Answer:
The area of the trapezoid is 57.5 square inches
Step-by-step explanation:
we know that
The trapezoid QRST can be divided into a rectangle QRDT and an isosceles right triangle RSD
see the attached figure to better understand the problem
step 1
The area of rectangle is given by the formula
we have
----> altitude
substitute
step 2
Find the area of the isosceles right triangle
The area of triangle is given by the formula
we have
---> because is an isosceles triangle
substitute
step 3
Adds the areas
Answer:
The length of the rectangle is 12cm and the area of the rectangle is 60cm2.
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. a2+b2=c2
52+b2=132
25+b2=169
25−25+b2=169−25
b2=144
√b2=√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=(5cm)(12cm)
A=60cm2
Answer:
Option D is correct.
13x = 39
Step-by-step explanation:
The system of equation is given:
....[1]
.....[2]
Multiply equation [1] by 5 to both sides we have;
.....[3]
Using elimination method:
Add [2] and [3] equations to eliminate y and solve for x, we have;
Divide both sides by 13 we get;
x = 3
Substitute x in [1] we have;
2(3)-y = -4
6-y = -4
Subtract 6 from both sides we have;
-y = -10
Divide both sides by -1 we have;
y = 10
⇒Solution: (3, 10)
Therefore, an equation can replace 3x+5y = 59 in the original system and still produce the same solution is,
13x = 39
Answer:
6 miles per hour
Step-by-step explanation:
speed = distance/time
speed = 1/2÷1/12 which is the same as
1/2 x 12/1 = 6
6 miles per hour.
or ou could change the 1/2 to become 0.5
and the 1/12 to become 0.083333333
and divide 0.5 ÷ 0.083333333 = 6.000000024
rounded to one decima place become 6.0
6 miles per hour
