Answer:
I answered it
Step-by-step explanation:
I answered it
The length and width of the rectangle is 11 in and 8 in respectively.
Step-by-step explanation:
Given,
The width of a rectangle is 3 in less than the length.
The area of each congruent right angle triangle = 44 in²
To find the length and width of the rectangle.
Formula
The area of a triangle with b base and h as height = 
bh
Now,
Let, the width = x and the length = x+3.
Here, for the triangle, width will be its base and length will be its height.
According to the problem,
×(x+3)×x = 44
or, 
or,
or, 
+(11-8)x-88 = 0
or, +11x-8x-88 =0
or, x(x+11)-8(x+11) = 0
or, (x+11)(x-8) = 0
So, x = 8 ( x≠-11, the length or width could no be negative)
Hence,
Width = 8 in and length = 8+3 = 11 in
Answer:
Final image L"M" will lie in the fourth quadrant.
Step-by-step explanation:
Coordinates of the ends of segment LM,
L → (-3, 4)
M → (-3, 2)
Rule to reflect a point across x-axis is,
(x, y) → (x, -y)
By this rule, coordinates of the image point of L and M will be,
L(-3, 4) → L'(-3, -4)
M(-3, 2) → M'(-3, -2)
Further these image points are translated along the vector <4, 1>
Rule for this translation will be,
(x, y) → (x + 4, y + 1)
Now the image points of the points L' and M' will be,
L'(-3, -4) → L"(-3 + 4, -4 + 1)
→ L"(1, -3)
M'(-3, -2) → M"(-3 + 4, -2 + 1)
→ M"(1, -1)
Therefore, final image L"M" will lie in the fourth quadrant.
Answer:
115
Step-by-step explanation:
angle DEF is an inscribed angle and arc DF is the arc it intercepts
if you didn't know an inscribed angle is equal to half the measure of the arc it intercepts
Hence angle DEF = 1/2 of arc DF
If arc DF = 230 then angle DEF = half of 230 or 230/2
230/2=115
Hence angle DEF = 115
Answer:
x = 2, y = 6
(2, 6)
Step-by-step explanation:
The system of equations is solved when we find the "x" and "y" pair that is true for both equations.
We can use elimination, which is when we eliminate one of the variables. This can be done when both equations have a variable that has the same number.
Make both equations have "12y". Multiply each term by the same number.
-7x + 4y =10 }x3 => -21x + 12y = 30
-5x + 3y = 8 }x4 => -20x + 12y = 32
Subtract the equations from each other to get rid of 12y.
. -20x + 12y = 32
<u>- -21x + 12y = 30</u>
. 1x + 0y = 2 0y is nothing and 1x is x.
. x = 2 We have solved for x.
Now solve for y.
Use one of the equations:
-5x + 3y = 8 Substitute x for 2
-5(2) + 3y = 8 Simplify
-10 + 3y = 8 Start isolating x. Add 10 to both sides
3y = 18 Divide both sides by 3
y = 6 Solved for y.
The system of equations intersect at (2, 6).
