Answers
they have equivalent sides and equivalent measurements
Triangles given in Options (b) and (c) are similar.
Theorems of similar triangles: If two angles of a pair of triangles are equal in measure, then the triangles will be similar by A-A property. If corresponding sides of two triangles are proportional, both the triangles will be similar.
From the picture attached,
a). In triangle ABC,
∠A + ∠B + ∠C = 180° [By triangle sum theorem]
60° + ∠B + 40° = 180°
∠B = 80°
Similarly, in ΔDEF,
∠D + ∠E + ∠F = 180°
60° + 85° + ∠F = 180°
∠F = 35°
Since, measure of angles of both the triangles are different in measures, triangles will not be similar.
b). In ΔABC,
∠A + ∠B + ∠C = 180°
45° + 50° + ∠B = 180°
∠B = 85°
In ΔDEF,
∠D + ∠E + ∠F = 180°
50° + 85° + ∠F = 180°
∠F = 45°
Hence, ∠C ≅ ∠D, ∠A≅ ∠F and ∠B ≅ ∠E
Since, measure of corresponding angles are equal, both the
triangles (ΔABC ~ ΔFED) will be similar.
c). Here, corresponding sides of both the triangles are proportional,
[tex]\frac{AB}{DE}= \frac{CA}{FD}= \frac{BC}{EF}[/tex]
[tex]\frac{14}{7}= \frac{12}{6}= \frac{16}{8}[/tex]
[tex]\frac{2}{1}= \frac{2}{1}= \frac{2}{1}[/tex]
Both the triangles ΔABC and ΔDEF will be similar.
Therefore, Option B and Option C are the correct options.
Learn more about the similarity of two triangles here,
https://brainly.com/question/2499350?referrer=searchResults
Related Questions
Which polynomial is in standard form?
A)
2x - 3x2 - 4x} + 6x4 + 8
B)
2x4 - 7x² - 6x² + 3x + 9
5 + 7x2 + 6x + 3x5 + x
D)
5 + 7x3 - 6x² + 3x + 9x
Answers
Answer:
A
Step-by-step explanation:
Simplify 0.05x + 1.02x.
Answers
Answer:
107x-
-------
100
Step-by-step explanation:
Find all points on the curve x=4cos(t),y=4sin(t) that have the slope of 12.
Answers
Answer:
[tex]\left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right )[/tex].
Step-by-step explanation:
We need to find all the points on the curve x=4cos(t),y=4sin(t) that have the slope of 1/2.
[tex]x=4cos (t)[/tex]
[tex]\dfrac{dx}{dt}=-4sin (t)[/tex]
[tex]y=4sin (t)[/tex]
[tex]\dfrac{dy}{dt}=4cos (t)[/tex]
Now,
[tex]\dfrac{dy}{dx}=\dfrac{dy}{dt}\times \dfrac{dt}{dx}[/tex]
[tex]\dfrac{dy}{dx}=4cos (t)\times \dfrac{1}{-4sin (t)}[/tex]
[tex]\dfrac{dy}{dx}=-\cot t[/tex]
So, slope of the curve is [tex]-\cot t[/tex].
[tex]-\cot t=\dfrac{1}{2}[/tex]
[tex]-\tan t=2[/tex]
[tex]\tan t=-2[/tex] ...(1)
Using [tex]\sec^2t=1+\tan^2t[/tex], we get
[tex]\sec^2t=1+(-2)^2[/tex]
[tex]\sec^2t=1+4[/tex]
[tex]\sec t=\pm \sqrt{5}[/tex]
[tex]\cos t=\pm \dfrac{1}{\sqrt{5}}[/tex]
Now,
[tex]\sin^2t=1-cos^2t[/tex]
[tex]\sin t=\pm \sqrt{1-\dfrac{1}{5}}[/tex]
[tex]\sin t=\pm \sqrt{\dfrac{4}{5}}[/tex]
[tex]\sin t=\pm \dfrac{2}{\sqrt{5}}[/tex]
It equation (1), tan(t) is negative. So, sin and cos have different signs.
If [tex]\sin t= \dfrac{2}{\sqrt{5}}[/tex], then [tex]\cos t=- \dfrac{1}{\sqrt{5}}[/tex].
[tex]x=4cos (t)=-\dfrac{4}{\sqrt{5}}[/tex]
[tex]y=4sin (t)=\dfrac{8}{\sqrt{5}}[/tex]
If [tex]\sin t=- \dfrac{2}{\sqrt{5}}[/tex], then [tex]\cos t= \dfrac{1}{\sqrt{5}}[/tex].
[tex]x=4cos (t)=\dfrac{4}{\sqrt{5}}[/tex]
[tex]y=4sin (t)=-\dfrac{8}{\sqrt{5}}[/tex]
Therefore, the two points are [tex]\left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right )[/tex].
I need help with this geometryyyy workkk
Answers
Answer:
Perpendicular
Step-by-step explanation:
For this problem, it is important to note two things. One line is completely vertical, and the other line is completely horizontal.
The line y=9 is completely horizontal at the y-value at 9. The line x = 2 is completely vertical at the x-value at 2.
Hence, these two lines would be perpendicular.
Cheers.
Answer:
Perpendicular.
Step-by-step explanation:
Since it makes a huge cross +, which we want it to be, we need the lines to intercept and it makes a right angle. That means it is perpendicular.
milo runs 4.5 miles around his house he has to run 6.7 miles how many miles does he have to run left
Answers
Answer:
2.2 miles
Step-by-step explanation:
6.7 - 4.5 = 2.2
Answer:
6.7 miles
Step-by-step explanation:
The sentence about 4.5 miles is extra info. you don't need. In the question it says he needs to run 6.7 miles, then continues to ask how many miles he needs to run.
I hope this answers your question and you understand! Have a great rest of your day! :)
i need a step by step explanation of how to solve this
Answers
Answer: x = 6
Step-by-step explanation:
Subtract 8 on both sides. The new equation should be -2x = -3x + 6.Now, add 3x on both sides. It should give you x = 6.Describe the transformation.
Answers
Answer:
C. reflection across the x-axis
Answer:
C
Step-by-step explanation:
This is a reflection across the x-axis because it is the same thing but reflected.
Hope this helps.
a seven sided number cube with sides numbered 1,2,3,4,5,6,7 is rolled. what is the probability that a 4 or odd number is rolled ? which fraction ? 5/7 2/7 3/7 4/49
Answers
The probablity of rolling a 4 = 1/7
There are 4 odd numbers, so the probablity of rolling an odd number = 4/7
4/7 + 1/7 = 5/7
please help me with these two questions ( show work plz )( it's ok if you only now one)
Answers
Answer:
1.8.09
2.-6
Step-by-step explanation:
1. 11b=89
b=89/11
8.09
2. 13+k/3=11
k/3=11-13
k/3=-2
k=-2*3
=-6
Answer:
Number 2 is - 6
Step-by-step explanation:
2. 13 + k/3 = 11
We can start off my subtracting 13 in both sides.
-13 + 13 + k/3 = 11 - 13
k/3 = -2. now we have to multiply 3 in both sides
3 x k/3 = -2 x 3
k = -6
Hope this helps!!
how does math play a role in the activities of your everyday life activities
Answers
Answer:
-Managing money $$$
-Balancing the checkbook.
-Shopping for the best price.
-Preparing food.
-Figuring out distance, time and cost for travel.
-Understanding loans for cars, trucks, homes, schooling or other purposes.
-Understanding sports (being a player and team statistics)
-Playing music.
These are things we do everyday that use Math.
Mathematics makes our life orderly and prevents chaos. Certain qualities that are nurtured by mathematics are power of reasoning, creativity, abstract or spatial thinking, critical thinking, problem-solving ability and even effective communication skills.
If n represents a number then write an expression for two less than one fourth of n
Answers
Answer: [tex]\frac{1}{4}n-2[/tex]
This is the same as [tex]\frac{n}{4} - 2[/tex] and it is also equivalent to [tex]0.25n-2[/tex]
=====================================================
Explanation:
n is some placeholder for a number
one fourth of that number is [tex]\frac{1}{4}n[/tex] which is the same as [tex]\frac{n}{4}[/tex] or [tex]0.25n[/tex] since 1/4 = 0.25
From here, we subtract off 2 to get [tex]\frac{1}{4}n-2[/tex] as one possible final answer.
A. B. 3(x+2) x+2 =18 =6 1) How can we get Equation BBB from Equation AAA? Choose 1 answer: Choose 1 answer: (Choice A) A Add/subtract the same quantity to/from both sides (Choice B) B Add/subtract a quantity to/from only one side (Choice C) C Multiply/divide both sides by the same non-zero constant (Choice D, Checked) D Multiply/divide only one side by a non-zero constant
Answers
Answer:
C. Multiply/divide both sides by the same non-zero constant
A. Yes
Just Did It On Khan Academy
Step-by-step explanation:
To get equation A from equation B multiply/divide only one side by a non-zero constant option (C) Multiply/divide only one side by a non-zero constant is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
It is given that:
Two linear equations:
A. 3(x + 2) = 18
B. x + 2 = 18
In equation B multiply by 3 on one side:
3(x + 2) = 18
Thus, to get equation A from equation B multiply/divide only one side by a non-zero constant option (C) Multiply/divide only one side by a non-zero constant is correct.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ2
Round 8,542,310 to the nearest million
Answers
Answer:
9,000,000
Step-by-step explanation:
Since the 5 next to the 8 is a number with a value of 5 or higher, you can round the 8 up to a 9 thus rounding to the nearest million.
Plz answer this as well. Thankyou.
Answers
Answer:
21
Step-by-step explanation:
(-5-2)(-3)
= (-7)(-3)
=21
6(m+2)+6m=-5(-7m-7) Solve for m.
Answers
Answer:
m = -1
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
m = -1
☽------------❀-------------☾
Hi there!
~
Let's solve your equation step-by-step.
[tex]6(m+2)+6m=-5(-7m-7)[/tex]
Step 1: Simplify both sides of the equation.
[tex]6(m+2)+6m=-5(-7m-7)[/tex]
[tex](6)^{(m)} + (6)(2)+6m= (-5)(-7m)+(-5)(-7)[/tex] (Distribute)
[tex]6m+12+6m=35m+35[/tex]
[tex](6m + 6m)+(12)=35m + 35[/tex] (Combine Like Terms)
[tex]12m + 12 = 35m + 35[/tex]
[tex]12m + 12 = 35m + 35[/tex]
Step 2: Subtract 35m from both sides.
[tex]12m + 12 - 35m = 35m + 35 - 35m[/tex]
[tex]-23m + 12 = 35[/tex]
Step 3: Subtract 12 from both sides.
[tex]-23m + 12 - 12= 35 - 12[/tex]
[tex]-23m = 23[/tex]
Step 4: Divide both sides by -23.
[tex]\frac{-23m}{-23} = \frac{23}{-23}[/tex]
[tex]m = 1[/tex]
❀Hope this helped you!❀
☽------------❀-------------☾
I give Brainliest to whom says this question is stupid. What is -2x-8
Answers
Answer:
No solution it IS STUPID.
Step-by-step explanation:
Answer:
that question is stupid.
The area, A, of a square with a side of length x is given by A = x^2? Use this relationship to verify that doubling the length of the side of a square floor increases the area of
the floor by a factor of 2^2
Answers
Answer:
Hi
Step-by-step explanation:
A basketball player averages 12.5 points per game. There are 24 games in a season. At this rate, how many points would the player score in an entire season?
Answers
Answer:
300
Step-by-step explanation:
hope this helps
Suppose that 14 inches of wire costs 70 cents. At the same rate, how many inches of wire can be bought for 35 cents?
Answers
Answer:
7
Step-by-step explanation:
35x2=70 14/2=7
about what is 4/5+8/9
Answers
Answer:
1.688 the 8 will keep repeating
Step-by-step explanation:
Answer:
76/45 or 1.69 (rounded)
Step-by-step explanation:
First, you want to find the LCM (Lowest Common Multiple) of the two fractions.
Here, the LCM would be 45 (5*9).
So the fraction would become:
[tex]\frac{4*9}{45} + \frac{8*5}{45} \\\\\frac{36+40}{45} \\\\\frac{76}{45}[/tex]
Steven wants to buy a $590 bicycle. Steven has no money saved, but will be able to deposit $50 into a savings account when he receives his paycheck each Friday. However, before Steven can buy the bike, he must give his sister $60 that he owes her. For how many weeks will Steven need to deposit money into his savings account before he can pay back his sister and buy the bike?
Answers
Answer:
13 weeks
Step-by-step explanation:
Add 590 and 60 together and then divide by 50 and you'll get 13
7¹² ÷ 7⁴ is equal to ___. A. 7³ B. 7⁸ C. 3 D. 1³
Answers
Answer:
B. 7⁸
Step-by-step explanation:
The four factors of 7 in the denominator cancel four of the twelve factors of 7 in the numerator, leaving 8. When a product consists of 8 factors of 7, we write it as ...
7⁸
Answer:
B
Step-by-step explanation:
7^12 / 7^4 = 7^8
The two rectangles in the sketch below are congruent. Which sequence exhibits their congruence? A rotation 90° clockwise about the origin followed by a reflection across the x-axis A rotation 90° counterclockwise about the origin followed by a reflection across the y-axis A rotation 90° counterclockwise about the origin followed by a reflection across the x-axis A rotation 180° counterclockwise about the origin followed by a reflection across the y-axis
Answers
Answer:
A rotation 90° counterclockwise about the origin followed by a reflection across the x-axis
Step-by-step explanation:
it's rotated about the origin counterclockwise by 90 degrees and then reflected over the X axis in order to find the shape there.
Write the fraction 12/28 in the simplest form
Answers
Answer: 3/7
Step-by-step explanation:
Answer:
12/28 is 3 /7 is your answer
2/7(x+4)=-6 what is the value of x?
Answers
Answer:
2/7 as decimal is 0.28
2/7(x+4)=-6
2/7x+ 1 1/4= -6
-6 - 1 1/4 = -7.25
0.28x = -7.25
x = -25.89
Hi can someone tell me how is the answer 113?? how do i type it in the calculator?? im confused can someone please explain ASAP!!!!!!!!
THANK YOU
Answers
You shouldn't need a calculator for this. The quadratic equation is written in standard form.
ax^2 + bx + c = 0
You substitute a, b, and c into the discriminant formula and solve as shown in the example in the picture you provided.
(-7)^2 - 4(2)(-8)
49 - 4(-16)
49 - (-64)
49 + 64
113
Best of Luck!
Solve with Foil, and show work (4x+3) (5x-4)
Answers
Answer:
[tex]20x^{2} + 12x -28[/tex]
Step-by-step explanation:
(4x+3) (5x-4)
= [tex]20x^{2} -16+15x-12[/tex]
(multiply 4x with (5x-4) and multiply 3 with (5x-4) )
= [tex]20x^{2} + 12x -28[/tex]
(rearrange the numbers and subtract 12 from -16)
Read the headline below and complete the instruction that follows. “Sloppy Play Sends Tigers to Final Loss” Determine which word indicates bias. Sloppy Tigers Final Loss
Answers
Answer:
Sloppy
_________
Answer:
sloppy
Step-by-step explanation:
it basically give a description that not everyone would think about it. if i described texas A&M as Trash not all people think that therefore making the statement an opinion and bias.
The temperature falls from 0 degrees to -12.4 degrees in 3 hours. Which expression finds the change in temperature
per hour?
Answers
Answer: should be 4.13
Step-by-step explanation: -12.4 divided by 3 is -4.13333333333 and goes on
Please emergency!!!
Please
Answers
Answer:
plane Q
Step-by-step explanation:
Please marke as a brainlist...