suppose a triangle has 2 sides of lengths 32 and 35 and that the angle between these 2 sides is 120 what is the length of the 3rd side of the triangle
Let the Vertices of the Δ be A , B , and C
We will follow the Usual Notation for Δ A B C , e.g., the side
opposite to the Vertex A will be denoted by a , m ∠ A = A , etc.
In this notation, let us assume that,
a = 32 , b = 35 , & , C = 120 ° & we have to find c
Using Cosine-Rule for Δ A B C , we have,
c²= a²+b² - 2 ab cos C = 32 ²+35² - 2 x 32 x 35 x cos 120° =
1024 + 1225 − 2240 cos ( 180 °− 60 °) = 2249 - 2240(-cos 60°)
2249+ 2240 (1/2)= 2249 + 1120= 3369
Answer: C= √3369 is about 58.04
Answer: 58.043087 (approximate)
===================================================
Explanation:
Refer to the diagram below. We can use the law of cosines to solve for c
c^2 = a^2 + b^2 - 2*a*b*cos(C)
c^2 = 32^2 + 35^2 - 2*32*35*cos(120)
c^2 = 3369
c = sqrt(3369)
c = 58.043087 which is approximate
Round this value however you need to.
Find the perimeter of ΔJKL. Round your answer to the nearest tenth if necessary
Answer:
Step-by-step explanation:
as angles of two triangles are equal, so they are similar.
x/17 =35/14=40/16
x/17=35/14
x=35/14×17=85/2=42.5
perimeter of ΔJKL=40+35+42.5=117.5
Find the length of side xx in simplest radical form with a rational denominator.
Answer:
Solution given:
Relationship base and hypotenuse is given by Cos angle
Now
Cos 60°=adjacent/hypotenuse=x/12
1/2=x/12
x=12/2
x=6
the value of x is 6.
2m^2-5m-3=0 by factorization
Answer:
M= 6, -1
Step-by-step explanation:
Factoring these numbers, it will result in (m-6)(m+1). So, m= 6,-1
helppppppppppppppppppppp plzzzzz
Answer:
B. 16/3
Step-by-step explanation:
f(2) = 1/3 · 4²
f(2) = 1/3 · 16
f(2) = 16/3
Round the $40435.29 to the nearest thousand dollar
Answer:
$40000
Step-by-step explanation:
The nearest thousand dollar is rounding the thousand value from its hundred value, which in this case is 4. Since 4 is less than half of 10, the thousand value must round down to $40000.
Answer:
$40000.00
Step-by-step explanation:
Report this answer if its incorrect ^_^
a^2×c^2/c^2×d^2+bc/ad reduce the algebraic
Answer:
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}= \frac{a^3 + bcd}{ad^2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}[/tex]
Required
Simplify
We have:
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}[/tex]
Cancel out [tex]c^2[/tex]
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}= \frac{a^2}{d^2}+\frac{bc}{ad}[/tex]
Take LCM
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}= \frac{a^3 + bcd}{ad^2}[/tex]
Which of the following are valid (necessarily true) sentences? a. (∃x x = x) ⇒ (∀ y ∃z y = z). b. ∀ x P(x) ∨ ¬P(x). c. ∀ x Smart(x) ∨ (x = x)
Answer:
b; ∀x P(x) ∨ ¬P(x)
Step-by-step explanation:
Suppose that we have a proposition p
Such that p can be true or false.
We can define the negation of p as:
¬p
Such that, if p is false, then ¬p is true
if p is true, then ¬p is false.
Also remember that a proposition like:
p ∨ q
is true when, at least one, p or q, is true.
Then if we write:
p ∨ ¬p
Always one of these will be true (and the other false)
Then the statement is true.
And if the statement depends on some variable, then we will have that:
p(x) ∨ ¬p(x)
is true for all the allowed values of x.
from this, we can conclude that the statement that is always true is:
b; ∀x P(x) ∨ ¬P(x)
Where here we have:
For all the values of x, P(x) ∨ ¬P(x)
a bag contains three red marbles five blue marbles and seven green marbles.what is the ratio of blue marbles to the total number of marbles
Answer:
5:15 simplified as 1:3
Step-by-step explanation:
A rectangular floor of area 360 m2 is going to be tiled. Each tile is rectangular, and has an area of 240 cm2. An exact number of tiles can be put into the space. How many tiles will be needed?
Answer:
1500
Step-by-step explanation:
The area of the regtangular floor is 360m². The floor is going to be retired with tiles having area of 240cm² . We need to find the number of times . Therefore ,
[tex]\implies 360m^2 = 360 \times 10^4 \ cm^2 [/tex]
And , the number of tiles required will be ,
[tex]\implies n =\dfrac{Area \ of \ floor}{Area \ of \ a \ tile }\\\\\implies n =\dfrac{ 360 \times 10^4 \ cm^2}{240 cm^2} \\\\\implies \underline{\underline{ n = 1,500 }}[/tex]
Hence the required answer is 1500 .
Help! What is the equation of the line shown in the graph?
Answer:
y = -x -2
Step-by-step explanation:
Slope = -1
y intercept is -2
Slope = [tex]\frac{-4-1}{2-(-3) }[/tex] = [tex]\frac{-5}{5}[/tex] = -1
what is the smiplest ratio for 75cm:1m:250 mm
Answer:
You need to convert all the units to one unit
What is the range of this set of heights in centimeters? {140, 166, 132, 165, 152, 168, 181, 158, 173, 171, 180, 182, 163, 177, 180, 142, 147, 149, 178} 38 41 46 50
Answer:
50
Step-by-step explanation:
Given:
140, 166, 132, 165, 152, 168, 181, 158, 173, 171, 180, 182, 163, 177, 180, 142, 147, 149, 178
Arranging in ascending order (from the lowest to the highest)
= 132, 140, 142, 147, 149, 152, 158, 163, 165, 166, 168, 171, 173, 177, 178, 180, 180 181, 182
Range = highest number - lowest number
= 182 - 132
= 50
Answer:
50
Step-by-step explanation:
None
Somebody please help me!!!
Randy walks his dog each morning. he walks 7/12 of a mile in 7 minutes how many miles does he walks in 1 minutes
Answer:
1/12 mile
Step-by-step explanation:
We can use a ratio to solve
7/12 miles x miles
---------------- = ---------------
7 minutes 1 minute
Using cross products
7 /12 * 1 = 7x
Divide each side by 7
7/12 * 1/7 = x
1/2 = x
[tex]\sf{\bold{\blue{\underline{\underline{Given}}}}}[/tex]
⠀Randy walks his dog each morning. he walks 7/12 of a mile in 7 minutes ⠀⠀⠀[tex]\sf{\bold{\red{\underline{\underline{To\:Find}}}}}[/tex]
⠀how many miles does he walks in 1 minutes⠀⠀⠀[tex]\sf{\bold{\purple{\underline{\underline{Solution}}}}}[/tex]
⠀
Randy walks 7/12 miles in 7 minutes
Sooo
He walks in one minutes is
7/12 miles in 7 minutes one minutes is [tex]\sf{\dfrac{\dfrac{7}{12}}{7} }[/tex] one minute =[tex]\sf{\dfrac{7}{12}×\dfrac{1}{7} }[/tex] one minute=[tex]\sf{\dfrac{1}{12} }[/tex][tex]\sf{\bold{\green{\underline{\underline{Answer}}}}}[/tex]
Hence,
he walks in 1 minutes is 1/12 miles.
HELP ASAP PLEASE!!!!!!!
Answer:
the answer is 2
Step-by-step explanation:
it doesn't match the other but is 2
If a > b and b > a, then ?
That's impossible. There are no solutions.
PLZ HELP
Which statement is an example of the reflexive property of congruence?
Find the angle marked with the ? mark
Answer:
53 degrees
Step-by-step explanation:
Angle N = angle E
because angle made by joining end points of same chord on circumference are always equal.
so angle E = 37
Angle D = 90 ( because angle made by diameter on circumference is 90 degrees)
Now in Triangle DEC. Sum if all the angles of triangle us 180
Angle D + angle E + ? = 180
37 + 90 + ? = 180
127 + ? = 180
? = 180 - 127
? = 53 degrees
HELP PLEASE! THIS IS MY LAST QUESTION ILL GIVE BRAINLIEST, NO LINKS. <3
Which of the following sets shows all the numbers from the set {1, 2, 3, 4} that are part of the solution to the inequality 7x + 6 > 20?
A) {1, 2, 3}
B) {2, 3, 4,}
C) {3, 4}
D) {4}
Answer: C {3, 4}
Step-by-step explanation:
Solve the inequality:
7x + 6 > 20
7x > 20 - 6
7x > 14
x > 2
Only 3 and 4 are greater than 2.
Helppp and explain thankyouuu
We have that
x - 3y = 12 and -x + y = 4
We add the 2 equations together
x - 3y + (-x + y) = 16
-> -2y = 16
-> y = -8 (1)
We plug y = -8 into -x + y =4
-> -x - 8 = 4
-> -x = 12
-> x = - 12 (2)
From (1) and (2) we could conclude that the answer is B
Answer this please:
I attached a file for you to see
Answer:
C Infinitely many solutions
Step-by-step explanation:
i think! Good luck!!
pls hurry!! helpppp i wil give brainliest..
Barbara, a school superintendent, asks the local school board for permission to hire an additional teacher whenever the student enrollment at a certain grade level within a school increases by 35 students beyond capacity. This is an example of which type of decision
Answer:
Programmed
Step-by-step explanation:
Programmed Decisons may be classified as those actions which are routinely carried out or performed based on existing rules and protocol. In programmed decision making, the rules are in place, therefore once the criteria or requirement for which the rule or routine is to be enforced arises, programmed Decisons are made. In the scenario, the superintendent required that a programmed Decison be made in cases or situations where enrollment increases by 35 student beyond capacity, Hence, with this, every time this occurs the additional teachers will be hired.
Given f(x)= 2^x and g(x)=x^2 answer the questions that follow
a. Your friend claims the graph of f(x)=2x increases at a faster rate than the graph of g(x)=x2 when x ≥ 0. Is your friend correct? Explain your reasoning.
b. How are the 2 functions different?
PLEASE HELP
Answer:
a. Yes it's correct, reasons;
I) let x=1, f(1)=2^1=2, g(x)=1^2=1 this proves that when a higher number is used the value of f(x) will be higher than g(x).
ii) As x approaches zero f(x) approaches 1, but g(x) approaches 0. Which will make the rate at which the graph of f(x) increase be faster than g(x)
b. f(x) has an infinite degree but g(x) has a finite degree of 2.
Which of the following is the explicit rule for a geometric sequence defined by
a recursive formula of a, - 138-1 for which the first term is 7?
Answer:
C
Step-by-step explanation:
What you wrote is not the same thing as what the question is, or at least I don't think so. I'll answer the printed question.
First of all, the 13 is what separates each of the terms. In other words 7 is the first term. 13 must be raised to the n - 1 power.
It is written like this
an = 7 * 13^(n - 1)
you want a1 to be 7. The only way that can happen is if 13^0 which gives you 1.
So the correct answer is C
GIVING BRAINLIEST!! Which of the following ordered pairs lies on the graph of y = tanx?
(5 pi, 0)
(-9pi/4, 1) <---- this is wrong
(-5pi, -1)
(pi/6, √3)
Answer:
[tex](5\pi ,0)[/tex]
The table below represents a linear function f(x), and the equation represents a function g(x): X) -1, 0, 1 F(x) -5, -1, 3 G(x)=4x+3
Part A. Write a sentence to compare the slope of the two functions and shows the steps you used to determine the slope of f(x) and g(x)
Part B which functions has greater y-intercept. Justify
Answer:
(a) g(x) has a greater slope
(b) g(x) has a greater y intercept
Step-by-step explanation:
Given
[tex]x \to -1,0,1[/tex]
[tex]f(x) \to -5,-1,3[/tex]
[tex]g(x) = 4x + 3[/tex]
Solving (a): Compare the slopes
Slope (m) is calculated as:
[tex]m =\frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, for f(x), we have:
[tex]m =\frac{-1- 0}{-5- -1}[/tex]
[tex]m =\frac{-1}{-4}[/tex]
[tex]m =\frac{1}{4}[/tex]
For g(x), we have:
Assume [tex]g(x) = mx + c[/tex] then the slope is m
Compare the above to [tex]g(x) = 4x + 3[/tex]
Then the slope of g(x) is 4
g(x) has a greater slope
Solving (b): Function with greater y intercept
Here we set [tex]x= 0[/tex]
From the table of f(x)
[tex]f(x) = -1[/tex] when [tex]x = 0[/tex]
From [tex]g(x) = 4x + 3[/tex]
[tex]g(0) = 4 * 0 + 3[/tex]
[tex]g(0) = 3[/tex]
Hence:
g(x) has a greater y intercept
What is the soution of (Image below)
Answer:
A
Step-by-step explanation:
Starting with the original equation:
[tex]\sqrt{1-3x} =x+3[/tex]
Squaring both sides to remove the root, and expanding the right side:
[tex]1-3x=(x+3)(x+3)[/tex]
Multiplying the right side:
[tex]1-3x=x^{2} +6x+9[/tex]
Combine like terms:
[tex]x^{2} +9x+8[/tex]
Factor:
(x+8)(x+1)
If x+8=0, then x= -8
If x+1=0, then x=-1
In ΔCDE, the measure of ∠E=90°, ED = 28, CE = 45, and DC = 53. What ratio represents the tangent of ∠C?
Explanation:
Angle E is 90 degrees. The segment DC = 53 is opposite this angle. Note how "DC" does not contain the letter "E". Furthermore, note how this is the largest side. So it's the hypotenuse.
The side ED = 28 is the opposite side of reference angle C, because "C" is nowhere to be found in the sequence "ED".
The side CE = 45 is the adjacent side because "E" is found in "CE".
The tangent ratio is...
tan(angle) = opposite/adjacent
tan(C) = ED/CE
tan(C) = 28/45
