9514 1404 393
Answer:
Step-by-step explanation:
The slope of a line is the tangent of the angle it makes with the x-axis. The given line has a slope of -1/3, so the lines we want will have slopes of ...
m1 = tan(arctan(-1/3) +45°) = 0.5 . . . . . using a calculator
m2 = tan(arctan(-1/3) -45°) = -2
Of course, these two lines are perpendicular to each other, so their slopes will have a product of -1: (0.5)(-2) = -1.
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We can use the point-slope form of the equation for a line to write the desired equations:
y = m(x -h) +k . . . . . line with slope m through point (h, k)
<u>Line 1</u>:
y = 1/2(x -2) +3
y = 1/2x +2
<u>Line 2</u>:
y = -2(x -2) +3
y = -2x +7
The answer is: Find the mean of the differences with the other numbers in the set<span>. Add the squared differences and then divide the total by the number of items in </span>data<span> in your </span>set; t<span>ake the square root of this mean of differences to </span>find<span> the standard </span>deviation.
Answer: he would receive a rebate of $1677.5
Step-by-step explanation:
A General Motors buyer-incentive program offered a 5.5% rebate on the selling price of a new car. This means that if the selling price of the new car is $x, the rebate (in dollars) that a customer would receive is
5.5/100 × x = 0.055 × x = 0.055x
Therefore, for a customer who purchased a $30,500 car under this program, the rebate that he would receive is
0.055 × 30500 = $1677.5
the cost for each of jelly beans and each pound of trail mix is $2.5 and $1.75
<u>Step-by-step explanation:</u>
Given A store is having a sale on jelly beans and trail mix. For 3 pounds of jelly beans and 2 pounds of trail mix, the total cost is $11. For 5 pounds of jelly beans and 6 pounds of trail mix, the total cost is $23 . We have to find the cost for each pound of trail mix and each pound of jelly beans.
Let the cost of each pound of trail mix is $y.
and the cost of each pound of jelly beans is $x.
According to question,
For 3 pounds of jelly beans and 2 pounds of trail mix, the total cost is $11.
⇒ 
→ (1)
For 5 pounds of jelly beans and 6 pounds of trail mix, the total cost is $23
⇒ 
→ (2)
Solving (1) and (2), we get
3(1 equation)-(2 equation)=0
⇒
⇒
hence,
⇒
⇒
Putting in we get ;
⇒
⇒ 
⇒ 
⇒ 
Hence, the cost for each of jelly beans and each pound of trail mix is $2.5 and $1.75 .
Answer:
10 in
Step-by-step explanation:
There are two ways to work this problem, and they give different answers. The reason for that is that <em>the data shown in the diagram is not consistent</em>.
<u>Method 1</u>
Use the area to determine the base length. The area formula is ...
A = (1/2)bh
20 in^2 = (1/2)(b)(4 in)
(20 in^2)/(2 in) = b = 10 in
The missing side dimension is 10 inches.
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<u>Method 2</u>
Use the Pythagorean theorem to find the parts of the base, then add them up.
Left of the "?" we have ...
left^2 +4^ = 6^
left^2 = 36 -16 = 20
left = √20 = 2√5
Right of the "?" we have ...
right^2 +4^2 = 8^2
right^2 = 64 -16 = 48
right = √48 = 4√3
So, the base length is ...
base = left + right = 2√5 +4√3
base ≈ 11.400 in
The missing side dimension is 11.4 inches. (The area is 22.8 in^2.)
