Question 8, triangle review

An equation for a line perpendicular to the line 2 = 10 can be found by finding the slope of that line and then finding the slope of the perpendicular line. The slope of the line 2 = 10 is 0, so the slope of the perpendicular line would be undefined.

The equation of a line with slope m passing through the point (x1, y1) can be written in the form:

y - y1 = m(x - x1)

Since the slope of the line is undefined, the equation of the line would be in the form:

x - x1 = constant

To find the equation of the line that passes through the point (3, 2), we substitute the values into the equation:

x - 3 = constant

So the equation of the line that is perpendicular to the line 2 = 10 and passes through the point (3, 2) is:

x - 3 = constant

or simply:

x = 3.

The value of 'w' in the solution of the following system of linear equations is -[tex]\frac{1}{6}[/tex]

we can solve for a variable say 'v' then put the value of 'v' in the other equations and solve them for the value of 'w'

5v + 4w = 1

5v = 1 - 4w

v = [tex]\frac{1-4w}{5}[/tex]

now, when we put the value of 'v' in the second equation, we get:

3([tex]\frac{1-4w}{5}[/tex] ) - 6w = 2

3([tex]\frac{1-4w}{5}[/tex] ) = 2 + 6w

[tex]\frac{3-12w}{5}[/tex] = 2 + 6w

3 - 12w = 10 + 30w

-42w = 7

w = [tex]\frac{7}{-42}[/tex]

w = -[tex]\frac{1}{6}[/tex]

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a. This is an example of continuous growth, as the functions for the GDPs of both countries are given as continuous functions of time.

(b) In the function for China's GDP, the parameter 1.35 represents the initial level of GDP in the year 2000, and the parameter 1.076 represents the annual rate of growth of GDP. In the function for the US's GDP, the parameter 10.4 represents the initial level of GDP in the year 2000, and the parameter 1.024 represents the annual rate of growth of GDP.

It should be noted that on order to calculate the projected level of GDP for each country for the years 2011, 2025 and 2047, we can substitute the corresponding values of t into the functions for YChina and YUSA:

For China:

YChina(11) = 1.35 * 1.076^11 ≈ 4.65 trillion dollars

YChina(25) = 1.35 * 1.076^25 ≈ 30.83 trillion dollars

YChina(47) = 1.35 * 1.076^47 ≈ 516.97 trillion dollars

For the US:

YUSA(11) = 10.4 * 1.024^11 ≈ 15.63 trillion dollars

YUSA(25) = 10.4 * 1.024^25 ≈ 30.19 trillion dollars

YUSA(47) = 10.4 * 1.024^47 ≈ 57.17 trillion dollars

So according to these projections, China's GDP has already surpassed the US's GDP as of 2025 and is expected to continue to grow at a much faster rate than the US's GDP in the future.

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The equation that describes the graphed function is given as follows:

A. y = f(-x + 3).

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

The parent function for this problem is given as follows:

[tex]y = \sqrt{x}[/tex]

The function was reflected over the y-axis, hence it is given as follows:

[tex]y = \sqrt{-x}[/tex]

Then it was moved 3 units right, hence the definition is given as follows:

[tex]y = \sqrt{-(x - 3)}[/tex]

[tex]y = \sqrt{-x + 3}[/tex]

Hence:

y = f(-x + 3), as x was replaced by -x + 3.

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The battery will last 2.73 hours when it is fully charged

The unit rate is the ratio of a certain number of units of one quantity to units of another quantity. Mathematically, the unit rate is one quantity divided by the other quantity

Since Cheryl's phone battery is 55% charged and it will last for another 1.5 hours. Thus, the rate will be:

rate =   1.5 hours/55% = 3/110 hour per %

When it is fully charged, that is 100%. Thus, it will take:

Time for 100% = (3/110) * 100% = 2 8/11 hours = 2.73 hours

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The zeros of the given polynomial function are 3

Zero of a polynomial are numerical values at which the polynomial will equal zero. In other words, zeros of a polynomial are numerical values of the variable which give zero when we plug into the polynomial.

For example, for a polynomial p(x) the zeros are the value of 'x' which satisfies p(x) = 0. This means by identifying the x-intercepts, we may determine the polynomial's zeros.

In the case of a graph, we can determine the zeros of a polynomial by observing the points at which the graph line will cut the x-axis. In simple words, we can say that the x-coordinates of the points where the graph meets the x-axis are the zeros of the polynomial.  

Here we have a graph

In the given graph the polynomial function meets the x-axis three times at three different points.

Therefore,

The zeros of the given polynomial function are 3

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The solution to the inequality are the region in the shaded area

From the question, we have the following parameters that can be used in our computation:

y < 3x+3

3x-y ≤ 4

Represent properly

y < 3x + 3

3x - y ≤ 4

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, one of the coordinates in the shaded area has a coordinate of (0.2, 2)

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The statement is true; Tests are weighed the most when determining a grade.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

Given in the question that:

Grade distribution

Quizzes, 30%

Homework 15%

Test, 30%

Classwork 25%

The total giving 100%.

A particular student scored the following;

87.9% on exams, 77.8% quiz, 90% Home work and 100%  on class participation

Calculating the percentages the student had for each

Exam total = 50 x 0.879 = 43.95% earned

Quiz = 30 x 0.778 = 23.34% earned

Home work = 15x 0.9 = 13.5% earned

Class participation = 5*1 = 5% earned

Total earned = 43.95+ 23.34 + 13.5+ 5 = 85.79%

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Answer:

340 CDs

Step-by-step explanation:

To answer this question, we're dealing with three functions for one problem, namely the revenue function, the cost function, and the profit function.

The revenue function is R(q) = pq, where p is the price of a certain good and q is the quantity sold.

The cost function is C(q) = variable cost + fixed cost, where variable costs changes depending on the quantity of goods produced and fixed cost is a one-time cost for the producer (e.g., an investment, rent, etc.).

The profit function is P(q) = R(q) - C(q) and is simply the cost function subtracted from the revenue function.

The "break-even point" is the point at which profit = $0 and the point at which cost = revenue.

From the problem, we see that Jason invested $3349 (once) for his CDs and each disk requires $3.65 for the materials so our cost function is C(q)  = 3.65q + 3349

Furthermore, we see that each disks sells for $13.50, so our revenue function is R(q) = 13.5q

Our profit function then is P(q) = 13.5q - (3.65q + 3349) = 13.5q - 3.65q - 3349 = 9.85q - 3349.

Thus, to find the break-even point, we set profit = 0 and solve for q:

[tex]0=9.85q-3349\\3349=9.85q\\340=q[/tex]

Answer:

Step-by-step explanation:

The probability that someone could guess the correct code for the car model with a keypad of 5 numbers is 1 in 120,000, or approximately 0.0000083.

To calculate this, we need to determine the total number of possible combinations of 5 numbers (without repetition) from a set of 5 numbers. This can be calculated as 5!/(5-5)! = 5! = 5x4x3x2x1 = 120.

So, the probability of guessing the correct code is 1/120 or 0.0000083. This means that the chances of guessing the correct code are very low and the car's security system is fairly secure.

The longest side of a triangle is always opposite the,

A. angle with the greatest measure.

If a² + b² < c² then it is an acute angle triangle.

If a² + b² = c² then it is a right-angle triangle.

If a² + b² ≥ c² then it is an obtuse angle triangle.

We know, The length of the largest side in a triangle is opposite to the largest angle.

The statement, The longest side of a triangle is always opposite the

angle with the greatest measure.

Because A longer angle will be more spread out and hence the opposite side will be longer too.

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The real zeroes of the polynomial function f(x) = 4x⁴ - 8x³ - 19x² + 23x - 6 are 1/2, 1, 3/2, and 2.

In mathematics, a polynomial is an expression consisting of variables and coefficients, which are combined using the operations of addition, subtraction, and multiplication. A polynomial can have one or more terms, where each term is the product of a coefficient and one or more variables raised to non-negative integer powers. For example, the polynomial 2x² - 3x + 1 has three terms: 2x², -3x, and 1.

For the given polynomial function, the constant term is -6 and the leading coefficient is 4. Therefore, the possible rational zeroes of the function are of the form p/q, where p is a factor of -6 and q is a factor of 4.

The factors of -6 are ±1, ±2, ±3, and ±6. The factors of 4 are ±1, ±2, and ±4. So the possible rational zeroes are:

±1/1, ±2/1, ±3/1, ±6/1, ±1/2, ±3/2

To determine which of these possible rational zeroes are actual zeroes, we can use synthetic division or long division to evaluate the function at each possible zero. Doing so, we find that the actual zeroes of the function are:

x = 1/2, x = 1, x = 3/2, x = 2

Therefore, the real zeroes of the polynomial function f(x) = 4x⁴ - 8x³ - 19x² + 23x - 6 are 1/2, 1, 3/2, and 2.

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Answer: C

Step-by-step explanation:

I am fairly certain this is the right answer. Good luck on your quiz!

Answer:C

Step-by-step explanation:

I remember this from class one time hope it helps:)

In this exercise we have to use the knowledge of excel to explain some functions that can be used, as:

In excel cell a division formula can be written as: =(A4+B4+C4+D4+E4)/5

If you track your daily earnings in an Excel spreadsheet, you can use the same spreadsheet to estimate your forecasted earnings for any period of time. You can use Excel's AVERAGE function to find out your average daily income. Multiply your average daily sales by the number of days specified to estimate how much profit you could make over time.

In mathematics, the average of a list of data represents the central value of the set of data. Mathematically defined as the ratio of the sum of all data and the number of items in the list. In statistics, the mean of a particular set of numerical data is also called the mean. For example, the average of 2, 3, 4 is (2+3+4)/3 = 9/3 =3. So here 3 is the center value of 2, 3, and 4. So the meaning of average is to find the average of a group of numbers.

mean = sum of values ​​/ number of values

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The truth table for the statement is

p     q     ~p    q ↔️ ~p   ~(q ↔️ ~p)

-------------------------------------

T     T     F     F        T

T     F     F     F        T

F     T     T     T        F

F     F     T     F        T

From the question, we have the following parameters that can be used in our computation:

~(q↔️~p)

To construct the truth table, we make use of the following notations

p, q, ~p, (q↔️~p) and ~(q↔️~p)

The truth table for the statement ~(q ↔️ ~p) is then represented as follows:

p     q     ~p    q ↔️ ~p   ~(q ↔️ ~p)

-------------------------------------

T     T     F     F        T

T     F     F     F        T

F     T     T     T        F

F     F     T     F        T

The condition for ↔ is that it is true if both statements are true

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The length of side f is 12.0 inches

From the question, we have the following parameters that can be used in our computation:

In ΔDEF, e = 9.2 cm, m m∠F=72° and m m∠D=61°

The sum of angles in a triangle is 180 degrees

Using the above as a guide, we have the following:

E = 180 - 72 - 61

E = 47

Using the law of sines, we have

f/sin(F) = e/sin(E)

substitute the known values in the above equation, so, we have the following representation

f/sin(72) = 9.2/sin(47)

So, we have

f = sin(72) * 9.2/sin(47)

Evaluate

f = 12.0

Hence, the length is 12.0 inches

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Answer:

Step-by-step explanation:

a

The value of lim x -> -1- f(x)= -1

The behavior of a function at a specific input is described by its limit, a crucial concept in calculus and analysis.

Hence,

As x approaches -1 from the left, the graph of f(x) leads you to the point (-1, 3), so the limit from the left is 3.

As x approaches -1 from the right, the graph leads to the point (-1, -3), so the limit from the right is -3.

The one-sided limits do not match, so the two-sided limit does not exist.

But f(x) is still defined at x = -1; this is indicated by the point (-1, -1). So f (-1) = -1.

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The graph below is the function f(x)

Find lim x -> -1- f(x)=

Answer:

12 and 5

Step-by-step explanation:

12+5=17

12x5=60

Answer:

Step-by-step explanation:

5 12 step by step

Angle b is equal to 35°, angle a and angle e are each equal to 145°

An angle is formed when two lines intersect at a point. Types of angles are acute angle, obtuse angle and right angle. Vertical opposite angles are always congruent to each other. The sum of angles along a straight line is supplementary (add up to 180 degrees)

From the diagram:

b = 35° (vertical opposite angles are congruent)

a + b = 180° (sum of angles along a straight line)

a + 35 = 180

a = 145°

a = e = 145° (vertical opposite angles are congruent)

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There was a 305.1% increase in the value from 2000 to 2010.

What is Percent?

To compute a percentage, divide the value by the entire amount and multiply the result by 100.

To calculate the percent increase, we need to determine the difference between the two values and divide it by the original value, then multiply by 100 to express it as a percentage.

For the year 2000:

Percent increase = (22.5 - 5.53) / 5.53 * 100 = 305.05%

And rounded to the nearest tenth of a percent, this would be 305.1%.

So, There was a 305.1% increase in the value from 2000 to 2010.

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Answer: no exact answer

Step-by-step explanation:

The value of x is 21.4.

What is right-angle triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.

The height of the right-angle triangle is 11. The hypotenuse of the right-angle triangle is x. The measure of the angle opposite to height is 31°.

The sine of an angle is the ratio of height to the hypotenuse.

Therefore,

sin 31° = height/hypotenuse

sin 31° = 11/x

Multiply x with both sides:

x sin 31° = 11

Divide sin 31° with both sides:

x = 11/ sin 31°

x = 21.35

x ≈ 21.4 units

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According to the information, it can be inferred that the total surface of the figure is 23.18yr². Additionally, the volume would be 7.8 yr³

To calculate the surface of the figure we must perform the following mathematical procedure.

We must find the surface of each of the faces that the figure has, we do this by multiplying base by height; in the case of triangles it is base times height divided in two.

Now we must multiply these values by the number of faces of this dimension:

Then we add all the surfaces to have the total surface

On the other hand, to find the volume of the figure we must multiply height by length by width; in the case of the triangle it is the same formula because it has a rectangular base.

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The total distance that Cami walked from home to school, then home, and then library, is 7. 46 miles

The distance walked by Cami, can be found to be :

= Distance from home to school + distance from school to home + distance from home to library

The distance in kilometers is:

= 5 + 5 + 2

= 12 kilometers

In miles, this is:

= 12 / 1. 60934 km per mile

= 7. 46 miles

In conclusion, the distance walked by Cami in miles, was 7. 46 miles.

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The shape is most specifically a trapezoid because it has a pair of parallel sides

From the question, we have the following parameters that can be used in our computation:

The figure

From the figure, we have the following highlights:

Using the above as a guide, we have the following:

The shape is most specifically a trapezoid

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Answer: 994 beads

Step-by-step explanation:

Red Beads = 275

Blue Beads = 825 (275 x 3)

825 + 275 = 1100 beads (total)

1100 - 156 = 994 beads

The equation of the line that contains diagonal AH is  y = -4/7 x + 51/14.

Rhombus is a parallelogram whose all sides are of equal lengths.

Its diagonals are perpendicular to each other and they cut each other in half( thus, they're perpendicular bisector of each other).

Its vertex angles are bisected by its diagonals.

The triangles on either side of the diagonals are isosceles and congruent.

Given;

The endpoints of the diagonal MT are M(0,-1) and T(4,6).

Now, The point that it passes through in this case is the midpoint of the diagonal MT. Using the midpoint formula you get

( (0+4)/2 , (-1+6)/2 ) = (2,2.5).

The slope of MT is (6--1)/(4-0) = 7/4.

We need this because the other diagonal must be perpendicular, which means that the slopes must be negative reciprocals. So the negative reciprocal of 7/4 is -4/7.

Now that we have the slope and the point, we can just use y=mx+b. We have an x and y value as well as the m....so we can substitute them in and calculate b.

2.5 = -4/7 (2) + b

5/2 = -8/7 + b

5/2 + 8/7 = b

35/14 + 16/14 = b

51/14 = b

Therefore, in the rhombus diagonal line has the equation will be y = -4/7 x + 51/14

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Answer:

5,144,079

Step-by-step explanation:

[tex]\displaystyle CI=\mu\pm z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\CI_{99.5\%}=\mu\pm2.807\biggr(\frac{80.8}{\sqrt{n}}\biggr)\\\\0.1=2.807\biggr(\frac{80.8}{\sqrt{n}}\biggr)\\\\0.1\sqrt{n}=226.8056\\\\\sqrt{n}=2268.056\\\\n=5144078.01914\\\\n=5144079[/tex]

Thus, you would need a sample size of 5,144,079 to be 99.5% confident that the true population mean is ±0.1 away from it with a population standard deviation of 80.8 (aka. our margin of error).