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
Volgvan
3 years ago
7

Solve the following system of equations algebraically: y = x2 - 6x + 9 y = -9x + 19

Mathematics
1 answer:
Ratling [72]3 years ago
3 0
{(-5,64), (2,1)}

linear equation: y = -9x + 19
quadratic equation: y = x² - 6x + 9

Substitute the y in the quadratic equation by the its value in the linear equation.

-9x + 19 = x² - 6x + 9
      -  19               - 19    *subtract 19 to both sides
-9x         = x² - 6x -10
+9x              + 9x            *add 9x to both sides
0            = x² + 3x - 10
0            = (x + 5) (x - 2) *Factor

Set each factor = 0 and solve
x + 5 = 0    ;      x - 2 = 0
x = -5         ;      x = 2

Find the corresponding value of y using the linear equation.
y = -9x + 19

x = -5                              x = 2
y = -9(-5) + 19               y = -9(2) + 19
y = 45 + 19                    y = -18 + 19
y = 64                            y = 1

(-5,64)                              (2,1)

Check each value on each equation.
y = x² - 6x + 9
(-5,64)                                                  (2,1)
64 = (-5)² - 6(-5) + 9                          1 = 2² - 6(2) + 9
64 = 25 + 30 + 9                                1 = 4 - 12 + 9
64 = 64                                               1 = 1

y = -9x + 19
64 = -9(-5) + 19                                  1 = -9(2) + 19
64 = 45 + 19                                      1 = -18 + 19
64 = 64                                              1 = 1

{(-5,64), (2,1)}

You might be interested in
A bakery uses 8 tablespoons of honey for every 10 cups of flour to make bread dough. Some days they bake bigger batches and some
Tamiku [17]
Your answer: A bakery uses 8 tablespoons of honey for every 10 cups of flour to make bread dough. Some days they bake bigger batches ... brainly.com/question/18026512
7 0
2 years ago
5 1/2 by 4 3/4 by 1/4 scale it down by 1/10
TiliK225 [7]

Answer:

(11/20 by 19/40 by 1/40) OR (0.55 by 0.475 by 0.025)

Step-by-step explanation:

To scale down a set of measurements, simply multiply the original measurement by the factors you're scaling it by. For example, take the first measurement of 5 1/2. To scale this down, I turned the value into an improper fraction (11/2) to make the multiplication process easier. Then, I multiplied 11/2 by the factor of 1/10.

After that, I got 11/20, which is the new first measurement.

7 0
3 years ago
A circular swimming pool has a diameter of 40 meters. The depth of the pool is constant along west-east lines and increases line
Nataliya [291]

Answer:

Volume is 2000\pi\ m^{3}

Solution:

As per the question:

Diameter, d = 40 m

Radius, r = 20 m

Now,

From north to south, we consider this vertical distance as 'y' and height, h varies linearly as a function of y:

iff

h(y) = cy + d

Then

when y = 1 m

h(- 20) = 1 m

1 = c.(- 20) + d = - 20c + d              (1)

when y = 9 m

h(20) = 9 m

9 = c.20 + d = 20c + d                  (2)

Adding eqn (1) and (2)

d = 5 m

Using d = 5 in eqn (2), we get:

c = \frac{1}{5}

Therefore,

h(y) = \frac{1}{5}y + 5

Now, the Volume of the pool is given by:

V = \int h(y)dA

where

A = r\theta

A = rdr\ d\theta

Thus

V = \int (\frac{1}{5}y + 5)dA

V = \int_{0}^{2\pi}\int_{0}^{20} (\frac{1}{5}rsin\theta + 5) rdr\ d\theta

V = \int_{0}^{2\pi}\int_{0}^{20} (\frac{1}{5}r^{2}sin\theta + 5r}) dr\ d\theta

V = \int_{0}^{2\pi} (\frac{1}{15}20^{3}sin\theta + 1000) d\theta

V = [- 533.33cos\theta + 1000\theta]_{0}^{2\pi}

V = 0 + 2\pi \times 1000 = 2000\pi\ m^{3}

7 0
3 years ago
HELP ME PLEASE!!,I WILL GIVE BRAINLIEST!!I PROMISE!!:)
Alja [10]
The answer is D, to get rid of a radical you multiply by the radical to cancel out
8 0
2 years ago
Read 2 more answers
In 2010 a family membership in a country club cost $18,000 if this cost increased $475 each year since 2010, then how much will
kvasek [131]

Answer:

21,800

Step-by-step explanation:

Because 475 x 8 equals 3800 you add 3800 to 18,000 and get 21,800

4 0
3 years ago
Other questions:
  • At a hospital, 56 percent of the babies born are boys. Of the baby girls born, 12 percent are premature. What is the probability
    15·1 answer
  • Which of the equations below could be the equation of this parabola?
    8·1 answer
  • Find the coordinates of the midpoint of the segment whose endpoints are H(6,4) and K(2,8).
    8·1 answer
  • Statement
    9·1 answer
  • If the temperature outside is 25 Celsius what clothing would be the most appropriate
    13·2 answers
  • 3x subtracted from 15x + x power of 2​
    9·1 answer
  • What are the possible values of x in 8x + 4x = -1
    9·1 answer
  • Need the value of P please
    13·1 answer
  • Translate each equation into slope-intercept form. Then, state the slope and y-intercept . 4y=2x+20
    6·1 answer
  • The scale model of a car is 5% of the size of the actual car. The length of
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!