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3 years ago

Find the equation of the line using the info given and write the answers in slope – intercept form.

Mathematics

2 answers:

Fittoniya [83]3 years ago

8 0

Step-by-step explanation:

Step 1: Find the slope of the new line

To find the slope of a line perpendicular, you need to find the opposite reciprocal. Which means that you flip the sign and put the number over 1.

Opposite → $y = -3$ → y = 3

Reciprocal → $y = 3$ → $y = \frac{1}{3}$

Step 1: Find the line

$(y-y_0) = m(x - x_0)$

$(y - 5) = \frac{1}{3}(x - 2)$

$y - 5+5 = \frac{1}{3}x-\frac{2}{3}+5$

$y=\frac{1}{3}x+\frac{13}{3}$

Answer: $y=\frac{1}{3}x+\frac{13}{3}$

Murrr4er [49]3 years ago

4 0

Answer:

y - 5 = 0(x - 2)

y - 5 = 0

y = 5

Step-by-step explanation:

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Find the sum of the first 25 terms in this geometric series: 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

Suppose you have a right triangle with side lengths 26, 24, and 10. Which lengths

solong [7]

Answer:

hypotenuse —>26

Legs —> 10 and 24

Step-by-step explanation:

Generally ,the hypotenuse is the longest side .

So in our triangle the hypotenuse is of length 26.

Consequently, the legs are of lengths 24 and 10.

Also ,we can verify that this is right triangle using the Pythagorean theorem:

26^2 = 676

24^2+10^2 = 676

Then

26² = 24²+10².

3 0

2 years ago

At a football game Jasmine bought a soft pretzel for $2.25 in a bottle of water for $1.50 she paid with a $5 bill how much thing

andrew11 [14]

Answer:

$1.25.

Step-by-step explanation:

We have been given that at a football game Jasmine bought a soft pretzel for $2.25 in a bottle of water for $1.50 she paid with a $5 bill.

First of all let us find how much Jasmine spent on soft pretzel and water bottle by adding the cost of both items.

$\text{Total amount spent on both items}=2.25+1.50$

$\text{Total amount spent on both items}=3.75$

To find the amount that Jasmine will get as a change we will subtract the amount spent on both items from 5.

$\text{Amount of change that Jasmine will get}=5-3.75$

$\text{Amount of change that Jasmine will get}=1.25$

Therefore, Jasmine will get $1.25 back as change.

3 0

3 years ago

Find the sum or difference. 81-3 3

yuradex [85]

Answer:

Step-by-step explanation:

81 - 33 = 48

8 0

3 years ago

Read 2 more answers

6. If b>6, then 3b + 3 could be A. 18 B. 19 C. 20 D. 21 E. 22

Gala2k [10]

Answer:

E. 22

Step-by-step explanation:

Hello!

We know that b>6, and we are asked to find the possible values for 3b + 3.

Let's directly substitute 6 for b:

3(6) + 3
18 = 3
21

Now, because b is greater than 6, and not equal to 6, any value greater than 21 will work.

The correct option is E. 22.

7 0

2 years ago