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3 years ago

Quadratic Functions: Standard Form

Mathematics

1 answer:

Anni [7]3 years ago

6 0

$f(x)=x^2+12x+11\\$

Find the x-intercept, f(x) = 0

$x^2+12x+11=0\\(x+11)(x+1)=0\\x=-11,-1$

There we get the x-intercepts, what about y-intercept? That's easy, (0,11). You don't even need to calculate to get the y-intercept as from

$f(x)=ax^2+bx+c$ (a=/0)

The y-intercept is "c" So if c = 2 then y-intercept is (0,2)

Or if you want to calculate for y-intercept.

then x=0

$f(0)=0^2+12(0)+11\\f(0)=0+0+11\\f(0)=11$

There, we get the y-intercept which is (0,11).

Therefore, x-intercepts are (-11,0) and (-1,0)

y-intercept is (0,11)

and yeah, you kinda of got it right.

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Box 1 contains 3 blue and 5 red balls, whereas Box 2 contains 2 blue and 4 red ball. A ball is randomly chosen from Box 1 and th

muminat

Answer:

0.32

Step-by-step explanation:

Let A be the event that the transferred ball was blue.

B be the event that the red ball is selected from box 2

C be the event that the transferred ball was red

Then:

P(A) be the probability that the transferred ball was blue, which is 3/8

P(C) be the probability that the transferred ball was red, which is 5/8

P(B|A) is the probability that selected ball is red, given that the transferred ball was blue, which is 4/7

P(B|C) is the probability that selected ball is red, given that the transferred ball was red, which is 5/7

P(B) is the probability that the selected ball is red, which there are 2 scenarios, given that the transferred ball is blue and red

P(B) = P(B|A)P(A) + P(B|C)P(C)

$P(B) = \frac{4}{7}\frac{3}{8} + \frac{5}{7}\frac{5}{8}$

$P(B) = \frac{3}{14} + \frac{25}{56} = \frac{37}{56}$

P(A|B) is the probability that the transferred ball was blue, given that a red ball is selected from Box 2, which can be solved using Bayes theorem

$P(A|B) = \frac{P(B|A)P(A)}{P(B)} = \frac{\frac{4}{7}*\frac{3}{8}}{\frac{37}{56}} = \frac{3}{14}\frac{56}{37} = \frac{12}{37} = 0.324$

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3 years ago

I would like help plz

Nuetrik [128]

the answer are b,d and e....

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3 years ago

Sheryl is choosing a briefcase. There are 6 leather cases, 8 vinyl cases, and 5 steel cases. How many choices for a briefcase do

Sedbober [7]

The answer would be 19...

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3 years ago

Read 2 more answers

A drone has an initial velocity of 38m/s. Five seconds later it reaches a velocity

timofeeve [1]

Answer:

The acceleration of the drone is 2.6 m/s²

Step-by-step explanation:

The acceleration is the rate at which the speed changes over time, therefore to solve this question we must divide the change of speed by the elapsed time in order to find the accelaration of the drone in that period. We have:

a = (Vf - Vi)/dt

Where a is the acceleration, Vf is the final velocity, Vi is the initial velocity and dt is the elapsed time. We have:

a = (51 - 38)/5 = 2.6 m/s²

7 0

3 years ago

((81x^3 y^(-1/3))^1/4)/(x^2 y)^1/4 simplify

malfutka [58]

$\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}
\\\\\\
\left.\qquad \qquad \right.\textit{negative exponents}\\\\
a^{-{ n}} \implies \cfrac{1}{a^{ n}}
\qquad \qquad
\cfrac{1}{a^{ n}}\implies a^{-{ n}}
\qquad \qquad 
a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\
-------------------------------\\\\$

$\bf \cfrac{\left( 81x^3y^{-\frac{1}{3}} \right)^{\frac{1}{4}}}{(x^2y)^{\frac{1}{4}}}\implies \cfrac{81^{\frac{1}{4}}x^{3\cdot {\frac{1}{4}}}y^{-\frac{1}{3}\cdot {\frac{1}{4}}}}{x^{2\cdot {\frac{1}{4}}}y^{\frac{1}{4}}}\implies
\cfrac{81^{\frac{1}{4}}x^{\frac{3}{4}}y^{-\frac{1}{12}}}{x^{\frac{2}{4}} y^{\frac{1}{4}}}$

$\bf \cfrac{81^{\frac{1}{4}}x^{\frac{3}{4}}x^{-\frac{2}{4}}}{ y^{\frac{1}{4}}y^{\frac{1}{12}}}\implies \cfrac{(3^4)^{\frac{1}{4}}x^{\frac{3}{4}-\frac{2}{4}}}{y^{\frac{1}{4}+\frac{1}{12}}}\implies \cfrac{3^{4\cdot \frac{1}{4}}x^{\frac{1}{4}}}{y^{\frac{4}{12}}}\implies \cfrac{3^{\frac{4}{4}}x^{\frac{1}{4}}}{y^{\frac{1}{3}}}
\\\\\\
\cfrac{3\sqrt[4]{x}}{\sqrt[3]{y}}$

7 0

3 years ago