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1 year ago

In the figure, all, and both lines are intersected by transversal & Complete the statements to prove that m≤1 = m25.

Mathematics

1 answer:

m_a_m_a [10]1 year ago

7 0

First blank: Substitution or transitive property of equality

Second blank: Subtraction property of equality

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Ava has 34 candy bars. If

aliya0001 [1]

$\bf Step-by-step~explanation:$

If Ava has 34 candy bars, and each box can hold 5 bars, then we need to find out how many boxes that are filled up.

$\bf Step~1:$

Divide the number of candy bars (34), by the number each box can hold (5)

$\bf\frac{34}{5}=6.8$

Since we cannot have 6.8 boxes, we have to round down to 6.

$\boxed{\bf Our~final~answer:~6~boxes}$

$\bf Check~our~answer:$

To check our answer, we multiply the number of boxes (6), by the number of bars in each box (5), to get 30. We add Ava's extra bars (4), and we get the number we started off with: 34. This proves our answer is correct!

4 0

3 years ago

Use the power series for 1 1−x to find a power series representation of f(x) = ln(1−x). What is the radius of convergence? (Note

Viktor [21]

a. Recall that

$\displaystyle\int\frac{\mathrm dx}{1-x}=-\ln|1-x|+C$

For $|x|$ , we have

$\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n$

By integrating both sides, we get

$\displaystyle-\ln(1-x)=C+\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}$

If $x=0$ , then

$\displaystyle-\ln1=C+\sum_{n=0}^\infty\frac{0^{n+1}}{n+1}\implies 0=C+0\implies C=0$

so that

$\displaystyle\ln(1-x)=-\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}$

We can shift the index to simplify the sum slightly.

$\displaystyle\ln(1-x)=-\sum_{n=1}^\infty\frac{x^n}n$

b. The power series for $x\ln(1-x)$ can be obtained simply by multiplying both sides of the series above by $x$ .

$\displaystyle x\ln(1-x)=-\sum_{n=1}^\infty\frac{x^{n+1}}n$

c. We have

$\ln2=-\dfrac\ln12=-\ln\left(1-\dfrac12\right)$

$\displaystyle\implies\ln2=\sum_{n=1}^\infty\frac1{n2^n}$

4 0

3 years ago

I need help with q5

Roman55 [17]

Percent increase = ((new number - original number) / (original number)) x 100.

percent increase = ((3000 - 2500) / 2500)) x 100 =
(500 / 2500)....x 100 =
0.2 x 100 =
20% increase <====

7 0

3 years ago

A rabbit and a turtle were to start a race at the same place. The rabbit was asleep when the turtle started. He slept for seven

Ierofanga [76]

Rabbit: y=5x-7
Turtle: y=x

use substitution

x=5x-7
-4x=-7
x=7/4=1.75

1.75hr

3 0

3 years ago

You are the treasurer for a local charity. At the beginning of the month the balance was $820.64. The charity received donations

dsp73

<span>ed donations of $500.00, $55.00 and $25.00. You have an electric bill of $40.64, bill for postage of $12.75, and rent for $445.00</span>

3 0

2 years ago

Read 2 more answers