Maria is going for a walk. She walks 6.4 miles in four hours. What is her speed?

Mathematics

1 answer:

borishaifa [10]3 years ago

3 0

Answer:

Hello,

1.6 mile by hour

Step-by-step explanation:

$\frac{6.4}{4} = 1.6$

1.6 mile in one hour

3.2 miles in two hours

6.4 miles in four hours

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Find the vertical, horizontal, and slant asymptotes, if any, for f(x)=5x^3-51x^2+77x+100/x^2-11x+24

liraira [26]

Answer:

Step-by-step explanation:

Given: f(x)=5x^3-51x^2+77x+100/x^2-11x+24

Please use parentheses to eliminate any ambiguity:

f(x) = (5x^3-51x^2+77x+100) / (x^2 - 11x + 24)

or (better yet):

5x^3-51x^2+77x+100

f(x) = ---------------------------------

x^2 - 11x + 24

The vertical asymptotes here are at the zeros of the denominator:

x^2 - 11x + 24 = 0, This quadratic equation has coefficients a = 1, b = -11 and c = 24. Thus, its roots (zeros) are:

-(-11) ± √( 121 - 4(1)(24) )

x = -------------------------------------

2(1)

or:

11 ± √( 25 )

x = --------------------

or: x = 8 and x = 3

The vertical asymptotes are x = 8 and x = 3.

If we attempt to divide x^2 - 11x + 24 into 5x^3 - 51x^2 + 77x + 100, we see that the first term of the quotient is 5x. As x increases or decreases without bound, 5x goes to either ∞ or -∞, so we conclude that there is no horiz. asymptote. Continuing this division results in:

5x + 4 + a fraction

This represents the slant asymptote, y = 5x + 4

7 0

3 years ago

Evaluate 8a+3b-10+c^2when a =2,b=5,and c=4

trasher [3.6K]

8a+3b-10+c^2when a =2,b=5,and c=4:

(8)(2)+(3)(5)−10+42

=16+(3)(5)−10+42

=16+15−10+42

=31−10+42

=21+42

=21+16

=37

3 0

4 years ago

Read 2 more answers

Please state the function for the corresponding data set

Lana71 [14]

Given:
x: [1 2 3 4 5 6 7]
y: [9 9.5 10.25 11.25 12.5 14 15.75]

Let the function which models the data be
y(x) = ax² + bx + c

Apply the function to the first three data points
a + b + c = 9 .(1)
4a + 2b + c = 9.5 (2)
9a + 3b + c = 10.25 (3)

Subtract (1) from (2).
3a + b = 0.5
or
b = 0.5 - 3a (4)
Subtract (1) from (3).
8a + 2b = 1.25 (5)
Substitute (4) into (5).
8a + 2(0.5 - 3a) = 1.25
2a = 0.25
a = 0.125
From (4),
b = 0.5-3*0.125 = 0.125
From (1),
c = 9 - 0.125 - 0.125 = 8.75

The function is
y = 8.75 + 0.125x + 0.125x²

Check that the function works for x=4,5,6,7.
From the calculator, obtain
y(4) = 11.25 Correct
y(5) = 12.5 Correct
y(6) = 14 Correct
y(7) = 15.75 Correct

The graph of the function is shown below.

Answer: y = 8.75 + 0.125x + 0.125x²