Answer:
BC=YZ
Step-by-step explanation:
The SAS Congruency states that if two sides and one angle in a triangle are equal then the triangles are said to be congruent.
It is given that,
angle B= angle Y
AB=XY
to prove they are congruent we need to show that BC=YZ
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Answer:
13 ft/s
Step-by-step explanation:
t seconds after the boy passes under the balloon the distance between them is ...
d = √((15t)² +(45+5t)²) = √(250t² +450t +2025)
The rate of change of d with respect to t is ...
dd/dt = (500t +450)/(2√(250t² +450t +2025)) = (50t +45)/√(10t² +18t +81)
At t=3, this derivative evaluates to ...
dd/dt = (50·3 +45)/√(90+54+81) = 195/15 = 13
The distance between the boy and the balloon is increasing at the rate of 13 ft per second.
_____
The boy is moving horizontally at 15 ft/s, so his position relative to the spot under the balloon is 15t feet after t seconds.
The balloon starts at 45 feet above the boy and is moving upward at 5 ft/s, so its vertical distance from the spot under the balloon is 45+5t feet after t seconds.
The straight-line distance between the boy and the balloon is found as the hypotenuse of a right triangle with legs 15t and (45+5t). Using the Pythagorean theorem, that distance is ...
d = √((15t)² + (45+5t)²)
The consecutive integers are -1
Area is length times width. Therefore, width is area divided by length. Convert 11 7/8 to the improper fraction 95/8 and convert 4 3/4 to 19/4. Then, you can fine 95/8 divided by 19/4 by flipping the second fraction and multiplying so that you have 95/8 times 4/19. 4 times 95 is 380 and 8 times 19 is 152. Therefore, the answer is 380/152. This is equivalent to 5/2 or 2.5.
Answer:
16 men would be needed to paint the room in 2 hours
Step-by-step explanation:
We can use proportion to solve the problem given, but first we need to determine whether it is a direct or indirect proportion.
If the number of men are increase, the time taken to do the work will decrease, If the number of men are decrease, the time taken to do the work will increase. Therefore, this is an indirect proportion.
We are going to arrange the data inversely.
Let x be the number of men needed to paint the room in two hours
8 hours = 2 hours
x = 4 men
Cross-multiply
2×x = 8×4
2x = 32
Divide both-side of the equation by 2
2x/2 = 32/2
x = 16 men
16 men would be needed to paint the room in 2 hours
