To establish congruence between two geometric figures, it is necessary to have information about their size and shape. This includes information about the lengths of their sides and the measures of their angles. It may also be necessary to know the relative positions of the figures, such as whether they are oriented in the same way or whether one is a reflection of the other.
To show that two figures are congruent, it is usually necessary to use one or more of the following techniques:
Superimpose the figures: This involves placing one figure directly on top of the other so that corresponding parts are aligned. If the figures are congruent, they will fit exactly on top of each other and no gaps or overlaps will be visible.
Use a ruler or other measuring tool: By measuring the lengths of the sides and angles of the two figures, it is possible to determine whether they are congruent. If all of the measures are the same, the figures are congruent.
Use transformations: Congruent figures can be obtained from each other through translations, rotations, and reflections. By applying these transformations to one of the figures, it is possible to determine whether it can be made to match the other figure.
Use geometric principles: There are various geometric principles that can be used to establish the congruence of two figures. For example, the AA (Angle-Angle) Congruence Postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are congruent.
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A quantity with an initial value of 980 decays exponentially at a rate of 0.3% every 6 decades. What is the value of the quantity after 49 decades, to the nearest
hundredth?
Answer:
956.73
Step-by-step explanation:
0.3% = 0.003
1-0.003 = 0.997
49/6 = 8 r1 (use 8 because decay is not continuous)
0.997^8 = 0.97625...
0.97625... x 980 ≈ 956.73
Answer: 956.25
Step-by-step explanation:
The area of a rectangle is equal to its length times its width. If the area of a rectangle
is 14x + 42 square feet, which option(s) could be the length and width of that rectangle?
Answer:
d
Step-by-step explanation:
Dwayne is having a birthday party with a total of 37 people (including himself). He needs to buy enough cases of soda to have 2 cans for each person. If a case of
soda contains 12 cans, how many cases will he need to buy?
Answer:
I do not know
Step-by-step explanation:
Anyone help me solve for y.
Answer:
y = - 4
Step-by-step explanation:
Given
y = 2x + ( - 2) , that is
y = 2x - 2 ← substitute x = - 1
y = 2(- 1) - 2 = - 2 - 2 = - 4
This is confirmed by the point (- 1, - 4 ) on the graph
Help this is due in 2 minutes
First, convert R as a percent to r as a decimal
r = R/100
r = 8.4/100
r = 0.084 rate per year,
Then solve the equation for A
[tex] A = P(1 + \frac{r} {n})^{nt} \\\\ A = 10,000.00(1 + \frac{0.084}{12})^{(12)(30)} \\\\ A = 10,000.00(1 + 0.007)^{(360)} \\\\ A = \$ 123,199.63[/tex]
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $10,000.00 at a rate of 8.4% per year compounded 12 times per year over 30 years is $123,199.63.
Please, nobody answered it!!! :C
Answer:
C. 59
Step-by-step explanation:
Hello There!
Remember the angles in a triangle add up to equal 180
So if we want to find a missing angle we subtract the given angles ( in this case 65 and 56) from 180
So missing angle = 180 - 65 - 56
180 - 65 = 115
115 - 56 = 59
So we can conclude that the missing angle has a measure of 59 degrees
Answer:
C: 59
Step-by-step explanation: His explanation is correct, I did it myself.
A new savings account is opened with $400 and gains 3% every year. What is the value of the account at 32 years?
Answer:
1072
Step-by-step explanation:
A .Write an equation for the trend line in slope -intercept form .
Given:
The graph of a trend line.
To find:
The equation of the trend line is slope intercept form.
Solution:
From the given graph it is clear that the equation of the trend line is passes through the points (0,25) and (5,50).
Slope of the line is:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{50-25}{5-0}[/tex]
[tex]m=\dfrac{25}{5}[/tex]
[tex]m=5[/tex]
The line passes through the point (0,25). So, the y-intercept of the line is 25.
Slope intercept form of a line is:
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
The slope intercept from of the line is:
[tex]y=(5)x+(25)[/tex]
[tex]y=5x+25[/tex]
Therefore, the equation for the trend line in slope -intercept form is [tex]y=5x+25[/tex].
A rectangular prism has a base with a length of 25, a width of 9, and a height of 12. A secod prism has a square base with a side of 15. If the volumd of the two prisms are equal, what is the height of the second prism?
Answer:
6cm
Step-by-step explanation:
correct for 100 points i swear
What is the geometric mean of 6 and 8?
Answer:
16 square root 6
Step-by-step explanation:
The geometric mean of 6 and 8 is [tex]4\sqrt{3}[/tex]
What is geometric mean?The geometric mean of two numbers [tex]x_1[/tex] and [tex]x_2[/tex] is given by the formula:
[tex]GM = \sqrt{x_1 \times \ x_2}[/tex]
The two given numbers are 6 and 8
That is, [tex]x_1=6[/tex] and [tex]x_2=8[/tex]
Substitute [tex]x_1=6[/tex] and [tex]x_2=8[/tex] into the formula [tex]GM = \sqrt{x_1 \times \ x_2}[/tex]
[tex]GM=\sqrt{6 \times 8}[/tex]
Simplifying further:
[tex]GM=\sqrt{48} \\\\GM=4\sqrt{3}[/tex]
Therefore, the geometric mean of 6 and 8 is [tex]4\sqrt{3}[/tex]
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Can someone please help me with math.
Answer:
B
Step-by-step explanation:
The solution to a system of equation is when two lines pass and intersect ona specific point. Here we are looking for (0,1).
we can see b intersects on (0,1) so that is out answer.
What is the scale factor from Figure A to Figure B?
find the surface area of the pyramid
Answer:
864cm squared
Step-by-step explanation:
The base is 16 x 16
The 4 lateral faces (Triangles) are [(19 x 16) / 2 ] x 4}
Which expression is not a polynomial?
Please answer the question bellow
No solution
because delta ( b^2 - 4ac ) is lower than 0(zero) .
James wants to cover a floor measuring 90 cm by 120 cm with square tiles of the same size.
Given that he uses only whole tiles, find the largest possible length of the side of each tile
Answer:
30cm
Step-by-step explanation:
Find L.C.M of 90 and 120
what is the product
4/6 x 9
13/16
36/54
3
6
Please help me out with this
Answer:
Step-by-step explanation:
surface area = 3^2 : 11^2
volume = 3^3 : 11^3
width = 3: 11
hmm I'm not sure what you can enter into the text boxes.. if it won't let you put in the exponentials just use your calculator to put in the number that they equal. But I like the exponential form better.
A grocery store is offering a sale on bread and soup. Khalil buys four cans of soup and three
loaves of bread for $11.67. Ronda buys eight cans of soup and one loaf of bread for $12.89.
Homework Help!
a. Write equations for both Khalil's and Ronda's purchases.
b. Solve the system to find the price of one can of soup and the price of one loaf of bread.
Answer:
a) For Khalil's purchase
4x + 3y = 11.67.....Equation 1
For Ronda's purchase
8x + y = 12.89......Equation 2
b) A can of soup = x = $2.09
Loaf of bread = y = $1.35
Step-by-step explanation:
A grocery store is offering a sale on bread and soup. Khalil buys four cans of soup and three
loaves of bread for $11.67. Ronda buys eight cans of soup and one loaf of bread for $12.89.
Homework Help!
Let us represent:
a can of soup = x
Loaf of bread = y
a. Write equations for both Khalil's and Ronda's purchases.
For Khalil's purchase
= Khalil buys four cans of soup and three loaves of bread for $11.67.
4x + 3y = 11.67.....Equation 1
Ronda buys eight cans of soup and one loaf of bread for $12.89.
8x + y = 12.89......Equation 2
b. Solve the system to find the price of one can of soup and the price of one loaf of bread.
We have:
4x + 3y = 11.67.....Equation 1
8x + y = 12.89......Equation 2
y = 12.89 - 8x
We substitute 12.89 - 8x for y in Equation 1
4x + 3(12.89 - 8x) = 11.67
4x + 38.67 - 24x = 11.67
38.67 - 11.67 = 24x - 4x
27 = 20x
x = 27/20
x = 1.35
y = 12.89 - 8x
y = 12.89 - 8 × 1.35
y = 12.89 - 10.8
y = 2.09
Therefore,
Solving for y
a can of soup = x = $2.09
Loaf of bread = y = $1.35
10. Mason earns $10 for each lawn he mows. How much will he earn if he mows 6 lawns?
A. Write and solve an equation to solve the problem. Show your
work.
Answer:
60
Step-by-step explanation:
just multiply 10 by 6 why is this in highschool math though.
Find the value of x.
Which one doesn’t belong?
Come up with one reason for at least 3 different boxes
Answer:
I think box #1 doesnt't belong because it say spend $100 and get $10 off
Step-by-step explanation:
What is 2 2/13 divided by 2/3
Answer:
3.23
Step-by-step explanation:
Answer:
the answer is 3.23 hahahhhhahahhahndjalid;jslakjsakl sorry needed that to submite the answer
HELP FAST I'LL MARK YOU BRAINLIEST
Which below is not always true about a Rhombus?
1. All side are equal
2. Opposite sides are equal and congruent
3. Consecutive angles are supplementary
4. Diagonals are congruent
Answer:
#4 is not always true, only when it's a square.
42. Use the Quadratic Equation to find the Roots of x2 + 3x - 3=0
Answer:
Step-by-step explanation:
The coefficients of the x terms are {1, 3, -3}, so the discriminant, b^2 - 4ac, is 3^2 - 4(1)(-3), or 9 + 12, or 21. The positive nature of the discriminant tells us that there are two real, unequal roots. Following the quadratic formula, we get:
-3 ± √21
x = -----------------
2
Someone pls help:( im new tysm if u doo!
additive inverse of 8/-13 pls help fast
Answer:
8/13
hope this answer helps you.....
identify the equation whose graph is a vertical line.
a) y=x/3-1
b) y=0
c) x=0
I need help I'm struggling :(
A triangular pyramid is formed from three right triangles as shown below.
Use the information given in the figure to find the length BD.
If applicable, round your answer to the nearest whole number.
The lengths on the figure are not drawn accurately.
ΔADC is a right angle triangle, we will use the Pythagorus Theorem to find the length CD.
Formula of the Pythagorus Theorem :
⇒ a² + b² = c²
⇒ AD² + CD² = AC²
The value of AD is 54 and the value of AC is 90:
54² + CD² = 90²
Solve for CD:
54² + CD² = 90²
CD² = 90² - 54²
CD² = 5184
CD = √5184
CD = 72
ΔADC is also a right angle triangle, we will use the Pythagorus Theorem to find the length BD.
Formula of the Pythagorus Theorem :
⇒ a² + b² = c²
⇒ BD² + CD² = BC²
The value of CD is 72 and the value of BC is 97:
BD² + 72² = 97²
Solve for BD:
BD² = 97² - 72²
BD² = 4225
BD = √4225
BD = 65
Answer: The length of BD is 65 units.