2015 > Chapter 1: Measuring and Constructing Angles > Section Exercises
11
Find the measure of ZCOD.
10 20
10 170 160 150
m/COD-
do 140 130 120 110 100
A
Classify ZCOD
-88
с
-88
O
100 110 120
LCOD is a(n) acute ✓angle.
D
E
a
B
15 20 10
170 10

Answer:

To estimate I would either do 6x220 then subtract 6 from that sum

Or you could do 6x200

6x10

6x9

And add that to get your answer but 6x219 is 1314

Step-by-step explanation:

The reasonable Domain and Range for the situation.

Given that

To find

So, according to the question

We have,

So, we can say that

          Total charges = 8 (total number of peoples in a party)

Let's assume

                                 Total charges = y , and

Total number of peoples in a party =  x

Then, we get a equation of this problem,

                y = 8x ------------(1)

So, the domain of this equation will be greater then and equal to 64. and range will be greater then and equal to 8 and less then and equal to 40.

Answer:

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To solve the inequality, divide both sides by 9. The solution is a < 5 or (∞, 5)

Tips to solve linear inequalities:

Interval notation is often used for the solution(s). Recall the differences between a bracket [ or ], and a parenthesis (  or ). A bracket means the endpoint is included in the solution while a parenthesis means the endpoint is not included in the solution. Remember, infinity ∞ always use a parenthesis.

Example:  x ≥ 2 can be written as [2, ∞), while

                x > 0 is written as (2, ∞)

The given problem:

9a < 45

Notice that the variable, a, is already isolated on the left side.  Divide both sides by 9: (Note that the inequality sign is not flipped since 9 is a positive number)

9a : 9 < 45 : 9

a < 5

Using the interval notation, the solution is (∞, 5)

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The product of three successive integers is represented by the symbol n3 n=(n1)(n)(n+1).

n3 n can be divided by 6.

Consecutive integers are the numbers that follow one another. They go either alphabetically or sequentially. For instance, a series of integers is a group of natural numbers. The term "consecutive" in mathematics refers to an unbroken flow or succession of numbers; hence, a sequence of consecutive integers is one where each following number is one more than the one before it. An array of consecutive integers (or numbers) has an identical mean and median. If x is a positive integer, then x + 1 and x + 2 are likewise positive integers. We shall learn in-depth details regarding formulas, characteristics, illustrations, and the significance.

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Answer:1) An operator is missing in your statement. Most likely the right expression is:

Step-by-step explanation:

              2x

f(x) = -------------

          3x^2 - 3

So, I will work with it and find the result of each one of the statements given to determine their validiy.

2) Statement 1: The graph approaches 0 as x approaches infinity.

Find the limit of the function as x approaches infinity:

                                   2x

Limit when x →∞ of ------------

                                3x^2 - 3

Start by dividing numerator and denominator by x^2 =>

     2x / x^2                         2/x

--------------------------- = ---------------

 3x^2 / x^2 - 3 / x^2       3 - 3/x^2

                                     2/∞             0          0

Replace x with ∞ =>  ------------ =  ------- =  ---- = 0

                                   3 - 3/∞        3 - 0      3

Therefore the statement is TRUE.

3) Statement 2: The graph approaches 0 as x approaches negative infinity.

Find the limit of the function as x approaches negative infinity:

                                       2x

Limit when x → - ∞ of ------------

                                    3x^2 - 3

Start by dividing numerator and denominator by x^2 =>

     2x / x^2                         2/x

--------------------------- = ---------------

 3x^2 / x^2 - 3 / x^2       3 - 3/x^2

                                       2/(-∞)           0            0

Replace x with - ∞ =>  ------------ =  ---------- =  ---- = 0

                                     3 - 3/(-∞)      3 - 0        3

Therefore, the statement is TRUE.

4) Statement 3: The graph approaches 2/3 as x approaches infinity.

FALSE, as we already found that the graph approaches 0 when x approaches infinity.

5) Statement 4: The graph approaches –1 as x approaches negative infinity.

FALSE, as we already found the graph approaches 0 when x approaches negative infinity.

Answer:

Step-by-step explanation:

56/89

The probability of scoring exactly four out of the given six shots is 0.311, calculated using the concept of binomial distribution in probability theory.

What is a Binomial Distribution?

Binomial Distribution in probability theory is defined as getting x number of successes on repetition of trial n times, the formula for binomial distribution is C(n,r) × (p)x × (q)n - r, where p denotes the probability of success and q denotes the probability of failure.

Calculation of the probability of scoring exactly four shots out of six

Let p denote the probability of success and q denote the probability of failure, which is equal to 1 - p.

Using Binomial Distribution, we get,

P(x = r) = C(n,x) × (p)x × (q)n - x

Taking r = 4,

P(x = 4) = C(6,4) × (0.6)4 × (0.4)2

= 6! / (4! 2!) × (0.6)4 × 0.16

= 0.31104

~ 0.311

Hence, the required probability using binomial distribution is 0.311.

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Answer:

Hello,

answer : 259269764699508231

Step-by-step explanation:

We must use permutations with repetitions

The properties used, in order, are:

We start by writing the linear equation:

3*(x + 2) = 4x + 1

The first step is using the distributive property to distribute the left product.

3x + 6 = 4x + 1

Then we use the addition property of equality to subtract 4x in both sides, we will get:

-x + 6 = 1

And we use it again to subtract 6 in both sides:

-x = 1 - 6 = -5

Finally, we multiply both sides by -1 (multiplication property of the equality)

x = 5

That is the solution of the linear equation.

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The total area under the normal curve is 1.

Why is there a standard deviation?

the total area under the normal curve is 1.

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Answer:

option C: 69

Step-by-step explanation:

We are to find approximately how many pink flowers are predicted to bloom on a shrub with 40 red flowers. The equation given is: y = 1.73x + 0.0924 and we see that red flowers are on the x-axis and pink flowers are on the y-axis.

Since we know there are 40 red flowers and red flowers are on the x-axis, x = 40. Plug into the equation:

y = 1.73x + 0.0924 where x = 40

y = 1.73(40) + 0.0924

y = 69.2  + 0.0924

y = 69.2924

best answer is C. 69.

Step-by-step explanation:

so, we have a kite here.

a kite is a quadrilateral, that is totally symmetric along one of its diagonals.

the sum of all internal angles of a quadrilateral is always 360°.

remember, the sum of all angles around one point on one side of a line is always 180°.

a full circle airways represents 360°.

the inner angle at 140° is

180 - 140 = 40°

the inner angle at 250° is

360 - 250 = 110°

the inner angles at x and its opposing corner are equal (due to the symmetry) and are in sum with the other 2 inner angles 360°.

so, we have for the inner angles

360 = 110 + 40 + 2×xinner

210 = 2×xinner

the inner angle of x = 105°.

x (the outer angle of the inner angle of x) is

x = 360 - 105 = 255°

There is an approximate average velocity. 0.1 m/s, or 0.222 m/h.

A vector quantity is average velocity. The change in position and otherwise displacement (x) divided by that of the time intervals (t) during which the displacement happens is the definition of average velocity. The average velocity may be either positive or negative depending on the displacement's direction.

The distance covered by the rubber ducks = 1600 miles.

The duration needed to cover this distance = 10 months.

The average ocean speed, according to definition, is

v = (1600 miles)/(10 months)

Now,

1 mile = 1609 m

10 months = (10 months)*(30 days/month) *(24 hours/day)

                 = 7200 hours (approx.)

                 = 7200*3600

                 = 2.592 x 10⁷ s

So that,

ν = [tex]\frac{(1600 \mathrm{~m}) *\left(1609 \frac{\mathrm{m}}{\mathrm{mi}}\right)}{(10 \mathrm{months}) *\left(2.592 \times 10^7 \frac{\mathrm{g}}{10 \mathrm{mon} t h}\right)}[/tex]

   = 0.0993 m/s

Also,

ν = 1600/7200

  = 0.222 mi/h

There is an approximate average velocity. 0.1 m/s, or 0.222 m/h.

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I understand that the question you are looking for is:

A severe storm on January 10, 1992, caused a cargo ship near the Aleutian Islands to spill 29,000 rubber ducks and other bath toys into the ocean. Ten months later hundreds of rubber ducks began to appear along the shoreline near Sitka, Alaska, roughly 1600 miles away.

What was the approximate average speed of the ocean current that carried the ducks to shore in m/s and in mi/h? (Rubber ducks from the same spill began to appear on the coast of Maine in July 2003.)

Answer:

7x

Step-by-step explanation:

Check to discover if an issue even exists before attempting to address it. not just to you, but also to those it will effect. You may create the criteria to compare and evaluate the potential remedies by developing an understanding of what makes this a problem in the first place.

Before programming starts, evaluation enables us to think through a problem's solution, ensure that it satisfies the original design requirements, yields the right answer, and is appropriate for the task at hand.

Three methods can be used to evaluate your problem-solving skills: asking for examples of times you've previously solved an issue; posing you with potential scenarios and asking you to reply; and observing how you use your problem-solving abilities in various exams and activities.

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The comparison of the numbers is that  -√7 is greater than -3.12345....

The numbers are given as:

-√7 and -3.12345....

Using a calculator, we have:

-√7 = -2.6457.....

-2.6457.... is greater than -3.12345....

This means that

-√7 is greater than -3.12345....

Hence, the comparison of the numbers is that  -√7 is greater than -3.12345....

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Answer:

25

Step-by-step explanation:

j(k + 2)

5(3 + 2)

5(5)

25

Answer:

[tex]10\frac{11}{20}[/tex]

Step-by-step explanation:

[tex]5\frac{1}{2} + 3\frac{4}{5} + 1\frac{1}{4}[/tex]

1.Find the LCM(Least Common Multiple).

That would be 20.

2.Multiply so all denominators are equal.

[tex]5\frac{10}{20} + 3\frac{16}{20} + 1\frac{5}{20}[/tex]

3. Add

[tex]9\frac{31}{20}[/tex]

4. Simplify

[tex]10\frac{11}{20}[/tex]

The vertex is (3,16) and the quadratic equation in vertex form is [tex]f(x)=(x-3)^{2}+16\\[/tex].

Any equation in algebra that can be put into standard form is called a quadratic equation (from the Latin quadratus, which means "square").

As well as being referred to as the roots or zeros of the expression on the left-hand side of the equation, the values of x that satisfy it are known as solutions of the equation. There are only two possible answers to a quadratic equation. A double root is said to exist if there is only one solution. In the case where all of the coefficients are real values, there are either two real solutions, one real double root, two complex solutions that are complex conjugates of one another, or all three of the aforementioned options. If complex roots are taken into account, then a quadratic equation will always have two roots, with a double root counting as one. An equivalent equation  can be created from a quadratic equation.

Calculations:

[tex]f(x)=x^{2} -6x+25\\ = x^{2} -2.x.3+(3^{2} )-(3^{2} )+25\\=(x-3)^{2} -9+25\\=(x-3)^{2}+16\\[/tex]

Comparing this from the vertex, y=[tex]a[/tex][tex](h-x)^{2} +k\\[/tex]

h=3 and k=16

Hence, vertex is (3,16).

[tex]f(x)=(x-3)^{2}+16\\[/tex]

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The distance between the zoo and library is 600 feet, as seen with the help of concept of applications of trigonometry.

Given: height of helicopter = 300√3 feet from the ground.

To find: Distance between zoo and library.

Finding:

(Refer to the image attached.)

Let the distance from the plane to the zoo and library be d1 and d2 respectively.

Then, with the help of concepts of applications of trigonometry,

[tex]tan(60) = \frac{300\sqrt{3}}{d1}[/tex]

=> [tex]\sqrt{3}=\frac{300\sqrt{3}}{d1}[/tex]

=> d1 = 300 feet

[tex]tan(30) = \frac{300\sqrt{3}}{d2}[/tex]

=> [tex]\frac{1}{\sqrt{3}}=\frac{300\sqrt{3}}{d2}[/tex]

=> d2 = 300 (3) = 900 feet

The distance between zoo and library = d2 - d1 = 900 - 300 = 600 feet.

Hence, the distance between the zoo and library is 600 feet, as seen with the help of concept of applications of trigonometry.

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The factors of the expression  w³ + 6w² - 40w = 0 is (w - 4) and (w + 10)

(w - 4) will be the height

(w + 10) will be the length

Given,

The length of the enclosure for the pancake tortoise will be greater than the height, that is: l > h

The volume of enclosure = w³ + 6w² - 40w

Where w is the width.

Now, factorize the expression:

w³ + 6w² - 40w = 0

10 - 4 = 6

10 × (-4) = -40

Therefore, the factors of the expression  w³ + 6w² - 40w = 0 is (w - 4) and (w + 10)

Here, we know that length is greater than height.

So, (w - 4) will be the height and (w + 10) will be the length.

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[tex]f + b = m \\ f + b - f = m - f \\ b = m - f[/tex]

The time required to work at temperature of75degree celsius is 56.25 minutes

If a machine starts working in 45 minutes at the temperature of 60degree celsius, the amount of time worked at a temperature of 1 degree is expressed as:

Unit rate = 45/60

Unit rate = 0.75degrees celsius/minute

Determine the time it required to work at temperature of 75degree celsius

Time required = 0.75 * 75

Time required = 56.25 minutes

Hence the time required to work at temperature of75degree celsius is 56.25 minutes

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Answer:

42 plants

might be easier to find how many plants are planted in 1 hour then multiply that by 6. In this case, 7 plants will be planted within an hour. So, multiply 7 x 6 to get 42.

Answer:

c

Step-by-step explanation:

192=4x-12

Problem 4

Let's define these point locations

Angle DBC is 90 degrees since it covers the upper right quadrant

Angle CBA is 45 degrees

Therefore, angle ABD is 90+45 = 135 degrees.

Check out the diagram below.

=========================================================

Problem 11

x = the unknown angle

angle x and 140 combine to a straight angle (180 degrees)

x+140 = 180

x = 180-140

x = 40

=========================================================

Problem 12

This time the angles add to 90

x+36 = 90

x = 90-36

x = 54

=========================================================

Problem 13

The two angles x and 90 combine to a 120 degree angle

x+90 = 120

x = 120-90

x = 30

Answer:

Z = ky/x where y=12, x=-12 and z=-6

-6= k(12)/-12

-k = - 6

K = 6

Answer:

34-5=29

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

hope it helps and have a nice day! :)