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3 years ago

What is parallel to y=-3x+12, passing through (4,2), written in point slope form and standard form?

Mathematics

1 answer:

kolezko [41]3 years ago

7 0

Answer:

$y = 4x - 18$

$y - 4x = -18$

Step-by-step explanation:

Given

$y = -3x + 12$

$Point:(4,2)$

Required

Determine the equation.

This is calculated as follows:

Since the line is parallel to $y = -3x + 12$ , then m = slope =-3

The point slope of a lin equation is:

$y -y_1 = m(x - x_1)$

This gives:

$y - 2 = 4(x - 4)$

$y - 2 = 4x - 16$

Solve for y

y = 4x - 16 - y

$y = 4x - 18$

To convert smileys into standard form, we have"

$Ax + by = c$

This gives

$y - 4x = -18$

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Classify each pair of numbered angles. Drag and drop the descriptions into the boxes to correctly classify each pair of numbered

Leona [35]

(i) Pairs of neighboring angles are supplementary and opposite angles have the same measure.

(ii) The two angles formed by a line coming out of another line are supplementary.

<h3>How to analyze pairs of angles</h3>

(i) When two straight lines pass through each other, then two pairs of opposite angles are constructed. A pair with angles of $(3\cdot x + 52)^{\circ}$ and another pair with angles of $(2\cdot x + 2)^{\circ}$ , each pair of angles with different measures are supplementary. $\blacksquare$

(ii) When a straight line comes out of another straight line, from a point distinct to any endpoint of the former, then we construct two supplementary angles. The largest angle has a value of $(10\cdot x + 20)^{\circ}$ , whereas the smaller one has a value of $(6\cdot x + 8)^{\circ}$ . $\blacksquare$

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2 years ago

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Gwar [14]

What do you mean? What’s the question?

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2 years ago

Read 2 more answers

How many terms of the arithmetic sequence {1,22,43,64,85,…} will give a sum of 2332? Show all steps including the formulas used

MA_775_DIABLO [31]

There's a slight problem with your question, but we'll get to that...

Consecutive terms of the sequence are separated by a fixed difference of 21 (22 = 1 + 21, 43 = 22 + 21, 64 = 43 + 21, and so on), so the n-th term of the sequence, a (n), is given recursively by

• a (1) = 1

• a (n) = a (n - 1) + 21 … … … for n > 1

We can find the explicit rule for the sequence by iterative substitution:

a (2) = a (1) + 21

a (3) = a (2) + 21 = (a (1) + 21) + 21 = a (1) + 2×21

a (4) = a (3) + 21 = (a (1) + 2×21) + 21 = a (1) + 3×21

and so on, with the general pattern

a (n) = a (1) + 21 (n - 1) = 21n - 20

Now, we're told that the sum of some number N of terms in this sequence is 2332. In other words, the N-th partial sum of the sequence is

a (1) + a (2) + a (3) + … + a (N - 1) + a (N) = 2332

or more compactly,

$\displaystyle\sum_{n=1}^N a(n) = 2332$

It's important to note that N must be some positive integer.

Replace a (n) by the explicit rule:

$\displaystyle\sum_{n=1}^N (21n-20) = 2332$

Expand the sum on the left as

$\displaystyle 21 \sum_{n=1}^N n-20\sum_{n=1}^N1 = 2332$

and recall the formulas,

$\displaystyle\sum_{k=1}^n1=\underbrace{1+1+\cdots+1}_{n\text{ times}}=n$

$\displaystyle\sum_{k=1}^nk=1+2+3+\cdots+n=\frac{n(n+1)}2$

So the sum of the first N terms of a (n) is such that

21 × N (N + 1)/2 - 20N = 2332

Solve for N :

21 (N ² + N) - 40N = 4664

21 N ² - 19 N - 4664 = 0

Now for the problem I mentioned at the start: this polynomial has no rational roots, and instead

N = (19 ± √392,137)/42 ≈ -14.45 or 15.36

so there is no positive integer N for which the first N terms of the sum add up to 2332.

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2 years ago

Solve the following system to find the point(s) of intersection. y = x² - 2x - 3 y = 2x - 3

omeli [17]

x=4 y=5

if we put two pharases together

the answer is as follows pic :

x=4 y=5

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2 years ago

Find the distance between the points a. 3 b. 4 c. 5 d. 6

Naily [24]

Answer:

B. 4

Step-by-step explanation:

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3 years ago