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Lelechka [254]
3 years ago
7

Given the function graphed below, what is the average rate of change between f(3) and f(7)?

Mathematics
1 answer:
Shkiper50 [21]3 years ago
6 0
Answer: choice D) 20

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

Explanation:

Locate 3 on the x axis number line. Draw a vertical line through 3 and this vertical line will cross the parabola at some point P. Mark this point P on the parabola. Then draw a horizontal line from P to the y axis. The horizontal line will land on y = 10. In short, this all shows us that (3,10) is a point on this parabola.

Repeat those steps above, but now for x = 7. You'll see that (7,90) is another point on this parabola.

We need to find the slope of the line through the two points (3,10) and (7,90). The average rate of change from x = 3 to x = 7 is the same as the slope of the line through those two points.

To find the slope, we use the slope formula
m = (y2 - y1)/(x2 - x1)
where (x1,y1) and (x2,y2) are the two points, and m is the slope

In this case,
(x1,y1) = (3,10) and (x2,y2) = (7,90)
further breaking down to
x1=3
y1=10
x2=7
y2=90
So we'll plug those four pieces of info into the equation and simplifying to get...
m = (y2 - y1)/(x2 - x1)
m = (90 - 10)/(7 - 3)
m = 80/4
m = 20

The slope of the line is 20, so therefore, the average rate of change is 20.

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Craig has a building block in the shape of a rectangular pyramid. A net of which is shown below.
Alex787 [66]

Answer:

the answer is D: 294 sq. cm

Step-by-step explanation:

first you want to split the net into 4 triangles and 1 rectangle

a = 12 cm

b =  6 cm

d = 13 cm

calculate the surface area of the pyramid...

1st find the area of the rectangle base

Rectangle base area

b x a = (6 cm) (12 cm)

= 72 sq. cm

next find the area of the triangle on the left

Left triangle

1/2(b)(d) = 1/2 (6 cm)(13 cm)

= 1/2 (78 sq cm)

= 39 sq. cm

Since all the triangles are congruent (same), you will need to multiply by 2 to get the combined area of the triangle on the left and on the right.

Area of left & right triangles

= 2 (39 sq. cm)

= 78 sq. cm

Find the area of the triangle on the bottom

Bottom triangle area = 1/2 (a)(a)

= 1/2 (12 cm) (12 cm)

= 1/2 (144 sq. cm)

= 72 sq. cm

Since the bottom of the triangle is congruent to the top triangle, multiply that by 2 to get a combined area of the triangle on the bottom and top

Area of top & bottom triangles

2 (72 sq. cm) = 144 sq. cm

Finally...add the area of the 4 triangles to the area of the rectangular base

72 + 78 + 144 = 294 sq. cm

3 0
3 years ago
For any integers x and y ,|x+y|=|x|+|y| Ture or False
Nutka1998 [239]

Answer:

yes because |x+y|=|x|+|y| is just the same equation just splitting the numbers

They both are the same absolute value equation

Step-by-step explanation:

|x+y|=|x|+|y|

x+y=|x|+|y|

x+y=x+y

7 0
3 years ago
A kilogram of seawater contains 1/40 kg of salt. How much salt is there in two buckets of seawater, which contain 500 liters of
never [62]

Two buckets of seawater contain 13\frac{28}{40} kg of salt.

Step-by-step explanation:

Amount of salt in 1 kg water = \frac{1}{40}\ kg

It is given that;

1 liter = 1\frac{12}{125} = \frac{137}{125}\ kg

500 liters = 500*\frac{137}{125} = \frac{68500}{125}

500 liters = 548 kilogram

As,

1 kg of seawater = \frac{1}{40}\ kg of salt

548 kilograms = \frac{1}{40}*548

548 kilograms = 13\frac{28}{40} kilograms of salt

Two buckets of seawater contain 13\frac{28}{40} kg of salt.

Keywords: unit rate, multiplication

Learn more about multiplication at:

  • brainly.com/question/10525991
  • brainly.com/question/10534381

#LearnwithBrainly

5 0
3 years ago
A rocket is launched from the top of a 90 foot cliff with an initial velocity of 140 feet per second. The height, h, of the rock
erastovalidia [21]
H=140s+90 s is seconds
7 0
3 years ago
Which inequality is represented by this graph?
erastovalidia [21]

Answer:the last one I’m not really sure

8 0
3 years ago
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