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
White raven [17]
3 years ago
6

1. What are the solutions (coordinate points) to the system of equations?

Mathematics
1 answer:
Leto [7]3 years ago
3 0

Question 1

The given system of equations is:

y =  {x}^{2}  + 5x + 6 \\ y = 3x + 6

Equate the two equations:

{x}^{2}  + 5x + 6 = 3x + 6

Rewrite in standard form:

{x}^{2}  + 5x - 3x + 6 - 6 = 0

{x}^{2}   + 2x = 0

x(x + 2) = 0

x = 0 \: or \: x =  - 2

When we put x=0, in y=3x +6, we get:

y = 3(0) + 6 = 6

One solution is (0,6)

When we put x=-2, into y=3x+6, we get:

y = 3( - 2) + 6 = 0

Another solution is (-2,0)

The solutions are; (0,6) and (-2,0)

Question 2:

The function is

f(x) =  {x}^{6}  -  {x}^{4}

Let us put x=-x,

f( - x) =  {( - x)}^{6}  -  {( - x)}^{4}

This gives:

f( - x) =  {x}^{6}  -  {x}^{4}

We can observe that:

f(x) = f( - x)

This is the property of an even function.

Question 3:

The given function is

f(x) =  {x}^{2}  + 3x - 2

The average rate of change of f(x) from x=a to x=b is given as:

\frac{f(b) - f(a)}{b - a}

This is the slope of the secant line connecting the two points on f(x)

From x=2 to x=6, the average rate of change

=  \frac{f(6) - f(2)}{6 - 2} \\   =  \frac{ {6}^{2}  + 3 \times 6 -  2 -  {2}^{2}   -  3 \times 2  + 2 }{4} \\   =  \frac{36 + 18 - 4  - 6}{4}  \\  =  \frac{44}{4}   \\ = 11

The average rate of change is 11

You might be interested in
What is the sum of the first 20 terms of the arithmetic sequence shown? \displaystyle \frac{1}{3} 3 1 ​ , \displaystyle \frac{2}
Murrr4er [49]

Answer:

70

Step-by-step explanation:

a_1 = First term = \dfrac{1}{3}

d = Common difference = \dfrac{2}{3}-\dfrac{1}{3}=\dfrac{1}{3}

n = Number of terms = 20

Sum of arithmetic progression is given by

S=\dfrac{n}{2}[2a_1+(n-1)d]\\\Rightarrow S=\dfrac{20}{2}\times (2\times \dfrac{1}{3}+(20-1)\dfrac{1}{3})\\\Rightarrow S=70

The sum of the first 20 terms of the arithmetic sequence is 70.

5 0
3 years ago
What is the fraction as a decimal for -4/7
Andrei [34K]

Answer:

-57.14%

Step-by-step explanation:

8 0
3 years ago
The ratio of Dobermans to terriers is 2:7. There are 774 dogs altogether.
kaheart [24]

Answer:

172-602 I think

Step-by-step explanation:

6 0
2 years ago
What is the equation of the line that passes through point [3,-1] and has a slope of 2
Savatey [412]

Answer:

y = 2x - 7

Step-by-step explanation:

lmk if you want an explanation

8 0
3 years ago
Jodi delivers 54 newspapers on Saturday and 78 on newspapers Sunday. She makes bundles of 6 newspapers for each of her delivery
Katarina [22]
First add 54+78 which is 132. Then do 132 divided by 6 which is 22. 22 is the answer! When u need help ask me ok
4 0
3 years ago
Other questions:
  • WILL GIVE BRAINEST <br>If f(x)=5x^2-3....
    8·1 answer
  • Greatest to least 0.04; 0.5; 0.021; 0.133
    8·2 answers
  • Please see attachment for the question.
    7·1 answer
  • What is (2/5 +1/5) - 3/10 ?
    5·2 answers
  • Convert 8.6 ha to km².<br> Remember to include units with your answer.
    7·1 answer
  • You spin a spinner that is equally divided into 7 parts. 2 parts white, 2 parts are speckled, and 3 parts are blue.
    5·1 answer
  • A number w increased by 6 is at least 24. Using an inequality
    13·2 answers
  • Solve the following equation q=1/3bh , for b
    15·1 answer
  • A bird flys 45 miles per hour. What is the speed in feet per second
    9·1 answer
  • 2 1/3 ÷ 1 3/4-2.6÷1.3<br> pls i rlly need help anything will help
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!