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Papessa [141]
2 years ago
6

Can anyone help me with this?​

Mathematics
1 answer:
Ivahew [28]2 years ago
4 0
I typed out everything and it won’t let me answer, love that for me !
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URGENT! (Grades close tomorrow and turning this in will boost my grade from a B to an A in College Algebra. I can't figure these
zvonat [6]

Answer:

  24.  see below for a drawing with axis intercepts labeled

  30.  the plane is parallel to the y-z plane. It is "x=4". The only axis intercept is (4, 0, 0).

Step-by-step explanation:

24. The axis intercepts are fairly easily found. You can do it a couple of ways.

<u>first way</u>

  • Set other variables to zero and divide by the coefficient of the variable of interest.

For 3x +5y +15z = 15, the x-intercept can be found by setting y and z to zero. This gives ...

  3x = 15

so, dividing by 3 tells you the x-intercept is ...

  x = 15/3 = 5

Likewise, the y- and z-intercepts are, respectively, ...

  y = 15/5 = 3

  z = 15/15 = 1

So, the points where the plane crosses the axes are ...

  (5, 0, 0), (0, 3, 0), (0, 0, 1) . . . . axes intercepts

__

<u>second way</u>

  • Divide by the constant on the right, and express all coefficients as denominators

Doing that gives ...

\dfrac{3x+5y+15z}{15}=1\\\\\dfrac{x}{5}+\dfrac{y}{3}+\dfrac{z}{1}=1

The denominators are the corresponding intercepts. (This is called the "intercept form" of the equation of the plane.)

From the above equation, we see the axis intercepts are ...

  (5, 0, 0), (0, 3, 0), (0, 0, 1) . . . . same as above

Actually, the math for these two methods is virtually identical. The second way does it "all at once", so can take fewer steps. Effectively, you're doing the math of the "first way" and expressing the result in the denominator.

__

Please note that when a variable is missing, there is no intercept for that axis. That is, the plane is parallel to that axis. (In problem 30, for example, the y- and z-variables are missing. The plane x=4 is parallel to the y- and z-axes (the y-z plane).)

_____

In the first attached drawing, the x-axis is red, the y-axis is green, and the z-axis is blue. The labeling of the points is difficult to see, but the axes are a different (lighter) color behind the plane than in front of it. This plane forms a triangle in the first octant (x, y, z > 0).

In the second attached drawing, the x=0 plane is blue; the y=0 plane is green, and the z=0 plane is red. The plane of the equation is yellow. This figure better shows the triangle in the first octant.

3-D graph paper (isometric graph paper) grids are available with a web search. Such might make it easier to draw the planes you need to draw. (See the third attachment for one example.)

3 0
3 years ago
In the graph shown, suppose that f(x) = ax, g(x) = bx, and h(x) = cx. Choose the true statement.
faltersainse [42]
Where a, b, and c are real numbers and a ≠ 0 . The quadratic term is ax 2 , the linear term is bx, and the constant term is c. Quadratic functions have degree two. The graph of a quadratic function is called a parabola. If a < 0, then the parabola opens downward, like function g. If a > 0, then the parabola opens upward like function f. If the parabola opens upward, then the vertex is the point whose yvalue is the minimum value of f. If the parabola opens downward, then the vertex is the point whose y-value is the maximum value of f. The vertical line that goes through the vertex is called the axis of symmetry of the parabola.
5 0
2 years ago
Read 2 more answers
Synthetic division!! Please help!!!<br> Fast!!
tatyana61 [14]
See that remainder in the lower, right hand corner of this array?  It's 2.  That is the value of f(-2).
3 0
3 years ago
People grapes
maksim [4K]

Answer:

1:6

5:30

?:426

You would take the ratio of each one which is simply 1:6, so to reduce ?:426 into 1:6, you would divide 426/6=71, so it would be

71:426

8 0
3 years ago
Kelvin plans to buy potato chips and coke with $50. If he buys 3 packs of potato chips and 2 cans of coke, $9 will be left. If h
Delicious77 [7]
Let the prices of a pack of potato chips and can of coke be x and y respectively
3x+2y=50-9
3x+2y=41........... (1)
4x+5y=50+21
4x+5y=71............(2)
Multiply (1) with 4 and (2) with3
12x+8y=164
12x+15y=213
On subtracting above eqs. we get
7y= 49
y=7
Putting value of y in (2)
4x+5(7)=71
4x+35=71
4x=36
x=9
x=$9
y=$7
MARK IT BRANLIEST PLZZZ....

7 0
3 years ago
Read 2 more answers
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