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Komok [63]
3 years ago
13

Which of the following graphs represents a proportional relationship?

Mathematics
1 answer:
topjm [15]3 years ago
4 0
The graph that is proportional is B because it goes through the origin and the ratio remains the same.
You might be interested in
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.

4 0
2 years ago
I need help on this problem!!! please help!!! ​
MA_775_DIABLO [31]
(0.1x-22)+(0.3x-54)=90

First combine like terms

0.4x - 76 = 90

Now add 76 on both sides

0.4x = 166

Divide by 0.4 on each side to isolate x

X= 415
7 0
3 years ago
A) Let f(x) = 4x + 2 and g(x) = 2x^2-4. Find the formula for the composition function gof
ollegr [7]

Answer:

g o f = g(f(x)) = 32x^2 + 32x + 4

Step-by-step explanation:

Given

f(x) = 4x +2

g(x) =2x^2 - 4

Required:

Find g o f

This is calculated as:

gof = g(f(x))

g(x) =2x^2 - 4

So:

g(f(x)) = 2(4x+2)^2 - 4

g(f(x)) = 2(4x+2)(4x+2) - 4

g(f(x)) = 2[ 16x^2 + 16x + 4)] - 4

g(f(x)) = 32x^2 + 32x + 8 - 4

g(f(x)) = 32x^2 + 32x + 4

5 0
3 years ago
The graph shows the amount of money paid when purchasing bags of peanuts at the zoo:
I am Lyosha [343]

Answer:

$4

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Help PLEASE (look at picture)
elena-14-01-66 [18.8K]

Answer:

16

Step-by-step explanation:

So for QR is 1-(-3)=4

QT:|-2-2|=4

TS: |-2-(-2)|=4

RS: 2-(-2)=4

and they plus together is 4x

4x4 = 16

I hope this helps, have a blessed day. :D

6 0
1 year ago
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