Step-by-step explanation:
Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. The correct option is C, -7/25.
What are Trigonometric Identities?
Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. There are several trigonometric identities relating to the side length and angle of a triangle.
Given that the value of tan(x) = -4/3 and x is in quadrant 2.
In order to find the value of cos(2x), we can use the trigonometric identity of cos(2x), therefore, for cos(2x) we can write,
\cos(2x) = \dfrac{1-\tan^2(x)}{1+\tan^2(x)}cos(2x)=
1+tan
2
(x)
1−tan
2
(x)
Since the value of tan(x) is known, substitute the value in the identity,
\begin{gathered}\cos(2x) = \dfrac{1-(-\frac{4}{3})^2}{1+(-\frac{4}{3})^2}\\\\\cos(2x) = \dfrac{1-(\frac{16}{9})}{1+(\frac{16}{9})}\\\\\end{gathered}
cos(2x)=
1+(−
3
4
)
2
1−(−
3
4
)
2
cos(2x)=
1+(
9
16
)
1−(
9
16
)
cos(2x) = (-7/9) × (9/25)
Cancelling 9 from the numerator and the denominator,
cos(2x) = -7/25
Hence, if tanx=-4/3 and x are in quadrant 2 then cos2x=-7/25.
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i need help with this i just need the answer.
We have to find the length of FH.
We know that G is on the line, and we know the length FG and GH, so we can represent this as:
We then, we can apply the rule that states that the length of a segment is equal to the length of the segments that are part of it:
[tex]FH=FG+GH=10+5=15[/tex]Answer: FH = 15
Find the value of x if T is the midpoint of segment XY. Segment XT = 3x-14, Segment XY = 8x-56
The value of x if T is the midpoint segment XY is 14.
How to find the mid point of a segment?The midpoint is the middle point of a line segment.
It is equidistant from both endpoints.
The midpoint is halfway between the two end points.
Therefore, the end point of the segment is XY.
The midpoint is T.
Hence,
XY = XT + YT
XT = 3x - 14 = YT
XY = 8x - 56
Let's find the value x.
Therefore,
8x - 56 = 3x - 14 + 3x - 14
8x - 56 = 6x - 28
8x - 6x = -28 + 56
2x = 28
divide both sides by 2
x = 28 / 2
x = 14
Therefore, the value of x is 14
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geometry!!!!! help please!!
Answer:
CD and BG
EF and AH
Step-by-step explanation:
Skew lines are a lines that are on different planes.
BC and CD are on the same plane, and EF and FG are on the same plane.
This leaves CD and BG, and EF and AH, which are on different planes, and thus skew lines.
I need to get this done I'm really behind I need answers today!! Please help
Answer: this is just the first one
y = -3.5x + 2
subtract the 7x from both sides to get 2y = -7x + 4
divide by 2 to get rid of the 2 so you get y = -3.5 + 2
For the third the mistake was adding 3.
You're meant to subtract the 10x from both sides to get -3y = -10x + 6
Divide everything by -3 to get y = 3.3 - 2
Write an equation for a parabola with x-intercepts at 0 and 1 and which passes through the point (2, -2).
I would greatly appreciate some help with this!
（っ＾▿＾）
Answer:
y = -x(x - 1).
Step-by-step explanation:
y = a(x - b)(x - c) where a is a constant and b and c are the x-intercepts.
y = a(x - 0)( x - 1)
y = ax(x - 1).
When x = 2, y = -2 so:
-2 = a(2) (2 - 1)
2a = -2
a = -1.
So the equation is y = -x(x - 1).
Answer:
[tex]y=-x^2+x[/tex]
Step-by-step explanation:
Intercept form of a quadratic equation:
[tex]y=a(x-p)(x-q)[/tex]
where:
p and q are the x-intercepts.a is some constant.Given:
x-intercepts: 0 and 1Point on the curve: (2, -2)Substitute the given values into the formula and solve for a:
[tex]\begin{aligned}y&=a(x-p)(x-q)\\\\\implies -2&=a(2-0)(2-1)\\-2&=a(2)(1)\\-2&=2a\\\dfrac{2a}{2}&=\dfrac{-2}{2}\\\implies a&=-1\end{aligned}[/tex]
Substitute the given x-intercepts and the found value of a into the formula:
[tex]y=-1(x-0)(x-1)[/tex]
Expand to standard form:
[tex]\implies y=-1(x)(x-1)[/tex]
[tex]\implies y=-x(x-1)[/tex]
[tex]\implies y=-x^2+x[/tex]
1.1 A tuck shop at a particular school sells soft drink cans. The economic friendly club of this school collected soft drink cans for recycling for a period of 20 days. The number of cans collected was recorded and the data is given below: 48 50 52 59 60 68 73 76 76 76 78 79 80 81 82 82 84 91 92 98
1.1.1 Determine the median of the cans collected. 76 91 76 92 76 98 (1)
The median of the cans collected by the tuck shop will be 77.
What is median?In statistics and probability theory, the median is the number that separates the upper and lower half of a population, a probability distribution, or a sample of data.
The middle score in the group is called the median. You follow these steps to determine the median:
Put the results in numerical order.
Subtract 2 from the final score.
If your total scores are odd, round them up to the next whole number to determine where the median falls. If your total scores are even, find the number that is in the middle and add it to the one that is higher up to get the median.
Total cans collected = 20
Dividing 20 by 2 we get 10, which is even.
To calculate the total of the two scores (76 + 78 = 154) add the score in the tenth position of the given data set to the number in the next position. Dividing 154 by 2, we get 77.
Therefore, 77 is the median in this instance.
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100 POINTS PLEASE ANSWER ASAP!
Answer: -2
Step-by-step explanation:
Answer: -2
Step-by-step explanation:
18x-51=9(4x+5)-6(3x-10)
[tex]18-51=36x+45-18x-60\\18x-51=36x-18x+45-60\\18x-51=18x-15\\18x-18x=-15+51[/tex]
∴ 18x-18x≠-15+51
THERE IS NO SOLUTION FOR THIS EQUATION
Suppose f(x)=4[[x-1]].
Find: f(1.7),f(-3.4), and f(9.8).
Answer:
I believe it should be
f(1.7) = 2.8
f(-3.4) = -17.6
f(9.8) = 35.
Step-by-step explanation:
Simply plug-in the different numbers for x.
Please help with this assignment
The result of the subtraction are-
13,2217,993693,00006What is defined as the subtraction?Subtraction in maths means to take something out of a group or a variety of items. When we deduct, the number of items in the group decreases or becomes smaller. A subtraction problem includes the minuend, subtrahend, and difference.Once we subtract two digits, we should use following terms from the subtraction expression:Minuend: The number that is subtracted from the other number.Subtrahend: The amount to be subtracted as from minuend.Difference: The outcome of subtracting the subtrahend as from minuend.The subtraction formula:
Minuend - Subtrahend = Difference
Part 1:
46,329
- 33, 108
_______
13,221
_________
Part 2:
8,695
- 702
_______
7, 993
_________
Part 3:
700,989
- 7,989
_______
693,000
_________
Part 4:
55
- 49
_______
06
_________
Thus, the result of the given subtractions are found.
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Let f= {(1,2),(2,3),(3,5),(4,7)}
What is f ⁻¹ ∘ f
Test of a horizontal line.Suppose f is a function.F does not have an inverse if any horizontal line crosses the graph of f more than once.F does have an inverse if no horizontal line crosses the graph of f more than once
How do you calculate f's inverse?
Finding a Function's InverseReplace f(x) with y first, then.Every x must be replaced with a y, and vice versa.Solve the y-part of the equation from step two.In place of y, write f1(x) f 1 (x).Check that (ff1)(x)=x (f f f 1) (x) = x and (f1f)(x)=x (f f 1 f) (x) = x are both true to validate your workf= {(1,2),(2,3),(3,5),(4,7)}
Dom(gof)=dom(f)={1,3,4}.
(gof)(1)=g{f(1)}=g(2)=3,
(gof)(3)=g{f(3)}=g(5)=1
(gof)(4)=g{f(4)}=g(1)
∴gof={(1,3),(3,1),(4,3)}.
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If f (x) = 4x² + 3x - 5, then f(x+h)-f(x)/ h is equal to which of the following?
Answer:
[tex]8x + 4h + 3[/tex]
Step-by-step explanation:
[tex]f(x)=4x^2 + 3x-5 \\ \\ f(x+h)=4(x+h)^2+3(x+h)-5 \\ \\ =4(x^2+2xh+h^2)+3x+3h+5 \\ \\ =4x^2+8xh+4h^2+3x+3h+5 \\ \\ f(x+h)-f(x)=(4x^2+8xh+4h^2+3x+3h+5)-(4x^2+3x+5) \\ \\ =8xh+4h^2+3h \\ \\ \frac{f(x+h)-f(x)}{h}=\frac{8xh+4h^2+3h}{h}=8x+4h+3[/tex]
What Is 4 1/5% of 50 write your answer as a decimal, make sure answer is fully reduced
Answer:
2.1
Step-by-step explanation:
Use a calculator then put in 4.2 (4 1/5)% then put 50
Example: 4.2%50 = 2.1
Describe the graph of y = -|x + 4| - 5.
please answer correctly this will help me pass my exam
The graph of the absolute value function is an inverted "V" such that the vertex is at (-4, -5) and opens downwards.
How to calculate the modular function?We call a modular function the function f(x) = |x|, in which its domain is given by the real numbers and its range is the positive real numbers. This is because, for every negative value on the y-axis, the modular function will make |-y| = -(-y) = y
Therefore, to plot the graph of a modular function, it is enough to adopt some values for x and apply them to the function f(x) = | x |, in order to obtain their respective values in y.
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There are 135 people in a sport centre.
77 people use the gym.
62 people use the swimming pool.
65 people use the track.
27 people use the gym and the pool.
23 people use the pool and the track.
31 people use the gym and the track.
4 people use all three facilities.
A person is selected at random.
What is the probability that this person doesn't use any facility?
We can conclude that the probability of the randomly selected person does not use any facility is 0.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes.Statistics is the study of events that follow a probability distribution. The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.So, the probability that the selected person does not uses any facility:
According to the given data, we can easily say that all the people use some or the other facility.So, there are 0 people present who do not use the facility.Then, the probability that the selected person does not use any facility will be 0.Therefore, we can conclude that the probability of the randomly selected person does not use any facility is 0.
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n(x) = -1-x+4
n(-2) =
n(0)=
n(5)=
Step-by-step:
n(x) = -1 - x + 4
n(-2) = -1 - (-2) + 4
= -1 + 2 + 4
= 5
___________________________
n(0)= -1 - 0 + 4
= 3
___________________________
n(5)= -1 - 5 + 4
= -2
i need help with this, thanks
Answer: 11
Step-by-step explanation:
8x + 7 = 9x - 4
7 = x - 4
11 = x
How do you do these?
Solve for s.
6/s = 2
Answer:
s=3
Step-by-step explanation:
So you have the equation: [tex]\frac{6}{s}=2[/tex]
If we multiply both sides by this "s" value we should maintain equality, and it conveniently cancels out our division by "s" on the left side giving us the following equation: [tex]6=2s[/tex]
The only "operation" on the value "s" is the coefficient of 2, which is multiplying the value of "s" by 2.
To undo this multiplication of 2, we simply divide by 2, since 2/2 = 1, and now we have a coefficient of 1 for the "s", which is the same as isolating "s"
But we want to divide both sides by 2 to maintain equality, so let's write out our expression
[tex]\frac{6}{2}=\frac{2s}{2}\implies3=\frac{2}{2}*s\implies 3=s[/tex]
We can double check this by plugging in this value for "s" in the original equation: [tex]s=3, \ \frac{6}{s}=2\implies \frac{6}{3}=2\implies 3=3[/tex] which is indeed true, so we have our solution!
Al's bowling center offers its customers 1 game for $4.40 or 2 games for $8.40. The games can be played by one bowler or by a group of bowlers. if a group wants to play 4 games, how much more will its members spend by buying the games on a time instead of buying the 2-game pack?
Answer:
148.4
Step-by-step explanation:
4.40x8.40x4=148.4
A recipe says that 6 spring rolls will serve 3 people. Complete the table.
number of spring rolls number of people
6 3
30
40
28
Here is the completed table:
number of spring rolls number of people
6 3
30 15
40 20
28 14
What is the relationship between the number of spring rolls and people?The first step is to determine the number of people that one spring roll would serve.
Number of people that one spring roll would serve = 3 / 6 = 1/2
Number of people that s spring rolls would serve = number of people that 1 spring roll would serve x s
Number of people that 30 spring rolls would serve = 1/2 x 30 = 15
Number of people that 40 spring rolls would serve = 1/2 x 40 = 20
Number of people that 28 spring rolls would serve = 1/2 x 28 = 14
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simplify 3 sqrt -64x^6y^9
When we simplify ³√(-64x⁶y⁹), the result obtained is written as -4x²y³
How do I simplify ³√(-64x⁶y⁹)?To simplify ³√(-64x⁶y⁹), do the following:
³√(-64x⁶y⁹)
Simplifying individual term, we have
³√(-64) = -4
³√(x⁶) = x²
³√(y⁹) = y³
Combining the individual simplification, we have
³√(-64x⁶y⁹) = -4 × x² × y³
³√(-64x⁶y⁹) = -4x²y³
Thus, from the above illustration, we can conclude that simplifying ³√(-64x⁶y⁹) results in -4x²y³
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a box contains 24 light bulbs of which four are defective. if one person selects 10 bulbs from the box in a random manner, and a second person then takes the remaining 14 bulbs, what is the probability that all four defective bulbs will be obtained by the same person?
The probability that all four defective bulbs will be obtained by the same person is 0.1140 .
In the question ;
it is given that
the total number of light bulbs in the box = 24 bulbs
total number of bulbs available for first person = 24 bulbs
number of defective bulbs = 4
So, the number of ways the first person can select 4 defective bulbs out of 10 selection = C(10,4)
total number of ways that first person can select 4 defective bulbs out of 24 bulbs = C(24,4)
So , the Probability that all four defective bulbs obtained by first person = C(10,4)/C(24,4) . .......(i)
Since 10 bulbs have been selected
So, total number of bulbs available for second person = 14 bulbs
number of defective bulbs = 4
So, the number of ways the first person can select 4 defective bulbs out of 14 remaining bulbs = C(14,4)
total number of ways that first person can select 4 defective bulbs out of 24 bulbs = C(24,4)
So , the Probability that all four defective bulbs obtained by second person = C(14,4)/C(24,4) . .....(ii)
Probability that all four of the defective bulbs will be obtained by the same person
= P(four defective bulbs obtained by first person) + P(four defective bulbs by second person)
Substituting the probabilities from (i) and (ii) , we get
= C(10,4)/C(24,4) + C(14,4)/C(24,4)
= (210/10626 )+(1001/10626) ...as C(10,4)=210 ,C(24,4)=10626, C(14,4)=1001
= 1211/10626
= 0.1139657
≈ 0.1140
Therefore , the probability that all four defective bulbs will be obtained by the same person is 0.1140 .
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container a holds 4 red balls and 6 green balls; containers b and c each hold 6 red balls and 4 green balls. a container is selected at random and then a ball is randomly selected from that container. what is the probability that the ball selected is green? express your answer as a common fraction.
Answer:
Step-by-step explanation:
There are three different possibilities for our first decision, each corresponding to which container we choose. So, if we choose container A, with 1/3 probability, we have a 6/10=3/5 probability of drawing green, which means we have a (1/3)(3/5)=1/5 of picking Container A and then picking a green ball. Similarly for container B the probability is (1/3)(4/10)=2/15, and the same for container C. So, the total probability is (1/5)+(2/15)+(2/15) = 7/15.
Question 5 (1 point)
Solve the problem.
LF and LG are supplementary
angles.
m/F = (4x + 22)° and m
Find m/F.
Please help me !:)
Answer: [A]: " 78 ° " .
_______
Step-by-step explanation:
Supplementary angles add up to 180 degrees.
So, given m∠F & m∠G are supplementary angles:
and given m∠F = (4x + 22) and: m∠G = (6x + 18) ;
Find m∠F ; which equals (4x + 22).
_______
So, add the 2 (two) supplementary angles;
set them as "equal to 180" ;
solve for x ;
then: plug that x value into:
(4x + 22) ; which is the m∠F ;
_______
4x + 22 + 6x + 18 = 180 ;
On the 'right-hand side of the equation" ;
"combine the like terms" :
+ 4x + 6x = + 10x ;
+ 22 + 18 = 40 ;
Then rewrite the equation:
10x + 40 = 180 ;
_______
Now:
Method 1):
Subtract 40 from Each Side of the equation:
10x + 40 − 40 = 180 − 40 ;
to get: 10x = 140 ;
Now: Divide Each Side of the equation by 10 ; to isolate x on one side of the equation; & to solve for x ;
10x / 10 = 140 / 10 ; to get: " x = 14 " ;
Method 2):
When we have: 10x + 40 = 180 ;
Divide the entire equation (i.e. Each Side of the equation) by 10 ;
to get rid of the "zeros" :
(10x + 40) / 10 = (180)/10 ;
to get:
(10x/10) + (40/10) = (180/10);
→ x + 4 = 18 ;
Subtract 4 from Each Side of the equation; to isolate x on one side of the equation; & to solve for x ;
x + 4 − 4 = 18 − 4 ;
to get: x = 14 .
_______
Now, find m∠F = 4x + 22 ;
Plug in 14 for x ; to solve:
m∠F = 4(14) +22 ;
= 56 + 22 ;
m∠F = 78°
which corresponds to:
Answer choice: [A]: 78° .
_______
Hope this is helpful to you!
Wishing you well!
_______
Answer:
A
Step-by-step explanation:
Angles that are supplementary add to 180°.
[tex]4x+22+6x+18=180 \\ \\ 10x+40=180 \\ \\ 10x=140 \\ \\ x=14 \\ \\ \therefore m\angle F=78^{\circ}[/tex]
please help!! it’s timed so please help
I am not in this grade but I think it is A
Step-by-step explanation:
if right please mark brainiest
At a garage sale, Petra priced her scooter for $15.50. She ended up selling it for $10.75. Find the percent of decrease in the price of the scooter. Round to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
Answer:
The percent of decrease in the price of the scooter is 30.6%.
Step-by-step explanation:
In order to calculate the percent of decrease, you have to divide the difference between the two numbers by the original number and multiply the result for 100:
% decrease=((10.75-15.50)/15.50)*100
% decrease=-0.306*100
% decrease= -30.6%
According to this, the answer is that the percent of decrease in the price of the scooter is 30.6%.
please help meeee!!! :c
Function A
f(x) = x − 9
Function B
graph of line going through ordered pairs negative 1, negative 3 and 2, 3
Which equation best compares the slopes of the two functions?
Slope of Function B = 2 x Slope of Function A
Slope of Function A = Slope of Function B
Slope of Function A = 2 x Slope of Function B
Slope of Function B = − Slope of Function A
The equation best compares the slopes of two functions is,
Slope of function B = 2 × Slope of function A
Given,
The function A, f(x) = x - 9
We have to find slope of Function B
The function is in the form of y = mx + b
Here, m is the slope.
y = x - 9
m is 1 and b is -9
Now, lets consider the graph of line passing through points (-1, -3) and (2, 3)
That is,
(x₁, y₁) = (-1, -3)
(x₂, y₂) = (2, 3)
Now we can find the slope of the line:
m = (y₂ - y₁) / (x₂ - x₁)
m = (3 - (-3)) / (2- (-1))
m = (3 + 3) / (2 + 1)
m = 6/3
m = 2
That is, the slope of function B is 2
Here,
Slope of function A is 1.
That is, slope of function B is twice the slope of function A.
Therefore, the equation best compares the slopes of two functions is,
Slope of function B = 2 × Slope of function A
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Determine the intercepts of the line.
Answer:
x- intercept: ( -10,0)
y- intercept: (0, -45)
Step-by-step explanation:
An x intercept can be determined from the graph above by recognizing where the given line crosses the x-axis. The same is true for the y intercept and the y-axis.
On this graph, we see that the line crosses the x axis at the point ( -10,0), making this our x intercept.
We also see that the line crosses the y axis at the point (0, -45), making this our y intercept.
HOPE THIS HELPS!!
According to a study published in the journal Social Psychological and Personality Science, people with
religious affiliations live longer, on average, than those without religious affiliations. The study analyzed
more than 1,000 obituaries and accounted for other variables like sex and marital status.
What type of study is this, and what is the explanatory variable?
The correct option is Option(c) An observational study where religious affiliation is an independent variable.
How is the study an observational study?According to a study published in the Journal Social Psychological and Personality Science, people with religious affiliations live longer, on average, than those without religious affiliations.Now, as we note, lifespan is said to be higher for people with religious affiliations.So, lifespan is claimed to be dependent on religious affiliation; so religious affiliation is independent and lifespan is dependent.Also, we cannot manipulate anyone's religious affiliation or lifespan; we just observe them by analyzing more than 1000 obituaries.Therefore, it is an observational study where religious affiliation is an independent variable.
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The complete question is: "According to a study published in the journal Social Psychological and Personality Science, people with religious affiliations live longer, on average, than those without religious affiliations. The study analyzed more than 1,000 obituaries and accounted for other variables like sex and marital status.
What type of study is this, and what is the explanatory variable?
A. A manipulative experiment where religious affiliation is an independent variable
B. A manipulative experiment where lifespan is an independent variable
C. An observational study where religious affiliation is an independent variable
D. An observational study where lifespan is an independent variable."
75 pts 8th grade science. WILL give brainliest.
On landing, the plane touches the runway with a speed of 65 m/s. After one second its 60 m/s.
?
Answer:
Not sure what you are looking for
Step-by-step explanation:
Acceleration = change in velocity / change in time
= (60 - 65) / 1 s = - 5 m/s^2