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d1i1m1o1n [39]
3 years ago
6

Use the graph that shows the solution to f(x)=g(x).

Mathematics
1 answer:
Inessa05 [86]3 years ago
6 0

9514 1404 393

Answer:

  x = 0, x = 3

Step-by-step explanation:

It appears your equations are intended to be ...

  f(x) = (7/3)x -3

  g(x) = 2^x -4

These are the equations that are graphed in your second attachment. The graphs cross at x=0 and x=3.

The solutions to f(x) = g(x) are x ∈ {0, 3}.

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Step by step instructions
alisha [4.7K]

Since there is a multiplier of 7 on the left, and both terms on the right are divisible by 7, I'd start by dividing the equation by 7

|8 - 3x| = 3x - 7

The absolute value function may or may not negate its argument. (The argument is negated if it is negative.) Hence this can resolve to two equations

-(8 -3x) = 3x -7

or

(8 -3x) = 3x -7

_____

Starting with the first of these, we can eliminate parentheses to get

... -8 +3x = 3x -7

Subtracting 3x from both sides gives the FALSE statement

... -8 = -7 . . . . FALSE

Thus, this version of the equation has No Solution.

Looking at the second of the equations above, we can add 3x to get

... 8 = 6x -7

Adding 7 and dividing by 6 gives

... (8 +7)/6 = x = 5/2

The solution is x = 5/2.

3 0
4 years ago
Verify the trig identity: tan^2 theta + cot^2 theta / csc^2 theta = sec^2 theta
Mars2501 [29]

Answer:

See proof below

Step-by-step explanation:

In trigonometry identity

tan^2 theta = sin^2 theta /cos^2 theta

cot^2 theta = cos^2 theta/sin^2 theta

csc^2 theta = 1/sin^2 theta

Substitute into the expression

(sin^2 theta /cos^2 theta )+ (cos^2 theta/sin^2 theta)/1/sin^2 theta

= [sin^4theta + cos^4theta/cos^2 theta sin^2 theta]÷(1/sin^2 theta)

= 1/cos^2 theta sin^2 theta÷(1/sin^2 theta)

= 1/cos^2 theta sin^2 theta * sin^2 theta/1

= 1/cos^2theta

= sec^2theta (Proved!)

3 0
3 years ago
Zack has 3/4 hours to play video games it's takes him 1/12hours to set up the system. Each round of his favorite game takes 1/6h
ladessa [460]

Answer: He can play 4 rounds of his favorite game

Step-by-step explanation:

Zack has 3/4 hours to play video games. This means that he cannot spend more than 3/4 hours playing video games. it takes him 1/12hours to set up the system before he starts playing. This means that the time left for him to play games would be the time he has to play - the time it takes him to set up the video game. It becomes

3/4 - 1/12 = 8/12

If each round of his favorite game takes 1/6 hours, the number of rounds he can play would be the time he has left to play/time per round of his favorite game. It becomes

8/12 ÷ 1/6

= 8/12 × 6/1

= 4

3 0
3 years ago
A fifth grade teacher gives homework every night in both mathematics and language arts. The time to complete the mathematics hom
kherson [118]

Answer:

0.82% probability that the average time it takes to complete both homework assignments is greater than 82 minutes

Step-by-step explanation:

When the distribution is normal, we use 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.

Math homework:

\mu_M = 30, \sigma_M = 3

Arts homework:

\mu_A = 40, \sigma_A = 4

What is the probability that the average time it takes to complete both homework assignments is greater than 82 minutes?

Here, we have a sum of normal variables. The mean will be the sum of the means, while the standard deviation is the square root of the sum of the variances. So

\mu = \mu_M + \mu_A = 30 + 40 = 70

\sigma = \sqrt{\sigma_M^2 + \sigma_A^2} = \sqrt{3^2+4^2} = 5

This probability is 1 subtracted by the pvalue of Z when X = 82. So

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

Z = \frac{82 - 70}{5}

Z = 2.4

Z = 2.4 has a pvalue of 0.9918

1 - 0.9918 = 0.0082

0.82% probability that the average time it takes to complete both homework assignments is greater than 82 minutes

3 0
3 years ago
On Monday, stock XYZ opened at $8.84. On Friday, it closed at $10.12. What is the rate of change of stock XYZ for this particula
Elenna [48]

p = amount of change in price

p = (final amount) - (starting amount)

p = 10.12 - 8.84

p = 1.28

The stock increased by $1.28

Divide the value of p over the original amount 8.84

(amount of change)/(original amount) = p/8.84 = 1.28/8.84 = 0.144796

Convert 0.1447 to percent form to get 14.4796% which rounds to 14.5%

Unfortunately 14.5% isn't listed. I think your teacher made an typo when s/he made the problem.

7 0
3 years ago
Read 2 more answers
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