Answer:
Sine, Cosine and Tangent are main functions used in Trigonometry .
They are based on a Right-Angled Triangle.
It helps to give a name to each side of a right triangle:
"Opposite" ; side opposite to the angle θ
"Adjacent"; side adjacent (next to) to the angle θ,
"Hypotenuse" ; the longest side
Step-by-step explanation:
Sine, Cosine and Tangent (are often shortened as sin, cos and tan)
They are used in calculation by;
[tex]Sin \alpha = \frac{Opposite}{Hypotenuse}\\ \\Cos \alpha = \frac{Adjacent}{Hypotenuse}\\ \\Tan \alpha = \frac{Opposite}{Adjacent}[/tex]
To remember how to apply them , we use
SOHCAHTOA
soh
Sin = Opposite / Hypotenusecah
Cosine = Adjacent / Hypotenusetoa
Tangent = Opposite / AdjacentI hope it helps :)the slope of a line parallel to the given line 8x-2y=5
Answer:
4x
Step-by-step explanation:
8x-2y=5
8x=2y+5
8x-5=2y
4x-5/2=y
The slope of the parallel line would be 4x because the slope doesn't change. Hope this helps.
3x + 4y = 14 x = 2y - 12 Which point satisfies both equations? A) (-2,-2) B) (-2,5) C) (-4,4) D) (2,2)
Answer:
B) (-2, 5)
Step-by-step explanation:
Perhaps easiest is to try the points to see what works. You can also graph the equations or solve by any of several other means.
Trying the points
A) 3(-2)+4(-2) = -6 -8 = -14 ≠ 14
B) 3(-2) +4(5) = -6 +20 = 14; -2 = 2(5) -12 = 10 -12 . . . . true
C) 3(-4) +4(4) = -12 +16 = 4 ≠ 14
D) 3(2) +4(2) = 6 +8 = 14; 2(2) -12 = -8 ≠ -2
__
Choice B ( -2, 5) is the only point that works in both equations.
Answer:
x = -2
y = 5
then:
B) (-2,5)
Step-by-step explanation:
3x + 4y = 14
x = 2y - 12
from te firs equation:
3x = 14 - 4y
x = (14-4y)/3
then:
2y - 12 = (14-4y)/3
3(2y-12) = 14 - 4y
3*2y + 3*-12 = 14 - 4y
6y - 36 = -4y + 14
6y + 4y = 14 + 36
10y = 50
y = 50/10
y = 5
from the second equation:
x = 2y - 12
x = 2*5 - 12
x = 10 - 12
x = -2
Check:
from the first equatión:
3x + 4y = 14
3*-2 + 4*5 = 14
-6 + 20 = 14
PLS ANSWER I WILL GIVE BRAINLIST AND A THANK YOU!!!! :)
Answer:
THE OTHER ANSWER IS WRONG
Step-by-step explanation:
90=20+6x-2
92=20+6x
72=6x
12=x
Hope this helps!
If y is inversely proportional to x and y = 15 when x= 3 Find x when y = 5.
X=5
X=8
X=9
X=1
Answer:
answer is 1
Step-by-step explanation:
y∝x
y=kx
15=3k
divide 3 both sides
k=5
so y=5x
when y is 5
5=5×x
divide 5 both sides
x=1
What is the slope of the line below (1, -2) (4, -2)
Answer:
0
Step-by-step explanation:
We can use the slope formula to find the slope
m = (y2-y1)/(x2-x1)
= ( -2 - -2)/( 4 -1)
= (-2+2)/( 4-1)
= 0/3
= 0
Answer:
Slope =0Step-by-step explanation:
[tex](1, -2) , (4, -2)\\m = ?\\x_1 =1\\y_1 =-2\\x_2 =4\\y_2 =-2\\\\m = \frac{y_2-y_1}{x_2-x_1} \\\\m = \frac{-2-(-2)}{4-1} \\m = \frac{-2+2}{3}\\ m = \frac{0}{3}\\ m = 0[/tex]
Jayden is driving on a long road trip. He currently has 11 gallons of gas in his car. Each hour that he drives, his car uses up 0.75 gallons of gas. How much gas would be in the tank after driving for 4 hours? How much gas would be left after t hours?
Answer:
a. 8 gallons
b. (11-0.75t) gallons
Step-by-step explanation:
a. Here in this question, we are told that the total amount of fuel in the fuel tank is 11 gallons and the car consumes 0.75 gallon per hour. We are interested in knowing the amount of fuel left in the tank after driving for four hours.
We proceed as follows;
Since 0.75 gallon is consumed in an hour, the amount of fuel consumed in 4 hours would be the amount consumed in an hour * 4 hours
Mathematically, that would be 0.75 * 4 = 3 gallon
Now, the amount of fuel left is simply the difference between the initial amount of fuel in the tank minus the amount of fuel present after 4 hours.
That would be; 11 - 3 = 8 gallons
b. Like above, we want to know the amount of fuel left after t hours.
Since 0.75 is used up per hour, the amount used up in t hours would be 0.75 * t = 0.75t
Now, the amount of fuel that would be left in the tank would be the difference between what we had initially and what was used up.
Mathematically, that would be 11- 0.75t
The cost for an upcoming field trip is $30 per student. The cost of the field trip C. in dollars, is a function of the number of students x.
Select all the possible outputs for the function defined by
C(x)=30
a. 20
b. 30
c. 50
d. 90
e. 100
Answer: B and D
Step-by-step explanation: since it is $30 per student the total cost would have to be a multiple of 30
Find the coefficient of third term of (2x−1)^6.
240
using pascals trianle
for the power 6 it is
1, 6,15,20, 15,6, 1
and for the third term (2x)^4 and (-1)^2
[tex]15 \times {(2x)}^{4} \times {( - 1)}^{2} [/tex]
[tex]240 {x}^{4} [/tex]
Since only the coefficient is needed
the answer is 240.
The required coefficient of third term is 480.
Coefficient of the third term of (2x−1)^6 to be determine.
Coefficient is defined as the integer present adjacent to the variable.
Here, (2x−1)^6
Using binomial expansion,
Third term = P(6,2)(2x)^6-2(-1)^2
= 6*5*16x^4
= 480x^4
Thus, the required coefficient of third term is 480.
Learn more about coefficient here:
https://brainly.com/question/2507029
#SPJ2
collen family plans to paint the window of their house. her father will paint twice as many window as her mother, and collen and her 2 brothers will paint an equal number of the rest of the windows. How many windows are there
Need Help Will Mark Brainlist
Answer:
21 windows
Step-by-step explanation:
collen family plans to paint the windows of their house. her father will paint twice as many windows as her mother, and collen and her 2 brothers will paint an equal number of the rest of the windows. Colleen decided to do her own share and her mother's share and paints 7 window, which is one less than her father's share. how many windows are in their house?
Answer: Let the number of window Collen father would paint be a while that of her mother be b. Since her father will paint twice as many window as her mother, therefore the number of windows painted by the father a = 2b
Let the number of windows that would be needed to be painted each by Colleen and her 2 brothers be c because they would paint the equal number of windows.
The total number of windows to be painted = 2b + b + c + c + c = 3b + 3c = 3(b + c).
Collen painted 7 windows as her mother and her own share which is one less than the fathers share. Therefore b + c = 7.
Also the fathers share a = 2b = 7 + 1 = 8 windows. Therefore b = 4 which is the mother share
Therefore the total number of windows = 3(b + c) = 3(7) = 21 windows
3b + 3c = 21
3(4) + 3c = 21
12 + 3c = 21
3c = 21 - 12
3c = 9
c = 3 which is collen and her brothers share
simplify;a/2(a+b)+b/2(a-b)
Answer:
[tex]\huge\boxed{\sf \frac{a^2+b^2}{2(a^2-b^2)}}[/tex]
Step-by-step explanation:
=> [tex]\sf \frac{a}{2(a+b)} + \frac{b}{2(a-b)}[/tex]
LCM = 2(a+b)(a-b)
=> [tex]\sf \frac{a(a-b)+b(a+b)}{2(a+b)(a-b)}[/tex]
Simplifying further
=> [tex]\sf \frac{a^2-ab+ab+b^2}{2(a^2-b^2)}[/tex]
=> [tex]\sf \frac{a^2+b^2}{2(a^2-b^2)}[/tex]
[tex]\dfrac{a}{2(a+b)}+\dfrac{b}{2(a-b)}=\\\\\dfrac{a(a-b)}{2(a+b)(a-b)}+\dfrac{b(a+b)}{2(a+b)(a-b)}=\\\\\dfrac{a^2-ab}{2(a^2-b^2)}+\dfrac{ab+b^2}{2(a^2-b^2)}=\\\\\dfrac{a^2+b^2}{2(a^2-b^2)}[/tex]
y=2/5x-12 is it liear or nolinear or both
Answer:
Step-by-step explanation:
y=2/5x-12 it is a linear equation in the form of y=mx+b
the best way to know is to graph the function
Please help me I promise I will mark brainliest, I need an answer asap!!!!!!!! please hurry!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! f(x) = 3x + 9, g(x) = 5x^2 Find (f + g)(x). A). -5x^2 + 3x + 9 B). Quantity three x plus 9 divided by five x squared. C). 15x^3 + 45x D). 5x^2 + 3x + 9
Answer:
D
Step-by-step explanation:
(f+g)(x) = f(x) + g(x)
=3x + 9 + 5x²
=5x² + 3x + 9
I also need to know this one pretty soon pleaseee
Answer:
128
Step-by-step explanation:
A family has four children. What is the probability that two children are girls and two are boys? Assume the the probability of having a boy (or a girl) is 50%.
Answer:The first issue one most notice is the words “at least” We are trying to find the probability of at least 2 girls.
The five possible outcomes for girls are 0,1,2,3,4. The odds of 1 girl out of 4 is .25 and the odds of 1 boy out of 4 is .25 (same as the odds of 3 out of 4 girls). Therefore the odds of 1 OR 3 girls must be .5 because 1 girl and 3 girls each has a .25 probability. If the probability of (1 OR 3 girls) equals .5, then the probability of 2 girls must be a different number.
The probability of 2 or more girls, is the sum of the probability of 4 girls (.06125)(—-.5 to the 4th power—— ), plus the probability of 3 girls (.25)——(the same as the probability of 1 boy)—- plus the probability of 2 girls. Since we know the probability of zero boys is .0625 (again, .5 to the 4th power) and the probability of 1 boy is .25 (the same as the probability of 3 girls )———then the probability of 2 girls is ((1 minus (the sum of the probability of 0 OR 1 boys) plus the (sum of the probability of 3 or 4 girls)), or 1-((.0625+.25)+(.0625+.25)), or .375. We had to derive the probability of two from the other known probabilities. Therefore .375+.25+.0625=.6875 is the probability of both AT LEAST 2 girls and also NO MORE than 2 boys. Notice this adds up to 1.375 because the probability of the central number 2 (i.e., .375) appears on both sides.
Write 37 99 as a decimal. A) 0.037 B) 0.37 C) 0.37 D) 3.73 (ALSO there are 2 of the .37 in the problem so im not sure what i have to do)
Answer:
Step 1: Address input parameters & values.
Input parameters & values:
The fraction number = 37/99
Step 2: Write it as a decimal
37/99 = 0.3737
0.3737 is the decimal representation for 37/99
Answer is 0.3737 repeating.
Hope this helps! Plz mark brainliest! ☜(ﾟヮﾟ☜)
Please help me understand this. Thank you! Gina has borrowed 100 songs from her friend. She plans to download an equal number of songs on her music player each week for 5 weeks. The graph shows the number of songs left to download, y, for a certain number of weeks, x: A graph titled Song Downloading shows the Number of Weeks on x-axis and Number of Songs Left to Download on the y-axis. The x-axis scale is shown from 0 to 5 at increments of 1, and the y-axis scale is shown from 0 to 140 at increments of 20. A straight line joins the ordered pairs 0, 100 and 1, 80 and 2, 60 and 3, 40 and 4, 20 and 5, 0. Part A: What is the rate of change and initial value of the function represented by the graph, and what do they represent in this scenario? Show your work to find the rate of change and initial value. (6 points) Part B: Write an equation in slope-intercept form to model the relationship between x and y. (4 points)
Answer:
Rate of Change/Slope = -20
Equation: y= -20x +100
Step-by-step explanation:
A. We know the rate of change is also known as the slope. If we used the slope formula to find the slope we can find the Rate of Change.
[tex]\frac{y2 - y1}{x2 - x1} = \frac{100-80}{1-2} = \frac{20}{-1} = -20[/tex]
B. Since we know the slope and 1 point on the graph we can substitute them in for 'b'
(0,100)
(100)=-20(0) + b
b = 100
Since we know the slope and the b value we can write the equation:\
y = -20x +100
The rate of change refers to the slope of the line, that is the change in y-axis per unit change in the value on the x-axis. Hence, the rate of change is :
Slope = - 20y = -20x + 100Slope = Rise / Run Rise = (y2 - y1) = (0 - 100) = - 100Run = (x2 - x1) = (5 - 0) = 5Slope = - 100 / 5 = - 20
General form of a slope - intercept relation :
y = bx + cThe intercept, c can be calculated thus:
100 = - 20(0) + c
100 = 0 + c
c = 100
Hence, the slope - intercept equation will be y = - 20x + 100
Learn more : https://brainly.com/question/18479471
if Angie’s gross pay for 21.5 hours was $282.08, what was her pay per hour?
Answer:
$13.12 per hour
Step-by-step explanation:
Take the total pay and divide by the number of hours
$282.08/21.5 hours
$13.12 per hour
Answer:
Step-by-step explanation:
21.5 hours - $282.08
1 - ?
$282.08/21.5 = $13.12
What does it mean when a polynomial equation is in standard form?
All terms are on one side of the equation, and zero is on the other side.
It is in the form Ax+Bx=C.
The polynomial is in factored form.
All terms with a variable are on one side of the equation, and the constant is on the other side of the equation.
Answer:
Standard form is Ax + By = C
Step-by-step explanation:
Answer:
The standard form is Ax + Bx = C
how do you solve for 5/6w = 2/3 (the answer is w= 4/5) I just don’t know how to show it.
Answer:
5/6w=2/3
5/6(4/5)=2/3
20/30=2/3
20/30=10/15=2/3=2/3
Proof:
5/6w=2/3
6/5*5/6w=2/3*6/5
30/30w=2/3*6/5
w=12/15=4/5
Hope this helps ;) ❤❤❤
If 2/3 inch on a map corresponds to an actual distance of 9 miles, what distance on the map will represent 21 miles?
Answer:
14/9 inches, or an inch and 5/9 of an inch.
Step-by-step explanation:
If 2/3 inch is the same as 9 miles, then x inches represents 21 miles. We can then set up a proportion.
[tex]\frac{\frac{2}{3} }{9} =\frac{x}{21}[/tex]
9 * x = (2/3) * 21
9x = 2 * 7
9x = 14
x = 14/9 inches.
Hope this helps!
Answer:
1 5/9 ich represent 21 miles
Step-by-step explanation:
Proportions:
2/3 inch ⇔ 9 miles
M inch ⇔ 21 miles
M = 21*(2/3) / 9
M = 14/9
14/9 = 9/9 + 5/9 = 1 + 5/9 = 1 5/9 inch
Factor completely, then place the answer in the proper location on the grid. 6x2 - 3x - 30
Answer:
3(2x-5)(x+2)
Step-by-step explanation:
Factor out the 3.
3(2x²-x-10)
Factor the remaining.
3(2x-5)(x+2)
(I don‘t know what grid they’re talking about.)
Which fractions are equal to 0.375? Select all that apply. A.) 375/1000 B.) 75/200 C.) 15/4 D.) 3/8 E.) 375/100
Answer:
A.) 375/1000, B) 75/200, D.) 3/8
Step-by-step explanation:
A number can be represented in many forms depending on the situation, it can be represented in form of ratio, decimals, fraction e.t.c.
Given the number 0.375 which is in its decimal form, this number can also be represented in the form of a fraction.
[tex]a)0.375=\frac{0.375}{1} \\ \\multiplying\ by\ \frac{1000}{1000}\ gives:\\\\\frac{0.375}{1}*\frac{1000}{1000}= \frac{375}{1000}\\\\ b) 0.375=\frac{0.375}{1} \\ \\multiplying\ by\ \frac{1000}{1000}\ gives:\\\\\frac{0.375}{1}*\frac{1000}{1000}= \frac{375}{1000}=\frac{5(75)}{5(200)} =\frac{75}{200} \\\\d) 0.375=\frac{0.375}{1} \\ \\multiplying\ by\ \frac{1000}{1000}\ gives:\\\\\frac{0.375}{1}*\frac{1000}{1000}= \frac{375}{1000}=\frac{125(3)}{125(8)}=\frac{3}{8} \\[/tex]
A united states presidential coin is made from an alloy of 4 metals-copper, zinc, manganese, and nickel- with weights in the ratio of 177:12:7:4 respectively. The coin weighs a total of 8 grams. What is the weight of the zinc in this coin?
Answer:
0.32 grams
Step-by-step explanation:
ratio of weight of -copper, zinc, manganese, and nickel = 177:12:7:4
let the
weight of copper = 177x
weight of zinc = 12x
weight of manganese = 7x
weight of nickel = 4x
Total weight of this alloy in terms of x = 177x + 12x+ 7x + 4x = 300x
given weight of alloy = 8 grams
thus,
weight of this alloy in terms of x =given weight of alloy
300x = 8 grams
x = 8/300 grams =
weight of zinc = 12x = 12 * 8/300 grams = 96/300 grams = 0.32 grams
Which angle is coterminal to StartFraction 3 pi Over 4 EndFraction radians? Negative StartFraction 5 pi Over 4 EndFraction radians Negative StartFraction 3 pi Over 4 EndFraction radians StartFraction 5 pi Over 4 EndFraction radians StartFraction 7 pi over 4 EndFraction radians
Answer:
The co-terminal angle of [tex]\frac{3\pi}{4}\ \text{radians}[/tex] is [tex]-\frac{5\pi}{4}\ \text{radians}[/tex].
Step-by-step explanation:
The angle provided is, [tex]\frac{3\pi}{4}\ \text{radians}[/tex].
Convert the angle into degrees as follows:
[tex]\frac{3\pi}{4}\ \text{radians}=\frac{3\times180^{o}}{4}=135^{o}[/tex]
Co-terminal angles are those angles that share the same terminal and initial sides.
To find the co-terminal angle of a provided angle, we just need to add or subtract 360° or 2π to it.
Determine the co-terminal angle of [tex]\frac{3\pi}{4}\ \text{radians}[/tex] as follows:
[tex]\text{Co-terminal Angle}=\frac{3\pi}{4}+2\pi[/tex]
[tex]=\frac{3\pi+8\pi}{4}\\\\=\frac{11\pi}{4}[/tex]
[tex]\text{Co-terminal Angle}=\frac{3\pi}{4}-2\pi[/tex]
[tex]=\frac{3\pi-8\pi}{4}\\\\=-\frac{5\pi}{4}[/tex]
Thus, the co-terminal angle of [tex]\frac{3\pi}{4}\ \text{radians}[/tex] is [tex]-\frac{5\pi}{4}\ \text{radians}[/tex].
Answer:
Its A
Step-by-step explanation:
edge
Find the point-slope equation for
the line that passes through the
points (7,-21) and (-4,23). Use
the first point in your equation.
y +[? ] = [ ](x + [ ])
Answer:
y+(21)=-4(x-7)
Step-by-step explanation:
the point slope equation , two point
m=y2-y1/x2-x1
m=23+21/-4-7=44/-11= -4
y+(21)=-4(x-7)
For a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 31 31 beats per minute, the mean of the listed pulse rates is x overbar x equals = 71.0 71.0 beats per minute, and their standard deviation is s equals = 12.6 12.6 beats per minute.
Complete question is;
For a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 31 beats per minute, the mean of the listed pulse rates is x over bar equals 71.0 beats per minute, and their standard deviation is s equals 12.6 beats per minute.
a. What is the difference between the pulse rate of 31 beats per minute and the mean pulse rate of the females?
b. How many standard deviations is that [the difference found in part (a)]?
c. Convert the pulse rate of 31 beats per minutes to a z score.
d. If we consider pulse rates that convert to z scores between minus 2 and 2 to be neither significantly low nor significantly high, is the pulse rate of 31 beats per minute significant?
Answer:
A) 40 beats per minute
B) 3.1746
C) z = -3.17
D) the pulse rate of 31 beats per minute is significantly low.
Step-by-step explanation:
A) The mean pulse rate is given as x bar = 71
Thus difference between this and pulse rate of 31 beats per minute is;
Difference = 71 - 31 = 40 beats per minute
B) number of standard deviations of the difference found in part a is given as;
number = difference/standard deviation(s)
number = 40/12.6
number = 3.1746
C) The z-score is calculated from;
z = (x - xbar)/s
z = (31 - 71)/12.6
z = -3.17
D) from the question we are told that the z scores between minus2 and 2 to be neither significantly low nor significantly high. However, we have a Z-score of -3.17 which doesn't fall into that range. Thus, the pulse rate of 31 beats per minute is significantly low.
does anyone know how to solve 182 6/8 divided by 3 .
Answer:
Step-by-step explanation:
Convert 182 6/8 into improper fraction
[tex]182\frac{6}{8}=\frac{1462}{8}[/tex]
[tex]\frac{1462}{8}[/tex]÷ 3 =[tex]\frac{1462}{8}*\frac{1}{3}=\frac{1462}{24}[/tex]
= 60 22/24
Mother wants to divide $36 between her daughters Ava and Charlotte in the ratio of their ages. If Ava is 15 years old and Charlotte is 12 years old, find how much Ava and Charlotte will get.
Answer:
Ava's share = $20
Charlotte's share = $16
Step-by-step explanation:
15x + 12x = 36 : multiply each girl's age by same amount and adding gives $36
27x = 36 : add x terms
x = 36 / 27 : divide both sides of equation by 27
x = 4 / 3
Ava's share = 15x = 15 * 4/3 = 20
Charlotte's share = 12x = 12 * 4/3 = 16
Need help please! Oh and the options are
A. 2/3
B. 1/5
C. 4/15
D. 2/7
Answer:
C. 4/15There are 15 spaces in total with 4 shaded columnsStep-by-step explanation:
Answer:
Hey there!
The answer would be C. 4/15.
4/5(1/3)=4/15
Let me know if this helps :)
Allison is rolling her hula hoop on the playground. The radius of her hula hoop is 35 \text{ cm}35 cm35, start text, space, c, m, end text. What is the distance the hula hoop rolls in 444 full rotations?
Answer: 880 cm
Step-by-step explanation:
Given: Radius of the hula hoop = 35 cm
Hula hoop is circular in shape
Then, Circumference = [tex]2\pi r[/tex] , where r = radius
Now , Circumference of hula hoop = [tex]2\times \dfrac{22}{7}\times35=220\ cm[/tex]
Now , the distance the hula hoop rolls in 4 full rotations = 4 × (Circumference of hula hoop)
[tex]= 4 \times 220=880\ cm[/tex]
Hence, the required distance = 880 cm
Answer:
880
Step-by-step explanation:
