Answer:
30 60 90 triangle
the hypotenuse is twice the length of the shorter leg length.
Rewrite the given function as an equivalent function containing only cosine terms raised to a power of 1.f(x)=7cos^2x
Answer:
Step-by-step explanation:
Using the double angle formulas,
cos(2x) = cos^2(x) - sin^2(x) ............(1)
1 = cos^2(x) + sin^2(x)............(2)
add (1) and (2)
1 + cos(2x) = 2 cos^2(x)
=> cos^2(x) = (1/2) (1+cos(2x)) ..............(3)
f(x) = 7 cos^2 (x)
substituting (3)
f(x) = (7/2) (1+cos(2x))
PLEASE HELP!! laboratory tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standard deviation of 75 hours. find the probability that a randomly selected light bulb will last between 900 and 975 hours.
Answer:
P = 0.0215 = 2.15%
Step-by-step explanation:
First we need to convert the values of 900 and 975 to standard scores using the equation:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
Where z is the standard value, x is the original value, [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation. So we have that:
standard value of 900: [tex]z = \frac{900 - 750}{75} = 2[/tex]
standard value of 975: [tex]z = \frac{975 - 750}{75} = 3[/tex]
Now, we just need to look at the standard distribution table (z-table) for the values of z = 2 and z = 3:
z = 2 -> p_2 = 0.9772
z = 3 -> p_3 = 0.9987
We want the interval between 900 and 975 hours, so we need the interval between z = 2 and z = 3, so we just need to subtract their p-values:
P = p_3 - p_2 = 0.9987 - 0.9772 = 0.0215
So the probability is 0.0215 = 2.15%
Answer:
2.35 babyyyyyyyyyyy
Step-by-step explanation:
Acellus sux
given that sin x equals to a over b then what is tan x
Answer:
Hey there!
Sine is equal to opposite/hypotenuse
Tangent is equal to opposite/adjacent
opposite=a
hypotenuse=b
adjacent=c
Thus, tangent x= a/c.
Hope this helps :)
Answer:
tan x = a/sqrt(b^2 - a^2)
Step-by-step explanation:
sin x = a/b = opp/hyp
tan x = opp/adj
adj^2 + opp^2 = hyp^2
adj^2 + a^2 = b^2
adj = sqrt(b^2 - a^2)
tan x = a/sqrt(b^2 - a^2)
A limited-edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15% per year, the poster is worth $20.70. Which equation can be used to find the value, y, after x years? (Round money values to the nearest penny.)
y = 18(1.15)x
y = 18(0.15)x
y = 20.7(1.15)x
y = 20.7(0.15)x
Answer: A) 18(1.15)x
Step-by-step explanation:
18 was the original cost, so the price will always be determined with this starting point. Sice there is an increasing value, that makes it 1.15 instead of .15. And it goes up by 15%, making it the coefficient.
Answer:
A) y = 18(1.15)x
Step-by-step explanation:
A una granja llegaron 54 ovejas 24 vacas 30 cerdos los cuales se quieren repartir en corrales con igual numero de animales de forma que haya la mayor cantidad posible en cada corral ¿cuantos animales posibles deben ir en cada uno de los corrales?
Answer: 6 animals should go in each pen.
Step-by-step explanation:
Total sheep = 54
Total cows = 24
Total pigs = 30
Highest number of animals are possible in each pen such that animals are distributed in pens with the same number = Greatest common divisior (54,24, 30)
54= 6 x 9
24= 6 x 4
30 = 6 x 5
So, Greatest common divisior (54,24, 30) = 6
Hence, 6 animals should go in each pen.
PLEASE HELP ASAP !! Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. QUESTION: Find the average rate of change of each function over the interval [0, 3]. Match each representation with its respective average rate of change 3, -3 ,-2,6,-1,5
Answer:
Average rate of change of functions r, q, p, s are 5, 3, -2 and 6 respectively.
Step-by-step explanation:
The formula for average rate of change of f(x) over [a,b] is
[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]
The given function is
[tex]r(x)=x^2+2x-5[/tex]
[tex]r(0)=(0)^2+2(0)-5=-5[/tex]
[tex]r(3)=(3)^2+2(3)-5=10[/tex]
Now,
[tex]m_1=\dfrac{r(3)-r(0)}{3-0}[/tex]
[tex]m_1=\dfrac{10-(-5)}{3}=5[/tex]
From the graph it is clear that q(0)=-4 and q(3)=5.
[tex]m_2=\dfrac{q(3)-q(0)}{3-0}[/tex]
[tex]m_2=\dfrac{5-(-4)}{3}=3[/tex]
It is given that function p has as x-intercept at (3,0) and a y-intercept at (0,6). It menas p(0)=6 and p(3)=0.
[tex]m_3=\dfrac{p(3)-p(0)}{3-0}[/tex]
[tex]m_3=\dfrac{0-6}{3}=-2[/tex]
From the given table it is clear that s(0)=-13 and s(3)=5.
[tex]m_4=\dfrac{s(3)-s(0)}{3-0}[/tex]
[tex]m_4=\dfrac{5-(-13)}{3}=6[/tex]
Therefore, the average rate of change of functions r, q, p, s are 5, 3, -2 and 6 respectively.
Which triangle’s area can be calculated using the trigonometric area formula?
Answer:
Triangle klm
Step-by-step explanation:
edg 2020
Help again 《Brainlist》
A six faced dice with numbers 1 thru 6 is thrown twice. No fee is charges to the throws. If the organizer of the game has to payout as many dollars as the result every time an even sum comes up and will receive from the player as many dollars as the result if the sum is odd, in the very long run, when 1 million throws are made,
approximately how much is the winning or loss to the organizer?
Answer:
win-263889 loss-236111
Step-by-step explanation:
1:the guys throws the dice twice no charge for this
2:for every face the first time there is a chance of getting the others or the same face e.g round 1-1 round 2-(either 123456)
3:I drew a probability tree to get the sum
like if I got 1and1 then sum is 2 I did it for the rest
4:I got P of (even)=17/36 and for (odd)=19/36
5:then the organizer has to pay if it's even and there 1 million throws Wich means the probability he will lose is the probability of getting an even sum for 500000 throws and for winning is the probability of getting odd sums in those 500,000 throws
6: 500k is because only after it's thrown twice were there charges
A cell phone company charges $60.00 a month for up to 1 gigabyte of data. The cost of additional data is $0.05 per megabyte. If d represents the number of additional megabytes used and c represents the total charges at the end of the month, write a linear equation that can be used to determine a user's monthly bill.
Answer:
60 + 0.05d
Step-by-step explanation:
Calculate the volume of the figure.
Answer: The volume is 33 cubic centimeters.
Step-by-step explanation:
First find the volume of the square pyramid on top of the cube. To find the volume of the square pyramid you use the volume a^2*h/3 a is the side length of the base of the square pyramid and h is the height all divide by 3.
So we can say that the side length of the base of the square pyramid is 3 because it has the same side length base as the cube.
V= 3^2 * 2 /3
V= 9 * 2 /3
V= 18/3
v= 6
So the volume of the square pyramid is 6 so now we need to find the volume of the cube and add them together.
Volume of the a cube uses the formula s^3 where s is the side length.
V= 3^3
v= 3*3*3
v= 27
The volume of the cube is 27.
Add 6 and 27 to find the total volume.
6 +27 = 33
John needs to find out the probability that he will sell all his cars by the end of the
year. He takes a sample of the customers that come in to see if they will buy a car.
How many customers should he sample to get an accurate probability?
a) 3 customers
b) 10 customers
c) 100 customers
d) 1000 customers
Answer:
c) 100
Step-by-step explanation:
This is the best choice because the number is not too low or too high. He will get an accurate probability.
Which graph represents the solution set for the system x+y greater than or equal to 5 and -3x+2y less than or equal than to -2
Step-by-step explanation:
in each equation once substitute the value of x as 0 and again y as zero by this way you will get two values of X and y .
then again find the slope for each equation by the formula
slope= -coefficient of x / coefficient of y
for example,
X+y is greater or equals to 5
or, X+y= 5
or, X=5-y
or, when y is equals to zero
X= 5
and when X is equals to zero
y= 5
then plot the above point in the graph with respect to its slope and the shaded part is the solution
X^4 -33x^2-108 which of the following is equal to the polynomial given above? A. (X+36)(x+v3i)(x-3) B. (X-36)(x+v3i)(x+3)
Answer:
Answer D I believe :)
Step-by-step explanation:
x^4-33x^2-108
rewrite as a difference
x^4+3x^2-36x^2-108
factor out x^2
x^2(x^2+3)-36x^2-108
factor out -36
x^2(x^2+3)-36(x^2+3)
factor out x^2+3
(x^2+3)(x^2-36)
factor x^2-36
(x^2+3)(x-6)(x+6)
set x^2+3 equal to 0
x^2+3=0
solve for x
x=+/-[tex]\sqrt{3}[/tex]i
set at factors
(x+6)(x-6)(x+[tex]\sqrt{3}[/tex]i)(x-[tex]\sqrt{3}[/tex]i)
I hope this helps.
A Prince came to an Evil Wizard to ask for the release of his beloved Princess, who is locked behind one of three doors. The Evil Wizard offered to release the Princess if the Prince was able to correctly guess which door she was behind. And with this offer, the Evil Wizard gave three hints: 1) The Princess is locked behind door 1 2) A fire-breathing Dragon is locked behind door 2. 3) There is also someone locked behind door 3 The Prince realized that all three hints were false, and with the help of logic, understood which door the Princess was locked behind. Which door was it?
Answer:
Princess is behind 2
Step-by-step explanation:
If all 3 hints are false, then the princess is not behind 1 ( so it must be 2 or 3)
The dragon is not behind 2 ( so it must be 1 or 3)
The is no one behind 3
That means the princess cannot be behind 3 and the dragon cannot be behind 3
The princess is behind 2 and the dragon is behind 1
x=y-y and 2x+4y=10 solve using substitution
Answer:
(0, 2.5)
Step-by-step explanation:
Well we substitute y-y into x in the following equation,
2x + 4y = 10
2(y-y) + 4y = 10
2y - 2y + 4y = 10
Combine like terms
2y - 2y = 0
4y = 10
10/4
y = 2.5
If y is 2.5 we can plug those into y.
2x + 4(2.5) =10
2x + 10 = 10
-10
2x = 0
0/2
x = 0
32. Mariah bought a shirt for $28.50 and a
belt. The total cost was $45.50. Which
of the following equations can be used
to find the cost of the belt?
A 28.50 +b=45.50
B 45.50 + b = 28.50
Cb= 28.50 - 45.50
D b= 28.50 x 45.50
Answer:
The correct answer is A because subtract 28.50 from 45.50 and you get the answer of 17$ for the belt
PLEASE HELP ILL GIVE BRAINLIEST!!
What is the solution to this system of equations?
Answer:
B. (4.75,-22)
Step-by-step explanation:
Step: Solve 3.2x+0.5y=4.2for x:
3.2x+0.5y=4.2
3.2x+0.5y+−0.5y=4.2+−0.5y(Add -0.5y to both sides)
3.2x=−0.5y+4.2
3.2x
3.2
=
−0.5y+4.2
3.2
(Divide both sides by 3.2)
x=−0.15625y+1.3125
Step: Substitute−0.15625y+1.3125 for x in−1.6x−0.5y=3.4:
−1.6x−0.5y=3.4
−1.6(−0.15625y+1.3125)−0.5y=3.4
−0.25y−2.1=3.4(Simplify both sides of the equation)
−0.25y−2.1+2.1=3.4+2.1(Add 2.1 to both sides)
−0.25y=5.5
−0.25y
−0.25
=
5.5
−0.25
(Divide both sides by -0.25)
y=−22
Step: Substitute−22 for y in x=−0.15625y+1.3125:
x=−0.15625y+1.3125
x=(−0.15625)(−22)+1.3125
x=4.75(Simplify both sides of the equation)
One polygon has a side of length 3 feet. A similar polygon has a corresponding side of length 9 feet. The ratio of the perimeter of the smaller polygon to the larger is
Answer:
1:3
Step-by-step explanation:
9/3 = 3
3 is the scale factor
What is the simplified form of m-4+m
Answer:
2m - 4
Step-by-step explanation:
Add m and m.
Hope this helps :)
Answer:
[tex]\boxed{2m+4}[/tex]
Step-by-step explanation:
[tex]m-4+m[/tex]
Combine like terms.
[tex]m+m-4[/tex]
[tex]2m-4[/tex]
Identify whether the relations given in the options are functions or not.
Answer:
Graphs 1, 2, and 3 are not functions. Graph 4 is a function.
Step-by-step explanation:
Use the vertical line test.
Imagine a vertical line moving from left to right.
If in any position of the vertical line, it intersects more than one point on the graph, then it is not a function.
In graphs 1 and 2 it is clear that there are many vertical lines than would intersect the graph at more than one point.
In graphs 3, a vertical line would intersect the vertical parts of the graph at more than 1 point, so graph 3 is not a function.
The only function is graph 4.
The relations given in options 1, 2, and 3 are not functions only Graph 4 is a function.
What is the function?A function is an expression, or rule that defined the relation between two variables.
If we use the vertical line test.
Imagine a vertical line moving from left to right.
If in any position of the vertical line, it intersects more than one point on the graph, then it is not a function.
In graphs 1 and 2 it is clear that there are many vertical lines than would intersect the graph at more than one point.
In graph 3, a vertical line would intersect the vertical parts of the graph at more than 1 point, so graph 3 is not a function.
Learn more about function here;
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The height of a right rectangular prism is 3 units greater than the length of the base. The edge length of the square base is x units.
Which expression represents the volume of the prism, in cubic units?
x3 + 9
x3 + 3x2
x3 + 3x + 3
x3 + 6x2 + 9x
Answer:
B. x^3 + 3x^2
Step-by-step explanation:
Volume of a rectangular prism=width * length * height
V=w*l*h
h=3 greater than the length of the base
h=x+3
Length of the base=x
Width=x
Substituting values into the formula
V=w*l*h
=(x)*(x)*(x+3)
Multiplying
=(x^2)(x+3)
=x^3 + 3x^2
Option B is the correct answer
The expression [tex]x^3 + 3x^2[/tex] represents the volume of the prism, in cubic units.
We have given that the,
The height of a right rectangular prism is 3 units greater than the length of the base.
The edge length of the square base is x units.
What is the volume of rectangular prism?[tex]Volume of a rectangular prism=width * length * height[/tex]
[tex]V=w*l*h[/tex] ......(1)
We have given that the
h=3 greater than the length of the base
and length of the base is x
Hence, [tex]h=x+3[/tex]
[tex]Length of the base=x[/tex]
[tex]Width=x[/tex]
Substituting values l h and w into the formula (1) we get,
[tex]V=w*l*h[/tex]
[tex]=(x)*(x)*(x+3)[/tex]
[tex]=(x^2)(x+3)[/tex]
[tex]=x^3 + 3x^2[/tex]
Therefore the expression
[tex]x^3 + 3x^2[/tex]
represents the volume of the prism, in cubic units.
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*HELP* Select the correct answer. What is the value of this expression when t = -12? -3|t − 8| + 1.5 A. 61.5 B. 13.5 C. -10.5 D. -58.5
Answer: D
Step-by-step explanation:
If we substitute -12 into this equation we get:
[tex]-3[-12-8]+1.5[/tex]
[tex]-3[-20]+1.5[/tex]
Because -20 is in absolute value, we simply just use 20.
Thus,
[tex]-3(20)+1.5\\= -60+1.5\\= -58.5[/tex]
Answer:
D
Step-by-step explanation:
Classify the following triangle. Check all that apply.
A. Obtuse
B. Isosceles
C. Scalene
D. Equilateral
E. Acute
F. Right
Answer:
isosceles
Step-by-step explanation:
which is the equation of a line that passes through the point (3,2) and is parallel to the line in the graph?
Answer:
A. 3x - 2y = 5
Step-by-step explanation:
Given line in the graph has the following properties:
using point (2,3)
m = slope = (y2-y1)/(x2-x1) = (5-2)/(2-0) = 3/2
New line passes through y0(3,2), so use the point-slope form
(y-y0) = m (x-x0)
substitute in value y0(3,2)
y - 2 = (3/2) (x - 3)
multiply by 2 on each side
2y - 4 = 3x - 9
simplify and rearrange
3x - 2y = -4 + 9 =5
3x - 2y = 5
Find the slope and y-intercept of each line:
a. (x+2)(x+3)=(x-2)(x-3)+y
b. x=my+b
Please show workings, and I won't accept nonsense answers! Don't answer the question if you don't know what it means!!
Answer:
See below
Step-by-step explanation:
Part A:
[tex](x+2)(x+3) = (x+2)(x-3) + y[/tex]
Resolving Parenthesis
[tex]x^2+3x+2x+6=x^2-3x-2x+6+y\\x^2+5x+6 = x^2-5x+6+y[/tex]
Subtracting [tex]x^2[/tex] and 6 to both sides
[tex]5x= -5x+y[/tex]
Adding 5x to both sides
[tex]y = 5x+5x\\y = 10x[/tex]
Comparing it with [tex]y = mx+b[/tex] where m is the slope while b is the y-intercept
So,
Slope = m = 10
Y-intercept = b = 0
Part B:
[tex]x = my+b[/tex]
Subtracting b to both sides
[tex]my = x-b[/tex]
Dividing both sides by m
[tex]y = \frac{x-b}{m}\\ y = \frac{x}{m} - \frac{b}{m}[/tex]
Comparing it with [tex]y = mx+b[/tex] where m is the slope while b is the y-intercept
So,
Slope = m = [tex]\frac{1}{m}[/tex]
Y-intercept = b = [tex]-\frac{b}{m}[/tex]
Si tienes 24 tubos de 6 metros de longitud cada uno para unir dos puntos que conducen agua , si los tubos fueran de 8 metros ¿ cuantos tubos se necesitarían?
Answer:
Se necesitarían:
18 tubos
Step-by-step explanation:
La longitud total de la tubería con 24 tubos de 6 metros cada uno es:
24*6 = 144 metros
si los tubos fuesen de 8 metros:
144/8 = 18
Se necesitarían:
18 tubos
The surface area of a cube is 24 square inches What us the side length of the cube ?
A=24in² this th ans because the side of cube is 24 cm
Rewrite [tex]\frac{200x - 300}{x}[/tex] as a sum of two fractions, and simplify.
Answer:
We can rewrite this as [tex]\frac{200x}{x} + \frac{-300}{x}[/tex].
[tex]\frac{200x}{x}[/tex] simplifies to 200 after eliminating x from the numerator and denominator and [tex]\frac{-300}{x}[/tex] becomes [tex]-\frac{300}{x}[/tex] so the final answer is [tex]200 - \frac{300}{x}[/tex].
A stone is dropped from the upper observation deck of a tower, 600 m above the ground. (Assume g = 9.8 m/s2.) (a) Find the distance (in meters) of the stone above ground level at time t. (b) How long does it take the stone to reach the ground? (Round your answer to two decimal places.) (c) With what velocity does it strike the ground? (Round your answer to one decimal place.) Remember that velocity requires direction. (d) If the stone is thrown downward with a speed of 7 m/s, how long does it take to reach the ground? (Round your answer to two decimal places.)
Answer:
a) [tex]D = 600 -4.9t^2[/tex]
b) 11.06 seconds
c) 108.39 m/s
d) 10.37 m/s
Step-by-step explanation:
Given:
Distance, s = 600 m
Acceleration, a = g = 9.8 [tex]m/s^2[/tex]
a) Distance of stone above ground level at time 't'.
First of all, we need to find the distance traveled in time 't' and then we will subtract it from 600 to find the answer.
The formula is given as:
[tex]s=ut+\dfrac{1}{2}at^2[/tex]
where u is the initial velocity which is 0 in this case.
[tex]s=0\times t+\dfrac{1}{2}\times 9.8 \times t^2\\s =4.9t^2[/tex]
Distance of stone above ground level at time 't',
[tex]D = 600 -4.9t^2[/tex]
b) Time taken by stone to reach the ground. i.e. D = 0
Using above equation, putting D = 0
[tex]0 = 600 -4.9t^2\\\Righttarow 4.9t^2 = 600\\\Rightarrow t = \sqrt{\dfrac{6000}{49}} = 11.06\ sec[/tex]
c) Velocity with which it strikes the ground i.e. [tex]v=?[/tex]
Using the formula:
[tex]v=u+at[/tex]
[tex]v = 0 +9.8 \times 11.06\\v = 108.39\ m/s[/tex]
d) If initial velocity, u = 7 m/s, time taken to reach the ground = ?
In this case total distance traveled = 600 m
[tex]s=ut+\dfrac{1}{2}at^2[/tex]
[tex]600=7 t+\dfrac{1}{2}\times 9.8t^2\\\Rightarrow 600=7 t+4.9t^2\\\Rightarrow 4.9t^2+7 t-600=0\\\Rightarrow 49t^2+70 t-6000=0[/tex]
Solving the above equation:
t = 10.37 seconds
The answers are:
a) [tex]D = 600 -4.9t^2[/tex]
b) 11.06 seconds
c) 108.39 m/s
d) 10.37 m/s
A) The distance (in meters) of the stone above ground level at time t is; d(t) = 600 - 4.9t²
B) The time it takes the stone to reach the ground is; t = 11.07 seconds
C) The velocity at which the stone strikes the ground is; v = -108.486 m/s
D) The time it takes to reach the ground when thrown downwards with a speed of 7 m/s is; t = 10.37 s
A) Using Newton's 2nd equation of motion, we have;
d(t) = d_o + ut - ½gt²
Plugging in the relevant values, we have;
d(t) = 600 + 0(t) - 0.5(9.8)t²
d(t) = 600 - 4.9t²
B) The time it takes for the stone to reach the ground is when d(t) = 0. Thus;
0 = 600 - 4.9t²
4.9t² = 600
t² = 600/4.9
t = √(600/4.9)
t = 11.07 seconds
C) Velocity at which is strikes the ground will be gotten from Newton's first equation of motion;
v = u - gt
v = 0 - (9.8 × 11.07)
v = -108.486 m/s
D) The stone is thrown downwards with a speed of 7 m/s.
Thus;
600 - 7t - 0.5(9.8t²) = 0
-4.9t² - 7t + 600 = 0
Using online quadratic equation solver gives;
t = 10.37 s
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Evaluate the following expression using the given values: (1 point) Find x − 3y if x = 3 and y = −2.
Answer:
9
Step-by-step explanation:
x − 3y
Let x =3 and y = -2
3 -3(-2)
3 + 6
9