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
slava [35]
2 years ago
5

1.) Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth .x squared minus 21 x equals n

egative 4 x
2.) Which kind of function best models the data in the table? Use differences or ratios.

x y
0 1.7
1 6.8
2 27.2
3 108.8
4 435.2

3.) Solve the system of equations algebraically. Show all of your steps.

y equals x squared plus two x; y equals three x plus twenty



PLEASE HELP!
Mathematics
1 answer:
Andrew [12]2 years ago
7 0
Part 1
We are given x^2-21x=-4x. This can be rewritten as x^2-18x=0.
Therefore, a=1, b=-18, c=0.
Using the quadratic formula
     x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{-\left(-18\right)\pm \sqrt{\left(-18\right)^2-4\left(1\right)\left(0\right)}}{2\left(1\right)}
     x=\frac{18\pm 18}{2}

The values of x are
     x_1=\frac{18-18}{2}=0
     x_2=\frac{18+18}{2}=18

Part 2
Since the values of y change drastically for every equal interval of x, the function cannot be linear. Therefore, the kind of function that best suits the given pairs is a quadratic function. 

Part 3.
The first equation is y=x^2+2.
The second equation is y=3x+20.

We have 
     x^2+2=3x+20
     x^2-3x-18=0
Factoring, we have 
     \left(x-6\right)\left(x+3\right)=0
Equating both factors to zero.
     x_1-6=0\rightarrow x_1=6
     x_2+3=0\rightarrow x_2=-3

When the value of x is 6, the value of y is 
     y=3\left(6\right)+20=38

When the value of x is -3, the value of y is 
     y=3\left(-3\right)+20=11

Therefore, the solutions are (6,38) or (-3,11)
You might be interested in
After distributing, which equation is equivalent to -4(3x + 2) = 10a.-12x -8 = 10b.-12x + 8 = 10c.-12x -6 = 10d.-12x + 6 = 1
rodikova [14]

Answer:

Option A: -12x-8=10 is the correct answer.

Step-by-step explanation:

Given equation is:

-4 (3x+2) = 10

We will distribute the equation by multiplying the terms inside the brackets with -4.

Therefore,

-4*3x + 2*-4 = 10

-12x +(-8) = 10

-12x - 8 = 10

The equation -4 (3x+2) = 10 will become -12x-8=10 after distributing.

Hence,

Option A: -12x-8=10 is the correct answer.

5 0
3 years ago
-6x-14y=-20<br> -3x-7y=-10
Alex Ar [27]
ANSWER:

x = 10 / 3

y = 0

STEP-BY-STEP EXPLANATION:

We will be using simultaneous equations to solve this problem. Let's first establish the two equations which we will be using.

Equation No. 1 -

- 6x - 14y = - 20

Equation No. 2 -

- 3x - 7y = - 10

First, we will make ( x ) the subject in the first equation and simplify accordingly.

Equation No. 1 -

- 6x - 14y = - 20

- 6x = - 20 + 14y

x = ( - 20 + 14y ) / - 6

x = ( - 10 + 7y ) / - 3

From this, we will make ( y ) the subject in the second equation and substitute the value of ( x ) from the first equation into the second equation to solve for ( y ) accordingly.

Equation No. 2 -

- 3x - 7y = - 10

- 7y = - 10 + 3x

- 7y = - 10 + 3 [ ( - 10 + 7y ) / - 3 ]

- 7y = - 10 + [ ( - 30 + 21y ) / - 3 ]

- 7y = - 10 + ( 10 - 7y )

- 7y = - 7y

- 7y + 7y = 0

0y = 0

y = 0

Using this, we will substitute the value of ( y ) from the second equation into the first equation to solve for ( x ) accordingly.

x = ( - 10 + 7y ) / - 3

x = [ - 10 + 7 ( 0 ) ] / - 3

x = [ - 10 + 0 ] / - 3

x = - 10 / - 3

x = 10 / 3
6 0
3 years ago
Pls help this is due very soon
Viefleur [7K]
10x16 = 160 cm

160x 3.14 = 502.4 cm

502.4 ≈ 500 cm

7 0
3 years ago
Read 2 more answers
Tyler used 6 gallons of paint to paint 4/7 of a fence. How many gallons will it take to paint the whole fences
vredina [299]

Answer:

Step-by-step explanation:

(6 gal)/(4/7 fence) = (21/2 gal)/fence = (10.5 gal)/fence

5 0
2 years ago
What is the value of (14)5?
valina [46]

Answer:

70

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • Which is bigger 2/3 or 20/27?
    11·1 answer
  • Trigonometry help please
    11·1 answer
  • Which is an example of an algebraic expression? A. m – 3 B. b &gt; –2 C. 4 c &gt; 1 D. 12 = a 6
    13·1 answer
  • How do I draw a shaded figure that represents 100%
    8·1 answer
  • How to evaluate s-r/-7 when r=-3 and s=4?
    13·1 answer
  • Is 7500000 meters greater than 750 kilometers
    11·1 answer
  • 20% of what number is 18​
    7·2 answers
  • What is 75 1/5+ 82/14
    8·2 answers
  • List and count all the outcomes for event E, in which the product of the two numbers rolled is odd.
    14·2 answers
  • Gotta need answers fast like asap, it’s geometry, just fill the blanks pls
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!