Answer:
See Below.
Step-by-step explanation:
We want to show that the Law of Cosines simplifies to the Pythagorean Theorem when the contained angle between the two known sides is 90°.
The Law of Cosines is given by:
[tex]c^2=a^2+b^2-2ab\cos(C)[/tex]
Where a and b are the two known sides, and C is the angle between them.
If C is 90° then we will have:
[tex]c^2=a^2+b^2-2ab\cos(90 ^\circ)[/tex]
Recall that the cos(90°)=0. Hence:
[tex]c^2=a^2+b^2-2ab(0)[/tex]
Simplify:
[tex]c^2=a^2+b^2[/tex]
So, we acquire the Pythagorean Theorem as desired.
How do you solve problems involving sequence? Discuss the mathematics concepts and principles applied when solving problems involving sequence
Step-by-step explanation:
Sequence is defined as arrangement f numbers in a specific or defined pattern. Sequence are categorized into
1) Arithmetic
2) Geometric
Arithmetic sequence are characterized by their common difference while Geometric sequence are characterized by their common ratio.
Given a sequance of numbers say;
T1, T2, T3...
The first term "a" of the sequence is T1
Common difference d = T2-T1 =T3-T2
Common ratio = T2/T1 = T3/T2
The formula for calculating nth term of an Arithmetic sequence is expressed as;
Tn = a+(n-1)d
a is the first term
n is the number of terms
d is the common difference
The nth term of a Geometric sequence is expressed as;
Tn = ar^{n-1}
r is the common ratio
Numbers are arranged in a sequence when they follow a predetermined or established pattern. Sequences can be divided into
1) Mathematics
2) Graphitic
Geometric sequences are characterized by their common ratio, whereas arithmetic sequences are distinguished by their common difference.
Suppose a sequence of numbers is given;
T1, T2, T3...
The sequence's initial term "a" is T1.
common distinction d = T2-T1 =T3-T2
T2/T1 Common Ratio T3/T2
The following is the formula for finding the nth term in an arithmetic sequence:
Tn = a+(n-1)d
The first term is a.
The number of terms is n.
d is the typical discrepancy
The nth term of a Geometric sequence is expressed as;
[tex]T_{n} =ar^{n-1}[/tex]
r is the common ratio
To learn more about information Sequence :
brainly.com/question/28015562
what do i say for this
please help :((((
Answer:
Step-by-step explanation:
Error 1) It should be divided by 5.
x - 5 = 0
x = 5
Error 2) -3 15 0 -1 5
coefficient of x² is 0 and it is not included
Solve this equation
3|6v+2|=-66
Derrick is placing a right triangle in the coordinate plane. He knows that the longer leg is 3 times the length of the shorter leg. He places the longer leg on the x-axis.
What coordinates should he assign to the third vertex of the triangle?
Answer:
Longer leg is placed on X axis.
Let the longer leg be at A(0,0) and B(3 a,0),or (-3 a,0), which is either base or altitude.
AB= 3 a
As longer leg = 3 × shorter leg
Shorter leg should be placed either at (0,a) or (0,-a) maintaining triangle as right angled triangle.
Step-by-step explanation:
calculate the value of the expression (-8)·(-1/3)
Answer:
8/3
Step-by-step explanation:
If we multiply it the subtraction will cut off and 8 will mulitply to 8/3.
Ratio to 6:3?? Write 2 other ways :))
Answer:
6/3, 6:3, and 6 to 3
Step-by-step explanation:
All of these answers above are correct!!!
May I have a Brainliest?
As a salesperson, you are paid $150 per week plus $5 per sale that you make. This week
you want your pay to be at least $225. Write and solve an inequality for the number of
sales you need to make
Answer:
15 Sales
Step-by-step explanation:
225 - 150 = 75
75 / 5 = 15
Solve the equation 2 + 4.7 = -9.3.
Answer: positive then greater than
Step-by-step explanation:
Tracy can type 45 words in 3 minutes. At that rate, how many minutes would it take Tracy to type 315 words?
Answer:
21 minutes
Step-by-step explanation:
The rate that she types is 15 words in a minute
315/15 =
21 or 21 minutes
Answer: It will take Tracy 21 minutes to type 315 words
Step-by-step explanation:
Set up a proportional relationship to solve for the number of minutes.
45 words = 3 mins
315 words = x mins.
[tex]\frac{45}{315} = \frac{3}{x}[/tex] Cross multiply
45x = 945 Divide both sides by 45
x = 21
O There are 15 students going on a field trip. If 3/5 of them pack their lunches, how many students pack their lunches?
Answer:
Students
Step-by-step explanation:
Consider these functions:
f(x)=3x - 7
g(t)=1+1
What is the value of f(g(3))?
A.-1
B.0
C.3
D. 5
Answer:
A(-1)
Step-by-step explanation:
First, we will replace any x in g(x) with 3
g(x)=(3+1)/(3-1)=4/2=2
Thwn replace any x in f(x) with 2
f(x)=3(2)-7=6-7=-1 ⇒A
hope this helps
What is the inverse of the function f(x) = x +3
Answer:
h(x) = x-3
Step-by-step explanation:
The inverse of a function works such that f(h(x)) = x. Also, f(h(x)) = h(x) + 3. Thus, x = h(x) +3 -> h(x) = x-3
i hope this helps!!! :)
all my points! PLZ help me on this and explain ur answer plzz
Find the perimeter of the figure. Round to the nearest tenth if needed.
a=50 b=83 c=65
Answer:
263
Step-by-step explanation:
50 + 83 + 65 + 65 = 263
i don’t know witch sides are which but here you go
Describe the end behavior of the polynomial function.
microzooplankton is _____ compared to macrozooplankton
a) smaller
b) bigger
c) faster
d) brighter in color
btw yes i put it on math because i feel like more people do math more
a ) smaller is correct answer
3x-y=6
-4x+2y=-8 solve using substitution method
Answer:
x= 3y+2
Step-by-step explanation:
The purchase price of an iPad is $625.00. There is a 15% discount and the tax rate is
8%. What is the total cost of the iPad?
Answer:
$573.75
Step-by-step explanation:
625.00x15%=93.75
625.00-93.75=531.25
531.25x8%=42.50
531.25+42.50=573.75
Answer: I think that the answer is $573.75
please correct me if im wrong.
Step-by-step explanation:
Quadrilateral MNOP is similar to quadrilateral SURT
Answer:
C is the anser i belive i im wrong im sorry
Step-by-step explanation:
What is the point-slope form of an equation passing through (0, -5) with a 5 points
slope of 2? *
Answer:
y=2x-5
Step-by-step explanation:
[tex]y-y_{1}=m(x-x_{1})[/tex]
[tex]x_{1}=0, y_{1}=-5\\[/tex], and m=2
[tex]y-(-5)=2(x-0)[/tex], -(-5)-Two negatives make it positive, and you distribute the 2
[tex]y+5=2x[/tex], you now subtract 5 to get y by itself to get your answer of
[tex]y=2x-5[/tex]
*NOTE* (0,-5) is the y-intercept, so you could have used the linear equation of y=mx+b, m=2, and b(y-intercept)=-5
giving you y=2x-5
Please help, I am bad at math and I don't know how to answer this question please help
How is solving equations with fractions similar to solving equations with whole numbers?
(Written Response)
(Sorry if this is easy, if you have already done this on edg, I don't mind if it is the sample response)
Answer:
You have to make the fraction into a whole number.
Step-by-step explanation:
Hope this helps. :)
Can you guys help me find the slope for the given graph and y-intercept
(pictures included)
Answer:
I believe the answer is
[tex]y = \frac{2}{3} x + 1[/tex]
slope = 2/3x
y-intercept = 1
Step-by-step explanation:
Hope this helps!
ILL MARK U BRAINLIEST HELP
Answer:
6x-y
Step-by-step explanation:
Add the two expressions
Answer:
6x + -y
Lets simplify this step by step:
2x + 7y + 4x −8y
2x + 7y + 4x + −8y
Then we combine like terms
=2x + 7y + 4x + −8y
=(2x + 4x) + (7y + −8y)
= 6x + −y
Juan needs to take an Uber to get to the movies. The Uber charges $1.50 for the first mile, and then $1.55 for each mile after that. If the total charge is $10.49, then how far was Juan’s Uber ride to the movie?
Answer:
5.8 miles were travelled by Juan's Uber ride to the movie.
Step-by-step explanation:
Let x = miles travelled by Juan
Charges for first mile = $1.50
Charges for each mile after first = $1.55
Total charge for Juan = $10.49
We need to find how many miles Juan covered?
The equation will be:
[tex]1.50+1.55(x)=10.49[/tex]
We will solve this equation to find value of x
Solving:
[tex]1.50+1.55(x)=10.49[/tex]
Subtracting 1.50 from both sides
[tex]1.50+1.55(x)-1.50=10.49-1.50\\1.55(x)=8.99\\x=\frac{8.99}{1.55} \\x=5.8[/tex]
So, 5.8 miles were travelled by Juan's Uber ride to the movie.
Each cable car at an amusement park can hold six Riders. There are 51 people in line to ride the cable cars. How many cable cars will the people in line fill? how many more people are needed to fill the next cable car?
Answer:
9 cable cars
Step-by-step explanation:
51 ÷ 6 = 8.5
8.5 rounds up to 9
Answer:
3
Step by step explanation:
54 ÷ 6 = 9
help helppppppppppppp
Answer:
4/15 = height of lamp/(15+5)
4/15 = height of lamp/20
20/15 = 1 5/15
1 5/15 times taller
lus
If f(x) = 3x + 7, find:
f(3) = [?]
Answer:
The answer is 16
Step-by-step explanation:
You substitute 3 in for x.
Please help me! Itll mean so much!
Please help asap!! Due today!
Answer:
No for the first
Step-by-step explanation:
Sorry i do not know the second one bt the first one is No it is not a right angle
Brett bought 2 shirts. One cost $4 more than 3 times the other. Together, the 2 shirts cost
him $72.
HELP PLEASE.
Answer:
one costs 17 dollars the other costs 55 dollars
Step-by-step explanation:
we have to make 2 equations using variables
x=shirt 1
y= shirt 2
y+x=72
x=3y+4
then substitute 3y+4 for x in the first equation
y+3y+4=72
subtract 4 and add y and 3y
4y=68
divide by 4
y= 17
use this for y in the second equation
x=3(17)+4
x=51+4
x=55