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DanielleElmas [232]
3 years ago
9

Write the quadratic equation in standard form. What is the value of b 2 - 4ac? 1 = 2x 2 + 7x 40 41 57

Mathematics
2 answers:
ella [17]3 years ago
5 0

Answer:

2x^2+7x-1=0

the value of b^2-4ac is 57

Step-by-step explanation:

1 = 2x^2 + 7x

Standard form of a quadratic equation is ax^2+bx+c=0

Subtract 1 on both sides to get the standard form of the equation.

2x^2+7x-1=0

Now we find the value of b^2-4ac

From the standard form, the value of a=2, b=7, c=-1

the value of b^2-4ac=(7)^2-4(2)(-1)=49+8=57

the value of b^2-4ac is 57

Likurg_2 [28]3 years ago
3 0
Hello : 
2x² +7x +1
a=2        b = 7      c =1
b²-4ac = (7)²-4(2)(1) =49 -8 =41
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2 years ago
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3 years ago
Using the scale of 5 cm: 25 m, find the actual length of the parking lot. Be sure to include units.
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Suppose X, Y, and Z are random variables with the joint density function f(x, y, z) = Ce−(0.5x + 0.2y + 0.1z) if x ≥ 0, y ≥ 0, z
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a.

f_{X,Y,Z}(x,y,z)=\begin{cases}Ce^{-(0.5x+0.2y+0.1z)}&\text{for }x\ge0,y\ge0,z\ge0\\0&\text{otherwise}\end{cases}

is a proper joint density function if, over its support, f is non-negative and the integral of f is 1. The first condition is easily met as long as C\ge0. To meet the second condition, we require

\displaystyle\int_0^\infty\int_0^\infty\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz=100C=1\implies \boxed{C=0.01}

b. Find the marginal joint density of X and Y by integrating the joint density with respect to z:

f_{X,Y}(x,y)=\displaystyle\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dz=0.01e^{-(0.5x+0.2y)}\int_0^\infty e^{-0.1z}\,\mathrm dz

\implies f_{X,Y}(x,y)=\begin{cases}0.1e^{-(0.5x+0.2y)}&\text{for }x\ge0,y\ge0\\0&\text{otherwise}\end{cases}

Then

\displaystyle P(X\le1.375,Y\le1.5)=\int_0^{1.5}\int_0^{1.375}f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy

\approx\boxed{0.12886}

c. This probability can be found by simply integrating the joint density:

\displaystyle P(X\le1.375,Y\le1.5,Z\le1)=\int_0^1\int_0^{1.5}\int_0^{1.375}f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz

\approx\boxed{0.012262}

7 0
3 years ago
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