Where is this function positive?

Answer:

12.649

Step-by-step explanation:

we can use Pythagoras to solve this; simply by forming a triangle of the difference between the x and y values. (I added a lil-sketch of it).

So, we just need to find the length of the two sides:

Vertical side: 12

Horizontal side: 4

Thus;

[tex]4^{2} + 12^{2} = c^{2} \\160 = c^{2}\\Side c is equal to 12.649 (in whatever unit given)[/tex]

The equation of the line in slope-intercept form passes through (5,-3), parallel to y = - 2x + 4 is  y = - 2x + 8 and  equation of the line passes through (3,5), perpendicular to y = 1/3x + 12 is  y = - 3x + 18.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and equation of a line in slope-intercept form is y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

We know that parallel lines have same slopes and perpendicular lines have slopes that are negative reciprocals of each other.

Given a line passes through (5,-3), perpendicular to y = - 2x + 4.

The slope of this line is - 2 and hence line parallel to it will also have a

slope of - 2.

∴ The equation of the line in slope-intercept form is,

- 3 = 5(-2) + b.

- 3 = - 10 + b.

b = 8.

The required line  is y = - 2x + 8.

Given a line passes through (3,5), perpendicular to y = 1/3x + 12.

The given line has a slope of 1/3 so the line perpendicular to it will have a slope of - 3 ( as the negative reciprocal of 1/3 is - 3/1 = - 3 ).

∴ The equation of the line in slope-intercept form is,

3 = 5(-3) + b.

3 = - 15 + b.

b = 18.

So, y = - 3x + 18.

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The coordinates of the vertices when rotated 270° counterclockwise around the origin are:

K' = ( 4, 1 )

L' = ( 7, 1 )

M' = ( 7, 0 )

N' = ( 4, 0 )

When a point P( a, b ) is rotated 270° counterclockwise around the origin, we flip a and b and reverse the sign of a.

Therefore,

The rule to rotate a point P ( a, b )  after a rotation 270° counterclockwise around the origin is:

P ( a, b ) → P' ( b, - a )

Now, consider the points on the graph:

L = ( - 1, 7 )

K = ( - 1, 4 )

N = ( 0, 4 )

M = ( 0, 7 )

When the coordinates are rotated 270° counterclockwise.

L ( - 1, 7 ) → L' ( 7, 1 )

K ( - 1, 4 ) → K' ( 4, 1 )

N ( 0, 4 ) → N' ( 4, 0 )

M ( 0, 7 ) → M' ( 7, 0 )

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The diameter of the speck of dust is written as;

⇒ 2 × 10⁻⁵ inches.

Option A is true.

What is Number system?

A way for system of writing to express the number is called number system.

Given that;

The diameter of the speck of dust = 0.00002 inches.

Now,

Find the estimate number of the diameter of speck of dust as;

Since, The diameter of the speck of dust = 0.00002 inches.

The number = 0.00002 inches

It can be written as;

0.00002 inches = 2 × 10⁻⁵ inches.

Therefore,

The diameter of the speck of dust is written as;

⇒ 2 × 10⁻⁵ inches.

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Explanation

The distributive property tells us how to solve expressions in the form of a(b + c)

Then,

Step 1

apply distributive property operate

Step 2

add similar terms

so, the answer is

I hope this helps you

A property of equality that you should apply to keep the equation 22 . a = 242 in balance when solving include the following: A. The division property of equality.

In Mathematics and Geometry, the subtraction property of equality states that the two (2) sides of an algebraic expression or equation would still remain equal even when the same number has been subtracted from both sides of an equality.

Based on the information provided above, we can logically deduce the following equation:

22 . a = 242

22 × a = 242

By applying the division property of equality, we have the following:

a = 242/22

a = 11.

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Step-by-step explanation:

22×(t + 18) - 7

t = 13

so,

22×(13 + 18) - 7 = 22×31 - 7 = 682 - 7 = 675

The value of N/10 is 372.

The characters can be chosen from the word "AIME" or the number "2007".

There are 7 different characters that can be picked, with 0 being the only number that can be repeated twice.

There are two possible cases.

The first case is given below :

If 0 appears 0 or 1 time in the sequence, the number of possible sequences is 7!/(7-5)!.

If 0 appears 0 or 1 time in the sequence, the number of possible sequences is 2520.

The second case is given below :

If 0 appears twice in the sequence, the number of places to fill 0 is 5C2.

If 0 appears twice in the sequence, the number of places to fill 0 is 10.

The number of ways to place the remaining three characters is 6!/(6-3)!.

The number of ways to place the remaining three characters is 120.

The total number of ways in the second case is 10*120 = 1200.

The total number of ways is 2520 + 1200.

The total number of ways is 3720.

N = 3720

We have to find the value of (N/10).

N/10 = 3720/10

N/10 = 372

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Answer:

First one is a function, second one is not, since it assigns more than one y value for x values.

Step-by-step explanation:

A function means for every x value, at most 1 y value exists. This is clearly not the case for the bottom figure. You can test it with an imaginary vertical line. There should be zero or one intersections.

After simplification this 5√3(2√3−3√7) we get, -38.71

5√3(2√3−3√7) is a linear equation.

What is linear equation?

An equation between two variables that, when plotted on a graph, produces a straight line or say first degree equation is known as linear equation.

Let's simply this 5√3(2√3−3√7)

=> 5√3 * 2√3 - 3√7 * 5√3

=> 5*2*√3*√3 - 3 * 5 √7 * √3

=> 10 * 3 - 15 * 1.732 * 2.645

=> 30 - 68.717

=> -38.717 or -38.71

Therefore, the value of  5√3(2√3−3√7), after simplification we get  -38.71

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Autumn bought 4 Donuts and 2 Cookies worth of 5 dollars.

We know two simultaneous equations have a unique solution when they intersect at a point,

when they are parallel they have no solution and when they are coinciding they have an infinite no. of solutions.

Given, Autumn and her children went into a bakery and she bought $5 worth of donuts and cookies.

Each donut costs $1 and each cookie costs $0.50. She bought a total of 6 donuts and cookies altogether.

Let us denote no. of Donuts by x and no. of Cookies by y.

∴ x + y = 6...(i) and x + 0.5y = 5...(ii).

Subtracting eqn(ii) from eqn(i) we get y = 2 and substituting the value of y in eqn(i) we get x = 4.

Autumn bought 4 Donuts and 2 cookies with 5 dollars.

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To solve a system of equations algebraically means that we will use some algebraic manipulation to find the solution(s). there are two techniques for solving algebraically: elimination and substitution.

The theory of linear systems serves as the foundation for the field of linear algebra, which is used in most branches of modern mathematics.

Hence the two ways an algebraic equation can be solved is by elimination and substitution.

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Answer:

C.

Step-by-step explanation:

You can assign each variable a ride, let's say the teacup is t, the roller coaster is r, and the spinning vortex is s. Now we can create algebraic expressions to find the values of each ride :

Kristen: 2t+2r+s=20

Jorge: t+r+3s=25

Lakesha: 5t+2r+s=29

Now we can use elimination to find each variable:

2t+2r+s=20

-2t-2r-6s=-50

The t and r cancel out, so find s

-5s=-30

s=6, so the spinning vortex is $6.

Now, substitution

2t+2r+s=20     -5t-2r-s=-29

2t+2r+6=20    -5t-2r-6=-29

2t+2r=14          -5t-2r=-23

2t=-2r+14

t=-r+7

Now plug in for t

-5(-r+7)-2r=-23

5r-35-2r=-23

3r=12

3r/3=12/3

r=4, which means the roller coaster is $4

Now we can just plug in both of those and solve for t with any equation

t+r+3s=25

t+4+3(6)=25

t+4+18

t+22=25

t=3

Now we know that the teacups have to be $3, the rollercoaster has to be $4, and the spinning vortex has to be $6. Marc's equation is:

3t+2r+2s = Money marc spent

Plug in the values

3(3) + 2(4) + 2(6) = Money marc spent

9+8+12 = Money marc spent

29 = Money marc spent

Marc spent $29, your answer is C

The value of the fraction expression 1/2 + 3/6 is 1.

The highest number that is a factor of all the numbers is known as the greatest common factor of two or more numbers.

The smallest number (non-zero) that is a multiple of all the numbers is known as the least common multiple of two or more numbers.

Consider the expression,

1/2 + 3/6 = x

Consider the fraction 3/6,

The factors of 3 are 1 and 3.

The factors of 6 are 1, 2, 3, and 6.

Therefore, the GCF or greatest common factor is 3.

Therefore,

3/6 = ( 3 ÷ 3 ) / ( 6 ÷ 3 ) = 1/2

So, the value of the expression will be:

x = 1/2 + 3/6

x = 1/2 + 1/2

As the denominators of the fractions are equal.

x = ( 1 + 1 )/ 2

x = 2/2

x = 1

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When a scale of 1 inch to 40 miles apart then distance = 112 miles .

We have been give that

If 1 inch = 25 miles,

Then 2.8 inches would be 25 miles multiplied by 2.8 since each of those 2.8 inches is 25 miles.

2.8 x 25 = 70.

70 miles.

The same two cities be on a map that has a scale of 1 inch to 40 miles

Then 1 inch= 40 miles,

then 2.8 inches would be 40 miles multiplied by 2.8 since each of those 2.8 inches is 40 miles.

2.8 x 40 = 112.

112 miles.

Hence , Distance equals 112 miles when measured on a scale of 1 inch to 40 miles apart.

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As x and y vary inversely as each other , if x=7 then y =  -8/7.

in the question ,

it is given that

x and y vary inversely ,

So , x * y = k

given that , when x = 4 , the value of y = -2 .

Substituting , 4 * (-2) = k

k = -8

so , the constant of variation (k) = -8 .

in order to find value of y when x = 7 ,

we substitute x=7 and k = -8 in the relation xy = k

we get , 7 * y = (-8)

Dividing both sides by 7 we get

7y/7 = -8/7

on simplifying we get ,

y = -8/7

Therefore , as x and y vary inversely as each other , if x = 7 then y = -8/7 .

The given question is incomplete , the complete question is

If y varies inversely as x, and y = -2 when x = 4 find y when x = 7  .

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Answer:

[tex]\frac{15}{2}[/tex]

Step-by-step explanation:

8 - [tex]\frac{1}{2}[/tex]

= [tex]\frac{16}{2}[/tex] - [tex]\frac{1}{2}[/tex]

= [tex]\frac{15}{2}[/tex]

Answer:

The answer is  17/2

Step-by-step explanation:

You get that by multiplying the whole number 8 by the denominator of the fraction, and that will be equal to 16 and the 1 from the numerator of the fraction 1/2, so the equation will look like 16+1=17. Your new numerator  17.

You have the following algebraic expression:

The previous expression can be simplified by taking into account, that for the simplification you sum or subtract (depending of signs) similar terms. Remind that similar terms are those one which has the same variable with the same exponent. In this case you have similar terms with variable x and exponent 4, furthermore you have similar terms with variable x and exponent 3. Then you sum this terms and you obtain:

where you have summed 8x^4 + 2x^4 = 10x^4, and 7x^3 + 4x^3 = 11x^3.

Hence, the simplied expression is 10x^4 + 11x^3 + 6

Answer:

25.

Step-by-step explanation:

At time 2, x(t) = 2(2)^2 + 2 = 10

At time 10, x(t) = 2(10)^2 + 10 = 210.

Average speed for this interval

distance / time

= (210 - 10) / (10 - 2)

= 200/8

= 25.

A function from set A to set B is a relation that pairs each element of set A to exactly one element of B.

Here, we are given two functions as shown in the figure. We can answer the questions as follows-

1. a. the given function represents the countries to which the chocolate companies belong to.

b. the function represents the square of the a number

2. Both the relations are functions because for every value in the first circle there is one and only one unique value in the second circle. This, is the basic property of a function.

3. a. Domain: (Neuhaus, Cote d'Or, Leonidas, Toblerone, Lindt, Hershey's, Baci)

Range: (Belgium, Switzerland, USA, Italy)

b. Domain: (1, -1, 2, -2, 5, -5)

Range: (1, 4, 5)

4. a. (Neuhaus, Belgium) is one ordered pair of the given function

b. (1, 1) is one ordered pair of the given function

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Answer:The order of operations tells us the order to solve steps in expressions with more than one operation.

Step-by-step explanation: First, we solve any operations inside of parentheses or brackets. Second, we solve any exponents. Third, we solve all multiplication and division from left to right.

Mia, this is the solution:

4 = 2 * 2

14 = 2 * 7

Therefore, we have:

2 = two ocurrences (the higher number)

7 = one ocurrence

LCM = 2 * 2 * 7

LCM = 28

The customer will pay $391.5 after it is marked up to 65% and the sale tax of 9%.

When a consumer buys a good or service from a retailer, sales tax, which is estimated as a percentage, is added to the cost of the item.

Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity exceeds the costs, costs, and taxes associated with maintaining that activity.

The wholesale price paid by a store owner is $225.

The store owner needs to make a profit of 65%.

Then, the profit will be:

=  225 × 65% = $146.25

And, amount of tax the customer will pay will be:

= $225 × 9% = $20.25

Therefore, the price at which the customer will buy the TV will be:

= $225 + profit + sales tax

= $225 + $146.25 + $20.25

= $391.5

Hence, the customer will pay $391.5 for the TV.

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The formula for calculating the total surface area of a rectangular pyramid using its length, width, and height is provided as T.S.A. = lw + l[(w/2)2 + h2] + w[(l/2)2 + h2], where l is the length of the rectangular base, w is its width, and h is its height.

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Yield testing is a technique for figuring out the precise quantity of raw materials required to make a specific quantity of finished product.

Therefore, yield testing is a method of determining the precise amount of raw materials needed to produce a certain amount of the final product.

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Answer:

The unit rate for the bottle is $0.023/oz

The unit rate for the cans is $0.025/oz

Step-by-step explanation:

Cans   oz/can Total oz     Price ($)        Cost ($/oz)  

  1          138          138               3.20              $0.023

 12         12           144       3.60              $0.025

The unit rate for the bottle is $0.023/oz

The unit rate for the cans is $0.025/oz

The unit rate for the bottle is $0.023/oz

The unit rate for the cans is $0.025/oz

Answer:

Below in bold.

Step-by-step explanation:

The sum of 17 terms is 107.1.

Sn = (n/2)[2a + (n-1)d]   where a = first term and d = common difference

(17/2) (2a + (17-1)(-4)) = 107.1

8.5(2a -64) = 107.1

17a - 544 = 107.1

17a = 651.1

a = 38.3 = First term

The last term is the 17th so

L = a + (n - 1) d

  = 38.3 + 16*-4

  = -25.7.