The coordinates of the three vertices of a square are (4,14) (10,14) and (4,8). What are the coordinates of the missing vertex

Answer:

Step-by-step explanation:

6x + 15 = x - 10

5x + 15 = -10

5x = -25

x = -5

The function has vertical asymptotes at x = -3/2 and x = 1, a horizontal asymptote at y = 0, and a y-intercept at (0, -2/3).

In mathematics, a function is a relation between two sets that associates each element of the first set, called the domain, with a unique element of the second set, called the range. In other words, a function maps each input value to a unique output value.

The notation used to represent a function is f(x), where f is the name of the function and x is the input value. The output value is then given by the expression f(x).

Functions can be represented in various ways, such as tables, graphs, equations, and verbal descriptions. They are used to model real-world phenomena, analyze data, and solve problems in various fields, including science, engineering, economics, and finance.

To find the intercepts of the rational function, we set the numerator equal to zero and solve for x:

2/(2x² - x - 3) = 0

2 = 0 (there is no solution for x that makes the numerator zero)

Therefore, the rational function has no x-intercepts.

To find the y-intercept, we set x = 0:

f(0) = 2/(2(0)² - 0 - 3) = -2/3

Therefore, the y-intercept is (0, -2/3).

To find the vertical asymptotes, we set the denominator equal to zero and solve for x:

2x² - x - 3 = 0

Using the quadratic formula, we get:

x = (1 ± √(1 + 24))/4

x = (1 ± 5)/4

x = -3/2, 1

Therefore, the rational function has vertical asymptotes at x = -3/2 and x = 1.

To describe the behavior at the vertical asymptotes, we can use limits. Let's consider the vertical asymptote at x = -3/2:

lim x → -3/2+ f(x) = 2/(2(-3/2)² - (-3/2) - 3) = -∞

lim x → -3/2- f(x) = 2/(2(-3/2)² - (-3/2) - 3) = +∞

This means that as x approaches -3/2 from the right, the function approaches negative infinity, and as x approaches -3/2 from the left, the function approaches positive infinity. Therefore, the function has a vertical asymptote at x = -3/2 with a vertical (or infinite) discontinuity.

Let's now consider the vertical asymptote at x = 1:

lim x → 1+ f(x) = 2/(2(1)² - (1) - 3) = +∞

lim x → 1- f(x) = 2/(2(1)² - (1) - 3) = -∞

This means that as x approaches 1 from the right, the function approaches positive infinity, and as x approaches 1 from the left, the function approaches negative infinity. Therefore, the function has a vertical asymptote at x = 1 with a vertical (or infinite) discontinuity.

To analyze and draw the graph of the rational function, we can use the intercepts, asymptotes, and behavior at the vertical asymptotes that we found earlier. We can also find the horizontal asymptote by looking at the degree of the numerator and denominator:

Degree of numerator = 0

Degree of denominator = 2

Therefore, the horizontal asymptote is y =0

As we can see from the graph, the function has vertical asymptotes at x = -3/2 and x = 1, a horizontal asymptote at y = 0, and a y-intercept at (0, -2/3). The behavior at the vertical asymptotes is a vertical (or infinite) discontinuity.

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The complete question is:

5/6 can be rewritten with a least common denominator of 6 as 10/12.

Fracture is  part of the whole. A fraction consists of two parts, the numerator and the denominator. Numerator: The numerator represents the number  above the fraction bar. For example, for 6/7, 6 is the numerator. Denominator: The denominator shows the number  placed under the fraction bar.  

We can write 5/6 in the lowest common denominator, we need to find the common multiple of 6. The smallest multiple  is 2. So we can write 5/6 with the lowest denominator  6 as follows:

5/6 = (5/6) x (2/2) = 10/12

Therefore, 5/6 can be rewritten as 10/12 with a lowest common denominator of 6.

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The possible rule of the polynomial function is f(x) = 1/2(x + 2)(x + 1)²(x - 1)²

From the question, we have the following zeros and multiplicities that can be used to derive the rule of the function

The possible rule of the function is represented as

f(x) = a(x - zero)^multiplicity

So, we have

f(x) = a(x + 2)(x + 1)²(x - 1)²

The graph passes through (0, 1)

So, we have

a(0 + 2)(0 + 1)²(0 - 1)² = 1

This gives

2a = 1

Divide

a = 1/2

Recall that

f(x) = a(x + 2)(x + 1)²(x - 1)²

So, we have

f(x) = 1/2(x + 2)(x + 1)²(x - 1)²

Hence, the function is f(x) = 1/2(x + 2)(x + 1)²(x - 1)²

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Answer:

4. b/c

Step-by-step explanation:

In a right-angled triangle with sides of lengths a, b, and c, where c is the hypotenuse (the side opposite the right angle), the sine of the angle opposite side b (angle B) is given by:

Sin theta : Opposite/hypotenuse

sin(B) = b/c

Therefore, the answer is 4. b/c

The area of circle is represented by quadratic expression A = π · x², for a radius x = 5 units, the area of circle equals 25π square units.

In this question we need to derive the area formula for a circle as a function of radius and compute the value of the figure for a given radius. According to geometry, the area of a circle (A), in square units, is described by following quadratic equation:

A = π · x²

Where x is the radius of the circle, in units.

If we know that x = 5, then the area of the circle is now computed:

A = π · 5²

A = 25π

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Answer:300

Step-by-step explanation:

We can find the answer the simple way.

There are 10 triangles in a regular pentagon

We used pythagorean theorm to find side b, 12

12*5*0.5 is 30

30*10 is 300

The original numbers multiplied by 10² are:

968

0.002

3.33

When a number is multiplied by 10², the position of the decimal point will move to the right by 2 steps. If the number does not have decimal point, two zeros is added to the back of the number .

6 * 10³  = 6,000

968 * 10² = 96,800

0.002 * 10² = 0.2

70,000 ÷ 10² = 700

3.33 * 10² = 333

Thus, the original numbers multiplied by 10² are 968, 0.002 and 3.33

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The missing step in the two column proof is

Statement              Reason

Δ DAC ≅ ΔBCA    ASA congruence theorem

The ASA theorem, also known as the angle side angle theorem, is a rule used in geometry to determine whether two triangles are congruent (meaning they have the same shape and size).

The angle side angle theorem states uses the side two parameters which includes:

The parameters are used for the theorem to say that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

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The distance from the top of the flagpole to the end of its shadow is approximately 10.02 feet.

Explain the term distance

Distance refers to the measurement of the space between two objects or points. It is typically measured in units such as meters, kilometres, miles, or feet. The distance can be calculated using various methods, including using maps, GPS technology, or mathematical formulas.

According to the given information

We can set up the following proportion:

h / 12 = d / 11

We can cross-multiply to get:

h x 11 = 12 x d

Simplifying further:

d = (h x 11) / 12

We need to solve for d, so we need to find the value of h. Using the Pythagorean theorem, we can set up the following equation:

h² + d² = 12²

Substituting d = (h x 11) / 12, we get:

h² + ((h x 11) / 12)² = 12²

Simplifying:

h² + (121h²) / 144 = 144

Multiplying both sides by 144/265:

265h² / 144 = 144

Solving for h:

h² = (144 x 144) / 265

h = √(20736 / 265)

h = √(78.113)

Now we can substitute this value into our earlier equation to find d:

d = (√(78.113) x 11) / 12

d ≈ 10.02 feet

Therefore, the distance from the top of the flagpole to the end of its shadow is approximately 10.02 feet.

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Answer:

(C) {-3, 2} is the correct answer.

The rectangle with largest area has length 3 and width 3/2, with an area of 9/2.

What is a rectangle?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. As a result, it is sometimes referred to as an equiangular quadrilateral. Because the opposing sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

The equation for the area of a rectangle is length * width. For us here, it would be x * y. We can substitute the equation of the line for y and get

A = x * (6-x)/2

A = 3x - x2/2

To find the maximum of this equation, we first need to find a critical point. So we take the derivative and find the zeros:

A' = 3 - x = 0

x = 3

So we have a critical point at 3, which happens to be the maximum of the area equation. We plug this back into the line equation to get y:

y = (6 - 3)/2 = 3/2

So the rectangle with largest area has length 3 and width 3/2, with an area of 9/2.

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The expression Negative 3 6/7 times negative 3 1/3 has a value of -12 6/7

We have the following statement as the given parameter

Negative 3 6/7 times negative 3 1/3

Next, we rewrite the above statement using numbers and operators

-3 6/7 * 3 1/3

The above statement is a product expression that multiplies the values of -3 6/7 and 3 1/3

Also, there is no need to check if there are like terms in the expression or not

This is  because we are multiplying the factors

So, we have

-3 6/7 * 3 1/3 = -27/7 * 10/3

Evaluate

-3 6/7 * 3 1/3 = -9/7 * 10

Rewrite as

-3 6/7 * 3 1/3 = -90/7

Simplify

-3 6/7 * 3 1/3 = -12 6/7

This means that the value of the expression is -12 6/7

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Answer:

b

Step-by-step explanation:

b

Answer: bellshaped

Step-by-step explanation:

Answer:

The answer to (m+3)(m-3) is m^2-9.

Step-by-step explanation:

We will use distributive law to solve this question.

m(m-3)+3(m-3)

= m^2-3m+3m-9

= m^2-9 (since, 3m-3m=0)

As an alternative method, we can use the direct rule learned in algebra: (a+b)(a-b)=a^2-b^2.

so, here a=m and b=3.

(m+3)(m-3)

=m^2-3^2

=m^2-9

Using the inequality rule we know that 11 is greater than -11, (11 > -11).

Mathematical expressions with inequalities are those in which the two sides are not equal.

Contrary to equations, we compare two values in inequality.

Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Two expressions in inequality aren't always equal, which is denoted by the symbols >, <, ≤, or ≥.

So, let's say the inequality equation looks like this: A

Right now, A is valued at

Let p be used to representing the initial number.

P equals 11, so

Let q be used to representing the second number.

Q has a value of -11.

-11 and 11 are both numbers that are greater than zero.

Then, 11 > -11 ... (1)

A has a value of 11 > -11.

Therefore, using the inequality rule we know that 11 is greater than -11, (11 > -11).

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Correct question:
Is 11 greater than, equal to, or less than -11?

The median the most useful measure of central tendency for these

times: is A) The median is not affected by an outlier.

The median is the middle value in a set of data when the values are arranged in order. In this case, the median of Brandon's climbing times would be 16, because it is the fourth value when the times are arranged in order:

13, 13, 14, 16, 17, 18, 35

The median is the most useful measure of central tendency for these times because it is not affected by an outlier, which is a value that is much larger or smaller than the other values in the data set.

In this case, the value 35 is an outlier, because it is much larger than the other values. If we were to use the mean as the measure of central tendency, the outlier would greatly influence the result. However, the median is not influenced by outliers, and therefore provides a better representation of the typical climbing time for Brandon.

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The woman invested $4,000 at 5% and $3,000 at 12%.

Let x be the amount invested at 5% and y be the amount invested at 12%. Then we have:

x + y = 7,000 (equation 1)

0.05x + 0.12y = 560 (equation 2)

To solve for x and y, we can use substitution method :

From equation 1, we have y = 7,000 - x. Substituting this into equation 2, we get:

0.05x + 0.12(7,000 - x) = 560

Simplifying and solving for x, we get:

0.05x + 840 - 0.12x = 560

-0.07x = -280

x = 4,000

Substituting x = 4,000 into equation 1, we get:

4,000 + y = 7,000

y = 3,000

Therefore, the woman invested $4,000 at 5% and $3,000 at 12%.

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The surface area of the triangular prism is 162 square inches.

In geometry, a prism is a three-dimensional solid shape that has two identical, parallel faces (called bases) and rectangular or parallelogram-shaped sides. The sides connect the bases, and their shape determines the type of prism.

To find the surface area of the triangular prism, we need to find the areas of all five faces and add them together.

The area of each triangular base is:

A = (1/2)bh

where b is the length of the base (which is equal to 4 in) and h is the height (which is equal to 3 in).

A = (1/2)(4 in)(3 in) = 6 in²

So the total area of both triangular bases is:

2A = 2(6 in²) = 12 in²

The area of each rectangular side is:

A = lw

where l is the length (which is equal to 10 in) and w is the width (which is equal to 5 in).

A = (10 in)(5 in) = 50 in²

So the total area of all three rectangular sides is:

3A = 3(50 in²) = 150 in²

Therefore, the total surface area of the triangular prism is:

12 in² + 150 in² = 162 in²

Thus, the surface area of the triangular prism is 162 square inches.

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The length of the tank should be approximately 150.4 inches in order to hold 450 gallons of water, with a width of 21 inches and a height of 33 inches.

To find the length of the tank, we first need to convert the volume of water from gallons to cubic inches, using the given conversion factor:

1 gallon = 231 cubic inches

Therefore, the volume of water in the tank is:

450 gallons * 231 cubic inches/gallon = 103950 cubic inches

We can then use the formula for the volume of a rectangular prism to find the length of the tank:

Volume = length * width * height

Substituting the given dimensions, and solving for the length, we get:

103950 cubic inches = length * 21 inches * 33 inches

length = 103950 cubic inches / (21 inches * 33 inches)

length ≈ 150.4 inches

Therefore, the length of the tank should be approximately 150.4 inches in order to hold 450 gallons of water, with a width of 21 inches and a height of 33 inches.

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From the circle graph of the survey, 52 more people prefer pigs than chickens.

A sort of data visualisation tool used to depict data as a circular chart is a circle graph, commonly referred to as a pie chart. Each slice of the circle graph, also known as a sector, represents a certain category or chunk of the entire. Each slice's size is proportional to how much data or what percentage it represents, and the sum of all slices is 100%.

Circle graphs are frequently used to depict percentages or categorical data, and they are especially helpful for comparing and illustrating relative proportions among several categories within a data collection.

From the circle graph we see that the percentage of people who prefer chickens are 29%.

Thus, 29/100 (400) = 116 people

Also, 16% people prefer pig:

Thus, 16/100 (400) = 64 people

Thus, the difference is:

116 - 64 = 52

Hence, from the circle graph of the survey, 52 more people prefer pigs than chickens.

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The complete question is:

Alpa must take out at least 19 T-shirts from the bag to be absolutely sure of having at least two T-shirts among them that differ only by size or only by color.

What is the Pigeonhole Principle?

The Pigeonhole Principle is a fundamental concept in combinatorics, which is a branch of mathematics that deals with counting and analyzing the properties of sets of objects. The principle states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon.

We can solve this problem using the Pigeonhole Principle, which states that if n+1 objects are distributed among n boxes, then there is at least one box that contains two or more objects.

In this case, we want to be sure that we have at least two T-shirts that differ only by size or only by color.

So we need to find the minimum number of T-shirts that we must take out of the bag to guarantee this.

Let's consider the worst-case scenario, where we take out all the T-shirts that are of one size or one color.

If we take out all 18 small red T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color (since we could still get a small black T-shirt).

Similarly, if we take out all 19 small black T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color.

If we take out all 13 large black T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color.

If we take out all 15 large red T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color.

So we need to take out at least 19 T-shirts to be sure that we have at least two T-shirts that differ only by size or only by color. (We add one to the largest number of T-shirts of one color or size.)

Therefore, Alpa must take out at least 19 T-shirts from the bag to be absolutely sure of having at least two T-shirts among them that differ only by size or only by color.

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The equivalent expression of log4 ( 1/4x²) is log4(1/4) + log4(x²) ( option D)

The logarithm is the inverse function to exponentiation. For example log2 (8) = 3 and 2³ = 8

The following are math logarithm rules:

loga (MN) = loga M + loga N.

loga (M/N) = loga M - loga N.

IogaMn = n Ioga M.

For example Log5 (5²) = Log5 (5) + Log5 (5)

= 1+1 = 2

this means Log5 ( 5²) = log5 ( 25) = 2

Therefore if loga (MN) = loga M + loga N.,

we can say that,

log4( 1/4x²) can also be written as ;

log4 (1/4) + log4 (x²) .

therefore the equivalent expressions for

log4 ( 1/4x²) is log4 (1/4) + log4 (x²) .

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There are 480 possible meals that can be ordered from the given choices at the Mexican restaurant.

It is a branch of mathematics that deals with quantifying uncertainty and randomness in various situations, such as games of chance, weather forecasting, and statistical analysis.

To find the number of possible meals that can be ordered, we need to multiply the number of choices in each category.

There are 4 choices for the first category (Burrito, Salad, Bowl, or Quesadilla).

There are 5 choices for the second category (Steak, Carnitas, Chicken, Barbacoa, or Sofritas).

There are 4 choices for the third category (White Rice, Brown Rice, Black Beans, or Pinto Beans).

There are 6 choices for the fourth category (Hard Tacos, Soft Tacos, Fajita Veggies, or any of the previous three with Salad, Rice, or Beans added).

Using the multiplication rule, we can find the total number of possible meals as:

4 x 5 x 4 x 6 = 480

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we should subtract (389/600) from (7/12) + (7/8) to obtain the multiplicative inverse of (4/3) - (2/9).

To find the multiplicative inverse of a fraction, we need to find another fraction that, when multiplied by the original fraction, results in a product of 1.

Let's start by finding the multiplicative inverse of the fraction (4/3) - (2/9):

(4/3) - (2/9) = (12/9) - (2/9) = (10/9)

The multiplicative inverse of (10/9) would be a fraction (a/b) such that:

(10/9) x (a/b) = 1

Multiplying both sides by (9/10) (the reciprocal of 10/9), we get:

(a/b) = (9/10) x (1/(10/9))

Simplifying the expression on the right-hand side, we get:

(a/b) = (9/10) x (9/10) = 81/100

So the multiplicative inverse of (4/3) - (2/9) is 81/100.

Next, we need to find what we should subtract from (7/12) + (7/8) to obtain 81/100.

We can first find a common denominator between (7/12) and (7/8), which is 24:

(7/12) = (7/12) x (2/2) = 14/24

(7/8) = (7/8) x (3/3) = 21/24

So, we can rewrite (7/12) + (7/8) as:

(14/24) + (21/24) = 35/24

To obtain the difference between 35/24 and 81/100, we subtract the smaller fraction from the larger one:

81/100 - 35/24 = (81/100) x (6/6) - (35/24) x (25/25)

= 486/600 - 875/600 = -389/600

Therefore, we should subtract (389/600) from (7/12) + (7/8) to obtain the multiplicative inverse of (4/3) - (2/9).

Final answer:

(7/12) + (7/8) - (389/600) = 1.0158 (rounded to four decimal places)

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number one take the second

The requried,  3025 bacteria are present after 12 hours.

To find the number of bacteria present after 12 hours, we simply need to substitute t=12 in the given equation:

[tex]n(12) = 500e^{(0.15*12)}[/tex]

[tex]n(12) = 500e^{1.8}[/tex]

n(12) ≈ 3024.82

Rounding this to the nearest whole number, we get:

n(12) ≈ 47,416 ≈ 3025

Therefore, there are approximately 3025 bacteria present after 12 hours.

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The mean low temperature in Ketchikan from Monday to Friday is given as follows:

b. -5.4 ºF.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

The five observations in the data-set are given as follows:

-10, -20, 5, 3 and -5.

Hence the mean of the data-set is given as follows:

(-10 - 20 + 5 + 3 - 5)/5 = -5.4 ºF.

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