Recall some identities:
tan(x) = sin(x) / cos(x)
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
cos(x - y) = cos(x) cos(y) + sin(x) sin(y)
sin(x - y) = sin(x) cos(y) - cos(x) sin(y)
This means we have
• cos²(90° - x) = [cos(90°) cos(x) + sin(90°) sin(x)]²
… = sin²(x)
• tan(180° - x) = sin(180° - x) / cos(180° - x)
… = [sin(180°) cos(x) - cos(180°) sin(x)] / [cos(180°) cos(x) + sin(180°) sin(x)]
… = sin(x) / (-cos(x))
… = -tan(x)
(and we also get sin(180° - x) = sin(x))
• cos(180° + x) = cos(180°) cos(x) - sin(180°) sin(x)
… = -cos(x)
So, the given expression reduces to
sin²(x) (-tan(x)) (-cos(x)) / sin(x) = sin²(x)
since tan(x) and cos(x)/sin(x) = 1/tan(x) will cancel.
PLEASE HELP THIS IS TRIGONOMETRY!!!
Answer:
7/25
Step-by-step explanation:
[tex]cos2θ = 1 - 2 {sin}^{2} θ \\ = 1 - {2(sinθ)}^{2} \\ = 1 - {2 (\frac{3}{5}) }^{2} \\ = \frac{7}{25} [/tex]
Which polynomials are prime? check all of the boxes that apply. x2 9 x2 – 9 x2 3x 9 –2x2 8
Prime polynomials cannot be factorized in smaller degree polynomials. The prime polynomials out of the considered option are:
Option 1: x^2 + 9Option 3: x^2 + 3x + 9What are prime polynomials?Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called prime polynomial.
(it is necessary that no factors exists having their coefficients are still integers and they're of lower degree)
Checking all the options for them being prime or not:
Option 1: [tex]x^2 + 9[/tex]Take [tex](x+a)(x+b) = x^2 + 9[/tex]
Then, expanding it gives:
[tex]x^2 + (a+b)x + ab = x^2 + 9 \implies a+b = 0, ab = 9[/tex]
or we get: [tex]a = -b, ab = -b^2 = 9, b^2 = -9[/tex]
Square of a real number doesn't exist, so this factor doesn't exist. Thus, it is prime polynomial.
Option 2: [tex]x^2 - 9[/tex]We have the identity [tex](a+b)(a-b) = a^2 - b^2[/tex]
and since 9 is square of 3, therefore, we get:
[tex]x^2 -9 = x^2 -3^2 = (x+3)(x-3)[/tex]
So it got factorized. Thus, not a prime polynomial.
Option 3: [tex]x^2 +3x + 9[/tex]Take [tex](x+a)(x+b) = x^2 + 3x + 9[/tex]
Then, expanding it gives:
[tex]x^2 + (a+b)x + ab = x^2 + 3x + 9 \implies a+b = 3, ab = 9[/tex]
That gives:
[tex]a = 3-b\\ab = b(3-b) = 3b - b^2 = 9\\b^2 -3b + 9 = 0[/tex]
Solving this quadratic equation by root formula gives:
[tex]b = \dfrac{-(-3) \pm \sqrt{(-3)^2 -4(1)(9)} }{2}\\\\b = \dfrac{-(-3) \pm \sqrt{-27} }{2}\\[/tex]
this makes 'b' a complex number and it doesn't remain a real number as its expression contains square root of a negative number.
Thus, this polynomial cannot be factorized in terms of smaller degree polynomials. Thus, its a prime polynomial.
Option 4: [tex]-2x^2 + 8[/tex]Taking -2 common out, we get:
[tex]-2(x^2 - 4) = -2(x^2 - 2^2) = -2(x-2)(x+2)[/tex]
Thus, it got factorized, and therefore not a prime polynomial.
Thus, the prime polynomials out of the considered option are:
Option 1: [tex]x^2 + 9[/tex]Option 3: [tex]x^2 + 3x + 9[/tex]Learn more about prime polynomials here:
https://brainly.com/question/10717989
Answer:
A) x2 + 9
C) x2 + 3x + 9
☆
EDGE2022; Good Luck :D!!!
A bag contains ten titles labeled B, C, D, E, F, G, H, I, J, and K. One time will be randomly picked. What is the probability of picking a vowel? Write your answer as a fraction in the simplest form.
On a coordinate plane, line M N goes through points (2, 3) and (negative 3, 2). Point K is at (3, negative 3). Which point could be on the line that is perpendicular to Line M N and passes through point K? (0, −12) (2, 2) (4, 8) (5, 13)
MN goes through
(2,3)(-3,2)Slope:-
m=2-3/-3-2=-1/-5=1/5Slope of perpendicular line:-
-5Passes through k(3,-3)
Equation in point slope form
y-y1=m(x-x1)y+3=-5(x-3)y+3=-5x+15y=-5x+12Check one by one
0=-5(-12)+12=60+12=722=-5(2)+12=-10+12=2Yes option B is correct
Answer:
(2, 2)
Step-by-step explanation:
First find the slope of the line MN, using the two given points:
[tex]\sf let\:(x_1,y_1)=(2,3)[/tex]
[tex]\sf let\:(x_2,y_2)=(-3,2)[/tex]
[tex]\implies \sf slope\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{2-3}{-3-2}=\dfrac15[/tex]
If two lines are perpendicular to each other, the product of their slopes will be -1.
Therefore, the slope (m) of the line perpendicular to MN is:
[tex]\implies \dfrac15 \times m=-1[/tex]
[tex]\implies m=-5[/tex]
Using the point-slope form of the linear equation with point K (3, -3), we can construct the linear equation of the line perpendicular to MN:
[tex]\sf y-y_1=m(x-x_1)[/tex]
[tex]\implies \sf y-(-3)=-5(x-3)[/tex]
[tex]\implies \sf y=-5x+12[/tex]
Now we have the equation of the line perpendicular to MN, we can input the x-values of the solution options to see which once is correct:
[tex]x=0\implies \sf y=-5(0)+12=12\implies (0,12)[/tex]
[tex]x=2\implies \sf y=-5(2)+12=2\implies (2,2)[/tex]
[tex]x=4\implies \sf y=-5(4)+12=12\implies (4,-8)[/tex]
[tex]x=5\implies \sf y=-5(5)+12=-13\implies (5,-13)[/tex]
Therefore, the point that is on the line that is perpendicular to MN and passes through point K is (2, 2)
The probability that juliana will take a particular type of dance class is shown in the chart below. She will definitely take either ballet or jazz, but not both. The probability that she will take jazz on wednesday night is 27%. If the probability that she will take ballet is 70%, what is the probability that she will take jazz on saturday morning?.
The probability that Juliana will take jazz on Saturday morning based on the decision tree given is 3%.
What is the probability that jazz is taken on Saturday morning?The probability that jazz is taken is:
= 1 - Probability of ballet
= 1 - 70%
= 30%
The probability that if jazz is taken, it will be taken on Wednesday is:
= Probability that jazz is taken on Wednesday night / Probability that Jazz is taken
= 27% / 30%
= 90%
The probability that Jazz is taken on Saturday morning is therefore:
= Probability that jazz is taken x (1 - Probability of Wednesday night)
= 0.3 x ( 1 - 90%)
= 3%
Find out more on probability at https://brainly.com/question/17930357?referrer=searchResults.
What is the surface area of the milk carton
to the nearest square inch? Check your
answer for reasonableness.
Answer:
280 in ^2
Step-by-step explanation:
Hi ok heres how I did this:
SA of rectangular prism: S = 2(lw + lh + wh)
SA of triangle top thing(whats it called???): Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 + S2+ S3)L + bh
So basically for the square part, the surface area is
2(4*4+4*12+4*12), or 224
For the triangle part, the surface area is
4+4+4, or 12*4+2*4, or 48+8, or 56
224+56=280
The thing is I don't know why it says round though. Theres a chance its incorrect if they want something with a decimal. Let me know.
Which of the following is an equivalent expression to the expression “T?
a
a
Answer:
a^1/12
Step-by-step explanation:
a ^1/3 / a^1/4 = a ^ (1/3 - 1/4) = a^ 1/12
Please answer this DO NOT POST A LINK I will report you if its a link. please help :(
Answer:
21
Step-by-step explanation:
10-(3×2²-23) = 21
10- -11
10+11=21
(1+10²)=101
2²×5²=100
101-100=1
²¹/1 = 21
Fleur has 32 collectable playing cards. 3/8 of the playing cards are red. 2/8 of the playing cards are blue. The rest were green. How many of the playing cards were green? Explain how you found your answer.
When the research hypothesis posits that there is a nondirect relationship between two variables, the test is ______. a. nondirectional b. one-tailed c. two-tailed d. negative
Answer:
c. two-tailed
Step-by-step explanation:
i think its this because i say so now trust :)
find the volume of the cylinder. round your answer to the nearest tenth. 7 inches and 6 inches.
[tex]\pi r^{2}[/tex]Answer:
You must know the radius but...
Step-by-step explanation:
The formula to find volume of a cylinder is: B*h
B= area of base
h=height
To find the area of the base you need to know the radius since the formula to find area of a circle is: [tex]\pi r^{2}[/tex]
Once you find the area of the base you just multiply it by the height
Can someone help me with this one
Answer:
15
Step-by-step explanation:
i belive its 15 i think you should look where the dot is
3.0 × 10^{8} ms− 1 i need the answer to this question please
Hey there!
3.0 * 10^8
= 3.0 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10
= 3.0 * 100 * 100 * 100 * 100
= 3.0 * 10,000 * 10,000
= 3.0 * 100,000,000
= 300,000,000
Therefore, your answer is:
300,000,000
Good luck on assignment & enjoy your day!
~Amphitrite1040:)
Please help
Workout a b and c
Answer:
a=21° b=70°
Step-by-step explanation:
a=21°(Vertically Opposite Angles)
b+110°=180° (linear pair)
b=180-110
b=70°
[please mark me brainliest]
Answer:
a = 21°
b = 70°
c = 89°
Step-by-step explanation:
angle of measure b and the angle of measure 110 are two supplementary angles
Then b + 110 = 180
Therefore b = 180 - 110 = 70°
angle of measure b and the angle of measure 21 are two opposite angles
Then a = 21
We Know that the sum of the interior angles of a triangle equal to 180
Then a + b + c = 180
Therefore c = 180 - a - b = 180 - 21 - 70 = 159 - 70 = 89°
Tell which letter shows the graph of the number.
Answer:
Your answer is correct. It is letter A
Step-by-step explanation:
7/9= 0.778
Hence, A
expand and simplify 2(3a-5b +4 (a+2b)
Answer:
14a + 6b
Step-by-step explanation:
To expand use distributive property. a*(b +c) =a*b +a *c
Simplifying an expression
2*(3a - 5b + 4*(a+2b) = 2*(3a -5b + 4*a +4*2b)
= 2*(3a - 5b + 4a + 8b)
= 2* (3a + 4a - 5b + 8b)
Combine like terms. To combine like terms, add or subtract the coefficient of the variables. 3a and 4a & (-5b) and 8b are like terms
= 2*( 7a + 3b)
= 2*7a + 2*3b
= 14a + 6b
Hey there!
2(3a - 5b) + 4(a + 2b)
= 2(3a - 5b) + 4(1a + 2b)
= 2(3a) + 2(-5b) + 4(1a) + 4(2b)
= 6a - 10b + 4a + 8b
= (6a + 4a) - (10b + 8b)
= 6a + 4a - 10b + 8b
= 10a - 2b
Therefore, your answer is: 10a - 2b
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
what two numbers that can multiply into 60 and add into 19
Answer:
15 and 4
Step-by-step explanation:
we must first find the Factors:
1, 2, 3, 4, 5
60, 30, 20, 15, 12
Now we can add them to find what adds to 19
1+60 = 61
2+30 = 32
3+20 = 23
4+15 = 19
Estimate 31+65 over 9.7
Answer:
9.9
Step-by-step explanation:
31
+ 65
96
96/9.7=
9.89 =
9.9
Hey there!
31 + 65 / 9.7
= 96 / 9.7
= 9.896907
31 ≈ 30
65 ≈ 70
9.7 ≈ 10
9.896907 ≈
30 + 70 / 10
= 100 / 10
= 10
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Kilograms represented by the mass defect for thorium-234 = 3.09 × 10-27 kg what is the nuclear binding energy for thorium-234? 2.78 × 10-10 j 3.36 × 10-14 j 1.67 × 1017 j 5.35 x 10-23 j
The nuclear binding energy for thorium -234 is 2.78 × 10-10 j
We have given that,
Kilograms are represented by the mass defect for thorium
-234 = 3.09 × 10-27 kg
To determine the nuclear binding energy for thorium -234.
What is the relation between Mass defect and binding energy?ΔE = Δmc^2
Where
ΔE = binding energy
Δm = mass defect
c = speed of light
mass defect = 3.09× 10^-27 kg
We know that the speed of light = 3 × 10^8 m /s
[tex]\Delta E \\= 3.09\times 10^{-27} kg (3 \times 10^8 m /s)^2 \\= 2.781 \times 10^{-10} J / Kg[/tex]
Therefore, the nuclear binding energy for thorium -234 is
2.78 × 10-10 j
To learn more about the energy visit:
https://brainly.com/question/9367965
.
Answer:
The nuclear binding energy for thorium -234 is 2.78 × 10-10 j
Step-by-step explanation:
Describe the behavior of the graph shown below.
A.
As the input increases, the output decreases at first until it reaches a minimum. After the minimum, the output increases as the input increases.
B.
As the input decreases, the output increases at first until it reaches a maximum. After the maximum, the output decreases as the input increases.
C.
As the input increases, the output increases for all values of x.
D.
As the input increases, the output decreases for all values of x.
Reset Submit
As the side of the curved line on the right increases in the x direction (input) the curved lines gets greater t words the left side . This means the output decreases.
answer:
D. As the input increases, the output decreases for all values of x.
Option A
It's a parabola having vertex (-1,-5)
As we can see the graph .
The curve first decreases until it reaches the vertex (-1,-5) then it increases on increase in x
As parabola is opening upwards Vertex is minimum
So option A is correct
find the value of x from the square
Answer:
X = 5
Step-by-step explanation:
From the given figure,
one length of a square(l)= x
Area of the square(A) = 25cm^2
We know,
Area of square(A)= l^2
or, 25=x^2
or, √25 = x
or, 5cm = x
Step-by-step explanation:
Side = x cmGiven, that the area of the square = 25cm^2
therefore,area of square = (side)^2
25 = x^2
x = √25
x = 5 cm.
Hope it helps you!!Can someone help me with this?
2u+14
hope it helps...!!!
what is pi and why do we need it
Answer:
Pi is a mathematical term we need under the circumstances of solving complex math problems.
Answer:
pi explains everything
Step-by-step explanation:
pi goes on forever, so u could look in pi and find your birthday and even your name (in letter/number code : a=1 z=26 etc...) its pretty cool
what is the volume of this shape
Answer:
C -- 72
Step-by-step explanation:
Formula B x W x H
B = base
W = with
H = hight
Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Also remember to rate answers to help other students, While leaving thanks to answers that help you. Have a great day!
what is the LCM for 9 and 12
5. Two buses leave Bangor at the same time and travel in opposite directions. One bus
averages 57 mi/h and the other bus averages 43 mi/h. After how many hours will the buses be
450 mi apart?
One sector has an area of 167 square inches and an arc measure of 110°.
The area of the circle that contains the sector is 546.5 in² (rounded to the nearest tenth)
Calculating area of a circleFrom the question, we are to determine the area of the circle.
The area of a circle can be determined by using the formula,
[tex]A = \pi r^{2}[/tex]
From the given information,
Area of the sector = 167 in²
Arc measure = 110°
Using the formula,
[tex]Area\ of\ sector = \frac{\theta}{360 ^\circ} \times \pi r^{2}[/tex]
Then,
[tex]167= \frac{110 ^\circ}{360 ^\circ} \times \pi r^{2}[/tex]
[tex]167= \frac{11}{36} \times \pi r^{2}[/tex]
[tex]\pi r^{2} =\frac{167 \times 36}{11}[/tex]
[tex]\pi r^{2} = 546.5 \ in^{2}[/tex]
Since area of the circle, A, is given by πr²
Then,
A = 546.5 in²
Hence, the area of the circle that contains the sector is 546.5 in²
Learn more on Calculating the area of a circle here: https://brainly.com/question/15673093
Here is the complete question:
Find the area of the circle that contains sector. Round to the nearest tenth, if necessary. One sector has an area of 167 square inches and an arc measure of 110°.
#SPJ1
Please answer number 8
Answer:
0.05%
Step-by-step explanation:
Last week, the price of apples at a grocery store was $1.06 per pound. This week, apples at the store are on sale at a 10% discount. What is the total price of 4/1/2 pounds of apples this week at the grocery store?
Answer: $6.48
Step-by-step explanation:
1.60 * 0.1 = $0.16
1.60 - 0.16 = $1.44
1.44 * 4.5 = $6.48
rewrite the equation by completing the square, 4x^2-4x+1=0,
Answer:
(x-0.5)^2=0
Step-by-step explanation:
x^2-x+0.25=0
(x-0.5)^2=0