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SpyIntel [72]
3 years ago
14

Given f (x) = 17 minus x squared, what is the average rate of change in f(x) over the interval [1, 5]?

Mathematics
2 answers:
PolarNik [594]3 years ago
8 0

Answer:

The average rate of change of the function over the given interval is -6

Step-by-step explanation:

The function we want to find its average rate of change is;

F(x) = 17 - x^2

Mathematically, the average rate of change of a function F(x) over an interval (a,b) can be calculated as;

{F(b) - F(a)}/(b-a)

According to this question, a = 1 and b = 5

F(a) = F(1) = 17 -(1)^2 = 17 -1 = 16

F(b) = F(5) = 17 - 5^2 = 17-25 = -8

So making the substitution; we have

(-8)-16/(5-1) = -24/4 = -6

Luda [366]3 years ago
8 0

Answer:

A: -6

Step-by-step explanation:

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In 1995, Hazel was 25 years older than her son Gary. In 2022, Hazel's age will be 150% of Gary's age. How old were they in 1995?
Kitty [74]
So find the difference between 1995 and 2022 to make it easier
2022-1995=27

so the rephrased question is
when hazel was x years old, she was 25 years older than son gary who was y old at that time (equation is x is 25 more than y or x=25+y)
in 27 years, (this means x+27 and y+27) hazel's age will be 150% of gary's age (x+27= 150% of y+27)
percent means parts out of 100  so 150%=150/100=15/10=1.5
'of' in math means multiply so
the equations are
x=25+y
x+27=1.5(y+27)
subsitute 25+y for x in second euation
25+y+27=1.5(y+27)
add like terms
y+52=1.5(y+27)
I personally dislike decimals to multiply both sides by 2 to make 2 0.5's or 1 (you are technically supposed to distribute or divide both sides by 1.5) so
2y+104=3(y+27)
distribute
2y+104=3y+81
subtract 2y from both sides
104=y+81
subtract 81 from both sides
23=y
subsitute
x=25+y
x=25+23
x=48


Hazel was 48 and Gary was 23 in the year of 1995
5 0
3 years ago
Find the equation of a line with slope 1/2 and y intercept -1
Mrac [35]
If you use slope-intercept form, Y =mx+b

m is equal to the slope,
and b is the y intercept.

Y= (1/2)x+ (-1)

or
Y = (1/2)x-1
4 0
3 years ago
Together, teammates Pedro and Ricky got 2682 base hits last season. Pedro had 282 more hits than Riley. How many hits did each p
pickupchik [31]

Pedro had 1482 hits and Riley had 1200 hits.

Step-by-step explanation:

Given,

Number of base hits = 2682

Let,

Number of Pedro's hits = x

Number of Riley's hits = y

According to given statement;

x+y=2682    Eqn 1

x = y+282    Eqn 2

Putting value of x from Eqn 2 in Eqn 1

(y+282)+y=2682\\y+282+y=2682\\2y=2682-282\\2y=2400

Dividing both sides by 2

\frac{2y}{2}=\frac{2400}{2}\\y=1200

Putting y=1200 in Eqn 2

x=1200+282\\x=1482

Pedro had 1482 hits and Riley had 1200 hits.

Keywords: linear equation, substitution method

Learn more about substitution method at:

  • brainly.com/question/9532142
  • brainly.com/question/9381080

#LearnwithBrainly

4 0
3 years ago
F(x) = 3x - 2x - 5<br><br> Factoring quadratics
bagirrra123 [75]

Answer:

(3x -5)(x+1)

Step-by-step explanation:

Factoring 3x^{2} -2x-5=0 results in (3x -5)(x+1)

4 0
2 years ago
10 boys share 7 cereal bars equally what fraction of the cereal bars does each boy get? show the work.
pochemuha

Answer:

1 43/100

Step-by-step explanation:

10 boys divide 7 cereal bars equally or

10 / 7 = 1.428571428571429

Or 1.43 rounded Or 1 43/100

7 0
3 years ago
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