help please!
Does mapping the triangle DEF onto triangle GHI prove the two triangles are congruent? Explain your reasoning.
Answers
Yes, and there are actually several methods to do so. One method to ensure congruency is to rotate and translate the triangle onto the other, which does not change the shape or size, only where it is. They perfectly match each other when rotated and translated, showing perfect congruency. Another way to ensure congruency is to find angle lengths/slope. Using the slope formula (rise/run), we can find both slopes (whch is the distance in this case) of each side length of both triangles. The angle lengths and slopes are equal to each other.
Mapping the triangle DEF onto triangle GHI gives the coinciding image so the length will be the same and thus it can prove congruency.
What is congruence?If two figures are exactly the same in sense of their length side all things then they will be congruent.
If it is possible to superimpose one geometric figure on the other so that their entire surface coincides.
As per the given graph,
Triangle GHI and triangle DEF are plotted.
If we map triangle DEF onto GHI since the length is the same and orientation will become the same so both triangles will coincide with each other.
And it is known that if the length of all sides of a triangle is the same then they will be called a congruent triangle.
Hence"Mapping the triangle DEF onto triangle GHI gives the coinciding image so the length will be the same and thus it can prove congruency".
To learn more about congruence,
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Related Questions
1.) What is the maximum number of zeros for the following function
f(x) = x - 2x2 - 11x + 12
Answers
Answer:
-14x+12
Step-by-step explanation
f(x)=-14
8n - 32 + 5m + 33 - 3
Answers
8n - 32 + 5m + 33 - 3
8n-32+5m+30
8n-32+30+5m ( rearranging)
8n-2+5m
answer:
5m+8n-2 or 8n+5m-2
Answer:
[tex]8n+5m-2[/tex]
Step-by-step explanation:
Simplify the expression by combining like terms:
[tex]-32+33-3\\\\1-3\\\\-2[/tex]
Insert:
[tex]8n+5m-2[/tex]
:Done
HELP ME THIS IS SO CONFUSING
Answers
Answer:
365 degrees :)
Step-by-step explanation:
It's a multiple of 5, but with no zeros, so that means the ones place is 5. The hundreds place is two less than 5, so that's 3. And the tens place is two times the 3, so that gives you 365!
Answer: 365
Step-by-step explanation: hope this helps bud
How can you tell, without multiplying, if the product of three or more integers will be positive or negative?
Answers
Answer:
divide, or write and equation and solve it
Step-by-step explanation:
What is the equation for the line in slope-intercept form? Enter your answer in the box.
Answers
Answer: y=-4x+5
Step-by-step explanation:
Answer:
y=-4x+5
Step-by-step explanation:
1. Find the slope by counting downward and over from one point to another point. Let's start from (-2,13) and go down to (0,5)
If you are worried about miscounting, you could also use the slope formula which is y2-y1/x2-x1
5-13/0--2
= -8/2
The slope is -4.
2. FInd where the line crosses the y-axis to get the y-intercept. Here it crosses it at 5.
3. Write the equation on slope-intercept form, which is y=mx+b where mx represents the slope and b represents the y-intercept.
y=-4x+5
1.
Divide:
x+3x+2 x +4x+4
x+1 x + 5x+4
Answers
Answer:
x
4
−5x
2
+4
To factor the expression, solve the equation where it equals to 0.
x
4
−5x
2
+4=0
By Rational Root Theorem, all rational roots of a polynomial are in the form
q
p
, where p divides the constant term 4 and q divides the leading coefficient 1. List all candidates
q
p
.
±4,±2,±1
Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.
x=1
By Factor theorem, x−k is a factor of the polynomial for each root k. Divide x
4
−5x
2
+4 by x−1 to get x
3
+x
2
−4x−4. To factor the result, solve the equation where it equals to 0.
x
3
+x
2
−4x−4=0
By Rational Root Theorem, all rational roots of a polynomial are in the form
q
p
, where p divides the constant term −4 and q divides the leading coefficient 1. List all candidates
q
p
.
±4,±2,±1
Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.
x=−1
By Factor theorem, x−k is a factor of the polynomial for each root k. Divide x
3
+x
2
−4x−4 by x+1 to get x
2
−4. To factor the result, solve the equation where it equals to 0.
x
2
−4=0
All equations of the form ax
2
+bx+c=0 can be solved using the quadratic formula:
2a
−b±
b
2
−4ac
. Substitute 1 for a, 0 for b, and −4 for c in the quadratic formula.
x=
2
0±
0
2
−4×1(−4)
Do the calculations.
x=
2
0±4
Solve the equation x
2
−4=0 when ± is plus and when ± is minus.
x=−2
x=2
Rewrite the factored expression using the obtained roots.
(x−2)(x−1)(x+1)(x+2)
Expand and simplify
1: (2 ) a) 9( 3 – 10n ) -3 ( 10n + 1 )
Answers
Answer:
Hope it can help you .......
Mark me as a brainlist and follow me.....
Jen and Kamlee are walking to school. After 20 minutes, Jen has walked 45 mile. After 25 minutes, Kamlee has walked 56 mile. Find their speeds in miles per hour. Enter the correct answers in the boxes.
Answers
Answer:
Jen's speed = 135 miles per hour (Approx)
Kamlee's speed = 134 miles per hour (Approx)
Step-by-step explanation:
Given:
Jen walk = 45 miles
Jen's time = 20 min = 20/60 = 0.333 hour
Kamlee walk = 56 miles
Kamlee's time = 25 min = 25/60 = 0.416667 hour
Find:
Speed
Computation:
Jen's speed = 45 / 0.333
Jen's speed = 135 miles per hour (Approx)
Kamlee's speed = 56 / 0.416667
Kamlee's speed = 134 miles per hour (Approx)
Bob’s monthly phone bill is made up of a $10 fee plus $0.05 per minute. Bob’s phone bill for July was $22. Write an equation to model the situation using m to represent the number of minutes. Solve the equation to determine the number of phone minutes Bob used in July.
Answers
Answer:
equation: 10 + 0.05x=22
Step-by-step explanation:
the next step after writing the equation would be to subtract 10 from both sides to get 0.05x=12. after this you would then have to divide 12 by 0.05 to get 240 minutes. you could check it by putting 240 in for x to get 10+0.05(240)=22. you would then multiply 0.05 by 240 to get 12 and then add 10 onto it to get 22 which was already given.
9514 1404 393
Answer:
equation: 10 +0.05m = 22
solution: Bob used 240 minutes in July
Step-by-step explanation:
Bob's bill is the total of the fixed fee and the charges based on minutes. The latter is 0.05m, where m is the number of minutes. Hence, Bob's July bill is ...
10 + 0.05m = 22 . . . . . total of charges for July is $22
__
The equation is solved by subtracting the constant and dividing by the coefficient of m.
0.05m = 12 . . . . . subtract 10
m = 12/0.05 = 240
Bob used 240 minutes in July.
In the supermarket, there were 434 boxes of cereal, 285 gallons of milk, and 176 cans of orange juice. About how many
breakfast items were there? Use rounding to the nearest hundred to estimate the total number of breakfast items.
Answers
Answer:
900
Step-by-step explanation:
434+285+176 is 895,895 to the nearest hundred is 900
Simplify.
6y + 5y
Please help me!!!!!!!
Answers
Answer:
11y
Step-by-step explanation:
The answer is 11y because is kinda like adding. You add 6 + 5 which is 11 and then you just convert the y so its 11y
Solve the system by substitution ( find the intersection)
y=-2x+18
y=8
Answers
Answer: x = 5
Step-by-step explanation:
the table below shoes the rates for two duplicating companies. quick copy copy place initial fee of $5.00 initial fee of $10.00 $0.06 per page $0.04 per page the total cost, c, is dependent on the number of pages, p, that are duplicated. which of these systems of equations represents this situation? p = 5 + 6c p = 10 + 4c ⊝ c = 5 + 6p c = 10 + 4p ⊝ p = 5 + 0.06c p = 10 + 0.04c ⊝ c = 5 + 0.06p c = 10 + 0.04p
Answers
Answer:
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The system of equations representing the rates for two duplicating companies are -
C[1] = 5 + 0.06x
C[2] = 10 + 0.04x
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the rates for two duplicating companies. There are two different rates as-
[1] > initial fee of $5 and $0.06 per page.
[2] > initial fee of $10.00 and $0.04 per page.
For the [1] company, we can write the equation as -
C[1] = 5 + 0.06x
For the [2] company, we can write the equation as -
C[2] = 10 + 0.04x
So, the system of equations will be -
C[1] = 5 + 0.06x
C[2] = 10 + 0.04x
Therefore, the system of equations representing the rates for two duplicating companies are -
C[1] = 5 + 0.06x
C[2] = 10 + 0.04x
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.Write the following number in expanded form using powers of 10: 67.938
Answers
Answer:
67.938 =
(6 * 10^1) + (7 * 10^0) + (9 * 10^-1) + (3 * 10^-2) + (8 * 10^-3)
Step-by-step explanation:
Here, we want to write the given number in expanded form
Mathematically that will be ;
60 + 7 + 0.9 + 0.03 + 0.008
Using the power of 10, that will be;
(6 * 10^1) + (7 * 10^0) + (9 * 10^-1) + (3 * 10^-2) + (8 * 10^-3)
EASY POINTS FOR Y'ALL!!!!!!
Answers
Answer:B
Step-by-step explanation:
Answer:
D, is the correct answer!!
Step-by-step explanation:
6. A rectangle has a length of (x + 2) and a width of (3x
an expression in simplest form for the perimeter of the rectangle,
Pleaseee urgent!! Thank youuu
Answers
x + 2 + x + 2 + 3x + 3x = 8x + 4
If you know that 84 is 70% of the whole, how can you use proportional reasoning to determine the whole?
A: 70100 shows 70% as a ratio. The ratio 84x compares 84 to the whole, x. Write an equation so that the first ratio is equal to the second ratio. Solve for x : x = 120.
B: 70100 shows 70% as a ratio. The ratio 84x compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 58.8.
C: 70100 shows 70% as a ratio. The ratio x84 compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 120.
D: 70100 shows 70% as a ratio. The ratio x84 compares 84 to the whole, x. Write an equation so that the first ratio is equal to the second ratio. Solve for x : x = 58.8.
Answers
Answer:
A. 70/100 shows 70% as a ratio...
Step-by-step explanation?
"If three angles and two sides of two triangles are congruent, are the triangles congruent? Why or why not?"
Answers
Answer:
yes
Step-by-step explanation:
because the corresponding angles are congruent, the triangles are congruent through CPCTC. If two sides are congruent and an included angle, then the triangles are congruent through the SAS postulate. And if two sides and a non-included angle are congruent then the triangles are congruent through the AAS postulate. Any way of looking at this proves congruency through various postulates, therefore the trianlges are congruent.
select Yes or No to indicate whether each of the ordered pairs is most likely a solution to the equation represented by the graph
Answers
Answer:
(-1, 4)
Step-by-step explanation:
From the graph we see that;
At x = 0, y has a value of 1
At x = 2, y has a value of 1
At x = 1, y has a value of 0
At x = -1, y has a value of 4
Looking at the given options, the only ordered pair that corresponds to a correct reading on the graph as earlier observed is; (-1, 4)
Answer:
no
no
yes
Step-by-step explanation:
Which graph shows 3x - y = 1?
Answers
Answer:
The graph below shows the graph of 3x - y = 1.
Hope this helps! :)
Wendy tasted 12 desserts from each bakery in her county. Each bakery has an equal number of desserts.
Is this sample of the desserts from the county's bakeries likely to be representative?
Answers
It is difficult to determine whether the sample of desserts that Wendy tasted is representative of all desserts from the county's bakeries without additional information.
First, it depends on the total number of bakeries in the county. If there are only a few bakeries, Wendy's sample of 12 desserts from each bakery may not be enough to accurately represent all the desserts in the county. On the other hand, if there are many bakeries, and Wendy tasted 12 desserts from each one, then her sample may be more representative.
Secondly, it is important to consider how the bakeries were selected. If Wendy only tasted desserts from certain types of bakeries or only in certain areas of the county, her sample may not be representative of all the county's bakeries.
Therefore, without more information on the total number of bakeries in the county and the selection process, it is difficult to determine whether Wendy's sample of desserts is representative of all the desserts from the county's bakeries.
To learn more about sample here:
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Find the slope of a line with a y-intercept of -5 that goes through the point (12,3).
Formula: y=mx+b
Answers
y=2/3x-5
What is the imagine point of (-1,-5) after a translation left 1 unit and up 4 units?
Answers
Answer:
-2, -1
Step-by-step explanation:
So moving left would affect the x-axis.
Left would move it to the negatives so -1 - 1 = -2.
Moving up would affect the y-axis.
Up would move towards the positive so -5 + 4 = -1.
-2, -1
what is an equivalent fraction to 9/28 ?
Answers
Answer:
18/56
Step-by-step explanation:
Answer:
18/56
Step-by-step explanation:
9/28= 18/56
for the top 1 I multiplied the numerator and denominator by 2 and then when you simplify it you get 9/28
I need help any help is appreciated please
Answers
Answer:
third option both cost the same after 2 months
Find the perimeter of the figure.
Answers
Answer:
17x-3
Step-by-step explanation:
6x+9 + 3x-2 = 9x+7
2(4x-5) = 8x-10
9x+7 + 8x-10 = 17x-3
Answer:
Step-by-step explanation:
Answer:
17x-3
Step-by-step explanation:
6x+9 + 3x-2 = 9x+7
2(4x-5) = 8x-10
9x+7 + 8x-10 = 17x-3
Please Help me :)))))))))))
Answers
Answer:
35
Step-by-step explanation:
if GFL = 34 and GEL = 36 FLG would be 35
Jenny earned 110 of a possible 148 points on a test. She lost 2 points for each incorrect answer. How many incorrect answers did she have?
Answers
Answer: She had 19 incorrect answers
Step-by-step explanation:
n = number of incorrect answers at 4 points per answer
110 = 148 - 2n
Solve for n
n = (148 - 110)/2 = 19
Part B: A triangle has vertices A (-2, 3), B (0, 0), and C (1, 2). What are the coordinates of the vertices if the original triangle is dilated by a scale factor of 3 and then reflected over the x-axis?
Answers
Answer:
(-6,-9) , (0,0) and (3,-6)
Step-by-step explanation:
Here, we want to find new coordinates after dilating by 3 and reflecting over x-axis
By dilating by a factor of 3, we multiply each term by 3
We have the following;
A’(-6,9) B’(0,0) and C’ (3,6)
Now if we want to reflect the point (x,y) over x-axis, what we shall have is (x,-y)
So the vertices will be as follows;
(-6,-9) , (0,0) and (3,-6)
Solve the given system using elimination.
Answers
Answer:
s = -1
r = 2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
2r + 8s = -4
7r = -6s + 8
Step 2: Rewrite Systems
2r + 8s = -4
Factor: 2(r + 4s) = -4Divide 2 on both sides: r + 4s = -2Subtract 4s on both sides: r = -4s - 2Multiply -7 on both sides: -7r = 28s + 14Step 3: Redefine Systems
-7r = 28s + 14
7r = -6s + 8
Step 4: Solve for s
Elimination
Combine equations: 0 = 22s + 22Isolate s term: -22 = 22sIsolate s: -1 = sRewrite: s = -1Step 5: Solve for r
Define equations: 2r + 8s = -4Substitute in s: 2r + 8(-1) = -4Multiply: 2r - 8 = -4Isolate r term: 2r = 4Isolate r: r = 2Answer:
r = 2, s = - 1
Step-by-step explanation:
Given the 2 equations
2r + 8s = - 4 → (1)
7r = - 6s + 8 ( add 6s to both sides )
7r + 6s = 8 → (2)
Multiplying (1) by 7 and (2) by - 2, then adding will eliminate the r- term
14r + 56s = - 28 → (3)
- 14r - 12s = - 16 → (4)
Add (3) and (4) term by term to eliminate r , that is
44s = - 44 ( divide both sides by 44 )
s = - 1
Substitute s = - 1 into either of the 2 equations and solve for r
Substituting into (1)
2r + 8(- 1) = - 4
2r - 8 = - 4 ( add 8 to both sides )
2r = 4 ( divide both sides by 2 )
r = 2
solution is r = 2 , s = - 1