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Advocard [28]
2 years ago
11

Please give a valid complete answer with steps. Given the information below, what is m ∠CBE?

Mathematics
1 answer:
Arte-miy333 [17]2 years ago
3 0

Answer:

42 + 5 x + 7x + 6 = 180 \\ 48 + 12x = 180 \\ 12x = 132 \\ x = 11 \\ 7x + 6 = 77 + 6 = 83

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If x varies directly with y and x = 6 when y = 15, find x when y= 20.
Kaylis [27]

Answer:

8

Step-by-step explanation:

Varies directly think y=kx

Varies indirectly think y=k/x

We have first option so y=kx

x=6 and y=15 means we have 15=k(6)

So k=15/6 or reducing gives=5/2

So we just found our constant of proportionality, this number never changes.  It stays the same no matter what x or y they give you...

So the equation is y=5/2 *x

Now what is x if y=20

Plug in 20=5/2 *x

So x=20*2/5=40/5=8

6 0
3 years ago
Find the area of the parallelogram
iogann1982 [59]

Answer:

The answer is 32.

Step-by-step explanation:

Just multiply the height by the base length. 4*8=32

8 0
3 years ago
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
A store has clearance items that have been marked down by 60% they having a sale, advertising an additional 30% off clearance it
bagirrra123 [75]

The original price is 100% of the price. If the price is marked 60% off, then you pay 40% of the original price.

An item costs x dollars.

With the 60% off discount, it now costs 40% of x, or 0.4x.

Now you apply a 30% discount.

For the second discount, consider the price 0.4x to be the new original price. If the price is now discounted 30%, you will pay 70% of the new original price.

Start with 0.4x.

Now calculate 70% of 0.4x.

70% of 0.4x = 0.70 * 0.4x = 0.28x

After applying the 60% discount and the 30% discount, the item that originally cost x now costs 0.28x. 0.28x is the same as 28% of x. The amount you pay is 28% of the original price.

Answer: 28%

3 0
3 years ago
When the sum of an unknown number z and twenty-two is divided by the same unknown number, the quotient is twelve. What is the un
Anika [276]
Z+22/z = 12
z+22=12z
22=11z
2=z

Hope this helps. Just say if you need more of an explanation.
4 0
3 years ago
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