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3 years ago

Who can answer this for me please

Mathematics

1 answer:

melamori03 [73]3 years ago

8 0

Answer:

Step-by-step explanation:

<u>Values of a function from a graph</u>

The graph of a function is usually a drawn line that joins a number of points that correspond to the ordered pairs (x,y), where x is a given value, and y is the value calculated through the rule of the function, usually a formula or equation.

If we want to know the value for a specific value of x, we find the corresponding x-coordinate, draw an imaginary vertical line until we meet the graph. The value of y at that point is the required value of the function.

For example, for x=0 the graph crosses the y-axis at y=2, thus the ordered pair is (0,2), and f(0)=2.

For x=2, the function has a value of y=-2, thus:

f(2)=-2

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An archaeologist is categorizing the artifacts he has discovered. Two-thirds of the artifacts are shards of pottery. One-eighth

Reika [66]

Answer:

Personal items=15

Step-by-step explanation:

We are given:

Total number of artifacts = 72.

We are told that 2/3 of total artifacts are shards of pottery.

$\text{Shards of pottery}=72*\frac{2}{3} =24*2=48$

We are also told that 1/8 of total artifacts are tools.

$\text{Tools}=72*\frac{1}{8}=9$

Now we will find out number of personal items by subtracting combined number of shards of pottery and tools from total number of artifacts.

$\text{ Personal items}=72-(48+9)$

$\text{ Personal items}=72-57=15$

Therefore, there are 15 personal items.

8 0

4 years ago

The number of miles that a commuter travels a car per day for one seven day work week is as follows: 19, 28, 17, 39, 22, 44, 56.

Aloiza [94]

Car:
19 + 28 +17 +39 + 22 + 44 + 56 = 225
225/7 = 32.14

bus:
32 + 26 +25 + 40 + 39 + 49 + 22 = 233
233/7 = 33.29

the bus has the higher average

4 0

3 years ago

Write a linear function $f$ with the values $f(0)=8$ and $\ f(4)=20$ .

lawyer [7]

Answer:

f(x) = 3x + 8 is the required linear function.

Step-by-step explanation:

We know that the slope-intercept form of linear equation is

y = mx+b

here

m is the slope of the line, and

b is the y-intercept

Given initial value

f(0) = 8

Meaning at x = 0, y = 8

Thus, the y-intercept = b = 8

Also given

at x = 4, f(4) = 20

Meaning at x=4, y = 20

substituting the point (4, 20) and y-intercept b=8 in the slope-intercept form to determine the slope

y = mx+b

20 = m(4) + 8

20 = 4m + 8

4m = 20-8

4m = 12

Dividing both sides by 4

m = 3

Thus, the slope = m = 3

Now, substituting m = 3 and b = 8 in the slope-intercept of linear function

y = mx+b

y = 3x + 8

f(x) = 3x + 8

Thus,

f(x) = 3x + 8 is the required linear function.

VERIFICATION:

Given the linear function

f(x) = 3x + 8

plug in x = 0

f(0) = 3(0) + 8

f(0) = 8

plug in x = 4

f(x) = 3x + 8

f(4) = 3(4) + 8

f(4) = 12+8

f(4) = 20

8 0

3 years ago

Circle two addends to add first. write the sum 7,3,3

Hitman42 [59]

7 + 3 = 10 those are the 2 addens

4 0

4 years ago

A right circular cone is undergoing a transformation in such a way that the radius of the cone is increasing at a rate of 1/2 in

Ivenika [448]

Answer:

The volume is decreasing at the rate of 1.396 cubic inches per minute

Step-by-step explanation:

Given

Shape: Cone

$\frac{dr}{dt} =\frac{1}{2}$ --- rate of the radius

$\frac{dh}{dt} =-\frac{1}{3}$ --- rate of the height

$r = 2$

$h = \frac{1}{3}$

Required

Determine the rate of change of the cone volume

The volume of a cone is:

$V = \frac{\pi}{3}r^2h$

Differentiate with respect to time (t)

$\frac{dV}{dt} = \frac{\pi}{3}(2rh \frac{dr}{dt} + r^2 \frac{dh}{dt})$

Substitute values for the known variables

$\frac{dV}{dt} = \frac{\pi}{3}(2*2*\frac{1}{3}* \frac{1}{2} - 2^2 *\frac{1}{3})$

$\frac{dV}{dt} = \frac{\pi}{3}(\frac{4}{3}* \frac{1}{2} - \frac{4}{3})$

$\frac{dV}{dt} = \frac{\pi}{3}(\frac{4}{3}(\frac{1}{2} - 1))$

$\frac{dV}{dt} = \frac{\pi}{3}(\frac{4}{3}*- 1)$

$\frac{dV}{dt} = -\frac{\pi}{3}*\frac{4}{3}$

$\frac{dV}{dt} = -\frac{22}{7*3}*\frac{4}{3}$

$\frac{dV}{dt} = -\frac{22}{21}*\frac{4}{3}$

$\frac{dV}{dt} = -\frac{88}{63}$

$\frac{dV}{dt} =-1.396in^3/min$

The volume is decreasing at the rate of 1.396 cubic inches per minute

3 0

3 years ago