Answers
Statement 1 and statement 3 contradict
======================================================
Explanation:
We'll start with statement 1 and try to build to statement 3, and you'll find that a contradiction happens.
If angle 1 and angle 2 are supplementary, then that must mean [tex]m \angle 1 + m \angle 2 = 180[/tex] because the angles can be combined to form a straight angle.
Add the measure of angle 3 to both sides
[tex]m \angle 1 + m \angle 2 = 180\\\\m \angle 1 + m \angle 2+m\angle 3 = 180+m\angle 3[/tex]
The left side matches with the left side in statement 3, but the right side is a bit off. That [tex]m\angle 3[/tex] term needs to be zero, so that the right side boils down to simply 180. However, statement 3 specifically mentions that angle 3 is nonzero. So angle 3 is some positive value.
That's why choice C is the answer.
------------------
Here's an example:
Let's say angles 1 and 2 are 50 and 130 degrees. The order doesn't really matter, but I'll make angle 1 to be the smaller angle.
This means,
[tex]m \angle 1 + m \angle 2 = 180\\\\50 + 130 = 180\\\\[/tex]
So we've made statement 1 to be true. The angles 50 and 130 are indeed supplementary.
Now let's add some nonzero value to both sides. This will represent the measure of angle 3. If we add say 10 degrees to both sides, then,
[tex]50 + 130 = 180\\\\50 + 130+10 = 180+10\\\\50 + 130+10 = 190\\\\m\angle 1 + m\angle 2 + m\angle 3 = 190\\\\[/tex]
we don't get 180 like we want in the equation of statement 3. This is where the contradiction happens, more or less. One right side is 180, the other right side is 190. The 190 will change if you use some other value for angle 3, but hopefully you can see that it's impossible to add up angles 1 through 3 to get 180. It's only possible if angle 3 were zero degrees.
We can think of it like angles 1 and 2 hog up all the oxygen, and use up 180 points of it, leaving no air for angle 3 to breathe so that's why angle 3 must be 0. Furthermore, it means that a triangle is not possible if exactly two angles are supplementary.
----------------------
Extra info:
Statements 1 and 2 can coexist just fine without any contradictions happening. If angle 1 is 110 degrees, then that makes angle 2 to be 70 degrees (110+70 = 180). That rules out choice A.Statements 2 and 3 are just fine as well, for similar reasoning as above. We can plug in 110 for angle 1, then subtract that from 180 to get 180-110 = 70. Then from here, just ensure that angles 2 and 3 add to 70. So there are infinitely many ways to do this. Choice B can be ruled out.Choice D is ruled out because we found choice C to be the answer, ie the contradicting two statements.Answer:
C) l and lll
Step-by-step explanation:
m∠1+∠2=180
m∠1+m∠2+m∠3=180
180+m∠3=180
m∠3=0 but m∠3=∦0
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Related Questions
Find the area of this circle. Use 3 for .
A = 7r2
18 in
[?] in2
Answers
Answer:
Area of a circle = πr^2 if pi here = 3
then (3 × 81) in^2 = 243 in^2
Hope it helps
Answer:
The area of circle is 254.34 in².
Step-by-step explanation:
Given :
[tex]\small\purple\bull[/tex] Diameter of circle = 18 inTo Find :
[tex]\small\purple\bull[/tex] Radius of circle [tex]\small\purple\bull[/tex] Area of circleUsing Formulas :
[tex]\star{\small{\underline{\boxed{\sf{\pink{R = \dfrac{D}{2}}}}}}}[/tex]
[tex]\blue\star[/tex] R = radius [tex]\blue\star[/tex] D = diameter[tex]\star{\small{\underline{\boxed{\sf{\pink{Area_{(Circle)} = \pi{r}^{2} }}}}}}[/tex]
[tex]\blue\star[/tex] π = 3.14 [tex]\blue\star[/tex] r = radiusSolution :
Here we have given that diameter of circle is 18 in. So, finding the radius of circle :
[tex]\implies{\sf{Radius = \dfrac{D}{2}}}[/tex]
[tex]\implies{\sf{Radius = \dfrac{18}{2}}}[/tex]
[tex]\implies{\sf{Radius = \cancel{\dfrac{18}{2}}}}[/tex]
[tex]\implies{\sf{Radius = 9 \: in}}[/tex]
[tex]\star{\underline{\boxed{\sf{\red{Radius = 9 \: in}}}}}[/tex]
Hence, the radius of circle is 9 in.
[tex]\rule{200}2[/tex]
Now, we know the radius of circle is 9 in. So, finding the area of circle by substituting the values in the formula :
[tex]\implies{\sf{Area_{(Circle)} = \pi{r}^{2}}}[/tex]
[tex]\implies{\sf{Area_{(Circle)} = 3.14\times {(9)}^{2}}}[/tex]
[tex]\implies{\sf{Area_{(Circle)} = 3.14\times {(9 \times 9)}}}[/tex]
[tex]\implies{\sf{Area_{(Circle)} = 3.14\times (81)}}[/tex]
[tex]\implies{\sf{Area_{(Circle)} = \dfrac{314}{100} \times 81}}[/tex]
[tex]\implies{\sf{Area_{(Circle)} = \dfrac{314 \times 81}{100}}}[/tex]
[tex]\implies{\sf{Area_{(Circle)} = \dfrac{25434}{100}}}[/tex]
[tex]\implies{\sf{Area_{(Circle)} = 254.34 \: {in}^{2} }}[/tex]
[tex]{\star{\underline{\boxed{\sf{\red{Area_{(Circle)} = 254.34 \: {in}^{2}}}}}}}[/tex]
Hence, the area of circle is 254.34 in².
[tex]\rule{300}{1.5}[/tex]
Function “p” is in the form y=ax^2 + C. If the values of “a” and “c” are both less than 0, which graph could represent “p”?
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Answers
Answer:
B
Step-by-step explanation:
Since the value of a is less than 0, the graph of the parabola would be opening downwards. Because of this we can rule out option C. In a quadratic equation, c represents the y-intercept, and, in this case c is negative, meaning the y-intercept is less than 0. Only option B has a downward-opening curve and a y-intercept less than 0, so it is the answer.
Answer:
B. Graph B
--------------------
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What is the circumference?
(radius = 4)
Answers
Answer:
25.13
Step-by-step explanation:
C = 2πr
C = 2π(4)
C = 25.13
Hope this helps!
Write the equation of the parallel line - x + 2y = 12 that goes through the
point (10,8).
Write your answer in in slope-intercept form,
y = m x +
b
slope
y-intercept
Answers
Answer:
Step-by-step explanation:
PLEASE ASAP ILL GIVE BRAINLIEST.
Answers
Answer:
It would be the fourth one
Step-by-step explanation:
Simplify the left side of equation so it looks like the right side. cos(x) + sin(x) tan(x) = sec (x)
Answers
Step-by-step explanation:
Consider LHS
[tex] \cos(x) + \sin(x) \tan(x) = \sec(x) [/tex]
Apply quotient identies
[tex] \cos(x) + \sin(x) \times \frac{ \sin(x) }{ \cos(x) } = \sec(x) [/tex]
Multiply the fraction and sine.
[tex] \cos(x) + \frac{ \sin {}^{2} (x) }{ \cos(x) } = \sec(x) [/tex]
Make cos x a fraction with cos x as it denominator.
[tex] \cos(x) \times \cos(x) = \cos {}^{2} (x) [/tex]
so
[tex] \frac{ \cos {}^{2} (x) }{ \cos(x) } + \frac{ \sin {}^{2} (x) }{ \cos(x) } = \sec(x) [/tex]
Pythagorean Identity tells us sin squared and cos squared equals 1 so
[tex] \frac{1}{ \cos(x) } = \sec(x) [/tex]
Apply reciprocal identity.
[tex] \sec(x) = \sec(x) [/tex]
Name all asymptotes: y =x−3/2x+8
Answers
Answer:
x=0
y= x + 8
Step-by-step explanation:
find the oblique asymptotes using long polynomial divison
Find h.
10 in.
h = [?] in.
5.
4 in.
PLEASE ILL DO ANYTHING
Answers
10 * 2 - 2 * 2= height*2
100- 4 = height *2
96= height *2
Under-root 96 = height
Answer:[tex]h=\sqrt{96}in.[/tex]
Step-by-step explanation:
.
Find the area and round it to the nearest hundredth if necessary
Answers
Answer:
16.28 squared inches
Step-by-step explanation:
Use the formula A = bh.
b = base
h = height
A = (4.4) (3.7)
A = 16.28
In ΔMNO, the measure of ∠O=90°, MN = 60 feet, and OM = 11 feet. Find the measure of ∠N to the nearest degree.
Answers
Answer:
I don't have the right calculator but if you type sin-1(11/60) it'll give you the answer
The line y = 6 - 2x passes through the point (2, 2)
is it correct?
Answers
Answer:
Yes
Step-by-step explanation:
We can substitute the point (2, 2) into the equation. So, in place of x would be 2 and in place of y would be 2 as well:
y = 6 - 2x
2 = 6 - 2(2)
2 = 6 - 4
2 = 2
Since the above is a true statement, the point (2, 2) must belong to the line y = 6 - 2x
Yes, the line y=6-2x passes through the point (2, 2).
Given that, the line y=6-2x passes through the point (2, 2).
What is the slope intercept form?The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.
Here, substitute (x, y)=(2, 2) is the given line y=6-2x, we get
2 = 6-2(2)
2 = 2
Since, LHS = RHS
Yes, the line y=6-2x passes through the point (2, 2).
To learn more about the slope intercept form visit:
brainly.com/question/9682526.
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The boys basketall team averages 52 points per game with a standard deviation of 7.0 points. What is the probability that the boys will score between -1.2 and 2.0 standard deviations of their average?
Answers
Answer:
0.6832
Step-by-step explanation:
Given :
Mean, m = 52
Standard deviation, s = 7
-1.2 standard deviation of average = 57 - 1.2(7) = 57 - 8.4 = 48.6
2 standard deviations of average = 57 + 2(7) = 57 + 14 = 71
Zscore = (48.6 - 52) / 7 = - 0.486
Zscore = (71 - 52) / 7 = 2.714
P < -0.486) = 0.31348
P < 2.714 = 0.99668
P < 2.714 - P < -0.486 = (0.99668 - 0.31348) = 0.6832
Which inequality is true when the value of u is 10?
u – 3<-6 , u-3>-6 , -u-3>6 , -u-3>-6
Answers
Answer:
The answer is: u-3>-6
This is because 10-3=7 and 7>-6
Mila graphs the point A (5, 0) on a coordinate plane.
Which of the following statements are true?
Select all that apply.
Point A is 5 units to the________(Please fill this box any of these choices in A-E)
A. right of the origin and up 1 unit.
B. The x-coordinate of point A is 5.
C. The y-coordinate of point A is 5.
D. Point A is on the y-axis.
E. Point A is on the x-axis.
Answers
Answer:
B,E
Step-by-step explanation:
(5,0) (5=x, 0=y)
A is false because y = 0
B is true because x=5
c is false because y = 0
D is false because again y = 0
E is true because 5,0 is on the x axis
- Gage Millar, Algebra 2 tutor
Solve each equation, explain how you figured it out. (No fake answers!!Proper ones pleaser!!)
A. 25 - 3x = 40
B. 2 (x - 10) = -4
Answers
Answer:
A. x= -5
B. x= 8
Step-by-step explanation:
A. 25 - 3x = 40
-3x = 40 - 25
-3x = 15
x= 15/-3
x= -5
B. 2 (x-10) = -4
x-10 = -4/2
x-10 = -2
x = 8
A. 25 - 3x = 40
-3x = 40 - 25
= 15
-x = 15/3
x = -5
Checking
25 - 3*-5 = 40
25 + 15 = 40
40 = 40
LHS = RHS
B. 2(x-10) = -4
2x - 20 = -4
2x = -4 +20
x = 16/2 = 8
Hope u understand
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Thank You
hey! please help i’ll give brainliest
Answers
Answer:
Your answer would be C: occurred during the same period of time
Step-by-step explanation:
PLS ANSWER!! +GIVING BRAINLIEST FOR 1ST CORRECT ANSWER
Answers
Answer:
18
Step-by-step explanation:
mark me as
brainliest
18
Answer:
144 ounces
Step-by-step explanation:
ahhhh someone help pls!!!!
Answers
Answer:
I may be wrong but I think it's 90 I may be wrong but hey I tryed.
Step-by-step explanation:
on a venn diagram shade the region
a'n(bnc)
Answers
Answer:
See the three attached images.
Step-by-step explanation:
image1 shows the intersection of b and c: [tex]b \cap c[/tex]. (green "football")
image2 shows the complement of a (outside a): [tex]a'[/tex] (yellow)
image3 shows the intersection of those sets: [tex]a'\cap (b\cap c)[/tex] (green "football with a bite out of it") :-)
What is the domain of the function y = l n (x + 2)
A. x < -2
B. x > -2
C. x < 2
D. x > 2
Answers
Answer:
Option B.
Step-by-step explanation:
For a function f(x), the domain is the set of all the possible values of x that can be used in the function.
We know that the natural logarithm is only defined for positive real numbers.
So, the function:
Ln(x + 2)
Works always that
x + 2 > 0
So we can just solve this inequality for x, and that will give us the domain of the function.
To isolate x, we just need to subtract 2 in both sides of the inequality.
x + 2 - 2 > 0 - 2
x > - 2
This is the domain of the function.
The correct option is B.
Answer:
b.x>-2
Step-by-step explanation:
edge 2021
ANYONE PLS HELP ASAP!!!
Answers
Part A answer- 2.5
Work: 5 divided by 2 which is just 2.5 which is your answer
Part B answer - 12.5
Work- 2 bags = 10 pounds (5x2=10)
We already know half a bag is 2.5 so just add 10+2.5= 12.5
How many 1/4 pound packages of cheese can the deli make with 12 pounds of cheese
Answers
Answer:
48 1/4 packages
Step-by-step explanation:
Apparantly this Math problem is impossible? Ive posted it like 10 times and yet nobody has answered
Answers
Answer:
Step-by-step explanation:
r=5 ×90/100=4.5 in
h=6×90/100=5.4 in
a.
volume of original cylinder=π×5²×6=150 π≈471.24 in³
b.
volume of new cylinder=π×4.5²×5.4=109.35 π in³≈343.53 in ³
c.
decrease in volume=150 π-109.35 π=40.65π
% decrease=(40.65 π)/150 π×100=4065/150=1355/50=27.1 %
Please help me with this question
Answers
Answer:
x = 11
Step-by-step explanation:
Since we are given triangle PQR is similar to triangle PTU, we can write a proportion to connect the side lengths:
PQ / PT = QR / TU = PR / PU
We don't really care about QR and TU because the are irrelevant to the problem, so we can remove them:
PQ / PT = PR / PU
Now, we can substitute the values given by the diagram:
70 / 30 = 49 / (x + 10)
We can cross multiply,
70(x + 10) = 30 * 49
And divide by 70 on both sides(too lazy to multiply :P)
x + 10 = 3 * 7
x + 10 = 21
x = 11
Find all vertical asymptotes of the following function f(x)=9x^2-64/2x+14
Answers
Answer:
Step-by-step explanation:
Was the latter half of this function, -64 / 2x + 14, meant to be:
-64 / 2x + 14, or
-64 / (2x + 14)?
In the first case the vertical asymptote is x = 0.
In the second, the vertical asymptote is the root of 2x + 14, or x = -7
Use parentheses in problems such as this one, to eliminate ambiguity.
I didn’t understand so I need a help
Answers
Answer:
y is 107° and z is 36°
Step-by-step explanation:
73° and y are supplementary angles so they add up to 180°
Answer:
y = 107
z = 36
Step-by-step explanation:
We are given that line o is parallel to line m, and we can notice line k is a transversal through them both. Using same side interior angles, we can say that:
y + 73 = 180
and
y = 107
Next, using vertical angles, we can say that:
5z - 73 = y
We already have y = 107, so we can substitute that in:
5z - 73 = 107
5z = 180
z = 36
For the given measure
, find the measure of the supplementary angle and the measure of a complementary angle, if possible. If not possible, type the word none in lowercase letters in the box.
82 degrees
Answers
Answer:
The supplementary angle is
153°.
The complementary angle is
63°.
Step-by-step explanation:
This is very right trust mne
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The measure of the supplementary angle and the measure of a complementary angle as follows; The supplementary angle is 153°. The complementary angle is 63°.
What are complementary angles?Two angles whose sum is 90° are called complementary angles.
Two angles whose sum is 180° are called supplementary angles.
If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line.
Those two-two angles are two pairs of supplementary angles.
That means, if supplementary angles are aligned adjacent to each other,
their exterior sides will make a straight line.
Therefore, The supplementary angle is 153°.
The complementary angle is 63°.
Learn more about complementary angles here:
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How many solutions does the equation
-2(x + 3) = 2x - (5 – x) have?
Answers
Step-by-step explanation:
-2(x + 3) = 2x - (5 – x)
-2x+6= 2x-5+x
-2x+6=3x-5
-2x-3x=-5-6
-5x=-11
x= 11/5
( 1 solution)
Answer:
Solution given:
-2(x + 3) = 2x - (5 – x)
-2x-6=2x-5+x
-6+5=2x+2x+x
5x=-1
x=[tex] \frac{-1}{5} [/tex]
It has one Solution.
Find all solutions to the equation. cos x = -1/2
Answers
Answer:
^^
Step-by-step explanation:
Answer:
You didn't add the range. I'll use (0<x<2π)
cosx = -1/2
x=-cos-¹(1/2)
x= -60°
Cosine is negative in the second and 3rd quadrants
180-x ---- Second quadrant
x+180 ----- 3rd quadrant
So
Our answer
180-(-60)=240° or 4π/3 second quad
180+(-60) = 120° or 2π/3---- 3rd quad
33%
The diagram shows a square ABDE and an isosceles triangle BCD.
Angle C = 40°
Work out the size of angle EBC.
А
B
40°
E
Answers
Answer:
ans = <ebc= 115°
hope this will help
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