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vivado [14]
4 years ago
8

Which of the following equations is perpendicular to y = 2x + 5 and passes through the point (4 , 6)? A. y = – 1 2x + 8 B. y = 2

x + 8 C. y = – 1 2x – 2 D. y = 2x – 2
Mathematics
1 answer:
MrMuchimi4 years ago
5 0

Answer:

The equation would be y = -1/2x + 8

Step-by-step explanation:

To find the equation of the line, we start by find the slope. Perpendicular slopes have opposite and reciprocal slopes. since the original slope is 2, then the perpendicular slope is -1/2.

Now, using the point and the slope in point-slope form, we can find the equation.

y - y1 = m(x - x1)

y - 6 = -1/2(x - 4)

y - 6 = -1/2x + 2

y = -1/2x + 8


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Inverse Function In Exercise,analytically show that the functions are inverse functions.Then use the graphing utility to show th
DanielleElmas [232]

Answer:

g^{-1}(x)=f(x)=e^{\frac{x}{3}}

Step-by-step explanation:

We have been given two functions as g(x)=\text{ln}(x^3) and f(x)=e^{\frac{x}{3}}. We are asked to show that both functions are inverse of each other algebraically and graphically.

Let us find inverse function of g(x)=\text{ln}(x^3) as:

y=\text{ln}(x^3)

Interchange x and y values:

x=\text{ln}(y^3)

Using log property \text{ln}(a^b)=b\cdot \text{ln}(a), we will get:

x=3\cdot \text{ln}(y)

\frac{x}{3}=\frac{3\cdot \text{ln}(y)}{3}

\frac{x}{3}=\text{ln}(y)

Using log definition; If \text{log}_a(b)=c, then b=a^c, we will get:

y=e^{\frac{x}{3}}

g^{-1}(x)=e^{\frac{x}{3}}

Therefore, we can see that function f(x)=e^{\frac{x}{3}} is inverse of function g(x)=\text{ln}(x^3).

We can see that both functions are symmetric about line y=x, therefore, both functions are inverse of each other.  

8 0
4 years ago
Anna has 3 3/4 cups of yogurt to make smoothies. Each smoothie uses 1/3 cup of yogurt. What is the maximum number of smoothies t
KiRa [710]
Turn 3 3/4 into an improper fraction, so it becomes 15/4. Then divide 15/4 by 1/3. Which would just be to multiple by the reciprocal, 15/4 times 3/1, to get 11 1/4, and since 1/4 is smaller than 1/3 the maximum number of smoothies is 11
4 0
3 years ago
A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance travelled on 1 gallon of fuel is
Darya [45]

Answer:

15.87% probability that the car travels more than 53 miles per gallon.

Step-by-step explanation:

Problems of normally distributed samples are 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 = 45, \sigma = 8

Find the probability of the following events: A. The car travels more than 53 miles per gallon. Probability

This is the pvalue of Z when X = 53. So

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

Z = \frac{53 - 45}{8}

Z = 1

Z = 1 has a pvalue of 0.8413

1 - 0.8413 = 0.1587

15.87% probability that the car travels more than 53 miles per gallon.

5 0
3 years ago
what is the measure of PLEASE HELP GIVING 50 POINTS!! <br><br> OPTIONS: <br> 90<br> 37<br> 143<br> 127
sineoko [7]

Answer:

Step-by-step explanation:

La answer es porque esa la respuesta 34 c  d #7 B = 9 37 134 127 la = 292-238 lan Angels Hope En help : )

6 0
3 years ago
Read 2 more answers
53 26 11 35 16 61 47 39 50 46 58 10 <br> what is the mean average
bonufazy [111]

Answer:

37.66

Step-by-step explanation:

7 0
4 years ago
Read 2 more answers
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