Find the sine and the cosine of 30°.
A. sin 30° =1/2, cos 30°= √3
B. sin 30°=1/2, cos 30° = √3/2
C. sin 30° = √3/3, cos 30°= √3/4
D. sin 30° = √3/3, cos 30° = √3/2

If x∆y = 3x - y², then

5∆1 = 3×5 - 1² = 15 - 1 = 14

and

14∆6 = 3×14 - 6² = 42 - 36 = 6

So (5∆1)∆6 = 6.

Answers:

2% bond: $11000

4% bond: $13000

========================================================

Explanation:

x = amount invested in the 4% bond

y = amount invested in the 2% bond

Amounts are in dollars

The two amounts add to $24,000 so

x+y = 24000

y = -x+24000 is one equation to set up

0.04x = interest earned from the 4% bond

0.02y = interest earned from the 2% bond

0.04x+0.02y = total interest earned = $700

0.04x+0.02y = 700 is another equation to set up

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The system of equations is

[tex]\begin{cases}y = -x+24000\\0.04x+0.02y = 700\end{cases}[/tex]

Apply substitution. Solve for x.

0.04x+0.02y = 700

0.04x+0.02(-x+24000) = 700

0.04x-0.02x+480 = 700

0.02x= 700-480

0.02x= 220

x= 220/(0.02)

x = 11000

Use this to find y

y = -x+24000

y = -11000+24000

y = 13000

Given the parameterization

[tex]\vec r(u,v) = u\cos(v) \, \vec\imath + u\sin(v) \,\vec\jmath + v \,\vec k[/tex]

take the normal vector to be

[tex]\vec n = \dfrac{\partial\vec r}{\partial u} \times \dfrac{\partial \vec r}{\partial v} = \sin(v) \,\vec\imath - \cos(v) \,\vec\jmath - u \,\vec k[/tex]

(The order of partial derivatives in the cross product doesn't matter since this a scalar line integral.)

Compute the magnitude of the normal vector.

[tex]\|\vec n\| = \sqrt{\sin^2(v) + (-\cos(v))^2 + (-u)^2} = \sqrt{1+u^2}[/tex]

so that the area element reduces to

[tex]dS = \|\vec n\| \, du\,du = \sqrt{1+u^2}\,du\,du[/tex]

Evaluate the integrand at [tex]\vec r[/tex] to get

[tex]\sqrt{1 + (u\cos(v))^2 + (u\sin(v))^2} = \sqrt{1 + u^2}[/tex]

The surface integral reduces to

[tex]\displaystyle \iint_S \sqrt{1+x^2+y^2} \, dS = \int_0^{2\pi} \int_0^1 (1+u^2) \, du \, dv = 2\pi \int_0^1 (1+u^2) \, du = \boxed{\frac{8\pi}3}[/tex]

The Gross pay which Derek gets is 690 dollars.

Gross pay is what employees earn before taxes, benefits and other payroll deductions are withheld from their wages. The amount remaining after all withholdings are accounted for is net pay or take-home pay.

Here, Total hours worked by Derek = 43 hours

Rate of pay = $15 per hour

Rate of pay beyond 40 hours = $30 per hour

Now,

Rate of pay for the first 40 hours = 40 X 15 = $ 600

Since the pay rate doubles after 40 hours,

Rate of pay for the remaining 3 hours = 3 X 30 = $ 90

Gross Pay = 600 + 90 = $ 690

Thus, the Gross pay which Derek gets is 690 dollars.

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Answer:

5√2, 5

Step-by-step explanation:

in a 90 45 45 triangle, each leg is the same legnth

the hypotenuse of a 90 45 45 triangle is x√2

x being the measure of the leg

Answer:

option b, y = 3/4x - 11

Step-by-step explanation:

Parallel lines have the same slope,

slope = rise / run where the rise is 3 and the run is 4

slope = 3/4

The line is in a upwards trend making the slope positive making choice c and d incorrect

The line passes through (8, -5)

y = 3/4x + b, (x, y)

-5 = 3/4(8) + b

-5 = 6 + b

-5 - 6 = 6 - 6 + b

-5 - 6 = b

-11 = b

y = 3/4x - 11

This can be represented by [tex]\boxed{10(x+y)}[/tex]

Answer:

8/3

Step-by-step explanation:

4 x 2 = 8, so (4 × 2)/2 = 8/3.

Answer:

22/7

Step-by-step explanation:

22/7 is not very close to pi, but it is sometimes used as an estimation for pi

Answer:

22/7 is estimation

y equals short dash 2 x minus 1

In other words, y = -2x - 1 is the equation

=========================================================

Explanation:

Slope = m = -2

Point on the line is (x,y) = (1, -3)

Use these three items to find the y intercept b

y = mx+b

-3 = -2*1 + b

-3 = -2 + b

-3+2 = b

-1 = b

b = -1

The slope intercept form of y = mx+b turns into y = -2x-1 after plugging m = -2 and b = -1

Answer:

Sorry I don't know the answer

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Answer:  [tex]\textsf{Option D, y = 2x - 3}[/tex]

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Given: [tex]\textsf{The graph}[/tex]

Find: [tex]\textsf{The equation in slope intercept form}[/tex]

Solution: Looking at the graph, we can see that the line intersects the y-axis at -3 therefore that is the y-intercept.  All we need to do now is find a second point so we can determine the slope.  The line crosses at (1, -1) so we will use that as the second point.  Then we just plug all of the values into the slope intercept form.

Determine the slope

Plug in the values

Therefore, the option that would best fit the graph that was provided would be option D, y = 2x - 3.

Step-by-step explanation:

3x - 2 is formatted in the formula y = mx + c

To substitute for 3x - 2

y = 3x -2

We found a counterexample, so the statement is false.

Let's use the matrix:

[tex]\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right][/tex]

This is a 4x4 matrix with determinant equal to -2.

The inverse matrix is:

[tex]\left[\begin{array}{cccc}1/2&0&0&0\\0&-1&0&0\\0&0&-1&0\\ 0&0&0&-1 \end{array}\right][/tex]

If we multiply it by 2, we get:

[tex]\left[\begin{array}{cccc}1&0&0&0\\0&-2&0&0\\0&0&-2&0\\ 0&0&0&-2 \end{array}\right][/tex]

The adjoint of that is the original matrix, actually:

[tex]\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right][/tex]

Which we already know, has a determinant of -2.

So the statement is false, as we found a counterexample.

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Answer:

The answer is 20 L

Step-by-step explanation:

if 1/2 minutes = 1 L

10 minutes = 20 L

Answer:

20 liters

Step-by-step explanation:

when working with math problems about the rate that something is happening, it is typically helpful to find the unit rate.

In this case, the unit rate will be how many liters are lost in 1 minute (per unit essentially means per "1" )

we know that 1 liter is lost in 1/2 minute

1/2 minute = 1 liter

×2                ×2  {multiply both sides by 2 to find "1 minute"}

1 minute = 2 liters

So, for every 1 minute, we lose 2 liters

if we have 10 minutes, we can multiply both sides by 10:

1 minute = 2 liters

×10           ×10

10 minutes = 20 liters

So, after 10 minutes, 20 liters are lost

hope this helps!!

Answer:

when (-1, -4) is substituted into the first equation it's true

when (-1, -4) is substituted into the second equation it's true

the ordered pair (-1, -4) is a solution to the systems of equation

Step-by-step explanation:

original equation

x-y=3

multiply both sides by 7

7x-7y = 21

add 7y to both sides

7x=7y + 21

substitute into second equation

(7y+21)-y=-3

simplify

6y+21=-3

subtract 21 from both sides

6y=-24

y=-4

substitute y into original equation

x-(-4) = 3

cancel out negative signs

x+4=3

subtract -4 from both sides

x=-1

Answer:

[tex]\fbox {77}[/tex]

Step-by-step explanation:

Given

⇒ a = 5

⇒ d = + 8

Solving :

⇒ a₁₀ = a + 9d

⇒ a₁₀ = 5 + 9(8)

⇒ a₁₀ = 5 + 72

⇒ a₁₀ = 77

Answer: [tex]x=0,x=-\frac{9}{2}, x=\frac{9}{2}[/tex]

Step-by-step explanation:

[tex]-3x(4x^2-81)(x^2+64)=0\\[/tex]

multiply the terms together

[tex]-12x^5-525x^3+15552x=0[/tex]

factor left side of the equation

[tex]3x(-x^2-64)(2x+9)(2x-9)=0[/tex]

set factors equal to 0

[tex]x=0,x=-\frac{9}{2}, x=\frac{9}{2}[/tex]

Answer:

y = -5x

Step-by-step explanation:

gradient = delta y / delta x

gradient = -10 / 2

gradient = -5

y = mx + b

5 = -5(-1) + b

5 = 5 + b

b = 0

y = -5x

Answer:

The answer is y = -4x+11

Answer:

0.0085× 100= 0.85℅

Step-by-step explanation:

okay so you want 3/8 from 44 as percentage but how can you put the 3/8 on top of the 44 to multilply it by 100 to get the percentage, ofcourse we will have to change the 3/8 into a whole number. To do that we are going to do the following.

= 3 ÷ 8 = 0.375, so here you got a number that you can put on the 44.

Now to get the percentage we are going to do this:

0.375/44 × 100

= 0.0085 × 100 ( I solved the 0.375/44 as you know that division always comes first in maths)

= 0.85℅ ( I solved the 0.0085 × 100)

°•°•° I hope this helped sorry for taking long °•°•° May I get brainliest if you liked my ans im trying to lvl up ty and its okay if you don't want to

Answer:

D)

Step-by-step explanation:

47 is the right answer! Have an cool day!

The area of the piece of red paper after the hole for the photograph has been cut is,

⇒ 47 square units.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Now, First, find the area of the two squares:

The photograph have vertices:

(-3, -2), (-2, 2), (2, 1), and (1, -3).

Since, The square is diagonally aligned, so we need to find the length between two points in order to find the area.

For (1, -3) and (2, 1).

There is a 1 unit length and a 4 unit height.

We can use the Pythagorean theorem to find the hypotenuse of the triangle, which is the length of the square's side:

1² + 4² = x²

1 + 16 = x²

x = √17

The side length for the square of the photograph is the square root of 17,

so the area of the photograph is 17 units²

Now, The red paper has side lengths of 8. The distance between (-4, 4) and (4, 4) is 8 units wide, so we do not need to use the Pythagorean theorem.

Now , we know the area of the red paper and photograph, you can subtract the area to find the red paper with the hole:

64 - 17 = 47 square units.

Thus, The area of the piece of red paper after the hole for the photograph has been cut is,

⇒ 47 square units.

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Answer:

1.37

Step-by-step explanation:

3^1=3/2=1.5

2^(1/3)=1.26

1.5×1.26=1.89

1.89^(1/2)=1.37

Answer:

x = 4

Step-by-step explanation:

6x - 8 = 16 (add 8 to both sides)

6x = 24 (divide by 6 on both sides)

x = 4

Brainliest, please :)

Step-by-step explanation:

6x=16+8

6x=24

6x/6=24/6

x=4

so the answer is 4

Answer:

Step-by-step explanation:

The statement is false, as the system can have no solutions or infinite solutions.

The statement says that a system of linear equations with 3 variables and 3 equations has one solution.

If the variables are x, y, and z, then the system can be written as:

[tex]a_1*x + b_1*y + c_1*z = d_1\\\\a_2*x + b_2*y + c_2*z = d_2\\\\a_3*x + b_3*y + c_3*z = d_3[/tex]

Now, the statement is clearly false. Suppose that we have:

[tex]a_1 = a_2 = a_3\\b_1 = b_2 = b_3\\c_1 = c_2 = c_3\\\\d_1 \neq d_2 \neq d_3[/tex]

Then we have 3 parallel equations. Parallel equations never do intercept, then this system has no solutions.

Then there are systems of 3 variables with 3 equations where there are no solutions, so the statement is false.

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Answer:

3

Step-by-step explanation:

we can think of the slope of a graph as [tex]\frac{rise}{run}[/tex]

the "rise" is the difference in y-values between two points (the change in y)

the "run" is the difference in x-values between two points (the change in x)

when we divide these (rise/run), we find the slope

you can choose any two well-defined points (with clear x and y values), here are the two we will be using:

(remember, points are written as (x, y)  )  

(0 , 2)

(-1 , -1)

for the "rise", we have risen 3 (difference between 2 and -1 = 3 [2- -1 = 3] )

for the "run" we have ran 1 (difference between 0 and -1 = 1) (0 - - 1 = 1)

so, the slope for this graph is: 3/1 ; which simplifies to 3

So, the slope of our graph is 3

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technical layout:

[tex]m=\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex]               (note: slope is called "m" in the format of y=mx + b)

[tex]y_{1}[/tex] means one y-value, [tex]y_{2}[/tex] means other y-value

[tex]x_{1}[/tex] means one y-value, [tex]x_{2}[/tex] means other x-value

{note: it is important to keep the y1 and x1 from the same point, and the y2 and x2 from a shared point}

our equation in this layout:

[tex]m=\frac{2 -(-1)}{0-(-1)}[/tex] = [tex]m=\frac{3}{1}[/tex]

                     m = 3

Answer:

16 x^14 / y^16

Step-by-step explanation:

Remember   ' PEDMAS '

Parentheses

Exponents

Division

Multiplication

Addition

Subtraction

 so do the stuff inside the parentheses to get

  y^8     ^-2

  4x^7  

Now do the exponents  ( the -2  one)

y^-16

4^-2 x^-14       then simplify

16 x^14 / y^16

Question 1

We want to choose a white marble, then a black marble.

Multiplying these probabilities, we get (9/24)(8/24) = 1/8.

Question 2

Thus, the probability is 5/10 = 1/2.

Question 3

Multiplying these probabilities, we get (7/24)(9/23) = 21/184.

Answer:

[tex]12a^5+15a^3b^2-24b^3a^2-30b^5[/tex]

Step-by-step explanation:

(3a³-6b³) (4a² + 5b²) -> Simplify not Multiply

Expand (3a³-6b³) (4a² + 5b²) using the FOIL Method.

Apply the distributive property.

[tex]3a^3(4a^2+5b^2)-6b^3(4a^2+5b^2)[/tex]

[tex]3a^3(4a^2)+3a^3(5b^2)-6b^3(4a^2+5b^2)[/tex]

[tex]3a^3(4a^2)+3a^3(5b^2)-6b^3(4a^2)-6b^3(5b^2)[/tex]

Simplify each term.

Rewrite using the commutative property of multiplication.

[tex]3*4a^3a^2+3a^3(5b^2)-6b^3(4a^2)-6b^3(5b^2)[/tex]

↓

[tex]12a^5+15a^3b^2-24b^3a^2-30b^5[/tex]

Equation Simplified.

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Hope this helped!