Write the slope-intercept form of the equation of the line through the given points.

Answer:

see explanation

Step-by-step explanation:

Using the sum/ difference → product formula

cos x - cos y = - 2sin( [tex]\frac{x+y}{2}[/tex])sin ([tex]\frac{x-y}{2}[/tex] )

sin x - sin y = 2cos ([tex]\frac{x+y}{2}[/tex] )sin ([tex]\frac{x-y}{2}[/tex] )

Given

(cosA - cosB)² + (sinA - sinB )²

= [ - 2sin([tex]\frac{A+B}{2}[/tex])sin([tex]\frac{A-B}{2}[/tex] ) ]² + [ 2cos([tex]\frac{A+B}{2}[/tex] )sin([tex]\frac{A-B}{2}[/tex] ) ]²

= 4sin² ([tex]\frac{A+B}{2}[/tex] )sin² ([tex]\frac{A-B}{2}[/tex] ) + 4cos² ([tex]\frac{A+B}{2}[/tex] )sin² ( [tex]\frac{A-B}{2}[/tex] )

= 4sin² ([tex]\frac{A-B}{2}[/tex] )[ sin² ( [tex]\frac{A+B}{2}[/tex] ) + cos² ( [tex]\frac{A+B}{2}[/tex] ) ← sin²x + cos²x = 1

= 4sin² ( [tex]\frac{A-B}{2}[/tex] ) × 1

= 4sin² ( [tex]\frac{A-B}{2}[/tex] ) = right side ⇒ proven

Answer:

use the straight line test

Step-by-step explanation:

use your pencil or draw a line horizontally (like this -> I )anywhere on the graph. If it's a function, it will only touch the line at one point no matter where you put the line.

it is B because the x value does not repeat twice

Answer:

the one in the middle

Step-by-step explanation:

why because if you see the x axis when you go over it the one that has a funtion dosent have two of the same number but the one that dosent haves two of the same numbers

Answer:

3 is the answer

mutiply and open bracket minus each other

Answer:

Function families are groups of functions with similarities that make them easier to graph when you are familiar with the parent function. They're useful because if you know the parent function, you can figure out another function from there

Step-by-step explanation:

Answer:

  right angles and obtuse angles

Step-by-step explanation:

We assume that anything that looks like a right angle is a right angle.

The angles at the left end of each horizontal line are right angles.

The angles at the right end of each horizontal line are obtuse angles.

The angle where the diagonal lines meet is a right angle.

The shape contains right angles and obtuse angles.

Answer:

66

Step-by-step explanation:

Plug in 5 for x

16 + 10(5)

16 + 50 = 66

Answer:

66

Step-by-step explanation:

So we have the expression:

[tex]16+10x[/tex]

To find the value of the expression when x is 5, substitute 5 for x:

[tex]=16+10(5)[/tex]

Multiply:

[tex]=16+50\\[/tex]

Add:

[tex]=66[/tex]

Answer:

you would need to find the area of the quantity of sheet metal needed for a roof

Step-by-step explanation:

The area is used to find the quantity of sheet metal needed for a roof.

We need to check whether the perimeter or area would be used to find the quantity of sheet metal needed for a roof.

Area: Area is defined as the amount of space that is occupied by any shape, object, or flat surface. The total number of square units that can fit into a shape or object or a flat surface defines the actual area.

Perimeter: The word 'perimeter' is derived from the Greek word 'Perimetron'. 'Peri' means 'around' and 'Metron' means 'measure'. The perimeter of a shape is calculated by adding up the length of all the sides or by measuring the outer boundary of a shape or an object.

Therefore, the area is used to find the quantity of sheet metal needed for a roof.

To learn more about an area visit:

https://brainly.com/question/27683633.

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Given :

All the natural numbers below 1000 that are multiples of 3 or 5 .

To Find :

The sum of all the multiples of 3 or 5 below 1000.

Solution :

Max multiple of 3 is 999 .

Max multiple of 5 id 995 .

So , number of multiple of 3 is :

[tex]999=a+(n-1)d\\\\999=3+3(n-1)\\\\n=333[/tex]

Similarly for 5 .

[tex]995=a+(n-1)d\\\\995=5+5(n-1)\\\\n=199[/tex]

Now , sum of all multiple of 3 is given by :

[tex]S_3=\dfrac{n}{2}(2a+(n-1)d)\\\\S_3=\dfrac{333\times (2\times 3+332\times 3)}{2}\\\\S_3=166833[/tex]

Also , sum of all multiple of 5 is :

[tex]S_5=\dfrac{n}{2}(2a+(n-1)d)\\\\S_5=\dfrac{199\times (2\times 5+198\times 5)}{2}\\\\S_5=99500[/tex]

Therefore , total sum :

[tex]T=S_3+S_5\\\\T=166833+99500\\\\T=266333[/tex]

Now , there are some common number which we add two times like :

15 , 30 , 60 ......

So , we should subtract the sum of all multiple of 15 from T .

Now , sum of all multiple of 15 is 33165 .

So ,

[tex]T=266333-33165\\\\T=233168[/tex]

Therefore , the  sum of all the multiples of 3 or 5 below 1000 is 233168 .

Answer:

8.4

Step-by-step explanation:

8 is a whole njmber, so it stays the same.

2/5 is equivalent to .4, so you put that at the end.

Your answer is 8.4 Hope this helps!

The decimal number is 8.4.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

8(2/5)

= (8 x 5 + 2) / 5

= (40 + 2) / 5

= 42/5

= 8.4

Thus,

The decimal number is 8.4.

Learn more about expressions here:

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Answer:

14

Step-by-step explanation:

5(2)² - 2 - 4 = 14

The required value of the given expression 5z²-z-4 is 14 when z = 2,

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers. Unknown variables, numbers, and arithmetic operators make up an algebraic expression. It contains no equality or inequality symbols.

The expression is given in the question below as:

5z²-z-4​

To determine the value of the expression 5z²-z-4 when z=2, we need to substitute 2 for every occurrence of z in the expression and then simplify the expression.

5z²-z-4 when z = 2 is :

= 5(2²)-2-4

= 5(4)-2-4

= 20-2-4

= 14

Therefore, the required value is 14.

Learn more about the algebraic expression here :

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Answer:

see below

Step-by-step explanation:

8- 2x - 5- 13x = 6

Combine like terms

-15x+3=6

Subtract 3 from each side

-15x+3-3=6-3

-15x = 3

Divide each side by -15

x = 3/-15

x = -1/5

Check

8 - 2(-1/5) -5 -13(-1/5) = 6

8 + 2/5 -5 +13/5 = 6

3 + 15/5 = 6

3+3=6

6=6

Answer:

It is on floor 2

Step-by-step explanation:

15-18=-3

-3+5=2

hope this helped :)

Answer:

it is on the 2nd floor

Step-by-step explanation: this is because it started at 15, then went down 18: 15-18

     -3

then it went up 5: -3+5  or 5-3

                                to end up at the 2nd floor

Answer:

£9318.96

Step-by-step explanation:

18000×0.7×0.86^(2)=£9318.96

Answer:

y = 2x + 2

Step-by-step explanation:

6x -3y = -6 (get y on one side of the equals sign by substracting 6x from both sides)

-3y = -6x - 6 (divide each side by -3 to get final value of y)

y = 2x + 2

Answer: The length of [tex]\overline{NP}[/tex] is 10 units.

Step-by-step explanation:

We are given that,

Point O is on line segment [tex]\overline{NP}[/tex] .

Then, [tex]\overline{NP}=\overline{NO}+\overline{OP}[/tex]   (i)

Since we have given that OP=8 units and NO=2 units .

Now we will substitute these values in (i), we will get

[tex]\overline{NP}=8\ units+2\ units\\\\\Rightarrow\ \overline{NP}=10\ units[/tex]

Hence, the length of [tex]\overline{NP}[/tex] is 10 units.

Answer:

u=5

Step-by-step explanation:

-29 = 5u + 6 - 12u        

-6             -6

-35 =5u - 12u

         -7u

-35 = 7u

-35 divided by 7 to get u by itself equals 5

therefore u =5

Step-by-step explanation:

Reorder the terms:

6+5u+ -12u= -29

u =5

Answer:

3.1415×10⁶

Step-by-step explanation:

Move the decimal point one digit at a time until it is after the first digit.  Count the number of times the decimal point moved.

In this case, we move the decimal point 6 places to the left.  So the scientific notation is:

3.1415×10⁶

Answer:

16

Step-by-step explanation:

You add 7, 4 and 5 to get 16.

Answer:

42+56+7.5h ≤ 300

≤ means less than or equal to and Julie does not want to go over 300 so this would be the correct symbol to use

Answer:

So we know the shop spent $250 on equipment and they also purchased 300 T-shirts  for $2 each.

Knowing this, we only have to add to the $250, what they have paid for the  T-shirts.

So if each T-shirt is purchased by $2 and they have bought 300, we multiply:

2 * 300 = $600

So we add the $600 spent on T-shirts to the $250:

600 + 250 = $850

We could also have done it with by replacing T for 300 in C = 2T + 250:

C = 2*300 + 250 --> C = 600 + 250 --> C = $850

Answer:

x-axis(independent) = 1.5

y-axis(dependant) = 75ft

Step-by-step explanation:

An INDEPENDENT variable is the variable yourself can not change, in this case its time. The DEPENDANT variable is the variable that is changed to affect data you are solving for. Idk if this helps you at all to understand for future references but i hope it did!

Answer:

x = 15

Step-by-step explanation:

Using the Altitude on Hypotenuse theorem

( leg of large Δ )² = (part of hypotenuse below it ) × ( whole hypotenuse )

Thus

x² = 9 × (9 + 16) = 9 × 25 = 225 ( take the square root of both sides )

x = [tex]\sqrt{225}[/tex] = 15

Answer:

x=8-y

Step-by-step explanation:

Answer:

See Explanation

Step-by-step explanation:

The options are not given; however, the solution is as follows;

[tex]3y = 27x[/tex]

Required

Determine relationships with the same constant of proportionality (k)

[tex]3y = 27x[/tex]

Divide both sides by 3

[tex]\frac{3y}{3} = \frac{27x}{3}[/tex]

[tex]y = \frac{27x}{3}[/tex]

[tex]y = 9x[/tex]

The relationship between y, x and k is:

[tex]y = kx[/tex]

Comparing [tex]y = kx[/tex] with [tex]y = 9x[/tex]; then

[tex]k = 9[/tex]

Hence, any of the options with k=9 answers the question.

Take for instance:

[tex]2y = 18x[/tex]

Dividing both sides by 2 gives

[tex]y = 9x[/tex] and hence; [tex]k = 9[/tex]

Answer:

The answers are A B and C

Step-by-step explanation:

I just got it right

Answer:

[tex]\Large \boxed{\displaystyle y=\sqrt{\frac{z \cdot w}{x}}}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{x}{w} =\frac{z}{y^2 }[/tex]

Cross multiplication.

[tex]x \cdot y^2 =z \cdot w[/tex]

Dividing both sides by [tex]x[/tex].

[tex]\displaystyle \frac{x \cdot y^2 }{x} =\frac{z \cdot w}{x}[/tex]

[tex]\displaystyle y^2 =\frac{z \cdot w}{x}[/tex]

Taking the square root of both sides.

[tex]\displaystyle \sqrt{y^2 } =\sqrt{\frac{z \cdot w}{x}}[/tex]

[tex]\displaystyle y=\sqrt{\frac{z \cdot w}{x}}[/tex]

Answer:

Yes

Step-by-step explanation:

You can find the answer to this question by finding the value of x in both equations.

Let's start off with the first equation: [tex]x+4=5[/tex]

To find the value of x, you're going to have to subtract 4 from both sides. This is because you're looking for the value of only x, not x + 4. To leave x alone, you'd have to subtract 4, leaving that side with just x.

[tex]x+4-4=5-4[/tex]

[tex]x=1[/tex]

The answer to the first equation is x = 1.

Now let's start on the second equation: [tex]2x+8=10[/tex]

Like before, you're looking for x alone and in this equation, 8 is being added to 2x. Although x itself isn't alone, you'll first start off with 2x since you can simplify it thrughout the process. In this equation, you're going to subtract 8 from both sides to leave the variable x alone.

[tex]2x+8-8=10-8[/tex]

[tex]2x=2[/tex]

Now you're left with 2x = 2. Since you're looking for the value of x alone, you're going to divide both sides by 2. Because x is being multiplied by 2(2 times x = 2x) you're going to divide(opposite of multiply), which will cancel out the 2(in 2x).

[tex]\frac{2x}{2} = \frac{2}{2}[/tex]

[tex]x = 1[/tex]

The answer to the second equation is x = 1.

Since both equations have the same solution, the answer to your question would be yes.

Hello There!

Yes

If you want to know if your two equations are equivalent, let's try finding the answer to both of them.

[tex]x+4=5[/tex]

Let's find x.

We all know addition and subtraction. So let's just do

[tex]5-4=x[/tex]

So 5-4 is equal to 1.

So the answer for this equation is

[tex]x=1[/tex]

Let's move on to your second equation.

[tex]2x+8=10[/tex]

Now we must subtract 8 from both sides.

[tex]2x+8-8=10-8[/tex]

And this equals

[tex]2x=2[/tex]

Let's divide the both sides by 2.

[tex]\frac{2x}{2}=\frac{2}{2}[/tex]

The fraction [tex]\frac{2}{2}[/tex] is gonna equal one.

So [tex]x=1[/tex]

Now you have your answer for the second equation. Both answers were the same.

So the answer to your question is YES.

Answer

Ex 3) - b

(-2, 19) (1,4)  

Ex 4) -b

(1, 3) (3, 5)