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gulaghasi [49]
3 years ago
15

Write the equation of the line, in standard form, that passes through the origin and is parallel to x + y= 6. Include your

Mathematics
1 answer:
hram777 [196]3 years ago
8 0

Answer:

x+y=0

Step-by-step explanation:

Hi there!

We're given the line x+y=6 and we want to write the equation of the line that's parallel to x+y=6 and passes through the origin (or the point (0,0)) in standard form

Standard form is given as ax+by=c, where a, b, and c are free integer coefficients (the values of a, b, and c are numbers).

Note that a CANNOT be 0 and CANNOT be negative

First, let's find the slope of the line that will be parallel to x+y=6, as parallel lines have the same slope.

We'll do this by converting x+y=6 from standard form into slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)

x+y=6

subtract x from both sides

y=-x+6

although there's no number in front of x, there's the negative sign, which means that the slope of x+y=6 is -1

Since parallel lines have the same slope, the slope of the new, parallel line is also -1

here's our equation so far in slope-intercept form:

y=-x+b

we need to find b

As the line will pass through (0,0), we can substitute it into the equation to solve for b

substitute 0 as x and 0 as y into the equation

0=-(0)+b

multiply

0=0+b

0=b

so the equation in slope-intercept form is y=-x+0

But remember! The problem asks for the answer in standard form

in that case, add x to both sides of the equation

<u>x+y=0</u>

Hope this helps!

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Answer: 97 students

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Simple! We need to split 388 into four equal parts, so

388 / 4 = 97

Hope this helps!

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3 years ago
Leena has 2/3 of a glass of milk with her. She gives 1/6 of it to her cat. How much of milk is left with her now?
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Answer:

1/2 glass milk is left.

Step-by-step explanation:

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2 years ago
In a recent contest, the mean score was 210 and the standard deviation was 25. a) Find the z-score of John who scored 190 b) Fin
denpristay [2]

Answer:

a) Z = -0.8

b) Z = 2.4

c) Mary's score was 241.25.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 210, \sigma = 25

a) Find the z-score of John who scored 190

Z = \frac{X - \mu}{\sigma}

Z = \frac{190 - 210}{25}

Z = -0.8

b) Find the z-score of Bill who scored 270

Z = \frac{X - \mu}{\sigma}

Z = \frac{270 - 210}{25}

Z = 2.4

c) If Mary had a score of 1.25, what was Mary’s score?

Z = \frac{X - \mu}{\sigma}

1.25 = \frac{X - 210}{25}

X - 210 = 25*1.25

X = 241.25

Mary's score was 241.25.

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3 years ago
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Step-by-step explanation:

y = 8x² + 8x - 96

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When y = 0, 8(x + 4)(x - 3) = 0.

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C is one of the answers
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