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Karo-lina-s [1.5K]
2 years ago
6

Write the equation of a line that is parallel to 4x-2y=3 and is passing through the point (2,1)

Mathematics
1 answer:
Temka [501]2 years ago
5 0

Answer:

y= 2x -3

Step-by-step explanation:

Let's rewrite the given equation into the form of y=mx+c, so that we can find the gradient of the line. In this form, m (coefficient of x) is the gradient.

4x -2y= 3

2y= 4x -3

<em>Divide</em><em> </em><em>by</em><em> </em><em>2</em><em> </em><em>throughout</em><em>:</em>

y = 2x - 1 \frac{1}{2}

Thus the gradient is 2.

Parallel lines have the same gradient thus the line would also have a gradient of 2.

Substitute m=2 into the equation:

y= 2x +c

To find the value of c, substitute a pair of coordinates.

When x=2, y=1,

1= 2(2) +c

1= 4 +c

c= 1 -4

c= -3

Thus, the equation of the line is y= 2x -3.

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h(n)=-13nh(n)=−13nh, left parenthesis, n, right parenthesis, equals, minus, 13, n Complete the recursive formula of h(n)h(n)h, l
mr Goodwill [35]

Answer:

h(1)=-13

h(n)=h(n-1)-13, n\geq 2

Step-by-step explanation:

We are given that

h(n)=-13n

We have to find the recursive formula of h(n).

Substitute n=1

h(1)=-13

n=2

h(2)=-13-13=-26=h(1)-13

n=3

h(3)=-13(3)=-39=-26-13=h(2)-13

h(4)=-13(4)=-52=-39-13=h(3)-13

:

:

:

h(n)=h(n-1)-13

Therefore, the recursive formula is given by

h(1)=-13

h(n)=h(n-1)-13, n\geq 2

5 0
3 years ago
The sum of three numbers is 3. if the second number is subtracted from the sum of the first and third numbers, the result is 9.
Margaret [11]
Let the three numbers be x, y, and z.

If the sum of the three numbers is 3, then x+y+z=3

If subtracting the second number from the sum of the first and third numbers gives 9, then x+z-y=9

If subtracting the third number from the sum of the first and second numbers gives -5, then x+y-z=-5

This forms the system of equations:
[1] x+y+z=3
[2] x-y+z=9
[3] x+y-z=-5

First, to find y, let's take do [1]-[2]:
x+y+z=3
-x+y-z=-9
2y=-6
y=-3

Then, to find z, let's do [1]-[3]:
x+y+z=3
-x+-y+z=5
2z=8
z=4

Now that you have y and z, plug them into [1] to find x:
x+y+z=3
x-3+4=3
x=2

So the three numbers are 2,-3, and 4.


5 0
3 years ago
A shirt boutique purchased 100 new shirts for $1072. The short-sleeved shirts cost $10 each and the long-sleeved shirts cost $12
Scilla [17]

Answer:

one equation would be S+ L=36for the number of shirts sold.

4 0
3 years ago
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In circle C, SQ = 10 cm. Which statements about the circle are correct? Check all that apply.
lbvjy [14]

Answer: A, B, D, E

Arc PQ is congruent to arc SR.

The measure of arc QR is 150°

Arc PS measures about 13.1 cm.

Arc QS measures about 15.7 cm.

Step-by-step explanation:

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2 years ago
Otto had two days to paint 9 paintings. He painted 5 1\5 yesterday. How many paintings does Otto need to paint today?
enot [183]

Answer:

He needs to paint 3 4/5 today.

Step-by-step explanation:

9 - 5 1/5 = 3 4/5

Otto will need to paint 3 4/5 today.

4 0
2 years ago
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