Answer:
The bench was $375 and the garden table was $284.
Step-by-step explanation:
Let x be the value of the bench, if the table is 91 less than the value of the bench then the equation can be:
x + x-91 = 659
2x -91 = 659
Add 91 to both sides of the equation to isolate the 2x:
2x - 91 + 91 = 659 + 91
2x = 750
Divide both sides by 2 to get 1x:
2x ÷ 2 = 750 ÷ 2
x = 375
This means the bench was $375 and the garden table was $284.
Hope this helps!
You have to use the distance formula.
Answer:
Unit rate = 1 1/2 cups per serving
Step-by-step explanation:
1/2 serving has 3/4 cup
1 serving
3/4 * 1/2 = 3/4 * 2/1 = 6/4 = 6/4 / 2 = 3/2 = 1 1/2
Answer:
Step-by-step explanation:
<u>Given points:</u>
The perpendicular bisector passes through the midpoint.
<u>Finding the coordinates of the midpoint first:</u>
- x = (-2 + 6)/2 = 2, y = (-2 + 0)/2 = -1
<u>Next finding the slope of AB:</u>
- m = (0 - (-2))/(6 - (-2)) = 2/8 = 1/4
The perpendicular lines have negative-reciprocal slopes.
<u>The line will have a slope of -4 and pass through the point (2, -1)</u>
- y - (-1) = -4(x - 2)
- y + 1 = -4(x - 2) - point-slope form
- y = -4x + 7 - slope-intercept form
Applying the angle of intersecting secants theorem, the measure of arc JML is: 262°.
<h3>What is the Angle of Intersecting Secants Theorem?</h3>
The angle of intersecting secants theorem states that when two lines form an external angle outside a circle, the measure of the angle is half the difference between the measure of the major and minor intercepted arcs.
Thus:
m∠JKL = (measure of arc JML - measure of arc JL)/2 => angle of intersecting secants theorem
m∠JKL = 8x - 6
measure of arc JML = 25x - 13
measure of arc JL = 360 - (25x - 13)
Plug in the values
8x - 6 = [(25x - 13) - (360 - (25x - 13))/2]
Solve for x
2(8x - 6) = [(25x - 13) - (360 - 25x + 13)]
16x - 12 = [(25x - 13) - (373 - 25x)]
16x - 12 = 25x - 13 - 373 + 25x
16x - 12 = 50x - 386
16x - 50x = 12 - 386
-34x = -374
x = 11
Measure of arc JML = 25x - 13
Plug in the value of x
Measure of arc JML = 25(11) - 13 = 262°
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