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My name is Ann [436]

3 years ago

9

What is the equation of the line that is parallel to the line y =1/3 x + 4 and passes through the point (6, 5)?

1 answer:

lianna [129]3 years ago

5 0

Answer:

y = $\frac{1}{3}$ x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = $\frac{1}{3}$ x + 4 ← is in slope- intercept form

with slope m = $\frac{1}{3}$

Parallel lines have equal slopes , then

y = $\frac{1}{3}$ x + c ← is the partial equation

To find c substitute (6, 5) into the partial equation

5 = 2 + c ⇒ c = 5 - 2 = 3

y = $\frac{1}{3}$ x + 3 ← equation of parallel line

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Match each series with the equivalent series written in sigma notation

PIT_PIT [208]

Answer:

$3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n$

$4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n$

$2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n$

$3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n$

Step-by-step explanation:

Given

See attachment for complete question

Required

Match equivalent expressions

Solving (a):

$3 + 12 + 48 + 192 + 768$

The expression can be written as:

$3 \to 3*4^{0$ --- 0

$12 \to 3 * 4^{1$ ---- 1

$48 \to 3 * 4^{2$ --- 2

$192 \to 3 * 4^{3$ ---- 3

$768 \to 3 * 4^{4$ ---- 4

For the nth term, the expression is:

$Term = 3 * 4^{n$ ---- n

So, the summation is:

$3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n$

Solving (b):

$4 + 32 + 256 + 2048 + 16384$

The expression can be written as:

$4 \to 4 * 8^0$ --- 0

$32 \to 4 * 8^1$ ---- 1

$256 \to 4 * 8^2$ --- 2

$2048 \to 4 * 8^3$ ---- 3

$16384 \to 4 * 8^4$ ---- 4

For the nth term, the expression is:

$Term \to 4 * 8^n$ ---- n

So, the summation is:

$4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n$

Solving (c):

$2 + 6 + 18 + 54 + 162$

The expression can be written as:

$2 \to 2 * 3^0$ --- 0

$6 \to 2 * 3^1$ ---- 1

$18 \to 2 * 3^2$ --- 2

$54 \to 2 * 3^3$ ---- 3

$162 \to 2 * 3^4$ ---- 4

For the nth term, the expression is:

$Term \to 2 * 3^n$ ---- n

So, the summation is:

$2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n$

Solving (d):

$3 + 15 + 75 + 375 + 1875$

The expression can be written as:

$3 \to 3 * 5^0$ --- 0

$15 \to 3 * 5^1$ ---- 1

$75 \to 3 * 5^2$ --- 2

$375 \to 3 * 5^3$ ---- 3

$1875 \to 3 * 5^4$ ---- 4

For the nth term, the expression is:

$Term \to 3 * 5^n$ ---- n

So, the summation is:

$3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n$

5 0

2 years ago

If four times the sum of a number and 3 is divided by 2, the quotient is 0: find the number

AveGali [126]

The other number is -3.

Step-by-step explanation:

Step 1; First we develop formulae for the given information. A number is added with 3 and the resulting sum is multiplied by 4. This number is then divided by 2 and the quotient is 0. Assume the unknown number is x, then the given information is as follows

The quotient of $\frac{4(x+3)}{2}$ is 0. So $\frac{4(x+3)}{2}$ = 0.

Step 2; Now we solve the above equation. The denominator is taken to the RHS and the RHS remains zero.

$\frac{4(x+3)}{2}$ = 0, 4(x+3)= 0, 4x+ 12 = 0, 4x = -12, x = $\frac{-12}{4}$ = -3.

So the other number is -3.

3 0

3 years ago

enton is shopping for clothes during a special event. He pays $24.99 for a pair of jeans and $5.25 for a clearance-priced shirt.

Marianna [84]

Answer$18.12

Step-by-step explanation:

24.99+5.25-12.12=$18.12

7 0

2 years ago

HELP PLEASEE!!! I just need help with the 2 boxes

Soloha48 [4]

Answer:

$y= x - 300$

$y = -246$ -- Her equivalent weight on earth

Step-by-step explanation:

Given

The attached table

Required

Fill in the gaps

(a) The equation

First, we calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

From the table, we can say that:

$(x_1,y_1) = (0,-300)$

$(x_2,y_2) = (300,0)$

So, we have:

$m = \frac{0 -(-300)}{300 - 0}$

$m = \frac{0 +300}{300}$

$m = \frac{300}{300}$

$m = 1$

The equation is then calculated using:

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

This gives:

$y - (-300) = 1(x - 0)$

$y +300 = 1(x)$

$y +300 = x$

$y= x - 300$

(b) When x = 54

Substitute 54 for x in $y= x - 300$

$y = 54 - 300$

$y = -246$

3 0

3 years ago

What is the slope<br> of the line in this graph?

jasenka [17]

5/7

explanation: (5-0)/(7-0) = 5/7

5 0

3 years ago