1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
salantis [7]
3 years ago
14

3x = -y + 12 2x + 3y = -6

Mathematics
1 answer:
tangare [24]3 years ago
3 0

Answer:

3x=-y+12

2x+3y=-6

collecting the like terms we have

3x+y=12

2x+3y=-6

to solve this simultaneous equation, we use substitution method

we make y the subject in equation one:

y=12-3x

then we put y=12-3x into 2x-3y=-6 in equation two

2x+3(12-3x)=-6

2x+36-9x=-6

-7x+36=-6

-7x=-6-36

-7x=-42

x=-42÷-7

x=6

then we put x=6 in y=12-3x:

y=12-3x

y=12-3(6)

y=12-18

y=-6

You might be interested in
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

4 0
3 years ago
On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these flowers rapid
Elza [17]

Answer:

L(t)=7600e^{0.2273t}

Step-by-step explanation:

-The locust population grows by a factor and can therefore be modeled by an exponential function of the form:

P=P_oe^{rt}

Where:

  • P is the population after t days.
  • P_o is the initial population given as 7600
  • r is the rate of growth
  • t is time in days

-Given that the growth is by a factor of 5( equivalent to 500%), the r value will be 5

-The population increases by a factor of 5 every 22 days. therefore at any time instance, t will be divided by 22 to get the effective time for calculations.

Hence, the exponential growth function will be expressed as:

P=P_oe^{rt},\ \ \ P=L(t)\\\\\therefore L(t)=7600e^{5\frac{t}{22}}\\\\=7600e^{0.2273t}

7 0
3 years ago
CAN SOMEONE PLEASE HELP ME WITH MY GEOMETRY HOMEWORK!!!! I DON'T UNDERSTAND WHAT I'M SUPPOSED TO DO SO CAN SOMEONE PLEASE HELP M
MAVERICK [17]

Answer:

  see attached

Step-by-step explanation:

Dilation is the transformation that changes the size of something. When you choose ×110% on a copy machine, you are making all the dimensions in the copy equal to 1.1 times the dimensions of the original, for example. That is dilation by a factor of 1.1, or 110%.

Here, you're asked to dilate triangle ABC by a factor of 3. That means all of the dimensions on the dilated figure will be 3 times their length on the original.

The center of dilation is point P. That means all the distances from point P are multiplied by 3.

In the attached figure, a gray arrow has been drawn from point P to each of the points A, B, and C. Then two more arrows of the same length are drawn in the same direction. The total distance at the end of the 3 arrows is 3 times the original distance from point P. These are the points A', B', and C' you are asked to draw. Connecting these points gives the dilated triangle A'B'C'.

___

You could think of point P (the center of dilation) as having coordinates (0, 0). Then points A, B, and C would have coordinates A(-4, 0), B(0, -3), and C(-4, -3). To dilate these points by a factor of 3, multiply each coordinate value by 3: A'(-12, 0), B'(0, -9), C'(-12, -9). You will see that these are the coordinates of the vertices of the dilated triangle.

4 0
3 years ago
you are about take an 8 question multiple choice test .each of these questions has 4 answers (A,B,C,D). how many ways can you an
Leviafan [203]

4^8=65536

5 0
3 years ago
Read 2 more answers
B) Complete the frequency polygon
masya89 [10]

Could you explain this better. Maybe in a picture or better format?

7 0
3 years ago
Other questions:
  • A survey was done that asked people to indicate whether they run or ride a bike for exercise.
    7·2 answers
  • What is exact value of cos7pi/6
    13·1 answer
  • Consider the two triangles shown. Which statement is true?
    15·2 answers
  • which of the following regular polygons can make a tessellation: a)septagon b)octagon c)square d)hexagon
    6·1 answer
  • I need help on number 1
    6·1 answer
  • ((3+10) −3) plus 10
    8·1 answer
  • Solve for x. Thank you
    12·2 answers
  • For every 3 strawberries, 1 banana needs to be added to the mixture. The ratio of strawberries to bananas is 3:1. Write this rat
    8·1 answer
  • Find the value of x in the parallelogram below.
    6·2 answers
  • 3 A bag contains red and blue marbles, such that the probability of drawing a blue marble is 8 An experiment consists of drawing
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!