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Assoli18 [71]
3 years ago
5

This month Erica saved $20 more than last month. For the two months, she saved a total of $70. How much did she save each month

Mathematics
1 answer:
skelet666 [1.2K]3 years ago
7 0
If its 20 more than last month that means x + $20 = $70, solve that and you get x = $50, last month she saved $50
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How to convert base two to base three​
sladkih [1.3K]

Consider this example: say we want to convert <em>x</em> = 11 0101 1001₂ to base 3.

The binary expansion of <em>x</em> is

<em>x</em> = 1×2⁹ + 1×2⁸ + 1×2⁶ + 1×2⁴ + 1×2³ + 1×2⁰

which in base 10 reduces to

<em>x</em> = 512 + 256 + 64 + 16 + 8 + 1 = 857

Recall the first several powers of 3:

3⁰ = 1; 3¹ = 3; 3² = 9; 3³ = 27; 3⁴ = 81; 3⁵ = 243; 3⁶ = 729

Now it's a matter of computing quotients and remainders. Pick the largest power of 3 that fits into the target number, then check the remainder and repeat.

• How many times does the 729 go into 857? 1 time, and it leaves a remainder of 128, or

857 = 1×729 + 128 = 1×3⁶ + 128

• How many times does 81 go into 128? Also 1 time, so

128 = 1×81 + 47 = 1×3⁴ + 47

• How many times does 27 go into 47? Also 1 time,

47 = 1×27 + 20 = 1×3³ + 20

• How many times does 9 go into 20? 2 times,

20 = 18 + 2 = 2×9 + 2 = 2×3² + 2

• How many times does 1 go into 2? Also 2 times,

2 = 2 + 1 = 2×1 + 0 = 2×3⁰

So we found

857 = 1×3⁶ + 1×3⁴ + 1×3³ + 2×3² + 2×3⁰

which is the ternary expansion of <em>x</em>,

<em>x</em> = 1 011 202₃

6 0
3 years ago
Can someone help me with this please
Anni [7]

Answer:

x = 61

Step-by-step explanation:

These 2 angles are supplementary which means they add up to 180:

2x - 6 + x + 3 = 180

3x - 3 = 180

3x = 183

x = 61

3 0
3 years ago
PLEASE HELP!!!!!!<br> idk
strojnjashka [21]

Answer:

5cm is a correct answer

5 0
3 years ago
Read 2 more answers
2^x=3^x+1 what are the exact approximate solutions
Mashcka [7]

Answer:

d.

Step-by-step explanation:

The goal of course is to solve for x.  Right now there are 2 of them, one on each side of the equals sign, and they are both in exponential positions.  We have to get them out of that position.  The way we do that is by taking the natural log of both sides.  The power rule then says we can move the exponents down in front.

ln(2^x)=ln(3^{x+1}) becomes, after following the power rule:

x ln(2) = (x + 1) ln(3).  We will distribute on the right side to get

x ln(2) = x ln(3) + 1 ln(3).  The goal is to solve for x, so we will get both of them on the same side:

x ln(2) - x ln(3) = ln(3).  We can now factor out the common x on the left to get:

x(ln2 - ln3) = ln3.  The rule that "undoes" that division is the quotient rule backwards.  Before that was a subtraction problem it was a division, so we put it back that way and get:

x(\frac{ln(2)}{ln(3)})=ln(3).  We can factor out the ln from the left to simplify a bit:

x[ln(\frac{2}{3})]=ln(3).  Divide both sides by ln(2/3) to get the x all alone:

x=\frac{ln(3)}{ln(\frac{2}{3}) }

On your calculator, you will find that this is approximately -2.709

6 0
3 years ago
What are the coordinates of the point on the directed line segment from (-6,9) to
brilliants [131]

Answer:

Step-by-step explanation:

difference of x-coordinates = 4-(-6) = 10

difference of y-coordinates = -1-9 = -10

partition the differences into a ratio of 1:4

10 × 1/(1+4) = 2

-10 × 1/(1+4) = -2

(-6+2,9-2) = (-4,7)

8 0
3 years ago
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