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
MAXImum [283]
3 years ago
14

Find the length of the segment AB if points A and B are the intersection points of the parabolas with equations y=−x^2+9 and y=2

x^2−3 .
Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
6 0

Answer:

The length of the segment AB is √48

Step-by-step explanation:

Given the two equations, the idea is to find the solution to the system

y = x² + 9

y = 2x² - 3

you can use the equality method to find the "x" and "y" of the solution.

x² + 9 = 2x² - 3 ⇒ x² - 2x² = -3 - 9 ⇒ -x² = -12 ⇒ x² = 12 ⇒ x = ±√12.

With this value we return to the original equations and replace it to find "y" values.

y = (±√12)² + 9 ⇒ y = 21

The solutions to the system are (-√12, 21) and (√12, 21). Now you need to find the distance between this points.

d= √[(x2-x1)² + (y2-y1)²] ⇒ d = √48.

The length of the segment AB is √48.

You might be interested in
Why is 3÷0.5 is 6, why is it?​
Alekssandra [29.7K]

Answer:

Step-by-step explanation:

A quick way to divide by 0.5 or ½ is to double the number (or multiply number by 2). The reason for this is that two halves go into a whole.

3 0
2 years ago
A triangle has sides of length 2, 2, and 3. Which of the following is the measure of the obtuse angle of the triangle?
kramer

Answer:

97.18^{\circ}

Step-by-step explanation:

An obtuse angle in the triangle is opposite to the greatest side. The greatest side in the triangle with sides lengths 2, 2 and 3 is side with length 3. By the cosine rule,

3^2=2^2+2^2-2\cdot 2\cdot 2\cdot \cos \alpha,\\ \\9=4+4-8\cos \alpha,\\ \\-8\cos \alpha=9-4-4=1,\\ \\\cos \alpha=-\dfrac{1}{8},\\ \\\alpha\approx 97.18^{\circ}.

7 0
3 years ago
HELPPPPP PLSSSS
Pavlova-9 [17]

Answer:

43:22

Step-by-step explanation:

start with the large ratio then divide both sides as much as possible:

86:44

43:22

4 0
2 years ago
PLEASE HELP ill Mark BRAINLIEST!
alisha [4.7K]

Answer:

im im give the anser in a sec

Step-by-step explanation:

4 0
3 years ago
A father is 38 years old. his sons are 13 and 5 years old, and his daughter is 8 years old. In how many years will the father be
nalin [4]

Answer:

6 years

Step-by-step explanation:

So each person's age can be represented as a linear equation, since each year our age increases by 1. It can be represented in the slope-intercept form: y=mx+b. The slope in this case is going to be 1, since the time is going to be years, and each year everyone's age goes up by 1 (of course if you're still alive...) and y-intercept in this case represents their current age.

So the father can be represented as: y=x+38

The sons can be represented as: y = x+13 and y=x+5

The daughter can be represented as: y=x+8

So adding up all his children you get:

(x+13)+(x+5)+(x+8)

This gives you the equation:

3x+26

Now set this equal to the father's age to solve for x (in this context it's years)

3x+26=x+38

Subtract from both sides

2x+26=38

Subtract 26 from both sides

2x=12

Divide both sides by 2

x=6

So in 6 years the father will be the same age as his children put together

8 0
2 years ago
Other questions:
  • *WILL GIVE BRAINLIEST TO WHOEVER HAS A DETAILED ANSWER*
    7·2 answers
  • Find the area of the following ellipse Use = 3.14 and round to nearest tenth. a = 7 in.; b = 9 in.
    15·1 answer
  • Anybody know the answer?
    9·2 answers
  • Classify each pair of angles as Complementary, Supplementary or neither.
    5·1 answer
  • Sea H = {(x, y, z, w) : x = y, w = 3y} y sea v = (−1, 2, 3, 1). Encuentre una base para su complemento ortogonal H⊥. Escriba v =
    12·1 answer
  • The Basketball Boosters Club plans a pancake supper to raise $1,200. They can serve 240 people. They
    5·1 answer
  • I need help with this please :)
    7·1 answer
  • Use the properties of equality to simplify the equation. Tell whether the equation has zero, one, or infinitely many solutions.
    11·1 answer
  • Sixety five divided by fifteen ​
    13·1 answer
  • Help <br><br> Dealing with corresponding write reasons as well pls
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!