Answer:
m<1 = 39
m<2 = 51
Step-by-step explanation:
For this problem, you need to understand that a little square in the bottom of two connecting lines represents a right-angle (an angle this 90 degrees). This problem, gives you two relationships for angle 1 and angle 2 within a right-angle. Using this information, we can solve for the measures of the two angles.
Let's write the two relations:
m< 1 = 3x
m< 2 = x + 38
And now let's right an equation that represents the two angles to the picture:
m<1 + m<2 = 90
Using this information, let's substitute the expressions we have for the two angles and solve for x. Once we have the value of x, we can find the measure of the two angles.
m< 1 + m< 2 = 90
(3x) + (x + 38) = 90
3x + x + 38 = 90
x ( 3 + 1 ) + 38 = 90
x ( 4 ) + 38 = 90
4x + 38 = 90
4x + 38 - 38 = 90 - 38
4x = 90 - 38
4x = 52
4x * (1/4) = 52 * (1/4)
x = 52 * (1/4)
x = 13
Now that we have the value of x, we simply plug it back into our expressions for the m<1 and m<2.
m<1 = 3x = 3(13) = 39
m<2 = x + 38 = 13 + 38 = 51
And we can verify this is correct with the relational equation:
m<1 + m<2 = 90
39 + 51 ?= 90
90 == 90
Hence, we have found the values of m<1 and m<2.
Cheers.
Answer:
length = 23 inches ; width = 18 inches.
Step-by-step explanation:
Length and width can be found from the following expression after solving for x. The expression is given by :
outside area - inside area = 148 square inches
(2·x - 1)·(x + 6) - (2·x - 5)·(x + 2) = 148 (On substitute length and width expressions. Each area is the product of length and width.)
⇒ 2·x² + 11·x - 6 - (2·x² - x - 10) = 148
⇒ 12·x + 4 = 148 .................(On simplifying the expression)
⇒ 12·x = 144
⇒ x = 12
Then the original length of the mat is given by substituting value of x in outside length expression :
2·x - 1 = 2·12 - 1 = 23 inches
and the original width of the mat is given by :
x + 6 = 12 + 6 = 18 inches
Hence, the overall dimensions of the original mat are 23 inches by 18 inches.
5 hours. 16 divided by 2 equals 8 40 divided b 8 equals 5
78 inches is the answer :-)
Answer:
1
Step-by-step explanation:
move up one and over one, 1/1 = 1
