Answer:
[tex] \sin(x) = \frac{1}{4} \\ { \sin }^{2} x = \frac{1}{16} \\ { \cos } x = \sqrt{1 - { \sin }^{2}x } \\ \cos(x) = \sqrt{1 - \frac{1}{16} } \\ \cos(x) = \sqrt{ \frac{15}{16} } \\ \tan(x) = \frac{ \sin(x) }{ \cos(x) } \\ \tan(x) = \frac{ \frac{1}{4} }{ \sqrt{ \frac{15}{16} } } \\ \tan(x) = 0.258[/tex]
The exact value of tan x is,
⇒ tan x = - 1/√15
What is mean by Ratio?A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.
Where, x and y are individual amount of two quantities.
And, Total quantity gives after combine as x + y.
First, we can use the fact that sin x = 1/4 to find the value of cos x.
We know that;
sin²x + cos²x = 1,
cos²x = 1 - sin²x
cos²x = 1 - (1/4)²
cos²x = 1 - 1/16
cos x = ±√(15/16)
But since we know that x is in the third quadrant , we know that cos x is negative.
Therefore, we can take:
cos x = -√(15/1`6)
Now we can use the fact that;
tan x = sin x / cos x
tan x = sin x / cos x
tan x = (1/4) / (-√(15/16))
tan x = - (1/4) * (4/√15)
tan x = - 1/√15
So, the exact value of tan x is,
⇒ tan x = - 1/√15
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Solve the quadratic equation by using a graphic approach. Round your answer to the hundredths place.
x² - 2x - 4= 0
a. x= 3.24 or x = -1.24
c. x = 4.24 or x = -0.24
b. x = 2.73 or x = -0.73
d. x= 5.24or x = -1.24
Pls explain I’m having a hard time understanding the lesson
Answer:
x = 3.24, x = -1.24
Step-by-step explanation:
The standard form for a quadratic equation is [tex]ax^2+bx+c=0[/tex]. For your equation a = 1, b = -2, c = -4. The quadratic formula you will be using is [tex]x=\frac{-b\pm \sqrt{b^{2} -4ac} }{2a}[/tex].
Plug in a = 1, b = -2, and c = -4 into the formula.
[tex]=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:1\cdot \left(-4\right)}}{2\cdot \:1}[/tex]
We'll do the top part first:
[tex]\sqrt{\left(-2\right)^2-4\cdot \:1\cdot \left(-4\right)}[/tex]
Apply rule [tex]- (-a) = a[/tex]
[tex]=\sqrt{\left(-2\right)^2+4\cdot \:1\cdot \:4}[/tex]
Apply exponent rule [tex](-a)^{n} =a^n[/tex] if [tex]n[/tex] is even
[tex](-2)^2=2^2[/tex]
[tex]=\sqrt{2^2+4\cdot \:1\cdot \:4}[/tex]
Multiply the numbers
[tex]=\sqrt{2^2+16}[/tex]
[tex]2^2=4[/tex]
[tex]=\sqrt{4+16}[/tex]
Add
[tex]=\sqrt{20}[/tex]
The prime factorization of 20 is [tex]2^2*5[/tex]
20 divides by 2. 20 = 10 * 2
[tex]=2*10[/tex]
10 divides by 2. 10 = 5 * 2
[tex]=2* \:2*5[/tex]
2 & 5 are prime numbers so you don't need to factor them anymore
[tex]=2*2*5[/tex]
[tex]=2^2*5[/tex]
[tex]=\sqrt{2^2\cdot \:5}[/tex]
Apply radical rule [tex]\sqrt[n]{ab} =\sqrt[n]{a} \sqrt[n]{b}[/tex]
[tex]=\sqrt{5}\sqrt{2^2}[/tex]
Apply radical rule [tex]\sqrt[n]{a^{n} } =a[/tex]; [tex]\sqrt{2^2} =2[/tex]
[tex]=2\sqrt{5}[/tex]
[tex]=\frac{-\left(-2\right)\pm \:2\sqrt{5}}{2\cdot \:1}[/tex]
Because of the [tex]\pm[/tex] you have to separate the solutions so that one is positive and the other is negative.
[tex]x=\frac{-\left(-2\right)+2\sqrt{5}}{2\cdot \:1},\:x=\frac{-\left(-2\right)-2\sqrt{5}}{2\cdot \:1}[/tex]
Positive x:
[tex]\frac{-\left(-2\right)+2\sqrt{5}}{2\cdot \:1}[/tex]
Apply rule [tex]-(-a)=a[/tex]
[tex]=\frac{2+2\sqrt{5}}{2\cdot \:1}[/tex]
Multiply
[tex]=\frac{2+2\sqrt{5}}{2}[/tex]
Factor [tex]2+2\sqrt{5}[/tex] and rewrite it as [tex]=2\cdot \:1+2\sqrt{5}[/tex]. Factor out 2 because it is the common term. [tex]=2\left(1+\sqrt{5}\right)[/tex].
[tex]=\frac{2\left(1+\sqrt{5}\right)}{2}[/tex]
Divide 2 by 2
[tex]x=1+\sqrt{5}[/tex] or [tex]x=3.24[/tex] (You'll probably have to use a calculator for the square root of 5)
^Repeating the process of positive x for negative x in order to get [tex]x=1-\sqrt{5}[/tex] or [tex]x=-1.24[/tex]
Plse help my grades go in tomorrow and I am currently struggling!!
C⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
factorise fully p^3 + p^2
Answer:
[tex]\huge\boxed{p^3+p^2=p^2(p+1)}[/tex]
Step-by-step explanation:
[tex]p^3+p^2\\\\p^3=p^{2+1}=p^2\cdot p\\\\p^3+p^2=p^2\cdot p+p^2\cdot1=p^2(p+1)[/tex]
Used:
[tex]a^n\cdot a^m=a^{n+m}\\\\\text{distributive property}:\ a(b+c)=ab+ac[/tex]
Translate into an inequality.
Negative nine is greater than or equal to the sum of two-fifths times a number and seven
Answer:
-9 ≥ (2/5x) + 7Step-by-step explanation:
the sign must have a line underneath itself to show that it can be equal and unequal. 2/5 times a number (from my understanding) is 2/5 times a variable, plus 7.
Translation into inequality of negative nine is greater than or equal to the sum of two-fifths times a number, and seven is -9 ≥ (2/5x) + 7.
What is inequality?The relationship between two non-equal values is defined by inequalities. Equal does not mean unequal, though. In most cases, the "not equal sign" is used.
Negative nine is greater than or equal to the sum of two-fifths times a number, and seven can be written as,
-9 ≥ (2/5x) + 7
Therefore, Translation into inequality of negative nine is greater than or equal to the sum of two-fifths times a number, and seven is -9 ≥ (2/5x) + 7.
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8 + (9 · 2 – 3) : 25 – 4 2 : 2
Answer:
14 : -17 : 2
Step-by-step explanation:
8 + (9 · 2 – 3) : 25 – 4 2 : 2
= 14 : -17 : 2
Answer:
- 12.4
Step-by-step explanation:
[tex]8 + \frac{9 * 2 - 3}{25} - \frac{42}{2}[/tex]
[tex]8 + \frac{18 - 3}{25} - 21[/tex]
[tex]8 + \frac{15}{25} - 21[/tex]
[tex]8 + \frac{3}{5} - 21[/tex]
[tex]8 \frac{3}{5} - 21[/tex]
[tex]-12 \frac{2}{5}[/tex]
Help please !!!!!!!!’
Step-by-step explanation:
everything can be found in the picture
When should a heart rate monitor be used?
Answer:
There are two simple, compelling reasons to use a heart-rate monitor: to train and race at the best pace for you. The table below shows you how to find your perfect paces for: (1) the three most important workouts in any training program; and (2) the four most popular road-race distances.
Step-by-step explanation:
Hope this helps :)
please help me!!!!! i need help with this, very urgent! ASAP
Step-by-step explanation:
QR--DE
RS--- EF
RQ-----DE
Find the number from which (– 66) is subtracted to get a difference of 100.
Answer:
-166
Step-by-step explanation:
4. Change 5 hours to minutes.
300 minutes
ОО
30 minutes
3000 minutes
ОО
3 minutes
Answer:
[tex]{ \tt{1 \: hour = 60 \: minutes}} \\ { \tt{5 \: hours = (5 \times 60) \: minutes}} \\ = 300 \: { \bf{minutes}}[/tex]
(Correct answers only)
A
B
C
Or D
Answer:
Division property of equality
Step-by-step explanation:
7q=49
Divide each side by 7
7q/7 = 49/7
q = 7
Solve for x. ЗХ - 14 = 46
Answer:
Step-by-step explanation:
3x - 14 = 46
+ 14 +14
3x = 60
3x/3 = 60/3
x = 20
pleaseeee helpppppp!!!!
Answer:
x=8
Step-by-step explanation:
The angles shown are vertical angles and vertical angles are equal
13x+19 = 16x -5
Subtract 13x from each side
13x-13x+19 = 16x-13x -5
19 = 3x-5
Add 5 to each side
19+5 = 3x-5+5
24 = 3x
Divide by 3
24/3 = 3x/3
8 = x
Answer:
x = 8
Step-by-step explanation:
The angles shown are vertical angles
Vertical angles are congruent
Hence, 13x + 19 = 16x - 5
We now solve for x using the equation we just created
13x + 19 = 16x - 5
Subtract 13 x from both sides
19 = 3x - 5
Add 5 to both sides
24 = 3x
Divide both sides by 3
x = 8
a 20 foot ladder leans against a building. if the ladder is 8 feet from the building, find to the nearest degree, the measure of the angle that the foot of the ladder makes with the ground
Answer:
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj/ hyp
cos theta = 8/20
cos theta = 2/5
Taking the inverse cos of each side
cos^-1 (cos theta) = cos ^-1 ( 2/5)
theta =66.42182152
To the nearest degree
theta = 66 degrees
The private school enrolled 1050 new students last year and the number of students enrolled this year decreased to 798.What was the percentage decrease in the number of students enrolled?
Answer:
Step-by-step explanation:
Decreased students = 1050 - 798 = 252
Decreased percentage = (decreased students ÷ number of last year students) * 100
= [tex]\frac{252}{1050}*100[/tex]
= 24%
Answer:
24%
Step-by-step explanation:
% change = [tex]\frac{difference}{original amount}[/tex] x 100
; 1050 - 798 = 252
% change = [tex]\frac{252}{1050}[/tex] x 100
% change = 0.24 x 100
% change = 24
the percentage decrease in the number of students enrolled is 24%
I just need to know the angle
Answer: B. DBC
Step-by-step explanation:
Answer: [tex]\angle DBC[/tex] (choice b)
================================================
Explanation:
When naming any angle, you need 3 points. The middle point is the vertex of the angle. The other two points can be in any order as long as they are on the lines or rays that we want.
We go for angle DBC, which we can write as [tex]\angle DBC[/tex], since B is at the vertex and points D and C are on either side of the vertex.
Angle ABD is adjacent to the marked angle, but it's not what we're after.
Angle BDC isn't drawn, so we cross this off the list as well.
Saying [tex]\angle B[/tex] is too vague in this context because it could mean either [tex]\angle ABD[/tex] or it could mean [tex]\angle DBC[/tex] since they both share the same vertex B.
If two lines are intersected by a third line, is the third line necessarily a transversal?
No, The third line does not necessarily be a transversal.
What is Equation of line?
The equation of line with slope 'm' and y intercept at point 'b' is given as;
⇒ y = mx + b
Given that;
Two lines intersected by a third line.
Since, When two lines are parallel to each other and two lines intersected by a third line then, third lines are transversal.
So, Here it is not given two lines are parallel.
Thus, Third line is not necessarily a transversal.
Hence, The third line does not necessarily be a transversal.
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If y=-0.8 when x=2 find the y when x=3
The manufacturer id number for proctor and gamble is (037000) and the item number for a box of bounce fabric softener is (80049). What is the valid upc? A- 0-37000-80049-9 B-0-37000-80049-1 C-1-37000-80049-1 D-1-80049-37000-0
Answer:
A. [tex]UPC = 0-03700-80049-9[/tex]
Step-by-step explanation:
Given
[tex]ID = 037000[/tex]
[tex]Item\ Number = 80049[/tex]
Required
The valid UPC
First, the UPC is represented as:
UPC = ID followed by item number followed by the checksum
So, we have:
[tex]upc = 0-03700-80049-X[/tex]
To calculate X (the checksum)
Add up digits at odd positions
[tex]Odd = (0 + 7 + 0) + (8 + 0 + 9)[/tex]
[tex]Odd = 24\\[/tex]
Multiply by 3
[tex]Product = Odd * 3[/tex]
[tex]Product = 24 * 3[/tex]
[tex]Product = 72[/tex]
Add up digits at even positions
[tex]Even = (3 + 0 + 0) + (0 + 4)[/tex]
[tex]Even = 7[/tex]
Add the product and the sum of even
[tex]Result = Product + Even[/tex]
[tex]Result = 72+7[/tex]
[tex]Result = 79\\[/tex]
The last digit of the UPC is 9.
Hence, the UPC is:
[tex]UPC = 0-03700-80049-9[/tex]
Write an equation to model the given scenario, then solve:
Each year the local country club sponsors a tennis tournament. Play starts with 128 participants. During each
round, half of the players are eliminated. How many players remain after 5 rounds?
Given:
Initial number of participants = 128
During each round, half of the players are eliminated.
To find:
The number of players remain after 5 rounds.
Solution:
It is given that, the initial number of participants is 128 and during each round, half of the players are eliminated.
If half of the players are eliminated, then half of the players are remained.
So, the initial value is 128 and the decay factor is [tex]\dfrac{1}{2}[/tex].
The general exponential decay model is:
[tex]y=a(b)^x[/tex]
Where, a is the initial value and b is the decay factor.
Putting [tex]a=128[/tex] and [tex]b=\dfrac{1}{2}[/tex] in the above model, we get
[tex]y=128\left(\dfrac{1}{2}\right)^x[/tex]
Here, y is the number of remaining players after x rounds.
Substituting [tex]x=5[/tex], we get
[tex]y=128\left(\dfrac{1}{2}\right)^5[/tex]
[tex]y=128\left(\dfrac{1}{32}\right)[/tex]
[tex]y=4[/tex]
Therefore, the required model is [tex]y=128\left(\dfrac{1}{2}\right)^x[/tex] and the number of players remain after 5 rounds is 4.
The surface of an air hockey table has a perimeter of 32 feet its area is 60 ft.what are the dimensions of the air hockey table
Tony and Michael ate 26 of 60 star apples that were in a basket. If the remaining star apples were shared equally between them, how much would each of them get?
A. 86
B. 17
C. 43
D. 34
D.
If Tony and Michael ate 26 you take that away from 60 which equals 34.
26-60=34
Find the Value of X in this Triangle
Answer:
x = -6
Step-by-step explanation:
All three angles are equal, so all three sides are equal, making this an equilateral triangle
5x+10 = 2x-8
Subtract 2x from each side
5x-2x +10 = 2x-8-2x
3x+10 = -8
Subtract 10 from each side
3x+10-10 = -8-10
3x = -18
Divide by 3
3x/3 = -18/-3
x = -6
Brainliest, 19 points (Running out of points to give)
Answer:
x^2-2x+5
Step-by-step explanation:
5x^2 -4x +8 + -4x^2 +2x -3
Combine like terms
5x^2-4x^2-4x+2x+8-3
x^2-2x+5
36A^4+16Y^2
Can someone help me
Answer:
4(9a^4+4y^2)
Step-by-step explanation:
factor out common term
Una caja en forma de prisma rectangular tiene 10cm3 de volumen.Si la longitud de cada arista se multiplica por 4, ¿cual sera el volumen de la caja?
The width of a rectangle is 5 3/4 inches. The length is three times its width. What is the perimeter?
Answer:
perimeter=46.5 inches
Step-by-step explanation:
[tex]width=2\frac{3}{4}[/tex]
[tex]=\frac{5*4+3}{4}[/tex]
=[tex]=\frac{23}{4}[/tex]
[tex]length=3(\frac{23}{4} )[/tex]
[tex]=\frac{23*3}{4}[/tex]
=[tex]\frac{69}{4}[/tex]
perimeter of rectangle =2(l+b)
[tex]=2(\frac{69}{4} +\frac{24}{4} )[/tex]
[tex]=2(\frac{69+24}{4} )[/tex] (since their denominator are same u can add their numerator)
[tex]=2(\frac{93}{4})[/tex]
[tex]=\frac{93*2}{4}[/tex]
[tex]=\frac{186}{4}[/tex]
[tex]=46.5[/tex] inches
factor the following
(a²+b²)²-18(a²+b²)-88
Answer:
[tex] \rm\displaystyle( {a}^{2} + {b}^{2} - 22)( {a}^{2} + {b}^{2} + 4)[/tex]
Step-by-step explanation:
we would like to factor the following:
[tex] \rm\displaystyle ( {a}^{2} + {b}^{2} {)}^{2} - 18( {a}^{2} + {b}^{2} ) - 88[/tex]
let a²+b²=x
thus substitute:
[tex] \rm\displaystyle x {}^{2} - 18x- 88[/tex]
rewrite the middle term as 4x-22x:
[tex] \rm\displaystyle x^{2} + 4x - 22x - 88[/tex]
factor out x:
[tex] \rm\displaystyle x( x^{} + 4)- 22x - 88[/tex]
factor out -22:
[tex] \rm\displaystyle x( x^{} + 4)- 22(x + 4)[/tex]
group:
[tex] \rm\displaystyle( x- 22)(x + 4)[/tex]
substitute back:
[tex] \rm\displaystyle( {a}^{2} + {b}^{2} - 22)( {a}^{2} + {b}^{2} + 4)[/tex]
and we are done!
pls help pls help pls help pls help
Answer:
The difference is 3 for 4-7, and 39 for 52-91. So basically its a change of 3 for every 4-7 I think this is what you ask for. Let me explain and show results and then pick what you need.
Step-by-step explanation:
So, we know 4 to 7 is 3.
52 to 91 is 39.
So one is a change in 3. the other is a change is 39.
However, could these be the same, just bigger?
Lets divide the 52 to 91 with a change of 39 by 4 to 7 with a change of 3:
52/4 to 91/7 with a change of 39/3 =
13 to 13 with a change of 13.
So this tells us that the 52 to 91 with a chang eof 3 is 13 times bigger than 4 to 7 with a change of 3.
Hope this helps!
Alex’s paycheck for the last two weeks totaled $239.64. He owes the cell phone company $44.87. How much money does he have left
Answer:
the answer would be 193.77
Step-by-step explanation:
literally, subtract 45.87 from 239.64.
you get 193.77.
(you put 44 instead of 45, so the sum with 44 would be 194, that is incorrect.)
