Lines j and k are parallel. m∠3 = (3x − 18)° and m∠4 = (y + 25)° and m∠7 = 75°. Find the values of x and y.

The domain for plotting the growth function will be [0, 5].

A function's domain is the set of its possible inputs or the set of input values for which the function is defined. The domain is the set of objects that the machine will accept as inputs in the function machine metaphor.

If the f(n) = 11.04 cm

By substituting the value in the equation,

11.04 = 10(1.02)n

(1.02)n = 11.04/10

(1.02)n = 1.104

Take log on both the sides,

log(1.02)n = log(1.104)

n[log(1.02)] = log(1.104)

n = 4.996 ≈ 5 years

Therefore, the span of the study was 0–5 years.

As a result, the domain for plotting the growth function will be [0, 5].

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The solutions of the trigonometric equation are π / 3, π / 2, 3π / 2 and 5π / 3.

In this problem we need to find the solutions of a trigonometric equation, which can be done by means of algebra properties and trigonometric formulas. Now we proceed to present the entire procedure:

Step 1 - Introduce the trigonometric equation:

cos 2x - cos x = - 1

Step 2 - Use the trigonometric formula cos 2x = cos² x - sin ² x:

cos² x - sin ² x - cos x = - 1

Step 3 - Use fundamental trigonometric formula:

cos² x - 1 + cos² x - cos x = - 1

2 · cos² x - cos x = 0

Step 4 - Use algebra properties to factor the expression:

cos x · (2 · cos x - 1) = 0

Step 5 - Find the solutions of the expression:

cos x = 0 → x = {π / 2, 3π / 2}

2 · cos x - 1 = 0

2 · cos x = 1

cos x = 1 / 2 → x = {π / 3, 5π / 3}

The solutions of the trigonometric equation are π / 3, π / 2, 3π / 2 and 5π / 3.

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Answer:

x=5, y=1

Step-by-step explanation:

you subtract  to get rid of 'y' in the equation like you are subtracting two numbers

7x+4y=39

2x +4y =14

5x=25

simplify to get 'x'

x=5

to get 'y' substitute the value of 'x' in one of the equations

2x+4y=14

(2x5)+4y=14

10+4y=14

subtract 10 to get 'y' on its own

4y= 4

simplify to get 'y'

y= 1

The function for the given situation is m=200+0.8t.

Given that, Leticia is selling raffle tickets for her class fundraiser. Her class receives four-fifths of the money raised from selling the raffle tickets.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, the amount of money in Leticia's class fund=m and  the amount of money Leticia has made from selling raffle tickets is t

Now, the function is

m=200+4/5 t

⇒m=200+0.8t

Therefore, the function for the given situation is m=200+0.8t.

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Answer: (6,1), (2,-1) etc

Step-by-step explanation:

Just pick any points on the graph and see if they aren't on the line and if they aren't, then you can pick that one.

To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.

So, inverse of the given statement is "If △ABC is not equilateral , then it is not  isosceles"

We have to find the inverse of the given statement:

" If ∆ABC is equilateral, then it is isosceles."

A triangle is said to be equilateral if all of the three sides are equal in measure and a triangle is said to be isosceles if two sides of a triangle are equal in measure.

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Answer:

  9 cm

Step-by-step explanation:

Given two beetles on a roof with a first face having a slope of -2/3 and the second face perpendicular to it. The first beetle travels down the first face twice as fast as the second beetle travels down the second face. You want to know their vertical separation when their horizontal separation is 72 cm.

In a given unit of time, the first beetle will travel 2×3 = 6 cm horizontally, and 2×(-2) = -4 cm vertically. The second beetle will travel 2 cm horizontally and -3 cm vertically in the same time, a perpendicular distance half as far.

After that one unit of time, the separation between the beetles is ...

  horizontally: 6 +2 = 8 cm

  vertically: -3 -(-4) = 1 cm

We notice the vertical separation is (1 cm)/(8 cm) = 1/8 of the horizontal separation. When the horizontal separation is 72 cm, the vertical separation will be ...

  (1/8)(72 cm) = 9 cm

The second beetle is 9 cm above the first when their horizontal separation is 72 cm.

__

Additional comment

The rise/run for the first face is given as (-2 cm)/(3 cm) = -2/3. The second face is perpendicular, so will have a rise/run = -1/(-2/3) = 3/2. That is, for a run of -2 cm, the rise will be -3 cm.

We note that the right triangles with legs "rise" and "run" are congruent for the two beetles. Traveling at the same speed, each beetle will cover a hypotenuse length in a given unit of time, hence the lengths "rise" and "run" on their respective roof faces. Since beetle 1 travels twice as fast, its distance will be 2·rise and 2·run in each time unit.

The attached diagram shows the geometry of the problem. The measures show beetle 1 has traveled twice as far as beetle 2 when they are separated horizontally by 72 cm. The grid is set so you can see the slopes are -2/3 and 3/2.

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The height of the mountain is 1.49 miles if in traveling across flat land you notice a mountain directly in front of you.

Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of a right-angle triangle.

It is given that:

In traveling across flat land you notice a mountain directly in front of you.

Applying tan ratio:

tan3.5 = h/(15+x)

Here h is the height of the mountain and x is the distance between the base of the mountain and to the second position of the car.

h = (15 + x) tan3.5

h = x tan9

(15 + x) tan3.5 = x tan9

x = 9.44

h = 9.44 tan9

h = 1.49 miles

Thus, the height of the mountain is 1.49 miles if in traveling across flat land you notice a mountain directly in front of you.

The complete question is:

In traveling across flat land you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5. After you drive 13 miles closer to the mountain, the angle of elevation is 9.

Approximate the height of the mountain. (Round your answer to one decimal place.)

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Zayne is right as Get Fit Gym is the better deal.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Zayne who wants to join a gym. Get Fit Gym charges a $140 enrollment fee and $50 per month. Fit R Us charges a $245 enrollment fee and $35 a month. He thinks Get Fit Gym is the better deal.

The price for one month at Get Fit Gym will be -

C[G] = 140 + 50 x 1 = 140 + 50 = $190

The price for one month at Fit R Us will be -

C[F] = 245 + 35 x 1 = 245 + 35 = $280

Therefore, Zayne is right, Get Fit Gym is the better deal.

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Answer: Correct, the answer is -28

Step-by-step explanation:

8-3=5

5-3=2

2-4=-2

-2-5=-7

-7-6=-13

-13-7=-20

-20-8=-28

Answer:

y=3x+19

Step-by-step explanation:

pls mark

The least common denominator for this pair of algebraic fractions: p/4 and p/16 is 16.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In the case, the fraction is illustrated as p/4 and p/16.

It should be noted that the lowest common multiple for 4 and 16 is 16. This is the denominator.

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Step-by-step explanation:

y + 4 = 8 ( x - 6 )

Multiple 8 by -6 and x

y+4 = 8x -48

Subtract 4 from both sides

y = 8x -52

Take two points from this equation, I took (7,4) and (8,12)

Find the slope with these points, which should give you 8

Step-by-step explanation:

when we have the equation in the form of

y = ax + b

then "a" is the slope.

in our equation

y + 4 = 8(x - 6)

the only thing that contributed to the factor of x is

8(x ...)

so, in the end the equation is (we sit need to bother about the rest)

y = 8x ...

so, the slope is 8.

question 9

this is trickier.

again, we want the form

y = ax + b

we have

6y - 3x = 12

6y = 3x + 12

y = 3/6 x + 2 = 1/2 x + 2

so, the slope is 1/2.

Answer:

The inverse of the function is 3+[tex]\sqrt[3]{x\x-2}[/tex].

What is inverse of the function?

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1. One should not confuse (-1) with exponent or reciprocal here.

Given, f(x) = (x − 3)³ + 2

replace f(x) with y

y = (x − 3)³ + 2

y-2 = (x − 3)³

∛y-2 = x-3

∛y-2 +3 = x

Put y =x

we get

∛x-2 +3 =y

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Answer:

6

Step-by-step explanation:

Answer:

72% are not freshmen.

Step-by-step explanation:

The not freshmen students are,

→ 50 - 14

→ 36 students

Then percent of not freshmen,

→ (36/50) × 100

→ 0.72 × 100

→ 72%

Hence, the answer is 72%.

The percentage of salt in green beans can is 2.89%.

It is important to know about the percentage first, the percentage is a part of the sample in the population. It can be determined by this formula

A% = x / N . 100%

where A% is the percentage, x is the sample and N is the total population

From the question above, we know that :

x = 11.5 grams

N = 14 ounce = 396.89 grams

By substituting the parameter to the equation, we get

A% = x / N . 100%

A% = 11.5 / 396.89 . 100%

A% = 2.89%

Hence, the total salt in the can is 2.89%

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Answer: Triangle FGH is an equilateral with values of x as 9.

Step-by-step explanation: The triangle given is an equilateral because all the given side are equal.  The value of x is 9.

Answer:

x = 9

Step-by-step explanation:

if x = 2 then

If x = 22.25 then

if x = 180 then

If x = 9 then

All the answers are correct, but the 5th one is wrong, the correct answer for the 5th question is y = 6.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.

A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

The answer of 5th question,

The given expression is,

(5y - 3)/63 = 9/21

105y -63 = 567

105y = 630

y = 630/105

y = 6.

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The basic calculation values are;

1. The largest number is 199

2. The score Vanessa needs is 99 points

3. Each person should raise approximately $471

4. The approximate minimum monthly payment is $374

5. The approximate monthly payment is $55.9

The interest is 123.[tex]\overline {6}[/tex]

Basic mathematical operations includes addition, subtraction, multiplication, division, and combinations of the above operations.

1. Let x represent the number, we have;

x - 46 ≤ 153

x ≤ 153 + 46 = 199

x ≤ 199

The largest integer that could be used for the number is 199

2. Vannesa's current scores are;

81 points, 91 points, 89 points

The score Vannesa requires so as to get an A is 360 points

The score Vannesa needs = 360 - (81+91+89) = 99

Vannesa needs 99 points to get an A

3. The number of members in the band = 105

The amount the band needs to raise = $49,500

The amount each one should raise therefore is 49500 ÷ 105 ≈ 471

Each one needs to raise $471

4. The down payment is $2,000

Number of monthly payment = 48

Least contract amount = $19,940

The monthly payment = (19,940 - 2,000)/48 ≈374

The least monthly payment ≈ $374

5. The cash price for the TV = $1,200

The down payment = $500

The charges = $1,484

Number of monthly payment = 48

Total payment = $1,200 + $1,484 = $2,684

The monthly payment = 2,684 ÷ 48 ≈ 55.9

The monthly payment is approximately $55.9

The interest is therefore;

[tex] \dfrac{1484}{1200}\times 100 = 123.\overline 6 \%[/tex]

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Answer:

$4375

Step-by-step explanation:

25 percent *17500 =

(25:100)*17500 =

(25*17500):100 =

437500:100 = 4375

Answer:

60

Step-by-step explanation:

All of the angles of a trapezoid add up to 360 degrees so,

2h+2h+h+h=360 degrees

6h=360 degrees

h = 60 degrees

2h=120degrees

Through subtraction method, we find out that the gallons of fuel used by Ravi is equal to 10.14 gallons.

It is given that -

The original gallons of fuel that Ravi had in the morning = 15.04 gallons

Now, the gallons of fuel left = 4.9 gallons

We have to find out the gallons of fuel used by Ravi.

The amount of fuel Ravi used =

Original gallons of fuel - Gallons of fuel left

= (15.04-4.9) gallons

= 10.14 gallons.

Thus, through subtraction method, we find out that the gallons of fuel used by Ravi is equal to 10.14 gallons.

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The number of home runs hit by player A nd player B are respectively 53 and 55which are consecutive odd integers.

Let the number of home runs hit by A is x.

Therefore the number of home runs hit by B is x+2 as they are consecutive odd numbers.

If x is odd then x + 1 is even and x+2 is odd.

The sum of their home runs is 108.

We will form a linear equation in x to represent this situation.

x + (x+2) = 108

now we will solve this equation to find the value of x.

or, 2x + 2 = 108

or, x + 1 = 54

or, x = 53

Hence the number of home runs hit by A is 53 .

Number of home runs hit by B = 53+2 = 55

Therefore the number of homeruns hit by players A and B are 53 and

55.

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The perimeter of the smaller triangle is 3m.

What is a perimeter of a triangle?

The total of a triangle's three sides is the perimeter. The Greek words "peri" (which means around) and "metron," which means measure, are combined to get the English word perimeter. The perimeter of any 2D shape is the total distance encircling it. Since a shape's perimeter indicates how long its boundary is, it is stated in linear units.

Here,

The ratio of given perimeters is 1:3 so the ratio of their sides and their altitudes will also be in the ratio of 1:3.

The ratio of the areas is 1^2/3^2=1/9. (ratio of their sides: a/b, ratio of their areas: a^2/b^2)

Now, we have 1/9=A/27

where A = area of the smaller triangle

Now, cross-multiply the given quantity

1*27=9*A

27=9A

A=27/9

A=3 m is the area of the smaller triangle.

Hence, the perimeter of the smaller triangle is 3m.

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The answer to following parts are and this can be solved by using probability.

a) 15,890,700 different samples can be chosen

b) 6,523,881 will contain at least one defective chip

c) 41.1%

What is probability?

A probability is the number of desired outcomes divided by the number of total outcomes.

Main body:

The order in which the microchips are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

Cₙ,ₓ is the number of different combinations of x objects from a set of n elements, given by the following formula.

Cₙ,ₓ =[tex]\frac{ n!}{x!(n-x)!}[/tex]

(a) How many different samples can be chosen?

Samples of 6 from a set of 50.

Then

C₅₀,₆ = [tex]\frac{50!}{6!(50-6)!}[/tex] =15,890,700

15,890,700 different samples can be chosen

(b) How many samples will contain at least one defective chip?

Either a sample contains no defective chip, or it contains at least one. From a), the sum of them is 15890700.

Then

No defective chips:

Four are defective.

So 50-4 = 46 are not.

This is samples of 6 from a set of 46.

C₄₆,₆ = 46!/6!*40!

9,366,819 samples contain no defective chips.

At least one:

9366819 + n = 15890700

n = 6523881

6,523,881 will contain at least one defective chip

(c) What is the probability (as a percent) that a randomly chosen sample of six contains at least one defective chip

6,523,881 out of 15,890,700

6,523,881/15,890,700 = 0.411

As a percent

41.1%

Hence the answer are as follows.

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