The exact value of cos 105° is equals to √2/4 - √6/4.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
In this case, 105 degrees, can be split into 45+60 (cos (45+60))
Use the sum formula for cosine to simplify the expression;
cos (A+B) = - (cos (A) cos (B) + sin (A) sin (B)).
The exact value of cos(60) is 1/2.
So, multiply 1/2 to cos (45) - sin (60) times sin (45).
The exact value of cos (45) is the square root of 2 over 2
(1/2) ⋅ (√2/2) - sin (60) ⋅ sin (45)
The Value of sin (60) is √3/2
(1/2) ⋅ (√2/2) - √3/2 ⋅ sin (45)
The exact value of sin (45) is √2/2
(1/2) ⋅ (√2/2) - √3/2 ⋅ √2/2
Therefore, The exact value of cos 105° is equals to √2/4 - √6/4.
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d. (x + y, 3x-2y) = (7,11)
Answer:
x = 5, y =2
Step-by-step explanation:
I guess the question is saying x+y = 7 and 3x-2y = 11?
then there are multiple ways but
I will multiply the first one by 2 so 2x+2y = 14
you add the equations to get 5x = 25 so x = 5 plug x into the first equation you get y = 2
if that isn't what the question means just comment and I'll change it
How many positive integers less than 1000 a) are divisible by 7? b) are divisible by 7 but not by 11?
Answer:
130
Step-by-step explanation:
The number of integers meeting the criteria can be found by counting them using a counting formula.
Divisible by 7Integers divisible by 7 will have the form (7n), where n is some positive integer. The number of them less than 1000 can be found from ...
7n ≤ 1000
n ≤ 142.857
There are 142 integers less than 1000 that are divisible by 7.
Divisible by 7 and 11Similarly, integers divisible by 7 and 11 will be of the form (77n), for some positive integer n.
77n ≤ 1000
n ≤ 12.987
There are 12 integers less than 1000 that are divisible by both 11 and 7.
Divisible by 7, not 11The number of integers less than 1000 that are divisible by 7, but not 11, will be the difference of these numbers.
142 -12 = 130 integers divisible by 7, but not 11.
Which digit is in the hundredths place?
18.36
8
3
1
6
Answer:
6.becuase after the decimal or "." it goes 00.tenth, hundredth, thousandth, and so on
Step-by-step explanation:
PLEASE GIVE BRAINLIEST OR 5 ⭐
Which word describes their measures? linear congruent complementary supplementary
what is 4^-2. ................................
Answer:0.0625
Step-by-step explanation:
Answer:
1/16.
Step-by-step explanation:
4 ^-2 = 1 / 4^2
= 1/16.
A sports teacher divided a class into two groups. Three-fifth of the first group and 80% of the second group play soccer.
What fraction of the class plays soccer?
Answer:
7/5
Step-by-step explanation:
80/100 = 0.8 = 8/10 = 4/5 (to the simplest fraction).(three-fifth) 3/5 + 4/5 = 7/57/5 of the class plays soccer ✅Hope this helpsGood luck ✅x(x-5) (x+5) - (x+2) (x^2 - 2x +4) = 17
x[x²-25] - [x³+8] = 17
x³- 25x - x³- 8 = 17
-25x = 17 + 8
-25x = 25
x = -1
The chart below shows conversion between kilometers and miles.
Conversion Chart
Kilometer
Miles
2
1.2
7
4.2
20
?
30
18
What is the missing value in the table?
The missing value in the table is 12.4
Conversion between UnitsFrom the question, we are to determine the missing value in the table
From the given information,
The chart shows conversion between kilometers and miles
The given table is
Kilometers Miles
2 1.2
7 4.2
20 ?
30 18
NOTE: 1 kilometer ≈ 0.62 miles
Then, 20 kilometer ≈ 20×0.62 miles
20 kilometer ≈ 12.4 miles
Hence, the missing value in the table is 12.4
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A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,320 ft Determine the flag's width and length if the length is 400 ft
greater than the width.
The flag's width is
_? ft. Its length is
_? ft.
Answer: 380 ft and 780 ft
Step-by-step explanation:
We can assume that the flag is a rectangle. If the width of the flag is w, then the length is w + 400.
The formula for the perimeter of a rectangle is [tex]2(l+w)[/tex]. Let's plug in the values we know.
[tex]P=2(l+w)\\2320=2(w+400+w)\\1160=2w+400\\760=2w\\w=380[/tex]
We know that the length is 400 more than the width, so let's find the length.
[tex]l=w+400\\l=380+400=780[/tex]
Hence, the flag's width is 380 ft and the length is 780 ft.
Find the equation of the linear function represented by the table below in slope-intercept form.
x 0 1 2 3 4
y 7 15 23 31 39
Answer:
y = 8x+7
Step-by-step explanation:
firstly reduce the equation to an arithmetic series starting from the 0th term so:
7, 15, 23, 31, 39....
Secondly, identify the common difference: 8
we now know that the answer must contain 8x
Thirdly, form the equation 8x + c = y where y is a constant. Afterwards insert the values of any given x and y so:
8*0 + c = 7
c = 7
Thusly we now know that the series and thus equation is 8x+7 = y
Answer:
y = 8x + 7
Step-by-step explanation:
the equation of a linear function in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2-y_{1} } }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1,15) and (x₂, y₂ ) = (2, 23) ← 2 ordered pairs from the table
m = [tex]\frac{23-15}{2-1}[/tex] = [tex]\frac{8}{1}[/tex] = 8
the ordered pair (0, 7 ) indicates c = 7
y = 8x + 7 ← equation of linear function
Joseph decided to solve the quadratic x² +8x=9. Which of the
following steps is where Joseph made his first mistake?
x² +8x=9
Step 1
Step 2
Step 3
0000
x+8x-9=0
(x+9)(x - 1) = 0
x= 9 and x = -1
Step 1
Step 2
Step 3
Joseph did not make any mistakes.
Answer:
he didn't mistake step 2
find the solution of systems of equations
8x-5y=-8 -7x-5y=82
Answer:
x = -6, y = -8
Step-by-step explanation:
8x - 5y = -8
-7x - 5y = 82
minus them
15x = -90
x = -90 / 15
x = -6
8(-6) - 5y = -8
-48 - 5y = -8
-5y = -8 + 48
-5y = 40
5y = -40
y = -40 / 5
y = -8
Variables y and x have a proportional relationship wher y=18 when x=2 what is the value of x when y=36
Answer:
4
Step-by-step explanation:
18 + 18 = 36
So you got 36 cuz you times by two so you times the same for x
which is
2 x 2 = 4
Answer:
4
Step-by-step explanation:
We can set up a proportion.
18:2 = 36: x
If we multiply 18 by 2, and multiply 2 by 2, we can get 18:2 = 36:4, so x is equal to 4
√32x+1
= 9x-2 minta tolong dengan ini
We have:
√32x + 1 = 9x - 2
<=> √32x - 9x = -2 - 1
<=> (√32 - 9)x = -3
<=> x = -3/(√32 - 9) = (27+12√2)/49
ANSWER: x = (27+12√2)/49
P/s: i'm not pretty sure
Ok done. Thank to me :3
The slope-intercept form given (6,-5) & perpendicular to -5x - 7y = -17.
Answer:
[tex]y=\dfrac{7}{5}x-\dfrac{67}{5}[/tex]
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
where:
m is the slope.b is the y-intercept.Rearrange the given equation so that it is in slope-intercept form:
[tex]\implies -5x-7y=-17[/tex]
[tex]\implies -7y=5x-17[/tex]
[tex]\implies y=-\dfrac{5}{7}x+\dfrac{17}{7}[/tex]
Therefore, the slope of the given equation is -⁵/₇.
If two lines are perpendicular to each other (at right angles), the product of their slopes will be -1. Therefore, their slopes will be negative reciprocals of each other.
Therefore, the slope of the line perpendicular to the given equation is:
[tex]\sf m=\dfrac{7}{5}[/tex]
Substitute the found slope and the given point (6, -5) into the slope-intercept formula and solve for b:
[tex]\implies -5=\dfrac{7}{5}(6)+b[/tex]
[tex]\implies -5=\dfrac{42}{5}+b[/tex]
[tex]\implies b=-\dfrac{67}{5}[/tex]
Substitute the found slope and the found value of b into the slope-intercept formula to create the equation for the perpendicular line:
[tex]\implies y=\dfrac{7}{5}x-\dfrac{67}{5}[/tex]
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If -3(x+8)= -21, then x = -1.
Step-by-step explanation:
-3(x+8)=-21
open the bracket
-3x-24=-21
-3x=-21+24
-3x=3
x=-3/3
x=-1
Graph h(x)= -4(x-3)(x-1)
Answer:
roots (1,0) (3,) the vertical intercept is (0,-12)
Step-by-step explanation:
A deli sells sliced meat and cheese. One customer purchases 4 pounds of meat and 5 pounds of cheese for a total of $30.50. A sandwich shop owner comes in and purchases 11 pounds of meat and 14 pounds of cheese for $84.50. The system of equations below represents the situation.
4x + 5y = 30.50
11x + 14y = 84.50
The variable x represents the
The variable y represents the
The deli charges $
The quantity of meat and cheese sold by the deli according to the description accounts in the task content are; 4.5 and 2.5 pounds respectively.
What is the quantity of meat and cheese sold by the deli?The quantity of meat sold by the deli as represented by the variable X in the task content can be calculated by solving the systems of equations.
The quantity of cheese sold by the deli as represented by the variable y in the task content can be calculated by solving the systems of equations.
Consequently, solving the system of equations by means of substitution, we have;
y = (30.50-4x)/5
Hence, we have;
11x + 14((30.50-4x)/5) = 84.50
x = 4.5 pounds of meat and
y = 2.5 pounds of cheese.
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What is the general form of the equation for the given circle centered at o(0, 0)? a. x2 y2 41 = 0 b. x2 y2 − 41 = 0 c. x2 y2 x y − 41 = 0 d. x2 y2 x − y − 41 = 0
The general form of the equation for the given circle centered at o(0, 0) is x² + y² - 41 = 0.
According to the question,
The general form of the equation for the given circle centered at o(0, 0) is (x-h)² + (y-k)² = r².
The given equation is x² + y² - 41 = 0 which is also represented by(x-0)² + (y-0)² = -(√41)². This is not possible.
The given equation is x² + y² - 41 = 0 which is also represented by (x-0)² + (y-0)² = (√41)²This means that the circle is centered at (0,0). Thus, the equation is correct The given equation is x² + y² +x+ y- 41 = 0 which is also represented by (x+1/2)² + (y+1/2)² = (√(83/2))²This means that the circle is centered at (-1/2,-1/2). Thus, this equation is incorrect. The given equation is x² + y² +x- y- 41 = 0 which is also represented by (x+1/2)² + (y-1/2)² = (√(83/2))²This means that the circle is centered at (1/2,-1/2). Thus, this equation is incorrect.Hence, the general form of the equation for the given circle centered at o(0, 0) is x² + y² - 41 = 0.
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14²-34 divided by -9+7.2
Answer:
Let's go part by part:
14 raised to 2 = 196
-9+7x2=-9+14 = 5
196/5= 39,2 (final result)
Answer:
-3.2
Step-by-step explanation:
14 SQUARED is 196
196 - 34 = 5.7647
- 9 + 7.2 = - 1.8
5.7647 / -1.8 = -3.2
-3.2 would be your answer.
You are playing a game with three cards. At the start, all three cards are face down. You know that a different real number is written on every card, but you do not know what the numbers are. The rules of the game are as follows: You can choose any card and turn it over (assuming that you have not already turned it over). You can either keep the card, or discard it. If you discard a card, then you cannot go back to it; you must choose a new card. If the card you have kept has the largest real number on it, then you win the game. If you use the optimal strategy, then what is the probability that you win the game
concluding, the idea is discarding cards until we get,at least, a 6, in that case, the smallest probability of winning the game is 0.59, which is more than in half of the cases.
How to find the probability?
Now, we know that there are 52 cards in a normal deck, if we only keep the ones with real numbers, there are 40.
These numbers go from 1 to 10.
5.5 is the average real number in the cards, so, having a 6 or more in a card is what we expect.
This means that if the card that we turn up is smaller than 6, we discard it.
If the card has the value 6 or larger, we keep it.
In this case, the probability of losing is if one of the other cards has a value larger than 6.
The probability that a random card has a value larger than 6 is:
p = (number of cards with a value larger than 6)/(total number of cards)
p = (16/39)
(The quotient is 39 instead of 40, because we already know one of the cards)
This means that if keep the 6, the probability of winning is:
1 - 16/39 = 0.59
If instead, we got a 7, obviously we keep it, in that case the probability of winning is:
1 - 12/39 = 0.69
And so on, concluding, the idea is discarding cards until we get,at least, a 6, in that case, the smallest probability of winning the game is 0.59, which is more than in half of the cases.
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The two hexagonal pyramids are similar. if the smaller pyramid has a surface area of 25.49 ft2, what is the surface area of the larger pyramid? round to the nearest hundredth. ft2
The largest pyramid's surface area is roughly 159.31 [tex]ft^2[/tex].
What is hexagonal pyramids?A hexagonal pyramid is one that has six isosceles triangles that meet at a point, each of which is supported by a hexagonal foundation. It is self-dual, just as any pyramid. It possesses C6v symmetry when the base of a right hexagonal pyramid is a regular hexagon.
A pyramid is a solid,
Additionally, the ratio of two solids' surfaces when they are comparable is equal to the square of the similarity scale factor.
The similarity scale factor in this instance
= (Hight of the larger pyramid)/(Height of smaller pyramid)
=15/6
Due to the aforementioned characteristic,
= (15/6)^2
Given that the smaller pyramid's surface area is 25.49 [tex]ft^2[/tex],
(The surface of larger pyramid)/(25.49) = 225/36
The surface of larger pyramid = (25.49*225)/36
= 5735.25/36
= 159.3125 ft^2
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The critical values for a 2-tailed sign test for 13-coin flips (alpha of. 05) is:_____.
The critical values for a 2-tailed sign test for 13-coin flips (alpha of. 05) is: ± 1.96
For given question,
We need to find the critical values for a 2-tailed sign test for 13-coin flips.
We have been given an alpha level of 0.05 that is 5%
⇒ α = 0.05
We know that in hypothesis testing, a critical value is a point on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis.
These are the points on the distribution which have the same probability as your test statistic, equal to the significance level α.
The critical values are assumed to be at least as extreme at those critical values.
Now we find 1 - α
⇒ 1 - α = 1 - 0.05
⇒ 1 - α = 0.95
Because it is a two-tailed test, we are going to divide 0.95 by 2.
⇒ 0.95/2 = 0.475
Now we look in the z-table to find out cutoff points.
For the area of 0.475, the critical values is ± 1.96 .
Therefore, the critical values for a 2-tailed sign test for 13-coin flips (alpha of. 05) is: ± 1.96
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how do you solve these two questions and what are the answers?
Answer:
a) -6/2
b) -9/2
Step-by-step explanation:
a) rearrange by making y the subject as y = mx+c
y = -6/2x-9/2
the gradient = -6/2
b) c is the y-intercept as it touch the y-axis, therefore -9/2 is where the line crosses the y-axis
The chart below shows conversion between kilometers and miles.
Conversion Chart
Kilometer
Miles
2
1.2
7
4.2
20
?
30
18
What is the missing value in the table?
Answer:Answer:
12 (D)
Step-by-step explanation:
The first one is 2:1.2 so i did x10 on it to get 20:12.
Step-by-step explanation:Oh and hey if it's right u have to make me brainliest i need award
Use a calculator to find tan 24°, round to the nearest hundredth.
Hi :)
To find the tan of a number, just type the number into your calculator and press [tex]\boxed{\tan}[/tex].
[tex]\tan 24=0.45[/tex], Rounded to the nearest hundredth, or 2 numbers after the decimal point, just like you asked
[tex]\textit{\textbf{Learn\;More;Work\;Harder}}[/tex]
:)
If a girl lifts a load of 60N to a height of 3m, find work.
Let the mass of the object exists at 60 N and the height exists at 3m then work
exists in 1764.
What is work?
The work done by a force exists determined to be the product of a component of the force in the direction of the displacement and the magnitude of this displacement.
Work can be estimated by multiplying Force and Distance in the direction of force as follows.
W = F × d. Unit.
Given data:
m = mass of the object = 60 N
h = height = 3 m
Work = Fh = mgh
g = gravity = 9.8 m/s²
work = Fh = mgh
[tex]= 60*3*9.8[/tex]
= 1764
Therefore, the work exists in 1764.
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Find the surface area of the cone to the nearest square unit. Use π = 3.14.
6 cm
3 cm
The surface area of the cone exists as πr² + πrl
= (3.14)(6)² + (3.14)(6)(3)
= 169.56 cm²
Therefore, the surface area of the cone exists at 169.56 cm².
How to find the surface area of the cone?
The surface of the cone consists of the lateral surface and the base area. So,
1. the lateral surface exists equal to πrs, where r exists the radius of the base and s exists the slant height of the cone.
2. the base area exists πr² (since the base exists a circle with radius r).
Then the surface area exists SA = πrs + πr²
The surface area of the cone exists as πr² + πrl
where "r" exists the radius, "l" exists the slant height
The radius of the cone exists at 6 cm
The slant height of the cone exists at 3 cm
To find the surface area of a cone
The surface area of a cone = πr² + πrl
= (3.14)(6)² + (3.14)(6)(3)
= 169.56 cm²
Therefore, the surface area of the cone exists at 169.56 cm².
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6;15; x; 45;....... is a quadratic number pattern (sequence). Determine the value of x.
Solving a system of equations, we conclude that the value of x is 28.
How to determine the value of x?
Here we have the quadratic number pattern:
6, 15, x, 45, ...
First, we have that:
15 - 6 = 9
So 9 is the first difference.
Then we will have:
x = 15 + 9 + a
(where a is the second difference, constant of the sequence).
And:
45 = x + 9 + a + a
Then we have a system of equations:
x = 15 + 9 + a
45 = x + 9 + a + a
We can isolate a on the first equation:
a = x - 24
We can replace that in the other equation:
45 = x + 9 + 2a
45 = x + 9 + 2*(x - 24)
Now we can solve that for x:
45 - 9 = x + 2*(x - 24)
36 = 3x - 48
36 + 48 = 3x
84 = 3x
84/3 = x = 28
The value of x is 28.
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Two children share 1/6 of a cake .what fraction does each get? answer in statement.
Fraction of cake each children's get 1/12.
What is Fraction?fraction: In mathematics, a number that is stated as a quotient in which the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.
According to the information:Cake available for Sharing = 1/6
The cake future divide into 1/2:
so,
= (1/6) x (1/2)
= 1/12
fraction of cake each children's get 1/12.
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