Solve for the Limit of Function by applying appropriate Limit Theorems

We are given a graph that shows the depth in meters (y) as a function of the time in minutes (x).

Part A:

Points A, B, and their projection in the point (2, 110) form a similar triangle with the triangle formed by points A, C, and the point (2, 66).

An example of the required quadratic equation is x(x+1)

What is an equation?

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign. Solving an equation with variables entails finding which variables' values make the equality true. The variables for which the equation must be solved are also known as unknowns, and the values of the unknowns that fulfill the equality are known as equation solutions. Identity equations and conditional equations are the two types of equations.

An example of the required quadratic equation is x(x+1)

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we have the equation

H = -16t^2 + 36t + 56

This equation represents a vertical parabola open downward, which means, the vertex is a maximum

The time t when the ball reaches its maximum value corresponds to the x-coordinate of the vertex

so

Convert the given equation into vertex form

H=a(t-h)^2+k

where

(h,k) is the vertex

step 1

Complete the square

H = -16t^2 + 36t + 56

Factor -16

H=-16(t^2-36/16t)+56

H=-16(t^2-36/16t+81/64)+56+81/4

Rewrite as perfect squares

H=-16(t-9/8)^2+76.25

the vertex is (9/8,76.25)

therefore

The store sells a total of 18 types of chairs (this is the sum of all the types of chairs in the two way frequency table). From this table we notice that only two of them are filled with beads and made from velvet. Then the probability of choosing this is:

Therefore the probability is 1/9

Using the Empirical Rule, the correct option regarding the skewness of the distribution is given as follows:

(A) No, the distribution is skewed to the right.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is given as follows:

In the context of this problem, the mean and the standard deviation are given as follows:

A huge percentage is within one standard deviation of the mean, and the distribution is not symmetric, hence it is not normal.

Since most values are at the lower bounds of the histogram, the distribution is right skewed and option a is correct.

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Step-by-step explanation:

due to AB being parallel to XZ, we know that ABY and XZY are similar triangles.

therefore, they have the same angles, and there is one common scale factor for all side lengths from one triangle to the other.

so,

AY / XY = AB / XZ

XY = AY + AX = 7 + 6 = 13

7/13 = 14/XZ

XZ×7/13 = 14

XZ×7 = 14×13

XZ = 14×13/7 = 2×13 = 26

The rational number is -91/100 or -0.91.

Any number of the form p/q, where p and q are integers and q is not equal to 0, is a rational number. The letter q stands for the set of rational numbers.

The word "ratio" is where the word "rational" first appeared. Rational numbers are therefore closely tied to the idea of fractions, which stand for ratios. In other terms, a number is a rational number if it can be written as a fraction in which the numerator and denominator are both integers.

Given:

We have to find the rational number between -1/3 and -1/2

Tale LCM for 3 and 2 = 6

-1/3 x 2/2 and -1/2 x 3/3

-2/6 and -3/6

Now, multiply 10

-2/6 x 10/10  and -3/6 x 10/10

-20/60 and -30/60.

Hence, the rational number is -21/60.

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step 1

Find out the circumference of the outer edge

Find out the radius

r=(650/2)+4

r=329 ft

so

step 2

Find out the circumference of the inner edge

r=650/2=325 ft

substitute

Find out the difference

2,066.12-2,041=25.12 ft

therefore

a)

In order to find a function M(t), first let's identify two ordered pairs that are solutions to the equation.

From the given information, we have the ordered pairs (1990, 1.16) and (2008, 1.4).

Using these ordered pairs, let's find the slope-intercept form of a linear equation (y = mx + b)

So the equation is M = 0.01333t - 25.3667

The independent variable represents the year (correct option: first one)

b)

The slope represents the change in M over the change in t, that is, it represents the change in attendance over a year (correct option: first one)

c)

For t = 2015, we have:

d)

For M = 1.5, we have:

we know that

The volume of a cone is equal to

In this problem

we have

V=75pi mm^3

h=9 m------> convert to mm

h=9,000 mm

substitute in the given equation

ANSWER

1.5(x)

EXPLANATION

The tree is originally x feet tall. If it grows 1/2 this height it means that now it is 1/2x taller, or we can express this as a decimal, 0.5x. If we add these two heights we'll have the new height of the tree:

From the given graph the line is passing through the points (-2,0) and (0,3).

Let,

From the option the equation of the line is y=2x+3

Since on subtituting (0,3) in the above expression the condition satisfys, also on substituting (-1.5,0) in the given expression the condition satisfys.

Thus, the correct option is option A.

We have that a group of points can be:

Coplanar: if they lie in the same plane

Collinear: if they lie in the same line

1.

It means multiply f(x) and g(x) and then put "2" into it. The solution is what we are looking for. So,

2.

For this we subtract f from g and put -1 into the expression. So

3.

We simply add f and g and put 2 into the final expression.

4.

We divide f by g and put -1 in the final expression. Shown below:

Now, please match each answer with each choice.

If we sum both equations, we have the next result:

Since we have this, we can say that the system has infinite solutions. We sum both equations, and we finally get that 0 = 0. In this case, the system has infinite solutions.

All these solutions are expressed by (solving for y):

For example, for a value of x = 1, y is a function of x; then, y = 1 + 5 = 6, or (1, 6), and so on.

For the next system of equations:

Adding both equations, we finally have:

Then, solving for x, we have (using the first equation):

Then, this last system has a unique solution, which is (3, 5) or x = 3 and y = 5.

Hello there. To solve this question, we'll have to remember some properties about inequalities and its graphs.

First, we have to determine the equation of the line. For this, we have to find, by inspection, two points contained in that line:

We can easily find the points (0, -6) and (2, -2).

With this, we can find the equation of the line using the point-slope formula:

Where (x0, y0) is a point of the line, as well as (x1, y1) and the slope m is given by:

Plugging the coordinates of the points, we get:

Such that:

Rearranging it in the ax + by = c form,

Multiply both sides of the equation by a factor of 2

Finally, notice that the values of y in the shaded region are greater than the values in the line, which means that the inequality we're looking for is:

All the point (x, y) satisfying this inequality are contained in the shaded region.

Solution:

The modulus of a complex number;

is denoted by;

Thus, given the complex number;

The modulus is;

ANSWER:

Solution

Why can the Vertical Angle Theorem NEVER be used to prove two triangles are congruent?

The Vertical angle theorem states that vertical angles are always congruent.

We can't use this to proof congruence between two triangles because this theorem not provide enough evidence to obtain the SSS, ASA, SAS, AAS, HHL. For this reason is not appropiate to use it for this case.

Conditional Probability

First, we must complete the totals in the table as follows:

The formula for the conditional probability is:

Where A is an event we know has already occurred, B is an event we want to calculate its probability of occurrence, and P∩A is the probability of both occurring.

We know a female student has been selected, so that is our known event and:

The probability that a female student is also a senior is:

Substituting:

The required probability is 3/16

To get 1 cup of pf trail mix, we need to mix 2 parts of cashew and 3 part of golden raisin. This means that to make one cup of pf trail mis, we are using 5 parts in total (2 cashew+3 golden raisin). Then, this means that out of one cup the exactly amount of golden raisin is 3/5 of the cups we have. So, having this fraction in mind, we only need to multiply the total number of cups to calculate the parts we are using. In this case, we have 30 cups. So if we want to calculate the parts of golde raisin we multiply 30 by the previous fraction. That is

So to make 30 cups of pf trail mix, jose needs 18 parts.

Solution:

Given:

Let the value of the car one year ago be represented by x.

If 20% has been depreciated, then it means the percentage left is;

100 - 20 = 80%

Hence,

Therefore, the value of the car one year ago was $23,750

The edible portion of the potato skins in ounces is = 0.8%

Potatoes are vegetable tubers that can be eaten with the skin when properly cooked.

The number of side dishes of skinless mashed potatoes= 150

Two orders of mashed potatoes = 8 ounce potato.

The potatoes with discarded skin = 90% yield

The potatoe skin= 10% of the 8 ounces

That is;

= 10/100×8

= 80/100 = 0.8 ounce

Therefore, the portion of the potatoes that consists of the skin in ounce is = 0.8 ounce

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ANSWER

EXPLANATION

The surface area of a cone can be found using the formula:

where l = slant height

r = radius

The diameter of the cone is given, but we can find the radius since the radius is half the diameter:

From the figure, the slant height of the cone is 10 units.

Hence, its surface area is:

The answer is option C.

The heptagon is a polygon of 7 sides and 7 angles

The heptagon is a closed figure formed from 7 sides

Since every 2 sides connected to form an angle, then

It contains also 7 angles

Then the answer is :

Angles: 7

Sides: 7

Thus,

80 cubes will have a volume of:

Hence, the volume of the prism is 10 cubic metre

In order to find the value of f(1.2), we just need to find the value of f(x) in the graph that corresponds to x = 1.2.

Looking at the graph, when x = 1.2, the function f(x) is equal to 2.

Then, to find the largest value of x for which f(x) = 1.5, we look for the value 1.5 in the vertical axis, then find the corresponding value of x.

For this value, we have two possible values of x: 1.2 and 3.6.

So the largest value is x = 3.6

We have the following rule for exponents:

then, in this case we have:

Step-by-step explanation:

what is the problem ?

all you need to do is put every different value of x into the spot of x and calculate the result.

x = -4

y = 3×-4 - 8 = -12 - 8 = -20

x = -2

y = 3×-2 - 8 = -6 - 8 = -14

x = 0

y = 3×0 - 8 = 0 - 8 = -8

x = 2

y = 3×2 - 8 = 6 - 8 = -2

x = 4

y = 3×4 - 8 = 12 - 8 = 4

1)

We can find the circumference using the formula

but remember that the diameter is 2 times the radius

So we can use the formula using radius or diameter, the problem gives us the diameter, so let's use it, so the formula will change a little bit

Where "d" is the diameter.

d = 40 yd, and π = 3.14, so the circumference will be

And to find out the area we can use this formula

Or if you prefer use the radius

Let's use the formula with the diameter again

Then the circumference is 125.6 yd and the area is 1256 yd^2

2)

Here we have a compounded figure, we have half of a circle and a triangle, so let's think about how we get the perimeter and the area.

The perimeter will be the sum of the sides of the triangle and half of a circumference, we already know the length of the triangle's side, it's 10.82, we got to find the half of a circle circumference and then sum with the sides.

We know that

And we can see in the figure that d = 12 mm, then

But that's a full circumference, we just want half of it, so let's divide it by 2.

Now we have half of a circumference we can approximate the perimeter of the figure, it will be

The area will be the area of the triangle sum the area of half of a circle

Then let's find the triangle's area first

The base "b" will be the diameter of the circle, and the height "h" will be 9 mm, then

And the half of a circle's area will be

Then the total area will be

Therefore, the perimeter and the area is

If Jaylen used a 20% discount on a pair of jeans that cost $70 before tax, then the price of the jeans will be $70 - 20%.

Let's calculate the 20% of $70.

So, the discounted price of the jeans before tax is $70 - $14 = $56.

Generally, sales tax is applied to the discounted price, so let's calculate the 6% of $56.

The sales tax is $3.36.

Therefore, the cost of the pair of jeans after tax is $59.36.