Answer:
(5, 1) and (-5, -7)
Step-by-step explanation:
Given the simultaneous equations
x^2– y^2 = 24 .... 1
x= 3 + 2y .... 2
Substitute 2 into 1
(3-2y)^2-y^2 = 24
Expand
9 - 12y + 4y^2 - y^2 = 24
9 - 12y + 3y^2 = 24
3y^2 - 12y + 9-24 = 0
3y^2 -12y -15 = 0
y^2-4y-5 = 0
y^2+5y - y - 5 = 0
y(y+5) - 1 (y+5) = 0
y-1 = 0 and y+5 = 0
y = 1 and -5
Substitute the values of y into 2
Recall that x = 3+3y
when y = 1
x = 3 + 2(1)
x = 5
when x = -5
x = 3 + 2(-5)
x = 3 - 10
x = -7
Hence the solutions are (5, 1) and (-5, -7)
***Not sure which one you want to be solved but some of the ones with answers are wrong, so I will be explaining those as well with answers; the questions will be labeled 1-4 from top to bottom as shown in your picture***
#1.
Answer:
y=3x+4
Explanation:
The slope is 3 because every 1 unit to the right, the next point is increased by 3. In other words, the line rises 3 every 1 across. Slope is calculated by rise divided by run, in this graph the rise is 3 and the run is 1.
Slope= rise/run=3/1=3
The slope is not negative because it rises upwards from left to right; not downwards as a negative slope would.
Slope-intercept form is y=mx+b with m being slope, b being the y-intercept, and (x,y) being the set of points. The y-intercept is found as the point that intersects on the y axis, here being 4. So, the answer is y=3x+4.
#2.
Answer:
y=(1/2)x+3
Explanation:
Again, y-intercept form is y=mx+b. Here we are given the slope and the x-intercept(the y is 0). Because the slope is given, we can plug that in the slope-intercept equation right away:
y=(1/2)x+b
Now, we just need to find b. So, how can we solve for b? We need to make b the only variable in this equation. This can be done by plugging in the given point, (-6, 0). Here is how b is solved:
y=(1/2)x+b
0=(1/2)(-6)+b
0=-3+b
3=b
So, the equation is y=(1/2)x+3.
#3.
Answer:
y=3x+7
Explanation:
Two points are given. Slope can be found given two points and we can use the slope to create an equation in point-slope form, before solving for the slope-intercept form. Slope can be found using the equation:
m=(y2-y1)/(x2-x1)
This equation basically finds the rise and run of the slope before dividing to find the slope. Plugging in the points given for this problem and find slope is shown below: ((-2, 1) and (1, 10) are the points btw)
m=(10-1)/(1+2)
m=9/3
m=3
Now that we know the slope, we can pick one number to create point-slope form and then move the variables around to create slope-intercept form.
Point-slope form: (y-y1)=m(x-x1)
With variables: (y-1)=3(x+2)
Now, we can use this equation to create slope-intercept form:
(y-1)=3(x+2)
y-1=3x+6
y=3x+7 <—Final Answer!
#4.
Answer:
(y+2)=1/6(x-9)
Explanation:
Given the point and a slope, we can create the point-slope equation. (9,-2) and m=1/6 is given. Refer back to point slope form (y-y1)=m(x-x1). m is the slope and (x1, y1) is the point plugged in.
So, when you plug in the slope and the points you get (y+2)=1/6(x-9).
The range is 8 and if you needed help finding the median it is 2 I think
Btw remember that median means middle, range means the difference between the highest and lowest number, the mode means what number have the most, and the mean is the total of all the values and then divide by the number of values :)
The formula to find the volume of a cylinder is
V=pi r∧2 h
so your answer should be 816.81
1. Off of the first deal, our discount is (20)(1-.15)=17. However, because we get two widgets from this offer, we have half the price per widget, so per widget we pay 17/2=$8.50.
2. 3 1/2 is 14/4 inches. Since 1/4 inches is equal to one foot in this scale, the wall is 14 feet long.
3. We see that $37 is a third of the cost of the bike, so the full cost is 37*3=$111.
