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slava [35]
3 years ago
12

How may times can 24 go into 50​

Mathematics
1 answer:
ale4655 [162]3 years ago
5 0

Answer:

Twice

Step-by-step explanation:

Because 24 x 24 would be 48

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(a) Find a vector parallel to the line of intersection of the planes −4x+2y−z=1 and 3x−2y+2z=1.
valentinak56 [21]

Find the intersection of the two planes. Do this by solving for <em>z</em> in terms of <em>x</em> and <em>y </em>; then solve for <em>y</em> in terms of <em>x</em> ; then again for <em>z</em> but only in terms of <em>x</em>.

-4<em>x</em> + 2<em>y</em> - <em>z</em> = 1   ==>   <em>z</em> = -4<em>x</em> + 2<em>y</em> - 1

3<em>x</em> - 2<em>y</em> + 2<em>z</em> = 1   ==>   <em>z</em> = (1 - 3<em>x</em> + 2<em>y</em>)/2

==>   -4<em>x</em> + 2<em>y</em> - 1 = (1 - 3<em>x</em> + 2<em>y</em>)/2

==>   -8<em>x</em> + 4<em>y</em> - 2 = 1 - 3<em>x</em> + 2<em>y</em>

==>   -5<em>x</em> + 2<em>y</em> = 3

==>   <em>y</em> = (3 + 5<em>x</em>)/2

==>   <em>z</em> = -4<em>x</em> + 2 (3 + 5<em>x</em>)/2 - 1 = <em>x</em> + 2

So if we take <em>x</em> = <em>t</em>, the line of intersection is parameterized by

<em>r</em><em>(t)</em> = ⟨<em>t</em>, (3 + 5<em>t</em> )/2, 2 + <em>t</em>⟩

Just to not have to work with fractions, scale this by a factor of 2, so that

<em>r</em><em>(t)</em> = ⟨2<em>t</em>, 3 + 5<em>t</em>, 4 + 2<em>t</em>⟩

(a) The tangent vector to <em>r</em><em>(t)</em> is parallel to this line, so you can use

<em>v</em> = d<em>r</em>/d<em>t</em> = d/d<em>t</em> ⟨2<em>t</em>, 3 + 5<em>t</em>, 4 + 2<em>t</em>⟩ = ⟨2, 5, 2⟩

or any scalar multiple of this.

(b) (-1, -1, 1) indeed lies in both planes. Plug in <em>x</em> = -1, <em>y</em> = 1, and <em>z</em> = 1 to both plane equations to see this for yourself. We already found the parameterization for the intersection,

<em>r</em><em>(t)</em> = ⟨2<em>t</em>, 3 + 5<em>t</em>, 4 + 2<em>t</em>⟩

3 0
3 years ago
Is (x +1) a factor of <br> f(x) = x3 + 2x2 −5x − 6 ?<br><br> Yes <br> No
sertanlavr [38]

Answer:

Yes.

Step-by-step explanation:

You can find it out by factoring but ill do it easier way.

(x + 1 ) = 0 put the first and second equation to 0

x = -1

x³ + 2x² - 5x - 6 = 0  Now plug in the x in the equation

(-1)³ + 2(-1)² - 5(-1) - 6 = 0

0 = 0

so (x + 1) is a factor.

5 0
3 years ago
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Brandon earns a rebate each month on his meals and movie tickets. He earns $0.50 for each movie ticket and $2 for each meal. Las
AURORKA [14]

Let ticket be x and meal be y

So $0.50 for each movie ticket = 0.50x

$2 for each meal = 2y


He purchased 22 tickets, so x = 22

0.50 * 22 = $ 11


Now the total value is $25 (with both ticket and meal)

total = t

0.50x + 2y = t

you know x = 22 and t = 25

11 + 2y = 25


Part A)

2y = 25 -11

y = 14/2

y = 7

Number of meal is 7


Part B)

(don't know about part B)

0.50x + 2y = 25

0.50(22) + 2(7) = 25

11 + 14 = 25

25 = 25

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3 years ago
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zepelin [54]

Answer:

a.

Step-by-step explanation:

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3 years ago
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torisob [31]
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2 years ago
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