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2 years ago

Write a quadratic equation in STANDARD FORM given the roots: 1, 1/2

Mathematics

1 answer:

Zigmanuir [339]2 years ago

5 0

Answer:

f(x) = 2x^2 - 3x + 1

Step-by-step explanation:

The root 1 is associated with the factor (x - 1).

The root 1/2 is associated with the factor (x - 1/2), which in turn is equivalent to (2x -1)

The quadratic in question is f(x) = (x - 1)(2x - 1). To write this in standard form, perform the indicated multiplication:

f(x) = 2x^2 - 2x - x + 1, or f(x) = 2x^2 - 3x + 1

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PLEASE HELP IS THIS RIGHT??????????AND EXPLAIN PLZZ

Anit [1.1K]

Add like terms

-4x+x=-3x
6-2=4

So the simplified term is 4-3x

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3 years ago

Marina walks from the police station at (-10, -4) to her friend Marissa’s house at (3, -8). She stops half way at a fast food re

Volgvan

$\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ -10}}\quad ,&{{ -4}})\quad 
% (c,d)
&({{ 3}}\quad ,&{{ -8}})
\end{array}\qquad
% coordinates of midpoint 
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)
\\\\\\
\left( \cfrac{3-10}{2}~~,~~\cfrac{-8-4}{2} \right)$

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2 years ago

Solve the rational equation 1/n-4 - 2/n = 3/4-n

Leokris [45]

Answer:

n=4

Step-by-step explanation:

Given equation: \[\frac{1}{n-4}-\frac{2}{n}=\frac{3}{4-n}\]

Simplifying the Left Hand Side of the equation by taking the LCM of the denominator terms:

\[\frac{n}{n*(n-4)}-\frac{2*(n-4)}{n*(n-4)}=\frac{3}{4-n}\]

=> \[\frac{n - 2*(n-4)}{n*(n-4)}=\frac{3}{4-n}\]

=> \[\frac{n - 2n + 8}{n*(n-4)}=\frac{3}{4-n}\]

=> \[\frac{8 - n}{n*(n-4)}=\frac{3}{4-n}\]

=> \[(8-n)*(4-n) =n*(n-4)*3\]

=> \[n-8 =3n\]

=> \[2n =8\]

=> n = 4

5 0

3 years ago

The heights of dogs, in inches, in a city are normally distributed with a population standard deviation of 3 inches and an unkno

Nitella [24]

Answer: 1.2703

Step-by-step explanation:

Given : Sample size : n= 17, which is a small sample (n<30), so we use t-test.

Significance level : $\alpha:1-0.90=0.1$

Then , Critical value : $t_{n-1,\alpha/2}=t_{16, 0.05}\pm1.745884$

Standard deviation: $s=3\text{ inches}$

The formula to find the margin of error : -

$E=t_{n-1,\alpha/2}\dfrac{s}{\sqrt{n}}\\\\\Rightarrow\ E=(1.745884)\dfrac{3}{\sqrt{17}}\\\\\Rightarrow\ E=01.27031720154\approx1.2703$

Hence, the error bound (EBM) of the confidence interval with a 90% confidence level.=1.2703

6 0

2 years ago

Find the equation f(x) = a(x - h)2 + k for a parabola containing point (3, 6) and having (1, -2) as a vertex. What is the standa

nlexa [21]

f(x) = 2 $x^{2}$ -4x

Step-by-step explanation:

Step 1 :

Given, f(x) = a(x - h)2 + k

Point on the parabola is (3, 6)

Vertex (h,k) = (1,-2)

Step 2:

Substituting the vertex in the equation we have,

f(x) = a(x-1)2 -2

Substituting the point (3,6) in this we have,

6 = a(3-1)2 - 2 => 6 = 4a -2

=> 4a = 8 => a = 2

Step 3 :

Substituting the value for a and the vertex in the given equation we have

f(x) = 2(x-1)2 -2 = 2(x2 - 2x + 1) -2 = 2x2 - 4x

=> f(x) = 2 $x^{2}$ -4x which is the standard form

8 0

2 years ago