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Gala2k [10]
3 years ago
9

4x+y-3z=45 6x-4y+3z=41 2x-7y-11z=85

Mathematics
1 answer:
photoshop1234 [79]3 years ago
7 0

Answer:

{x,y,z} = {8,-2,-5}

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Write an inequality that would include the point (3,78), (0,312), (5,10) to be part of the solution.
just olya [345]

Answer:

We want to write an inequality with the points (3, 78), (0, 312) and (5, 10) as solutions.

Then the set of the x-values is {0, 3, 5}

The set of the y-values is {10. 78. 312}

So if we wrote an inequality like:

y > 5

It would include all these solutions, because:

10 > 5

78 >  5

312 > 5

And this has no restriction on the x-variable, so all the x-value range can be a solution, meaning that the points (3, 78), (0, 312) and (5, 10) are solutions to that inequality.

Another one (also trivial) can be:

x < 9

because:

3 < 9

0 < 9

5 < 9

And we have no restriction on the y-values, then the points (3, 78), (0, 312) and (5, 10) are solutions to that inequality.

8 0
3 years ago
What is the discriminant of the quadratic equation 0 = –x2 4x – 2? a.–4 b.8 c.12 d.24
MrMuchimi
X^2 - 4x + 2
d = b^2 - 4ac, where a = 1, b = -4 and c = 2
d = (-4)^2 - 4 x 1 x 2
d = 16 - 8
d = 8
4 0
3 years ago
A skate ramp is 4.2 meters long. It rises up 1.7 meters. What’s is the angle of elevation to the nearest tenth of a degree?
Kipish [7]
Θ
=
arcsin
(
.7
4.2
)
≈
10
∘
Explanation:
We view the ramp as a right triangle. The hypotenuse is 4.2 and the vertical side .7, which is opposite the angle
θ
we seek.
sin
θ
=
.7
4.2
=
1
6
I'm going to finish the problem but I'll note if we were actually building the ramp we don't need to know the angle; this sine is sufficient.
θ
=
arcsin
(
1
6
)
θ
≈
10
∘
which I think is a pretty steep ramp for a wheelchair.
There will be another inverse sine that is the supplementary angle, around
170
∘
, but we can rule that out as a value for a ramp wedge angle.
4 0
3 years ago
Peter baked 18 cookies. He gave 2/3 of the cookies to his friend. How many cookies did Peter give to his friend
andre [41]

Answer:

12

thStep-by-step explanation:

4 0
3 years ago
Read 2 more answers
Find The art length of a sector with an area of 8 square units.
frez [133]
\bf \textit{area of a sector of a circle}\\\\&#10;A=\cfrac{\theta \pi r^2}{360}\quad &#10;\begin{cases}&#10;r=radius\\&#10;\theta =angle~in\\&#10;\qquad degrees\\&#10;------\\&#10;A=8\\&#10;r=4&#10;\end{cases}\implies 8=\cfrac{\theta \pi 4^2}{360}\implies \cfrac{8\cdot 360}{4^2\pi }=\theta &#10;\\\\\\&#10;\cfrac{2880}{16\pi }=\theta \implies \boxed{\cfrac{180}{\pi }=\theta }\\\\&#10;-------------------------------\\\\

\bf \textit{arc's length}\\\\&#10;s=\cfrac{\theta \pi r}{180}\quad &#10;\begin{cases}&#10;r=radius\\&#10;\theta =angle~in\\&#10;\qquad degrees\\&#10;------\\&#10;\theta =\frac{180}{\pi }\\&#10;r=4&#10;\end{cases}\implies s=\cfrac{\frac{180}{\underline{\pi} }\underline{\pi} \cdot 4}{180}\implies s=\cfrac{\underline{180}\cdot 4}{\underline{180}}&#10;\\\\\\&#10;\boxed{s=4}

if you do a quick calculation on what that angle is, you'll notice that it is exactly 1 radian, and an angle of 1 radian, has an arc that is the same length as its radius.

that's pretty much what one-radian stands for, an angle, whose arc is the same length as its radius.
6 0
3 years ago
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