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olga55 [171]
2 years ago
7

Line AB passes through points A(−6, 6) and B(12, 3). If the equation of the line is written in slope-intercept form, y=mx+b, the

n m=m equals negative StartFraction 1 Over 6 EndFraction.. What is the value of b? −6 −5 5 6
Mathematics
2 answers:
NeX [460]2 years ago
5 0

Answer:

m = -1/6.

b = 5.

Step-by-step explanation:

Slope m =  (3 - 6) / (12 - -6)

=  -3 / 18

= -1/6.

y = -1/6 x + b

when x = 12 y = 3 so

3 = -1/6 * 12 + b

b =  3 + 2 = 5.

Aloiza [94]2 years ago
3 0

Answer: 5

Step-by-step explanation:

We can find our intercept b from the equation of the straight line:

y - y₁ = m (x-x₁ )

point A(-6, 6)

x₁ = -6 and y₁ =6

m= -1/6 (as stated in the question)

Inputing this values in our equation, we have;

y - 6 = -1/6 ( x - -6)

y - 6 = -1/6(x+6)

y - 6 = -1/6x -1

y = -1/6x - 1 + 6

y= -1/6x + 5

comparing y= mx+b with the equation above; b=5

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2 years ago
Simplify the expression insert √96/8
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I hope this answers your question :)
6 0
2 years ago
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According to government​ data, the probability that an adult was never in a museum is 10​%. In a random survey of 60 ​adults, wh
lutik1710 [3]

Answer:

\text{Mean}=)=6\\\\\text{Standard deviation}=2.324

Step-by-step explanation:

Given : The probability that an adult was never in a museum is : p=0.10

The number of adults randomly surveyed: n = 60

In Binomial distribution , the formula to find the mean and the standard deviation is given by :-

\text{Mean}=np\\\\\text{Standard deviation}=\sqrt{np(1-p)}

Then , the mean and standard deviation of the number that were never in a​ museum will be :-

\text{Mean}=60(0.10)=6\\\\\text{Standard deviation}=\sqrt{60(0.10)(1-0.1)}=2.3237900077\approx2.324

5 0
2 years ago
Find the number a such that the line x = a bisects the area under the curve y = 1/x2 for 1 ≤ x ≤ 4. 8 5​ (b) find the number b s
IceJOKER [234]

a. We're looking for a such that

\displaystyle\int_1^a\frac{\mathrm dx}{x^2}=\int_a^4\frac{\mathrm dx}{x^2}

-\dfrac1x\bigg|_{x=1}^{x=a}=-\dfrac1x\bigg|_{x=a}^{x=4}

1-\dfrac1a=\dfrac1a-\dfrac14

\dfrac54=\dfrac2a\implies\boxed{a=\dfrac85}

b. Integrating with respect to y will make things easier.

y=\dfrac1{x^2}\implies x=\dfrac1{\sqrt y}

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Now we want to find b such that

\displaystyle\int_0^b\frac{\mathrm dy}{\sqrt y}=\int_b^1\frac{\mathrm dy}{\sqrt y}

2\sqrt y\bigg|_{y=0}^{y=b}=2\sqrt y\bigg|_{y=b}^{b=1}

2\sqrt b=2-2\sqrt b

4\sqrt b=2\implies\boxed{b=\dfrac14}

3 0
2 years ago
Joanne has a goal of buying a townhome and saved for 5 years. She expected to have the down payment of $15,000 saved by now but
serg [7]

Answer:


Step-by-step explanation:

Average amount saved per year = \frac{15,000}{5}

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So on average Joanne has saved $3000 per year. She only needs $2000 more which will not even take a year to save.

How many months it will take to save $2000:

\frac{12}{3000} \times2000

= 8 Months.

It will only take Joanne 8 moths to save $2000.

If she really wants to buy the home now she can always go for a home loan scheme for $2000. Any interest rate less than 50% per year is fine as she can save $3000 per year.


6 0
2 years ago
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