Pythagoras theorem is a formula that helps us determine the missing side of a triangle, with the measure of two sides, given.
The Pythagoras theorem formula is expressed as:
[tex](\small\text{Hypotenuse})^{2} = (\small\text{side}_{1} )^{2} + (\small\text{side}_{2} )^{2}[/tex]
Now, let us take an example to understand the concept better.
Example:A triangle with longest side given as 15 centimeters. The base of the triangle has a length of 9 centimeters. What is the measure of the height?
Solution:We are given the following:
Longest side (hypotenuse of the triangle) = 15 cm Base of the triangle (Not the longest side) = 9 cmWhen we plug the hypotenuse and the base, in the formula, we get;
⇒ 15² = 9² + (side₂)²Subtract 9² on both sides of the equation to isolate (side₂)².
⇒ 15² = 9² + (side₂)²⇒ 15² - 9² = 9² + (side₂)² - 9²We can use the rule [a² - b² = (a - b)(a + b)] to simplify the L.H.S
⇒ (15 - 9)(15 + 9) = (side₂)²⇒ (6)(24) = (side₂)²⇒ 144 = (side₂)²Now, take square root on both sides of the equation to determine the measure of the missing side (height of triangle).
⇒ √144 = √(side₂)²⇒ 12 = side₂Therefore, the measure of the height is 12 centimeters.
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There are 7 seniors on the high school soccer team. Two of them will be
chosen to be co-captains. How many ways are there to choose the co-
captains?
Decide if this is a permutation or a combination, and then find the number of
ways to choose the co-captains.
The two co-captians can be chosen in 21 different ways.
How many ways are there to choose the co-captains?
If the two co-capitans are equivalent, then we need to find combinations.
So we want to find how many combinations of 2 elements we can make out of a set of 7 elements.
This is given by:
[tex]C(7, 2) = \frac{7!}{(7 - 2)!*2!} = \frac{7*6}{2} = 21[/tex]
So the two co-captians can be chosen in 21 different ways.
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Marcus deposited his paycheck in the amount of $625.84. he’ll use the check register to record his transaction. what will be his new balance?
Based on the fact that Marcus has deposited his paycheck in the amount of $625.84, his new balance will be $1,266.15.
What is the paycheck about?A pay check is known to be a cheque that is given to a person for a job done.
Note that Marcus Beginning balance: $640.31
He then Deposit of : $625.84
When you add both together,
His New Balance will be: $1,266.15
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Answer:
$1,266.15.
Step-by-step explanation:
edge
application factorise 5x²-20
5x²-20
5(x²-4)
hope it helps...!!!
can somene answer this
Answer:
Use the pythagorean theorem.
[tex]a^2 + b^2 = c^2[/tex]
The length of one leg, a is 11, and the length of the hypotenuse, the longest side (or c) is 17. Substitute
[tex]11^2 + b^2 = 17^2 \\121 + b^2 = 289\\[/tex]
Subtract 121 from both sides to isolate B
[tex]b^2 + 121 - 121 = 289 - 121\\b^2 = 168[/tex]
Take the square root of both sides to isolate b
[tex]\sqrt{b^2} =\sqrt{168} \\b = 12.961[/tex]
Factor
please help :)
Answer: Heyaa! :)
Your Answer Is.. (3w+7)² Or is 1 depending on if u want the GCF (GFC means to.. Find the prime factors of each term in order to find the greatest common factor (GCF).
Step-by-step explanation:
Factor using the perfect square rule.
Step-by-step explanation:
9w²+42w+49
since this is in (a-b)² form
3²w²+2*3w*7+7²
(3w+7)²
The government conducted a study and collected the given data. use the
data to answer the following questions.
speed (mph) 45 55 65 75
fuel (mpg) 43 45 38 32
find the quadratic regression model that represents the relationship
between speed and fuel. round your answer to two decimal places
The quadratic regression equation is y = -0.02x^2 + 2x - 6
How to determine the quadratic regression?The table of values is given as:
speed (mph) 45 55 65 75
fuel (mpg) 43 45 38 32
Next, we determine the regression equation using a graphing calculator (see attachment)
From the graphing calculator, we have:
a = -0.02, b = 2 and c = -6
A quadratic regression is represented as:
y = ax^2 +bx + c
So, we have:
y = -0.02x^2 + 2x - 6
Hence, the quadratic regression equation is y = -0.02x^2 + 2x - 6
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ruby was out at a restaurant for dinner when the bill came. her dinner came to $27.
after adding in a tip, before tax, she paid $34.29. find the percent tip.
Answer:
I think it's 21.26%
Step-by-step explanation:
tip: 34.29-27=7.29$
the percent tip: (7.29×100)/34.29=21.26 (approximately)
What is the perimeter of a triangle whose sides are 3.8 cm. 4.7 cm and 5.6 cm!
Answer:
Step-by-step explanation:
Easy, add up all the numbers. 3.8+4.7+5.6 which is 14.1!
Finding the area is the same thing, x*x, but dividing it all by two, (x*y)/2
Answer:
14.1 cm
Step-by-step explanation:
Perimeter : sum of the sides
3.8 + 4.7 + 5.68.5 + 5.6 14.1 cmCan somebody help me on this
Answer:
7 + 7 = 14
you have 7 apples and add 7 more thats 14
Step-by-step explanation:
I am a bit confused on how to solve it so please explain
Answer:
Step-by-step explanation:
You could do it either way, but I have attached an image with one way to do it.
Then, using the exterior angle theorem, you can do:
(180-4x) + 100 = 3x
280 - 4x = 3x
280 = 7x
x = 40
From there, don't forget to plug in the numbers if you need to do so :)
1/12
Is this good?please help me I’m dying
Answer:
hey its fine but just add one more line in the between somewhere because it should be total 12 sectors and you have only 11.
Step-by-step explanation:
check the pic for reference
Answer:
I think it should be good =D
Step-by-step explanation:
Find the measure of all sides. Round to the nearest tenth.
Answer:
the value of x=9 and AB(h)=9.396
What's for b). Help me
Answer:
Step-by-step explanation:
Remark
First take a look at A. It is a pretty good idea always to write the formula you are using before you begin a solution and go step by step from the formula. Also write your givens. I know it sounds like a lot of work. It really isn't. You are creating a habit.
Givens
n = 8
Sn = ?
d = -6
a = 90
Formula
S8 = a + (n - 1)*d
Solution
s8 = 90 + (8-1)*-6
s8 = 90 + 7 * -6
S8 = 80 - 42
S8 = 38
Part B
Here's where the formula is your friend. Let's suppose it is. Then solve for n. If we get an integer for the term number, then all is well. If we don't, and we get some kind of fraction, then 5 is not a member of the sequence.
Givens
Sn = 5
n = ?
d = -6
Formula
Sn = a + (n - 1)*d
Solution
5 = 90 + (n - 1)*-6 Subtract 90 from sides
5-90 =90-90 +(n - 1)*-6 Combine
-85 = (n -1)*-6 Divide by - 6
-85/-6 = (n - 1)-6/-6
14 1/6 = n - 1 Add 1 to both sides
14 1/6 +1 = n - 1 + 1 Combine
15 1/6 = n
But a fraction is not permitted. So 5 is not a member of the sequence
What is the equivalent expression to (-18)-64n? A. -2(9-32n) B. 2(9-32n) C. -2(9+32n) D. 2(9+32n)
Answer:
C. -2(9 + 32n)
Step-by-step explanation:
-2(9 + 32n)
= -2*9 - 2*32n
= (-18) - 64n.
help me for 10 points
edge= 5 in
to find:the surface area of the given cube.
solution:[tex]s.a = 6 {a}^{2} [/tex]
[tex]s.a = 6 \times {5}^{2} [/tex]
[tex]s.a = 150 \: {in}^{2} [/tex]
hence, the surface area of the given cube is 150 square inches.
P(Head, Diamond AND Head, Heart) = ?
The probability of drawing a head card of diamonds and then a head card of hearts is:
P = 0.003
How to find the probability?
Here we assume that we have a deck of 52 cards, and we want to find:
P(Head, Diamond AND Head, Heart)
This is the probability of drawing a head of diamonds and then a head of hearts.
Remember that for each suit has 3 head cards, J, Q, and K.
Then for the first card, the probability of getting a head of diamonds is equal to the quotient between the number of cards with these properties (3) and the total number of cards (52).
P = 3/52
Then we need to draw a head of hearts, the probability is computed in the same way, but before we drew a card, so now the total number of cards is 51, so we get:
Q = 3/51
Then the joint probability is:
p = (3/52)*(3/51) = 0.003
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Please help ASAP!!
see attachment below!
-3/5, 6/5, -12/5 whats the next term of the geometric sequence?
Answer:
24
Step-by-step explanation:
The numerators are being multiplied by -2
helppppop this is 7th grade math
the answer is B, D and F. I hope this was helpful
What does each line on the protractor stand for?
one-half of a degree
ten degrees
one degree
five degrees
Answer: I'm a fourth grader Here's my answer One degree
I hope This helps and yes It will make sense because Each on line is one degree and I got A test And it was right Any questions just type In the comments
SOMEONE HELP ME PLEASEEE
Answer:
2
Step-by-step explanation:
First, you have to find the change in the sides you know the numbers of. 21/3 is 7, so it's being increased/decreased by 7 units. Now, just divide 14 by 7 to get your answer (2).
Hope this helps!
x+4>3
Help, solve for x, give the interval notation...
Solution:
[tex]x > - 1[/tex]
[tex]\huge\mathfrak\colorbox{white}{}[/tex]
Interval Notation:
x ∈ (-1,∞)
Point S is the midpoint of RT the coordinates of point R and point T are listed below R(-11,-12) T(-7,-4) what are the coordinates of point S
Answer:
S (- 9, - 8 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here the endpoints are R (- 11, - 12 ) and T (- 7, - 4 ) , then
midpoint = ( [tex]\frac{-11-7}{2}[/tex] , [tex]\frac{-12-4}{2}[/tex] ) = ( [tex]\frac{-18}{2}[/tex] , [tex]\frac{-16}{2}[/tex] ) = (- 9, - 8 )
HELP QUICK ILL GIVE BRAINLEST
Answer:
C) 15, 20, 25
Step-by-step explanation:
If you plug this in pythagorean theorem, it works. The others don't.
IF a universal set U = {x:x belongs to N , x less or equal to 10} , A ={y:y = 2n , n belongs to N , n less than 5} and B ={z:z = 3n , n belongs to N , n less than 4}
Answer:
your answer is N = {xxx: =9n
If f(x) = x² — 2x and g(x) = 6x + 4, for which value of x does (f + g)(x) = 0?
4
-2
2
04
Answer:
-2
Step-by-step explanation:
Given that;
f(x) = x² -2x
and g(x) = 6x + 4
(f + g)(x) = x²-2x+6x+4
:- x² +4x + 4 = 0
x² +2x +2x + 4 = 0
x(x + 2)+2(x + 2) = 0
(x + 2)(x + 2) = 0
:- x = -2
PLEASE HELP ME OUT
8.)
Using special right triangles, what will be the y-coordinate of the point below?
a.)
5√3
b.)
5
√3
30°
10 units
(0,0)
c.)
d.)
Step-by-step explanation:
the answer is b 5 according to the graph
I need help with this pls!!
Answer:
Second choice
Step-by-step explanation:
This is a circle with center at 0,0
radius = sqrt 100 = 10
19-29 find the derivative of the function using the definition of derivative. state the domain of the function and the domain of its derivative.
19. [tex]f(x)=3 x-8[/tex]
Answer:
The derivative of that function is 3x.
The domain of f(x) = x∈ℝ
The domain of f(x) is also x∈ℝ
Step-by-step explanation:
–51 ≤ x + 38 I need help please finals are tomorrow....
Answer:
x ≥ - 89
Step-by-step explanation:
−51 ≤ x + 38
Step 1: Flip the equation.
⇒ x + 38 ≥ - 51Step 2: Subtract 38 from both sides.
⇒ x + 38 - 38 ≥ - 51 - 38x ≥ - 89 ====> Answer