James runs the 400 meter for his school’s track team. He beat his best time by 2. 7 seconds in the meet today with a time of 53. 6 seconds

Answer:

Step-by-step explanation:

use SOH CAH TOA to remember tangent sin and cosine equations

Sin = opposite over hypotenuse Cosine Adjacent over Hypotenuse Tangent Opposite over Adjacent

tangent is also equal to sin/cos

tan B = opposite of B/adjacent of B = 3/5

cos B = adjacent/hypotenuse = 5/sqrt(34)

Sin A = opposite/hypotenuse = 5/sqrt(34)

tan A = opposite/adjacent = sin/cos = [ 5/sqrt(34) ]/ [ 3/sqrt(34) ] = 5/3

Step-by-step explanation:

3. D

it looks the same left and right from the line x = -0.5.

but not, when we turn the graph by 180° around one of these points.

4. A

as we clearly see the graph never every (on neither side) goes below -6.5 or so.

it goes on both sides to +infinity.

Using trigonometric identity, the solutions of x = 5π/6, 11π/6, π/3, and 4π/3 and  2θ is equal -2πn + π

Solution 1:

We start by simplifying the given equation:

2sin2 x = 1 + cos x

2(2sin x cos x) = 1 + cos x

4sin x cos x - cos x = 1

cos x (4sin x - 1) = 1

cos x = 1 / (4sin x - 1)

Since we are looking for solutions in the interval [0, 2π), we can use the unit circle to determine the values of sin x and cos x for each possible solution.

For sin x = 1/2, we have x = π/6 and x = 5π/6.

For sin x = -1/2, we have x = 7π/6 and x = 11π/6.

For cos x = 1/3, we have x = π/3 and x = 5π/3.

For cos x = -1/3, we have x = 2π/3 and x = 4π/3.

We need to check each of these values to see if they satisfy the original equation:

For x = π/6: 2sin2 (π/6) = 1/2 and cos (π/6) = √3/2, so the equation is not satisfied.

For x = 5π/6: 2sin2 (5π/6) = 1/2 and cos (5π/6) = -√3/2, so the equation is satisfied.

For x = 7π/6: 2sin2 (7π/6) = 1/2 and cos (7π/6) = -√3/2, so the equation is not satisfied.

For x = 11π/6: 2sin2 (11π/6) = 1/2 and cos (11π/6) = √3/2, so the equation is satisfied.

For x = π/3: 2sin2 (π/3) = 3/2 and cos (π/3) = 1/2, so the equation is satisfied.

For x = 5π/3: 2sin2 (5π/3) = 3/2 and cos (5π/3) = -1/2, so the equation is not satisfied.

For x = 2π/3: 2sin2 (2π/3) = 3/2 and cos (2π/3) = -1/2, so the equation is not satisfied.

For x = 4π/3: 2sin2 (4π/3) = 3/2 and cos (4π/3) = 1/2, so the equation is satisfied.

Therefore, the solutions to the equation are:

x = 5π/6, 11π/6, π/3, and 4π/3.

solution 2

We start by using the trigonometric identity sin (a + b) = sin a cos b + cos a sin b to rewrite the given equation:

(cos 3θ)(cos θ) + 1 = (sin 3θ)(sin θ)

cos 3θ cos θ + sin 3θ sin θ = 1

cos (3θ - θ) = 1

cos 2θ = 1

2θ = 2πn or 2θ = -2πn + π

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The area of the dish, a, can be represented by the product of its length and width. Thus, we can write:

a = (279/10) cm x (178/10) cm

Simplifying this expression, we get:

a = 4953/100 cm^2

So, the correct equations are:

B) 178/10 x 279/10 = a

and

D) a ÷ 178/10 = 279/10

Answer:

Rewriting \(6^{-2}\) without an exponent we get \(\mathbf{\frac{1}{36}}\)

Step-by-step explanation:

We need to rewrite the following without an exponent. \(6^{-2}\)

We need to solve the exponent to find the result.

We know the exponent rule: \(a^{-b}=\frac{1}{a^b}\)

Now using this rule to solve the equation:

\(6^{-2}\\=\frac{1}{6^2}\\We \:know \:that\:6^2 = 6\times 6=36\\=\frac{1}{36}\)

So, Rewriting \(6^{-2}\) without an exponent we get \(\mathbf{\frac{1}{36}}\)

The vertex is a maximum if the leading coefficient is negative and it is a minumum, if leading coefficient is positive

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

The required details are not given

So, I will provide a general explanation

A parabola is represented as

y = a(x - h)² + k

Where

a ≠ 0 and vertex = (h, k)

The required conditions are:

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A 1-gigabyte flash drive has 1000 times more storage space than a 1-megabyte flash disk. The right response is thus "1,000 times greater."

We need to find the ratio between the two capacities.

Given that there are \(10^9\) bytes in a gigabyte and\(10^6\) bytes in a megabyte, we can calculate the ratio as follows:

Ratio = (1 GB) / (1 MB)

= \((10^9 bytes) / (10^6 bytes)\)

= \(10^(9 - 6)\)

=\(10^3\)

= 1000

Therefore, A 1-gigabyte flash drive has 1000 times more storage space than a 1-megabyte flash disk. The right response is thus "1,000 times greater."

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Answer:

175% increase

Step-by-step explanation:

Awnser: Its D uhm yea...

Step-by-step explanation:

The point-slope form of a line is (y-y1)=m(x-x1). Therefore, option C is the correct answer.

Given that, slope (m)=4/5 and the point on line=(-2, 1).

A slope is, a numerical measure of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).

The point-slope form of a line formula is (y-y1)=m(x-x1).

Now, (y-1)=4/5(x+2).

Therefore, option C is the correct answer.

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Answer: Yes

Step-by-step explanation:

Most fractions can be simplified into smaller fractions, while some are in it's simplest form. When putting a bit in its simplest form it is much easier to compare to other fractions  

What I did first tried to simplify all the factions, starting with 1 1/2.

After looking at 1 1/2, I can see that it is in its simplest form.

Then looking at 1 2/4 I can see that it can be simplified into 1 1/2.

Lastly looking at 1 3/6 I can see that it can be simplified into 1 1/2.

Answer:

y = 3/7+0

Step-by-step explanation:

This is what I got, hope this helps.

Answer: The flowchart is shown below.

Explanation:

Each box is a different statement. The reason for the statement is provided below the box. The arrows on the flowchart direct the flow of how the proof is laid out. Typically the flow is left to right, top to bottom, or a mix of both. This is to match the reading order of many western countries. Though I would imagine the flow is reversed for countries that read from right to left.

The structure of any type of proof is to start with what you are given. Then use the previously established, or previously proven, theorems to make your way to what you want to prove.

In this case, we start off with MN and KL being parallel line segments. This is shown by the arrows on MN and KL. Because the segments are parallel, we then can determine these two facts:

Both of those will have the reasoning of "corresponding angles theorem"

We have two pairs of angles which are congruent. This then directly leads to the triangles being similar. Refer to the AA (angle angle) similarity theorem for more information.

Feel free to use symbols in place of some words. For example, instead of saying something like "Triangle NMJ is similar to Triangle LKJ", you could write \(\triangle \text{NMJ} \sim \triangle \text{LKJ}\)

If you're curious what app I used to make the flowchart, the app is called "LucidChart". They have 3 options: 1 free and the other 2 are paid versions. I went with the free version and it worked just fine. But it's up to you which you prefer most.

It has taken me 32 minutes to drive 48 km. If the total length of my journey is 146 km and I maintain the same speed,  then you can estimate that you will be driving for approximately 65.344 minutes longer to complete the remaining 98 km of your journey.

To estimate how much longer you will be driving for, we can use the concept of proportionality. We know that the time taken to drive 48 km is 32 minutes. Let's use this information to find the time it would take to drive 146 km.

We can set up a proportion to find the time:

(time taken for 48 km) / (48 km) = (time taken for 146 km) / (146 km)

Let's solve for the time taken for 146 km:

(time taken for 146 km) = (time taken for 48 km) * (146 km / 48 km)

Substituting the given values:

(time taken for 146 km) = 32 minutes * (146 km / 48 km)

Calculating the value:

(time taken for 146 km) ≈ 32 minutes * 3.042

(time taken for 146 km) ≈ 97.344 minutes

Therefore, it would take approximately 97.344 minutes to drive 146 km at the same speed.

To estimate how much longer you will be driving for, we can subtract the initial time of 32 minutes from the estimated time of 97.344 minutes:

Additional time = 97.344 minutes - 32 minutes

Additional time ≈ 65.344 minutes

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Answer:

1. Prepare the journal entries to close your temporary accounts.

the journal entries required to close the temporary accounts are:

December 31, 2019, closing of temporary revenue accounts

Dr Fees earned 136,000

    Cr Income summary 136,000

December 31, 2019, closing of temporary expense accounts

Dr Income summary 88,200

    Cr Salaries expense 66,000

    Cr Rent expense 14,200

    Cr Supplies expense 1,600

    Cr Depreciation expense 4,000

    Cr Utilities expense 2,400

December 31, 2019, closing of temporary income summary account

Dr Income summary 88,200

    Cr Retained earnings 88,200

December 31, 2019, closing of drawings account

Dr Retained earnings 10,000

    Cr Sean McCann, Drawing 10,000

2. Prepare an income statement and a statement of owner’s equity for the year ended December 31, 2019 and a classified balance sheet as of December 31, 2019.

          Sean McCann, CPA

            Income Statement

For the Year Ended December 31, 2019

Fees earned                                 $136,000

Salaries expense                         ($66,000)

Rent expense                               ($14,200)

Supplies expense                          ($1,600)

Depreciation expense                  ($4,000)

Utilities expense                           ($2,400)

Net income                                   $47,800

retained earnings = net income - drawings = $47,800 - $10,000 = $37,800

                     Sean McCann, CPA

                          Balance Sheet

         For the Year Ended December 31, 2019

Assets

Current assets:

Cash                                    $33,800

Accounts receivable          $28,000

Supplies                                $7,000

Total current assets                       $68,800

Non-current assets:

Equipment                         $130,000

Accumulated dep. (equip)-$32,000

Total non-current assets               $98,000

Total assets                                                    $166,800

Liabilities and equity

Current liabilities:

Accounts payable             $10,600

Salaries payable                $6,000

Total current liabilities                    $16,600

Long term liabilities:

Mortgage payable            $6,400

Total long term liabilities:                $6,400

Equity

Sean McCann, capital    $106,000

Retained earnings           $37,800

Total equity                                   $143,800

Total liabilities and equity                            $166,800

            Sean McCann, CPA

      Statement of Owner’s Equity

For the Year Ended December 31, 2019

Sean McCann, capital 1/1/19         $106,000

Net income                                     $47,800

Subtotal                                         $153,800

Drawings during the year             -$10,000

Sean McCann, capital 1/1/19         $143,800

Scores between 23 & 59 will give Paul a C for the semester (an average between 70 and 79).

The sum of the scores on the first three, hundred point tests

= 82 + 88 + 87 = 257.

The total score required in four 100-point tests to get an average score of 70 = 70X4= 280.

The total score required in four 100-point tests to get an average score of 79 = 79X4= 316.

Therefore, the score on the fourth test should be between (280-257) & (316-57) i.e, 23 & 59 to get an average score of 70 & 79.

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Answer:

Step-by-step explanation:

To solve this problem, we can use the formula:

Number of wheel revolutions = Distance traveled / Circumference of the wheel

First, we need to convert 1,200 meters to inches. Since 1 meter is approximately equal to 39.3701 inches, we have:

1,200 meters ≈ 1,200 * 39.3701 inches = 47,244.12 inches (rounded to the nearest inch)

The circumference of the wheel is given by the formula:

Circumference = π * Diameter

Substituting the given diameter of 12 inches and using π ≈ 3.14, we have:

Circumference = 3.14 * 12 = 37.68 inches

Now we can calculate the number of wheel revolutions:

Number of wheel revolutions = 47,244.12 inches / 37.68 inches ≈ 1,254 (rounded to the nearest whole number)

Therefore, approximately 1,254 wheel revolutions are needed to travel 1,200 meters. Option D is the correct answer.

The diameter of a child's bicycle wheel is 12 inches. Given Diameter of wheel = 12 inches

Circumference of the wheel = πd = 3.14 × 12 = 37.68 inches (approx.)

One meter = 39.3701 inches

Let's convert 1,200 meters into inches.

1200 meters. 1200 × 39.3701 = 47244.12 inches

We know that the circumference of the wheel = distance covered in one revolution  Let's find revolutions of the wheel will it take to travel 1,200 meters .

Number of revolutions of the wheel required = (distance covered / circumference of the wheel) = 47244.12 / 37.68 = 1254

revolutions (approx.)Therefore, 1,254 revolutions.

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Answer:

32

Explanation:

We can multiply the numerator by the number and leave the denominator as: (2 x 48) / 3 = 96/3 = 32.

Answer:

number7 9452.425 and number 4 2 hrs

Step-by-step explanation:

85+15 is 100 so to get one hundred percent you alr have 85 but you need to find 15

find what 30percent of 400 it is 120 if hes going 60 mph:

120/60 is 2

so it took him 2 hrs

Answer:

Its wrong the correct answer is the last one

Step-by-step explanation:

Multiply the numbers 3x9=27

Ergo, the answer is the last one.

Hope this helps if you have additional questions message me! :)

Answer: To factor the expression -14 - (-8) completely using the distributive law, we need to simplify it first.

Remember that when we subtract a negative number, it is equivalent to adding the positive number. Therefore, -(-8) is the same as +8.

So the expression becomes:

-14 + 8

To factor it further using the distributive law, we can rewrite the addition as multiplication by distributing the -14 to both terms:

(-14) + (8) = -14 * 1 + (-14) * 8

This can be simplified as:

-14 + 8 = -14 * 1 + (-14) * 8 = -14 + (-112)

Finally, we can add the two negative numbers to get the result:

-14 + (-112) = -126

Therefore, the expression -14 - (-8) factors completely as -126.

Answer:

W > 2

Step-by-step explanation:

-2W + 17 < 13

-2W < -4

W > 2

Answer:

A. has a right angle

thats one

Answer:

I think it is A and D. Not 100% sure tho.

Answer:

\(1\frac{3}{5}\) meter is the difference in depths of locations diver dove.

Step-by-step explanation:

With the help of "The Twelve Days of Christmas” song 364 is the total gifts in 12 days of Christmas.

Total 364 Christmas gifts were given in total.

Total 78 gifts were given on the 12th day.

"The Twelve Days of Christmas”: is one of the most famous and most often sung Christmas carols of all.

So, how many presents are there altogether?

Partridges: 1 × 12 = 12

Doves: 2 × 11 = 22

Hens 3 × 10 = 30

Calling birds: 4 × 9 = 36

Golden rings: 5 × 8 = 40

Geese: 6 × 7 = 42

Swans: 7 × 6 = 42

Maids: 8 × 5 = 40

Ladies: 9 × 4 = 36

Lords: 10 × 3 = 30

Pipers: 11 × 2 = 22

Drummers: 12 × 1 = 12

i) we have to calculate how many gifts total in 12 days of Christmas.

We observe from above that we have the same number of partridges as drummers (i.e 12) ; doves and pipers (i.e 22 ); hens and lords (i.e 30 ) etc. So the simplest way to count our gifts is to add up to the middle of the list and then double the result = (12 + 22 + 30 + 36 + 40 + 42) × 2 = 364.

ii)How many gifts were given in total :

On day one this is simple; just the one gift.

On day two, we get 1 + 2 = 3 gifts.

On day three, we get an additional three gifts on top of day two's three. We receive 3 + 3 = 6 gifts.

On day four, we add four to the previous day's total getting 6 + 4 = 10.

similarly, as we going on words the

we find out that total gifts were given are 364.

iii) The formula which is used to determine the how many gifts given on each day is

n x (n+1) ÷ 2 where n -->a particular day

we have to calculate total gifts were given on 12th day.

So, n x (n+1) ÷ 2 = 12(12+1)/2 = 13× 6 = 78

Hence, total received gifts on 12 days of Christmas is 364.

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The area of the poster in inches is,

⇒ A = 4 inches²

We have to given that;

A rectangular poster is 50 centimeters long and 25 centimeters wide.

Here, 1 centimeter is approximately 0.4 inches

Hence, Lenght = 50 cm

Lenght = 50 x 0.4

            = 2 inches

Width = 25 cm

          = 25 x 0.4

           = 1 inches

Thus, The area of the poster in inches is,

⇒ A = 1 x 4

⇒ A = 4 inches²

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Answer:

green

Step-by-step explanation:

11a^3−4a^2−14a−7

Answer:

11a³-4a²-14a-7

(The light blue/green one)

Step-by-step explanation:

We'll need to combine like terms (terms with the same variables and exponents)

(4a³-8a-4a²)+(7a³-7-6a)

add/subtract

we'll keep -4a² and -7 as is as there aren't any other terms like them

11a³-14a-4a²-7

put into standard form:

11a²-4a²-14a-7

(The light blue/Green one)

Hope this helps!

Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

The completed blanks in Nyala's solution that is used to prove that the measure of angle x is 40° is as follows;

If we perform a 180° rotation about the point O the following happens

Ray \(\overleftrightarrow{EF}\) maps unto ray \(\overleftrightarrow{GH}\)

Ray \(\overleftrightarrow{GH}\) maps unto ray \(\overleftrightarrow{FE}\)x

\(\overleftrightarrow{FG}\) maps unto itself

Therefore, the image of angle x will be exactly where the pre-image of 40° was. Since rotation preserve angle measure, the measure of angle x must be 40°.

The measure of an angle is the degree of rotation between the initial side and the terminal side of the angle.

The details of the method Nyala used to prove that the measure of the angle x is 40° can be found as follows;

The rotation of a line 180° about the center of the line maps onto itself, and the rotation of a line about a non colinear point, is parallel to the original line.

Whereby the center of rotation of the line \(\overleftrightarrow{EF}\) is equidistant from both the line \(\overleftrightarrow{GH}\) which is parallel to the line \(\overleftrightarrow{EF}\), the image of the line \(\overleftrightarrow{EF}\) maps to the line \(\overleftrightarrow{GH}\) following a 180° rotation about the point O, and the rotation of the line \(\overleftrightarrow{FG}\) about the point O maps unto itself, such that the angle x maps to the angle 40°, therefore;

∠x ≅ 40° (A rotation transformation is a rigid transformation)

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