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kramer
2 years ago
14

Find the measure of the missing angles

Mathematics
1 answer:
vovikov84 [41]2 years ago
4 0

Answer:

∠c = 33°

∠b= 147°

Step-by-step explanation:

A line is 180°, and ∠c + 147° make up a linear pair.

180 - 147 = 33°

∠c is 33°.

∠b and 147° angle are vertical angles, meaning that they have the same angle measure.

∠b = 147°.

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determine the point of intersection of the following pair of lines ............2x-3y-4=-13 and 5x=-2y+25. 3x+2y-7=0 and 2x=12-5y
grandymaker [24]

Answer:

  1. (x, y) = (3, 5)
  2. (x, y) = (1, 2)

Step-by-step explanation:

A nice graphing calculator app makes these trivially simple. (See the first two attachments.) It is available for phones, tablets, and as a web page.

__

The usual methods of solving a system of equations involve <em>elimination</em> or <em>substitution</em>.

There is another method that is relatively easy to use. It is a variation of "Cramer's Rule" and is fully equivalent to <em>elimination</em>. It makes use of a formula applied to the equation coefficients. The pattern of coefficients in the formula, and the formula itself are shown in the third attachment. I like this when the coefficient numbers are "too messy" for elimination or substitution to be used easily. It makes use of the equations in standard form.

_____

1. In standard form, your equations are ...

  • 2x -3y = -9
  • 5x +2y = 25

Then the solution is ...

  x=\dfrac{-3(25)-(2)(-9)}{-3(5)-(2)(2)}=\dfrac{-57}{-19}=3\\\\y=\dfrac{-9(5)-(25)(2)}{-19}=\dfrac{-95}{-19}=5\\\\(x,y)=(3,5)

__

2. In standard form, your equations are ...

  • 3x +2y = 7
  • 2x +5y = 12

Then the solution is ...

  x=\dfrac{2(12)-5(7)}{2(2)-5(3)}=\dfrac{-11}{-11}=1\\\\y=\dfrac{7(2)-12(3)}{-11}=\dfrac{-22}{-11}=2\\\\(x,y)=(1,2)

_____

<em>Note on Cramer's Rule</em>

The equation you will see for Cramer's Rule applied to a system of 2 equations in 2 unknowns will have the terms in numerator and denominator swapped: ec-bf, for example, instead of bf-ec. This effectively multiplies both numerator and denominator by -1, so has no effect on the result.

The reason for writing the formula in the fashion shown here is that it makes the pattern of multiplications and subtractions easier to remember. Often, you can do the math in your head. This is the method taught by "Vedic maths" and/or "Singapore math." Those teaching methods tend to place more emphasis on mental arithmetic than we do in the US.

7 0
3 years ago
A certain type of digital camera comes in either a 3-megapixel version or a 4 megapixel version. A camera store has received a s
Morgarella [4.7K]

Answer:

a) Hyper-geometric distribution

b1) P(X=2) = 0.424

b2) P(X>2) = 0.152

C1) Mean of X = 1.67

C2) Standard Deviation of X = 0.65

Step-by-step explanation:

b1) P(X = 2) = (5C2 * 7C2)/(12C4) = (10 * 21)/(495) = 210/495

P(X=2) = 0.424

b2) P(X>2) = 1 - P(X≤2) = 1 - [P(X=0) + P(X=1) + P(X=2)]

P(X=0) = (7C4)/(12C4) = 35/495 = 0.071

P(X=1) =  (5C1 * 7C3)/(12C4) = (5 * 35)/(495) = 175/495 = 0.354

P(X=2) = 0.424

P(X>2) = 1 - P(X≤2) = 1 - [0.424 + 0.071 + 0.354]

P(X>2) = 0.152

C1) Mean of X = nk/N

k = number of 3-megapixel cameras = 5

n = number of selected cameras = 4

N = Total number of cameras = 12

Mean of X = 5*4/12

Mean of X = 1.67

C2) Standard Deviation of X

Standard deviation of X=(nk/N*(1-k/N)*(N-n)/(N-1))1/2

Standard Deviation of X=(4*(5/20)*(1-5/12)*((12-4)/(12-1))^1/2 =0.65

Standard Deviation of X = 0.65

4 0
3 years ago
Use rounding to estimate the product.<br><br> 8.24 × 5.88<br><br> 40<br> 45<br> 48<br> 85
marin [14]
The answer would be 48. I hope that helped
8 0
3 years ago
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mixer [17]

Answer: 3

Step-by-step explanation:

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2 years ago
State whether the number is a solution to the giving inequality.
Sloan [31]
Yes -14 is greater than -17
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