Will Give Brainliest Please Help!

Will Give Brainliest Please Help!

Answers

Answer 1
Since the transversals are parallel, angle 10 and 1 are supplementary (add up to 180)
this means that if angle 10 is 113 degrees, then angle 1 is 180-113 degrees which is 67 degrees

Related Questions

What is the range of the set of coordinates shown below?
(-10, 2), (-5, 3), (-7,4), (0, 0), (-10, 3), (3, 8)

Answers

Answer:

{0,2,3,4,8}

Step-by-step explanation:

given this equation, what is the value of y at the indicated point?
(6,y)
y^2 = x - 3
Please Help. am very stuck!

Answers

The value of y at the indicated point is √3.

What is a square root function?

In Mathematics and Geometry, a square root function refers to a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

In this scenario and exercise, we would determine the y-value by substituting the x-value into the given square root function as follows;

y² = x - 3

By taking the square root of both sides of the square root function, we have:

y = √(x - 3)

When x = 6, the y-value is given by;

y = √(6 - 3)

y = √3

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can someone help me with this question please?

Answers

The value of the missing angle x is: 38°

How to find the angle of the parallelogram?

We know that the sum of angles in a triangle is 180 degrees and as such:

∠DAE = 180 - (82 + 68)

∠DAE = 30°

Now, we know that alternate angles are congruent. Thus:

∠DAE ≅ ∠ADC = 30°

Opposite angles of a parallelogram are equal (or congruent) Consecutive angles are supplementary angles to each other (that means they add up to 180 degrees).

Thus:

∠BAE = ∠BDE = 82 + 30

= 112°

Thus:

∠ABC = ∠ACB = 68°

Thus:

∠BAC = 180 - 2(68)

∠BAC = 44°

Thus:

x = 112 - (44 + 30)

x = 112 - 74

x = 38°

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Mark brought $43.00 to the state fair. He bought a burger, a souvenir, and a pass. The burger was
1
4
as much as the souvenir, and the souvenir cost
2
3
the cost of the pass. Mark had $4.50 left over after buying these items.
What was the cost of each item?

Answers

The cost of the burger is $10.50, the cost of the souvenir is $28.00, and the cost of the pass is $42.00.

Let's assume the cost of the pass is x dollars.

According to the given information:

The burger costs 1/4 of the souvenir, so the burger's cost is[tex](1/4) \times x[/tex]dollars.

The souvenir costs 2/3 of the pass, so the souvenir's cost is [tex](2/3) \times x[/tex]dollars.

Mark had $4.50 left over after buying these items, so we can set up the following equation:

[tex]43.00 - [(1/4) \times x + (2/3) \times x] = $4.50[/tex]

Simplifying the equation, we have:

[tex]43.00 - [(1/4) \times x + (2/3) \times x] = $4.50[/tex]

[tex]43.00 - (1/4 + 2/3) \times x = $4.50[/tex]

[tex]43.00 - (3/12 + 8/12) \times x = $4.50[/tex]

[tex]43.00 - (11/12) \times x = $4.50[/tex]

To solve for x, we'll isolate the variable on one side of the equation:

$43.00 - $4.50 = (11/12) * x

$38.50 = (11/12) * x

Now, we can solve for x by multiplying both sides of the equation by (12/11):

[tex](12/11) \times $38.50 = x[/tex]

$42.00 = x

Therefore, the cost of the pass is $42.00.

Now we can find the costs of the burger and the souvenir:

The burger costs 1/4 of the souvenir, so its cost is (1/4) * $42.00 = $10.50.

The souvenir costs 2/3 of the pass, so its cost is (2/3) * $42.00 = $28.00.

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Enterprise,a car rental company charges $40 per day to rent a car and $.50 per mile. Hertz charges $20 per day and $0.75 per mile. At what number of miles do both companies charge the same for a 1 day rental? ASAP PLS

Answers

call the number of miles driven "m".

For Enterprise, the cost of renting a car for one day would be:

$40 (daily rate) + $0.50 (cost per mile) x m (number of miles driven) = $40 + $0.50m

For Hertz, the cost of renting a car for one day would be:

$20 (daily rate) + $0.75 (cost per mile) x m (number of miles driven) = $20 + $0.75m

To find the number of miles at which both companies charge the same for a one day rental, we can set the two equations equal to each other and solve for "m":

$40 + $0.50m = $20 + $0.75m

Subtracting $0.50m from both sides:

$40 = $20 + $0.25m

Subtracting $20 from both sides:

$20 = $0.25m

Dividing both sides by $0.25:

m = 80

Therefore, at 80 miles, both Enterprise and Hertz would charge the same amount for a one day rental.

What is the slope of line represented by 5x-12y=24

Answers

Answer:

5/12

Step-by-step explanation:

add 12 y to both sides:

5x = 24 + 12y

subtract 24 from both sides:

12y = 5x - 24

divide all by 12:

y = (5/12)x - 2.

slope is the number in front of x.

slope is (5/12).

A cylinder with a diameter 6 of mi and a height of 7 mi

Answers

With the values provided, we can find both the volume and surface area.

Volume:

Formula = pi x r^2 x h

---r is the radius, h is the height

Volume = pi x (3)^2 x 7

Volume = pi x 36 x 7

Volume = 252pi mi^3 = 791.68 mi^3

Surface Area:

Formula = 2 x pi x r x h + 2 x pi x r^2

---r is the radius, h is the height

Surface Area = 2 x pi x 3 x 7 + 2 x pi x (3)^2

Surface Area = 42pi + 18pi

Surface Area = 60pi mi^2 = 188.50 mi^2

Hope this helps!

The values in the table show the relationship between times
measured in seconds and distances measured in meters.
Seconds
5
10
15
20

Meters
20
40
60
80
What is the unit rate, In meters per second, of the relationship
shown in the table?
Enter your answer in the box.
meters per second

Answers

the unit rate is 4 meters per second, meaning that for every second that passes, the distance increases by 4 meters.

The table shows the relationship between time and distance time is measured in seconds and distance is measured in meters.

The table provides us with the data points of time and distance allows us to examine the relationship between these two variables.

The table as time increases the distance also increases.

This suggests that there is a positive relationship between time and distance.

The unit rate of the relationship tells us how much distance changes for every unit of time.

The unit rate is 4 meters per second meaning that for every second that passes, the distance increases by 4 meters.

The relationship shown in the table is not necessarily a linear relationship.

A linear relationship would mean that the distance changes by the same amount for each unit of time.

The increase in distance is not constant over time.

From 5 seconds to 10 seconds the distance increases by 20 meters but from 10 seconds to 15 seconds the distance increases by 20 meters again and from 15 seconds to 20 seconds the distance increases by 20 meters yet again.

The table provides us with a snapshot of the relationship between time and distance and by examining the data we can identify patterns and relationships that can help us understand the behavior of these variables.

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8x^5+3x^4-23x in standard form

Answers

Answer:

Step-by-step explanation:

[tex]8x^5 + 3x^4 - 23x\\= 8x^5+3x^4+0x^3+0x^2-23x+0[/tex]

The box plot represents the number of tickets sold for a school dance.

A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.

Which of the following is the appropriate measure of center for the data, and what is its value?

The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.

Answers

The correct answer is: The median is the best measure of center, and it equals 19.

A box plot, also known as a box-and-whisker plot, is a graph that displays the distribution of a dataset.

The box represents the middle 50% of the data, with the bottom of the box being the first quartile (Q1) and the top of the box being the third quartile (Q3). The line inside the box represents the median.

The "whiskers" extend from the box to the dataset's minimum and maximum values or, in the case of outliers, a specific distance from the box (often 1.5 times the interquartile range).

The box plot in this instance reveals that the median number of tickets sold was 19, with the middle 50% of the data falling between 17 and 21 tickets sold.

A minimum of 10 and a maximum of 27 tickets may be sold before the whiskers are removed.

The median is the most suitable measure of the center for this dataset since it is the measure of the center that represents the middle of the dataset.

In light of this, the answer is "The median is the best measure of center, and it equals 19."

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Gillians net worth is 90,500 based on the information in the table what is the amount of money gillans owens student loans

Answers

The amount of money Gillians owes for student loans is $12,250

How to determine this

When Gillians net worth = $90,500

House(Current value) = $87,900

Checking account = $950

Credit- card = -$2,650

Automobile(current value) = $10,300

Student loans = ?

Investment = $5,000

Personal loans = 1,200

Savings account = $2,450

To calculate the money Gillians Owen owes student loans

Let x represent the student loans

$90,500 = $87,900 + $950 - $2,650 + $10,300 + x + $5,000 - $1,200 + $2,450

$90,500 = $102,750 + x

Collect like terms

x = $90,500 - $102,750

x = 12,250

Therefore, the money Gillians owes student loans is $12,250

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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Answers

The correct statement is the center of the circle does not lie on the x-axis or the y-axis.

Given the equation of a circle, x² + y² – 2x – 8 = 0. Transform this equation in standard form of equation of circle

The standard form of the equation is (x – 1)² + y² = 8, and the radius of this circle is not the same as the radius of the circle whose equation is x² + y² = 9. Also, the center of the circle does not lie on the x-axis or the y-axis.

Therefore, the correct statement is the center of the circle does not lie on the x-axis or the y-axis.

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Is x-1
a factor of
x^5-3x^4-2x^3-5x^2+5x+12?
Correct The remainder when you divide is

Answers

The remainder theorem indicates that remainder when the polynomial x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by (x - 1) is 8

What is the remainder theorem?

The remainder theorem specifies the relationship between the division of a polynomial by a linear factor to the value of the polynomial at a specified point

The remainder when the polynomial expression; x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by x - 1, can be found using the remainder theorem by plugging in x = 1 in the function as follows;

f(1) = 1⁵ - 3 × 1⁴ - 2 × 1³ - 5 × 1² + 5 × 1 + 12 = 8

The remainder when x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by (x - 1) therefore is 8

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Mary pays income tax according to the graduated schedule shown below.
If taxable income
But not over-
The tax is:
is over-
10% of the amount over 50
$782.50 plus 15% of the amount over 7,825
$4,386 25 plus 25% of the amount over 31,850
$15.698.75 plus 28% of the amount over
77,100
SO
$7,825
$31,850
$77,100
$160,850
$349,700
$7,825
$31,850
$77,100
$160,850
$349,700
Mark this and return
no limit
$39,148.75 plus 33% of the amount over
160,850
$101.469 25 plus 35% of the amount over
349,700
If Mary's taxable income is $68,562, how much income tax does she owe, rounded to the nearest dollar?
a. $13,564
b. $17,140
c. $21,527
d. $12,349
Save and Exit
Next
3
Submit

Answers

Mary's taxable income falls in the fourth tax bracket, which ranges from $39,148.75 to $160,850. To calculate her income tax, we first need to find out how much of her income falls within this bracket:

$68,562 - $39,148.75 = $29,413.25

Mary's income tax is then calculated as follows:

$39,148.75 x 0.33 = $12,912.75
$29,413.25 x 0.35 = $10,294.36
$12,912.75 + $10,294.36 = $23,207.11

Rounded to the nearest dollar, Mary owes $23,207 in income tax. Therefore, the correct answer is not one of the given options.

We find that Mary owes $13,564 in income tax. So the correct option is (a) $13,564. Option a

Mary's taxable income falls between $31,850 and $77,100. This means we apply the tax rate relevant to this bracket, which is $4,386.25 plus 25% of the amount over $31,850.

First, we need to subtract $31,850 from Mary's income to find the amount that we need to apply the 25% tax rate to:

$68562 - $31850 = $36712

Next, we take 25% of this result:

0.25 * $36712 = $9178

Then we add the base tax for this bracket ($4,386.25) to this result to get the total tax:

$4386.25 + $9178 = $13564.25

Rounding this to the nearest dollar, we find that Mary owes $13,564 in income tax. So the correct option is (a) $13,564.

Option  a

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Solve 125 + 20w− 20w = 43 + 37w− 20w

Answers

Answer:

[tex]w=\frac{82}{17}[/tex]

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Decimal form: 4.82352941

having a great day and thx for your inquiry :)

Quinn is baking sweet potato pies. The table shows the ratio of cups of sugar to number of pies.


Number of Pies 3 5 9
Cups of Sugar 1 and one half 2 and one half 4 and one half


How many cups of sugar will Quinn need to make 12 pies?

Answers

The answer should be 8 cups.

what is the median for 31,35,28,31,37​

Answers

Answer:

31

Step-by-step explanation:

Answer:

The median is the middle value in a set of numbers. To find the median for the given set of numbers 31, 35, 28, 31, and 37, we first need to arrange them in numerical order: 28, 31, 31, 35, 37.


Since there are an odd number of values in this set, the median is simply the middle value which is **31**.


MARK AS BRAINLIEST, I DID EXPLANATION AND TOOK A LOT OF TIME!

Helpppp pleaseeeee :(

Answers

Answer:

[tex]\large {\mbox{R = 3.6}}[/tex]

Step-by-step explanation:

The formula for finding a magnitude of an earthquake on the Richter Scale is given as
[tex]R = \log\left(\dfrac{A}{A_0}\right)\\[/tex]

[tex]\rm{where}\\\textrm{A - measure of amplitude of quake wave}\\\textrm{$A_0$ = amplitude of smallest detectable wave}\\[/tex]

Given A = 0.3954 and A₀ = 0.0001, we can plug in these values into the R equation to get

[tex]R = \log\left(\dfrac{0.3954}{0.0001}\right)\\\\= \log(3954)\\\\= 3.597\\\\= 3.6\text { rounded to the nearest tenth}[/tex]

Triangle D has been dilated to create triangle D'. Use the image to answer the question.
6
D
04
Determine the scale factor used.
3
10
13
24

Answers

The scale factor from triangle D to triangle D' is 4

Calculating the scale factor from Dto D'?

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

The triangles

From the triangles, we have the following parameters

Side length of D = 8Corresponding side length of D' = 32

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

Scale factor of the dilation = Corresponding side length of D' / Side length of D

So, we have

Scale factor of the dilation = 32/8

Evaluate

Scale factor of the dilation = 4

Hence, the scale factor of the dilation is 4

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175
m/1 =
m/2=
160°
determine the requested value below

Answers

The measures of angle 1 and angle 2 are 12.5 degrees

We have to find the measures of angle 1 and angle 2

The circle will have 360 degrees

The unknown arc length be taken as x

175+160+x=360

Add the like terms

335+x=360

Subtract 335 from both sides

x=360-335

x=25

So angle m∠1 = 1/2(25)

m∠1 is 12.5

m∠1 = m∠2 as both are equal.

m∠2 = 12.5 degrees

Hence, the measures of angle 1 and angle 2 are 12.5 degrees

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Chess player moves a knight from the location (3,2) to (5,1) on a chessboard. If the bottom-left is labeled (1,1) the translation made is ____. If the player moves the knight from (5,1) to (6,3), the translation made is

Answers

1) The translation made is 2 units up, 1 units left.

2) The translation made is 2 units right, 1 unit up.

Since, A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

We have to given that;

Chess player moves a knight from the location (3,2) to (5,1) on a chessboard.

And, the player moves the knight from (5,1) to (6,3),

Since, Translation for (3,2) to (5,1|) is,

⇒ 2 units up, 1 units left.

And, Translation for (5,1) to (6,3) is,

⇒ 2 units right, 1 units up.

Hence, When a player moves a knight from the location (3, 2) to (5, 1) on a chessboard the translation made is 2 units up, 1 units left.

And, When the player moves the knight from (5, 1) to (6, 3), the translation made is 2 units right, 1 units up.

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jeremiah spends at least $14.50 on dinner everyday. Write an inequality to repersent the amount jeremiah spends. then write two examples of amounts jeremiah might spend. Please help

Answers

The inequality representing the amount Jeremiah spends on dinner daily is x ≥ $14.50. Two examples of amounts Jeremiah might spend are $16.75 and $22.00.

1. To represent the amount Jeremiah spends on dinner daily, we can use the inequality symbol "≥" (greater than or equal to) since it says "at least." Let's use the variable x to represent the amount.

2. The inequality representing the amount Jeremiah spends is x ≥ $14.50.

3. Example 1: Jeremiah might spend $16.75 on dinner, which satisfies the inequality since $16.75 is greater than $14.50.

4. Example 2: Jeremiah might spend $22.00 on dinner, which also satisfies the inequality as $22.00 is greater than $14.50.

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help with number 6 please

Answers

The diameter of the second pile of phosphate is found to be approximately 62.6 feet.

The volume of a right circular cone is given by the formula,

V = (1/3)πr²h where volume is V, radius of the base is r, height is h, and π is approximately 3.14159. For the first pile of phosphate,

h = 15.3 feet

d = 48.6 feet

r = d/2 = 24.3 feet

Using the formula for the volume of a cone,

V = (1/3)πr²h

V = (1/3)π(24.3)²(15.3)

V = 24,249.8 cubic feet

For the second pile of phosphate,

h = 15.3 - 3.6 = 11.7 feet

r = ? (to be determined)

Using the same formula for the volume of a cone,

V = (1/3)πr²h

V = (1/3)πr²(11.7)

Since the volume of both piles is the same, we can set the two volume formulas equal to each other,

(1/3)π(24.3)²(15.3) = (1/3)πr²(11.7)

Simplifying,

(24.3)²(15.3) = r²(11.7)

r² = (24.3)²(15.3)/11.7

r = 31.3 feet (rounded to the nearest tenth)

Therefore, the diameter of the second pile of phosphate is d = 2r = 62.6 feet (rounded to the nearest tenth).

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Complete question - As phosphate is mined, it moves along a conveyor belt, falling off of the end of the belt into the shape of a right circular cone, as shown.

Height of the cone is 15.3 feet

Diameter of the base of cone is 48.6 feet

A shorter conveyor belt also has phosphate falling off of the end into the shape of a right circular cone. The height of the second pile of phosphate is 3.6 feet shorter than the height of the first. The volume of both piles is the same. To the nearest tenth of a foot, what is the diameter of the second pile of phosphate?

251,400 kilometers. What do you estimate is the circumference of the moon’s orbit around the earth?

Answers

The estimated circumference of the Moon's orbit around the Earth is approximately 1,579,896.8 kilometers.

The circumference of the Moon's orbit around the Earth can be estimated using the given distance of 251,400 kilometers.

The circumference of a circle is calculated using the formula:

Circumference = 2 × π × Radius

The Moon's orbit around the Earth can be considered as a circular path.

We can estimate the circumference by considering the given distance as the radius of the circle.

Circumference ≈ 2 × π × 251,400 kilometers

Using an approximate value of π as 3.14, we can calculate the estimated circumference:

Circumference ≈ 2 × 3.14 × 251,400 kilometers

Circumference ≈ 1,579,896.8 kilometers

The stated distance of 251,400 kilometres can be used to calculate the circumference of the Moon's orbit around the Earth.

In order to determine a circle's circumference, use the following formula:

Circumference equals two radii.

It is possible to think of the Moon's orbit around the Earth as a circle.

By using the specified distance as the circle's radius, we can calculate the circumference.

Approximately 251,400 km around.

We may determine the approximated circumference using an approximation of as 3.14:

= 2 × 3.14 × 251,400 kilometers around the earth.

1,579,896.8 km around the circumference

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Match each absolute value inequality on the left side with its solution set on the right

Answers

The inequality 2|x - 3| + 6 > 10 has the solution set:

x < 1 or x > 5

To solve the inequality 2|x - 3| + 6 > 10, we need to isolate the absolute value expression |x - 3|.

We can do this by subtracting 6 from both sides of the inequality:

2|x - 3| > 4

Then we can divide both sides by 2:

|x - 3| > 2

Now we need to consider two cases, one where x - 3 is positive, and another where it is negative:

When x - 3 is positive, the inequality |x - 3| > 2 becomes:

x - 3 > 2

Solving for x gives:

x > 5

When x - 3 is negative, the inequality |x - 3| > 2 becomes:

-(x - 3) > 2

Solving for x gives:

x < 1

Therefore, the solution set for the inequality 2|x - 3| + 6 > 10 is:

x < 1 or x > 5

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The complete question:

Match each absolute value inequality on the left side with its solution set on the right

2|x - 3| + 6 > 10 - 2

3. In the right triangle below, what is the measure of RST?
A 10°
B. 30°
C. 60°
D. 90°

Answers

The measure of angle RST is 90°.

option D.

What is the measure of RST?

The measure of angle RST is calculated by applying the principle of a right angle triangle as shown below;

A right-angled triangle, also known as a right triangle, is a triangle in which one of the angles measures exactly 90 degrees. The side opposite the right angle is called the hypotenuse, while the other two sides are known as the legs.

From the given diagram, the measure of angle RST is calculated as follows;

∠S = 90 (since this angle has a symbol of right angle)

So the other two angles, R and T are complementary.

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How many ways are there to construct a string of 4 digits if numbers cannot be repeated?

Answers

Answer:

The number of ways to construct a string of 4 digits without repetition can be found using the permutation formula.

The formula for finding the number of permutations of n objects taken r at a time without repetition is:

P(n, r) = n! / (n - r)!

Where n is the total number of objects and r is the number of objects being chosen.

In this case, we have 10 digits (0-9) to choose from, and we need to choose 4 digits without repetition. Therefore, the number of ways to construct a string of 4 digits without repetition is:

P(10, 4) = 10! / (10 - 4)!

P(10, 4) = 10! / 6!

P(10, 4) = (10 × 9 × 8 × 7) / (4 × 3 × 2 × 1)

P(10, 4) = 10,080

Therefore, there are 10,080 ways to construct a string of 4 digits without repetition using the digits 0-9.

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Please help as soon as possible

Answers

The exact values are:

sin(α + β) = (-6√5 - 8)/25

cos(α + β) = (4√5 - 6)/25

sin(α - β) = (-6√5 + 8)/25

tan(α - β) = (-9√5 + 45)/4

We have,

Recall the trigonometric identities:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

tan(a - b) = (tan(a) - tan(b))/(1 + tan(a)tan(b))

Using these identities, we can find the exact values of the expressions given.

(a) Sin (α + β)

sin(α + β) = sin(α)cos(β) + cos(α)sin(β)

= (√5/5)(-3/5) + (2/5)(-4/5) (using the values given for sin and cos)

= -6√5/25 - 8/25

= (-6√5 - 8)/25

(b) Cos (α + β)

cos(α + β) = cos(α)cos(β) - sin(α)sin(β)

= (2/5)(-3/5) - (√5/5)(-4/5) (using the values given for sin and cos)

= -6/25 + 4√5/25

= (4√5 - 6)/25

(c) Sin (α - β)

sin(α - β) = sin(α)cos(β) - cos(α)sin(β)

= (√5/5)(-3/5) - (2/5)(-4/5) (using the values given for sin and cos)

= -6√5/25 + 8/25

= (-6√5 + 8)/25

(d) tan (α - β)

tan(α - β) = (tan(α) - tan(β))/(1 + tan(α)tan(β))

= ((√5/5) - (-4/5))/(1 + (√5/5)(-4/5)) (using the values given for sin and cos)

= (9√5/5)/(1 - 4/5√5)

= (-9√5 + 45)/4

Therefore,

The exact values are:

sin(α + β) = (-6√5 - 8)/25

cos(α + β) = (4√5 - 6)/25

sin(α - β) = (-6√5 + 8)/25

tan(α - β) = (-9√5 + 45)/4

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how can i do that? thanks.​

Answers

The limit as n approaches infinity of ((n+1)⁶-(n-1)⁶)/((n+1)⁵+(n-1)⁵) is 6.

To evaluate the limit as n approaches infinity of the expression ((n+1)⁶-(n-1)⁶)/((n+1)⁵+(n-1)⁵), we can simplify it using algebraic manipulations.

Let's expand the numerator and denominator using the binomial:

Numerator:

((n+1)⁶-(n-1)⁶) = [n⁶ + 6n⁵ + 15n⁴ + 20n³ + 15n² + 6n + 1] - [n⁶ - 6n⁵ + 15n⁴ - 20n³ + 15n² - 6n + 1]

= 12n⁵ + 40n³ + 12n

Denominator:

((n+1)⁵+(n-1)⁵) = [n⁵ + 5n⁴ + 10n³ + 10n² + 5n + 1] + [n⁵ - 5n⁴ + 10n³ - 10n² + 5n - 1]

= 2n⁵ + 20n³ + 2n

Now, let's simplify the expression by canceling out common terms:

((n+1)⁶-(n-1)⁶)/((n+1)⁵+(n-1)⁵) = (12n⁵ + 40n³ + 12n) / (2n⁵ + 20n³ + 2n)

As n approaches infinity, we can see that the highest power of n in the numerator and denominator is n⁵.

We can divide all terms by n⁵ to determine the limit:

lim(n→∞) [(12n⁵ + 40n³ + 12n) / (2n⁵ + 20n³ + 2n)]

= lim(n→∞) [(12 + 40/n² + 12/n⁴) / (2 + 20/n² + 2/n⁴)]

= 12/2

= 6

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the ratio of a surface area between two similar solids is 36:49. what is the ratio of the volume between the 2 figures?
PLEASE HELP

Answers

The ratio of the volumes between the two similar solids is 216:343.

If two solids are similar, their corresponding sides are proportional. Let's assume that the ratio of the linear dimensions between the two similar solids is k:

If the ratio of the surface areas between the two solids is 36:49, then the ratio of the areas of corresponding surfaces is also 36:49.

Since the surface area of a solid is proportional to the square of its linear dimensions, we can write:

(Linear dimensions of first solid)² : (Linear dimensions of second solid)² = 36:49

Simplifying this equation, we get:

k² : 1 = 36:49

Solving for k, we get:

k = √(36/49) = 6/7

Therefore, the ratio of the volumes between the two similar solids is:

k³ : 1³ = (6/7)³ : 1 = 216/343 : 1

Simplifying this expression, we get:

216:343

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