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kirza4 [7]
3 years ago
5

100^a x 1000^b can be written in the form 10^w Show that w = 2a + 3b

Mathematics
1 answer:
Elena L [17]3 years ago
3 0
100^a \time 1000^b = 10^{2a} \times 10^{3b} = 10^{2a + 3b}

10^{w} = 10^{2a + 3b}

w = 2a + 3b \text { (shown)}
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Which expression below is equivalent to the one below? 3 (2x+5)-(-5x+4)
Vinil7 [7]

Answer:

D) 11x + 9

Step-by-step explanation:

3(2x + 5) - (-5x + 4) = (6x + 15) - (-5x + 4) = 6x + 15 + 5x - 4

add like terms:

(6x + 5x) + (15 - 4) = 11x + 9

8 0
3 years ago
Read 2 more answers
Anyone know what the answer is ?
alina1380 [7]
A perpendicular bisector
this means the length IJ=JK and the angles IJB, BJK are 90° (and their congruent angles too)

but this does not mean AB=IK, because their lengths can be arbitrary
for a similar reason AJ=IJ is wrong, essentially the same statement but with half lengths
BI=BK is true, because it is a bisector of IK this means the sides IJ=JK and JB is a shared side, therefore also having the same length. We also know IJB and BJK are congruent angles, so all in all these are congruent triangle and therefore also share the side length
BI=AK is false, because we don't know where the intersection point j is on AB, it could split the length into any arbitrary ratio, in case these are two equal sides then it would be true, but it doesn't hold for all other possibilities

so BI=BK is the solution
3 0
3 years ago
Let
Digiron [165]

What I gather from the question is that X has second moment E(X^2)=81 and variance V(X) = 58, and you're asked to find the expectation and variance of the random variable Y=2X+10.

From the given second moment and variance, we find the expectation of X :

V(X) = E(X^2) - E(X)^2 \implies E(X) = \sqrt{E(X^2) - V(X)} = \sqrt{23}

Expectation is linear, so

E(Y) = E(2X+10) = 2 E(X) + 10 = \boxed{2\sqrt{23} + 10}

Using the same variance identity, we have

V(Y) = V(2X+10) = E((2X+10)^2) - E(2X+10)^2

and

E((2X+10)^2) = E(4X^2 + 40X + 100) = 4E(X^2) + 40E(X) + 100 = 424 + 40\sqrt{23}

so that

V(Y) = V(2X+10) = (424 + 40\sqrt{23}) - (2\sqrt{23} + 10)^2 = \boxed{232}

Alternatively, we can use the identity

V(aX+b) = a^2 V(X) \implies V(2X+10) = 4V(X) = 232

5 0
2 years ago
25 penalties decreased by 32%?
SCORPION-xisa [38]
Kut 32% off  25

100-32=68% left

=25*0.68

=17
6 0
3 years ago
Jessica paid $170 for an item that was originally priced at $260. What percent of the original price
worty [1.4K]

Answer:

260x = 170

x=170/260 * 100% = 65.4 %

Step-by-step explanation:

8 0
3 years ago
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