Answer:
[tex] \rm\cos({600}^{ \circ} ) =-1/2 [/tex]
Step-by-step explanation:
we would like to solve the following using double-angle formula:
[tex] \displaystyle \cos( {600}^{ \circ} ) [/tex]
there're 4 double Angle formulas of cos function which are given by:
[tex] \displaystyle \cos(2 \theta) = \begin{cases} i)\cos^{2} ( \theta) - { \sin}^{2}( \theta) \\ii) 2 { \cos}^{2}( \theta) - 1 \\iii) 1 - { \sin}^{2} \theta \\ iv)\dfrac{1 - { \tan}^{2} \theta}{1 + { \tan}^{2} \theta } \end{cases}[/tex]
since the question doesn't allude which one we need to utilize utilize so I would like to apply the second one, therefore
step-1: assign variables
to do so rewrite the given function:
[tex] \displaystyle \cos( {2(300)}^{ \circ} ) [/tex]
so,
[tex] \theta = {300}^{ \circ} [/tex]Step-2: substitute:
[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2 \cos ^{2} {300}^{ \circ} - 1[/tex]
recall unit circle thus cos300 is ½:
[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2 \left( \dfrac{1}{2} \right)^2 - 1[/tex]
simplify square:
[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2\cdot \dfrac{1}{4} - 1[/tex]
reduce fraction:
[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = \dfrac{1}{2} - 1[/tex]
simplify substraction and hence,
[tex] \rm\cos({600}^{ \circ} ) = \boxed{-\frac{1}{2}}[/tex]
The measures of two angles of a triangle are 36 degree and 75 degree . The length of the shortest side of a triangle is 10 cm . The length of longest side of the triangle is:?
Abby made the following conjecture: The sum of a multiple of 7 and a multiple of 8 will be an
odd number. Do you agree or disagree? Briefly justify your decision with a counterexample if
possible.
Answer:
Disagree. As long as the odd number (7) is multiplied by an even number, the sum of multiples of an odd and even number in general will add to be even.
Step-by-step explanation:
Assume you have a=7 and b=8.
Now there are 4 combinations since there are only two types of numbers: even and odd.
Combination 1 would consist of an ODD amount of multiples of a, and and ODD amount of multiples of b.
See: 3a + 3b
3(7) + 3(8) = 45
*Combination 2 would be an EVEN amount of a and an EVEN amount of b.
2a + 2b
14 + 16 = 30
HERE, in combination 2, the claim is already debunked.
Combination 3 is an ODD amount of a and an EVEN amount of b
1a + 2b
7 + 16 = 21
*Combination 4 is an EVEN amount of a and an ODD amount of b
2a + 1b
14 + 8 = 24
HERE, in combination 4, the claim is justified again
What is the sum of the angles 'a' and 'b' from the diagram below.
Answer:
90+ 135= 225
Step-by-step explanation:
a can be found with formula (n-2)×180/n, where n is number of sides
a= 135
b=90
The graph of a line is shown below. What is the equation of the line, in slope-intercept form, that is parallel to this line and has a y-intercept of 1?
Answer:
[tex]y = - \frac{3}{2} x + 1[/tex]
Step-by-step explanation:
Slope -intercept form: y= mx +c, where m is the slope and c is the y-intercept.
Parallel lines have the same slope. Let's find the slope of the given line.
Given points: (-2, 0) and (0, -3)
[tex]\boxed{slope = \frac{y1 - y2}{x1 - x2} }[/tex]
slope of given line
[tex] = \frac{0 - ( - 3)}{ - 2 - 0} [/tex]
[tex] = \frac{0 + 3}{ - 2} [/tex]
[tex] = - \frac{3}{2} [/tex]
[tex]y = - \frac{3}{2} x + c[/tex]
Given that the y- intercept is 1, c= 1.
[tex]y = - \frac{3}{2} x + 1[/tex]
Which of the following is equal to the fraction (4/5)^6 A. 6•(4/5)
В.4^6/5^6
С. 4^6/5
D. 24/30
Answer:
b
Step-by-step explanation:
when raising a fraction to a power both the numerator and denominator has to be raised to that power
The diameter of a circle is 12 m. Find its area in terms of pi
Answer:
36 pi m^2
Step-by-step explanation:
The diameter of a circle is 12
The radius is 1/2 of the diameter, d/2 = 12/2 = 6
The area of a circle is given by
A = pi r^2
A = pi (6)^2
A = 36 pi m^2
The area under the standard normal curve to the right of z = -0.51 is 0.6950. What is the area to the left of z = 0.51?
Answer:
0.305
Step-by-step explanation:
We are told that area under the standard normal curve to the right of z = -0.51 is 0.6950
Thus, to get the area to the left, we just subtract 0.6950 from 1.
Thus;
area to the left of z = 0.51 is;
P( z < 0.51) = 1 - 0.6950 = 0.305
find the value of trigonometric ratio
Answer:
We know that Sin,
[tex]=\frac{perpendicular}{hypotenuse}[/tex]
[tex]SinA=\frac{BC}{AC}[/tex]
[tex]SinA=\frac{9}{41}[/tex]
OAmalOHopeO
Answer problem below
Answer:
A = 2, B = 1, C = 28Step-by-step explanation:
Find the slope of the line AB.
The slope:
m = (11 - 9)/(11 - 7) = 2/4 = 1/2Since the altitude is perpendicular to AB, it has a slope of -2.
The line with the slope of -2 and passes through point C(6, 16).
Use point-slope equation to find the line:
y - 16 = -2(x - 6)y - 16 = -2x + 12y + 2x = 16 + 122x + y = 28A = 2, B = 1, C = 28
Answer:
Solution given:
A(7,9)
B(11,11)
C(6,16)
Slope of AB=[tex]\frac{11-9}{11-7}=\frac{2}{4}=½[/tex]
since altitude is perpendicular to it .
so its slope becomes negative reciprocal to the slope of base
so
slope of altitude(m) =-2
now
equation of a line passing through C(6,16) perpendicular to its base is:
By using formula
[tex]y-y_{1}=m(x-x_{1})[/tex]
y-16=-2(x-6)
solve it
y-16=-2x+12
y+2x=12+16
in the form of Ax +By=C is:
2x+y=28
:.
A=2B=1
C=28
A recipe for eight flapjacks needs 2oz of butter, 3oz of sugar, and 4 oz of rolled oats. How many flapjacks can I make if I have 14 oz of butter, 15 oz of sugar, and 16 oz of rolled oats?
Answer:
Step-by-step explanation:
Eight flapjacks
2oz of butter
3oz of sugar
4 oz of rolled oats.
Each flapjack
Butter = 2/8 = 1/4 oz
Sugar = 3/8 oz
Rolled oats = 4/8 = 1/2 oz
How many flapjacks can I make if I have
14 oz of butter,
15 oz of sugar, and
16 oz of rolled oats?
Butter
= 14 oz ÷ 1/8 oz
= 14 × 8/1
= 112 flapjack
Sugar
= 15 oz ÷ 3/8 oz
= 15 × 8/3
= 120/3
= 40 flapjacks
Rolled oats
16 oz ÷ 1/2 oz
= 16 × 2/1
= 32 flapjack
Therefore,
Considering the quantity of rolled oats available, the number of flapjacks that could be made is 32
Determine what type of transformation is represented. A. translation B. reflection C. none of these D. rotation
Answer:
D. rotation
uhhhh I need 20 characters so
Rotation is correct because the triangle ABC is rotated about the mid-point of B and B'. Then the correct option is D.
What is a transformation of geometry?A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.
Reflection does not change the size and shape of the geometry. But flip the image.
Rotation does not change the size and shape of the geometry. But change the orientation of the image.
Translation does not change the size and shape of the geometry. But change the location of the shape.
Check all the options.
Translation is incorrect because orientation of the triangle is changed.
Reflection is incorrect because the line of the reflection is not possible for the triangles.
Rotation is correct because the triangle ABC is rotated about the mid-point of B and B'.
Then the correct option is D.
More about the transformation of geometry link is given below.
https://brainly.com/question/22532832
#SPJ5
find the missing length for the following trapezoid
Answer:
KL = 18
Step-by-step explanation:
The midsegment TU is half the sum of the parallel bases , that is
[tex]\frac{KL+JM}{2}[/tex] = TU
[tex]\frac{KL+34}{2}[/tex] = 26 ( multiply both sides by 2 )
KL + 34 = 52 ( subtract 34 from both sides )
KL = 18
Pleassse help with this
The length of a rectangle is 10 feet longer than it is wide. If each side is increased 10 feet, then the area is multiplied by 2. What was the size of the original rectangle?
Answer:
Size of the original rectangle is 30*20=600
Step-by-step explanation:
Let the length and width of rectangle be x+10 and x. After increasing the dimensions, the new length and width are x+20 and x+10
ATQ, (x+20)(x+10)=2(x+10)(x), x=20.
which of the following one is true
Kathryn plants two different types of tomato plant. She records the number of tomatoes that she picks from each plant every day. Her records are shown below:
Plant A: 4, 6, 7, 3, 5, 2, 1, 3, 6, 5
Plant B: 5, 6, 7, 6, 8, 9, 6, 7, 7, 9
Which plant has the more consistent yield of tomatoes?
Answer:
plant B
Consistent means better so plant be had more better yields
Rectangle ABCD is similar to rectangle JKLM. AB = 12, BC = 8, CD = 12, DA = 8, and JK = 15. What is the scale factor from JKLM to ABCD? Reduce all answers.
Answer:
4/5 or 0.8
Step-by-step explanation:
this problem description is not very precise. it leaves out the definition what corners or sides of JKLM correspond to corners and sides of ABCD.
I assume J and K correlate to A and B, and JK is a long side of JKLM.
so, we are going from JKLM to ABCD.
that means we are going from larger to smaller (as JK = 15 and therefore larger than AB = 12).
what is the scale factor to go from 15 to 12 ?
15 × x = 12
x = 12/15 = 4/5 or 0.8
Find the value of x. PLEASE HELP ASAP!
A.4
B. 16
С. 5
D. 12
Answer: x>12
so i think x is 16.
• What is the smallest distance, in meters, needed for an airplane touching the runway with a velocity of 360 km/h and an acceleration of -10 m/s2 to come to rest? HELP
Answer:
i think ..................
Step-by-step explanation:
society idsbwj ja
16. Sandra is choosing an Internet service provider.
• Smart Dot Company costs $12 per month plus $0.50 for each hour of Internet used.
• Communication Plus costs $2.50 for every hour of Internet used.
a. Create an equation to represent the cost of using the internet with each company. (2 marks) Let C represent the cost of using internet in any month.
Let t represent the number of hours used.
Answer: See explanation
Step-by-step explanation:
Since Smart Dot Company costs $12 per month plus $0.50 for each hour of Internet used, the equation to represent the cost of using the internet with them will be:
C = 12 + 0.5t
Since Communication Plus costs $2.50 for every hour of Internet used, the equation to represent the cost of using the internet with them will be:
C = 2.5t
Instructions: Find the missing side of the triangle.
12
16
X
х
=
Answer:
x = 20
Step-by-step explanation:
c^2 = a^2 + b^2
a = 12
b = 16
c = ?
c^2 = 12^2 + 16^2
c^2 = 144 + 256
c^2 = 400
sqrt(c^2) = sqrt(400)
c = 20
find H.C.F OF 4x²y and xy²
Answer:
xy
Step-by-step explanation:
The HCF is known as the highest common factor. To find the HCF of two values, we have to take the greatest number that fits into all of their factors.
To start, we can list each value's factors.
For 4x²y, this can also be written as 4*x²*y = 4*x*x*y. In multiplication, we can take the factors of each value that is multiplied. Therefore, we can start with the factors of 4 and then go to the factors of x² and so on. Our factor list is thus 1,2,4,x,x²,y
Similarly, for xy² = x*y*y, our factors are x, y, and y²
The common factors for each of these are x and y. Assuming all values are positive and greater than 1, the x*y will be greater than either x or y. Therefore, the highest common factor would be x*y = xy
Look at the figure. Which step should be taken next to construct a line through point R that is perpendicular to ST ?
Answer:
where is the figure without figure how to find out
“Use the equation 2p-7=25 to find the weight of your uncles backpack”
Answer:
the equation is 2p-7=25 // p = 16
Answer:
Your uncle's backpack weighs 16 pounds.
Step-by-step explanation:
1.) Add 7 to each side
2p=32
2.) Divide each side by 2
p = 16
3.) That is your answer.
Please help and show work. 60 points
Answer:
18.
Domain: X E \{-3,2}
Y-Intercept: 1/2
X-Intercept: 3
19.
Domain: (I think it's none)
Y-Intercept: -2
X-Intercept: 2
20.
Domain: X E R\ {-3,1}
y-INTERCEPT: 2/3
x-INTERCEPT: -1
Step-by-step explanation:
Help plz and thanks
Answer:
6b
Step-by-step explanation:
The graph shows the function f(x) = 2*
What is the value of x when f(x) = 8?
Ay
10-
A. 3
B. 2
C. 0
D. 1
Answer:
A
Step-by-step explanation:
Equate f(x) to 8 , that is
[tex]2^{x}[/tex] = 8 = 2³
Since bases on both sides are equal, both 2, then equate exponents
x = 3
The value of the x when the exponential function shown in the graph f(x) = 2ˣ is 8 is when x = 3, which is option A.
Here, given the graph of the function,
f(x) = 2ˣ
We have to find the value of x when f(x) = 8.
In order to find the value of x, when f(x) = 8, we have to write as,
f(x) = 8
2ˣ = 8
Now write 8 as an exponent with base 2.
2ˣ = 2³
Hence the value of x = 3
Learn more about Exponential Functions here :
https://brainly.com/question/9919887
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What is the equation of the following line? Be sure to scroll down first to see all answer options.
A.
y = 18x
B.
y = 9x
C.
y = -9x
D.
y = - x
E.
y = -18x
F.
y = x
Answer:
a
Step-by-step explanation:
i took this and got a 100
Answer:
y = 9x
Step-by-step explanation:
other person is so wrong, hope this helps.
how long will the sum of Rs 5,000 take to reach the amount RS 8750 at the rate of 15% per annum
Answer:
It will take 5 yrs the sum of 5000 will take to reach Rs 8750 at the rate 15%
Step-by-step explanation:
T= ?
Amount = Rs 8750
R = 15%
P = Rs 5000
so
I = A-P
= 8750 - 5000
= Rs 3750
so
I = PTR/100
3750 = (5000*15*T)/100
or, 375000 = 75000*T
or, T = 375000/75000
so T = 5 yrs
4. Which of the following is an algebra tiles representation of 3x - 2 = -5?
Answer:
Equation
ans = -1
Step-by-step explanation:
3x-2=-5
3x=-5+2
3x=-3
x=-3/3
x=-1
