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lesya692 [45]
3 years ago
8

solve the system of equations below by graphing both equations with a pencil and paper. what is the solution y = x - 1 y = 1/2x

+ 1

Mathematics
1 answer:
Elan Coil [88]3 years ago
6 0

Answer:

(4,3)

Step-by-step explanation:

(x-1) = \frac{1}{2}x +1

(x-\frac{1}{2}x)-(-1+1)=(\frac{1}{2}x-\frac{1}{2}x)+(1+1)

(\frac{1}{2}x/\frac{1}{2})=(2/\frac{1}{2})

x=4

y=(4)-1

y=3

y=\frac{1}{2}(4)+1

y=2+1

y=3

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You invest $5000 in an account at 5.5% per year simple interest. How much will you have in the account at the beginning of the 6
NeX [460]

Answer:

The amount in the account in the  beginning of the 6th year is $6375 .

Step-by-step explanation:

Formula

Simple\ interest = \frac{Principle\times Rate\ times Time}{100}

As given

You invest $5000 in an account at 5.5% per year simple interest.

Principle = $ 5000

Rate = 5.5 %

Time = 5 years

(As calculate amount in the account for beginning of 6th year.)

Putting all the values in the formula

Simple\ interest = \frac{5000\times 5.5\times 5}{100}

Simple\ interest = 50\times 5.5\times 5

Simple interest = $ 1375

Amount =  Principle + Simple interest

Putting values in the above formula

Amount =  $5000 + $1375

Amount = $ 6375

Therefore the amount in the account in the  beginning of the 6th year is $ 6375 .

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3 years ago
If the coordinates of the endpoints of a diameter of the circle are​ known, the equation of a circle can be found.​ First, find
Evgesh-ka [11]

Answer:

The equation of the circle is (x+3)^2+(y-5)^2 = 17

Step-by-step explanation:

The complete question is

If the coordinates of the endpoints of a diameter of the circle are​ known, the equation of a circle can be found.​ First, find the midpoint of the​ diameter, which is the center of the circle. Then find the​ radius, which is the distance from the center to either endpoint of the diameter. Finally use the​ center-radius form to find the equation.

Find the center-radius  form of the circle having the points (1,4) and (-7,6) as the endpoints of a diameter.

Consider that, if both points are the endpoints of a diameter, the center of the circle is the point that is exactly in the middle of the two points (that is, the point whose distance to each point is equal). Given points (a,b) and (c,d), by using the distance formula, you can check that the middle point is the average of the coordinates. Hence, the center of the circle is given by

(\frac{1-7}{2}, \frac{4+6}{2}) = (-3,5).

We will find the radius. Recall that the radius of the circle is the distance from one point of the circle to the center. Recall that the distance between points (a,b) and (c,d) is given by \sqrt[]{(a-c)^2+(b-d)^2}. So, let us use (1,4) to calculate the radius.

r = \sqrt[]{(1-(-3))^2+(4-5)^2} = \sqrt[]{17}.

REcall that given a point (x_0,y_0). The equation of a circle centered at the point (x_0,y_0) is

(x-x_0)^2+(y-y_0)^2 = r^2

In our case, (x_0,y_0)=(-3,5) and r=\sqrt[]{17}. Then, the equation is

(x-(-3))^2+(y-5)^2 = (x+3)^2+(y-5)^2 = 17

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3 years ago
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There are 10 hours and 45 minutes until the bus leaves.

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Part a, intersecting. Part B is one solution

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