the numbers are x=58 & x+2=60 , i.e. 58 and 60 .
<u>Step-by-step explanation:</u>
Here we have , Consecutive integers are 1,2,3,4 and so on. Consecutive even integers are 2,4,6,8 and so on. The sum of an integer and twice the next consecutive even integer is 178. We need to Write and solve an equation to find the two integers. Let's find out:
Let the integer be x , and the next consecutive even integer be x+2 .Now , According to question , The sum of an integer and twice the next consecutive even integer is 178 i.e.
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Therefore , the numbers are x=58 & x+2=60 , i.e. 58 and 60 .
<em><u>The required average on next two tests are:</u></em>
<em><u>Solution:</u></em>
An A grade will be given to students having at least 450 total test points
Let p represent her present test point total, and t represent the necessary average on the next two tests
There are two more tests to take before the semester is over
Therefore,
A grade is given to students having at least 450 total test points
"at least" means greater than or equal to
So we have used greater than or equal to symbol
Solve the inequality for "t"
Thus the required average on next two tests are:
Well seeing as how its around the park we think perimeter.
P= 2L +2W
P= 2(150)+ 2(125)
P= 300 + 250
P= 550
so we know the perimeter of the park is 550 yards but she walks this perimeter twice so 550*2 gives you 1100 yards that she walked.<span />
RX is + XS is the hypotenuse of the right triangle RTS, then:
(RX + XS)^2 = (RT)^2 + (ST)^2
=> (4+9)^2 = (RT)^2 + (ST)^2
=> 13^2 = (RT)^2 + (ST)^2 .....equation (1)
Triangle RTX and XST are also right triangles.
RT is the hypotenuse of RTX and ST is the hypotenuse os SXT.
Then, (RT)^2 - (RX)2 = (TX)^2 and (ST)^2 - (SX)^2 = (TX)^2
=> (RT)^2 - (RX)^2 = (ST)^2 - (SX)^2
=> (RT)^2 - (ST)^2 = (RX)^2 -(SX)^2
=> (RT)^2 - (ST)^2 = 4^2 - 9^2 = 16 - 81 = - 65
=> (ST)^2 - (RT)^2 = 65 ..........equation (2)
Now use equations (1) and (2)
13^2 = (RT)^2 + (ST)^2
65 = (ST)^2 - (RT)^2
Add the two equations:
13^2 + 65 = 2(ST)^2
2(ST)^2 =178
(ST)^2 = 234/2 = 117
Now use (ST)^2 - (SX)^2 = (TX)^2
=> (TX)^2 = 117 - 81 = 36
=> (TX) = √36 = 6
Answer: 6