Degrees and Radians
any steps.

Required  the equation of the line is y = -5/7 *x -4.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

the line through the point (7,-9) with slope -5/7

so, m= -5/7

now, y= mx+c

solving with the given values we get,

c=  -9 +5

 = -4

Hence, Required  the equation of the line is y = -5/7 *x -4.

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a) The measure of <ABC is 131 degree.

According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle.

The total of a triangle's three internal angles is 180 degrees, as stated by the angle sum feature of a triangle.

Given:

a) As <ACD= 90

and Triangle BCD is an equilateral triangle then each of its angle measure 60 degree.

So, <ACD= 90

<ACB + <BCD = 90

<ACB = 90 - 60

<ACB = 30

and, <BAC = 19

Using Angle sum property in Triangle ACB

19 + <ABC + 30 = 180

<ABC = 180 - 49

<ABC = 131 degree.

b) Bow, In Triangle HEF using Angle sum property

<E + <F + <EHF = 180

<EHF = 180 - (69+ 40)

<EHF = 71 degree.

Then, <GHE + <EHF + <FHI

= 72 + 71 + 37

= 180, which forms on straight line.

Thus, GHI is a straight line.

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The answers to each part is given above.

Given is that when an object is thrown upward with an initial velocity of v{0}, then its approximate height is given by this quadratic function -

S = - 4.9t² + [tex]$v_{o} ^{t}[/tex] + h

The approximate height is given by this quadratic function -

S = - 4.9t² + [tex]$v_{o} ^{t}[/tex] + h

{ 1 } - For the maximum height :

dS/dt = 0                                        ... Eq{ 1 }

dS/dt = -9.8t + [tex]$3.1^{t}[/tex] log(3.1) + 0 = 0

- 9.8t + [tex]$3.1^{t}[/tex] log(3.1) = 0

Refer to the graph attached. At t = 3.8 {possible value}, the function is 0.

So we get -

t = 3.8 s                                         ... Eq{ 2 }  

Maximum height achieved -

h{max} = - 9.8t + [tex]$3.1^{t}[/tex] log(3.1) + 15

h{max} = - 9.8 x 3.8 + [tex]$3.1^{3.8}[/tex] log(3.1) + 15

h{max} =  - 37.24 + 73.65 x 0.50 + 15

h{max} =  14.585 m

{ 2 } -

0 = 3.1 t + 9.8/2 t²

0 = 3.1 t + 4.9 t²

Solving graphically, we get -

|t| = 0.6 s

Total time taken to reach ground -

T = 2 x 3.8 + 0.6

T = 8.2 seconds                                       ... Eq{ 3 }

Therefore, the answers to each part is given above.

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[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=8 \end{cases}\implies S=180(8-2)\implies S=1080 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{just one angle is}}{\cfrac{1080}{8}\implies 135^o}\hspace{5em}\stackrel{\textit{for six angles}}{(6)(135)\implies \boxed{810^o}}[/tex]

Probability that the shopper selected at random was satisfied with the service they received is 845 / 1522.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Total number of customers = 1522

Out of these,

Number of customers made a purchase = 624

Number of customers not made a purchase = 898

Number of customers who purchased satisfied with the service = 130

Number of customers who does not purchase satisfied with the service = 715

Total number of customers who are satisfied with the service = 130 + 715 = 845

Probability that the randomly selected shopper satisfied with the service = 845 / 1522

Hence the probability is 845 / 1522.

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The value of sin A is, 7/25.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

The terminal side of angle A goes through the point (−24/25,7/25) on the unit circle.

Now, By definition we get;

⇒ cos A = - 24/25

⇒ Sin A = 7/25

Thus, The value of sin A is, 7/25.

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Answer:

1 quarter, 3 dimes, 1 nickel, 1 penny

Step-by-step explanation:

25c + 10c+10c+10c+5c+1c =61c

The volume of the sculpture is 92.316 feet³.

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is (1/3)πr²h.

We have,

Cone-shaped sculpture:

Height = 5 feet

Base circumference = 26.376

This means,

2πr = 26.376

r = 26.376/(2 x 3.14)

r = 4.2 feet

Now,

The volume of the sculpture.

= 1/3 x 3.14 x 4.2 x 4.2 x 5

= 92.316 feet³.

Thus,

92.316 feet³ is the volume of the sculpture.

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The price of vase next year is $2090.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

We need to Write the percent as a fraction in simplest form

16.24%

So, we can rewrite it as;

16.24 / 100

16 and 24/100 or 16 6/25

So the percent as a fraction is 16 6/25

Given;

An antique vase costs $2000

Its price increases by 4.5%

Now,

Let the 4.5% of price be x

x*100/2000=4.5

x=20*4.5

x=90

Therefore, the price next year by 4.5 percent increase will be $2090.

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Answer:

Step-by-step explanation:

it equals 90

On solving the provided question, we can say that ratio is = 2:5:7 => 2x + 5x + 7x = 84 => x =  6 and A gets = 2x = 12 rs.

Ratios show how often one number is contained in another in mathematics. For instance, the ratio of oranges to lemons in a fruit dish is 8 to 6 if there are 8 oranges and 6 lemons present. In a similar vein, the proportion of oranges to whole fruit is 8, while that of lemons to oranges is 6:8. A ratio is an ordered pair of numbers a and b that is expressed as a / b, with b not equal to zero. An equation equating two ratios is known as a ratio. The ratio can be expressed as 1:3, for instance, if there is 1 boy and 3 girls (for every boy she has 3 girls) 3/4 are girls, while 1/4 are boys.

ratio is = 2:5:7

2x + 5x + 7x = 84

14x = 84

x = 84/14 = 6

a gets = 2x = 12 rs.

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The properties are used to manipulate equations in order to isolate a variable, find a solution, or simplify the equation

What are the properties of equality?

The "division property of equality" states that if you divide both sides of an equation by the same non-zero number, the two sides will remain equal.

The "simplification" step is used to simplify an expression by combining like terms, reducing fractions, or performing other operations to simplify the expression.

The "multiplication property of equality" states that if you multiply both sides of an equation by the same non-zero number, the two sides will remain equal.

The "addition property of equality" states that if you add the same number to both sides of an equation, the two sides will remain equal.

The "subtraction property of equality" states that if you subtract the same number from both sides of an equation, the two sides will remain equal.

These properties are used to manipulate equations in order to isolate a variable, find a solution, or simplify the equation.

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the slope of the line means in this situation "a. The cost is $4 per T-shirt".

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, Seth owns a printing shop that makes customized T-shirts.

Since The cost to make T-shirts is proportional to the number of T-shirts he makes.

Thus,

The y-intercept of the line will be 0 cause the line is passing through the origin point.

The general formula of the equation of a line:

y=mx+b,

where m is the slope

b is the y-intercept

since, slope = (y - y')/(x -x')

In our case,

b = 0

m = (8 - 4)(2-1)

m = 4

And m represents The cost is $4 per T-shirt.

therefore,  the slope of the line means in this situation "a. The cost is $4 per T-shirt".

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In a market economy, option C. all consumers collectively have a great influence on the price of goods and services.

A market economy is an economic system in which goods and services are traded in a market, and prices are determined by supply and demand. The decisions of individual consumers and producers, operating through the market mechanism, determine what goods and services are produced and how they are distributed.

Therefore, the correct answer is as given above. It could be concluded that market economy allow individuals to influence the price of goods and services

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For the linear equation y = -3.5x + 50 the graph is plotted with points (0,50) and (14.28,0).

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The linear equation is y = -3.5x + 50.

An arcade deducts 3.5 points from a 50-point game card for each game played.

The graph will represent the x axis as number of games played.

The graph will represent the y axis as points earned.

Substitute the value x = 0 in the equation -

y = -3.5(0) + 50

y = 50

The coordinate point is (0,50).

Substitute the value y = 0 in the equation -

0 = -3.5x + 50

-50 = -3.5x

x = 14.28

The coordinate point is (14.28,0).

Plot both the coordinate points and join the line.

Therefore, the graph is plotted for the linear equation.

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Answer:

[tex]2\frac{7}{8}[/tex]

Step-by-step explanation:

size 10 dress requires 2 1/4 yards of fabric while a jacket requires 1 5/8 yards so we add them

2 1/4+1 5/8

we make similar fractions and turn the denominator to 8

2 2/8+ 1 5/8

and now we can add the whole numbers first

2+1=3

now the fractions

2/8+5/8

7/8

final answer is 2 7/8

hopes this helps

Han should expect to pay $90 for the ticket if he buys it the day of the game.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Han should expect to pay $90 for the ticket if he buys it the day of the game

The current ticket fee = $30

The markup = 200%

The markup = 200% of the current price

Markup = 200/100 ×30

= $60

The ticket fee on the game day = The current fee + The markup

The ticket fee on the game day = $30  +  $60

The ticket fee on the game day = $90

Hence, Han should expect to pay $90 for the ticket if he buys it the day of the game.

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Answer:

C.

Step-by-step explanation:

The answer is C (-1, 1/2)

Answer:

7/15

Step-by-step explanation:

Answer:

2w^2.

Step-by-step explanation:

Let "w" be the width of the walkway. Then, the length of the garden is 6.5(6x + 6) - 2w and the width of the garden is 6.5(6x + 6) - 2w.

The area of the garden is 6(4.5x + 2.5) = 6 * 4.5 * x + 6 * 2.5 = 27x + 15

The area of the garden and walkway is (6.5(6x + 6) - 2w)^2 = 27x + 15 + 2w^2

Equating the two expressions for the area of the garden:

27x + 15 = 27x + 15 + 2w^2

Thus, the area of the walkway is:

On solving the provided question, we can say that by solving the interest  the amount after his 21st birthday =  $ 10,806

Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it. The majority of the time, interest is calculated as an annual percentage of the loan balance. This proportion is referred to as the loan's interest rate.

P = $6000

Rate=  4 %

Time, t= 12 years  

Formula of Compound Interest

[tex]A = P(1+R/100)^T\\A = 6000(1+4/100)^{12}\\A = 9606.19332[/tex]

On his 19 th birthday

[tex]A = P(1+R/100)^T\\A = 6000(1+4/100)^{13}\\A = 9990. 44106[/tex]

After 21st year S. I is

S. I =  10390.058700 × 4/100

S. I = 415.602348

A= 415.602348 + 10390.058700

A = $ 10,805.661.

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Answer:

At an x-intercept

Step-by-step explanation:

y = sin x

y = sin 0

y = 0

(0,0) is an x-intercept but not it's maximum or minimum.

The size of the crowd that is 5 feet deep on both sides of the street along a 3-mile section of a parade route is 44000 people.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, the size of a crowd that is 5 feet deep on both sides of the street along a 3-mile section of a parade route,

The number of people that can fit comfortably in a 6 feet by 6 feet area = 10

The ratio of the number of people per unit area = 10/(6 × 6) = 10/36

The area, A, occupied by the crowd = 5 feet × 3 mile × 2

3 miles = 15840 feet

∴ A = 5 feet × 15840 feet × 2 = 158400 ft²

We then have;

Number of people / 158400 = 10/36

Number of people = 44000

Hence, the size of the crowd that is 5 feet deep on both sides of the street along a 3-mile section of a parade route is 44000 people.

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The correlation between the amount of rain (mm) in the summer and the amount of water (m2) used for watering the lawn is directly proportion to each other

Based on the grain size, the classification of rain is divided into four, namely:

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The total amount to lay down the pebbles in the seating area would be - ${(A/5) x 8.99}.

Given is that one bag of pebbles covers 5 ft² and costs $8.99​​.

Assume that the area of the seating place is A ft². Now -

1 bag will cover - 5 ft²

1 ft² will be covered in (1/5) bags

A ft² will be covered in (A/5) bags

The total cost of laying the pebbles -

(A/5) x 8.99

Therefore, the total amount to lay down the pebbles in the seating area would be - ${(A/5) x 8.99}.

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Answer:

50

Step-by-step explanation:

The number of fifty dollars with the manager are 31.

Two or more expressions with an Equal sign is called as Equation.

Given that a convention manager finds that she has $1370, made up of twenties and fifties.

20x+50y=1370

She has a total of 46 bills.

x+y=46

x=46-y

Now we have to plug in x value in equation 1

20(46-y)+50y=1370

920-20y+50y=1370

920+30y=1370

Subtract 920 on both sides

30y=450

Divide both sides by 30

y=15

Now plug in y value in x+y=46

x+15=46

Subtract 15 on both sides

x=46-15

x=31

Hence, the number of fifty dollars with the manager are 31.

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Answer:

7.40

Step-by-step explanation:

4.58+2.82 = 7.40

Answer: 241

300 / 3 = 100

321 / 3 = 107

241 / 3 = 80.333

8.910 / 3 = 2.97

Answer: A baker needs to make a dessert for a party. The recipe calls for 1 3/4 cups of sugar, but the baker only has 1/2 cup measuring cups. How many measuring cups does the baker need to measure out the sugar for the recipe?

We can start by converting the mixed number 1 3/4 into an improper fraction: 1 3/4 = 7/4. Then, we can divide 7/4 by 1/2:

7/4 ÷ 1/2 = 7/4 * 2/1 = 14/4 = 3 1/4

The baker needs 3 1/4 measuring cups to measure out the sugar for the recipe.

[Image: Three and a quarter measuring cups filled with sugar]

Step-by-step explanation:

The length of the trail on the map would be 3.7 cm when a bike trail is 7.40km.

Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions on the actual figure or object

On a map, 1.00 cm represents 2.00 km.

Let the required length of the trail on the map would be x cm, when a bike trail is 7.40km

As per the information, we can write the ratio would be as:

1.00 cm : 2.00 km = x cm : 7.40km

1/2 = x/7.40

Apply cross-multiplication operation, and we get

x = 7.40/2

x = 3.7

Thus, the required length of the trail on the map would be 3.7 cm.

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