To determine which of the choices is lies on the line represented by the equation, 2x + 5y = 4, substitute the values of the abscissas to the x of the equation and solve for y. Evaluate if the y calculated is equal to the ordinate of the ordered pair. Calculations are shown below.
A. (7, -2) ; 2(7) + 5y = 4 ; y = -2 ; EQUAL
B. (0,-1) ; 2(0) + 5y = 4 ; y = 0.8 ; NOT EQUAL
C. (0,1) ; 2(0) + 5y = 4 ; y = 0.8 ; NOT EQUAL
D. (3, -2) ; 2(-3) + 5y = 4 ; y = 2 ; NOT EQUAL
Thus, the answer is letter A. (7, -2)
Answer:
quadrant II
Step-by-step explanation:
quadrant III is located bottom left/ (-x, -y). Rotated 90° clockwise it would go to the right just like a clock which would end up in quadrant II which is too left quadrant (-x, y)
Answer:
108°
Step-by-step explanation:
The area of a sector is given by the formula ...
A = (1/2)r²θ . . . . . where θ is in radians
Solving for θ, we find ...
θ = 2A/r²
For your given sector, the central angle is ...
θ = 2(30π cm²)/(10 cm)² = 0.6π . . . . radians
π radians is 180°, so the central angle in degrees is ...
θ = (0.6)(180°) = 108°
The central angle measure of the sector is 108°.
Answer:
First question would be 11/7
Second question 1/42
Answer:
x = 7
Length = 4 inches , Width = 15 inches
Step-by-step explanation:
<em>PART</em><em> </em><em>1</em><em> </em><em>:</em>
Area of rectangle = Length × Width
A = L × W
L = x - 3
W = x + 8
Therefore:
A = L × W
60 = ( x - 3 ) ( x + 8 )
( x - 3 ) ( x + 8 ) - 60 = 0
x^2 + 8x - 3x - 24 - 60 = 0
x^2 + 5x - 84 = 0
x^2 + 12x - 7x - 84 = 0
x ( x + 12 ) - 7 ( x + 12 ) = 0
( x + 12 ) ( x - 7 ) = 0
THEREFORE:
x = - 12 , x = 7
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<em>PART</em><em> </em><em>2</em><em> </em><em>:</em>
L = x - 3
L = ( - 12 ) - 3
L = - 15
OR
L = ( 7 ) - 3
L = 4
THEREFORE:
Length can not be a negative number. Hence, L can not equal to - 15.
L = 4 inches
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W = x + 8
W = ( 7 ) + 8
THEREFORE:
W = 15 inches
