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4 years ago

Which expression is equivalent to that

Mathematics

2 answers:

kari74 [83]4 years ago

6 0

Answer:

3. 9x

4. D. -5v + 4

Step-by-step explanation:

3. (-3+12)v

= 9v

4. Combine like terms:

(-2v - 3v) + (8 - 4)

= -5v + 4

olchik [2.2K]4 years ago

4 0

Hope that somehow helps.

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0.6875 as a fraction

Eva8 [605]

0.6875 converted to a fraction is 11/16

7 0

3 years ago

Please help :c the first word is find

xeze [42]

Answer:

The values of $r_{2}$ and $\alpha_{2}$ are 2 and 150º.

Step-by-step explanation:

The complete statement is:

Find $\alpha_{2}$ and $r_{2}$ such that $\sin \theta - \sqrt{3}\cdot \cos \theta = r_{2}\cdot \cos (\theta - \alpha_{2})$ .

We proceed to use the following trigonometric identity:

$\cos (\theta - \alpha_{2}) = \cos \theta \cdot \cos \alpha_{2} +\sin \theta \cdot \sin \alpha_{2}$ (1)

$\sin \theta -\sqrt{3}\cdot \cos \theta = r_{2}\cdot \cos \theta \cdot \cos \alpha_{2}+r_{2}\cdot \sin \theta \cdot \sin \alpha_{2}$

By direct comparison we derive these expressions:

$r_{2}\cdot \sin \alpha_{2} = 1$ (2)

$r_{2}\cdot \cos \alpha_{2} = -\sqrt{3}$ (3)

By dividing (2) by (3), we have the following formula:

$\tan \alpha_{2} = -\frac{1}{\sqrt{3}}$

$\tan \alpha_{2} = -\frac{\sqrt{3}}{3}$

The tangent function is negative at second and fourth quadrants. That is:

$\alpha_{2} = \tan^{-1} \left(-\frac{\sqrt{3}}{3} \right)$

There are at least two solutions:

$\alpha_{2,1} = 150^{\circ}$ , $\alpha_{2,2} = 330^{\circ}$

And the value of $r_{2}$ :

$r_{2}^{2}\cdot \sin^{2}\alpha_{2} + r_{2}^{2}\cdot \cos^{2}\alpha_{2} = 4$

$r_{2}^{2} = 4$

$r_{2} = 2$

The values of $r_{2}$ and $\alpha_{2}$ are 2 and 150º.

5 0

3 years ago

The maximum weight allowed per car on The Twister carnival ride is 263 pounds. Your friend weighs 86 pounds. To be able to ride

Kazeer [188]

Your weight: x lb
Friend's wt.: 86 lb
Max wt. allowed: 263 lb

Then x + 86 ≤ 263, with x in lb. You could weigh a max. of 177 lb and still be able to go on this ride.

4 0

4 years ago

Revenue flows into a company at a rate of f(t) = 3000 1 + 5t , where t is measured in years and f(t) is measured in dollars per

Igoryamba

Answer:

$F = 388500\,dollars$

Step-by-step explanation:

The revenue flows has the following function:

$f(t) = 3000\cdot (1+5\cdot t)$

The total revenue obtained in the first seven years is obtained by using the concept of definite integral:

$F = 3000\int\limits^7_0 {(1+5\cdot t)} \, dt$

$F = 3000\cdot t|_{0}^{7}+7500\cdot t^{2}|_{0}^{7}$

$F = 21000+367500$

$F = 388500\,dollars$

4 0

3 years ago

10. (Section 4.7) John filled his gas tank and noted that the odometer read 38,320.8 miles. After the next filling, the odometer

hodyreva [135]

Find the number of miles he drove by subtracting the odometer readings:

38735.5 - 38320.8 = 414.7 miles.

Now divide the number of miles driven by the number of gallons:

414.7 / 14.5 = 28.6 miles per gallon.

6 0

3 years ago