Which ordered pair is the solution to the system of equations below? 4x+3y=31 2y=22-3x (A) (4,5) (B) (5,4) (C) (6,2) (D) (7,1)

Determine which function has the greatest rate of change over the interval [0, 2].

ruslelena [56]

Remember that the average rate of change of a function over an interval is the slope of the straight line connecting the end points of the interval. To find those slopes, we are going to use the slope formula: $m= \frac{y_{2}-y_{1}}{x_2-x_1}$

Rate of change of $a$ :
From the graph we can infer that the end points are (0,1) and (2,4). So lets use our slope formula to find the rate of change of $a$ :
$m= \frac{y_{2}-y_{1}}{x_2-x_1}$
$m= \frac{4-1}{2-0}$
$m= \frac{3}{2}$
$m=1.5$
The average rate of change of the function $a$ over the interval [0,2] is 1.5

Rate of change of $b$ :
Here the end points are (0,0) and (2,2)
$m= \frac{2-0}{2-0}$
$m= \frac{2}{2}$
$m=1$
The average rate of change of the function $b$ over the interval [0,2] is 1

Rate of change of $c$ :
Here the end points are (0,-1) and (2,0)
$m= \frac{0-(-1)}{2-0}$
$m= \frac{1}{2}$
$m=0.5$
The average rate of change of the function $c$ over the interval [0,2] is 0.5

Rate of change of $d$ :
Here the end points are (0,0.5) and (2,2.5)
$m= \frac{2.5-0.5}{2-0}$
$m= \frac{2}{2}$
$m=1$
The average rate of change of the function $d$ over the interval [0,2] is 1

We can conclude that the <span>function that has the greatest rate of change over the interval [0, 2] is the function a.</span>

4 0

2 years ago

A map has a scale of 2 inches : 12 miles. Two cities on the map are 6.5 inches apart. Find the actual distance between the two c

almond37 [142]

Answer:

39

Step-by-step explanation:

2in:12m = 6.5in:?m

6.5 / 2 = 3.25

3.25 x 12

39

6 0

1 year ago

Square root of 22801 by long division method

mezya [45]

First step: partition the number you want to square root into a block of 2 digits, starting from the last digit (first diagram)

Second step: As our number is a five-digits, we ends up with 2 28 01. Pick a number that could be squared to get the first partition, 2. This number is 1, since 1×1=1

Third step: Write 1 on the top and on the side, as shown in the second graph

Fourth step: Double the number on the side, which is 1+1=2 and use this number as the first digit for the next multiplier. Meanwhile, subtract 1 from 2 inside the root sign to get 1, then pull the other two digits, 28

Fifth step: We need a value in the boxes that when we multiply together will give a number less than 128. We choose 5 as 25×5=125

Sixth step: Subtract 125 from 128 to give 3, and as the same concept with long division, bring down the 0 and the 1. So we have 301

Seventh step: Add 5 to the multiplier on the left, so 20+5=30, which we will use on the side as the hundred and ten digits.

Final step: Find a number to fit in the boxes. We choose 1 since 301×1=301

And hence the square root of 228801 is 151

3 0

2 years ago

If someone can help me with this question please?

Katyanochek1 [597]

9514 1404 393

Explanation:

The three Reasons tell you what to look for to put in the Statement blank.

1. We are given that RE = 2AR and RT = 2GR.

2. The only vertical angles in the figure are ...

∠GRA ≅ ∠TRE

3. Using the given relation between the sides, we can write the proportion ...

RE/RA = RT/RG = 2

It is nice, though maybe not absolutely essential, to write the segment names in order of corresponding vertices.

4. Having shown that two sides are proportional and the angle between them is congruent, we can claim similarity using the SAS Theorem.

8 0

2 years ago

Which of the following functions is graphed below?

Vladimir [108]

Answer:

Step-by-step explanation:

The answer is D because the parabola is an empty circle and is positive which would mean its greater than 1 and the line has a solid point and is negative which means less than or equal to.

5 0

2 years ago