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Ne4ueva [31]
2 years ago
6

The table below shows points that are on the graph of the function h(x). 0 1 2 3 4 5 h(2) 2 5 8 11 14 17 Select the point that i

s on the graph of the inverse function h-'(x). А (1, - 1) B (2,0) С (3,11) D (4, 10)​
Mathematics
1 answer:
sukhopar [10]2 years ago
7 0

9514 1404 393

Answer:

  B.  (2, 0)

Step-by-step explanation:

We understand the points on the graph of h(x) to be ...

  (0, 2), (1, 5), (2, 8), (3, 11), (4, 14), (5, 17)

The points on the graph of the inverse function will have the x- and y-coordinates reversed:

  (2, 0), (5, 1), (8, 2), (11, 3), (14, 4), (17, 5)

The one that appears among the answer choices is ...

  (2, 0)

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Excursion boat on the river takes 2 1/2 hours to make the trip to a point 12 miles upstream and to return if the rate at which t
Mama L [17]

Answer:

Let the current speed be "c";

Then the boat speed in still wate is "5c":

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

Upstream speed:

distance = 12 miles ; rate = 5c-c = 4c mph ; time = 12/4c = 3/c hrs

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

Downstream speed:

distance = 12 miles ; rate = 5c+c = 6c mph ; time = 12/6c = 2/c hrs

Step-by-step explanation:

Equation:

time + time = 2 1/2 hrs

3/c + 2/c = 5/2

Multiply thru by 2c to get:

6 + 4 = 5c

c = 2 mph (speed of the current)

5c = 10 mph (speed of the boat in still water)

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2 years ago
!Extremely Urgent!
ira [324]

Answer:

B. slope: 3/2, y-intercept: 5

Step-by-step explanation:

Rewrite in slope-intercept form. The slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

3 0
3 years ago
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siniylev [52]

Answer:

b

Step-by-step explanation:

7 0
3 years ago
How many sets of three consecutive integers are there in which the sum of the three integers equals their product?
skad [1K]

Answer:

3

Step-by-step explanation:

since the 3 integers are consecutive, we are dealing with x, x+1, x+2.

and their sum is the same as their product :

x + (x + 1) + (x + 2) = x(x + 1)(x + 2)

3x + 3 = x(x² + 3x + 2) = x³ + 3x² + 2x

x³ + 3x² - x - 3 = 0

this is a polynomial of third degree.

and as such it has 3 solutions.

of course, it could be that some of them are the same or are even in the realm of complex numbers (i = sqrt(-1)), but usually these 3 solutions are different real numbers.

I tried x=1 just to see, and, hey, it is a solution for this equation.

x = 1 means that the other 2 consecutive integers are 2 and 3.

and indeed, 1+2+3 = 1×2×3 = 6.

now it is easier to find the other 2 solutions, as a zero solution can be expressed as a factor of the whole expression.

for x = 1 the factor term is (x - 1), as this term is then turning 0, when x = 1.

I can divide the main expression by this factor and then analyze the quotient about the other 2 solutions.

x³ + 3x² - x - 3 : x - 1 = x² + 4x + 3

- x³ - x²

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

0 4x² - x

- 4x² - 4x

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

0 + 3x - 3

- 3x - 3

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

0 0

so, the original expression can be written as

(x² + 4x + 3)(x - 1).

now we need to find the 2 zero solutions for x²+4x+3

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 4

c = 3

so,

x = (-4 ± sqrt(4² - 4×1×3))/(2×1) =

= (-4 ± sqrt(16 - 12))/2 = (-4 ± sqrt(4))/2 =

= (-4 ± 2)/2 = -2 ± 1

x1 = -2 + 1 = -1

x2 = -2 - 1 = -3

so, we have the additional solutions :

-1 0 1

-3 -2 -1

-1 + 0 + 1 = -1×0×1 = 0

-3 + -2 + -1 = -3×-2×-1 = -6

and there we have it fully proven :

there are 3 different sets of 3 consecutive integers with the same sum as product.

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2 years ago
224 fl oz equals how many gallons
Eddi Din [679]
1.75 google got you
3 0
3 years ago
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