Answer:
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Find a point-slope form for the line that satisfies the stated conditions. Slope , passing through (-5,4)
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I don't see a value for the slope. We need that to set the equation, otherwise I can write an unlimited number of equations that pass through (-5,4).
I'll assume a slope so that you can see how the procedure would work. I like 6, so we'll assume a slope of 6.
The equation for a straight line has the form y = mx + b, where m is the slope and y is the y-intercept, the value of y when x = 0. We want a line that has slope 6, so:
y = 6x + b
We need to find b, so substitute the point (-5,4) that we know is on the line:
4 = 6*(-5) + b and solve for b
4 = -30 + b
b = 34
The line is y = 6x + 34
<h3>
Answer: x = 19</h3>
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Explanation:
Arc XPZ = 271 is shown in the diagram below as the blue arc. The red arc is the remaining bit minor arc XZ. The term "minor arc" refers to any arc that is less than 180 degrees.
Subtract the measure of arc XPZ from 360 to get
360 - (arc XPZ) = 360 - 271 = 89
So minor arc XZ is 89 degrees. Central angle ZCX is also 89 degrees because this central angle cuts off (or subtends) minor arc XZ.
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We are told that angle XYZ circumscribes the circle. This is just another way of saying that segments XY and YZ are tangent to the circle. Tangent segments form 90 degree angles with the radius. Therefore, angles CXY and CZY are both 90. I have marked both angles with square angle markers in the diagram below.
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We know three angles of quadrilateral CXYZ.
- angle ZCX = 89
- angle CXY = 90
- angle CZY = 90
The only thing we don't know is angle XYZ, which we'll just call some variable for now. Let's use M. So M = measure of angle XYZ.
For any quadrilateral, the four angles always add up to 360 degrees
(angleZCX)+(angleCXY)+(angleCZY)+(angleXYZ) = 360
89+90+90+M = 360
269+M = 360
269+M-269 = 360-269
M = 91
angle XYZ = 91 degrees
Set this equal to (4x+15), which is what angle XYZ is also equal to, then solve for x
4x+15 = 91
4x+15-15 = 91-15
4x = 76
4x/4 = 76/4
<h3>x = 19</h3>
Answer:
a)
b)
c)
d)
Step-by-step explanation:
a) If the coins are all the same, we have a combination of 35 identical coins in 5 persons.
The amount of combinations is
being n the number of coins and r the number of grandchildren.
b) If the coins are different, the number of combinations can be calculated as:
c) If the coins are all the same, and each grandchild gets the same number of coins, there is only one combination for that (everyone gets 35/5=7 coins)
d) If the coins are all distinct, but each of the grandchildren get the same numer of coins, the expression to calculate this is:
Answer:
D.
Step-by-step explanation: