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2 years ago

A triangle has three different integer side lengths and a perimeter of 20 units. What is the max length of any one side?

1 answer:

3 0

X + x+1 + x + 2 = 20
3x + 3 = 20
3x = 17 but can't start with x = 6 because 6+7+8 > 20,
so have start with 5 + 6 + 7 = 18 are the 3 sides.

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Help! What is the average rate of change of f(x)=x^2+3x+6 over the interval -3 less-than-or-equal-to x less-than-or-equal-to 3?

Makovka662 [10]

Answer:

The average rate of change of the function over the interval is 5.

Step-by-step explanation:

Average rate of change of a function:

The average rate of change of a function f(x) over an interval [a,b] is given by:

$A = \frac{f(b)-f(a)}{b-a}$

Interval -3 less-than-or-equal-to x less-than-or-equal-to 3

This means that $a = -3, b = 3$

$f(x) = x^2 + 3x + 6$

$f(b) = f(3) = (3)^2 + 3(3) + 6 = 9 + 9 + 6 = 24$

$f(a) = f(-3) = (-3)^2 + 3(-3) + 6 = 9 - 9 + 6 = 6$

Average rate of change

$A = \frac{f(b)-f(a)}{b-a} = \frac{24+6}{3-(-3)} = \frac{30}{6} = 5$

The average rate of change of the function over the interval is 5.

8 0

2 years ago

Mrs. Gomes found that 40% of students at her high school take chemistry. She randomly surveys 12 students. What is the probabili

VMariaS [17]

Binomial formula is :
$P ( k = 4 ) = nCk * p ^{k}(1-p) ^{n}= \\ =495 * 0.4 ^{4}* ( 0.6 ) ^{8}=$
= 495 * 0.0256 * 0.0167961 =
= 0.21284 ≈ 0.213
Answer: C ) 0.213

3 0

3 years ago

Read 2 more answers

Which graph shows the solution to the system of linear inequalities? x – 4y < 4 y < x + 1 Image for option 1 Image for opt

slava [35]

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

$x-4y$ ----> inequality A

solve for y

$-4y$

$4y>x-4$

$y> (x/4)-1$

The solution of the inequality A is the shaded area above the dashed line

The slope of the dashed line is positive

The y-intercept is the point $(0,-1)$

The x-intercept is the point $(4,0)$

$y< x+1$ ----> inequality B

The solution of the inequality B is the shaded area below the dashed line

The slope of the dashed line is positive

The y-intercept is the point $(0,1)$

The x-intercept is the point $(-1,0)$

Using a graphing tool

The solution of the system of inequalities in the attached figure

7 0

3 years ago

ZC and ZD are vertical angles with mZC = -3x+58 and mZD= x - 2.

kogti [31]

Answer:

×=-2

0=×-2

×=-2

33333333

3 0

2 years ago

Given f(x) 2^x -7 find the x intercepts

brilliants [131]

Be sure to include the "=" sign: <span>f(x) = 2^x -7

To find the x-intercepts, set f(x) = 0 and solve for x: 2^x - 7 = 0,
or
2^x = 7

Take the common log of both sides: x log 2 = log 7
log 7
Solve for x: x = --------- = 2.81 (approx)
log 2

</span>

7 0

2 years ago