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4 years ago

1) Find the length of point A(-3,1) and B(2,6). Leave your answer in RADICAL FORM ONLY.

Mathematics

1 answer:

elena-14-01-66 [18.8K]4 years ago

7 0

Answer: The length of point A(-3,1) and B(2,6) is $5\sqrt{2}\text{ units}$ .

Step-by-step explanation:

We know that the distance between the two points (a,b) and (c,d) is given by :-

$d=\sqrt{(a-c)^2+(b-d)^2}$

Given points = A(-3,1) and B(2,6)

Therefore the distance between the points A(-3,1) and B(2,6) is given by :-

$d=\sqrt{(-3-2)^2+(1-6)^2}\\\\\Rightarrow\ d=\sqrt{(-5)^2+(-5)^2}\\\\\Rightarrow\ d=\sqrt{25+25}\\\\\Rightarrow\ d=\sqrt{50}\\\\\Rightarrow\ d=\sqrt{25\times2}\\\\\Rightarrow\ d=\sqrt{5^2\times2}\\\\\Rightarrow\ d=5\sqrt{2}\text{ units}$

Hence, the length of point A(-3,1) and B(2,6) is $5\sqrt{2}\text{ units}$ .

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Hello,

A: roots: -1,-3
a point (-2,1)
Vertex=((-2,1)

y=k*(x+1)(x+3) using roots
but k*(-2+1)(-2+3)=1==>k*(-1)*1=1==>k=-1

eq: y=-(x+1)(x+3)
==>y=-(x²+3x+x+3)
==>y=-x²-4x-3
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==>y=-(x+2)²+1

Answer :A--> R,K

B)
y=k(x+4)²-2 and k=-1/2
y=-1/2(x+4)²-2
y=-1/2x²-4x-10

answer B--> I,≈W if it is written -1/2*x² (square has been forgotten)

C:
y=2x²-16x+30
y=2(x-4)²-2
answer : C-->S,J

D:
y=-(x+3)(x+1)
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answer D--> V,L

E:
Here there is a problem: or the graph is wrong, or 2 equations are missing!

y=1(x+1)(x-3) using roots
y=x²-2x-3 ≈ T si it were -2x and not +2x.

y=(x-1)²-4 ≈H is it were -1 in place of +1 [H:y=(x+1)²-4]

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A circle is inscribed in a square. A point in the figure is selected at random. Find the probability that the point will be in t

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P of selecting point on the shaded region = shaded area/whole area
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P of selecting point on the shaded = ( 4 * ( π * x^2/16 ) )/ x^2 
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P of selecting point on the shaded = x^2( π/4 )/ x^2 
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4 years ago

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Step-by-step explanation:

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3 years ago

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According to an NRF survey conducted by BIGresearch, the average family spends about $237 on electronics (computers, cell phones

Usimov [2.4K]

Answer:

(a) Probability that a family of a returning college student spend less than $150 on back-to-college electronics is 0.0537.

(b) Probability that a family of a returning college student spend more than $390 on back-to-college electronics is 0.0023.

(c) Probability that a family of a returning college student spend between $120 and $175 on back-to-college electronics is 0.1101.

Step-by-step explanation:

We are given that according to an NRF survey conducted by BIG research, the average family spends about $237 on electronics in back-to-college spending per student.

Suppose back-to-college family spending on electronics is normally distributed with a standard deviation of $54.

Let X = back-to-college family spending on electronics

SO, X ~ Normal( $\mu=237,\sigma^{2} =54^{2}$ )

The z score probability distribution for normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean family spending = $237

$\sigma$ = standard deviation = $54

(a) Probability that a family of a returning college student spend less than $150 on back-to-college electronics is = P(X < $150)

P(X < $150) = P( $\frac{X-\mu}{\sigma}$ < $\frac{150-237}{54}$ ) = P(Z < -1.61) = 1 - P(Z $\leq$ 1.61)

= 1 - 0.9463 = 0.0537

The above probability is calculated by looking at the value of x = 1.61 in the z table which has an area of 0.9463.

(b) Probability that a family of a returning college student spend more than $390 on back-to-college electronics is = P(X > $390)

P(X > $390) = P( $\frac{X-\mu}{\sigma}$ > $\frac{390-237}{54}$ ) = P(Z > 2.83) = 1 - P(Z $\leq$ 2.83)

= 1 - 0.9977 = 0.0023

The above probability is calculated by looking at the value of x = 2.83 in the z table which has an area of 0.9977.

(c) Probability that a family of a returning college student spend between $120 and $175 on back-to-college electronics is given by = P($120 < X < $175)

P($120 < X < $175) = P(X < $175) - P(X $\leq$ $120)

P(X < $175) = P( $\frac{X-\mu}{\sigma}$ < $\frac{175-237}{54}$ ) = P(Z < -1.15) = 1 - P(Z $\leq$ 1.15)

= 1 - 0.8749 = 0.1251

P(X < $120) = P( $\frac{X-\mu}{\sigma}$ < $\frac{120-237}{54}$ ) = P(Z < -2.17) = 1 - P(Z $\leq$ 2.17)

= 1 - 0.9850 = 0.015

The above probability is calculated by looking at the value of x = 1.15 and x = 2.17 in the z table which has an area of 0.8749 and 0.9850 respectively.

Therefore, P($120 < X < $175) = 0.1251 - 0.015 = 0.1101

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4 years ago