A picture which measures 30cm by 40cm is surrounded by a frame which is 11/2 wide. find the area of the frame ​

Answer:

Step-by-step explanation:

Our interval is 180 to 270 so that's quadrant III. In quadrant 3, both x and y are negative. If we set up our right triangle in this quadrant and label it accordingly with the values given for tangent theta, we find that the missing length is the hypotenuse. Solve for that using Pythagorean's Theorem. Doing that gives us that the hypotenuse is [tex]\sqrt{61}[/tex].  Now we can solve for your other identities. First,

[tex]cos(2\theta)=2cos^2\theta-1[/tex] (There are 3 identities for cos(2θ) and regardless of which one you pick, the answer will be the same every time...promise!)

Filling in now:

[tex]cos(2\theta)=2(\frac{-5}{\sqrt{61} })^2-1[/tex] and simplified a bit:

[tex]cos(2\theta)=2(\frac{25}{61})-1[/tex] and a bit more:

[tex]cos(2\theta)=\frac{50}{61}-\frac{61}{61}[/tex] giving us, finally:

[tex]cos(2\theta)=-\frac{11}{61}[/tex]

Now for b. We have an identity for the half angle of sin:

[tex]sin(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{1-cos\theta}{2} }[/tex]  and filling in:

[tex]sin(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{1-(-\frac{5}{\sqrt{61} } )}{2} }[/tex] which simplifies a bit to:

[tex]sin(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{1+\frac{5}{\sqrt{61} } }{2} }[/tex] and a bit more to:

[tex]sin(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{\sqrt{61}+5 }{2\sqrt{61} } }[/tex]  I'm not sure if this is the form you need it in, but this is the answer, as convoluted and crazy as it may look.

As for the cosine half-angle, the identity is the same, except there's a + sign in the numerator of the identity instead of a -, giving us the solution:

[tex]cos(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{\sqrt{61}-5 }{2\sqrt{61} } }[/tex]

Answer:

{4 |8}. 96. 24

sin4B{3. |9}= ___. = ___ = cos2A

{10|10} 100. 25

{9 |9}

Answer:

y= -2x +8

Step-by-step explanation:

perpendicular lines have a negative reciprocal gradient so

1/2 becomes -2/1 which is the gradient

sub in the values of x and y

2= -2 (3) +C

2= -6 + C

8=C

y=-2x +8

Answer:

y = -2x + 8

Step-by-step explanation:

for me the easiest way is simply to transform the slope and then just determine the y-intersect.

the slope of the original line is 1/2.

it is always the factor of x and represents the y/x ratio of the function (how many units is y changing when x changes a certain number of units).

a perpendicular line (90 degree angle) simply reverses x and y and the sign of the original slope.

so, the slope of the perpendicular line is -2, and the equation is

y = -2x + c

and c we get by using the point coordinates :

2 = -2×3 + c

2 = -6 + c

c = 8

so, we have

y = -2x + 8

Answer:

(i) 7/10

(ii) 3/10

(iii) 1/5

(iv) Rs 40,000

Step-by-step explanation:

The fraction of the salary spent on food = 1/2

The fraction of the salary spent on rented house fee = 1/5

(i) The fraction spent for both food and rental fee = (1/2) + (1/5) = (5 + 2)/10 = 7/10

(ii) The remainder (rest) of the salary = 1 - 7/10 = 3/10

The fraction of the remainder spent for children's education = 1/3

The fraction of the total salary spent for the children's education = (1/3) × (3/10) = 1/10

(iii) The remaining portion deposited in the bank = 1 - (1/10 + 7/10)) = 2/10 = 1/5

(iv) The amount equal to portion of 1/5 of his salary deposited in the bank is Rs 8000

Let x represent his whole salary, we have;

(1/5) × x = Rs 8,000

x = 5 × Rs 8,000 = Rs 40,000

His whole salary is Rs 40,000.

Answer:

true

Step-by-step explanation:

Answer:

11:35

Step-by-step explanation:

add 13 hour and 45 minutes to 1:50 giving you 4:35 and since the time is 7 hours ahead add another 7 hours and tada

The arrival time in Colombo is 10:35 pm.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Now, First, we need to convert 13 hours and 45 minutes to just hours.

We can do this by dividing the minutes by 60:

45 minutes ÷ 60 = 0.75 hours

So the total flight time is,

13 + 0.75 = 13.75 hours.

Next, we need to add the time difference between London and Colombo. Since Colombo is 7 hours ahead of London, we need to add 7 hours to the total flight time:

13.75 hours + 7 hours = 20.75 hours

Now we need to convert this to a time.

Since the flight left at 01:50, we can add 20 hours and 45 minutes to find the arrival time in Colombo:

01:50 + 20:45 = 22:35

So, the arrival time in Colombo is 10:35 pm.

Learn more about the addition visit:

https://brainly.com/question/25421984

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6 It is divisible by 2 and by 3.

4 it is divisible by 4...

The divisibility rules of 4 and 6 are completely different. In the divisibility rule of 4, if the last two digits are zeros or the number formed by the last two digits is exactly divisible by 4, then we can say that a number is divisible by 4.

HOPE ITS HELPFUL FOR U MATE

Answer: 83 degrees

Step-by-step explanation:

(16^2 + 8^2 - 17^2)/(2)(16)(8) = 83

For a geometric sequence

a, ar, ar ², ar ³, …

the n-th term in the sequence is ar ⁿ ⁻ ¹.

The first sequence is

1, 3, 9, 27, …

so it's clear that a = 1 and r = 3, and so the n-th term is 3ⁿ ⁻ ¹.

The second sequence is

400, 200, 100, 50, …

so of course a = 400, and you can easily solve for r :

200 = 400r   ==>   r = 200/400 = 1/2

Then the n-th term is 400 (1/2)ⁿ ⁻ ¹.

Similarly, the other sequences are given by

3rd: … 4 × 2ⁿ ⁻ ¹

4th: … 400 (1/4)ⁿ ⁻ ¹

5th: … 5ⁿ ⁻ ¹

6th: … 1000 (1/2)ⁿ ⁻ ¹

7th: … 2 × 5ⁿ ⁻ ¹

Answer: A

Step-by-step explanation:

The graph has a vertical asymptote at x = -2. In this situation, vertical asymptotes happen when the denominator equals zero, which leaves the function undefined. Therefore, find the answer choice whose denominator equals zero when x = -2.

A would be correct because when x = -2,

[tex]F(-2)=\frac{1}{-2+2}=\frac{1}{0}[/tex], which is undefined.

Answer: 6 Painters

Step-by-step explanation:

Total painters needed to paint 7-room house = 3 painters

Rooms painted by each painter = 3/7

Total painters needed to paint 14-room house = 3/7×14

= 42/7

= 6 painters

Therefore it will require 6 painters to paint 14-room house

please click thanks and mark brainliest if you like :)

Perimeter:-4a

[tex]\\ \large\sf\longmapsto 4(5)=20in[/tex]

[tex]\boxed{\sf LSA=Height\times Perimeter}[/tex]

[tex]\\ \large\sf\longmapsto LSA=10\times 20[/tex]

[tex]\\ \large\sf\longmapsto LSA=200in^2[/tex]

Answer:

9 books

Explanation:

Number of animal books = 43

Number of art books = 29

So, total number of books

= Number of animal books + Number of art books

= 43 + 29

= 72

Number of books in each shelf, if divided equally

= Total number of books/Number of shelfs

= 72/8

= 9

So, each shelf has 9 books in it.

Answer:

Step-by-step explanation:

Volume of a cuboid = length × breadth × height

lenth = 7

Breadth = 10

Height = 9

7 x 10 x 9

= 630 yd^2

Answered by G a u t h m a t h

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Answer:

6x + 3 + 2y

Step-by-step explanation:

The GCF is 6 as thats the largest factor, so you divide the numbers by 6.

6x + 3 + 2y

Answer:

Hello,

We don't need vw(x) !

[tex]w^{-1}(x)=\dfrac{x-1}{2}[/tex]

Step-by-step explanation:

[tex]w(x)=2x+1=y\\\\2y+1=x \ exchanging \ x\ and\ y\\\\y=\dfrac{x-1}{2} \\\\w^{-1}(x)=\dfrac{x-1}{2}[/tex]

Answer:

- 14

Step-by-step explanation:

a = 3

a^2 - 6a - 5

= 3^2 - 6 ( 3 ) - 5

= 9 - 18 - 5

= 9 - 23

= - 14

Answer: [tex]9\times 11\ ft^2[/tex]

Step-by-step explanation:

Given

Height is [tex]2\ ft[/tex] more than its width

Suppose the width is [tex]x[/tex]. So, height becomes [tex]x+2[/tex]

Area of the painting is [tex]99\ ft^2[/tex]

Area is the product of width and height

[tex]\therefore 99=x(x+2)\\\Rightarrow 99=x^2+2x\\\Rightarrow x^2+2x-99=0\\\Rightarrow x^2+11x-9x-99=0\\\Rightarrow (x+11)(x-9)=0\\\Rightarrow x=-11,9[/tex]

Neglect the negative values

[tex]\text{Width =}9\ ft\\\text{height =}9+2=11\ ft[/tex]

Answer:

$64

Step-by-step explanation:

Let the pay of Bella be x and Glen be y.

ATQ, 7x-5y=46 and 6x+5y=188, x=18, y=16.

Glen earned 4*16=64 bucks on Friday.

[tex]x - 12 = 14 \\ x = 14 + 12 \\ x = 26[/tex]

it was help to you ❤︎❤︎❣︎❣︎★★★

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{x - 12 = 14}[/tex]

[tex]\huge\text{ADD 12 to BOTH SIDES}[/tex]

[tex]\huge\textsf{x - 12 + 12 = 14 + 12}[/tex]

[tex]\huge\boxed{\bullet}\huge\text{ CANCEL out: 12 - 12 because it gives}\\\huge\text{you 0}[/tex]

[tex]\huge\boxed{\bullet}\huge\text{ KEEP: 14 + 12 because it gives you}\\\huge\text{the RESULT of the x-value}[/tex]

[tex]\huge\textsf{a = 14 + 12}\\\huge\boxed{\rightarrow}\huge\textsf{ 14 + 12 = a}[/tex]

[tex]\huge\textsf{14 + 12 = \bf 26}[/tex]

[tex]\boxed{\huge\textsf{Therefore, your answer is: a = 26}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]

2^2 + 2^2 = h^2

8 = h^2

√8 = h

h = 2.82mm

Answered by Gauthmath must click thanks and mark brainliest

Answer:

[tex]{26}[/tex]

Step-by-step explanation:

[tex] \sqrt{(0 - ( - 5) ){}^{2} + (0 - 1) {}^{2} } [/tex]

[tex] = \sqrt{ {(5)}^{2} + {( - 1)}^{2} } [/tex]

[tex] = \sqrt{25 + 1} [/tex]

[tex] = \sqrt{26} [/tex]

Answered by GAUTHMATH

Answer:

26

Step-by-step explanation:

(-5, 1) (0, 0)

sqrt(5^2 + (-1^2))

sqrt(25 + 1)

sqrt(26)

So, 26 goes under the radical.

Answer:

13 and 39

Step-by-step explanation:

The sum of two numbers = 52

One number is 3 times as large as the other

Equation:

x + 3x = 52

4x = 52

52 / 4 = x

x = 13

13 * 3 = 39

The numbers are 13 and 39

If my answer is incorrect, pls correct me!

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-Chetan K

f(x)=3x²+x-3x-1

=x(3x+1)-(3x+1)

=(x-1)(3x+1)

[tex]\\ \sf\longmapsto 20°+2p=70[/tex]

[tex]\\ \sf\longmapsto 2p=70-20[/tex]

[tex]\\ \sf\longmapsto 2p=50[/tex]

[tex]\\ \sf\longmapsto p=\dfrac{50}{2}[/tex]

[tex]\\ \sf\longmapsto p=25[/tex]

Answer:

12

Step-by-step explanation:

bc it is

5:-c

The 3multiples are 25,50,75

6:-c

[tex]\\ \sf\longmapsto 6\:of\:2+9-5[/tex]

[tex]\\ \sf\longmapsto 6(11-5)[/tex]

[tex]\\ \sf\longmapsto 6(6)[/tex]

[tex]\\ \sf\longmapsto 36[/tex]

7:-a

12,17

8:-c

HCF=2×2×11=44

9:-c

LCM of 9 and 5 is 45 hence its true

10:-c

HCF of two consecutive numbers is 1

Given:

The equation is:

[tex]2540=\dfrac{22}{7}r^2(20)[/tex]

To find:

The solution for the given equation.

Solution:

We have,

[tex]2540=\dfrac{22}{7}r^2(20)[/tex]

It can be written as:

[tex]\dfrac{2540\times 7}{22\times 20}=r^2[/tex]

[tex]\dfrac{17780}{440}=r^2[/tex]

[tex]\dfrac{889}{22}=r^2[/tex]

Taking square root on both sides, we get

[tex]\sqrt{\dfrac{889}{22}}=r[/tex]               [Radius cannot be negative]

[tex]r=6.3568145[/tex]

[tex]r\approx 6.36[/tex]

Therefore, the value of r is about 6.36 cm.

Answer:

(-4, -4)

Step-by-step explanation:

On a 2D graph, moving to the right means going up the x axis, to the left means down the x axis, up means up the y axis, and down means down the y axis.

The point is translated 2 units to the right. This means that it is going up the x axis by two units. As it is going up, we can say that it is increasing. Therefore, on a coordinate (x,y), going up the x axis means we add to the x value. For the point (-6, -4), we add 2 to the x value, or -6, to get -6+2 = -4 as our new x value.

Our new end value is (-4, -4)