Answer:
The larger number is 5.
Step-by-step explanation:
Let the numbers be represented by x and y. Then:
x + y = 8 is their sum, and
x² + y² = 34 is the sum of their squares.
Let's solve this system of equations using substitution. Since x + y = 8,
x = 8 - y. Subbing this 8 - y for x into the second equation, we get:
(8 - y)² + y² = 34, or
64 - 16 y + y² + y² = 34
Simplifying, we get first: 30 - 16y + 2y² = 0, and then:
2y² - 16y + 30 = 0, and after reducing, y² - 8y + 15 = 0.
This factors into (y - 3)(y - 5) = 0, and so y = 3 and y = 5.
The larger number is 5.
Answer:
The surface area of the square pyramid is 
Step-by-step explanation:
we know that
The surface area of the square pyramid is equal to
where
B is the area of the base
P is the perimeter of the base
h is the height of the pyramid
<u>Find the area of the base B</u>
<u>Find the perimeter of the base P</u>
The height is 
substitute the values
3x^7 will be your answer
hope this helps!
First, 5 students and 2 teachers is 7 different people. That means there are 7! Ways they can stand in a line. (7! Means 7x6x5x4x3x2x1)
That is 5040 ways.
Having the teachers on either side with the five students in the middle splits the question. There are 2 ways the teachers could stand (TA on left, TB on right or vice versa). There are 5! Ways to arrange the students in the middle. That is, 120. So combined, there are 2x120 ways to have them lined up with the teachers on either side. 240 ways.
Out of the 5040 ways for all of them to line up, one teacher will be in the middle 3 spaces 3/7 of the time. The second teacher will be on one of the remaining 2 central spaces 2/6 (1/3) of the time. 3/7x1/3 = 1/7. That means 1/7 or 14.29% of the time, the two teachers will occupy two of the three middle slots.
Let the three consecutive odd numbers be x,x+2,x+4.
Given, their sum =219
Therefore, x+x+2+x+4=219
⇒3x+6=219
Subtract 6 from both the sides,
⇒3x+6−6=219−6
⇒3x=213
⇒x=71
The other numbers are x+2=71+2=73 and x+4=71+4=75.
Therefore, threee odd numbers are 71,73 and 75.
