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3 years ago

What is an equation of the line that passes through the point (-1, 4) and is parallel

Mathematics

1 answer:

vesna_86 [32]3 years ago

3 0

Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the parallel line we must first find the slope of the original line

The original line is 2x + y = 1

We must first write the equation in the general form above

That's

y = - 2x + 1

Comparing with the general equation above

Slope = - 2

Since the lines are parallel their slope are also the same

Slope of parallel line = - 2

So the equation of the line using point

( - 1 , 4) and slope - 2 is

We have the final answer as

Hope this helps you

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According to the empirical (69-95-99.7) rule, if a random variable z has a standard normal distribution, then approximately 95%

Dmitry_Shevchenko [17]

Using z-scores, it is found that the value of z is z = 1.96.

-----------------------------

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula, which for a measure X, in a distribution with mean $\mu$ and standard deviation $\sigma$ , is given by:

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

It measures how many standard deviations the measure is from the mean.
Each z-score has an associated p-value, which is the percentile.

The normal distribution is symmetric, which means that the middle 95% is between the <u>2.5th percentile and the 97.5th percentile</u>.
The 2.5th percentile is Z with a p-value of 0.025, thus Z = -1.96.
The 97.5th percentile is Z with a p-value of 0.975, thus Z = 1.96.
Thus, the value of Z is 1.96.

A similar problem is given at brainly.com/question/16965597

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2 years ago

Based only on the information given in the diagram, which congruence

Wewaii [24]

Answer:

Option B

Option E

Step-by-step explanation:

By the use of following postulates we can prove the two right triangles to be congruent.

1). HA - [Equal hypotenuse and an cute angles]

2). LL - [Two legs should be equal]

3). LA - [One leg and one angle must be equal]

4). ASA - [Two angles and the side containing these angles should be equal]

In the given right triangles,

1). OJ ≅ IL

2). ∠O ≅ ∠I

3). ∠J ≅ ∠L

Therefore, two postulates HA, ASA will be applicable for the congruence of the two triangles given.

Options A and E will be the answer.

3 0

4 years ago

Read 2 more answers

The axis of symmetry for the graph of the function f start bracket x end bracket equals one-quarter x square plus b x plus 10 is

zimovet [89]

The value of b is -3.

<h3>What is axis of symmetry?</h3>

Axis of symmetry is a line that divides an object into two halves,thereby creation a mirror like reflection of either side of the object.

Now the given function is,

f(x) = 1/4 x^2 bx + 10

and axis of symmetry is at x = 6

Now the quadratic function in standard form is given as,

f(x) = a x^2 bx + c

By comprison we get,

a = 1/4

c = 10

Since axis of symmetry is a vertical line

x = -b/2a

Therefore,

6 = -b/2*(1/4)

-b = 6*2*(1/4)

or, b = -12/4

or, b = -3

Hence,The value of b is -3.

More about axis of symmetry :

brainly.com/question/3514150

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2 years ago

How many places do you need to move the decimal to the left to write the

NikAS [45]

Answer: 6 x 10^12

Step-by-step explanation:

Move the decimal to the left so there is one non-zero digit number left of the decimal point. This will be the exponent placed on 10

3 0

3 years ago

A teacher places n seats to form the back row of a classroom layout. Each successive row contains two fewer seats than the prece

Alex_Xolod [135]

Answer:

The number of seat when n is odd $S_n=\frac{n^2+2n+1}{4}$

The number of seat when n is even $S_n=\frac{n^2+2n}{4}$

Step-by-step explanation:

Given that, each successive row contains two fewer seats than the preceding row.

Formula:

The sum n terms of an A.P series is

$S_n=\frac{n}{2}[2a+(n-1)d]$

$=\frac{n}{2}[a+l]$

a = first term of the series.

d= common difference.

n= number of term

l= last term

$n^{th}$ term of a A.P series is

$T_n=a+(n-1)d$

n is odd:

n,n-2,n-4,........,5,3,1

Or we can write 1,3,5,.....,n-4,n-2,n

Here a= 1 and d = second term- first term = 3-1=2

Let $t^{th}$ of the series is n.

$T_n=a+(n-1)d$

Here $T_n=n$ , n=t, a=1 and d=2

$n=1+(t-1)2$

⇒(t-1)2=n-1

$\Rightarrow t-1=\frac{n-1}{2}$

$\Rightarrow t = \frac{n-1}{2}+1$

$\Rightarrow t = \frac{n-1+2}{2}$

$\Rightarrow t = \frac{n+1}{2}$

Last term l= n,, the number of term $=\frac{ n+1}2$ , First term = 1

Total number of seat

$S_n=\frac{\frac{n+1}{2}}{2}[1+n}]$

$=\frac{{n+1}}{4}[1+n}]$

$=\frac{(1+n)^2}{4}$

$=\frac{n^2+2n+1}{4}$

n is even:

n,n-2,n-4,.......,4,2

Or we can write

2,4,.......,n-4,n-2,n

Here a= 2 and d = second term- first term = 4-2=2

Let $t^{th}$ of the series is n.

$T_n=a+(n-1)d$

Here $T_n=n$ , n=t, a=2 and d=2

$n=2+(t-1)2$

⇒(t-1)2=n-2

$\Rightarrow t-1=\frac{n-2}{2}$

$\Rightarrow t = \frac{n-2}{2}+1$

$\Rightarrow t = \frac{n-2+2}{2}$

$\Rightarrow t = \frac{n}{2}$

Last term l= n, the number of term $=\frac n2$ , First term = 2

Total number of seat

$S_n=\frac{\frac{n}{2}}{2}[2+n}]$

$=\frac{{n}}{4}[2+n}]$

$=\frac{n(2+n)}{4}$

$=\frac{n^2+2n}{4}$

4 0

3 years ago