Answer:
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.
The exterior angle of a triangle is equal to the sum of the other 2 oposite interior angles
therfor
95=4x-8+3x-18
95=7x-24
add 24 both sides
119=7x
divide both sides by 7
17=x
sub back
4x-8
4(17)-8
68-8
60=∠F
3x-16
3(17)-16
51-16
35=∠G
x represents the number of lawns weeded by Gwen and y represents the number of dogs walked by Fabio.
Gwen charges $12 each time she weeds a yard and Fabio charges $9 each time he walks a dog.
So, for x number of weeds, Gwen earned 12x and for y number of dogs walked, Fabio earned 9y.
They need at least $510 to purchase the new gaming station.
Therefore,
12x + 9y ≥ 510
Also, the number of dog walks that Fabio has scheduled should not be more than twice the number of yards Gwen has scheduled to weed.
Therefore,
y ≤ 2x
Also, Fabio will walk at least 25 dogs.
Therefore,
y ≥ 25
Hence, the constraints are:
12x + 9y ≥ 510
y ≤ 2x
y ≥ 25
Problem 11
Answer: Angle C and angle F
Explanation: Angle C and the 80 degree angle are vertical angles. Vertical angles are always congruent. Angle F is equal to angle C because they are alternate interior angles.
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Problem 12
Answer: 100 degrees
Explanation: Solve the equation E+F = 180, where F = 80 found earlier above. You should get E = 100.
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Problem 13
Answer: 80 degrees
Explanation: This was mentioned earlier in problem 11.
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Problem 14
Answers: complement = 50, supplement = 140
Explanation: Complementary angles always add to 90. Supplementary angles always add to 180. An example of supplementary angles are angles E and F forming a straight line angle.
Answer:
7/2 =x
Step-by-step explanation:
The triangles are similar so we can write a ratio to solve
2 4
---- = -------
x 7
Using cross products
2*7 = 4x
14 = 4x
14/4 = 4x/4
7/2 =x
