Answer:
cos(2x)
Step-by-step explanation:
The simplified expression is
How to evaluate trigonometric expression?
A Trigonometric expression consists of sin, cos and various other parameters which can be simplified using identities.
Given expression:
cos(x){cos(x)-tan(x)sin(x)}
Evaluation:
[tex]cos(x)(cos(x)-\dfrac{ sin(x)*sin(x)}{cos(x)})[/tex]
[tex]cos(x)(\frac{cos^{2} x-sin^{2}x}{cos(x)} )[/tex]
[tex]cos^{2}x-sin^{2}x[/tex]
[tex]cos2x[/tex]
Therefore, the given expression simplifies to cos2x.
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John was visiting four cities that form a rectangle on a coordinate grid at A(0, 4), B(4, 2), C(1, -4) and D(-3, -2). What is the area of the space that cities enclose? Round your answer to the nearest whole number. Do not include units in your answer.
Answer:
[tex]Area = 30[/tex]
Step-by-step explanation:
Given
Rectangle coordinates
[tex]A = (0,4)[/tex]
[tex]B = (4,2)[/tex]
[tex]C = (1,-4)[/tex]
[tex]D =(-3,-2)[/tex]
Required
The area of the rectangle
The area is calculated as:
[tex]Area = Length* Width[/tex]
The length of the rectangle will be represented as:
[tex]Length = AB = CD[/tex]
And the width is:
[tex]Width = BC = AD[/tex]
Calculate distance AB using:
[tex]AB = \sqrt{(x_1 - x_2)^2 +(y_1 - y_2)^2 }[/tex]
Where:
[tex]A = (0,4)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]B = (4,2)[/tex] [tex]--- (x_2,y_2)[/tex]
[tex]AB = \sqrt{(0 - 4)^2 +(4 - 2)^2 }[/tex]
[tex]AB = \sqrt{(- 4)^2 +(2)^2 }[/tex]
[tex]AB = \sqrt{16 +4 }[/tex]
[tex]AB = \sqrt{20}[/tex]
Calculate distance BC using:
[tex]BC = \sqrt{(x_1 - x_2)^2 +(y_1 - y_2)^2 }[/tex]
[tex]C = (1,-4)[/tex] [tex]---(x_1,y_1)[/tex]
[tex]B = (4,2)[/tex] [tex]--- (x_2,y_2)[/tex]
[tex]BC = \sqrt{(1 - 4)^2 +(-4 - 2)^2 }[/tex]
[tex]BC = \sqrt{(- 3)^2 +(-6)^2 }[/tex]
[tex]BC = \sqrt{9 +36}[/tex]
[tex]BC = \sqrt{45}[/tex]
So, the area is:
[tex]Area = Length * Width[/tex]
[tex]Area = AB * BC[/tex]
[tex]Area = \sqrt{20} * \sqrt{45}[/tex]
[tex]Area = \sqrt{20 * 45}[/tex]
[tex]Area = \sqrt{900[/tex]
[tex]Area = 30[/tex]
Find the length of the hypotenuse. Round your
answer to the nearest hundredth.
A. 11.00
B. 9.95
C. 8.06
D. 3.32
HELP NOW PLEASE !!!!!
Answer:
C: 8.06
Step-by-step explanation:
c=a^2+b^2=42+72≈8.06226
Answer:
8.06
Step-by-step explanation:
C2= a2+ b2
C2= 7 squared + 4 squared
C2= 49+16
C2=65
C is the square root of c2
square root 65
C= 8.06
c= 8
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Answeryou need to write your question better
Which expression is equivalent to x with the power of 2 +2x+2?
Answer:
The answer is the fourth one
Step-by-step explanation:
5. To prove that triangle PQR is isosceles, a student began by stating that
since Q is on the segment perpendicular to PR, Q is equidistant from the
endpoints of PR. What is the error in the student's reasoning ?
A yacht is anchored 90 feet offshore from the base of a lighthouse. The angle of elevation from the boat to the top of the lighthouse is 26 degrees . The distance between the yacht and the top of the lighthouse is about 100 feet. Which of these is nearest to the height of the lighthouse ?
Pls solve this I will give more points
Answer:
x=4
Step-by-step explanation:
7(2x+8)=4(28)
14x+56=112
14x=112-56
14x=56
x=4
determine if the given shapes are polygons or not if polygons name the classification according to sides
Rewrite the equation by completing the square.
f(x)=x^2+x-30
f(x)=_(x+_)^2+_
pls helppppp
Answer:
f(x)= (x-5)(x+6)
Step-by-step explanation:
First, we find the factors of -30 that add up to +1
We can use 6 and -5
6+(-5)=1
f(x)= x^2+6x - 5x-30
then, we do group factorization
f(x)= x(x+6)- 5(x+6)
f(x)= (x-5)(x+6)
i hope this helps <3
Can someone help me with this figure? I cannot figure out its area.
Answer:
85.13 inches^2 (2dp)
Step-by-step explanation:
Area semi circle:
πr^2/2
π * 4^2 / 2
25.1327412
Area parallelogram
bh
b x h
10 x 6 = 60
60 + 25.1327412 = 85.1327412
A weight of 270 pounds falls
A. Below the 3rd quartile
B.between the 1st and 2nd quartile
C.between the 2nd and 3rd quartile
D.above the 3rd quartile
Answer:
D
Step-by-step explanation:
above the third quartile. because it is upper 25% of the data.
Answer:
C.between the 2nd and 3rd quartile
what equation is solved by graphed systems of equations
Answer:
its 7x+3=x-3
Step-by-step explanation:
it is
A cylinder with radius 333 units is shown below. Its volume is 86 cubic units.
Find the height of the cylinder.
Use 3.143.143, point, 14 for \piπpi and round your final answer to the nearest hundredth.
Answer:
3.04 units
Step-by-step explanation:
h = volume / (3.14 x r^2)
86 / (3.14 x 3^3) = 3.04 units
A triangular prism and its dimensions are shown in the
diagram. What is the lateral surface area of this triangular
prism in square centimeters?
Select one
192cm?
144cm?
0
128cm
O
152cm
Consider this equation.
cos(θ) = 4sqrt41/41
If θ is an angle in quadrant IV, what is the value of sin(θ) ?
Answer:
A. -5√41/41Step-by-step explanation:
Let the horizontal leg = 4√41 and the hypotenuse = 41 as
cosine = adjacent leg / hypotenuse.Then the vertical leg is:
√(41² - 16*41) = √25*41 = 5√41Since the vertical leg is below the x-axis, its value is -5√41
Then we have:
sin (θ) = -5√41/41Correct choice is A
Answer:
Step-by-step explanation: i just take the test
Tenemos 2000 baldosascon las que nos proponrmos embaldosar dos habitaciones.Para la 1ª gastamos 3/5 de ellas,y con la 2ª,3/4de las que qudaron.¿Cuántas utilizamos para cada habitación y cuántas sobraron?
Answer:
En la primera habitación son usadas 1200 baldosas.
En la segunda habitación son usadas 600 baldosas.
Sobraron 200 baldosas.
Step-by-step explanation:
Tienes 2000 baldosas, con las que se propone embaldosar dos habitaciones.
Para la primera habitación se han gastado [tex]\frac{3}{5}[/tex] de las baldosas. Esto se expresa como:
[tex]\frac{3}{5}*2000[/tex]
Para multiplicar una fracción por un número entero, el número entero n se puede escribir como la fracción [tex]\frac{n}{1}[/tex]. Luego se multiplica los numeradores y denominadores. En este caso:
[tex]\frac{3}{5}*2000=\frac{3}{5}*\frac{2000}{1} =\frac{3*2000}{5*1} = \frac{6000}{5}[/tex]
Para reducir la fraccion, divide 40 entre 10
[tex]\frac{6000}{5} =[/tex] 6000 ÷5= 1200
Entonces en la primera habitación son usadas 1200 baldosas. Por lo que las que quedan se calcula como:
2000 - 1200= 800 baldosas
De esta cantidad de baldosas que quedaron, [tex]\frac{3}{4}[/tex] son usadas para embaldosar la segunda habitación. Esto se expresa como:
[tex]\frac{3}{4}*800[/tex]
Resolviendo de igual manera que en el caso de la primer habitación se obtiene:
[tex]\frac{3}{4}*800=\frac{3}{4}*\frac{800}{1} =\frac{3*800}{4*1} =\frac{2400}{4}[/tex]= 2400 ÷ 4= 600
Entonces en la segunda habitación son usadas 600 baldosas. Por lo que, teniendo en cuenta que se tenían 800 baldosas que quedaron de la primera habitación, las baldosas restantes se calculan como:
800 - 600= 200 baldosas
Sobraron 200 baldosas.
Can you guys help me with this?
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the concept of Angles.
Here we apply the concept of the Adjacent angles and linear pair of the angles.
1.) Angle 1 = 90° and Angle 2 = 60°
2.) Angle 4 = 90° and Angle 3 = 70°
3.) Angle 6 = 90° and Angle 5 = 65°
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
Answer:
The numbers are blurry on the graph
N-
Question 4
Indicate the answer choice that best completes the statement or answers the question,
Triangle XYZ has vertices X(4,2), Y(4,4), and Z(0, 2).
13
У
Y(4.4)
16
7
18
19
2 (0,24
X(4,2)
10
X
What are the coordinates of the image of point Y after a reflection over the y-axis?
Oa. Y'(4.4)
Ob. Y(4,-4)
Oc. Y'(-4,4)
Od. Y(0,2)
Answer:
The answer is (0, 2)
Step-by-step explanation:
Ive also had this question and viewed iver it and said it was right this was some time ago but im glad to help :)
The triangles below are similar.
Answer:
Step-by-step explanation:
Answer:
ΔFGH ~ ΔKLJStep-by-step explanation:
Determine the corresponding sides by the same opposite angles.
Opposite sides to 24° angle are FG and KL.
Correct expression is A:
ΔFGH ~ ΔKLJHey can you help me fast!!! I will give brain list if the Answer is right!
Answer:
-6.5cm/s
Step-by-step explanation:
-19.5/3
The same-side interior angles formed when two parallel lines cut by a transversal are 45° and x. Find x. a 45° b 90° c 135° d 180°
Answer: b
Step-by-step explanation:
Rewrite as equivalent rational expressions with denominator (x+3)(x−4)(x+4)
An equivalent rational expressions with denominator (x+3), (x−4) and (x+4) is (3x²+6x-16)/(x³+3x²-16x-48).
The given denominator are (x+3), (x−4) and (x+4).
What is a rational expressions?A mathematical expression that may be rewritten to a rational fraction, an algebraic fraction such that both the numerator and the denominator are polynomials.
Here, an equivalent rational expressions is
[tex]\frac{1}{x+3}+\frac{1}{x-4} +\frac{1}{x+4}[/tex]
The LCM of denominators is (x+3)(x-4)(x+4)
= (x+3)(x²-16)
= x(x²-16)+3(x²-16)
= x³-16x+3x²-48
= x³+3x²-16x-48
Now, [tex]\frac{(x-4((x+4)+(x+3)(x+4)+(x+3)(x-4)}{x^3+3x^2-16x-48}[/tex]
= (x²-16+x²+7x+12+x²-x-12)/(x³+3x²-16x-48)
= (3x²+6x-16)/(x³+3x²-16x-48)
Hence, an equivalent rational expressions with denominator (x+3), (x−4) and (x+4) is (3x²+6x-16)/(x³+3x²-16x-48).
Learn more about the rational expressions here:
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Given that x = 7.4 m and 0 = 26°, work out AB rounded to 3 SF.
B
o
A
С
x х
The diagram is not drawn accurately.
AB =
m
Answer:
3.24m
Step-by-step explanation:
SOH
sin(26)=O/7.4
O=7.4 sin(26)
O=3.24 (3sf)
Naomi is going to drive from her house to City A without stopping. Let D
represent Naomi's distance from City A t hours after leaving her house. A
graph of D is shown below. Write an equation for D then state the slope of
the graph and determine its interpretation in the context of the problem.
Answer:
I'm not sure of the answer
The price of a 32 pack of water at heb is $2.98. The tax rate is 8% what is the final cost of the water
Answer:
The final cost of the water is $3.22.
Step-by-step explanation:
In order to find the answer, you have to add the tax to the price of the 32 pack of water by calculating 8% of the price and adding that amount to it.
2.98*8%=0.24
2.98+0.24=3.22
According to this, the answer is that the final cost of the water is $3.22.
When rolling a die, determine the probability of rolling a number greater than 4.
a. Which outcome or outcomes make up the event of rolling a number greater than 4?
Answer:
The probability that the result of one die roll is greater than 4 is the number of events in set A divided by the total number of possible outcomes (the size of the sample space S) and so the probability of getting a number greater than 4 on one die roll is 2/6 which reduces to 1/3 .
Step-by-step explanation:
Assuming you mean “greater”, rather than “greater than or equal to”, the “successful” rolls are 5 and 6. That’s two out of six choices, so the probability is 2/6 or 1/3.
It gets more interesting when you want the total of several dice to be above a certain number, or to get that number on M of N dice rolls.
But the two basic probability formulas work - 1) add up all possible successful results and all possible results, then divide the number of successes into the total. 2) Multiply all the failure probabilities together, then subtract the result from 1 (100%) to get the success probability. With these two rules, you can solve most simple probability problems.
Playing D&D, and want to know the chance of scoring a 17 or 18 total when rolling 3 dice? You can only get an 18 one way - 6 6 6. You can get a 17 three ways - 6 6 5, 6 5 6, or 5 6 6. So that’s 4 chances out of 6 x 6 x 6 possibilities, which is 216. That’s about 1.85%. With quite a bit more work, you can discover the chance of getting a 17 or better when rolling 4 dice and adding the 3 highest.
which transformation(s) must map the square exactly onto itself? choose all that apply.
Answer:
Step-by-step explanation:
The first four
Two numbers have these properties Both numbers are greater than 8 The HCF is 8 The LCM is 80 Find the two numbers
Answer:
10 and 64.
16 and 40
Step-by-step explanation:
The product of the two numbers is equal to the product of LCM and HCF
Number 1* Number 2= LCM * HCF
Number 1* Number 2= 8*80
Number 1* Number 2= 640
Both the numbers are greater than 8. Suppose one number is 10 then the other number will be 640 ÷ 10= 64
so the two numbers will be 10 and 64.
Similalrly the two numbers can also be 16 and 40 and like wise.
Any number greater than 8 dividing 640 will give the second number also.
Which function describes the vertical shift up 2 units and left 2 units to the original function: f(x) = ex
Answer:
g(x) = e^(x + 2) + 2
Step-by-step explanation:
First, let's describe the shifts.
Vertical shift.
For a function f(x), a vertical shift of N units is written as:
g(x) = f(x) + N
If N is positive, then the shift is upwards.
If N is negative, then the shift is downwards.
Horizontal shift.
For a function f(x), a horizontal shift of N units is written as:
g(x) = f(x - N)
If N is positive, the translation is to the right
If N is negative, the translation is to the left.
Now let's solve the question.
f(x) = e^x
First, we have a vertical shift up of 2 units, then:
g(x) = f(x) + 2
Now we have a shift to the left of 2 units:
g(x) = f(x - (-2)) + 2
g(x) = f(x + 2) + 2
Then:
g(x) = e^(x + 2) + 2