Answer:
The length of the rectangle is
12
c
m
and the area of the rectangle is
60
c
m
2
.
Explanation:
By definition, the angles of a rectangle are right. Therefore, drawing a diagonal creates two congruent right triangles. The diagonal of the rectangle is the hypotenuse of the right triangle. The sides of the rectangle are the legs of the right triangle. We can use the Pythagorean Theorem to find the unknown side of the right triangle, which is also the unknown length of the rectangle.
Recall that the Pythagorean Theorem states that the sun of the squares of the legs of a right triangle is equal to the square of the hypotenuse.
a
2
+
b
2
=
c
2
5
2
+
b
2
=
13
2
25
+
b
2
=
169
25
−
25
+
b
2
=
169
−
25
b
2
=
144
√
b
2
=
√
144
b
=
±
12
Since the length of the side is a measured distance, the negative root is not a reasonable result. So the length of the rectangle is
12
cm.
The area of a rectangle is given by multiplying the width by the length.
A
=
(
5
c
m
)
(
12
c
m
)
A
=
60
c
m
2
Answer:
4. -6
5. -5
6. 2
Step-by-step explanation:
4.
2x + 3 <= -9
2x <= -9 - 3
2x <= -12
= x <= -6
5.
3p + 4 > -11
3p > -11 -4
3p > -15
p > -5
6.
5x + 6 >= 16
5x >= 16 - 6
5x >= 10
x >= 2
Answer:
(u + 1)(u - 1)(u² + 8)
Step-by-step explanation:
<u>Here is the steps:</u>
- u⁴ + 7u² - 8 =
- u⁴- u² + 8u²-8 =
- u²(u² - 1) + 8(u² -1) =
- (u² - 1) (u² +8) =
- (u + 1)(u - 1)(u² + 8)
Mr. Brown can make fewer than 6 full groups to give presentations.
<h3>Inequality</h3>
Inequality is an expression used to show the non equal comparison of two or more numbers and variables.
Let x represent how many full groups Mr. Brown can make.
He wants each group to have 4 students. There are fewer than 24 students in class today, hence:
Mr. Brown can make fewer than 6 full groups to give presentations.
Find out more on inequality at: brainly.com/question/11613554
Answer:
g(x)=x-1 if translated 4 units to the left
Step-by-step explanation:
