To prove the converse of the Pythagorean theorem, it must be assumed that the Pythagorean theorem is true. This assumption is fundamental to the proof. Option A is correct answer.
The proof of the converse of the Pythagorean theorem.
To prove the converse of the Pythagorean theorem, it is important to start by assuming that the Pythagorean theorem itself holds true.
Therefore, option A is the correct answer: It must be assumed that the Pythagorean theorem is true.
This fundamental assumption is crucial since the converse states that if the sum of the squares of two sides of a triangle is equal to the square of the third side, then the triangle is a right triangle.
This is a direct implication assuming the Pythagorean theorem's validity.
An essential part of a mathematical proof, especially in geometry, involves using established theorems and logical deductions.
It's also worth mentioning Euclid's proposition that states, "Any two sides of a triangle are together greater than the third side." While this proposition is relevant to the properties of triangles, it is not a component of the proof for the converse of the Pythagorean theorem.
Which is the correct solution for the system?
3y = 6 − 2x
8x = 3y − 1
Answer:
the answer is c
Step-by-step explanation:
just took the test
Answer:
its a
Step-by-step explanation:
Please Help!!!!!
Which method can you use to prove these triangles congruent?
Answer: The HL Theorem.
Step-by-step explanation: We are given that the triangles have a congruent 90 degree angle and two congruent sides. This would indicate towards SAS but in this case, that doesn't work because the angle is not in between the two congruent sides. We know that the triangles are right, and that their hypotenuses are congruent and that one leg is congruent. Thus, the answer must be HL (hypotenuse & leg).
Answer:
The HL Theorem.
Step-by-step explanation:
Make 24 using the numbers 1,5,7,8
Answer:
1+7+8+8
Step-by-step explanation:
Answer:
1+7+8+8
Step-by-step explanation:
what is the nth term for 7,11,15,19
Answer:
[tex]a_{n}[/tex] = 4n + 3
Step-by-step explanation:
Note there is a common difference d between consecutive terms, that is
d = 11 - 7 = 15 - 11 = 19 - 15 = 4
This indicates the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 7 and d = 4, thus
[tex]a_{n}[/tex] = 7 + 4(n - 1) = 7 + 4n - 4 = 4n + 3
Please please answer this correctly please label the numbers correctly and please write down your answers correctly
Answer:
My explanation -->
Step-by-step explanation:
Go over to the left on the -4 and up 5 times and mark a dot on it.
Next, go up half a mark from 0 and put a dot there.
Then, go over to the left between the -2 and -4 and go up 5 times.
Lastly, from the 0, go down half way until the next horizontal line and place a dot there.
To make Kool-Aid, the ratio of cups of water to cups of powder is 8 to 2. If I use
12 cups of water, how many cups of powder do I need? *
Answer:
3 cups of powder
Step-by-step explanation:
8/2 divided by 2=
4/1
4/1 x 3= 12/3
the 12 represents the water and the 3 represents the powder
Answer: 3 cups of powder
Step-by-step explanation
8 12. first you cross multiply so the equation would be 8x = 24
2 X. The you do division to get the answe for x X = 3
x represents the amount of powder that is needed so you just replace x for cups of powder! And done!
Which of the following is the best estimate for the direction of the given vector?
a.
60° N of E
c.
60° W of S
b.
60° E of N
d.
60° S of W
Please select the best answer from the choices provided
A
B
C
D
Answer:
The answer is B
Step-by-step explanation:
The answer is B on edg2020. Hope this helps. #classof2020
Answer:
The answer is B
Step-by-step explanation:
The answer is B on edg2020. Hope this helps. #classof2023
Circle A: center (2, 3) and radius 5. Circle B: center (-1, 4) and radius 10. Which of the
following is the necessary transformation (translation; dilation) from B to A to prove
that the two circles are similar?
Answer:
see explanation
Step-by-step explanation:
The centre of circle B requires to be coincident with centre of circle A
(- 1, 4 ) → (2, 3 )
That is a translation of < 3, - 1 >
This ensures that the circles are concentric ( have the same centre )
radius of B is 10 and radius of A is 5, thus
dilatation = [tex]\frac{5}{10}[/tex] = [tex]\frac{1}{2}[/tex]
Guilherme observed the number of minutes in an hour his dormmates spent on social media sites while they were at the library. He reported his data in the following table. Dormmate Number of minutes on social media Vera 131313 Timothy 000 Manueala 141414 Khaled 363636 Yash 181818 Fernanda 161616 How many dormmates spent less than 202020 minutes on social media sites?
Guilherme observed the number of minutes in an hour his dormmates spent on social media sites while they were at the library. He reported his data in the following table. Dormmate Number of minutes on social media Vera 131313 Timothy 000 Manueala 141414 Khaled 363636 Yash 181818 Fernanda 161616 How many dormmates spent less than 202020 minutes on social media sites?
Answer:
15.5
Step-by-step explanation:
First, let's add up all of the minutes on social media.
13+0+14+36+18+12=93 min
Now we need to divide the total by the number of dormmates.
93/6
15.5
What is the volume of this sphere?
Use ≈ 3.14 and round your answer to the nearest hundredth.
4 ft
Rounded to the nearest hundredth, the volume of the sphere with a radius of 4 ft is approximately 267.95 cubic feet.
The formula for the volume V of a sphere is given by:
[tex]\[V = \frac{4}{3} \pi r^3\][/tex]
Given:
Radius r = 4 ft
Let's calculate the volume using the given radius:
[tex]\[V = \frac{4}{3} \times 3.14 \times 4^3\][/tex]
[tex]\[V = \frac{4}{3} \times 3.14 \times 64\][/tex]
[tex]\[V = \frac{4}{3} \times 200.96\][/tex]
[tex]\[V \approx 267.95\][/tex]
Solve the equation 1/4 a =3
Answer:
a=12
Step-by-step explanation:
To solve, we need to isolate the variable, a
1/4a =3
To do this, divide both sides by 1/4, or multiply both sides by the reciprocal of 1/4: 4/1
4(1/4a)=3(4)
The 4 and 1/4 will cancel out
a=12
Answer:
a = 12
Step-by-step explanation:
1/4 a = 3
Multiply each side by 4
1/4a*4 = 3*4
a =12
What is the surface area of the triangular prism?
Answer:
168ft
Step-by-step explanation:
1/2(6)(4)=12
1/2(6)(4)=12
(9)(5)=45
(9)(5)=45
(9)(6)=54
12+12+45+45+54=168
50 Points + 50 points +
1. Find the measurements of DE
2. Find the lengths of BC EC
3. Find the 1) width, 2) height only workings.
Do not need perimeter or area for question 3. So just need exact workings
for 1, 2 and 3 width and height parts.... if answering questions.
Answer:
see below
Step-by-step explanation:
Angle ACE = DCE since they are vertical angles
Angle A = Angle E parallel lines cut by a transversal form congruent alternate interior angles
Angle B = Angle D parallel lines cut by a transversal form congruent alternate interior angles
When all three angles are equal, the triangles are similar.
We can use ratios to find DE
DE CE
------- = ----------
AB AC
DE 8
------- = ----------
12 10
Using cross products
10 DE = 8*12
10 DE = 96
Divide by 10
DE = 9.6
2nd problem
Angle ADE is congruent to ABC because corresponding angles are conguent when parallel lines cut by a transversal
Angle AED is congruent to ACB because corresponding angles are conguent when parallel lines cut by a transversal
Angle A equals angle A by the reflexive property
When all three angles are equal, the triangles are similar.
We can use ratios to find BC
AD DE
------- = ----------
AB BC
8 5
------- = ----------
8+6 BC
Using cross products
8 BC = 5 (14)
8 BC =70
Divide each side by 8
BC =8.75
We can use ratios to find EC
AD AE
------- = ----------
AB AC
8 4.2
------- = ----------
8+6 4.2+EC
Using cross products
8 (4.2+EC) = 4.2*14
33.6 +8EC = 58.8
Subtracting 33.6
8EC =25.2
Dividing by 8
EC =3.15
787,000 in scientific notation
Answer:
7.87 × 10 ^6
Step-by-step explanation:
787,000 in scientific notation is 7.87 × 10⁶.
What is a scientific notation?In Mathematics and Statistics, any numerical data (number) can be written in scientific notation as shown below:
[tex]a \times b^{n}[/tex]
Where
a represent a real number.b represent an integer.787,000 = 700,000 + 87,000
By counting the number of digits, we can logically deduce that they are equal to six (6). In this context, the given number can be written in scientific notation as shown below:
787,000 = 7.87 × 10⁶
Read more on scientific notation here: brainly.com/question/22369512
#SPJ6
Which is the best estimate for the area of the circle shown below?
A. 66 square meters
B. 121 square meters
C. 380 square meters
D. 726 square meters
Answer:
c) 380 m²
Step-by-step explanation:
A = π·r²
= 3.14×121
= 379.94
≈ 380 m²
Which table represents a linear function?
What do changes in a graphs slopes on a distance-versus-time graph mean?
Answer:quadratic formula
simple method
Consider the sequence shown.
A, E, I, …
Jorge reasons that the next letter in the sequence is M, since three letters of the alphabet are
skipped between each listed letter.
Should Marci agree with Jorge's inductive reasoning?
A
No; the sequence could be listing the vowels in alphabetical order.
B
No; sequences with only three terms are too short to use to find patterns.
C
Yes; this is the only reasonable pattern that can be identified from the terms.
D
Yes; inductive reasoning is a valid method for determining terms of a sequence.
Yes; inductive reasoning is a valid method for determining the terms of a sequence. Option D is correct.
Given that,
A, E, I, …
Jorge reasons that the next letter in the sequence is M since three letters of the alphabet are skipped between each listed letter. Should Marci agree with Jorge's inductive reasoning is to be determined.
Inductive reasoning is a form of definining determinations by proceeding with patterns specific to the usual. It's generally distinguished with deductive reasoning, there it proceeds from general knowledge to specific conclusions.
Here,
Jorge reasons that the next letter in the sequence is M in A, E, I, … since three letters of the alphabet are skipped between each listed letter.
And Yes, Marci agrees with Jorge's inductive reasoning is a valid method for determining the terms of a sequence.
Thus, Yes; inductive reasoning is a valid method for determining the terms of a sequence. Option D is correct.
Learn more about inductive reasoning here:
https://brainly.com/question/8419798
#SPJ2
The probability that Babe Ruth hits a home run on any given at-bat is 0.12, and each at-bat is independent.
Part A: What is the probability that the next home run will be on his fifth at-bat? (5 points)
Part B: What is the expected number of at-bats until the next home run? (5 points)
Answer:
A) 0.072 = 7.2%
B) 8.3333 at-bats (8 to 9 at-bats)
Step-by-step explanation:
A)
If the chance of hitting a home run is 0.12, the chance of not hitting a home run is 1 - 0.12 = 0.88.
To find the probability of the next home run being in the fifth strike, we need the four other strikes to not be a home run, so the probability is:
P = (0.88)^4 * 0.12 = 0.072 = 7.2%
B)
To find the expected number of at-bats until the next home run, we just need to divide 100% by the probability of hitting a home run (0.12 = 12%):
100/12 = 8.3333
So the expected number is 8 to 9 at-bats
how do you expand (5x+ 1)(5x-1)
Step-by-step explanation:
Multiply both numbers so
25x2 - 6x + 6x - 1
25x2 - 1
Answer:
25x power of 2 subtract 1
Step-by-step explanation:
The sum of one and the product of four and a number x.
The sum of one and the product of four and a number looks like this: 1 + (4n) or 1 + (4 x n) whatever you prefer.
Gabriel is at the grocery store, and wants to figure out his total cost before he gets to the register. He bought 2.5 pounds of apples that are x dollars a pound and 2 bags of lettuce for y dollars each. Which expressions would represent his total cost?
Answer:
I KNOW IT!!^^
Step-by-step explanation:
All right the answer would be 2.5x+2y=? so basically since x represents the cost of one pound of apples and y represents the cost of one bag of lettuce i had 2 this 2 last year i hope this helped u!!^^
Jeremy can stand on one leg for 3.8 minutes. Express that time in seconds.
Answer:
He can stand on one leg for 228 seconds.
Step-by-step explanation:
You multiply the 3.8 seconds by 60.
So, 3.8 * 60 = 228
Hope this helps :)
A coin is flipped 200 times. The results are 102 heads and 98 tails. What is the relative frequency of getting a tail? Question 2 options: 2% 49% 51% 98%
Answer:
98/200= 49% B.
Which expression is equivalent to 9x + 3y
Answer:
3(3x + y)
Step-by-step explanation:
Sorry if its wrong
The diameter of a circle is 4 cm. Find its area to the nearest tenth.
Answer:
12.57cm²
Step-by-step explanation:
Hopefully this helps :)
The area of a circle with a diameter of 4 cm is found by using the formula A = πr² with the radius being half the diameter. After calculation, the area of the circle is 12.56 cm², which is rounded to 12.6 cm² to the nearest tenth.
The question requires us to find the area of a circle when given its diameter, which is 4 cm. To calculate the area, we will use the formula A = πr², but first, we need to determine the radius of the circle. As the radius is half the diameter, for our circle, the radius (r) is 2 cm (half of 4 cm). Substituting this value into the area formula:
A = πr²
= 3.14 × (2 cm)²
= 3.14 × 4 cm²
= 12.56 cm²
To provide the answer to the nearest tenth, we round the area to 12.6 cm². Therefore, the area of the circle is 12.6 cm²
when rounded to the nearest tenth.
The sum of three consecutive integers is 9.
1. Determine the variable.
2. Identify key words and translate their meanings.
3. Write the multistep equation for the scenario.
Use the variable n to represent the first integer. Finish translating to identify the third integer.
1st integer: n
2nd integer: n + 1
3rd integer: n + _
To solve for three consecutive integers whose sum is 9, we can express the integers as n, n + 1, and n + 2. Using the equation n + (n + 1) + (n + 2) = 9, we find that n = 2. Therefore, the three consecutive integers are 2, 3, and 4.
Explanation:To solve for three consecutive integers whose sum is 9, we can start by expressing the integers in terms of a variable. Let's use the variable n to represent the first integer.
The second integer would then be n + 1, and the third integer would be n + 2.
The sum of these three integers is given as 9, so we can write the equation n + (n + 1) + (n + 2) = 9.
Simplifying the equation by combining like terms, we get 3n + 3 = 9. Subtracting 3 from both sides, we have 3n = 6. Finally, dividing both sides by 3, we find that n = 2.
Therefore, the three consecutive integers are 2, 3, and 4.
A camp needs 100 students to help with the 4-year old campers. Eight students from 4 different classes have agreed to help. How many more students are needed? Show your work.
Answer: if i can get brainliest that would be great
x = Students
100=8(4)+x
Equation:
100=32+x
-32 -32
68=x
68 students are needed
Answer:
the answer is 92
Step-by-step explanation:
You have to subtract 8 students that signed up from the amount of students needed.
Translate the expression with rational exponents into a radical expression. Simplify if necessary.
(233) -
Look at the attached picture⤴
Hope it will help u..
Answer and Step-by-step explanation:
Whenever we have a fractional exponent, the numerator is always going to be the exponent, and the denominator will be the root.
Here, the numerator is 4, so we taking 343 to the fourth power. At the same time, since the denominator is 3, we are taking the cube root of 343. Thus, we can write the expression as:
[tex]\sqrt[3]{343^4}[/tex]
We want to simplify this. We need to complete both operations, but it doesn't matter what order we do them in. In fact, I would do the cube root first because that won't lead to gigantic numbers:
[tex](\sqrt[3]{343} )^4=7^4=2401[/tex]
Thus, the answer is, I believe, 2401 (although it's not in radical form, the problem asked for the simplified answer, which is this).
Hope this helps!
Write the smaller solution first, and the larger solution second. h(x)=-5x^2 +180h(x)=−5x 2 +180
Answer:
x = -6,6
Step-by-step explanation:
h(x)=−5x^2 +180
Assuming you want to find the zero's
0 =−5x 2 +180
Subtract 180 from each side
0-180=−5x^2 +180-180
-180 = -5x^2
Divide each side by -5
-180/-5 = -5x^2/-5
36 = x^2
Take the square root of each side
±sqrt(36) = sqrt(x^2)
±6 = x
x = -6,6
Answer:
-6, 6
Step-by-step explanation:
h(x) = -5x² + 180
-5x² + 180 = 0
x² = 36
x = -6, 6