Could someone help me solve this?

tan(x + kπ) = 0.4 where  k∈Z

What do you mean by trignometry?

Trigonometry is one of the important branches in the history of mathematics that studies the relationship between the sides and angles of right triangles.

Trigonometric ratios of triangles are also called trigonometric functions. Sine, cosine, and tangent are three important trigonometric functions, abbreviated sin, cos, and tan

It is given that tan(x) = 0.4

Also, tan(x + kπ) = tanx where  k∈Z

Therefore,  tan(x + kπ) = 0.4 where  k∈Z

Hence, option D is correct.

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The length of the JU would be 60 units.

What is the Basic Proportionality Theorem?

The basic Proportionality Theorem (can be abbreviated as BPT) states that, if a line is parallel to a side of a triangle that intersects the other sides into two distinct points, then the line divides those sides in proportion.

In the given figure side TU is parallel to side LK

If JK = 64 and JU = -4 + 4x

then UK = JK - JU

              = 64 - (-4 + 4x)

               =68 - 4x

Similarly,if JL = 72 and JT = 27

then TL = JL - JT

             = 72 - 27

             = 45

Now by using the property of the basic proportionality theorem, we can write

              [tex]\frac{JT}{TL} =\frac{JU}{UK}\\\\ \frac{27}{45} =\frac{-4+4x}{68 - 4x}\\\\\frac{3}{5} = \frac{-4+4x}{68 - 4x}\\\\3(68-4x) = 5(-4+4x)\\\\204 - 12x=-20+2x\\\\204+20=14x\\\\x=\frac{224}{14}\\\\x=16[/tex]

Now we can calculate the length of JU = -4 + 4x

                                                                 = -4 + 4(16)

                                                                 = -4 + 64 = 60

Hence, the length of the JU would be 60 units.

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(a) The system of equations that could be used to find the weight (in kilograms) of each type of box is

3x + 5y = 116  

9x + 7y = 238

(b)

Weight of each large box: 15.75 kilograms

Weight of each small box: 13.75 kilograms

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Given that, the weight of 3 large boxes and 5 small boxes is 116 kilograms.

The weight of 9 large boxes and 7 small boxes is 238 kilograms.

Let x be the weight (in kilograms) of each large box.

Then the weight of 3 large boxes is 3x kilograms.

Then the weight of 9 large boxes is 9x kilograms.

Let y be the weight (in kilograms) of each small box.

Then the weight of 5 large boxes is 5y kilograms.

Then the weight of 7 large boxes is 7y kilograms.

The weight of 3 large boxes and 5 small boxes is 3x + 5y kilograms.

The weight of 9 large boxes and 7 small boxes is 9x + 7y kilograms.

Therefore,

3x + 5y = 116  .....(i)

9x + 7y = 238  .....(ii)

Solve equation by using elimination method:

Multiplying equation(i) by 3  and subtract equation (ii) from it:

9x + 15y = 348

9x + 7y = 238

(-)  (-)       (-)

_____________

       8y = 110

       y = 13.75

Putting  y = 13.75 in equation (i)

3x + 5×(13.75) = 116

3x = 47.25

x = 15.75

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The mathematical model that gives the stopping distance d in terms of speed v is

d = 1/(40 x 5280²) v²

The stopping distance when v is 59 miles per hour is 87.03 feet.

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

The stopping distance d is directly proportional to the square of the speed v.

This can be written as,

d ∝ v²

Now,

Converting 40 miles into feet.

1 mile = 5280 feet

40 miles = 40 x  5280 feet

40 miles = 211200 feet

Now,

40 feet ∝ 211200 feet per

Now,

The stopping distance is 40 feet when the speed is 40 miles per hour

d = 40 and v = (40 x 5280) feet per hour

d = k v²

k = d/v²

k = 40/(40 x 5280)²

k = 1/(40 x 5280²)

The mathematical model that gives the stopping distance d in terms of speed v is

d = 1/(40 x 5280²) v²

The stopping distance when v is 59 miles per hour

v = (59 x 5280) feet per hour

d = 1/(40 x 5280²) x (59 x 5280)²

d = (59 x 59) / 40

d = 87.03 feet

Thus,

The mathematical model that gives the stopping distance d in terms of speed v is

d = 1/(40 x 5280²) v²

The stopping distance when v is 59 miles per hour is 87.03 feet.

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4 - 6x is linear equation .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

What makes an equation linear?

A linear equation's graph almost always takes the shape of a straight line.

                Definition of a Linear Equation: Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

let the number be =x

        4 - 6x

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Answer:

  c  The first two hours cost $4, between two hours and six hours cost $2 per hour, and all hours after that cost $1.

Step-by-step explanation:

You want an interpretation of the graph that is a constant 4 up to x=2, has a slope of 2 for 2 ≤ x < 6, and a slope of 1 for x ≥ 6. The vertical axis is labeled dollars, and the horizontal axis is labeled hours.

The constant value of y = 4 for x < 2 means the cost of parking is $4 for the first two hours.

The slope of 2 from x=2 to x=6 means the cost of parking is $2 per hour between 2 and 6 hours.

The slope of 2 for x ≥ 6 means the cost of parking is $1 per hour for more than 6 hours.

The description of c applies.

__

Additional comment

The slope, or "unit rate", is the ratio of "rise" to "run". It can be simpler to choose a "run" of 1 and look at the corresponding "rise".

From x=2 to x=3, the cost rises from $4 to $6, a rise of 2 for the run of 1. That is why we say the slope is 2, or the "unit rate" in dollars per hour is $2 per hour.

Answer:

b

Step-by-step explanation:

4y = 2x

y = 2/4  x

y = 1/2 x               where y = kx    then k = 1/2

The number of different routes she can take from City Upper C to City Upper G​ is 18

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

Routes from City Upper C to City Upper D = 3 routes

Routes from City Upper D to City Upper G = 6 routes

The number of different routes she can take is calculated as

Routes = Routes from City Upper C to City Upper D x Routes from City Upper D to City Upper G

Substitute the known values in the above equation, so, we have the following representation

Routes = 3 * 6

Evaluate

Routes = 18

Hence, the number of routes is 18

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The second pair of coordinates on the line parallel to q that passes through (0,1) is (1,-4/5) and that of (3,5) is (1,7).

The general form of the equation of a line is y=mx+c

where

m=slope

c is a constant

The equation of the line is

m= [tex]\frac{y-y_{1} }{x-x_{1} }[/tex]

M=[tex]\frac{5-4}{3+2}[/tex]

m=1/5

From the slope formula

m = -1/5

X₎=0

y₎=1

substitute these in the formula for slope

[tex]\frac{-1}{5} =\frac{y-1}{x-0}[/tex]

x=5y-5

x-5y=5

Now, with the above-derived equation, we need to find the other co-ordinate as these coordinates will satisfy this equation.

when x=1,

x-5y=5

1-5y=5

-5y=5-1

y=[tex]\frac{-4}{5}[/tex]

The other coordinate is (1,-4/5)

11.   In the second line (3,5)

Using the slope formula

m=[tex]\frac{Y_{2}-Y_{1} }{X_{2}-X_{1} }[/tex]

[tex]\frac{-1}{5} =\frac{y-5}{x-3}[/tex]

x-3=-y+2

x+y=5+3

x+y=8

Also, with the above-derived equation, we need to find the other co-ordinate as these coordinates will satisfy this equation.

when x=1,

x+y=8

1+y=8

y=8-1

y=7

Therefore the second coordinate is (1,7)

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For given 30-60-90 triangle, the measure of the shorter leg = 5.78 units and hypotenuse = 11.55 units

In this question we have been given 30-60-90 triangle with a measure of 10 (longer leg)

We need to find the hypotenuse and shorter leg.

We know that longer leg of 30-60-90 triangle is opposite to angle 60

Consider the sine of angle 60

sin(60) = 10/hypotenuse

(√3)/2 = 10/hypotenuse

hypotenuse = 10 * (2/√3)

hypotenuse = 11.55 units

By Pythagoras theorem,

hypotenuse² = (longer leg)² + (shorter leg)²

11.55² = 10² + (shorter leg)²

(shorter leg)² = 11.55² - 10²

shorter leg = √(33.4025)

shorter leg = 5.78 units

Therefore, shorter leg = 5.78 units and hypotenuse = 11.55 units

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Answer:

2.0 acres

Step-by-step explanation:

C(x) = 270 ln(x+1) + 1900 = 2200

270 ln(x+1) = 300

ln(x+1) = 10/9

x+1 = e^(10/9)

x = e^(10/9) - 1 = 2.0377

The simplified form of the given expression, 4(3x^2y^4)3 / (2x^3y^5) ^4, is 27/x⁶y⁸

From the question, we are to simplify the given expression

From the given information,

The expression is

4(3x^2y^4)3 / (2x^3y^5) ^4

First, we will write the given expression properly

The given expression written properly is

4(3x²y⁴)³ / (2x³y⁵)⁴

Simplifying the expression

4(3x²y⁴)³ / (2x³y⁵)⁴

4 × (3x²y⁴)³ / (2x³y⁵)⁴

4 × (3)³(x²)³(y⁴)³ / (2)⁴(x³)⁴(y⁵)⁴

4 × (3)³ × (x²)³ × (y⁴)³ / (2)⁴ × (x³)⁴ × (y⁵)⁴

4 × 27 × x⁶ × y¹² / 16 × x¹² × y²⁰

108 × x⁶ × y¹² / 16 × x¹² × y²⁰

This can be further expressed as

108/16 × x⁶/x¹² × y¹²/y²⁰

27/4 × 1/x⁶ × 1/y⁸

= 27/x⁶y⁸
Hence, the simplified expression is 27/x⁶y⁸

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Answer:

Maria can buy at most 2 bottles of cranberry juice and 7 lemon-lime soda bottles.

Step-by-step explanation:

For this problem, we can set up an algebraic expression to represent the price, and this will help us solve the problem.

So firstly, let's assign the number of cranberry juice bottles to the variable  "C". We could technically represent this as the variable name "cranberry juice bottles", but "C" is a bit more easier to write when writing an algebraic expression while still making it easy to distinguish. Let's also assign the number of lemon-lime soda to the variable "L".

Now let's find a way to express the price of each. The price of buying a certain amount of items, can generally be expressed as: [tex](\text{items bought})*(\text{item price})[/tex], since you have to pay the item price for each item bought, also known as, multiplication.

Since we know that the price of a cranberry juice bottle is $3.80 then that means the total amount used towards cranberry juice can be expressed as: [tex]3.80C[/tex]. We're just multiplying the number of cranberry juice bottles times the price. Likewise, we can represent the total amount used towards lemon-lime soda as: [tex]1.40L[/tex]. The same logic is being applied here.

Now if we add both of these, we get the total amount that will be spent which is: [tex]3.80C + 1.40L = T[/tex], and in this case I just set it equal to "T" which just represents the total spent.

Now there's two more things to do. Generally we can't really solve two-variable equations and we want to express one variable in terms of the other, so that we can rewrite the equation as a one-variable equation.

There is one piece of information given that allows us to do this. "The recipe calls for 3.5 times as many bottles of lemon-lime soda as cranberry". So we can represent the numbers of lemon-lime soda bottles as 3.5 times the amount of cranberry juice bottles. We can express it as: [tex]L=3.5C[/tex]

So now let's plug this into the equation, instead of "L". This gives us: [tex]3.80C + 1.40(3.5C) = T[/tex]

let's multiply the 1.40 by the 3

[tex]3.80C + 4.9C= T[/tex]

now let's add up the values.

[tex]8.7C=T[/tex]

Now lastly, this represents the total amount that is going to be spent. Since Maria only has $17.40, we want this total to be less than or equal to 17.40 (assuming there is no sales tax, but this was never given). this gives us our final expression we will be using: [tex]8.7C\le 17.40[/tex]

From here solving the problem is actually pretty easy. Think of the inequality as a linear equation, we can still apply the same (for the most part) algebraic manipulations we apply to linear equations. We just divide both sides by 8.7 to isolate the C

[tex]\frac{8.7C}{8.7}\le\frac{17.40}{8.7}\\\\C\le 2[/tex]

So Maria can buy a maximum of 2 bottles of cranberry juice. From this we can actually determine the number of lemon-lime soda bottles.

So we know that:

[tex]C=2[/tex]

From this we can determine what L is, since remember the equation we set up earlier?

[tex]L = 3.5C[/tex]

Let's just plug C into the equation, and we get:

[tex]L=3.5(2)[/tex]

Multiply

[tex]L=7[/tex]

So Maria can buy at most 2 bottles of cranberry juice and 7 lemon-lime soda bottles.

Answer:

For the problem with the horse: 10,000 grams

For the problem with the hiker labeled 11: 2 feet

I hope these answers are of use to you!

Step-by-step explanation:

Okay, for the horse problem I understood that it was a horse eating exactly 10 kg per day. If she does, then you just convert 10 kilograms to grams. To do this, you multiply the amount of kilograms by 1,000, since that is how it works.

10 x 1,000 = 10,000 grams.

For the problem labeled 11 with the hiker, you divide 120 ft by 60 since there are 60 seconds in a minute.

120 divided by 60 = 2 feet

Mr. Dillon balance at the end of month is $809.

In a financial institution, a checking account is a deposit account that permits both deposits and withdrawals.

Money kept or held in any bank account is referred to as a deposit.

A withdrawal entails taking money out of a trust, pension, savings plan, or bank account.

As Mr. Dillon opened a checking account, so balance is $0 in starting.

When he deposits $1530, $896, $571, $472

Total deposit= $1530+$896+$571+$472

             = $ 3,469

Check is a kind of withdrawal.

He wrote check of $32 , $981 , $825 , $661 , $224

Total withdrawal= $32+$981,$825+$661+$224

                             = $2,660

Balance= Total deposit - Total withdrawal

             = $3,469 - $2,660

             = $809

Therefore, balance is $ 809.

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Answer:

y=2(x-4)^2+9

Step-by-step explanation:

Vertex form: y=a(x-h)^2+k

The vertex represents the h and k variables.

Z-tests are closely related to t-tests, but t-tests are best performed when the data consists of a small sample size, i.e., less than 30. The given statement is true.

Does critical value depend on sample size?

The sample size and the crucial value that the researcher employed must be connected. The variations in critical values between the t-distribution and the normal-shaped sampling distribution, however, are minimal for sample sizes bigger than 30.

Z-tests and t-tests are closely related, but t-tests work best with small sample sizes of data, or those with fewer than 30 participants. Additionally, whereas z-tests assume that the standard deviation is known, t-tests assume that it is unknown.

You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct.

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The perimeter of the scale floor is 56 inches.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape.

To solve, we can set up fractions:

34/17 = 22/x

Cross multiply and you get:

34x = 374

Divide each side by 34:

x = 11

Since we are trying to find the perimeter of the floor, you can use this equation:

2w + 2l = p

Substitute to solve:

2 ( width = 11 )

2 ( length = 17 )

2 ( 17 ) + 2 ( 11 ) = p

34 + 22 = p

p = 56

Hence, the perimeter is 56inches

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Brielle uses 1/3 of a cup of nuts for 1 cup of oatmeal.

What is unitary method?

The unitary method is a process of finding the value of a single unit, and based on this value finding the required solution.

According to the given question:

Brielle uses 2/3 cup of nuts for every 2 cups of oatmeal to make granola bars.

To find the fraction cup of nuts required for 1 cup of oatmeal, using unitary method

2 cups ----- 2/3 cup of nuts

1 cup ------- [tex]\frac{2/3}{2}[/tex] cup of nuts = 1/3 cup of nuts

Therefore Brielle uses 1/3 of a cup of nuts for 1 cup of oatmeal.

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Answer:

Step-by-step explanation:

I think its 40

The triangle is isosceles so the left and right side are equal in length.

you would equal 4x+4=6x-14 and solve, getting 18=2x the 9=x

The measure of the arc length of the sector will be 1.047 units. Then the correct option is A.

Let r is the radius of the sector and θ be the angle subtended by the sector at the center. Then the arc length of the sector of the circle will be

Arc = (θ/2π) 2πr

The radius of the sector is 1 unit and the central angle is π/3. Then the measure of the arc length of the sector will be given as,

Arc = [(π/3)/2π] 2π(1)

Simplify the equation, then we have

Arc = [(π/3)/2π] 2π(1)

Arc = (1/6) × 2π

Arc = π/3

Arc = 1.047 units

The proportion of the circular segment length of the area will be 1.047 units. Then, at that point, the right choice is A.

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he is supposed to lose an average of 1.36$ per roll

Answer:

Sammy loses $3.47 on average

Step-by-step explanation:

When you roll two number cubes, the number of possible combinations is 36 ( 6 * 6 ).

The only way to get a sum of two is rolling snake eyes (two ones), which means there's only one combination that gets this sum.

The chances of winning is 1/36 whilst the chance of losing is 35/36

$50*(1/36) - $5(35/36) = $1.39 - $4.86 = -$3.47

which means Sammy loses $3.47 on average

Answer:

a) 3-5*2=-7

b)3-5*-4=23

c)3-5*0=3

Step-by-step explanation:

you would plug each of them into the equation because they give you x so

a) 3-5*2=-7    x=2

b) 3-5*-4=23  x=-4

c) 3-5*0=3      x=0

By using linear inequation it can be calculated that-

The shaded region right of the y axis and above the x axis gives all possible solution.

The required linear inequation is

1310g + 20s < 900

What is linear inequation?

Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by >, <, ≥, ≤

A one degree inequation is known as linear inequation

Let the alloy has g ounces of gold and s ounces of silver

An ounce of gold costs $1310 and an ounce of silver costs $20.

Cost of the alloy should be less than $900

The required linear inequation is

1310g + 20s < 900

The graph has been attached

The shaded region right of the y axis and above the x axis gives all possible solution.

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The equation has two solutions, on is extraneous and x = 7, and the real solution is x = -8.

Here we have the following equation:

x + 8x/(x - 7) = 56/(x - 7)

This is the original equation, notice that if x = 7, we will have a zero on the denominators, and we can't divide by zero, thus, x can't be equal to 7.

Now let's multiply all the equation by (x - 7)

(x - 7)*x + 8x = 56

Now we have a quadratic equation:

x^2 - 7x + 8x - 56 = 0

x^2 + x - 65 = 0

Using the quadratic formula we will get the two solutions:

[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*1*-56} }{2*1} \\\\x = \frac{-1 \pm15}{2*1}[/tex]

Then the two solutions are:

x = (-1 + 15)/2 = 7  (this one is an extraneous solution, we can discard this one)

x = (-1 - 15)/2 = -8

This is our solution.

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The equation of the line that passes through the point (2, -2) and is parallel to the graph of y = -x - 2 is y = -x - 4.

What is the system of linear equations?

A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).

To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (b).

To find the slope of the line, we can use the slope formula:

m = (y2 - y1)/(x2 - x1)

The equation y = -x - 2 is in slope-intercept form, so the slope of the line is -1.

The y-intercept is the point where the line intersects the y-axis. This point is (0, b), where b is the y-intercept.

Since the given line passes through the point (2, -2), we can substitute these values into the slope-intercept form of the equation to find the y-intercept:

-2 = -1 * 2 + b

Solving for b gives us:

b = -4

Therefore, the equation of the line that passes through the point (2, -2) and is parallel to the graph of y = -x - 2 is y = -x - 4.

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The distance of the foot of the ladder from the wall is 10.58m, the distance can find using pythagoras theorem states that in a right-angled triangle.

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.

Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula. The Pythagorean theorem can be rewritten as d=√((x_2-x_1)²+(y_2-y_1)²) to calculate the separation between any two points.

Let AC be the ladder and A be the window.

Given: AC=15m, AB=12m, CB=am

In right angled triangle ACB,

(Hypotenuse) ²  =(Base)² +[Perpendicular)²   [By Pythagoras theorem]

⇒(AC)²   =(CB)² +(AB)²

⇒(16)²   =(a)²  +(12)²

⇒256 = a²  + 144

⇒ a = √112 = 10.58cm.

The distance of the foot of the ladder from the wall is 9m.

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Answer:

No

Step-by-step explanation:

x > -9y-3/7 (Solve for X)

_____________________________________________________

y > -7x/9 - 1/3 (Solve for Y)

_____________________________________________________

Therefore, (-3, 2) is not a solution.