Answer:
yes
Step-by-step explanation:
for it to be a right triangle you should be able to add two of the sides and it be greater than the third side. 7 + 24 > 25
24 + 25 > 7
7 + 25 > 24 therefore it is indeed a right triangle
Answer:
(x,y) = (3, 1/2)
Step-by-step explanation:
This pair of linear equations may be solved simultaneously by using the elimination method. This will involve ensuring that the coefficient of one of the unknown variables is the same in both equations..
To solve this, add the equations;
x + 2x + 2y - 2y = 4 + 5
3x = 9
x = 3
substitute the value of x into the first equation,
3 + 2y = 4
2y = 4 -3
2y = 1
y = 1/2
For a geometric sequence
<em>a</em>, <em>ar</em>, <em>ar</em> ², <em>ar</em> ³, …
the <em>n</em>-th term in the sequence is <em>ar</em> <em>ⁿ</em> ⁻ ¹.
The first sequence is
1, 3, 9, 27, …
so it's clear that <em>a</em> = 1 and <em>r</em> = 3, and so the <em>n</em>-th term is 3<em>ⁿ</em> ⁻ ¹.
The second sequence is
400, 200, 100, 50, …
so of course <em>a</em> = 400, and you can easily solve for <em>r</em> :
200 = 400<em>r</em> ==> <em>r</em> = 200/400 = 1/2
Then the <em>n</em>-th term is 400 (1/2)<em>ⁿ</em> ⁻ ¹.
Similarly, the other sequences are given by
3rd: … 4 × 2<em>ⁿ</em> ⁻ ¹
4th: … 400 (1/4)<em>ⁿ</em> ⁻ ¹
5th: … 5<em>ⁿ</em> ⁻ ¹
6th: … 1000 (1/2)<em>ⁿ</em> ⁻ ¹
7th: … 2 × 5<em>ⁿ</em> ⁻ ¹
Answer:
-28(2z - 1)
Step-by-step explanation:
Looking at the coefficients -56 and 28 in -56z + 28, we see that -28 is common to both and can be factored out:
-56z + 28 = -28(2z - 1).
Answer:
1
Step-by-step explanation:
f(x) = x² + 3x
g(x) = 5x + 2
f(3) = 3² + 3 x 3
f(3) = 9 + 9
f(3) = 18
g(3) = 5(3) + 2
g(3) = 15 + 2
g(3) = 17
(f - g)(3) = 18 - 17
(f - g)(3) = 1.
