Which of the following statements is true?
a.
sin 30° = cos 30°
b.
sin 35° = cos 55°
c.
sin 60° = cos 60°
d.
sin 55° = cos 25°

Answer:

-12 - 51i

Step-by-step explanation:

[tex]original:(-6-3i)*(5+6i)\\FOIL:(-6)(5)+(-6)(6i)+(-3)(5)+(-3i)(6i)\\Multiply:(-30)+(-36i)+(-15i)+(18i^2)\\Combine\ Like\ Terms:(-30) + (-51i)+(-18i^2)\\i^2\ =\ -1:(-30)+(-51i)+(-18)(-1)\\Multiply:(-30)+(-51i)+(18)\\Combine\ Like\ Terms:(-12) + (-51i)\\Simplify:-12-51i[/tex]

Thing to remember:

[tex]i = \sqrt{-1} \\i^2 = \sqrt{-1}*\sqrt{-1} = \sqrt{-1}^2 = -1\\i^3 = \sqrt{-1}*\sqrt{-1}*\sqrt{-1} = i^2 * i = (-1)*i = -i\\i^4 = \sqrt{-1}*\sqrt{-1}*\sqrt{-1}*\sqrt{-1} = \sqrt{-1}^2*\sqrt{-1}^2 = (-1)*(-1) = 1\\[/tex]

And all powers over 4 repeat such that [tex]i^x\ such\ that\ x\mod4 = y[/tex] is the same as [tex]i^y\\[/tex]:

i.e.:

[tex]i^6 = i^{4+2}= i^4*i^2 = 1*-1 = -1\\\\i^9 = i^{4+4+1}=i^4*i^4*i^1=(1)(1)(i) = i[/tex]

NOTE: x mod 4 simply means the remainder when x is divided by 4.

i.e.:

[tex]7\mod4 = 3\\8\mod4 = 0\\13\mod4 = 1[/tex]

The computation shows that the tons of sugar when they'll have same price is 18 tons.

The first company charges $5500 to rent trucks plus an additional fee of $200.25. Thai will be:

= 5500 + (200.25 × s)

= 5500 + 200.25s

where s = tons of sugar

The second company charges $5041 to rent trucks plus an additional fee of $225.75 for each ton of sugar. This will be:

5041 + 225.75s

Then we will equate both of them. This will be:

5500 + 200.25s = 5041 + 225.75s

5500 - 5041 = 225.75d - 200.25s

459 = 25.5s

s = 459/25.5

s = 18

At 18 tons, they'll have same price.

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The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $5500 to rent trucks plus an additional fee of $200.25 for each ton of sugar. The second company charges $5041 to rent trucks plus an additional fee of $225.75 for each ton of sugar. For want mount if sugar do they charge the same price.

Answer:

38/39

Step-by-step explanation:

P=s/(s+f)

P=38/(38+1)

P=38/39

Answer:

x = 1, x = 4

Step-by-step explanation:

First, let x = u^(2/3)

The problem given has a third power and also a 1.5 power. That is just oof! So choosing "u to the 2/3 power" to substitute in for x will make this equation be a straightforward quadratic that you can factor and solve.

see image.

Substitute

x = u^(2/3)

This gives you:

u^2 - 9u + 8 = 0

Factor.

(u - 1)(u - 8) = 0

Solve.

u-1 = 0 and u-8=0

u = 1 and u = 8

Substitute back into

x = u^(2/3)

x = 1^(2/3) and

x = 8^(2/3)

Remember some exponent rules and definitions. The 2 in the 2/3 will square the base number and the 3 (actually 1/3) will cuberoot the base number. See image. Hope this helps.

Answer:

C) 2.7 x 10-15

Step-by-step explanation:

Sorry if I'm wrong. hope you're having a great day

The computation shows that the value of (9 x 10−13) − (6.3 x 10−15) is C. 2.7 x 10−15

Simplify (9 x 10−13) − (6.3 x 10−15).

This will be solved as follows. It should be noted that one just have to subtract the values.rhat are given based on the information above.

Therefore, (9 x 10−13) − (6.3 x 10−15).

= 2.7 x 10−15

In conclusion, the correct option is C.

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Answer:

i don't know how to attach the file

The length of the square in centimetres in algebraic expression is 25m

The perimeter of a square is m meters.

The length of the each side of the square in centimetres can be represented in an algebraic expression as follows:

Therefore,

perimeter of a square = 4l

where

Therefore,

m = 4l

where

l = m / 4 meters.

Therefore, the side length of the square in centimetres is as follows:

1 meters = 100 cm

m / 4 meters  = ?

cross multiply

length of the square in meters = m / 4 × 100

length of the square in meters = 100m / 4

length of the square in meters = 25m

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a. It takes the robot 4/35 hour to complete one tasks

b. The number of tasks the robot can complete in one hour is 8 3/4 tasks

From the question, we are to determine how long it takes the robot to complete one task

From the given information,

A robot can complete 7 tasks in 4/5 hour

If the robot can complete 7 tasks in 4/5 hour

Then,

The robot will complete 1 task in 4/5 ÷ 7 hour

4/5 ÷ 7

= 4/5 × 1/7

= 4/35  

Hence, it takes the robot 4/35 hour to complete one tasks

b.

Let the number of tasks the robot can complete in one hour be x

If the robot can complete 7 tasks in 4/5 hour

Then,

The robot will complete x tasks in 1 hour

4/5 × x = 7 × 1

4/5 × x = 7

4 × x = 7 × 5

4x = 35

x = 35/4

x = 8 3/4

Hence, the number of tasks the robot can complete in one hour is 8 3/4 tasks

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Answer: 16 ft

Step-by-step explanation: The ratio given is 2ft=1in, therefore 2ft/1in=1. Multiplying anything by 1 equals itself, so multiplying 8in*(2ft/1in)=16ft where the number of inches cancel out.

Answer:

B.

Step-by-step explanation:

any arithmetic operation with functions just means to do this operation with the functional expressions.

f/g is really just the expression of f divided by the expression of g.

so, this results in a fraction with the denominator (bottom part) = 2x + 1

as you know, a division by 0 is not a valid operation, and therefore we have to forbid any value for x that would create a 0 in the denominator.

so, for what x do we get

2x + 1 = 0

2x = -1

x = -1/2

therefore, we have to exclude x = -1/2.

The solution to  function f(x) = 4 is 2 1/5.

Given that, f(x) = 5x - 7

Now, function  f(x) = 4 implies that

i.e. 5x - 7 = 4

i.e. 5x = 4 + 7

i.e. 5x = 11

i.e. x = 11/5

x =2 1/5

So, option (4) is correct. ​​​​​

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

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The function is f(x)= 5x-7. The solution to f(x)=4 is when x is 11/5.

Given that,

The function is f(x)= 5x-7

A function is nothing but in mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain),where there is exactly one output for every input, and the output can be connected to its input.

f(x), where x is the input, is a common way to refer to a function. A function represented as y = f(x).

We have to find the solution to f(x)=4

Take 5x-7 in the place of f(x) because they are equal.

5x-7=4

5x=4+7

5x=11

x=11/5

Therefore, the solution x value is 11/5.

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Answer:

length= 12 width=6

Step-by-step explanation:

when adding perimeter you add the length and width twice each so divide 36 by two and get 18

if the length is twice the width then you could make the equation w+2w=18

by adding like terms you get 3w=18

to get n by itself you divide 18 by 3 and get w=6

if the width is 6 and the length is twice that then the length is 12

Answer:

A=72

Step-by-step explanation:

The length of a rectangle is TWICE it's width meaning 2 times. (Note that L= length, W=width, and A=Area)

L=2w

4w+2w=36

6w=36 <- ( 6 is width)

then

2x6=12

Then

12x6=72

So the area of the rectangle is 72.

Hope that makes sense!

Step-by-step explanation:

the absolute value function always delivers the positive value of the internal expression, no matter if it is actually negative or already positive.

so,

|-25| = 25

therefore,

-7 + 25 = 18

Answer:

4) Larger/smaller, Size

5) Whichever are larger then the original, depends on if green or blue is original

Step-by-step explanation:

Answer:4 to 5 times a day

Step-by-step explanation:

Answer:

For the 60-30-90 degree triangle:

x=12

y=[tex]12\sqrt{3}[/tex]

For the 30-60-90 degree triangle:

x=16

y=[tex]8\sqrt{3}[/tex]

For the 45-45-90 degree triangle:

x=7

y=[tex]7\sqrt{2}[/tex]

Step-by-step explanation:

For 30-60-90 triangles, the side opposite the 30 degree angle is x, while the side opposite the hypotenuse is 2x, while the side opposite the 60 degree angle is [tex]x\sqrt{3}[/tex].

For 45-45-90 triangles, the sides opposite the 45 degree angles are x, while the hypotenuse is [tex]x\sqrt{2}[/tex].

Using the distance formula, the diameter has a length of

[tex]\sqrt{(-2-6)^2 + (-1-3)^2}=4\sqrt{5}[/tex]

The radius is half the diameter, so the answer is

[tex]\frac{4\sqrt{5}}{2}=\boxed{2\sqrt{5}}[/tex]

The domain is the set of all integers lying in the interval [0 , 200] and range is the set of all reals lying in the interval [800 , 2800].

What is a function?

A function defined from A to B, associates each and every element of the set A tò the element of set B. In mathematics, it is represented using the symbol, f : A -> B. Here, set A is called the domain of the function while set B is called the range of a function.

Calculation of domain and range of a given function

The domain is the set of all possible values of x.  According to this question, the domain of N lies in the interval [0 , 200] i.e. all the integers lying in the given interval. Only integers are chosen because the number of books cannot be in fraction.

The range is the set of possible costs and lies in the interval [800 , 2800] i.e. all the reals lying in the given interval.

Hence, the domain is the set of all integers lying in the interval [0 , 200] and range is the set of all reals lying in the interval [800 , 2800].

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scale factor of triangle is 20/7 = 2.8571 .

To get the scale factor of two triangles, follow these steps:

1. Check that the two triangles are similar.

2-If the triangles are similar, identify the sides that match.

3. Subtract any known angle from the triangle and multiply the result by the matching (also known) angle in the second triangle.

As a result,

4- the scale factor is equalized by the division.

∵ To find scale factor of two triangle we divide the sides of the both sides

∴ the scale factor of triangle given will be 20/7 = 2.8571 .

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Some of the 20th century's biggest market shifts were sparked by technological breakthroughs that impacted market supply curves.

The supply curve illustrates the relationship between the price of an item or service and the volume delivered over a specific time period.

In a typical scenario, the amount supplied will be shown on the horizontal axis and the price will be shown on the left vertical axis.

It should be noted that some of the 20th century's biggest market shifts were sparked by technological breakthroughs that impacted market supply curves.

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The least common multiple of 10 and 4 is 20.

L.C.M is defined as Least Common multiple. The Least Common multiple of two numbers is the least possible number that can be divisible by both the numbers. Or, in simple words, the least common multiple of two or more numbers is the smallest number among all common multiples of the given numbers.

We need to find the L.C.M of two numbers which are 10 and 4

First we will find out few multiples of 10 and 4which are:

       multiples of 10 : 10,20,30,40,50,60,70,80.....

       multiples of 4 : 4,8,12,16,20,24,28,32,36,40,......

Then we will filter out the common multiple.

common are : 20 and 40

From these two number the least number is 20.

Hence the least common multiple of 10 and 4 is 20.

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The expression with the y subject is y=(x²-w)/2z.

Given that,

The expression is x²-2yz

We have to express in the y as subject

In algebraic formulations, numbers are represented by letters or alphabets without their numerical values being specified. The fundamentals of algebra taught us how to represent an unknown value using letters like x, y, and z. Here, these letters are referred to as variables. A mathematical expression may have both variables and constants. A coefficient is any value that is introduced before and increased by a variable.

Let take w= x²-2yz

2yz=x²-w

Divide the equation by 2z.

2yz/2z=(x²-w)/2z

y=(x²-w)/2z

Therefore, The expression with the y subject is y=(x²-w)/2z.

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The function y = -x² + 3x + 4 is negative when - 1 > x > 4.

A function is made up of three parts: a set of inputs, a set of outputs, and a rule that links the components of the input set to the components of the output set so that each input is paired with exactly one output.

Consider the function,

y = - x² + 3x + 4

For the function to be negative y < 0.

Therefore,

- x² + 3x + 4 < 0

- ( x² - 3x - 4 ) < 0

- (  x² - 4x + x - 4 ) < 0

- [ x ( x - 4 ) + 1 ( x - 4 ) ] < 0

- ( x + 1 ) ( x - 4 ) < 0

Multiplying by -1 on each side of the inequality.

- ( x + 1 ) ( x - 4 )(-1) > 0( - 1 )

( x + 1 ) ( x - 4 ) > 0

x < - 1 or x > 4

Therefore, the function is negative when - 1 > x > 4.

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Answer:

the scientific notation of 83300 is 8.33*10^4

Answer:

9. 5 is the other number in the sum of two numbers

:(

hope it will help

Answer:

5

Step-by-step explanation:

because I give him and the answer is incorrect I know but I gave him believe me

Answer:

Step-by-step explanation:

Answer:

There is no solution.  The lines are parallel.  They will never intercept.  There will be no point that is on both lines.

Step-by-step explanation: