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3 years ago

N bisects MO. MN = 7x - 15, NO = 2x + 5. Find x

Mathematics

1 answer:

mrs_skeptik [129]3 years ago

4 0

Answer:

x = 4

Step-by-step explanation:

I don't see a picture, so I'm assuming that M, N, O are points on a line segment with endpoints M and O.

Point N bisects segment MO, so it's in the middle of that segment. That means the distance from M to N and the distance from N to O are equal.

7x - 15 = 2x + 5

5x - 15 = 5

5x = 20

x = 4

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Step-by-step explanation:

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3 years ago

Read 2 more answers

Find the indicated nth partial sum of the arithmetic sequence.<br> −7, −3, 1, 5, . . ., n = 30

TiliK225 [7]

Step-by-step explanation:

Given the Arithmetic sequence

$-7, -3, 1, 5, . . .$

An arithmetic sequence has a constant difference d and is defined by

$a_n=a_1+\left(n-1\right)d$

$\mathrm{Compute\:the\:differences\:of\:all\:the\:adjacent\:terms}:\quad \:d=a_{n+1}-a_n$

$-3-\left(-7\right)=4,\:\quad \:1-\left(-3\right)=4$

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

$d=4$

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

$a_1=-7$

$a_n=a_1+\left(n-1\right)d$

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

$a_n=4\left(n-1\right)-7$ ∵ $d=4$

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

$n\left(a_1+\frac{d\left(n-1\right)}{2}\right)$

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

$n=30,\:\space a_1=-7,\:\spaced=4$

$=30\left(-7+\frac{4\left(30-1\right)}{2}\right)$

$=30\left(58-7\right)$ ∵ $\frac{4\left(30-1\right)}{2}=58$

$=30\cdot \:51$

$=1530$ ∵ $\mathrm{Multiply\:the\:numbers:}\:30\cdot \:51=1530$

Therefore, the indicated nth partial sum of the arithmetic sequence is 1530.

ANOTHER METHOD

$a_n=4\left(n-1\right)-7$

n = 30

$\sum _{n=1}^{30}\:4\left(n-1\right)-7$

$=\sum _{n=1}^{30}4n-11$

$\mathrm{Apply\:the\:Sum\:Rule}:\quad \sum a_n+b_n=\sum a_n+\sum b_n$

$=\sum _{n=1}^{30}4n-\sum _{n=1}^{30}11$

$\sum _{n=1}^{30}4n=1860$

and

$\sum _{n=1}^{30}11=330$

$=1860-330$

$=1530$

7 0

3 years ago

What is the difference between whole numbers and real numbers ?

kirza4 [7]

Hello there! :)

Whole numbers are all positive numbers and zero.

Real numbers are negative numbers, fractions, positive numbers and zero.

Hope this helps!

~Just a felicitous girlie

#HaveAnAmazingDay

$SilentNature :)$

4 0

3 years ago

Find the exact value of sine [2 cosine Superscript negative 1 Baseline (- StartFraction StartRoot 2 EndRoot/2 EndFraction )] = n

Nady [450]

Answer:

$\frac{3\pi}{2}$ .

Step-by-step explanation:

The given expression is

$2\cos^{-1}\left(-\frac{\sqrt{2}}{2}\right)$

It can be rewritten as

$2\cos^{-1}\left(-\frac{1}{\sqrt{2}}\right)$

$2\left [\pi-\cos^{-1}\left(\frac{1}{\sqrt{2}}\right)\right]$ $[\because \cos^{-1}(-x)=\pi-\cos^{-1}(x), x\in [-1,1]]$

$2\left [\pi-\cos^{-1}\left(\cos \frac{\pi}{4}\right)\right]$

$2\left [\pi-\frac{\pi}{4}\right]$

$2\left [\frac{4\pi-\pi}{4}\right]$

$\frac{3\pi}{2}$

Hence, the exact value of given expression is $\frac{3\pi}{2}$ .

3 0

3 years ago