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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.

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gogolik [260]

1):  Answer  =====>  Letter Choice, (B),  The rate in which you walked home, The slope is the same, as the Rate of Change, In Distance Divided by the Change in Time  =====>    d    =     4   -1/15t(4) / 1/15t

 

2):   The Equation:  d     =       -1/15t     +     4

The more the Number of Minutes:  Larger the Negative Quantity;  ====>   -1/15t

The Larger the Negative Quantity in Equation:  D value is Smaller:

Therefore your Answer ===>  The Distance from home (d), Decreased with Minute Walked (t)  ====>  So, Letter Choice,  (C)



2):   Towards your home, The slope is Negative, and the Distance (y - value), Decreases, as the Time  (x- Values),  Increases. Notice the Slope is Negative, Because, you are getting closer to home.






Hope that helps!!!!                                           : )

7 0
3 years ago
Can someone help w number 4
strojnjashka [21]

Answer:

angle DFG = 49 degrees

angle JKL = 41 degrees

Step-by-step explanation:

When angles are complementary with each other, it means that if you add both of the angles up, it adds up to 90 degrees.

In this question, you would have to add up angle DFG and angle JKL and find the x that makes the equation equal to 90 degrees.

angle DFG = x + 5

angle JKL = x - 3

(x + 5) + (x - 3) = 90

2x + 2 = 90

2x = 90 - 2

2x = 88

x = 44

But since we have to find out the angle measures, we have to the "x = 44" with the x's in the DFG and JKL angles.

DFG = (44) + 5 = 49

JKL = (44) - 3 = 41

7 0
3 years ago
Match each graph to the equation of its line.
Serjik [45]

Answer:

b

Step-by-step explanation:

5 0
3 years ago
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<u>Answer:</u>

Lamar will charge\$7 to the comic dealer for a comic book.

<u>Solution:</u>

It is given that lamar purchases a comic book for \$4. He then marks up the price of a comic book by 75\% which means he increases the price of the book by 75\% and then sells it to the comic dealer.

We have to find out how much will he charge the comic book dealer.

New price of the book after lamar marks up the price is given by

New price =  \$4 + \frac{75}{100} \times \$4

=\$4 + \$3= \$7

Thus, lamar will charge \$7 to the comic dealer for a comic book.

4 0
3 years ago
What is the base of the exponential function?
jeka94

Answer:

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4 0
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