MATHEMATICS HIGH SCHOOL

THE SUM OF TWO NUMBERS IS 54. IF THE SMALLER NUMBER IS 6 LESS THAN THE BIGGER ONE, FIND THE NUMBERS. (STEP BY STEP PLZ)

Answers

Answer 1

Answer:

Answer:

24 and 30

Step-by-step explanation:

The sum of two numbers is 54. Let's use the variables x and y to represent theses numbers:

x + y = 54

The smaller number is 6 less than the bigger one. Let's say that x is the smaller number and y is the bigger number:

y - 6 = x

Now we know that x is equivalent to y - 6. So, let's replace x with y - 6 in the original equation:

x + y = 54

y - 6 + y = 54

Combine like terms:

2y - 6 = 54

Now we can solve for y:

2y - 6 = 54

Add 6 to both sides of the equation to isolate the 2y:

2y = 60

Divide both sides by 2 to find the value of y:

y = 30

Now that we know the value of y, we can solve for x:

y - 6 = x

30 - 6 = x

24 = x

The value of the two numbers is 24 and 30.

Related Questions

sixty people will be attending and needs 60% of the memos to be blue 20% to be red 15% to be green and 5% to be yellow how many green memos do you need to print
A colony of bacteria is growing exponentially according to the function below, where t is in hours. What will the approximate number of bacteria after 7 hours? B(t)=4*e^0.8t Answers: A. 45,674 / B. 1082 / C. 270 / D. 635,818
Corinne is 6 years younger than her brother. Which of the following expressions shows the sum of their ages if b represents Corinne's brother's age?
Round .0091 to the thousandths
Find the supplement of each, (a) 136 degreeâ€‹

How do you factor: x^3 - 8 (x cubed minus 8)

Answers

$x^3 - 8 =x^3-2^3 = (x-2) (x^2 + 2x + 2^2)=(x-2) (x^2 + 2x + 4)\n \n \na^3 - b^3 = (a - b) (a^2 + ab + b^2)$

Answer: (x - 2)(x² + 2x + 4)

Step-by-step explanation: In this problem, we're asked to factor x³ - 8.

Notice that x³ is a perfect cube and 8 is a perfect cube because 8 is 2 × 2 × 2 or 2³. So we have the difference of two cubes.

To factor the difference of two cubes, we use the following formula.

a³ - b³ can be factored as (a - b)(a² + ab + b²) and in this problem, since a³ is represented by x³, the value of a is x and since b³ is represented by 8, the value of b is 2.

So substituting x and 2 into the formula for a and b, we have

[(x) - (2)][(x)² + (x)(2) + (2)²] and notice that we changed the parentheses in the formula to brackets so that we're not dealing with too many sets of parentheses.

Next, simplifying inside the second set of brackets and changing the brackets back to parentheses, we have (x - 2)(x² + 2x + 4) which is our final answer.

A student earns $7.50 per hour at her part-time job. She wants to earn at least $200.Enter an inequality that represents all of the possible numbers of hours (h) the student could work to meet her goal.

Enter the least whole number of hours the student needs to work in order to earn at least $200

Answers

Answer: 7.50 h ≥200

She needs to work 27 hours to earn at least $200.

Step-by-step explanation:

Hi, to write the inequality we have to analyze the information given:

Earnings per hour : $7.50

Hours : h

She wants to earn at least $200.

So, she earns $7.50 per hour, the expression that represents the statement is $7.50h.

She wants to earn at least $200, "at least" means more or equal (≥200).

Mathematically speaking:

$7.50 h ≥200

This is the inequality that represents all of the possible numbers of hours (h) the student could work to meet her goal.

For the second part we simply solve the inequation:

7.50 h ≥200

h ≥200/7.50

h ≥ 26.67

Rounded to the nearest whole number:

h ≥ 27

She needs to work 27 hours to earn at least $200.

Total amount of cash the student earns per hour is $7.5, let the time taken to earn $200 be h, thus the inequality representing this will be:
7.5h≤200
thus
h≤80/3
writing in whole numbers we shall have:
h≤27

Line WY is a Tangent. Find WY. It's a right triangle inside a circle..any help?

Answers

For this question, you can do Pythagorean Theorem to solve WY. Since WY is tangent to the circle, we know that the triangle is a right triangle.

We know one leg is 9 and the other leg, WY is unknown. But, we do know the hypotenuse.

XY is 6 but PX is unknown. If you think about it, PX is a radius of the circle and we know that the radius is 9 since PW is also a radius of the circle. So, the hypotenuse is 6 + 9 = 15.

We know one leg is 9 and the hypotenuse is 15. We need to find the other leg and we can.

Pythagorean Theorem states that

a^2 + b^2 = c^2 where a and b are the sides of the triangle and where c is the hypotenuse. Using basic algebra, we can alter the equation to find a leg using the hypotenuse and one other leg.

c^2 - b^2 = a^2

All I did was solve for one leg and it doesn't matter what leg you solve for. Let's plug in the numbers.

15^2 - 9^2 = a^2
225 - 81 = a^2
144 = a^2
Take the square root on both sides to get "a" by itself with raising it to the second power.

12 = a

So, the last leg is 12. Hope this helped and good luck!

I don't have answer for this but I m seeing you not answering a lot of stuff,you should start lessening :)

What are two contributions to math that Leonardo Fibonacci made

Answers

Fibonacci is famous for his contributions to number theory.

In his book, Liber abaci he introduce the Hindu-Arabic place-valued decimal systems and the use of Arabic Numerals into Europe.He introduced the bar we use in fractions, previous to this, the numerator has quotations around it. The square root notation is also is Fibonacci method.

Use integration by parts to integrate sin2x between pi and 0

Answers

Answer:

$\displaystyle \int\limits^0_(\pi) {\sin (2x)} \, dx = 0$

General Formulas and Concepts:

Calculus

Integration

Integrals

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

U-Substitution

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int\limits^0_(\pi) {\sin (2x)} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution.

Set u: $\displaystyle u = 2x$
[u] Differentiate: $\displaystyle du = 2 \ dx$
[Bounds] Switch: $\displaystyle \left \{ {{x = 0 ,\ u = 2(0) = 0} \atop {x = \pi ,\ u = 2 \pi}} \right.$

Step 3: Integrate Pt. 2

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^0_(\pi) {\sin (2x)} \, dx = (1)/(2) \int\limits^0_(\pi) {2 \sin (2x)} \, dx$
[Integral] U-Substitution: $\displaystyle \int\limits^0_(\pi) {\sin (2x)} \, dx = (1)/(2) \int\limits^0_(2 \pi) {\sin u} \, du$
Trigonometric Integration: $\displaystyle \int\limits^0_(\pi) {\sin (2x)} \, dx = (1)/(2)(-\cos u) \bigg| \limits^0_(2 \pi)$
Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^0_(\pi) {\sin (2x)} \, dx = (1)/(2)(0)$
Simplify: $\displaystyle \int\limits^0_(\pi) {\sin (2x)} \, dx = 0$