The length of the hypotenuse of a 45 45 90 triangle with one side of length 8 is 8√2.
The length of the hypotenuse of a 45 45 90 triangle can be calculated using the Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse. This can be expressed mathematically as a2 + b2 = c2, where a and b represent the lengths of the two sides and c represents the length of the hypotenuse.
In a 45 45 90 triangle, both sides are equal in length. This means that the mathematical equation simplifies to a2 + a2 = c2 or 2a2 = c2. To calculate the length of the hypotenuse, we can solve for c by taking the square root of both sides, resulting in c = √2a.
In this particular example, if the length of one of the sides is 8, then the length of the hypotenuse can be calculated as c = √2(8) = 8√2. Therefore, the length of the hypotenuse of a 45 45 90 triangle with one side of length 8 is 8√2.
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A postulate is something in geometry that must be proven true before you can use it.
Answer:
Statements Reasons
AB¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ Given
∠ADB and ∠CDB are right angles Given
ΔADB and ΔCDB are right triangles definition of right triangles
BD¯¯¯¯¯¯¯¯≅BD¯¯¯¯¯¯¯¯ reflexive property
ΔADB≅ΔCDB HL≅
AD¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯ CPCTC (corresponding parts of congurent triangles must be congurent)
Step-by-step explanation:
Most of the geometry concepts and theorems that are learned in high school today were first discovered and proved by mathematicians such as Euclid thousands of years ago. Given that these geometry concepts and theorems have been known to be true for thousands of years, why is it important that you learn how to prove them for yourself?
Theorems and Proofs
In geometry, a postulate is a statement that is assumed to be true based on basic geometric principles. An example of a postulate is the statement “through any two points is exactly one line”. A long time ago, postulates were the ideas that were thought to be so obviously true they did not require a proof. A theorem is a mathematical statement that can and must be proven to be true. You've heard the word theorem before when you learned about the Pythagorean Theorem. Much of your future work in geometry will involve learning different theorems and proving they are true.
What does it mean to “prove” something? In the past you have often been asked to “justify your answer” or “explain your reasoning”. This is because it is important to be able to show your thinking to others so that ideally they can follow it and agree that you must be right. A proof is just a formal way of justifying your answer. In a proof your goal is to use given information and facts that everyone agrees are true to show that a new statement must also be true.
Suppose you are given the picture below and asked to prove that AD¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯. This means that you need to give a convincing mathematical argument as to why the line segments MUST be congruent.
Here is an example of a paragraph-style proof. This is similar to a detailed explanation you might have given in the past.
AB¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ because it is marked in the diagram. Also, ∠ADB and ∠CDB are both right angles because it is marked in the diagram. This means that △ADB and △CDB are right triangles because right triangles are triangles with right angles. Both triangles contain segment BD¯¯¯¯¯¯¯¯. BD¯¯¯¯¯¯¯¯≅BD¯¯¯¯¯¯¯¯ because of the reflexive property that any segment is congruent to itself. △ADB≅△CDB by HL≅ because they are right triangles with a pair of congruent legs and congruent hypotenuses. AD¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯ because they are corresponding segments and corresponding parts of congruent triangles must be congruent.
There are two key components of any proof -- statements and reasons.
The statements are the claims that you are making throughout your proof that lead to what you are ultimately trying to prove is true. Statements are written in red throughout the previous proof.
The reasons are the reasons you give for why the statements must be true. Reasons are written in blue throughout the previous proof. If you don't give reasons, your proof is not convincing and so is not complete.
When writing a proof, your job is to make everything as clear as possible, because you need other people to be able to understand and believe your proof. Skipping steps and using complicated words is not helpful!
There are many different styles for writing proofs. In American high schools, a style of proof called the two-column proof has traditionally been the most common (see Example 3). In college and beyond, paragraph proofs are common. An example of a style of proof that is more visual is a flow diagram proof (see Example 4). No matter what style is used, the key components of statements and reasons must be present. You should be familiar with different styles of proof, but ultimately can use whichever style you prefer.
Learning to write proofs can be difficult. One of the best ways to learn is to study examples to get a sense for what proofs look like.
Answer:
False
Step-by-step explanation:
It doesn't need to be proven in order to be used. We can just assume the postulate is true.
Help me please it’s due right now
Answer:
1. -3/2
2. 8
Step-by-step explanation:
Plug the number in with x to find the answer, then solve using PEMDAS as normal.
Which situation would be represented by the integer -8? A hole 8 feet deep. An 8-yard pass. You earn $8. A temperature of 8°F.
Answer:
A
Step-by-step explanation:
another helluva boss meme
Fill in the blank so that the ratios are equivalent. : 6 and 7:2
Answer:
x = 21
Step-by-step explanation:
x : 6 = 7 : 2
x/6 = 7/2
x/6 = 21/6
x = 21
Chen rode his skateboard 3 1/4 miles in 1/2 of an hour. What was his average speed in miles per hour.
Answer:
6.5 MPH
Step-by-step explanation:
Since he rode his skateboard for half an hour, you must multiply 2, that way he rode 1 hour. Since you multiply the 1/2 hour, you must also multiply 3 1/4, to get 6 1/2, or 6.5. Even though we know he didn't ride a full hour, if he had, and at the same rate, he would have rode 6.5 miles per hour.
Hope this helps! ;)
While walking past a flag pole, Tommy looked down and noticed his shadow. Use the diagram below to
find the length of his shadow.
PLS HELP
Answer: 30ft
Step-by-step explanation:
pls hurry i need the answer
9514 1404 393
Answer:
slope: 9/5
graph: C
Step-by-step explanation:
In a proportional relationship, the slope is the ratio of y to x. Here, that is ...
slope = y/x = 9/5
__
The graph of a proportional relationship goes through the origin. (eliminates graph B)
For this relationship, y is greater than x. (eliminates graph A)
The appropriate graph for y = 9/5x is graph C.
The number in front of a variable or term is called a .
Answer:
Coefficient. For example, in the term -3x, -3 serves as the coefficient of x.
The number in front of a variable or term is called a coefficient.
The coefficient represents the numerical factor by which the variable or term is multiplied. In an algebraic expression, the coefficient is the number that appears directly in front of the variable.
For example, in the expression 5x, the coefficient of x is 5. Similarly, in the expression 3y², the coefficient of y² is 3. The coefficient helps determine the magnitude or scale of the variable or term within the expression.
Therefore, the number in front of a variable or term is called a coefficient.
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PLZ HELP!!! WILL GIVE HIGHEST POINTS IF THE ANSWER IS CORRECT!!!
Answer:
ab multiplied by ( A -B)
Step-by-step explanation:
please help me on this will give you brainliest
Answer:
1.41 x 10 to the 7th power
Step-by-step explanation:
3 x 10 to the fifth is 300000
300000 x 47 = 14100000 in 47 seconds
14100000 = 1.41 x 10 to the 7th power
Hope that helps!
Answer:
1.41*10^7 or 14,100,000
Step-by-step explanation:
3*10^5*47=1.41*10^7
Jennifer and Ashley went to the store. Jennifer bought 1.2
pounds of apples. Ashley bought 0.75 pound of grapes. How
many pounds of fruit did they buy in all? Make sure to write your equation to receive credit.
Answer:
1.2+0.75=1.95 pounds
Step-by-step explanation:
Work out the percentage change to 2 decimal places when a price of £220 is decreased to £210.
Answer:
the answer is 4.54%
Can someone help me with this please .
Answer:
4
Step-by-step explanation:
78
what value of x is quadrilateral CDEF a parallelogram
Answer:
x = 2
Step-by-step explanation:
CDEF is a parallelogram.
CE and FD are its diagonals.
Diagonals of a parallelogram bisects each other.
Therefore,
10x - 5 = 4x + 7
10x - 4x = 7 + 5
6x = 12
x = 12/6
x = 2
Thus, for x = 2, CDEF is a parallelogram.
In the quadrilateral CDEF, the value of x is 2.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Quadrilateral CDEF is a parallelogram.
Here, CE and FD are its diagonals.
We know that;
Diagonals of a parallelogram bisects each other.
Therefore, We can formulate;
⇒ 4x + 7 = 10x - 5
Solve for x as;
⇒ 7 + 5 = 10x - 4x
⇒ 12 = 6x
⇒ x = 12/6
⇒ x = 2
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EXPRESA EN METROS :
A= 3 km 8 hm 5 dam
B= 8 dam 5 m 7 cm
C= 1 m 4 dm 6 cm 7mm
Answer:b
Step-by-step explanation:
Find the value of x, Round to the nearest tenth.
19
16
X
please help mee
Write an equivalent expression for 3(3x + 5). Explain what property you used to write your equivalent expression.
Answer:
9x+15, and I used the distributive property
Step-by-step explanation:
Answer:
distributive property
9x+15
Step-by-step explanation:
The distributive property is whenever you have () and distribute until you have zero of these ()
The equivalent expression simply means write this equation differently.
Andy learns in school that plants grow best when they receive an optimal range of water, sunlight, and nutrients. He decides to do an experiment with bean plants to test this idea. Over the course of a month, he is planning on giving five bean plants different amounts of water. His watering schedule is outlined below.
Plant
Amount of Water
Every Week
A
0 mL
B
10 mL
C
100 mL
D
1,000 mL
E
10,000 mL
What will be the most likely result of his experiment?
Question 2 options:
A. Plant A will die, while all of the other plants will flourish.
B. There will be no difference between the plants by the end of the fourth week.
C. Plant A and Plant E will die.
D. Plant E will grow faster than all of the other plants.
Question 3 (1 point)
Answer:
C. Plant A and Plant E will die.
Step-by-step explanation:
A0 mL
B 10 mL
C 100 mL
D 1,000 mL
E 10,000 mL
Plant A will get no water so it will Die
Plant E will be overwatered so it will rot and die
Please help due today
Answer:
1) unlikely 1/8 12.5%
2) equally likely 4/8 50%
3) likely 5/8 62.5%
4)impossible 0/10 0%
5) unlikely 3/8 37.5%
The measures of the angles of a triangle are shown in the figure below. Solve for x.
39
(9x-3)
Answer:
23.56
Step-by-step explanation:
i thin if not then 13,67
HELP! ITS EASY BUT I CANT DO IT!! Find the volume of a rectangular prism with length = 8.4mm, width = 3.5mm and height = 5.6mm. Length = 8.4mm
Answer:
164.64
Step-by-step explanation:
you just have to multiply
8.4 x 3.5= 29.4 then you do 29.4 x 5.6 = 164.64
¿Por qué creen que la cantidad de almidones es
la misma si el cereal se come solo o con leche? ayuda :(
Answer:
mira aveces el cereal se come con leche y aveces se come con yogurt a quienes lo hacen así claro el cereal tiene almidones
word problem that represents 8 times -0.25
Answer:
If bob buys 8 choclates, which each of them are 0.25 dollars each, how much money does he have if he has 0 dollars?
Step-by-step explanation:
A computer store bought a program at $10 and sold it at a selling price of $12 find the percent makup
Answer:
20%
Step-by-step explanation:
12-10=2
changed ÷ original x 100
2 ÷ 10 x 100
=20%
Sara uses 7.6 pints of blue paint and white paint to paint her bedroom walls. 3 4 of this amount is blue paint, and the rest is white paint. How many pints of white paint did she use to paint her bedroom walls?
Answer:
1.9
Step-by-step explanation:
7.6/4= 1.9
1.9*1= 1.9
ans is 1.9 pints
A 133.5 kg crate, sliding on the floor, is brought to a stop by a 54.5 N force. What is the deceleration of the crate?
Answer:
0.40m/s^2
Step-by-step explanation:
Given data
Mass= 133.5kg
Force F= 54.5N
The expression for the force acting is
F=ma
substitute
54.5=133.5*a
]Divide both sides by 133.5
a= 54.5/133.5
a= 0.40 m/s^2
Hence the acceleration is 0.40m/s^2
Bonjour, je bloque sur un exercice de mon DM pouvez vous m'aider s'il vous plaît ? Voici l'énoncé : Ce tremplin a la forme de la parabole de la fonction carré dans un repère orthonormé (unité : 1m). Il est haut de 0,5 m d'un côté et de 2m de l'autre. Calculer sa largeur l en m et arrondir au dixième. Merci d'avance.
2. The dimensions of a triangular pyramid are shown on the figure below. The height of the pyramid is
15 inches. What is the volume in cubic inches?
11
16 in
20 in
25.6 in
Answer:
he should be in 11 inches
A line has equation 2x + y=20 and a curve has equation y=a+
18/x-3, where a is a constant.
Find the set of values of a for which the line does not intersect the curve
Answer:
we have two equations:
2*x + y = 20
y = a + 18/x - 3
We want to find the values of a such that the graphs of the equations do not intersect.
The first step is to isolate y in the first equation.
now we get:
y = 20 - 2*x
Then we have the system of equations:
y = 20 - 2*x
y = a + 18/x - 3
If the line intersects the curve at a point (x, y), then at that point both functions have the same value of y, then:
20 - 2*x = y = a + 18/x- 3
We want to find a value of such that this does not happen.
Let's solve that equation and see what we can find.
20 - 2*x = a + 18/x - 3
20 + 3 = a + 18/x + 2*x
23 = a + 18/x + 2*x
(23 - a) = 18/x + 2*x
if we multiply all values by x, we get:
(23 - a)*x = 18 + 2*x^2
Then we have a quadratic equation, we can write this as:
2*x^2 - (23 - a)*x + 18 = 0
Now, remember that if the determinant of the quadratic function is smaller than zero, then the function does not have any real solution, then we need to find a such that the determinant of this quadratic equation is smaller than zero.
Remember that for a quadratic equation:
a*x^2 + b*x + c = 0 is:
b^2 - 4*a*c
In this case, the determinant is:
(-(23 - a))^2 - 4*2*18
(23 - a)^2 - 144
And this must be smaller than zero, then:
(23 - a)^2 - 144 < 0
23^2 - 2*23*a + a^2 - 144 < 0
529 - 46*a + a^2 - 144 < 0
a^2 - 46*a + 385 < 0
Notice that the function has a positive leading coefficient, then the arms of the function go upwards, then the region of the function that is smaller than zero is the values of a that are between both roots of a.
Then we need to solve:
a^2 - 46*a + 385 = 0
We can use the Bhaskara's equation to find the roots, the roots are given by:
[tex]a = \frac{-(-46) +- \sqrt{(-46)^2 - 4*1*385} }{2*1} = \frac{46 +-24}{2}[/tex]
Then the two roots are:
a₁ = (46 + 24)/2 = 35
a₂ = (46 - 24)/2 = 11
Then for all the values of a suc that:
11 < a < 35
The line does not intersect the curve.
I need help please
And if u don’t know the answer don’t comment because i'm really looking for help! ):
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The points form a right triangle. The circumcenter is the midpoint of the hypotenuse of a right triangle. Here, that is the midpoint of AC:
O = (A +C)/2
O = ((1, 1) +(10, 8))/2 = (11, 9)/2 = (5.5, 4.5)
The circumcenter is (5.5, 4.5).