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
Ksju [112]
2 years ago
5

Find the distance between the points of intersection of the graphs of the functions.

Mathematics
2 answers:
svlad2 [7]2 years ago
8 0

Answer:

Below in bold.

Step-by-step explanation:

1) y=x^2-3x+4 and y=x+1

Using substitution for y :

x + 1 = x^2 - 3x + 4

x^2 - 4x + 3 = 0

(x - 3)(x  - 1) = 0

x = 1, 3.

If x = 1,  y = 1-3+4 = 2 and

if x = 3, y = 9-9+4 = 4.

So the points of intersection are (1, 2) and (3, 4)

Distance between them = √[(3-1)^2 + (4-2)^2 ] = √8.

2) y=x^2-4 and y=2x-4

2x - 4 = x^2 - 4

x^2 - 2x = 0

x(x - 2) = 0

x = 0, 2

When x = 0,  y = -4 and

when x = 2,  y = 0

So the points are (0,-4) and (2, 0)

So distance between the 2 points = √[(2-0)^2 + (0--4)^2)] = √20.

Viefleur [7K]2 years ago
7 0

Answer:

Find the value of x and y in coordinate form, that'll be the point of intersection.

Question 1

{ \rm{y =  {x}^{2} - 3x + 4 }} \\ { \boxed{ \tt{but \: y = x + 1 \: }}} \\  \\ { \rm{(x + 1) =  {x}^{2} - 3x + 4 }} \\  \\ { \rm{ {x}^{2} - 4x + 3 = 0 }} \\  \\ { \rm{(x - 3)(x - 1) = 0}} \\  \\ { \boxed{ \rm{x_{1} = 3 \:  \: and \:  \: x _{2}  = 1}}} \\  \\ { \boxed{ \tt{remember \: y = x + 1}}} \\  \\ { \rm{y _{1} = 4 \:  \: and \:  \: y _{2}  = 2 }}

Therefore, points of intersection are two

Answer: <u> </u><u>(</u><u>3</u><u>,</u><u> </u><u>4</u><u>)</u><u> </u><u>and</u><u> </u><u>(</u><u>1</u><u>,</u><u> </u><u>2</u><u>)</u>

Question 2:

Following the steps as in question 1

{ \rm{y =  {x}^{2}  - 4}} \\  \\{ \rm{2x - 4 =  {x}^{2}  - 4}} \\  \\ { \rm{ {x}^{2} = 2x }} \\  \\ { \boxed{ \rm{x = 2}}} \\ { \tt{remember : \: y = 2x - 4 }} \\ { \boxed{ \rm{y = 0}}}

Answer: <u>(2, 0)</u>

You might be interested in
Write an expression to represent: The sum of ten and the quotient of a number x and 6.
Minchanka [31]
Let us break it down. A sum of ten. That is just 

+10

Then, we will add that to the quotient (which is the number after dividing) of a number x and 6. We can write that as 

+ x/6

The slash means division here. Thus your final answer is 


10 + x/6
8 0
2 years ago
The circumference of jj's basketball is 29.6 inches. Will it go through the basket that is 10 inches in diameter?
Olenka [21]

Step-by-step explanation:

circumference of jj's basketball = 29.6 inches

Circumference of basket = 3.14 * 10 = 31.4 inches

Because

circumference of jj's basketball < Circumference of basket

Therefore ball will go through the basket.

7 0
3 years ago
Read 2 more answers
A researcher was testing the number of popcorn kernels that popped out of a mini bag of 100 kernels after being cooked for the s
Lelechka [254]

Answer:

The percentage of the bag that should have popped 96 kernels or more is 2.1%.

Step-by-step explanation:

The random variable <em>X</em> can be defined as the number of popcorn kernels that popped out of a mini bag.

The mean is, <em>μ</em> = 72 and the standard deviation is, <em>σ</em> = 12.

Assume that the population of the number of popcorn kernels that popped out of a mini bag follows a Normal distribution.

Compute the probability that a bag popped 96 kernels or more as follows:

Apply continuity correction:

P( X\geq 96)=P( X>96+0.50)

                 =P( X>96.50)\\=P(\frac{X-\mu}{\sigma}>\frac{96.50-72}{12})\\=P(Z>2.04)\\=1-P(Z

*Use a <em>z</em>-table.

The probability that a bag popped 96 kernels or more is 0.021.

The percentage is, 0.021 × 100 = 2.1%.

Thus, the percentage of the bag that should have popped 96 kernels or more is 2.1%.

3 0
3 years ago
What are the Horizontal and vertical shift of <br> y = x+2-3
Nana76 [90]
If the equation is y=(x+2)-3 then the shifts are
3 down and 2 to the left
7 0
2 years ago
The area of a rectangular pool is 6992 m².
Nina [5.8K]

Step-by-step explanation:

area=6992m2

length=92m

Now,

area of rectangle=6992

3 0
2 years ago
Other questions:
  • Evaluate the given integral by making an appropriate change of variables, where R is the region in the first quadrant bounded by
    15·1 answer
  • Factor the common factor out of –12 + 15x. A. x(–8 + 5x2) B. 3(–4 + 5x) C. x(–12 + 15x) D. 3x(–4 + 5x)
    9·2 answers
  • Solve the equation for solutions in the interval [0, 2 π). Use algebraic methods and give exact values. Support your solution gr
    9·2 answers
  • HELP ME PLEASE!!! I SWEAR I'LL GIVE YOU THE BRAINLIEST ANSWER
    5·1 answer
  • Find the volume of the cone
    13·1 answer
  • What is 3 times 1/3 and subtract 5
    11·2 answers
  • 3+3+67+7+4+6+78+68+22+71+100-100=<br> FIND THE ANSWER
    12·2 answers
  • How to calculate angle which is 25 degree?
    8·1 answer
  • Use graphing technology to find the range of the function f(x)=-x^2+4.f(x)=−x <br> 2<br> +4.
    6·1 answer
  • On a snowy day 85% of the students of Wilson high school were present. If 572 of the students were present, how many students we
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!