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Answer:

[tex]sin\theta_1 = \dfrac{\sqrt{217}}{19}[/tex]

Step-by-step explanation:

It is given that:

[tex]cos\theta_1 = -\dfrac{12}{19}[/tex]

And we have to find the value of [tex]sin\theta_1 = ?[/tex]

As per trigonometric identities, the relation between [tex]sin\theta\ and \ cos\theta[/tex] can represented as:

[tex]sin^2\theta + cos^2\theta = 1[/tex]

Putting [tex]\theta_1[/tex] in place of [tex]\theta[/tex] Because we are given

[tex]sin^2\theta_1 + cos^2\theta_1 = 1[/tex]

Putting value of cosine:

[tex]cos\theta_1 = -\dfrac{12}{19}[/tex]

[tex]sin^2\theta_1 + (\dfrac{12}{19})^2 = 1\\\Rightarrow sin^2\theta_1 + \dfrac{144}{361} = 1\\\Rightarrow sin^2\theta_1 = 1-\dfrac{144}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{361-144}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{217}{361}\\\Rightarrow sin\theta_1 = +\sqrt{\dfrac{217}{361}}, -\sqrt{\dfrac{217}{361}}\\\Rightarrow sin\theta_1 = +\dfrac{\sqrt{217}}{19}, -\dfrac{\sqrt{217}}{19}[/tex]

It is given that [tex]\theta_1[/tex] is in 2nd quadrant and value of sine is always positive in 2nd quadrant. So, the answer is.

[tex]\Rightarrow sin\theta_1 = \dfrac{\sqrt{217}}{19}[/tex]

Answer:

−  square root 15/4

Step-by-step explanation:

Answer:

The correct answer is the third expression.

Step-by-step explanation:

We have the following equation:

[tex]4*x^2 + 4*y^2 + 16*x - 24*y = 34[/tex]

Let's organize it by variables, putting together the ones that have the same letter or no letter at all. We have:

[tex]4*x^2 + 16*x + 4*y^2 - 24*y = 34[/tex]

We can extract the common factor on the left side by dividing them by 4, we have:

[tex]4*(x^2 + 4*x) + 4*(y^2 - 6*y) = 34[/tex]

We need to complete the squares on the parenthesis without changing the value of the equation, to do that we will sum the proper values inside the parenthesis and those multiplied by four on the other side of the equation, we have:

[tex]4*(x^2 + 4*x + 4) + 4*(y^2 - 6*y + 9) = 34 + 16 + 36\\4*(x + 2)^2 + 4*(y - 3)^2 = 86[/tex]

The correct answer is the third expression.

Answer:  

9 diagonals  

Bit by bit clarification:  

Number of Diagonals = n(n-3)/2  

For instance, in a hexagon, the complete sides are 6.

Along these lines, the complete diagonals will be 6(6-3)/2 = 9.

Answer:

9 diagonals hope its helpful

Answer:

$30.74

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

To find the constant

take the coefficient of x

10

divide by 2

10/2 =5

Square it

5^2 =25

Add this

x^2 +10x+25

Answer:

65 = <JKL

Step-by-step explanation:

There are two expressions that represent the same thing.

The diagram shows that <JKL = 45 + x

The question states that JKL = 3x + 5

The two expressions must be equal since they represent the same thing.

3x + 5 = x + 45

Subtract 5 from both sides

3x + 5 -  5 = x + 45 - 5

3x = x + 40                     Subtract x from both sides

3x - x = x - x + 40

2x = 40                          Divide by 2

2x/2 = 40/2

x = 20

So x + 45 = 20 + 45 = 65

or

3x + 5 = 3*20 + 5 = 60 + 5 = 65

Answer:

The answer is option D

Took the quiz

Answer: They are equivalent because when x=2, the two expressions have the same value.

Step-by-step explanation:

Answer:

82 degrees

Step-by-step explanation:

First set 10x+8 equal to 12x-10 to find that the variable is equal to 9. Then solve for 10(9)+8 which equals 98. Since angle 1 is supplementary to angle two and supplementary angles add up to 180 degrees, subtract 98 from 180 to find that your answer is 82 degrees.

Answer:

9 cubic feet

Step-by-step explanation:

Assuming that the garden box is a rectangular prism, its volume is:

[tex]4\dfrac{1}{2} \cdot 4 \cdot \dfrac{1}{2}=9 \text{ ft}^3[/tex]

Hope this helps!

Solution,

Length(L)=4 1/2 ft

Breadth(b)= 4 ft

Height(H)=1/2 ft

Now,

Volume=L*B*H

= 4 1/2*4*1/2

=9/2*4*1/2

= 9 cubic feet

Hope it helps

Good luck on your assignment

Answer:

400

Step-by-step explanation:

Answer:

The dimensions of the driveway are 21 ft x 47 ft, which is option "D" in your list of possible answers

Step-by-step explanation:

Notice that the length "L" of the driveway can be written in terms of its width as:

L = 2 w + 5

based on the given information.

Please see the attached diagram to understand the geometry of the problem, and what the area of the brick walkway involves (depicted in brick color) as the addition of the area of two rectangles:

1) one of length L= 2 w + 5 (w being the width of the driveway - depicted in grey) times 3 feet (the width of the brick walkway

and the other one:

2) w + 3 times 3

Therefore the total area of the brick walkway is given by the formula:

(2 w + 5) * 3 +(w + 3) * 3 = 213 square feet

Now we can solve for "w" in the above equation:

6 w + 15 + 3 w + 9 = 213

9 w + 24 = 213

9 w = 213 - 24

9 w = 189

w = 189/9

w = 21 feet

We can now solve for the L of the driveway, using the first formula we created:

L = 2 w + 5

L = 2 (21) + 5

L = 42 + 5

L = 47 feet

Therefore the driveway's width is w = 21 feet

and its length is L = 47 feet

The expression [tex](8 + 2 \times 6)^2[/tex], following PEMDAS, simplifies to 400.

Let's break down the steps in solving the expression [tex](8 + 2 \times 6)^2[/tex] in more detail (Follow PEMDAS).

Step 1: MultiplicationWe start by evaluating the multiplication operation, which is 2 x 6. The result of this operation is 12.

Step 2: AdditionNext, we evaluate the addition operation, which is 8 + 12. The sum of 8 and 12 is 20.

Step 3: SquaringFinally, we square the result of the addition, which is 20. Squaring a number means multiplying it by itself. In this case, [tex]20^2[/tex] means 20 multiplied by 20, which equals 400.

Therefore, the expression [tex](8 + 2 \times 6)^2[/tex] simplifies to 400.

Learn more about PEMDAS here:

https://brainly.com/question/36185

#SPJ4

Answer:

The equation of the relationship is y = 1.25x + 6.5

Step-by-step explanation:

I graphed the ordered pairs on the graph below and found the slope and y-intercept of the line.

The price per game is $7.75. (If needed)

Answer:

Step-by-step explanation:

This problem is on the mensuration of flat shape, a circle.

we know that the circumference of a circle is expressed as

[tex]C= 2\pi r[/tex]

Given that radius = 12 ft

The circumference can be solved for by substituting the value of r in the formula

C=2*3.142*12

C= 75.408ft

to 2 d.p the circumference is 75.41 ft

Answer:

easy just find the total of how many people work there then put that no. as a denominator and put 12 on the numerator then times it by 100 and the answer should be 52.2% or 52.17%

Answer:

52.2% or 52.17%

12 men

Total = 23

12 / 23 =

Answer:

275 ft

Step-by-step explanation:

The formula given to use for the slant height l of the cone is ;

l = (s - πr^2)/π

Now substituting the parameters given in the question, 500 π for area and radius of 15, we have

l = {500π-15^(2)π}/π

l =( 500 π -225 π)/π

l = 275 π/π

l = 275 ft

Answer:

275

Step-by-step explanation:

^ and what they said

Answer:

see below

Step-by-step explanation:

2* (4*8) = (2*4) * 8

This is the associative property of multiplication

Answer:

Step-by-step explanation:

rectangle + semicircle

= 8*6 + pi r^2/2

=48 + 22/7 * 3/2 * 3/2

then simplyn..

Answer:

The figure is a rectangle and a semicircle

Step-by-step explanation:

Answer:

12.85

Step-by-step explanation:

P=1/2(3.14xd)+d

P=1/2x15.7+5

P=12.85

Answer:

192 cubes.

Step-by-step explanation:

The volume of each cube  = (side)³  = (1/4)³  = 1/64 units ³

Next is to find how many cubes are needed to fill the prism.

The number of cubes  that will fill the prism  :

Vol. of prism / Vol. of cube = 3 / [tex]\frac{1}{64}[/tex]

                                            =192 cubes.

Therefore, it takes 192 cubes to fill the prism.

Answer:

W

Step-by-step explanation:

The input is the x-axis.

The output is the y-axis.

Make them coordinates. Hope this helped!

Answer:

8/17

Step-by-step explanation:

total balls= 9 + 18 + 2 + 5 = 34

balls drawn should NOT be Orange.

so, 34 - 18 (as there are 18 orange balls)

16 balls

probability= 16/34 = 8/17

answer = 8/17

Answer:

i think its c idk if im wrong im sorry

Step-by-step explanation:

Answer:

9 spoons knives =12

9 spoons cost= £ 82.80

total no of 1 knife = 12x9 = 108

1 knife = 82.80 x 108 = 8,94, 240

so, 1 knife Cost's =£ 8,94,240

｡☆✼★ ━━━━━━━━━━━━━━  ☾  

4 : 5

300 : ?

Divide 300 by 4 to find out what '1 part' would count as:

300/4 = 75

Multiply this by 5

75 x 5 = 375

Add the two values together

375 + 300 = 675

There are 675 students

Have A Nice Day ❤    

Stay Brainly! ヅ    

- Ally ✧    

｡☆✼★ ━━━━━━━━━━━━━━  ☾

Step-by-step explanation:

Number of boys=300

Ratio of boys to girls=4:5

let the number of girls=y

300/y=4/5

Cross multiply

300×5=4×y

1500=4y

Divide through both sides by 4

1500/4=4y/4

374=y

Number of girls is 375

Total number of students=Number of boys+Number of girls

Total number of students=300+375

Total number of students=375

Answer:

3.2 ft

Step-by-step explanation:

The initial distance from the base of the ladder to the wall is:

[tex]20^2=16^2+d^2\\d=12\ ft[/tex]

After moving the ladder, the distance from the base to the wall is 12 - 2x while the height of the ladder is 16 + x. The distance x is given by:

[tex]20^2 = (12-2x)^2+(16+x)^2\\400 = 144-48x+4x^2+256+32x+x^2\\5x^2-16x=0\\5x=16\\x=3.2\ ft[/tex]

Therefore, the top of the ladder is  3.2 ft higher now.

Answer:

3.2ft higher

Step-by-step explanation:

Answer:

Felipe's answer is 8.

6 divided by 3/4

= 6 * 4/3

= 24/3

= 8

Answer:

8

Step-by-step explanation:

6÷3/4=6×4/3=8

Answer:

-9.661

Step-by-step explanation:

In the given equation, a and b are negative. The values of a and b are given. If you insert the values into the given formula, the values become negative because of "-" in front of the a and b values.

-a + (-b)   =   -6.05 + (-3.611)

Because the second value is negative, the plus sign references to adding BOTH negative values together so it is just the same as saying:

-6.05 - 3.611

This gives you -9.661

Hope this helps!

Answer:

g(x) has a greater y intercept than f(x)

Step-by-step explanation:

f(x) = 6x^2 + 18x +3

f(0) = 0+0+3

The y intercept is 3

g(x) crosses the y axis at 6

The y intercept is 6

g(x) has a greater y intercept than f(x)

Answer:

g(x) has a greater y intercept than f(x)

Step-by-step explanation:

f(x) = 6x^2 + 18x +3

f(0) = 0+0+3

The y intercept is 3

g(x) crosses the y axis at 6

The y intercept is 6

g(x) has a greater y intercept than f(x)

hope I could help