Answer:
Step-by-step explanation:
We can solve this in either of two approaches: Mathematically or Graphically.
<u>Mathematically</u>
y=-(3/4)(x-4)^2+12 where y is the height of the ball, and x is the time, in seconds.
We want to know how many seconds for the height to be 0, so y=0.
0 = -(3/4)(x-4)^2+12
-12 = -(3/4)(x-4)^2
12*(4/3) = (x-4)^2
16 = (x-4)^2
x = 8 and 0 (the initial point).]
It will reach the ground in 8 seconds
<u>Graphically</u>
Plot the function and find the time, x, when the graph passes through the x axis (after t = 0). Attached.
Answer:
The answer to your question should be B. OC
The correct answer is: [B]: " ∠C ≅ ∠F " .
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Note: We are given that:
"I<span>n △ABC, m∠A=38° and m∠B=67 " .
Since a triangle has three (3) angles (by definition) ; and since all 3 angles in any triangle must add up to 180</span>°<span> (by definition); we can solve for:
m</span>∠C ;
m∠C = 180 − (38 + 67) = 180 <span>− 105 = 75 .
</span>m∠C = 75° ;
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Likewise, given △DEF, m∠D=38° and m∠E=67 ; we find m∠F as follows:
m∠F = 180 - (38 + 67) = 180 − 105 = 75 .
m∠F = 75° .
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So, let us consider the answer choices given:
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Choice [A]: "m∠F = 67° " ; is incorrect. We know that "<span>m∠F = 75° " .
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Choice [B]: " </span>∠C ≅ ∠F " is correct. We know that ΔABC ≅ ΔDEF ; and that;
m∠A = m∠D = 38° ; and that: m∠B = m∠E = 67° ; and that:
m∠C = m∠F = 75° ; and as such:
∠A ≅ D ; and ∠B ≅ ∠E ; and ∠C ≅ ∠F .
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Choice [C]: "<span>m∠C = 75° only" ; is incorrect. While it is correct that:
"m</span><span>∠C = 75° " ; this answer choice is INCORRECT; since this answer choice is not the ONLY answer choice provided that holds true. In fact, we have already determined that answer choice: [B] (see above) is a correct statement.
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Choice [D]: "</span><span>∠C is not necessarily congruent to ∠F. " ; This answer choice is INCORRECT; as explained in Answer choice: [B]: (see above).
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Choice [E]: "</span>It is not possible to determine m∠F." ; This answer choice is INCORRECT. We know that " m∠F = 75° " .
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Choice [F]: " <span>It is not possible to determine m∠C." ; This answer choice is
INCORRECT. We know that " m</span>∠C = 75° " .
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The correct answer is: [B]: " <span>∠C ≅ ∠F " .
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Step-by-step explanation:
solved in the diagram above
I hope it helps you
Answer:
74
Step-by-step explanation:
Using linear equations, we are given two equations from the questions:
4x +7y=30 from day one and 3x +5y=22 from day two
Multiply the first equation by 3 and second by 4 giving us
12x +21y=90 and 12x +20y=88. Minus both equations.
12x - 12x +21y - 20y= 90 - 88, Gives you y=2,
You can now use the value of y to find x.
4x + 7y = 30
4x + 7(2)= 30
4x + 14= 30. Minus 14 on both sides giving you
4x=16. Divide both sides by 4.
x=4
Now use both values to find how much money is needed on the third day.
10x + 17y
=10(4) + 17(2)
=40 +34
=74
