Given:
The expression is
[tex]2\cos^2(\dfrac{x}{2})-\cos (x)[/tex]
To find:
The expression which is equivalent to the given expression.
Solution:
We have,
[tex]2\cos^2(\dfrac{x}{2})-\cos (x)[/tex]
We know that,
[tex]\cos x=2\cos^2 (\dfrac{x}{2})-1[/tex]
Using this formula, the given expression can be written as
[tex]2\cos^2(\dfrac{x}{2})-\left(2\cos^2(\dfrac{x}{2})-1\right)[/tex]
[tex]=2\cos^2(\dfrac{x}{2})-2\cos^2(\dfrac{x}{2})+1[/tex]
[tex]=1[/tex]
Therefore, the given expression is equivalent to 1.
Answer:
B
Step-by-step explanation:
A bell tolls every 30 minutes on the
hour and at half past the hour. How
many times does the bell toll
between the times of 11.45a.m. and
3.10p.m.?
Factors of 121 what do you think ???
Step-by-step explanation:
[tex]121 = 11 \times 11[/tex]
1, 11 and 121
What is the point- slope equation of the line through the point (-5, 5) that is perpendicular to the line whose equation is y= (5/3)x + 2? URGENT
Please find the x, thank you!
Answer:
X=8
Step-by-step explanation:
Hope this helps
What is an equation of the line that passes through the points (4,1) and (8,-3)?
PLZZ HELPP MEE!!
Answer:
y=-x+5
Step-by-step explanation:
(4,1)
(8,-3)
1)a slope of a line is (y2-y1)/(x2-x1)
so (-3-1)/(8-4)
-4/4=>m=-1
2)to find y-int replace any points in the equation by x and y
so 1=-1(4)+b
1=-4+b
1+4=b
so b= 5
therefore the equation is y=-x+5 so d
-4/9 divided by 2/3 what would the answer be?
Answer:
-4/9*3/2
-4*3/9*2
-12/18
-2/3
Answer:
-2/3
Step-by-step explanation:
-4/9 divided by 2/3
you turn divided into multiplied and flip the second number
-4/9*3/2
you can cross multiply.
once you have simplified you should have
-2/3*1/1
simplified further to
-2/3*1
so,
-2/3 is the answer :)
12.
Question 19 (5 points)
2 - (-8) + (-3) =
15
OA) 1
18
B) 14
12
O
D) 7
Answer:
The answer is d because 10-3 is 7
Answer:
D)7
Step-by-step explanation:
2 - (-8) + (-3) =
10-3 =7
Maria deposited $5,700 in an account that earns 8% simple interest. How much will be in her account after 6 years?
Answer:
,$456 paid in her account after 6 year
Can anyone find the simplest radical form
Answer:
C.) [tex]55[/tex]
Step-by-step explanation:
Simplify the expression by finding the square root of 25:
[tex]\sqrt{x} =x*x\\\\\sqrt{25} =5*5\\\\11*5=55[/tex]
The answer is 55
:Done
What kind of function describes this situation?
Answer: A
Step-by-step explanation:
because she's deducting 10 points every day the slope is constant so it has to be a linear equation
I really don’t understand this can someone pls help this is due soon and I will mark brainliest do not answer if your not sure
Answer:
|-3|=3
|0|=0
|3|=3
|-5|=5
Which of the following functions has the function rule y=x+4? (-2, 2), (-1,-5), (3.7)} {(-3, 1), (0.4), (2. 6)) (12.6). (-3.-7), (0.4) (0.2).(-2,-6). (1.5))
Answer:
b. {(-3, 1), (0, 4), (2, 6)}
Step-by-step explanation:
Marty swans 36 yards in 42 seconds. If he continues to swim at the same rate, how long will it take him to swim 500 yards
Whats the slope and how do i / where do i graph it
Answer:
The slope is 3. graph it every time the line hits an exact point
Step-by-step explanation:
PLEASEEEEEEEEEEE HELP MEH WILL GIVE BRAINLIST PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE HURRYYYYYYYYYY
Answer:
the awnser is b
.........
4.5.36
A smoke jumper jumps from a plane that is 1500 ft above the ground. The function h= -16? + 1500 gives the jumper's height hin feet during the free fall att seconds
a. How long is the jumper in free fall if the parachute opens at 1000 ft?
b. How long is the jumper in free fall if the parachute opens at 940 ft?
c. What is a reasonable domain and range for the function h? no
Answer:
Step-by-step explanation:
Given function is h(t) = -16t² + 1500
a). For h(t) = 1000 feet,
1000 = -16t² + 1500
1000 - 1500 = -16t² + 1500 - 1500
-500 = -16t²
t² = [tex]\frac{500}{16}[/tex]
t = [tex]\sqrt{31.25}[/tex]
t = 5.59 sec
b). For h(t) = 940 feet,
940 = -16t² + 1500
940 - 1500 = -16t² + 1500 - 1500
-16t² = -560
t² = [tex]\frac{-560}{-16}[/tex]
t = [tex]\sqrt{35}[/tex]
t = 5.92 sec
c). For domain and range of the function,
When the jumper comes down to the ground,
h = 0
0 =-16t² + 1500
t² = [tex]\frac{1500}{16}[/tex]
t = [tex]\sqrt{93.75}[/tex]
t = 9.68 sec
Since, x-values on the graph vary from x = 0 to x = 9.68,
Domain : [0, 9.68]
Vertex of the quadratic function: (0, 1500)
Since, coefficient of the highest degree term is negative, parabola will open downwards.
Therefore, y-values of the function will vary in the interval y = 0 to y = 1500
Range: [0, 1500]
Pedro & Samuel are training for a race. The ratio of miles Samuel runs is 2:3. If Samuel logs 27 miles, then how many miles did Pedro train
Answer:
18
Reason:
the ratio is 2:3, and samuel is the 3 part. We can put this as for every 2 miles that pedro gets, samuel gets 3 miles. Samuel got 27 miles, so you do 27/3 which is 9, and then 9 * 2, which is 18.
Una parte de 25 000 dólares se invierte al 10% de interés, otra parte al 12 % y el resto al 16%. El ingreso anual total de las tres inversiones es de 3200 dólares. Además, el ingreso de la inversión al 16% es igual al ingreso de las otras dos inversiones combinadas. ¿Cuánto se invirtió a cada tasa de interés?
Answer:
$5000 at 10%, $10000 at 12% and 10000 at 16%Step-by-step explanation:
One part of $ 25,000 is invested at 10% interest, another part at 12%, and the rest at 16%. The total annual income from the three investments is $ 3,200. Also, the income from the investment at 16% is equal to the income from the other two investments combined. How much was invested at each interest rate?==================
Let the parts be x, y and z
As per given we get below system of equations:
x + y + z = 250000.1x + 0.12y + 0.16z = 32000.1x + 0.2y = 0.16zSubstitute 0.1x + 0.2y in the second equation:
0.16z + 0.16z = 32000.32z = 3200z = 3200/0.32z = 10000Now we have:
x + y + 10000 = 25000 ⇒ x + y = 15000and
0.1x + 0.12y + 0.16*10000 = 3200 ⇒ 0.1x + 0.12y = 1600Multiply the second equation and then subtract the first one:
10(0.1x + 0.12y) = 10(1600) ⇒ x + 1.2y = 16000x + 1.2y - (x + y) = 16000 - 150000.2y = 1000y = 10000Then
x = 15000 - 10000 = 5000So the parts are:
$5000 at 10%, $10000 at 12% and 10000 at 16%What is the first step equation=6x – 4x + 3 = 15
A.
Add 4x to both sides of the equation.
B.
Subtract 4x to both sides of the equation.
C.
Combined the variable terms on the left side of the equation.
D.
Combine the constant terms on the right side of the equation.
6. Which equation or inequality represents the following description? & Multiply the quantity 2 more than a number by 8. The result is at least 12 times the number subtracted from 76.
A. 8(2n) < 76 - 12
B. 8n + 2 = 12n - 76
C. 8(n + 2) > 76 - 12n
D. 8(2n) = 76 – 12n
Answer:C it’s bc it says at least 12 time the number subtracted from 76
Step-by-step explanation:
If it’s wrong sry if your gonna be mean to me just work it by your self don’t use brainly
I need to know the explanation will mark Brainliest
Answer:
the value of x is 23
Step-by-step explanation:
plz mark brainly
PLS HELP ME FAST WILL GIVE POINTS
Triangle PQR is transformed to triangle P′Q′R′. Triangle PQR has vertices P(9, 0), Q(6, 3), and R(−3, −6). Triangle P′Q′R′ has vertices P′(3, 0), Q′(2, 1), and R′(−1, −2). Plot triangles PQR and P′Q′R′ on your own coordinate grid.
Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P′Q′R′? Explain your answer. (4 points)
Part B: Write the coordinates of triangle P′′Q′′R′′ obtained after P′Q′R′ is reflected about the y-axis. (4 points)
Part C: Are the two triangles PQR and P′'Q′'R′' congruent? Explain your answer. (2 points)
Answer:
The scale factor of the dilation that transforms the triangle is 1/3
Step-by-step explanation:
9x1/3 is 3. 6x1/3 is 2, etc.
Suppose you are a civil engineer, specializing in traffic volume control for the City of Grand Rapids. Your department has been receiving a multitude of complaints about traffic wait times for a certain intersection in the heart of downtown. To see if these claims are valid, you want to monitor the true average wait time at that intersection. Over the course of a few months, you record the average number of minutes a car waits at the intersection between 4:00 PM and 5:00 PM. With a sample size of 14 cars, the average wait time is 6.313 minutes with a standard deviation of 1.6509 minutes. Construct a 90% confidence interval for the true average wait time for a car at the intersection between 4:00 PM and 5:00 PM. 1) (4.542, 8.084).2) (5.536, 7.09). 3) (-5.532, 7.094).4) (5.532, 7.094).5) (5.872, 6.754).
Answer:
90% Confidence Interval = (5.532, 7.094)
Step-by-step explanation:
With a sample size of 14 cars, the average wait time is 6.313 minutes with a standard deviation of 1.6509 minutes. Construct a 90% confidence interval for the true average wait time for a car at the intersection between 4:00 PM and 5:00 PM. 1) (4.542, 8.084).2) (5.536, 7.09). 3) (-5.532, 7.094).4) (5.532, 7.094).5) (5.872, 6.754).
We are given the sample size = 14 cars
This sample size is small so instead of using z score , we would use the t score critical value
First we need to calculate our degree of freedom
Degrees of freedom = n - 1
= 14 - 1 = 13
The t score for 90% confidence interval with a degree of freedom of 13 =
= 1.771
Hence, Confidence Interval =
Mean ± t score × standard deviation/√n
= 6.313 ± 1.771 × 1.6509/√14
= 6.313 ± 1.771 × 0.4412215843
= 6.313 ± 0.7814034257
Confidence Interval
= 6.313 - 0.7814034257
= 5.5315965743
≈ 5.532
= 6.313 + 0.7814034257
= 7.0944034257
≈ 7.094
90% Confidence Interval = (5.532, 7.094)
How long would 8 thousand trillion trillion trillion trillion trillion trillion trillion trillion years be if typed out?
Answer:
100 digits
Step-by-step explanation:
One trillion is 10¹², so it adds 12 zeros.
8000 adds 4 digits.
8 trillions add 8·12 = 96 zeros.
So in total you have 96+4 = 100 digits
This number would also be called 8 googol, since 1 googol is 10¹⁰⁰
a = 65 – 100n
Find a
39
Simplify each term. please help!! 30 points + brainliest :)
1. -(-3y)³
2. (2c)⁵
3. (-2m)⁴
4. (4g)³
5. (7j)²
6. (-5z)⁵
Answer:
1. 27y^3
2. 32c^5
3. 16m^4
4. 64g^3
5. 49j^2
6. -3125z^5
Step-by-step explanation:
Can you help answer my question too, please?
sec²A-cosec²A=(tanA+cotA)(tanA-cotA)
Answer:
Step-by-step explanation:
Sec²A-cosec²A=(tanA+cotA)(tanA-cotA)
Tan^2A+1-cot^2A-1=(tan^2A-cot^2A)
tan^2A-cot^2A=tan^2A-cot^2A
L.H.S=R.H.S
Hence proved.
Determine whether the graph represents a function?
None are correct
The relation is a function
The relation is not a function
Pls answer professionally or with the right answer I’m beg you
Answer:
Step-by-step explanation:
Hello friend!!!
here's ur answer
1) <y = 180 - 74 = 106° ( linear pair )
<x = <y ( alternate angles )
therefore, <x = <y = 106°
2) <x = 68° ( corresponding angles )
<y = 180 - 68 = 112° ( linear pair )
<z = 112° ( vertically opposite angles )
Hope this helps
plz mark as brainliest!!!!!
10 workers produce 30 complex elements in 10 days. In how many days would 5
workers produce 24 elements?
Given:
10 workers produce 30 complex elements in 10 days.
To find:
The number of days, in which 5 workers produce 24 elements.
Solution:
According to the question, let as assume
[tex]n_1=10[/tex]
[tex]w_1=30[/tex]
[tex]d_1=10[/tex]
[tex]n_2=x[/tex]
[tex]w_2=24[/tex]
[tex]d_2=5[/tex]
where, n is number of workers, w is work done, and d is number of days.
We have, a formula,
[tex]\dfrac{n_1\times d_1}{w_1}=\dfrac{n_2\times d_2}{w_1}[/tex]
Substituting the values in the above formula, we get
[tex]\dfrac{10\times 10}{30}=\dfrac{x\times 5}{24}[/tex]
[tex]\dfrac{10}{3}=\dfrac{5x}{24}[/tex]
Isolate variable x.
[tex]\dfrac{10}{3}\times \dfrac{24}{5}=\dfrac{5x}{24}\times \dfrac{24}{5}[/tex]
[tex]\dfrac{240}{15}=x[/tex]
[tex]16=x[/tex]
Therefore, the required number of days is 16.