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ser-zykov [4K]
4 years ago
12

How many solutions does the system of equations have 3x+15y=35 and y=-1/5x+7/3

Mathematics
1 answer:
Alja [10]4 years ago
5 0
We can to make the method of substitution.

Look:

3x + 15y = 35

Isolating 3x

15y = 35 - 3x

Dividing both the sides by 15

y = 35/15 - 3x/15

Simpliting:

y = 7/3 - x/5

Now let's equate this expression with the other

7/3 - x/5 = - x/5 + 7/3

0 = 0

Oh noOo!

There is solution infinatly to this question!

Because, the two equation are the same.


Hope this helps!
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Answer:

Step-by-step explanation:

\[a_{n}=a{1}r^{n-1}\]

r=16/8=2

a_{12}=8(2)^{12-1}

a_{12}=8(2)^{11}=16384  

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3 years ago
A line goes through the points (4,16) Ana (7,19). Write a linear function rule in terms of x and y for this line
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Linear function rule in terms of x and y for this line is y = x + 12

<em><u>Solution:</u></em>

Given that a line goes through the points (4, 16) and (7, 19)

To find: linear function rule in terms of x and y for this line

A linear function is a function of the form f(x) = ax + b, where a and b are real numbers. Here, a represents the slope of the line, and b represents the y-axis intercept

<em><u>The slope intercept form is given as:</u></em>

y = mx + c

Where "m" is the slope of line and "c" is the y - intercept

Let us first find slope of line

<em><u>The slope "m" of a line is given as:</u></em>

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

\text {Here } x_{1}=4 \text { and } x_{2}=7 \text { and } y_{1}=16 \text { and } y_{2}=19

m=\frac{19-16}{7-4}=\frac{3}{3}=1

Thus the slope of line is 1

Substitute m = 1 and (x, y) = (4, 16) in y = mx + c

16 = 1(4) + c

c = 16 - 4 = 12

Substitute c = 12 and m = 1 in slope intercept form

y = 1x + 12

y = x + 12 is the required linear function rule

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3 years ago
Solve using the quadratic formula.<br>-v^2 + 9v - 5 = 0​
timama [110]

Answer:

v = 9/2 + sqrt(61)/2 or v = 9/2 - sqrt(61)/2

Step-by-step explanation:

Solve for v over the real numbers:

-v^2 + 9 v - 5 = 0

Multiply both sides by -1:

v^2 - 9 v + 5 = 0

Subtract 5 from both sides:

v^2 - 9 v = -5

Add 81/4 to both sides:

v^2 - 9 v + 81/4 = 61/4

Write the left hand side as a square:

(v - 9/2)^2 = 61/4

Take the square root of both sides:

v - 9/2 = sqrt(61)/2 or v - 9/2 = -sqrt(61)/2

Add 9/2 to both sides:

v = 9/2 + sqrt(61)/2 or v - 9/2 = -sqrt(61)/2

Add 9/2 to both sides:

Answer: v = 9/2 + sqrt(61)/2 or v = 9/2 - sqrt(61)/2

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