Dewight is proving the sum formula for the sine function. He has started his proof, what property should he use to complete the next line?

Answer:

Part 1) The sum of the interior angles is equal to 180 degrees

Part 2) The measure of angle N is ∠N=60°

Part 3) The measure of angle M is ∠M=120°

Part 4) The sum of the the exterior angles is 360°

Step-by-step explanation:

Part 1) What is the sum of the interior angles of the equilateral triangle?

we know that

The sum of the interior angles of any triangle must be equal to 180 degrees

Part 2) What is the measure of ∠N?

we know that

An equilateral triangle has three equal sides and three equal internal angles ( each internal angle measure 60 degrees)

so

In this problem

∠N=60°

Part 3) What is the measure of ∠M? Explain your reasoning.

we know that

∠M+∠N=180° -----> by supplementary angles (linear pair)

we have

∠N=60°

substitute

∠M+60°=180°

∠M=180°-60°=120°

Part 4) What is the sum of the exterior angles of the equilateral triangle ∠M + ∠R + ∠X?

we know that

The sum of the the exterior angles of any polygon is equal to 360 degrees

In this problem

we have

∠M=∠R=∠X=120°

so

∠M+∠R+∠X=120°+120°+120°=360°

Answer:

Step-by-step explanation:

The sum of the interior angles is equal to 180 degrees. The measure of angle N is ∠N=60°. The measure of angle M is ∠M=120°. The sum of the the exterior angles is 360°

Answer:

Step-by-step explanation:

9x⁴ – 2x² – 7 = 0

Let's say that u = x²:

9u² – 2u – 7 = 0

Factor:

(u – 1) (9u + 7) = 0

u = 1, -7/9

Since u = x²:

x² = 1, -7/9

x = ±1, ±i √(7/9)

By using the substitution method, the solutions of this equation (polynomial) is equal to C. x = ±1 and ±i√(7/9).

In order to determine the solutions of this equation (polynomial), we would let "u" be equal to x² and then substitute this value into the equation as follows:

9x⁴ - 2x² - 7 = 0

Substituting the value of "u" into the equation (polynomial), we have:

9u² - 2u - 7 = 0

Factorizing the equation (polynomial), we have:

(9u + 7)(u - 1) = 0

u = 1 and -7/9

Since, u = x²:

x² = 1 and -7/9

x = ±√(1 and -7/9)

x = ±1 and ±i√(7/9).

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Answer:

• linear angles

• supplementary angles (all linear angles are supplementary)

Step-by-step explanation:

If the angles share a side and are measured in opposite directions from that side, the non-common edges of these angles form a straight line, so these angles are sometimes called "linear" angles.

Since their sum is 180°, they are always "supplementary" angles. (Supplementary angles need not share a vertex or a side.)

I don’t know what the answer is I wish I could help

Answer:

The sum of the first 100 terms is 60400

Step-by-step explanation:

* Lets revise the arithmetic sequence

- There is a constant difference between each two consecutive

  numbers

- Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….

# 5  ,  10  ,  15  ,  20  ,  …………………………

# 12  ,  10  ,  8  ,  6  ,  ……………………………

* General term (nth term) of an Arithmetic sequence:

- U1 = a  ,  U2  = a + d  ,  U3  = a + 2d  ,  U4 = a + 3d  ,  U5 = a + 4d

- Un = a + (n – 1)d, where a is the first term , d is the difference

 between each two consecutive terms n is the position of the

 number

- The sum of first n terms of an Arithmetic sequence is calculate from

 Sn = n/2[a + l], where a is the first term and l is the last term

* Now lets solve the problem

- We will use method (1)

- From the table the terms of the sequence are:

 10 , 22 , 34 , 46 , 58 , 82 , 94 , ............., where 10 is the first term

∵ an = a1 + (n - 1) d ⇒ explicit formula

∵ a1 = 10 and a2 = 22

∵ d = a2 - a1

∴ d = 22 - 10 = 12

- The 100th term means the term of n = 100

∴ a100 = 10 + (100 - 1) 12

∴ a100 = 10 + 99 × 12 = 10 + 1188 = 1198

∴ The 100th term is 1198

- Lets find the sum of the first 100 terms of the sequence

∵ Sn = n/2[a1 + an]

∵ n = 100 , a = 10 , a100 = 1198

∴ S100 = 100/2[10 + 1198] = 50[1208] = 60400

* The sum of the first 100 terms is 60400

Answer:

A. 1 rational root and 2 complex roots

Step-by-step explanation:

The equation [tex]x^3+x^2=x-1[/tex] has the expression [tex]x^3+x^2[/tex] in the left side and the expression [tex]x-1[/tex] in the right side.

when ypu plot the graphs of the functions [tex]y=x^3+x^2[/tex] and [tex]y=x-1,[/tex] the number of intersection points shows the number of real solutions. These two graphs intersect only once, so the equation has one real solution. The third power equation should have three solutions, thus, two remaining solutions are complex.

Answer:

The answer is A

Step-by-step explanation:

Answer:

Step by step explanation

the equation is 225=27x-18

the first step is to add the 18 to the other side to get

243=27x

now divide by 27 on both sides

243/27=27x/27

solve to get

9=x

Answer:

step one: product of powers

step 2:power of powers

step 3: quotient of powers

Step-by-step explanation:

The rule of exponents was applied in each step will be multiplication rule,division rule and inverse of exponent rule.

Arithmetic is a branch of mathematics that studies numbers and the many operations that may be applied to them. The four basic math operations are addition, subtraction, multiplication, and division.

The given expression is;

[tex]\frac{(2)^3(2)^4}{2^{10}}[/tex]

Step 1; Multiplication rule of exponents;

[tex]\frac{(2)^3(2)^4}{2^{10}} \\\\ \frac{2^{3+4}}{2^{10}} \\\\\frac{2^7}{2^{10}}[/tex]

Step 2;Division rule of exponents;

[tex]\frac{2^7}{2{10}} \\\\ (2)^{7-10}\\\\ (2)^{-3}[/tex]

Step 2;Inverse rule of exponents;

[tex](2)^{-3}\\\\ \frac{1}{2^3} \\\\\frac{1}{8}[/tex]

Hence, the rule of exponents was applied in each step will be multiplication rule,division rule and inverse of exponent rule.

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Answer:

C and E

Step-by-step explanation:

Let's factor this the "old fashioned" way.  The standard form of a quadratic is

[tex]y=ax^2+bx+c[/tex]

If you're familiar with the quadratic formula I'd say throw it into that, but if not, again, let's do it the "old fashioned" way.  

We need to find the product of our a and c.  Our a = 2 and our c = -3.  So that gives us a -6.  Now we have to find the factors of 6 (the negative right now doesn't matter so much).  The factors of 6 are 1, 6  and 2, 3.  Both of those possibilities will work to give us a +5, which is the linear term.  Puttng in the 2, 3 first:

[tex]0=2x^2+3x+2x-3[/tex]

Now group the terms together into groups of 2:

[tex]0=(2x^2+3x)+(2x-3)[/tex]

The idea is to factor out something common in each term so that what's left over in the parenthesis in both terms is exactly the same.  In the first term we can factor out a common x, and in the second term, the only thing common is a 1.  So that looks like this:

[tex]x(2x+3)+1(2x-3)[/tex]

What's inside those parenthesis are not actually identical, so 2 and 3 won't work.  Lets try 1 and 6.  For those 2 numbers to equal a +5, the 6 is positive and the 1 is negative.  So let's try that:

[tex](2x^2+6x)+(-x-3)[/tex]

In the first term we can factor out the common 2x and in the second term we can factor out the common -1:

2x(x + 3) - 1(x + 3)

Now what's common is (x + 3), so we can factor THAT out and what is left over is 2x - 1:

(x + 3)(2x - 1) = 0

If x + 3 = 0, then x = -3

and if 2x - 1 = 0, then 2x = 1 and x = 1/2

Answer: m<c, m<b + m<d

Step-by-step explanation: If you use the given information, you can find that

m<a = 60

m<b = 30

m<c = 60

m<d = 30

The angles that will produce an acute angle in the given diagram are;  m<c, and m<b + m<d.

Acute angles are angles that measure less than 90 degrees.

From the image we observe the following;

m<a = 60

m<b = 30

m<c = 60

m<d = 30

Thus, the angles that will produce an acute angle in the given diagram are;  m<c, and m<b + m<d.

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Okay, so there are nickels and pennies in this jar.

So, let's call the number of pennies X

Since there are 161 coins altogether, the number of nickels is (161 - X)

So now we solve the equation:

.01X + .05(161 - X) = 3.09

.01X + 8.05 - .05X = 3. 09

4.96 = .04X

124 = X

So, there are 124 pennies

Therefore, there are 161 - 124 = 37 nickels

Let's check our answer:

124 x .01 + 37x .05 = 1.24 + 1.85 = 3.09

It works!

I think it is 18

nickels for $3.09

4x + 7 = 31

    -7    -7

4x = 24

/4     /4

x = 6 (Answer)

Prove.

4(6) + 7 = 31

24 + 7 = 31

31 = 31

True.

The solution to the given equation 4x + 7 = 31 is x = 6, which is determined by subtraction.

The equation is given as follows:

4x + 7 = 31

To solve the equation 4x + 7 = 31 for x, we want to isolate the variable x on one side of the equation.

First, we can begin by subtracting 7 from both sides of the equation:

4x + 7 - 7 = 31 - 7

Simplifying, we get:

4x = 24

Next, we want to isolate x, so we divide both sides of the equation by 4:

4x/4 = 24/4

This simplifies to:

x = 6

Therefore, the solution to the equation 4x + 7 = 31 is x = 6.

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Answer:

400

Step-by-step explanation:

Just take 10% of 4,000 flashlights.  400 flashlights are likely to be defective.

Answer:

  1

Step-by-step explanation:

"Complementary events" by definition have probabilities that total 1. An event is complementary to another if it occurs when the other one doesn't, and vice versa. That is, the outcome is always one or the other of the complementary outcomes--never both, never neither.

The sum of the probabilities of two complementary events is equal to 1.

In probability theory, mutually exclusive events are events that cannot occur simultaneously. The sum of the probabilities of two complementary events is equal to 1. If events A and B are mutually exclusive, then the probability that at least one occurs (A or B) is equal to the sum of their individual probabilities (PA + PB).

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Answer:

[tex]\frac{10x^2+6x}{6x^2}[/tex] and [tex]\frac{21x}{6x^2}[/tex].

Step-by-step explanation:

The given expression is:

[tex]\frac{5x+3}{3x}[/tex] and [tex]\frac{7x}{3x^2}[/tex].

The least common denominator is: [tex]6x^2[/tex].

We collect  LCM for the denominator to obtain;

[tex]\frac{2x(5x+3)}{6x^2}[/tex] and [tex]\frac{3(7x)}{6x^2}[/tex].

We multiply out the parenthesis to obtain;

[tex]\frac{10x^2+6x}{6x^2}[/tex] and [tex]\frac{21x}{6x^2}[/tex].

Therefore the correct answer is B or the second option.

Answer:

A) Δ RQP ↔ ΔUTS

Step-by-step explanation:

Answer:

Option A) is correct

Step-by-step explanation:

Given : [tex]\Delta PQR \leftrightarrow  \Delta STU[/tex]

We need to find which correspondence is equivalent to [tex]\Delta PQR \leftrightarrow  \Delta STU[/tex] .

Solution :

One to one correspondence means measure of each side and each angle of one triangle is equal to the side and angle of the other triangle .

Here, we observe that option A) is equivalent to [tex]\Delta PQR \leftrightarrow  \Delta STU[/tex] as explained below :

As per [tex]\Delta PQR \leftrightarrow  \Delta STU[/tex] ,

[tex]PQ=ST\,,\,QR=TU\,,\,PR=SU\\\angle P=\angle S\,,\,\angle Q=\angle T\,,\,\angle R=\angle U[/tex]

Also, as per [tex]\Delta RQP \leftrightarrow  \Delta UTS[/tex] , we have

[tex]PQ=ST\,,\,RQ=UT\,,\,PR=SU\\\angle P=\angle S\,,\,\angle Q=\angle T\,,\,\angle R=\angle U[/tex]

Therefore,

[tex]\Delta RQP \leftrightarrow  \Delta UTS[/tex] is equivalent to [tex]\Delta PQR \leftrightarrow  \Delta STU[/tex]

So, option A) is correct .

Answer:

A)

15 hours

B)

108 hours

C)

2074.29 miles

Step-by-step explanation:

Under the assumption the earth is a perfect circle, then in one complete rotation about its axis ( 24 hours) the Earth will cover 360 degrees or 2π radians.

A)

In every 24 hours the earth rotates through 360 degrees ( a complete rotation). We are required to determine the length of time it will take the Earth to rotate through 225 degrees. Let x be the duration it takes the earth to rotate through 225 degrees, then the following proportions hold;

(24/360) = (x/225)

solving for x;

x = (24/360) * 225 = 15 hours

B)

In 24 hours the earth rotates through an angle of 2π radians (a complete rotation) . We are required to determine the length of time it will take the Earth to rotate through 9π radians. Let x be the duration it takes the earth to rotate through 9π radians, then the following proportions hold;

(24/2π radians) = (x/9π radians)

Solving for x;

x = (24/2π radians)*9π radians = 108 hours

C)

If the diameter of the earth is 7920 miles, then in a day or 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle;

circumference = 2*π*R = π*D

                         = 7920*3.142

                         = 24891.43 miles

Therefore a point on the equator covers a distance of 24891.43 miles in 24 hours. This will imply that the speed of the earth is approximately;

(24891.43miles)/(24 hours) = 1037.14 miles/hr

The distance covered by the point in 2 hours will thus be;

1037.14 * 2 = 2074.29 miles

Answer:

262 m³

Step-by-step explanation:

The volume (V) of a cone is calculated as

V = [tex]\frac{1}{3}[/tex] πr²h ( r is the radius of the base and h the height )

here diameter = 10 m, hence radius = 5 m

V = [tex]\frac{1}{3}[/tex]π × 5² × 10

   = [tex]\frac{1}{3}[/tex] π × 250 = [tex]\frac{250\pi }{3}[/tex] ≈ 262 m³

Ari will water and weed his garden on the same day again in 21 days by finding the Least Common Multiple (LCM) of the watering and weeding cycles, which are 3 and 7 days respectively.

The question asks us to find out how many days will pass until Ari once again waters and weeds his garden on the same day. This problem can be solved by finding the Least Common Multiple (LCM) of the watering and weeding cycles. Ari waters his garden every 3 days and weeds it every Saturday, which suggests a 7-day cycle for weeding.

To find the LCM of 3 and 7, we list the multiples of each number:

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, ...

The smallest multiple they both share is 21. Therefore, Ari will water and weed his garden on the same day again in 21 days.

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Answer:

The test statistic supports the claim

Step-by-step explanation:

413 out of 1588 people says that they smoked.

So, we can find that that is 413/1588 ≈ 0.26 = 26%.

This proves that the test statistic is supporting the claim, since the two are similar.

Answer:

2 nickels 3 dimes 5 quarters

Step-by-step explanation:

We know it cannot be the second option because there are only 7 coins and Kim has 10. It also cannot be the first option because the coins add up to $1.60, and Kim has $1.65. It could not be the last option either because the coins add up to $1.15, and Kim has $1.65.

Answer: Third option

Why? The third option has a total of $1.65, which is what Kim has. There are 10 coins all together, which is also what Kim has. And the number of nickels and dimes combined (5) is equal to the number of quarters (5).

Answer:

1/9

Step-by-step explanation:

6/9+ 2/9= 8/9

then we subtract 8/9 from 1

1-8/9

then we have to convert 1 into a fraction

9/9-8/9

this leaves 1/9

Answer:

1/9

Step-by-step explanation:

We can make an equation that looks like this:

2/9+6/9+x/9=9/9

Let's cancel out the denominator:

2+6+x=9

Then combine like terms:

8+x=9

Then solve for x:

x=1

Then add in the denominator we canceled out:

x=1/9

Hope I helped, soz if I'm wrong!

~Potato.

Copyright Potato 2019.

P.S. Why would your friend clean your room lel :P

The answer is D 3/5

if you can pick 4 and odd it will be 1,3,4,5,7,9

that is 6 numbers, 3/5 5*2 is 10 so 3*2 is 6

3/5

You can solve this by using trial and error. When doing so I came with a conclusion of 8,4, and 2.

The dimensions of a rectangular prism with a volume of 64 cubic inches can be any combination of length, width, and height whose multiplication result is 64, including possibilities of 1x1x64, 2x2x16, 4x4x4 and many more.

The volume of a rectangular prism is calculated by multiplying the length, width, and height of the prism (Volume = Length x Width x Height).

If we know that the volume of the prism is 64 cubic inches, there can be several possible dimensions for the rectangular prism. To find these, we would look for different combinations of length, width and height that when multiplied, equal 64. Here are a few examples:

Length = 1 inch, Width = 1 inch, Height = 64

Length = 2 inches, Width = 2 inches, Height = 16 inches

Length = 4 inches, Width = 4 inches, Height = 4 inches

There can be many more possible dimensions, including fractions as well.

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Final answer:

The standard deviation of the data set is 2.98, calculated by finding the mean, squaring the differences, averaging them, and taking the square root. One standard deviation below the mean is 2.52.

Explanation:

To find the standard deviation of the data set 8.2, 10.1, 2.6, 4.8, 2.4, 5.6, 7.0, 3.3, follow these steps:

Calculate the mean (average) of the data set.

Subtract the mean from each data point and square the result.

Calculate the average of these squared differences.

Take the square root of the average to find the standard deviation.

Using a calculator or computer:

The mean of the data set is 5.5

The squared differences would be (8.2-5.5)^2, (10.1-5.5)^2, etc.

The average of these squared differences is approximately 8.86.

The square root of 8.86 gives us the standard deviation of approximately 2.98.

Therefore, the standard deviation of the data set, rounded to the nearest hundredth, is 2.98.

To find the value that is one standard deviation below the mean, you subtract the standard deviation from the mean:

5.5 - 2.98 = 2.52.

It would have to be 3/5

Answer:

We use the combination formula:

combinations = n! / r! * (n-r)!

n = 5 and r =3

combinations = 5! / 3! * 2!

combinations = 5! / 12

combinations = 5 * 4 * 3 * 2 * 1 / 12

combinations = 5 * 2 = 10

Step-by-step explanation:

Answer: 30.01 feet.

Step-by-step explanation:

You need to remember this identity:

[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]

Observe the figure attached, where [tex]h_t[/tex] is the height in feet of the tree.

You need to calculate [tex]h_1[/tex] of the Triangle 1, where:

[tex]\alpha= \alpha_1=42\°\\opposite=h_1\\adjacent=20[/tex]

Substitute values into [tex]tan\alpha=\frac{opposite}{adjacent}[/tex] and solve for [tex]h_1[/tex]:

[tex]tan(42\°)=\frac{h_1}{20}\\\\h_1=20*tan(42\°)\\h_1=18[/tex]

Now you need to calculate [tex]h_2[/tex] of the Triangle 2, where:

[tex]\alpha= \alpha_2=31\°\\opposite=h_2\\adjacent=20[/tex]

Substitute values into [tex]tan\alpha=\frac{opposite}{adjacent}[/tex] and solve for [tex]h_2[/tex]:

[tex]tan(31\°)=\frac{h_2}{20}\\\\h_2=20*tan(31\°)\\h_2=12.01[/tex]

Then the height in feet of the tree is:

[tex]h_t=h_1+h_2\\h_t=(18+12.01)ft\\h_t=30.01ft[/tex]

The height of the tree can be determined by the trigonometric ratio of tan angle.

The height of the tree is 30 feet.

Given that,

Mariela is standing in a building and looking out a window at a tree.

The tree is 20 feet away from Mariela,

Mariela's line of sight creates a 42-degree angle of elevation, and her line of sight creates a 31 degree of depression.

We have to determine,

What is the height, in feet, of the tree?

According to the question,

Let, the height of the tree be h

The tree is 20 feet away from Mariela,

First, we have to calculate the length of BD which is x,

Then,

The length of BD is given by,

[tex]\rm Tan\theta = \dfrac{Opposite \ side}{Adjacent \ side}\\\\Tan\theta = \dfrac{BD}{AD}\\\\Tan42 = \dfrac{x}{20}\\\\x = tan42 \times 20\\\\x = 0.9 \times 20\\\\x = 18[/tex]

The measurement of x is 18 feet.

Again we have to calculate the length of y,

Then,

The length of DC is given by,

[tex]\rm Tan\theta = \dfrac{Opposite \ side}{Adjacent \ side}\\\\Tan\theta = \dfrac{DC}{AD}\\\\Tan31 = \dfrac{Y}{20}\\\\y = tan31 \times 20\\\\x =0.6 \times 20\\\\y = 12[/tex]

The measurement of y is 12 feet.

Therefore,

The height of the tree is given by,

[tex]\rm h= x +y\\\\h = 18+12\\\\h = 30 \ feet[/tex]

Hence, The height of the tree is 30 feet.

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3:7

Taxes are 30c and one dollar is 100c then the net income is 70c, making the income 30:70. this can be simplified to 3:7.

Answer:

This is the answer : (answer given in the picture)

Answer:

vertex = (- 3, 24)

Step-by-step explanation:

Given a quadratic in standard form y = ax² + bx + c : a ≠ 0, then

The x- coordinate of the vertex is

[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]

y = - x² - 6x + 15 ← is in standard form

with a = - 1, b = - 6, thus

[tex]x_{vertex}[/tex] = - [tex]\frac{-6}{-2}[/tex] = - 3

Substitute x = - 3 into the function for corresponding value of y

y = - (- 3)² - 6(- 3) + 15 = - 9 + 18 + 15 = 24

vertex = (- 3, 24)

ANSWER

[tex]\theta = \frac{\pi}{2} ,\frac{3\pi}{2},\frac{\pi}{4} , \frac{5\pi}{4} [/tex]

EXPLANATION

We want to solve the equation;

[tex] \cos( \theta) - \tan( \theta) \cos( \theta) = 0[/tex]

We factor to get:

[tex] \cos\theta(1 - \tan\theta) = 0[/tex]

Either

[tex]\cos\theta = 0[/tex]

Or

[tex]1 - \tan \theta = 0[/tex]

For

[tex]\cos\theta = 0[/tex]

We gave

[tex] \theta = \frac{\pi}{2} ,\frac{3\pi}{2}[/tex]

When

[tex]\tan \theta = 1[/tex]

Then,

[tex] \theta = \frac{\pi}{4} , \frac{5\pi}{4} [/tex]

Therefore the solution on the interval

[tex]0 \leqslant \theta \: \leqslant 2\pi[/tex]

is

[tex]\theta = \frac{\pi}{2} ,\frac{3\pi}{2},\frac{\pi}{4} , \frac{5\pi}{4} [/tex]