The triangles can be proven similar by the congruent theorem of triangles
What are Congruent Triangles?
Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
Given data ,
Let the two triangles be ABC and DEF
Now , the two triangles will be similar if
The three sides are equal
So , AB = BC = CD and
DE = EF = FD
And the two triangles are congruent if
By ASA theorem - two angles are the same and a corresponding side is the same
And ,
By SAS theorem : Two sides are equal and the angle between the two sides is equal
And ,
By RHS theorem : A right angle, the hypotenuse and a corresponding side are equal
Hence , the triangles ABC and DEF is similar ΔABC ≅ ΔDEF
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Mike's younger brother likes to ride his bike. If the wheels have a radius of 25 cm, determine how far the wheel travels in 2 revolutions.
Answer:
Intwo full revolutions,the wheel will travel 314 cm
Step-by-step explanation:
Recall that in one full revolution, the wheel will tavel the length of the wheel's circumference, That is:
In each revolution the wheel will cover 2 pi R = 2 * 3.14 * 25 cm = 157 cm
Therefore, in2 full revolutions, the wheel will cover twice this amount:
In 2 revolutions the wheel will travel: 2 * 157 cm = 314 cm.
Answer:
410
Step-by-step explanation:
PLZ HELPPPPPPPPPPPPPPPP
Three out of every seven candies sold were chocolate. If 210 candies were sold,
how many were chocolate?
Answer: 90
Step-by-step explanation:
210/7 is 30 times 3 is 90
Alecia had save 60% of the cost of a new cell phone. If she has saved $105, what is the full price of the cell phone?
[8-(-12)]÷(2x-2)-(-8)
Answer:
3
Step-by-step explanation:
Use order of operations to simplify 6 squared - (5 -4) + 2( 8 - 2 squared) divided by 8
Is one half greater than four fifths
Answer:
No, it is not greater than four fifths.
Step-by-step explanation:
Well 1/2 of 4/5 would be about 2.5/5. So summing it up. . .
if f(6)=7 what is f(-2)
Answer:
1 is correct answer or not please reply me
Three boys won $6000. They shared the money so that one boy gets $1200 more than the other two boys. Calculate how much money each boy gets?
Answer:
3200
Step-by-step explanation:
take 6000 and divide it by 3 then add 1200 to that!
12b – 5 = 3b
How do you solve for b
Answer:
b=5/9
Step-by-step explanation:
Joan climbed down 330 feet to the bottom of a cave. Next, she climbed up 385 feet. What was her final elevation? Joan was
feet above sea level
I NEED HELP ASAP PLEASE HELP ME
Answer:
102
Step-by-step explanation:
Has to equal up to 180° so 180-78 gives you 102.
Plz help me!!
I have no clue how to do this because my teacher moves to fast for me. If you can help out that would be really appreciated!!
Answer:
1. x = 65
2. x = 40
3. x = -7
4. x = -4
5. x = -7
6. x = 4
Step-by-step explanation:
Angles in a triangle always add up to 180 degrees.
Thus, for each triangle you can write an equation setting the sum of the three angles equal to 180, and solving for x.
1. 180 = 80 + 35 + x
180 - (80 + 35) = x
180 - 115 = x
65 = x
2. 180 = 70 + 70 + x
180 - (70 + 70) = x
180 - 140 = x
40 = x
3. 180 = 76 + 41 + (x+ 70)
180 - (76 + 41) = x + 70
180 - 117 = x + 70
63 = x + 70
63 - 70 = x
-7 = x
4. (the red square means its a right angle = 90 degrees)
180 = 90 + 25 + (x + 69)
180 - (90 + 25) = x + 69
180 - 115 = x + 69
65 = x + 69
65 - 69 = x
x = -4
5. 180 = 50 + (57 +x) + (x + 87)
180 - 50 = (57 +x) + (x + 87)
130 = (57 +x) + (x + 87)
combine like terms
130 = 144 + 2x
130 - 144 = 2x
-14 = 2x
-7 = x
6. 180 = 80 + (9x + 4) + (16x - 4)
180 - 80 = (9x + 4) + (16x - 4)
100 = (9x + 4) + (16x - 4)
combine like terms
100 = 25x + 0
100 = 25x
4 = x
10.(06.01 LC)
The following set of coordinates represents which figure?
(3,-5), (5,-2), (10,-4), (8, -7) (6 points)
Rectangle
O Rhombus
O Parallelogram
O Square
Answer:
It's a Rhombus
Step-by-step explanation:
4. If Sean has about 130 pieces of candy, what
are 3 amounts of candy he could actually
have?
on
Answer:
EXPLAIN
Step-by-step explanation:EXPLAIN
EXAMPLE
This table shows the number of marbles in a bag by color. If one marble is randomly selected from the bag, what is the
probability that it will be a blue or a red marble?
Answer:
I would say it would be in the middle
Step-by-step explanation:
Answer: the answer would be 52% :)
Step-by-step explanation:
“Half of a number (n) is at least 22."
translate and solve
Answer:
n >_44
Step-by-step explanation:
1/2n>_22
(times 2 on both sides)
n >_44
*** >_ is greater than or equal to sign
Ugh I need so much help please
Answer:
Step-by-step explanation:
Remember the SAS rule is that you know the measure of 2 sides and their angle in between. (Note that SSA side side angle DOESN'T work.) For the first question we know that sides JH and LM are congruent, and sides GJ and MK are as well. Secondly, we know that angles M and J are congruent. The question is; does this problem follow the SAS (side angle side) rule? Yes, their are two proven congruent sides on the two triangles, and the angle between them is proven congruent as well.
Second one is congruent because it follows the SSS rule (side side side) ie: all sides are congruent, so therefore the triangles are congruent.
Think about the third one. Is it congruent or not. (To be congruent it has to follow SSS, or SAS) Comment below so I can correct you.
simplify this expression
-1/2 (15/6 + 1/3)
Answer:
-17/12
Step-by-step explanation:
A marching band has 80 members.
The ratio of members who play wind instruments to all others is 2 to 3.
How many members play wind instruments?
Answer:
30 members will play wind instruments
Answer:
30 would be the answer to the ?
Amelia started with $54, and spent $6 each day at camp. She has $18 left. Write and solve an equation to find how many days d Amelia was at camp
Someone please help
Answer:
100
Step-by-step explanation:
360 is the total degree for every quadrilateral. 80+75+105=260. 360-260=100.
PLEASE HELP!! Write an equation of g(x) that represents an exponential base “e” parent function with the following transformations:
Reflect over y-axis, shift right 7, vertical stretch by 12
Answer:
[tex]g(x) = 12 {e}^{ - x - 7} [/tex]
Step-by-step explanation:
The parent function is
[tex]g(x) = e {}^{x} [/tex]
First it is asked to reflect over the y axis so using the rule
[tex]g(x) = g( - x)[/tex]
Our function looks like
[tex]g(x) = e {}^{ - x} [/tex]
Then we are asked to shift the equation to the right 7. When shifting to the right or move the x axis, instead of adding 7 we would want to subtract 7 since the x axis is the independent variable and we must respect the y axis which is the dependent so using the rule
[tex]g(x) = g(x - h)[/tex]
When subtracting a 7 it looks like now
where h is the number we move . Now we are asked to apply a vertical stretch of 12. Since vertical stretch refers to the y axis, we are just going to multiply the function by 12 using the rule
[tex]g(x) = a \times g(x)[/tex]
where a is the vertical stretch. So now it would look like
[tex]g(x) = 12 {e}^{ - x - 7} [/tex]
Ira and his wife's monthly payment included $1,256.61 for principal and interest, as well as
one twelfth of the annual property taxes of $3,478.50 and one twelfth of the annual
insurance premium on the property of $1,186. What will the total monthly payment be?
Answer:
its 1,645.32
Step-by-step explanation:
search one twelfth of 3,478.50, then one twelfth of 1,186 and add those answers with 1,645.32
Make x the subject of y=x/3
This simply means moving everything possible thing off x and isolate it.
y=x/3
We see x is stuck with a divide by 3 so we need to get rid of that by multiplying by 3 on both sides.
y*3=x/3*3
switch left and right side and simplify
x=3y
Done! as simple as that.
Which point could be on the line that is parallel to line KL and passes through point M?
(–10, 0)
(–6, 2)
(0, –6)
(8, –10)
Answer:
D. (8, –10)
Step-by-step explanation:
(8, -10) passes through this line.
The correct option is D
What is Coordinate Geometry?
By using graphs with curves and lines, coordinate geometry (also known as the analytic geometry) explains how geometry and algebra are related.
As per the given data:
We are given a line KL in the diagram, and we have to find out which point out of the given options will satisfy the equation of the line which is parallel to KL and passes through M.
Using the intercept form equation of line KL:
x/a + y/b = 1 [a and b are x and y intercepts respectively]
x/6 + y/4 = 1
4x + 6y = 24
Slope of this line = -a/b = -4/6 = -2/3
The line parallel to this will have the same slope and should pass through (-4, -2)
y - (-4) = (-2)/3 [x - (-2)]
y + 4 = (-2/3)[x + 2]
3y + 12 = -2x - 4
2x + 3y + 14 = 0
Clearly (8, -10) passes through this line.
2(8) + 3(-10) + 14 = 0
Hence, (8, -10) passes through this line.
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Find the number of groups and the number left over of 11÷3
I also need help with this one so pls help me
Answer:
the answer is 39
Step-by-step explanation:
you take 300 - 271 and you get 39
Answer:
29? or I'm just gullible.
Step-by-step explanation:
It seems like 29 so hopefully it is
help me out not all just what you can
9514 1404 393
Answer:
1e. 2t² +8t -6
2h. a² +2ab -3b²
3b. 8r +4
4b. 6x +4y -11
5b. e -3
Step-by-step explanation:
1e. Combine like terms.
(3t² +3t -6) +(-t² +5t) = t²(3 -1) +t(3 +5) -6
= 2t² +8t -6
__
2h. (2a² +3ab -4b²) -(a² +ab -b²)
Use the distributive property to eliminate parentheses. Note that all signs change in the second set of parentheses.
= 2a² +3ab -4b² -a² -ab +b² = a²(2 -1) +ab(3 -1) +b²(-4+1)
= a² +2ab -3b²
__
3b. The hash marks indicate sides of the same length. The perimeter is the sum of all side lengths.
P = (4r -2) +2(2r +3)
P = 4r -2 +4r +6 . . . . . . eliminate parentheses
P = 8r +4 . . . . . . . . . . . . combine like terms
__
4b. (3x +4y) +(5x -8) -(2x +3)
Note that the distributive property changes the sign of all terms in the last parentheses.
= 3x +4y +5x -8 -2x -3 . . . . eliminate parentheses
= x(3+5-2) +y(4) +(-8-3) . . . group like terms
= 6x +4y -11
__
5b.
Bill's age - Erin's age = (2e-3) -(e) = e -3
The difference in their ages is (e -3).
Please hurry; Which function increases the fastest? A. y 5 14x B. y 5 23 · 17x C. y 5 120x D. y 5 2275x^x
a y = 14^x
b y = -3 (17)^x
c y = 120x
d y = -275x
Answer: y = 14^x
Step-by-step explanation:
Here the options are:
a y = 14^x
b y = -3*(17)^x
c y = 120x
d y = -275x
to see which function increases the fastest (or which function is steeper) we need to look at the first derivations of each one of these, and see which one is larger for every value of x:
the derivations are:
a y = x*14^(x - 1)
b y = -x*3*(17)^(x - 1)
c y = 120
d y = -275
So we can already discard options c and d, because have constant rate of change.
Then we keep options a and b.
Always when we have an exponential function, like a^x and b^x
The one with the larger base will be steeper.
So if a > b, then:
a^x is steeper than b^x
In this case, the function:
y = -3*(17)^x
has a larger base, but, this function is negative.
This means that as x increases, our function will decrease, then this function will not "increase the fastest" (because it does not increase)
Then the left option (a: y = 14^x)
Will be the correct one.
(this will happen after some value of x, because two of the options have constant derivatives, these may be steeper for smaller values of x, and as x increases, we will see that y = 14^x is the one that increases the fastest)