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3 years ago

How many dots will figure n have? Explain how you know this.

Mathematics

2 answers:

Firdavs [7]3 years ago

6 0

Up to the table everything is right at the exception of the n value (in the table).

How many dots... figure 10: You found it it's 49 (and not 9)

How many dots... figure 25: You found it it's 109 (and not 24). Expanding it gives : 13+24x4

How many dots... figure 100: You found it it's 409 (and not 99). Expanding it gives : 13+99x4

How many common difference are added to 13 for figure 100. It's easy you also found it, it's 99, the common difference being 4 so it's 99x4

Now let's calculate the number of dots in figure "n" which is:

a(n) = a₁ + (n-1)x4 (4 being the common difference and a₁ = 1st term)

explanation: lookup again at your table and compare the FIG # part with the EXPAND part:

FIG # EXPAND (and notice the figures in the parenthesis)
--------- -----------
1 13 + (0)x4    = 13 (for fig# 1 we have (0)
2 13 + (1)x4    = 17  (for fig# 2 we have (1)
3 13 + (2)x4 = 21    (for fig# 3 we have (2)
4 13 + (3)x4 = 25    (for fig# 4 we have (3)
.    ........................
. .........................
.    ........................
n 13 + (n-1)x4            (for fig# we have (n-1)

As you notice the number in the parenthesis is always = fig # - 1

Hope that you understand this formula of an arithmetic progression with first term a = 13 and 4, the common difference. Note that n is the number of terms

LenKa [72]3 years ago

5 0

N = ((n-1) + 4) + 4, to my understanding.
although your answers seem right written in the columns, but your method of applying numbers to equation seems incorrect in 'expand' column. for example, answer for 3 should be something like this...
3 21 17+4
4 25 21+4
hope it helps.

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What is the equation of the line that passes through (-2,3) and is parallel to 2x+3y=6?

Vsevolod [243]

Answer:

Step-by-step explanation:

$\bold{METHOD\ 1:}$

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

Let $k:y=m_1x+b_1,\ l:y=m_2x+b_2$

then

$l\ \parallel\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}$

We have the equation of a line:

$2x+3y=6$

Convert to the slope-intercept form:

$2x+3y=6$ subtract 2x from both sides

$3y=-2x+6$ divide both sides by 3

$y=-\dfrac{2}{3}x+2\to m_1=-\dfrac{2}{3}$

therefore the slope is $m_2=-\dfrac{2}{3}$

Put the value of the slope and the coordinates of the point (-2, 3) to the equation of a line:

$3=-\dfrac{2}{3}(-2)+b$

$3=\dfrac{4}{3}+b$ subtract 4/3 from both sides

$\dfrac{9}{3}-\dfrac{4}{3}=b\to b=\dfrac{5}{3}$

Finally:

$y=-\dfrac{2}{3}x+\dfrac{5}{3}$

Convert to the standard form (Ax + By = C):

$y=-\dfrac{2}{3}x+\dfrac{5}{3}$ multiply both sides by 3

$3y=-2x+5$ add 2x to both sides

$2x+3y=5$

$\bold{METHOD\ 2:}$

Let $k:A_1x+B_1y=C_1,\ l:A_2x+B_2y=C_2$ .

Lines k and l are parallel iff

$A_1=A_2\ \wedge\ B_1=B_2\to\dfrac{A_2}{A_1}=\dfrac{B_2}{B_1}$

We have the equation:

$2x+3y=6\to A_1=2,\ B_1=3$

then the equation of a line parallel to given lines has the equation:

$2x+3y=C$

Put the coordinates of the point (-2, 3) to the equation:

$C=2(-2)+3(3)\\\\C=-4+9\\\\C=5$

Finally:

$2x+3y=5$

4 0

3 years ago

A linear function contains the following points: 0,-3 and 6,15.

9966 [12]

The slope of the linear function is 3 and the y-intercept is -3 if the linear function contains the following points: (0,-3) and (6,15)

<h3>What is the slope?</h3>

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

$\rm m =\dfrac{y_2-y_1}{x_2-x_1}$

We have:

A linear function contains the following points: (0,-3) and (6,15)

The slope:

$\rm m =\dfrac{15-(-3)}{6-0}$

m = 18/6

m = 3

The equation of a line:

y = mx + c

Plug x = 0, y = -3

-3 = c

Thus, the slope of the linear function is 3 and the y-intercept is -3 if the linear function contains the following points: (0,-3) and (6,15)

Learn more about the slope here:

brainly.com/question/3605446

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4 0

2 years ago

An English professor assigns letter grades on a test according to the following scheme. A: Top 15% of scores B: Scores below the

lisabon 2012 [21]

Answer:

59 to 66

Step-by-step explanation:

Mean test scores = u = 74.2

Standard Deviation = $\sigma$ = 9.6

According to the given data, following is the range of grades:

Grade A: 85% to 100%

Grade B: 55% to 85%

Grade C: 19% to 55%

Grade D: 6% to 19%

Grade F: 0% to 6%

So, the grade D will be given to the students from 6% to 19% scores. We can convert these percentages to numerical limits using the z scores. First we need to to identify the corresponding z scores of these limits.

6% to 19% in decimal form would be 0.06 to 0.19. Corresponding z score for 0.06 is -1.56 and that for 0.19 is -0.88 (From the z table)

The formula for z score is:

$z=\frac{x-u}{\sigma}$