2.
We have a transversal across parallel lines so we get the usual array of congruent and supplementary angles. We just have to figure out which is which, and the diagram, even though not to scale, makes it pretty obvious.
Angle x isn't the same as the 40° angle so it must be its supplement.
Answer: C 140°
3.
r=1.2, h=2.9, V = (1/3) πr²h
Nothing hard here, we just plug in the numbers,
V = (1/3) π (1.2)² (2.9) ≈ 4.37310
Answer: B. 4.4 cubic inches
4.
Dilation by .5 makes a similar triangle, and reflection is an isomorphism (i.e. it doesn't change the size or shape) so the answer is
Answer: B similar not congruent
5.
The corresponding interior and exterior angles of a triangle form a linear pair, so supplementary angles. x=180-110 = 70°
Answer: A 70°
Hiya! So instead of the word "what", I am going to use 't' as the missing term in this equation
So basically, 14= t x 2/3
1. As you would do with any type of solve-for-x equation, you have to divide 2/3 on both sides of the equation.
To divide a by a fraction, you must turn it into a
reciprocal: <span>"a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity." (via Google definition)
Trust me, it's not as hard as it looks.
To turn the fraction into a reciprocal, you have to flip the numerator and denomonater.
2 = numerator
-
3 = denominator
When you flip it, you get:
3
-
2
If you are still confused, look at this: https://www.mathsisfun.com/reciprocal-fraction.html
2. As simple as that. After you turn the fraction into a reciprocal, you must multiply that fraction.
Multiply 3/2 by 14.
3 14 42
- x - = - = 21
2 1 2
21 = t x 2/3
Since to have to multiply on both sides, you have to divide 2/3 by 3/2 which cancels itself out.
21 = t x 2/3 divide by 2/3
It poofs out of existance.
Dont ask why.
So now we are left with:
t = 21
That is the answer. Viola!
To check your work, fill in the 't' value with 21 into the orginal problem!
14 = t x 2/3
14 = (21) x 2/3
(You are not dividing the fraction anymore so there is not need to create the reciprocal)
In the end, 14 = 14, which proves the problem to be correct. Hope this helped, if you have any questions just ask in the comments!</span>
Answer:
(0.25x, 0.25y)
Step-by-step explanation:
Since the origin is the center of the scale factor of dilation, we don't need to add or subtract anything
Multiplying the x and y values of the ordered pair by 0.25 represents what the value would be with the scale factor, meaning multiplication.
7m+2n=21
-7m -7m
<u>2n</u>=<u>21-7m</u>
2 2
n=<u>21-7m
</u> 2
<u>
</u>10m+4(21-7m/2)= -10
<u />-10m -10m
4(21-7m/2)= -10-10m
(84-28m/2)= -10-10m
x2 x2
84-28m = -20-20m
+20+28m +20+28m
<u>104</u> = <u>8m
</u>8 8
m=13
10(13) + 4n = -10
-130 -130
<u>4n</u> = <u>-140
</u>4 4
<u>
</u>n= -35
If anything is unclear please feel free to ask.
