In 10 words or fewer, write your own definition of slope.

The graph of the linear inequality  [tex]y\geq -3x+4[/tex] is given below.

What is linear inequality?

The expressions that compare two linear expressions using inequality symbols are referred to as linear inequalities. A linear inequality, which is an inequality including at least one linear algebraic expression, is when a polynomial of degree 1 is compared to another algebraic expression of a degree less than or equal to 1. There are numerous ways to depict various kinds of linear inequalities.

Given linear inequality is [tex]y\geq -3x+4[/tex] for which y region will be in the positive range.

Hence, the graph of the given linear inequality is given below.

To learn more about linear inequality

https://brainly.com/question/17060040

#SPJ1

Answer:

2x^2 - 12*x/2= Area For Shaded Region

Step-by-step explanation:

This works because you find tha area of both and subtract the shaded area by the unshaded area

Answer: Expression for the area of shades region of the figure = 2[tex]x^{2}[/tex] - 6x

Step-by-step explanation: Area of shaded region = Area of big rectangle - Area of small rectangle

Area of rectangle = length.breadth

Area of big rectangle = 2x.x                                  { . means multiply}

                                     = 2[tex]x^{2}[/tex]

Area of small rectangle = 12.(x/2)

                                         =6x

∴ Area of shaded region = 2[tex]x^{2}[/tex] - 6x

To learn more about area of rectangle,

https://brainly.com/question/2607596

The shopping mall has 65,625 square feet of total leasable area. As stated in the problem, this indicates that the fitness club takes up 16% of the total leasable space.

According to the information provided, a fitness club occupies 10,500 square feet or 16% of the total leasable area at a sizable shopping mall. We can use the proportional and percentage approaches to determine the total leasable area.

Let's assume that the variable "x" stands for the whole amount of leasable space. Since we are aware that the area leased by the gym is 16% of the total leasable area, we can create the following equation:

10,500 = 0.16x

To solve for "x", we can divide both sides of the equation by 0.16:

10,500 / 0.16 = x

Simplifying this expression gives us:

x = 65,625

Therefore, The shopping mall has 65,625 square feet of total leasable area. As stated in the problem, this indicates that the fitness club takes up 16% of the total leasable space.

To learn more about square feet, visit the link below:

https://brainly.com/question/15468175

#SPJ4

Answer:

4x - 5y - z

Step-by-step explanation:

3x − 4y + z − 2z + x − y

Add like terms

= 4x - 5y - z

Answer: 4x-5y-z

Step-by-step explanation: 3x + x -4y-y -2z + z

It becomes a lot easier to simplify if you reorganize the equation so that the same variables are next to each other

The equation that represents the given scenario is 35 + 0.45d = 63.80

The linear equation is a mathematical statement that is solved for an unknown value. The linear equation is straight in a graph where the variable will represent an unknown value in the given problem.

To find the required equation, first calculated the charge according to the given problem and form the linear equation using the given variable.

Here we have

Cam will be charged a flat fee of $35.00 plus $0.45 for each day of storage.

If Cam stores her possessions for d days then the charge = $ 0.45d

After adding the fee the total charge will be $ 35 + $ 0.45d  

Given that the total charge is $63.80

From the above calculations,

=> $ 35 + $ 0.45d  = $ 63.80

=> 35 + 0.45d = 63.80

Therefore,

The equation that represents the given scenario is 35 + 0.45d = 63.80

Learn more about Linear equations at

https://brainly.com/question/29739212

#SPJ1

1. To get System BBB from System AAA, we can divide both sides of the first equation in System AAA by -3:

-3x + 12y = 15

-3x/ -3 + 12y/ -3 = 15/ -3

x + 4y = -5

So System BBB is obtained by dividing both sides of the first equation in System AAA by -3.

2. Are Systems AAA and BBB equivalent?

Yes, Systems AAA and BBB are equivalent. This means that they have the same solution set, despite having different coefficients in their equations. Equivalent systems of linear equations are systems that have the same solution set, regardless of the coefficients of the equations.

Answer:

To solve it, you need to use vectors. Let me show you how.

To find the vector that describes the translation, we need to subtract the coordinates of point A from the coordinates of the translated point. Let the vector be v. Then we have:

v = (-1, -3) - (-4, 2)

v = (-1 + 4, -3 - 2)

v = (3, -5)

To write this vector as a column vector, we write it vertically with square brackets. So we have:

v = [3

   -5]

Therefore, the vector that describes the translation is [3

   -5].

Step-by-step explanation:

Given the angle bisector, the statements and reasons for the proof are explained.

A bisector splits a given line or angle into two equal parts. A straight line is said to be an angle bisector if it divides a given angle into two equal measures. Such that on comparison, the sum of the angles formed is equal to the measure of the bisected angle.

The statements and reasons for the proof are given below;

      STATEMENT                                                    REASONS

1. MK bisects <HKO and <HMO                           Given

2. m<HMK = m<OMK and m<HKM = m<OKM    Definition of angle bisector

3. HK ≅ KO, and HM ≅ OM                                 Congruent side property

4. ΔHMK ≅ ΔOMK                                               Angle-Angle-Side theorem

Learn more about angle bisector at https://brainly.com/question/24334771

#SPJ1

Answer:The price of 10 pounds of cheese is 15.84$

Step-by-step explanation:

It's simple

Using compounding we know that after 30 years, the account balance has changed by $345.31.

Theoretically, continually compounded interest indicates that interest is continuously earned on an account balance as well as reinvested into the balance so that additional interest is generated.

So, a business owner put $7,000 into a Treasury bond paying a semiannual compound interest rate of 4.3%.

The bond's value after 30 years is $25,084.20.

Instead of compounding twice a year, the investment made by the business owner was made continuously.

After 30 years, we must determine the difference in the account balance.

Think of the continuously compounding recipe:

A = Pe∧rt

We have, p = 7000.

r = 4.3% = 0.043

t = 30

Then,

A = 7000e∧(0.043*30) = 25429..51

A = $25429.51

Therefore, using compounding we know that after 30 years, the account balance has changed by $345.31.

Know more about compounded continuously here:

brainly.com/question/14303868

#SPJ1

Correct question:

A business owner invested $7,000 in a treasury bond paying 4.3% compounded semiannually. After 30 years, the value of the bond will be $25,084.20. If the business owner's investment was compounded continuously instead of twice per year, what would be the difference in the account balance after 30 years?

The estimate for the mean book thickness is 3.2 mm.

What is mean?

In arithmetic, mean is the sum of all the added values of all the data in a set divided by the number of data in the set.

To find the mean book thickness, we can use the formula for the mean (also known as the average):

mean = (sum of all data points) / (number of data points)

Since we don't have the exact thickness of each book, but rather intervals of thickness and the number of books in each interval, we can use a weighted mean to estimate the mean thickness.

Here is the calculation:

First, we'll find the midpoint of each interval:

Interval 1: [0, 2]  -> midpoint: x1 = 1

Interval 2: [2, 4]  -> midpoint: x2 = 3

Interval 3: [4, 6]  -> midpoint: x3 = 5

Next, we'll find the weight of each interval by multiplying the midpoint by the frequency:

Interval 1: x1 * f1 = 1 * 5 = 5

Interval 2: x2 * f2 = 3 * 8 = 24

Interval 3: x3 * f3 = 5 * 7 = 35

Finally, we'll sum up the weights and divide by the total frequency to find the weighted mean:

Weighted mean = (5 + 24 + 35) / (5 + 8 + 7) = 64 / 20 = 3.2

So, the estimate for the mean book thickness is 3.2 mm.

To know more about mean visit,

https://brainly.com/question/1136789

#SPJ1

An item priced at $200 has a fee of $12. An item priced at $150 has a fee of $9. The restocking fee for an item priced at $180 is $10.

To solve this problem, we need to use a proportion to relate the item price to the restocking fee. The problem provides two pairs of corresponding item prices and restocking fees: $200 and $12, and $150 and $9. We can set up a proportion using these pairs:

$200/$12 = $150/$9

We can simplify this proportion by dividing both sides by 3:

$200/$4 = $150/$3

Now we can use the simplified proportion to find the restocking fee for an item priced at $180. We'll use cross-multiplication:

$200 x $3 = $150 x $4

$600 = $600

This tells us that the ratios are equivalent, and the restocking fee for an item priced at $180 is $10.

In other words, the restocking fee is proportional to the item price, and we can use the given pairs of prices and fees to find the fee for any given price using a proportion.

To learn more about price click on,

https://brainly.com/question/30647340

#SPJ4

Answer:

See below.  The answer is 8.8 feet, but none of the options offers this value.

Step-by-step explanation:

I get 8.8 feet.

2^2 + x^2 = 9^2

4 + x^2 = 81

x^2 = 77

x = 8.77496 to be exact.

Answer:

Step-by-step explanation:Class Trip Fund Calculation

The class figured out that if the percent increase is 99% from the beginning of the year, the class will have enough money for every student to go on the field trip. How much money will the class need to raise for every student to go

To calculate the amount of money that the class needs to raise, you can use the formula for calculating the amount after a percent increase:

amount = original amount + (original amount * percent increase / 100)

Let's assume that the original amount is x. After a 99% increase, the new amount will be:

x + (x * 99 / 100) = x * 199 / 100

So, to find the original amount, you can set up an equation:

x * 199 / 100 = amount needed for the field trip

And then solve for x:

x = amount needed for the field trip * 100 / 199

So, the class needs to raise an amount equal to the amount needed for the field trip * 100 / 199 to have enough money for every student to go on the field trip.

The complete question:

A baker uses the equation y = 12x to predict the revenue generated from selling a cakes. She uses equation y= 450 +4.5x to

model the cost to produce a cakes:

What does (60, 720), the solution of the system -450 +4.5x &

y=12x represent?

Solution:-

The solution of the system (-450 + 4.5x, y = 12x) at (60, 720) represents :

a. The point where the revenue generated from selling 60 cakes is 720 dollars

b. The cost to produce those 60 cakes is 720 dollars.

In geometry, A system of equations is a collection of two or more equations with the same set of unknown variables. In solving a system of equations, we try to calculate values for each of the unknowns that will satisfy each and every equation in the system.

The given system of equations is:

y = 12x (equation 1)

y = 450 + 4.5x (equation 2)

where x represents the number of cakes produced and sold, y represents the revenue generated from selling x cakes, and 450 + 4.5x represents the cost to produce x cakes.

To find the solution of the system, we can substitute equation 1 into equation 2, and solve for x as follows:

12x = 450 + 4.5x

7.5x = 450

x = 60

Substituting this value of x into equation 1 gives us:

y = 12(60)

y = 720

To know more about system of equations check:

https://brainly.com/question/90105

#SPJ9

The dilated figure coordinates will be A(-6,6); B(3,3); C(3,-3); D(-3,0) E.g. If a figure is drawn by the help of lines and the length of all the four lines are equal, then the resultant figure is known as Square Shape.

Figures are nothing but a kind of drawing which we make using lines and arcs. Figures can be 2-D or 3-D. In mathematics these figures are studied by calculating their's area, perimeter, surface area, volume, etc.

In mathematics when we draw a figure using line and arcs and the resultant figure has some specific pre-defined properties then such figures are called shapes.

The coordinates of the given figure ABCD are

A=(-2,2); B=(1,1); C=(1,-1) and D=(-1,0)

As we have to dilate the figure by the factor of 3 from the origin which means we have to enlarge the figure 3 times with same origin, then we simply multiply the coordinates of the given figure by 3.

Dilated coordinates will be

A=(-2×3,2×3)=(-6,6)

B=(1×3,1×3)=(3,3)

C=(1×3,-1×3)=(3,-3)

D=(-1×3,0×3)=(-3,0)

Therefore, New dilated coordinates of the figure are A(-6,6); B(3,3); C(3,-3) and D(-3,0).

Learn more about dilate figures here:

https://brainly.com/question/22258562

#SPJ1

Answer:

1.  2^n + 1.

2. (n +1)/(n + 4)

Step-by-step explanation:

1. 3 5 9 17....

3 = 2^1 + 1

5 = 2^2 + 1

9 = 2^3 + 1

17 = 2^4 + 1

Therefore the nth term is

2^n+ 1 .

2. Looking at the fractions we see that:

Numerators are 2, 3, 4 ,5..

and denominators are  5, 6, 7, 8

So the nth term is

(n + 1) / (n + 4)

Answer:

75.50 + 14x - (35.50 + 9x) = 40 + 5x

Step-by-step explanation:

From the graphs below, we can see that the solution of the given system of linear equations is (3,0.5).

What is meant by a system of linear equations?

A collection of one or more linear equations containing the same variables is known as a system of linear equations. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation is invariably a straight line equation. A group of diverse straight line equations make up a system of linear equations.

We are given two linear equations:

y = -1/2 x + 2

y = 1/2x - 1

As mentioned earlier, these are equations of two straight lines with slopes -1/2 and 1/2.

Now the solution of the equation is the intersecting point of these straight lines. We graph these equations and found the intersecting point.

Therefore, from the graphs below, the solution of the given system of linear equations is (3,0.5).

To learn more about the system of equations, follow the link.

https://brainly.com/question/13729904

#SPJ1

Based on your knowledge of the two data sets described below, would you expect a scatter plot describing the two data sets to have a no correlation.

Based on my knowledge, I would not expect there to be a strong correlation between hourly pay and total number of sick days allowed. These two variables are not directly related to each other and there is no clear reason to expect a positive or negative correlation between them. Therefore, I would expect the scatter plot to show no correlation between the two variables. However, it's worth noting that without actually seeing the data, it's difficult to definitively determine whether there is any correlation present.

To learn more about correlation here:

https://brainly.com/question/28898177

#SPJ4

The hare can afford to nap for a maximum time of 3,690 seconds without losing the race if his speed is 15 m/s.

After running for 7 seconds, the hare has covered a distance of:

[tex]distance = speed \times time\\distance = 15 \times 7\\[/tex]

distance = 105m

The hare is now 895 m away from the starting line and 100 m away from the finish line.

The hare needs to cover a distance of 100 m to reach the finish line, while the tortoise needs to cover a distance of 895 m.

calculate the time it would take the tortoise to reach the finish line:

[tex]time = \frac{100}{0.27}[/tex] = 3704 seconds

The maximum speed of the hare is 15 m/s, which means the time it would take the hare to cover the distance is:

[tex]time = \frac{100}{15}[/tex] = 6.67 seconds

so, the time hare have to nap so that he does not lose race = 3704 - (7+6.67) ≅3690 seconds

To know more about speed

https://brainly.com/question/30670429

#SPJ4

The equation can be solved using the quadratic formula when the following expression is used: [tex]$x=\frac{-(-4)+-\sqrt{(-4)^2-4(1)(3)}}{2(1)}$[/tex]

The quadratic formula in elementary algebra is a formula that gives the solution(s) to a quadratic equation. In addition to the quadratic formula, there are various methods for solving quadratic equations, including factoring (direct factoring, grouping, and the AC technique), completing the square, graphing, and others.

The following general quadratic equation is given:

ax² + bx + c = 0

As a result, a polynomial equation with exponent two is referred to as a quadratic ("square-like") equation. Quadratum is the Latin word for square, and since the area of a square with side length x is given by x2, this is the case.

A quadratic equation's solution(s) can be found using the quadratic formula in elementary algebra. Graphing, factoring (direct factoring, grouping, AC technique), completing the square, and other methods can be used to solve a quadratic equation in addition to the quadratic formula.

The given equation is x² - 4x + 3 = 0

When compared to the quadratic equation's general equation, we get a = 1, b = -4, c = 3.

When the coefficient values for the Sridhar Acharya formula are put in,[tex]$x=\frac{-(-4)+-\sqrt{(-4)^2-4(1)(3)}}{2(1)}$[/tex] which gives Option (A).

To learn more about quadratic formula, refer to:

https://brainly.com/question/1214333

#SPJ1

Answer:

348.75

Step-by-step explanation:

Answer:

Step-by-step explanation:

From a hot-air balloon, Violet measures a 24

∘

∘

 angle of depression to a landmark that’s 806 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary.

Answer:

Area = 200ft²

Step-by-step explanation:

Perimeter of a rectangle = 2(length+width)

Area of a rectangle = length * width

Then:

g = 2w           Eq. 1

60 = 2(g+w)   Eq. 2

g = length

w = width

From Eq. 2

60 = 2g + 2w

60 - 2g = 2w      Eq. 3

matching Eq. 1 and Eq. 3

g = 60 - 2g

g + 2g = 60

3g = 60

g = 60/3

g = 20 ft

From Eq. 1

g = 2w

20 = 2w

20/2 = w

w = 10 ft

Area

area = length * width

area = 20ft * 10 ft

area = 200ft²

The distance is a function of time and the slope of the distance time graph will give the speed

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the first quantity be represented as Distance D

Let the second quantity be represented as Time T

Now , the function is given as

The distance D is a function of time and the slope of the line between the x and y axis of the distance time graph will give us the speed

Substituting the values in the equation , we get

Let the y axis represent the distance D

And , let the x axis represent the time T

So , Slope m = y / x

On simplifying the equation , we get

Slope m = Distance / Time = Speed

Hence , the distance is a function of time

To learn more about function rule click :

https://brainly.com/question/3760195

#SPJ1

The linear function representing the depth of the submarine after t seconds is given as follows:

d(t) = -15 - 0.5t.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The parameters for this problem are given as follows:

Hence the function is given as follows:

d(t) = -15 - 0.5t.

The problem asks for the linear function representing the depth of the submarine after t seconds.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Rudy has 3003 different ways to choose 6 toppings from a menu of 14 toppings if each topping can only be chosen once.

The number of ways to choose 6 toppings from a menu of 14 toppings where each topping can only be chosen once is 14!/(14-6)! = 14!/(8!) = 3003. This is because for the first topping, Rudy has 14 options, for the second topping he has 13 options, for the third topping he has 12 options, and so on. To calculate the total number of combinations, we use the formula n!/(n-r)! where n is the number of items and r is the number of items to choose. This formula gives us the number of ways to choose r items from a set of n items without regard to order, which is the number of combinations.

The formula for combinations is given by n!/(n-r)! where n is the number of items and r is the number of items to choose. Here, n = 14 (the number of toppings on the menu) and r = 6 (the number of toppings Rudy wants to choose). So, the number of combinations is 14!/(14-6)! = 14!/(8!).

The factorial (!) is the product of all positive integers up to that number. For example, 4! = 4 x 3 x 2 x 1 = 24.

So, 14! = 14 x 13 x 12 x ... x 2 x 1 = 87178291199, and 8! = 8 x 7 x 6 x ... x 2 x 1 = 40320.

Now, to calculate the number of combinations, we divide 14! by 8!: 14!/(8!) = 87178291199/40320 = 3003.

Therefore, Rudy has 3003 different ways to choose 6 toppings from a menu of 14 toppings if each topping can only be chosen once.

To learn more about toppings please click on below link.

https://brainly.com/question/29858706

#SPJ4