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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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Simplify the following complex fraction.(3/7---1/3)2/3-----1/7
Yakvenalex [24]
Please retype this fraction.  If by "---" you mean "subtraction," type 3/7-1/3.

Let's assume that the problem is as follows:  (3/7-1/3)(2/3)-1/7;
first, find the LCD of 3/7 and 1/3 and then combine 3/7 and -1/3).
second, multiply your result by (2/3).
third, subtract 1/7 from your result.

If, however, your "---" and "-----" mean "division, then the above is all wrong.

If that's the case, then please retype your whole question.

You could express "the quotient of 2/3 and 1/6" as follows:
   
            2
          ----
            3

------------------------
            1
          -----
             6

Is that what you meant?

Sorry to be picky, but it's very important that you express math properly.





4 0
3 years ago
Please help I need an answer ASAP !
Mila [183]
Well, 4+1=5, so we need to first find:
150 \div 5 = 30
Ivan gets
30 \times 4 = 120
Tanya gets
30 \times 1 = 30
120 - 30 =  \boxed{90}

6 0
3 years ago
Find the distance between these points.<br> R(-1,0), S(8,6)<br> V(26)<br> V(85)<br> 3V(13)
Thepotemich [5.8K]

Answer:

The distance is equal to 3\sqrt{13}\ units

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

we have

R(-1,0)\\S(8,6)  

substitute the values

d=\sqrt{(6-0)^{2}+(8+1)^{2}}

d=\sqrt{(6)^{2}+(9)^{2}}

d=\sqrt{36+81}

d=\sqrt{117}\ units

Simplify

d=3\sqrt{13}\ units

4 0
3 years ago
3. The diagonal of a rectangular field is 169 m. Ifthe ratio of the length to the width is 12:5, find the: (a) (b) dimensions; p
Kazeer [188]

The dimensions of the rectangle are length 156 m and a width of 65m, and a perimeter P = 442m

<h3>How to find the dimensions of the rectangle?</h3>

For a rectangle of length L and width W, the diagonal is:

D = \sqrt{L^2 + W^2}

Here we know that the diagonal is 169m.

And the ratio of the length to the width is 12:5

This means that:

W = (5/12)*L

Replacing all that in the diagonal equation:

169 = \sqrt{((5/12)^2*L^2 + L^2} \\\\169^2 = (25/144)*L^2 + L^2 = ( 25/144 + 1)*L^2\\\\\frac{169}{\sqrt{25/144 + 1} } = L = 156

So the length is 156 meters, and the width is:

W = (5/12)*156 m = 65m

Finally, the perimeter is:

P = 2*(L + W) = 2*(156 m + 65m) = 442m

If you want to learn more about rectangles:

brainly.com/question/17297081

#SPJ1

8 0
1 year ago
How many real roots does a quadratic equation have if the discriminant is -3?
soldier1979 [14.2K]

\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ y=\stackrel{\stackrel{a}{\downarrow }}{a}x^2\stackrel{\stackrel{b}{\downarrow }}{+b}x\stackrel{\stackrel{c}{\downarrow }}{+c} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\stackrel{\textit{no real roots}}{\textit{no solution}}\quad \checkmark \end{cases}

6 0
3 years ago
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