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3 years ago

Decide if the expressions in each pair are equivalent. Explain how you know.

2 answers:

8 0

The first expression is true because x+x+x+x= 4x. It is like addition but with a variable. The second isn’t true because 5x= x+x+x+x+x whereas x+5 is x plus five. Not 5x. Hope this helps.

marysya [2.9K]3 years ago

4 0

Answer:

20x²+5x+5

Step-by-step explanation:

any more help just ask

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Trigonometry problem

IgorC [24]

Answer:

The values are x = 0° or x = 60°

Step-by-step explanation:

Given:

$\cos x + \frac{1}{\sqrt{3} }\times \sin x = 1$

Let it be in the form of

$a\cos x + b\sin x = 1$ such that

a = 1

$b=\frac{1}{\sqrt{3} }$

We have

$\sqrt{(a^{2}+b^{2} )}=\sqrt{(1^{2}+(\frac{1}{\sqrt{3} }) ^{2} )}\\=\sqrt{\frac{4}{3}}\\=\frac{2}{\sqrt{3} }$

Now, Dividing both the side by $\frac{2}{\sqrt{3} }$ we get

$\frac{\sqrt{3} }{2}\cos x + \frac{1}{2}\sin x =\frac{\sqrt{3} }{2}\\$

We Know

$\sin 60 =\frac{\sqrt{3} }{2}\\and\\\cos 60 = \frac{1}{2}$

Now by replacing with above values we get

$\sin 60\times \cos x + \cos 60\times \sin x = \frac{\sqrt{3} }{2}\\$

Also we have formula

$\sin A\times \cos B + \cos A\times \sin B = \sin (A+B)$

By applying the above Formula we get

$\sin (60+x)=\frac{\sqrt{3} }{2}\\$

Also ,

$\sin (60)=\frac{\sqrt{3} }{2}\\and\\\sin (120)=\frac{\sqrt{3} }{2}$

Comparing we get

60 + x = 60 or 60 + x = 120

∴ x = 0° ∴ x = 120 - 60 = 60°

Therefore, the values are x = 0° or x = 60° i.e between 0° to 360°

5 0

3 years ago

In a recent contest, the mean score was 210 and the standard deviation was 25. a) Find the z-score of John who scored 190 b) Fin

denpristay [2]

Answer:

a) $Z = -0.8$

b) $Z = 2.4$

c) Mary's score was 241.25.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 210, \sigma = 25$

a) Find the z-score of John who scored 190

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{190 - 210}{25}$

$Z = -0.8$

b) Find the z-score of Bill who scored 270

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{270 - 210}{25}$

$Z = 2.4$

c) If Mary had a score of 1.25, what was Mary’s score?

$Z = \frac{X - \mu}{\sigma}$

$1.25 = \frac{X - 210}{25}$

$X - 210 = 25*1.25$

$X = 241.25$

Mary's score was 241.25.

3 0

3 years ago

Read 2 more answers

The formula can be used to find the velocity v in feet per second of an object that has fallen h feet. Find the velocity of an o

Otrada [13]

I assume you are looking for the formula, and the velocity.

The formula:
v1^2-v0^2=2aS

where
v0=initial velocity (0 if object falls from rest), ft/s
v1=velocity reached after falling a distance S, ft/s
S=distance from initial position, positive downwards (for falling objects), ft
a=acceleration due to gravity, 32.2 ft/s^2 in imperial units

So substituting numbers, assuming initial velocity is zero (from rest), then
S=25 ft
v1^2-0^2=2*32.2*25
v1^2=1610
v1=sqrt(1610)
=40.1 ft/s

3 0

3 years ago

-5x-14=6y written in standard form

elixir [45]

Answer:

5x + 6y = -14

Step-by-step explanation:

Standard form means the x term will be on the farthest left, then the y term next, set equal to the constant (plain number) all by itself on the right.

Like this:

Ax + By = C

So you have

-5x - 14 = 6y

Add 14 to both sides.

-5x = 6y + 14

Subtract 6y from both sides.

-5x - 6y = 14

Also multiply both sides by -1, to make sure your A value (number next to the x) is positive.

5x + 6y = -14

7 0

3 years ago

3x-5=-8(6+5x)<br> Solve by substitution

OLga [1]

Answer:

x = -1

Step-by-step explanation:

3x - 5 = - 8 (6 + 5x)

3x - 5 = - 48 - 40x

3x + 40x = - 48 + 5

43x = - 43

x = - 43/43

x = - 1

5 0

3 years ago