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Marizza181 [45]
2 years ago
12

On a coordinate plane, 2 exponential functions are shown. f (x) decreases from quadrant 2 to quadrant 1 and approaches y = 0. It

crosses the y-axis at (0, 4) and goes through (1, 2). g (x) increases from quadrant 3 into quadrant 4 and approaches y = 0. It crosses the y-axis at (0, negative 4) and goes through (1, negative 2).
Which function represents g(x), a reflection of f(x) = 4(one-half) Superscript x across the x-axis?

g(x) = −4(2)x
g(x) = 4(2)−x
g(x) = −4(one-half) Superscript x
g(x) = 4(one-half) Superscript negative x
Mathematics
1 answer:
aliina [53]2 years ago
3 0

Answer: -4\left(\frac{1}{2} \right)^{x}

Step-by-step explanation:

To reflect the graph of a function across the x-axis,

y=f(x) \longrightarrow y=-f(x)

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An opaque bag contains 5 green marbles 3 blue marbles and 2 red marbles. If a marble is drawn at random what are the odds of dra
melamori03 [73]

Answer:

Odds are 3 to 7

Step-by-step explanation:

The odds are defined as the probability that the event will occur divided by the probability that the event will not occur.

Let's find:

Probability of blue marble = 3/10 [ 3 blue and 10 in total]

Probabilty of NOT blue marble = 7/10 [7 marbles are red and green (not blue) and 10 in total]

Hence,

Odds of drawing a blue marble = \frac{\frac{3}{10}}{\frac{7}{10}}=\frac{3}{10}*\frac{10}{7}=\frac{3}{7}

The odds are 3 to 7

3 0
3 years ago
The gradient of the curve is given by the equation and a point on the curve is also given. Find the equation of the curve with w
IgorC [24]

Answer:

4 x^(3/2)         + 5x -32

Step-by-step explanation:

This problem involves definite integration (anti-derivatives).

If dy/dx = 6x^(1/2) - 5, then dy = 6x^(1/2)dx - 5dx.

                                        (1/2) + 1

This integrates to y = 6x                        

                                   ----------------                      

                                      (1/2) + 1             x^(3/2)

                                                      =  6 ------------ + C

                                                                 3/2

             

or:        4 x^(3/2) + C

and the ∫5dx term integrates to 5x + C.

The overall integral is:  

4 x^(3/2) + C + 5x + C. better expressed with just one C:

4 x^(3/2)         + 5x + C

We are told that the curve represented by  this function goes thru (4, 20).

This means that when x = 4, y = 20, and this info enables us to find the value of the constant of integration C:

20 = 4 · 4^(3/2)         + 5·4 + C, or:

20  =  4  (8)           + 20 + C

Then 0 = 32 + C, and so C = -32.

The equation of the curve is thus   4 x^(3/2)         + 5x -32

                   

           

                                      (1/2 + 1)

7 0
3 years ago
Benny grew 5 watermelons. Joan grew 2 watermelons. How many<br>watermelons did they grow in all ?​
Alenkinab [10]

Answer:Benny and Joan grew 7 watermelons Total

3 0
3 years ago
Read 2 more answers
In ΔKLM, the measure of ∠M=90°, the measure of ∠L=76°, and LM = 99 feet. Find the length of KL to the nearest tenth of a foot.
hram777 [196]

Answer:

The length of KL is 409.2 foot

Step-by-step explanation:

Firstly, please check attachment for diagrammatic representation.

From the diagram, we can see that we are asked to calculate the value of the hypotenuse KL. Kindly note that the hypotenuse is the longest side of the right-angled triangle and it faces the angle 90 at all times.

Looking at what we have, we can see that we have adjacent and we are asked to calculate hypotenuse.

The trigonometric identity to use here is the Cosine

Cosine = length of adjacent/length of hypotenuse

cos 76 = 99/hypotenuse

hypotenuse = 99/cos76

hypotenuse = 99/0.24192

hypotenuse = 409.22 which is 409.2 to the nearest tenth of a foot

7 0
3 years ago
find the equation of the linear function which passes through the points (1,-3) and (4,-2) give your answer in y=mx+b form
Tpy6a [65]
To solve this problem, we first have to find the slope of the two given points. To find the slope, we have to use slope intercept form, which is y₂ - y₁ divided by x₂ - x₁. We substitute each variable for its corresponding value, and we'll get -2 - (-3) divided by 4-1. If we simplify the expression, we'll get 1/3. Next, we plug in the slope and one ordered pair into the equation and we get -3 = 1/3 * 1 + b. We should solve for b and we end up with -3 1/3 = b. Therefore, the equation is y = 1/3x - 3 1/3.
5 0
3 years ago
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