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3 years ago

10 less than 5 times a number is less than 6 times the number decreased by eight

Mathematics

1 answer:

-BARSIC- [3]3 years ago

8 0

Answer:

The Answer is: the Number is -2

Step-by-step explanation:

Let n = the number.

Five times the number minus 10 is less than 6 times the number minus eight:

5n - 10 = 6n - 8

-1n = -8 + 10

-n = 2

n = -2, the value of the number is -2.

Proof:

5(-2) - 10 = 6(-2) - 8

-10 - 10 = -12 - 8

-20 = -20

Hope this helps! Have an Awesome Day!! :-)

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nancy spent 7/8 hour working out at the gym she spent 5/7 of that time lifting weights what fraction of an hour did sje spentld

Juli2301 [7.4K]

$\frac{9}{56}\\$ Fraction of hour was spent by NAncy in lifting weights

Step-by-step explanation:

Time spent at the gym by Nancy = $\frac{7}{8}\,hour$

Time spent at lifting weights = $\frac{5}{7}\,hour$

What fraction of hour she spent in lifting weights?

Solving:

Fraction of hour she spent in lifting weights= Time spend at the gym-Time spent at lifting weights

Fraction of hour she spent in lifting weights= $\frac{7}{8}\,hour-\frac{5}{7}\,hour$

$=\frac{49}{56}-\frac{40}{56}\\=\frac{49-40}{56}\\=\frac{9}{56}\\$

So, $\frac{9}{56}\\$ Fraction of hour was spent by Nancy in lifting weights

Keywords: Word Problems involving Fractions

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3 years ago

Describe several methods you could use to determine the rational zeros of a polynomial function. Which would you choose to use f

barxatty [35]

Answer:

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6 0

3 years ago

If 180° < α < 270°, cos⁡ α = −817, 270° < β < 360°, and sin⁡ β = −45, what is cos⁡ (α + β)?

eduard

Answer:

$cos(\alpha+\beta)=-\frac{84}{85}$

Step-by-step explanation:

we know that

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

Remember the identity

$cos^{2} (x)+sin^2(x)=1$

step 1

Find the value of $sin(\alpha)$

we have that

The angle alpha lie on the III Quadrant

The values of sine and cosine are negative

$cos(\alpha)=-\frac{8}{17}$

Find the value of sine

$cos^{2} (\alpha)+sin^2(\alpha)=1$

substitute

$(-\frac{8}{17})^{2}+sin^2(\alpha)=1$

$sin^2(\alpha)=1-\frac{64}{289}$

$sin^2(\alpha)=\frac{225}{289}$

$sin(\alpha)=-\frac{15}{17}$

step 2

Find the value of $cos(\beta)$

we have that

The angle beta lie on the IV Quadrant

The value of the cosine is positive and the value of the sine is negative

$sin(\beta)=-\frac{4}{5}$

Find the value of cosine

$cos^{2} (\beta)+sin^2(\beta)=1$

substitute

$(-\frac{4}{5})^{2}+cos^2(\beta)=1$

$cos^2(\beta)=1-\frac{16}{25}$

$cos^2(\beta)=\frac{9}{25}$

$cos(\beta)=\frac{3}{5}$

step 3

Find cos⁡ (α + β)

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

we have

$cos(\alpha)=-\frac{8}{17}$

$sin(\alpha)=-\frac{15}{17}$

$sin(\beta)=-\frac{4}{5}$

$cos(\beta)=\frac{3}{5}$

substitute

$cos(\alpha+\beta)=-\frac{8}{17}*\frac{3}{5}-(-\frac{15}{17})*(-\frac{4}{5})$

$cos(\alpha+\beta)=-\frac{24}{85}-\frac{60}{85}$

$cos(\alpha+\beta)=-\frac{84}{85}$

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3 years ago

If Dion was to purchase all 171 ticktes, then it would cost him $25.

Masteriza [31]

Answer:

He would need to purchase 8 ticket books. 8*24=192

Step-by-step explanation:

171/24=7.125 so he would need 8 books

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3 years ago

Round 75.434 to the nearest hundredth

nordsb [41]

Answer:75.43

Explanation:

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2 years ago

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