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3 years ago

Nena thinks that because 4<6, it must also be true that 1/4<1\6. Explain to nena why this is incorrect

Mathematics

2 answers:

Snowcat [4.5K]3 years ago

4 0

When the numerator are the same, which ever fraction's denominator is smaller is the larger number.

olga nikolaevna [1]3 years ago

4 0

If you have two identical and symmetrical objects and divide one into 4ths and the other into 6ths, the pieces of the object divided into 4ths will be larger than the pieces of the object divided into 6ths.

1/4 = 25 4/4 = 100
1/6 = 16.66... (17) 6/6 = 100
25 > 17

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dawn has a rug with a perimeter of 32 feet the width of her rug is 6 feet what is the length in feet of dawns rug

puteri [66]

6*2=12
32-12=20
20/2=10.
Perimeter is all the way around an object. So take 6 two times and minus that from 32. Answer of that divide by 2 to get the length. Length of one side is 10 ft.

7 0

3 years ago

Find the sum of the first 25 terms in this geometric series:<br> 8 + 6 + 4.5...

Ksivusya [100]

Step-by-step explanation:

Given the geometric sequence

8 + 6 + 4.5...

A geometric sequence has a constant ratio and is defined by

$a_n=a_1\cdot r^{n-1}$

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}$

$\frac{6}{8}=\frac{3}{4},\:\quad \frac{4.5}{6}=\frac{3}{4}$

$\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}$

$r=\frac{3}{4}$

$\mathrm{The\:first\:element\:of\:the\:sequence\:is}$

$a_1=8$

$\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:$

$a_n=8\left(\frac{3}{4}\right)^{n-1}$

$\mathrm{Geometric\:sequence\:sum\:formula:}$

$a_1\frac{1-r^n}{1-r}$

$\mathrm{Plug\:in\:the\:values:}$

$n=25,\:\spacea_1=8,\:\spacer=\frac{3}{4}$

$=8\cdot \frac{1-\left(\frac{3}{4}\right)^{25}}{1-\frac{3}{4}}$

$\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}$

$=\frac{\left(1-\left(\frac{3}{4}\right)^{25}\right)\cdot \:8}{1-\frac{3}{4}}$

$=\frac{8\left(-\left(\frac{3}{4}\right)^{25}+1\right)}{\frac{1}{4}}$

$\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$

$=\frac{8\left(-\frac{3^{25}}{4^{25}}+1\right)}{\frac{1}{4}}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{\frac{b}{c}}=\frac{a\cdot \:c}{b}$

$=\frac{\left(1-\frac{3^{25}}{4^{25}}\right)\cdot \:8\cdot \:4}{1}$

$\mathrm{Multiply\:the\:numbers:}\:8\cdot \:4=32$

$=\frac{32\left(-\frac{3^{25}}{4^{25}}+1\right)}{1}$

$=\frac{32\cdot \frac{4^{25}-3^{25}}{4^{25}}}{1}$ ∵ $\mathrm{Join}\:1-\frac{3^{25}}{4^{25}}:\quad \frac{4^{25}-3^{25}}{4^{25}}$

$=32\cdot \frac{4^{25}-3^{25}}{4^{25}}$

$=\frac{\left(4^{25}-3^{25}\right)\cdot \:32}{4^{25}}$

$=\frac{2^5\left(4^{25}-3^{25}\right)}{2^{50}}$ ∵ $\mathrm{Factor}\:32:\ 2^5$ , $\mathrm{Factor}\:4^{25}:\ 2^{50}$

$=\frac{4^{25}-3^{25}}{2^{45}}$ ∵ $\mathrm{Cancel\:}\frac{\left(4^{25}-3^{25}\right)\cdot \:2^5}{2^{50}}:\quad \frac{4^{25}-3^{25}}{2^{45}}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a\pm \:b}{c}=\frac{a}{c}\pm \frac{b}{c}$

$=\frac{4^{25}}{2^{45}}-\frac{3^{25}}{2^{45}}$

$=32-\frac{3^{25}}{2^{45}}$ ∵ $\frac{4^{25}}{2^{45}}=32$

$=32-0.024$ ∵ $\frac{3^{25}}{2^{45}}=0.024$

$=31.98$

Therefore, the sum of the first 25 terms in this geometric series: 31.98

3 0

3 years ago

How can you recognize linear change from a graph, an equation, a table, or in a real world situation?

Stolb23 [73]

In linear change, the two variables keep increasing or decreasing at the same speed.

7 0

3 years ago

Pamela and Debbie are shelving books at a public library. Pamela shelves 26 books at a time, whereas Debbie shelves 7 at a time.

Ira Lisetskai [31]

If both Pamela and Debbie can shelf the same number of books at the end, the smallest number of books each could have shelved is 182

The number of books that Pamela can shelf at a time = 26

The number of books that Debbie can shelf at a time = 7

If both Pamela and Debbie can shelf the same number of books at the end, the smallest number of books each could have shelved is the least common multiple of 26 and 7

The Least common multiple of 26 and 7 = 182

Therefore, if both Pamela and Debbie can shelf the same number of books at the end, the smallest number of books each could have shelved is 182

Learn more on Least Common Multiple here: brainly.com/question/363238

8 0

3 years ago

Can someone help me with this math homework please!

jolli1 [7]

Answer:

(-3,-6) and (-3,2)

Step-by-step explanation:

A line with an undefined slope is vertical. In this case it must have x coordinates equal to -3

4 0

3 years ago