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3 years ago

0.51 (1 repeating) as a fraction simplest form

1 answer:

4 0

Answer: 23/45

step-by-step explanation:
write out your equation equal to x
x = 0.51 with a repeating 1
count the repeating decimal (1) and multiply each sides of the equation by 10^1
10x = 5.11 with a repeating 1
9x = 4.6 subtract the first equation from the second
solve for x
x = 4.6/9
eliminate the 1 decimals by multiplying the numerator and denominator by 10^1
4.6/9 • 10/10 = 46/90
find the greatest common factor
46/2 / 90/2 = 23/45
the fraction is already simplified at 23/45
i hope this helps :)

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3 years ago

If y varies directly as x, and y is 18 when x is 5, which expression can be used to find the value of y when x is 11?

Rzqust [24]

Y=kx is the direct variation equation
First plug in the x, y values given to find K
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3 years ago

A long jumper lifts off 3 m after starting his run, and lands 6 m later. When he is 8 m from the start line, he is 5 cm above an

slega [8]

Answer:

The equation of the parabola that models the path of the long jumper through the air is $y = -x^{2}+12\cdot x -27$ .

Step-by-step explanation:

Mathematically, we know that parabolas are second-order polynomials and every second-order polynomials, also known as quadratic functions, can be constructed by knowing three different points of the curve. The standard form of the parabola is:

$y = a\cdot x^{2}+b\cdot x + c$

Where:

$x$ - Horizontal distance from the start line, measured in meters.

$y$ - Height of the long jumper, measured in meters.

$a$ , $b$ , $c$ - Polynomial constants, measured in $\frac{1}{m}$ , dimensionless and meters, respectively.

If we know that $(x_{1},y_{1}) = (3\,m, 0\,m)$ , $(x_{2},y_{2}) = (8\,m, 0.05\,m)$ and $(x_{3}, y_{3}) = (9\,m, 0\,m)$ , this system of linear equations is presented below:

$9\cdot a + 3\cdot b + c = 0$ (Eq. 1)

$81\cdot a + 9\cdot b + c = 0$ (Eq. 2)

$64\cdot a + 8\cdot b + c = 0.05$ (Eq. 3)

The coefficients of the polynomial are, respectively:

$a = -\frac{1}{100}$ , $b = \frac{3}{25}$ , $c = -\frac{27}{100}$

The equation of the parabola that models the path of the long jumper through the air is $y' = -\frac{1}{100}\cdot x^{2}+\frac{3}{25}\cdot x -\frac{27}{100}$ .

But we need $y$ measured in centimeters, then, we use the following conversion:

$y = 100\cdot y'$

Then, we get that:

$y = -x^{2}+12\cdot x -27$

Where $x$ and $y$ are measured in meters and centimeters, respectively.

The equation of the parabola that models the path of the long jumper through the air is $y = -x^{2}+12\cdot x -27$ .

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4 years ago

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