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QveST [7]
3 years ago
12

Toko follows a budget to buy supplies to paint his room. He spends 1/2 of his budget on a roller, a tray, and tape. He spends $1

2.27 on paint, and of the remaining money, he spends 2/3 on a trim brush, which costs $3.82. How much money had he budgeted?
Mathematics
1 answer:
Natasha_Volkova [10]3 years ago
3 0
The answer is $36.

B - budget
So the calculation is as following:
B= \frac{1}{2}B + 12.27 +  \frac{3.82}{ \frac{2}{3} } = \frac{1}{2}B + 12.27 + \frac{3.82*3}{2}=   \frac{1}{2}B + 12.27 +5.73
B= \frac{1}{2} B + 18
B- \frac{1}{2}B = 18
\frac{1}{2}B = 18
B = 18*2=36
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Which sequence of transformations confirms congruence by mapping shape I onto shape II?
Lubov Fominskaja [6]

Answer:

  • Neither of the choices is correct.

Explanation:

<u>1. Coordinates of the vertices of the figure I (preimage):</u>

  • (10, - 5)
  • (15, -5)
  • (10, - 10)
  • (15, -10)

<u />

<u>2. Coordinates of the vertices of the figure II (image):</u>

  • (0,10)
  • (0,15)
  • (-5,10)
  • (-5, 15)

Since many different rigid transformations can map the figure I into the figue II, you will need to use trial and error.

The most important is to do it in an educated way.

I will start by eliminating some options.

The first option, a reflection across the x-axis and 15 units left, does not work, because the reflection across the x-axis would shift the figure to a lower position than what you need.

The third option, a 90º counterclokwise rotation about the origin then a translation 10 units up, would move the figure to the second quadrant, and we need it in the third quadrant.

I will try now with the second choice, a 90º clockwise rotation and then 25 units up:

First, a 90º clockwise rotation, which is the same that a 270º counterclockwise rotation, follows the rule (x, y) → (y, -x)

Then, that results in:

  • (10, - 5) → (-5, -10)
  • (15, -5) → (-5, -15)
  • (10, - 10) → (-10, -10)
  • (15, -10) → (-10, -15)

Now, you can see that shifting 25 units up will not work, because you need that two x-coordinates become 0 (zero). So, this is not the correct set of transformations either.

A 180º rotation about the origin and a translation 10 units right follow this chain of rules:

  • (x, y) → (-x, -y) → (-x + 10, -y)

That means:

  • (10, - 5) → (-10,5) → (-10 + 10, 5) = (0, 5)
  • (15, -5) → (-15, 5) → (-15 + 10, 5) = (-5, 5)
  • (10, - 10) → (-10, 10) → (-10 + 10, 10) = (0, 10)
  • (15, -10) → (-15, 10) → (-15 + 10, 10) = (-5, 10)

        These last points do not coincide either with the vertices of the figure II.

In conclusion, neither of the choices gives the correct answer to the question.

8 0
3 years ago
Read 2 more answers
The number of 8th graders in choir is three times the number of the 7th graders. if there are 48 8th graders choir how.many 7th
stira [4]
Divide 48 by 3, for every three 8th graders, there is one 7th grader in choir
48÷3=16
There's 16 7th graders in choir !!
7 0
3 years ago
System of conics help
ZanzabumX [31]

Answer:

Solutions are (6,3) and (-2,3).

Step-by-step explanation:

From the first equation given we can write:

(x-2)^{2} = 16-(y-3)^{2}\\  

substituting for (x-2)^{2} in the second equation given we get

\frac{16-(y-3)^{2}}{16} + \frac{(y-3)^{2}}{64} = 1

\frac{-(y-3)^{2}}{16} + \frac{(y-3)^{2}}{64} =0

∴ y=3

Putting y=3 in the first equation we get

(x-2)^{2} = 16

x-2 = ±4

Hence x=6 or x=-2.

7 0
3 years ago
Help me please, kinda lost
Dmitry_Shevchenko [17]

Answer:

400cm^2

Step-by-step explanation:

For this question, you need to find the surface areas of both objects, then add them together.

For the cube:

56cm for the front

56cm for the back

42cm for the side

42cm for the other side

48cm for the top

48cm for the bottom

SA for the cube: 292cm^2

For the triangle, things are a little different. We do the same process that we did to find the SA of the cube, but we do not have to find the SA of the top side (because there isn't a top side) and we have to divide the total SA by 2 because it's a triangle.

For the triangle:

42cm for the front

42cm for the back

54cm for the slanted side

42cm for the other side

36cm for the bottom

SA for the triangle: (216/2)^2=108cm^2

292+108=400cm^2

the SA of the composite figure is 400cm^2

8 0
3 years ago
As you can see, I already answered part A. That part is easy, like kindergarten level. But I don't remember learning how to do p
drek231 [11]

Answer:

Length: 10 units.

Width:6 units

Step-by-step explanation:

Part a has 1 unit =40 yards. When we have 1 unit = 20 yards, we have divided the original numbers, 40, in half, getting 20. That means that we need to double the original amount of units, like you see above.

3 0
3 years ago
Read 2 more answers
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