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3 years ago

Determine the equation of the line that goes through points (1.1) and (3.7).

Mathematics

1 answer:

ValentinkaMS [17]3 years ago

4 0

Answer:

The equation of the line that goes through points (1,1) and (3,7) is $\mathbf{y=3x-2}$

Step-by-step explanation:

Determine the equation of the line that goes through points (1,1) and (3,7)

We can write the equation of line in slope-intercept form $y=mx+b$ where m is slope and b is y-intercept.

We need to find slope and y-intercept.

Finding Slope

Slope can be found using formula: $Slope=\frac{y_2-y_1}{x_2-x_1}$

We have $x_1=1, y_1=1, x_2=3, y_2=7$

Putting values and finding slope

$Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{7-1}{3-1}\\Slope=\frac{6}{2}\\Slope=3$

We get Slope = 3

Finding y-intercept

y-intercept can be found using point (1,1) and slope m = 3

$y=mx+b\\1=3(1)+b\\1=3+b\\b=1-3\\b=-2$

We get y-intercept b = -2

So, equation of line having slope m=3 and y-intercept b = -2 is:

$y=mx+b\\y=3x-2$

The equation of the line that goes through points (1,1) and (3,7) is $\mathbf{y=3x-2}$

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This graph shows transformations between f(x) = 10x and g(x) = a · 10x. Identify the following functions. p(x) = 4 · 10x q(x) =

wel

Anwers:

1. line A

2. line D

3. line B

4. line C

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.

Please have a look at the attached photo.

My answer:

Given the original function:

f(x) = 10x

and g(x) = a · 10x is the general from of all transformed functions from the above original function.

p(x) = 4 · 10x

The graph of this function is stretched vertically => line A

q(x) = –4 · 10x

The graph of this function is stretched vertically and is reflected through the x-asix => line D.

r(x) = (1/4) x 10x

The graph of this function is compressed vertically => line B

s(x) = (-1/4) x 10x

The graph of this function is compressed vertically and is reflected through the x-asix => line C

Hope it will find you well.

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Answer: 45.

Step-by-step explanation:

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2 years ago

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What is the radical form of the expression (2x^4y^5)^3/8

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We are given expression: $(2x^4y^5)^{3/8}$

Let us distribute 3/8 over exponents in parenthesis, we get

$(2^{3/8}x^{4\times 3/8}y^{5\times 3/8}) = (2^{3/8}x^{12/8}y^{15/8})$

$= (2^{3/8}x^{1\frac{4}{8}} y^{1\frac{7}{8}} )$

We can get x and y out of the radical because, we get whlole number 1 for x and y exponents for the mixed fractions.

So, we could write it as.

$(2^{3/8}x^{1\frac{4}{8}} y^{1\frac{7}{8}} ) = xy(2^{\frac{3}{8} }x^{\frac{4}{8}} y^{\frac{7}{8}} )$

Now, we could write inside expression of parenthesis in radical form.

$xy\sqrt[8]{2x^{3}x^4y^7}$

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3 years ago

1. Draw a quadrilateral with 2 parallel sides. It should have 2 pairs of perpendicular lines.

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Answer:

draw a rectangle

Step-by-step explanation:

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2 years ago

Findℒ{f(t)}by first using a trigonometric identity. (Write your answer as a function of s.)f(t) = 12 cost −π6

allsm [11]

Answer:

$L(f(t)) = \dfrac{6}{S^2+1} [\sqrt{3} \ S +1 ]$

Step-by-step explanation:

Given that:

$f(t) = 12 cos (t- \dfrac{\pi}{6})$

recall that:

cos (A-B) = cos AcosB + sin A sin B

∴

$f(t) = 12 [cos\ t \ cos \dfrac{\pi}{6}+ sin \ t \ sin \dfrac{\pi}{6}]$

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$L(f(t)) = L ( 6 \sqrt{3} \ cos \ (t) + 6 \ sin \ (t) ]$

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