Answer:
Step-by-step explanation:
hello :
y= 5x + 9
y = -x +3
so : 5x+9 = -x+3
5x+x= 3-9
6x=-6
x=-6/6 = -1
A.) Since there are no restrictions as to the dimensions of the candle except that their volumes must equal 1 cubic foot and that each must be a cylinder, we have the freedom to decide the candles' dimensions.
I decided to have the candles equal in volume. So, 1 cubic foot divided by 8 gives us 0.125 cubic foot, 216 in cubic inches.
With each candle having a volume of 216 cubic inches, I assign a radius to each: 0.5 in, 1.0 in, 1.5 in, 2.0 in, 2.5 in, 3.0 in, 3.5 in, and 4.0 in. Then, using the formula of the volume of a cylinder, which is:
V=pi(r^2)(h)
we then solve the corresponding height per candle. Let us let the value of pi be 3.14.
Hence, we will have the following heights (expressed to the nearest hundredths) for each of the radius: for
r=2.5 in: h=11.01 in
r=3.0 in: h= 7.64 in
r=3.5 in: h= 5.62 in
r=4.0 in: h= 4.30 in
r=4.5 in: h= 3.40 in
r=5.0 in: h= 2.75 in
r=5.5 in: h= 2.27 in
r=6.0 in: h= 1.91 in
b. each candle should sell for $15.00 each
($20+$100)/8=$15.00
c. yes, because the candles are priced according to the volume of wax used to make them, which in this case, is just the same for all sizes
Range of values of x is 25°<x<27°.
<u>Step-by-step explanation:</u>
An angle is formed when two rays, a line with one endpoint, meet at one point called a vertex.Alternate interior angles are formed when a transversal passes through two lines. The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles. The Alternate Interior Angles theorem states, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
In above question, sides are equal and so alternate interior angles are equal i.e. 2x + 10° = 62° ⇒ 2x = 52° ⇒ x =26°
∴ range of values of x is 25°<x<27°
Hi!
An obtuse angle is one greater than 90 degrees, a right angle one that is 90, and acute less than 90.
An obtuse triangle is one with one obtuse angle, all the rest being acute. A right triangle is one with one right angle, all the rest acute. And finally, an acute triangle is one with three acute angles.
In this case, the angles measure 83 degrees, 31 degrees, and 66 degrees. All of them are acute angles, as they're all less than 90 degrees.
Therefore, the triangle is an acute triangle.
Hope this helped!
