Length\ and\ high\ make\ with\ horizontal\ rectangular\ triangle\n\n Length \is \ hypotenuse\ \n\ high\ and\ horizontal\ are\ cathetuses.\n\n \angle\ \alpha\ between\ length\ and\ horizontal=?\n sin \alpha =(10)/(44)\n sin \alpha \approx0,227\n \alpha \approx\ arcsin0,227\approx\ 13^\circ

Pete is conducting a survey to determine his customers’ overall satisfaction about the quality of his company’s products. He sends out surveys to the 5 customers who have purchased the largest number of items over the past year. Are his results likely to be representative of the population he is trying to analyze?

Answers

No.
Because, when to do some sort of analysis (such as this one), you need to take (for example) a RANDOM SAMPLE from the POPULATION of the problem that is being analyzed. In this example (problem), Pete wants to evaluate OVERALL satisfaction of customers, so he should NOT send the surveys ONLY to the customers who have purchased the LARGEST number of items, but to the randomly selected customers, in order to obtain REPRESENTATIVE results of the OVERALL satisfaction. If he sends the surveys only to the customers who have bought the largest number of items, he will obtain VERY HIGH satisfaction of customers, as results, of course, and this will not be representative results.

No.

When trying to analyze an overall satisfaction with Quality of service. The number of population he is analyzing should not be limited to a certain factor. This would cause a narrow data information gather and would not represent the entire population. The surveys should be based randomly to avoid data bias/filters and actual results would be realistic.

41,004 mL = _____ cm3

Answers

 41,004 milliliters is 41,004 cubic centimeters
41,004 mL = 41,004 cm³
good homeworks

Explain your answerSimplify the difference.

(4w2 - 7w - 6) - (8w2 + 2w - 3)
Choose one answer.
a. -4w2 - 9w - 3
b. 12w2 + 9w + 3
c. -4w2 - 5w - 9
d. 12w2 - 5w - 9

Answers

(4w^2-7w-6)-(8w^2+2w-3)\n -(a\pm b)=-1(a\pm b)\ \ \ \ |use\ a\ distributive\ property: a(b\pm c)=ab\pm ac\n\n\=4w^2-7w-6-8w^2-2w-(-3)\n\n = 4w^2-7w-6-8w^2-2w-(-3)\n\n=(4w^2-8w^2)+(-7w-2w)+(-6+3)\n\n=\boxed{-4w^2-9w-3}
(4w² - 7w - 6) - (8w² + 2w - 3)
(4w² - 8w²) + (-7w - 2w) + (-6 + 3)
-4w² - 9w - 3
The answer is A.

A painter charges $35 per hour for labor plus $40 for a ladder rental when he paints a house. the customer provides the paint. the total charge to paint a customer's house was $950.how many hours did the painter spend painting this house?

Answers

Answer:

The painter spent 26 hours painting the house.

Step-by-step explanation:

If the painter charged $ 950 for painting a house, and he charges $ 35 per hour plus $ 40 for the ladder rental, in order to determine how many hours of work it took to paint the house, we must make the following calculation:

950 (total charge) - 40 (ladder rental) = Total work charge

910 (total charge per work) / 35 (charge per hour) = Total hours of work

910 / 35 = 26

It took 26 hours to the painter for painting the entire house.
the painter worked for 26 hours because 26*35=910+40 =950
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