Let us evaluate each pair of expressions one at a time.
8. (n²+4) - n² and 4n.
(n²+4) - n² = n²+ 4 - n² = 4 which is not equal to 4n.
NOT EQUIVALENT
9. 3x + 5 and 2(x + 3)
2(x + 3) = 2x + 6 which is not equal to 3x + 5.
NOT EQUIVALENT
10. 15 - 6x and 15(1 - 6x)
15(1 - 6x) = 15 - 90x which is not equal to 15 - 6x
NOT EQUVALENT
11. (y + y + 2 + y) + 3y and 6y + 2
(y +y +2 + y) + 3y = y+y+y +2 + 3y = 3y + 2 + 3y = 6y + 2.
It matches the other expression.
EQUIVALENT
12. 8y - 3 + 10y and 3(6 - 1)
8y - 3 + 10y = 8y + 10y - 3 = 18y - 3
3(6 - 1) = 3(5) = 15
The two expressions do not match.
NOT EQUIVALENT.
Answer: Only the expressions in number 11 are equivalent.
Answer: 99.07$
Steps: First turn 32% into a decimal by moving the decimal right 2 places. You get 0.32. Then multiply 75.05$ by your decimal. You get 24.016. Add that to 75.05 and round your cent up, getting 99.07$ Sorry if i am incorrect this is my first answer. Hope I helped :)
Answer: D
Step-by-step explanation:
Set up
Let the dimes = d
Let the pennies = p
Let the quarters = q
Equations
You cannot mean that the pennies and dimes have equal numbers. That would mean that each had 21.5 members. Now could you mean that the dime and penny amount could be the same with 43 coins that total 4.00. Four dollars means that you need 40 dimes alone. It must mean that you are including quarters.
p + d + p = 43 (1)
p = d (2)
p +10d +25q = 451 (3)
Note how this last equation = was derived. You have to multiply the dimes by 10 and he quarters by 100 and the total by 100 to get the numbers all in pennies.
Put the results of 2 into 1.
2p + q = 43 (4)
You need to modify equation 3 as well.
p + 10p + 25q = 451
11p + 25q = 451 (5)
Solve the new equations
2p + q = 43 (4)
11p + 25q = 451 (5)
Multiply 4 by 25
25(2p- + q = 43)
50p + 25q = 1075 (6) Subtract (5) from (6)
<u>11p + 25q = 451
</u>39p = 624 Divide by 39
p = 624 / 39
p = 16
Since the pennies and dimes are equal there are 16 dimes
p + d + q = 43
16 + 16 + q = 43
32 + q = 43
q = 11
Check
16 + 10*16 + 11*25 = ?
16 + 160 + 275 = ?
451 = ?
Nice problem. Thanks for posting.
Answer:
<u>The measure of the arc CD = 64°</u>
Step-by-step explanation:
It is required to find the measure of the arc CD in degrees.
So, as shown at the graph
BE and AD are are diameters of circle P
And ∠APE is a right angle ⇒ ∠APE = 90°
So, BE⊥AD
And so, ∠BPE = 90° ⇒(1)
But it is given: ∠BPE = (33k-9)° ⇒(2)
From (1) and (2)
∴ 33k - 9 = 90
∴ 33k = 90 + 9 = 99
∴ k = 99/33 = 3
The measure of the arc CD = ∠CPD = 20k + 4
By substitution with k
<u>∴ The measure of the arc CD = 20*3 + 4 = 60 + 4 = 64°</u>
