Please help! I’m this figure, which angles are congruent? Find the measure of all the angles if m< 2= 76 degrees
Answers
Problem 1.
Yes it is true that vertical angles are congruent, but that's not what your teacher is asking. Instead, your teacher is asking basically how the term "congruent" is defined.
Two segments are congruent if they are the same length. Two angles are congruent if they are the same measure. Two triangles are congruent if they have the same angles and sides.
So in short, "congruent" just means "same". You can think of having mirror copies.
==========================================
Problem 2.
Angles 2 and 4 are one pair of vertical angles. They are opposite one another in this X shape formed by the two lines. The other pair of vertical angles are angle 1 and angle 3.
Angle 2 is given to be 76 degrees, so this means angle 4 is this measure as well.
Angle 1 = 180 - (angle 2) = 180 - 76 = 104, which is also the measure of angle 3 as well. I'm using the idea that the adjacent angles form a straight angle. This is known as a linear pair (ie the angles form a straight line).
==========================================
Problem 3.
If all three angles are the same (all 60 degrees), then we have an equilateral triangle. We could say it's equiangular, but it's also equilateral as well meaning all 3 sides are the same length. "equi" means "equal", "angular" means what you'd expect, and "lateral" means "side".
If only two angles are equal with the third one different, then we have an isosceles triangle. An isosceles triangle is one where only two sides are the same length.
If none of the angles are the same, then we have a scalene triangle. As you probably expect, none of the sides are the same length with a scalene triangle.
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If all three angles are less than 90 degrees, then the triangle is acute
If one angle is 90 degrees, then we have a right triangle
If one angle is over 90 degrees (but less than 180), then the triangle is obtuse
---
Often you'll see the terms of the previous two sections combined. For instance, we could have an isosceles right triangle. Or we might have an obtuse scalene triangle. Any equilateral triangle is acute (as all three angles are less than 90).
To solve this problem we have to understand what congruent angles are and then find the angles that are congruent to one other in this given question.
What are Congruent Angles?Congruent angles are angles that are equal to one another and in the given question, we were given m<2 = 76 degrees.
Data;
m<2 = 76 degreesIf we look critically at the angles, we can use opposite angle theorem here to predict angles that are congruent to another here.
angles 2 and angle 4 are congruent to one another while angle 1 and angle 3 are congruent to one another.
This implies that
m<2 = 76°m<4 = 76°Let's solve for other angles.
But the some of angles at a point is equal to 360°
Applying that theorem here,
[tex]m > 1=x\\m > 2 = 72^0\\m > 3 = x\\m > 4 = 72^0[/tex]
Let's substitute the values and solve.
[tex]x+ x + 72+72 = 360\\2x + 144 = 360\\2x = 360 - 144\\2x = 216\\x = \frac{216}{2} \\x = 108^0[/tex]
This can be further summarized as
m<1 = 108°m<2 = 72°m<3 = 108°m<4 = 72°Learn more on corresponding angles here;
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Related Questions
2*cosx*(2x+30°) + √3=0
Answers
Answer: x ≈ 1.59688927, −1.60312387, −4.67045686, 4.69039614, 7.872914, −7.91513776, −10.89002194
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Simplify 2*cosx*(2x+30°) + √3=0
Simplify each term.
Apply the distributive property.
2 cos ( x ) ( 2 x ) + 2 cos ( x ) * 30 ° + √ 3 = 0 Multiply 2 by 2 4 cos ( x ) x + 2 cos ( x ) *30 ° + √ 3 = 0 Multiply 30 °by 2 4 cos ( x ) x + 60 cos ( x ) + √ 3 = 0Reorder factors in 4 cos ( x ) x + 60 cos ( x ) + √34xcos(x)+60cos(x)+√3=0Graph each side of the equation. The solution is the x-value of the point of intersection. x ≈ 1.59688927 , − 1.60312387 , − 4.67045686 , 4.69039614 , 7.872914 , − 7.91513776 , − 10.89002194
Answer:
Step-by-step explanation:
please click thanks and mark brainliest if you like :)
Which of the following has all the justifications Kelsey used to solve this equation?
(9th grade Algerbra 1)
Answers
Find the product (4x-3y)(2x+5)
Answers
Answer:
8x²−6xy+20x−15y
Step-by-step explanation:
(4x−3y)(2x+5)
=(4x+−3y)(2x+5)
=(4x)(2x)+(4x)(5)+(−3y)(2x)+(−3y)(5)
=8x²+20x−6xy−15y
=8x²−6xy+20x−15y
Urgent Help. The circle shown above has a radius of 5 units
Answers
Area enclosed in [tex] 2\pi[/tex] radians =$\pi r^2$
so area enclosed in $\theta$ radians=$\theta \times \frac{\pi r^2}{2\pi}= \frac{1}2\theta r^2$
does this answer your question?
===================================================
Explanation:
2pi radians is equal to 360 degrees.
The shaded region has a central angle 2pi/5 radians
Divide 2pi/5 over 2pi to end up with 1/5. The "2pi" terms cancel.
The shaded region is 1/5 of the full circle.
The full circle area is pi*r^2 = pi*5^2 = 25pi square units
Taking 1/5 of that leads to (1/5)*25pi = 5pi which is the area of the shaded region.
find the transpose of matrics.
Q=[789]
Answers
Answer:
[7]
[8]
[9]
Step-by-step explanation:
according to your question
your answer is
[7]
[8]
[9]
you must be write this answer in one bracket
solve the equation: sin(2x)= sin x
Answers
Answer:
Below
Step-by-step explanation:
sin(2x) = 2 ×cos(x)× sin(x)
● sin(x) = 2 × cos(x) × sin(x)
● 2 × cos(x) = 1
● cos (x) = 1/2
So we can deduce that:
● x = Pi/3 + 2*k*Pi
● or x = -Pi/3 + 2*k*Pi
K is an integer
The Solution of x:
x = π/3 + 2πn, where n is an integer.
x = 2π/3 + 2πn, where n is an integer.
In degrees:
x = 60° + 360°n, where n is an integer.
x = 120° + 360°n, where n is an integer.
To solve the equation sin(2x) = sin(x), we can use the properties of trigonometric functions.
First, let's simplify the equation using the double angle identity for sine:
sin(2x) = 2sin(x)cos(x).
Now we can rewrite the equation as:
2sin(x)cos(x) = sin(x).
2cos(x) = 1.
Dividing both sides of the equation by cos(x), we get:
2 = 1/cos(x).
Now, we can find the value of cos(x) by taking the reciprocal of both sides:
cos(x) = 1/2.
From the unit circle or trigonometric values,
we know that cos(x) = 1/2 corresponds to angles of π/3 or 2π/3 (in radians) or 60° or 120° .
So, the solutions for x are:
x = π/3 + 2πn, where n is an integer.
or
x = 2π/3 + 2πn, where n is an integer.
In degrees:
x = 60° + 360°n, where n is an integer.
or
x = 120° + 360°n, where n is an integer.
Learn more about Trigonometry here:
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A set of circular cups are placed so that they are touching rim to rim, as close together as possible. It is not possible to fit more cups inside the group if the longest straight line is five cups long, how many cups are there altogether?
Answers
Answer:
The total number of cups in arranged in an hexagonal area = 19 cups
Step-by-step explanation:
The pack the most circles within an area, the arrangement with the densest packing is the hexagonal lattice structure similar to the bee's honeycomb as has been proved Gauss and Fejes Toth.
Therefore, we pack the circles in an hexagonal lattice structure in an assumed hexagonal area where we have;
The longest straight line is five cups the next on either side are four cups and the final line on either side has three cups
The total number of cups = 3 + 4 + 5 + 4 + 3 = 19 cups
The total number of cups = 19 cups.
Megan has some cards. She gives away 8 cards. Now she has 41 cards.
How many cards did Megan start with? Enter the answer in the box.
Answers
Answer:
c = 49
Step-by-step explanation:
Let c = number of cards originally
give away 8 cards
c-8
Now she has 41
c-8 = 41
Add 8 to each side
c-8+8 = 41+8
c = 49
Answer:
49
Step-by-step explanation:
In the end, if she now has 41 cards you have to do inverse operation. Since you subtracted to take away those 8 cards she gave away, you have to add back in 8 cards to the 41 if you want to find what she had before. So, 8 + 41 = 49
Hope this helps! :)
9.
Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 + 2x = 15
A. 3, –5
B. 3.74, 4
C. 4, –4
D. 15, –17
Answers
Answer:
x = 3 , x = -5
Step-by-step explanation:
Given x^2 +2x=15 add 1 to both sides to get:
x^2 + 2x + 1 =16
(x+1)^2 = 16
x + 1 = ± [tex]\sqrt{16}[/tex] = ± 4
x = -1 ± 4
x = 3 or x = -5
What is the midpoint of PQ?
Answers
Answer:
I think it is (2,0)
Step-by-step explanation:
Because in it 2 lies in the mid of x either y
Explanation:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
In this case:
((-4+8)/2, (6+(-6))/2)
= (2,0)
Hope this helps!
In an effort to persuade customers to reduce their electricity consumption, special discounts have been offered for low consumption customers. In Florida, the EPA estimates that 70% of the residences have qualified for these discounts. If, instead, a sample of 20 residences is selected, what is the probability 12 or more will have qualified for the discounts
Answers
Answer:
please mark me brainlist
Step-by-step explanation:
p = proportion of residents qualified for discounts = 0.70
Sample size = 20
If X is the no of residences selected for discounts then x is binomial with (20,0.7)
P(X>=12) = 0.8867
find the radius of a circle for which an arc 6 cm long subtends an angle of 1/3 radians at the center?
plz some one can help to solve the question??
Answers
Step-by-step explanation:
Eueydhhdgdgdbdbddbdbhd
Answer:
Hello,
[tex]R=\dfrac{18}{\pi}\ (cm)[/tex]
Step-by-step explanation:
[tex]Formula: \ L=\theta*R\\[/tex]
[tex]R=\dfrac{6}{\dfrac{\pi}{3} } =\dfrac{6*3}{\pi} =\dfrac{18}{\pi}\ (cm)[/tex]
PLS HELP ASAP!!
Solve the inequality for 0
√2sinx+√2cosx>0
a. 0
b. 3π/4
c. 0
d. 0
Answers
Answer:
2
Step-by-step explanation:
w
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Answers
Answer:
Option C, 93.6 mi³
Step-by-step explanation:
Volume of the triangular prism,
base area × height
= (8×3.9/2)×6
= 93.6 mi³
if a + b + c = 9 and ab + bc + ca = 26 find the value of a^2 + b^2 + c^2
Answers
[tex](a+b+c)^2=a^2 + 2 a b + 2 a c + b^2 + 2 b c + c^2\\a^2+b^2+c^2=(a+b+c)^2-2ab-2ac-2bc\\a^2+b^2+c^2=(a+b+c)^2-2(ab+ac+bc)\\\\a^2+b^2+c^2=9^2-2\cdot26=81-52=29[/tex]
The members of an Olympiad team contributed
a total of $ 1.69 for refreshments for their
weekly practices. Each member contributed the
same amount and paid for his or her share in
five coins. How many nickels were contributed
by all of the members?
Answers
Answer:
26 nickels
Step-by-step explanation:
Given that
Total contributed = $1.69
Number of coins = 5
based on the above information,
The number of nickels to be contributed is
Here first we have to determine the prime factors of 169 i.e 13 and 13
This represents that there are 13 member gives their $0.13 per person so it would be $1.69
Also there are 13 cents out of which 3 cents would be 3 pennies the remaining 10 cents would be 2 nickels
So the 13 people contributed to 2 nickels
Therefore, it would be
= 13 × 2
= 26 nickels
Bruno is designing his next skateboard. The skateboard store has 3 types of grip tape, 13 types of decks, 7 types of trucks, 4 types of bearings, and 2 types of wheels. How many different skateboards can Bruno create? Assume each skateboard will contain only one type of each component.
Answers
Answer:
2184 different combinations
Step-by-step explanation:
To find how many different combinations are possible, multiply all of the values:
3 * 13 * 7 * 4 * 2 = 2184 different combinations
Answer:
2,184 different skateboards.
Step-by-step explanation:
You would have to multiply
3 x 13 x 7 x 4 x 2 = 2184
If it helps you then please mark it as brainliest!
i need help :( please answer
Answers
Answer:
[tex] = - ( \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} )[/tex]
Step-by-step explanation:
[tex] - {(3)}^{ - 4} = \\ - ( { 3}^{ - 4} )= \\ - (\frac{1}{ {3}^{4} } )[/tex]
[tex] = - ( \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} )[/tex]
[tex] = - \frac{1}{81} [/tex]
I hope it helps
Can someone plz help me
Answers
Answer:
37500
Step-by-step explanation:
pattern is multiplying by -5.
-7,500*-5 = 37,500
Have a nice day! :-)
Find the perimeter of the following rectilinear figure.
Answers
Answer:
54
Step-by-step explanation:
see attached
Write equation of a line in slope intercept form with the given information p=(1,2) m=4
Answers
Answer:
[tex]y=4x-2[/tex]
Step-by-step explanation:
Hi there!
Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
We're given that the slope is 4. Plug this into [tex]y=mx+b[/tex] as m:
[tex]y=4x+b[/tex]
Now, to determine the y-intercept, plug in the given point (1,2) and solve for b:
[tex]2=4(1)+b\\2=4+b\\b=-2[/tex]
Therefore, the y-intercept is -2. Plug this back into [tex]y=4x+b[/tex] as b:
[tex]y=4x+(-2)\\y=4x-2[/tex]
I hope this helps!
Figure a is a scale image of figure b. what is the value of x? please answer asap!
Answers
Answer:
[tex]\boxed{x = 20}[/tex]
Step-by-step explanation:
Hey there!
Well to find x we need to set up the following.
[tex]\frac{10}{12.5} = \frac{16}{x}[/tex]
Cross multiply
10x = 200
Divide both sides by 10
x = 20
Hope this helps :)
Two angles are adjacent and form an angle of 160. Their difference is 34. Find the angles
Answers
Answer:
The angles are 63 , 97
Step-by-step explanation:
Let one angle be x
As sum of two angles is 160, the other angle = 160 - x
Their difference = 34
x - [160- x] = 34
Use distributive property to remove the brackets
x - 160 + x = 34
Add like terms
x + x - 160 = 34
2x - 160 = 34
Add 160 to both sides
2x = 34 + 160
2x = 194
Divide both sides by 2
2x/2 = 194/2
x = 97°
One angle = 97°
Other angle = 160 - 97 = 63°
An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?
Answers
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Hope this can help you.
Answer:
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Step-by-step explanation:
On a recent math test. Samantha scored 3 points for each of the 18 multiple choice que non se
answered correctly and 5 points for each of the 6 short response questions she answered correctly
She scored an additional 4 points for the bonus question. Write an expression for her total score on
the test and then find her score.
Answers
The required expression will therefore be:
(3×18) + (5×6) + 4
Her total score is 88points :
From the question given, we are told that Samantha scored 3 points for each of 18multiple questions his means that the total points made here is expressed as:
(3 × 18) ...1
If she got 5 points for each of the 6 short responsmultiple choice questione questions she answered
correctly, the total point made will be expressed as;
(5×6) ... 2
Total score for an additional 4 points for the bonus question will be "4"
Expression for her total score will be the sum of all the expression above as thus:
(3×18) + (5×6) + 4
Taking the sum, her score will be:
= (3×18) + (5×6) + 4
= 54 + 30 + 4
= 84 + 4
= 88 points
The required expression will therefore be:
(3×18) + (5×6) + 4
Her total score is 88points
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Put the following equation of a line into slope-intercept form, simplifying all
fractions.
4x + 2y = -18
Answers
4x + 2y = -18
2x + y = -9
y = -2x - 9
Ray is making his reward winning lemonade recipe for a party he is comparison shopping for lemons at super pioneer supermarket he can buy 4 lemons for 1.60 ray visits keyfood and found 3 lemons cost 1.80 use the table below to compare the values
Answers
Step-by-step explanation:
Super Pioneer:
If at the Super Pioneer Store he can get 4 lemons for 1.6 dollars, 1 lemon should cost:
4: 1.6
1:. X
4x = 1.6
X = 1.6/4
X = 0.4
1 lemon costs 0.4 dollars
How many lemons could we get from $2.4?
1 : 0.4
X : 2.4
0.4x = 2.4
X = 2.4/0.4
X = 6
2.4 dollars would get you 6 lemons
8 lemons would cost= 8x0.4 = $3.2
Keyfood Supermarket
3 lemons cost 1.8$, so how mucb does 1 lemon cost?
3: 1.8
1 : X
3x = 1.8
X = 1.8/3
X = 0.6
If 1 lemon costs 0.6, how many lemons could you buy from $3?
1: 0.6
X : 3
3 = 0.6x
X = 3/0.6
X = 5
If 1 lemon cost 0.6$, 8 lemons would cost:
8 x 0.6 = $4.8
(I have also edited the answers on the table, but sorry if they seem a bit messy)
Answered by G a u t h m a t h
solve for x. you must show all of your work to receive credit.
Answers
Answer:
x = 6
Step-by-step explanation:
The tangent- tangent angle WVU is half the difference of the measure of the intercepted arcs. , that is
5x + 17 = [tex]\frac{1}{2}[/tex] (37x + 5 - (23x - 5) )
5x + 17 = [tex]\frac{1}{2}[/tex] (37x + 5 - 23x + 5)
5x + 17 = [tex]\frac{1}{2}[/tex] (14x + 10) ← multiply both sides by 2 to clear the fraction )
10x + 34 = 14x + 10 ( subtract 14x from both sides )
- 4x + 34 = 10 ( subtract 34 from both sides )
- 4x = - 24 ( divide both sides by - 4 )
x = 6
Could you help me???
It’s year8 maths
Answers
Answer:
go on doubtnut app
The average weight of the three lion cubs at the zoo was 288 pounds. Two of the cubs weighed 261 and 252 pounds. What was the weight of the third cub?
Answers
Answer:
351 pounds
Step-by-step explanation:288 x 3 = 864 pounds
864 - 261 - 252 = 351 pounds
Therefore (261 + 252 + 351)/3 = 288.
So the answer is 351 pounds