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3 years ago

What is an equation of the line that passes through the poin (-4,3) and is parallel that line 4x-5y=20

Mathematics

2 answers:

Oksanka [162]3 years ago

7 0

Answer:

y = 4/5x + 6 1/5

Step-by-step explanation:

First, rearrange the equation to put it in the form y = mx + b. Once you put it in that form, m will be the slope and b will be the y-intercept (for example, if the equation is y = 3x - 1 then 3 is the slope and -1 is the y-intercept)

4x - 5y = 20

subtract 4x from both sides

-5y = -4x + 20

divide both sides by -5

y = 4/5 * x - 4

This means the slope of this line is 4/5

Parallel lines always have the same slope, so again you can put your new equation in the form y = mx + b and you have that the slope, or m, = 4/5 so this would be:

y = 4/5x + b

Now, you know that (-4, 3) is a solution so if you plug in x = -4 and y =3 the equation should be true:

3 = 4/5 * -4 + b

3 = -16/5 + b

6 1/5 or 6.2 = b

So the equation is y = 4/5x + 6 1/5 or y = 0.8x + 6.2

Anestetic [448]3 years ago

4 0

Answer:

y = 4/5x + 31/5

Step-by-step explanation:

parallel lines have the same gradient(m)

and the straight like equation is y=mx +c

so to find m , make y the subject.

m will equal to 4/5.

The x and y values are given substitute them and the value to y=mx + c , to find c.

After you have c, place the value of m and c in their places and you'll get: y=4/5x + 31/5

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1/2 +b=1 3/4 What does b represent and how to solve it?

LenKa [72]

Answer:

b= 5/4 or 1 1/4

Step-by-step explanation:

First I will make 1 3/4 into an improper fraction

1/2 + b = 7/4

Then I will make the fractions have common denominators

2/4 + b = 7/4

I subtract 2/4 from 7/4

b= 5/4

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3 years ago

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To the nearest hundredth, what is the value of x? 36.08 41.51 47.81 72.88

Crazy boy [7]

Answer:

Step-by-step explanation:

Using the law of sines, we can make a proportion.

But first, we'll need to solve for the unknown angle.

We add up the two known angles and subtract that by 180.

90 + 41 = 131

180 - 131 = 49

So the unknown angles is 49.

Then, we can use the law of sines.

Make the equation.

sin(90)/55 = sin(49)/x

Simplify this using a calculator and you get around 41.51 or option B.

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2 years ago

Use a calculator to find the r-value of these data. Round the value to three decimal places.

Sindrei [870]

Answer:

-0.985

Step-by-step explanation:

Refer to the image below for explanation:

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2 years ago

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A prticular type of tennis racket comes in a midsize versionand an oversize version. sixty percent of all customers at acertain

svetlana [45]

Answer:

a) P(x≥6)=0.633

b) P(4≤x≤8)=0.8989 (one standard deviation from the mean).

c) P(x≤7)=0.8328

Step-by-step explanation:

a) We can model this a binomial experiment. The probability of success p is the proportion of customers that prefer the oversize version (p=0.60).

The number of trials is n=10, as they select 10 randomly customers.

We have to calculate the probability that at least 6 out of 10 prefer the oversize version.

This can be calculated using the binomial expression:

$P(x\geq6)=\sum_{k=6}^{10}P(k)=P(6)+P(7)+P(8)+P(9)+P(10)\\\\\\P(x=6) = \binom{10}{6} p^{6}q^{4}=210*0.0467*0.0256=0.2508\\\\P(x=7) = \binom{10}{7} p^{7}q^{3}=120*0.028*0.064=0.215\\\\P(x=8) = \binom{10}{8} p^{8}q^{2}=45*0.0168*0.16=0.1209\\\\P(x=9) = \binom{10}{9} p^{9}q^{1}=10*0.0101*0.4=0.0403\\\\P(x=10) = \binom{10}{10} p^{10}q^{0}=1*0.006*1=0.006\\\\\\P(x\geq6)=0.2508+0.215+0.1209+0.0403+0.006=0.633$

b) We first have to calculate the standard deviation from the mean of the binomial distribution. This is expressed as:

$\sigma=\sqrt{np(1-p)}=\sqrt{10*0.6*0.4}=\sqrt{2.4}=1.55$

The mean of this distribution is:

$\mu=np=10*0.6=6$

As this is a discrete distribution, we have to use integer values for the random variable. We will approximate both values for the bound of the interval.

$LL=\mu-\sigma=6-1.55=4.45\approx4\\\\UL=\mu+\sigma=6+1.55=7.55\approx8$

The probability of having between 4 and 8 customers choosing the oversize version is:

$P(4\leq x\leq 8)=\sum_{k=4}^8P(k)=P(4)+P(5)+P(6)+P(7)+P(8)\\\\\\P(x=4) = \binom{10}{4} p^{4}q^{6}=210*0.1296*0.0041=0.1115\\\\P(x=5) = \binom{10}{5} p^{5}q^{5}=252*0.0778*0.0102=0.2007\\\\P(x=6) = \binom{10}{6} p^{6}q^{4}=210*0.0467*0.0256=0.2508\\\\P(x=7) = \binom{10}{7} p^{7}q^{3}=120*0.028*0.064=0.215\\\\P(x=8) = \binom{10}{8} p^{8}q^{2}=45*0.0168*0.16=0.1209\\\\\\P(4\leq x\leq 8)=0.1115+0.2007+0.2508+0.215+0.1209=0.8989$

c. The probability that all of the next ten customers who want this racket can get the version they want from current stock means that at most 7 customers pick the oversize version.

Then, we have to calculate P(x≤7). We will, for simplicity, calculate this probability substracting P(x>7) from 1.

$P(x\leq7)=1-\sum_{k=8}^{10}P(k)=1-(P(8)+P(9)+P(10))\\\\\\P(x=8) = \binom{10}{8} p^{8}q^{2}=45*0.0168*0.16=0.1209\\\\P(x=9) = \binom{10}{9} p^{9}q^{1}=10*0.0101*0.4=0.0403\\\\P(x=10) = \binom{10}{10} p^{10}q^{0}=1*0.006*1=0.006\\\\\\P(x\leq 7)=1-(0.1209+0.0403+0.006)=1-0.1672=0.8328$

7 0

3 years ago

Please help! i do not understand my homework!

Verizon [17]

Answer:

I believe the answer is A.

8 0

3 years ago

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