Work out the length x in the triangle below. If your answer is a decimal, give it to 1 d.p.

area = 42 m²

​

Answer:

y=4x-30

Step-by-step explanation:

Expression is equivalent to ³√27x + ³√x, if x # 0, The correct answer is A. 4³√x.

To find the equivalent expression, we can factor out the common term of ³√x from both terms in the original expression:

³√27x + ³√x = ³√x(³√27 + 1)

Next, we can simplify the term ³√27 by finding the cube root of 27, which is 3:

³√x(3 + 1) = ³√x(4)

Finally, we can simplify the expression by multiplying ³√x and 4:

³√x(4) = 4³√x

Therefore, the equivalent expression is 4³√x, or answer choice A.

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[tex] \sf 36 \degree = 3x[/tex]

[tex] \sf36 \div 3 = 3x \div 3 \\ \tt \: x = 12[/tex]

The wavelength of the wave is 0.125 m.

A periodic wave's wavelength is its spatial period, or the length over which its shape repeats. It is a property of both traveling waves and standing waves as well as other spatial wave patterns. It is the distance between two successive corresponding locations of the same phase on the wave, such as two nearby crests, troughs, or zero crossings.

A sinusoidal waveform's wavelength (λ) is determined by the equation

λ= ν/f,

where ν denotes the wave's phase speed (or magnitude of the phase velocity) and f denotes its frequency.

According to the given information,

Speed of transverse wave, ν = 25 m/s

Frequency, f = 200 Hz

We know the formula, λ= ν/f

By substituting the values, we get

λ = 25/200

λ = 0.125m

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This question is related to Physics.

Answer:false

Step-by-step explanation:

Answer:

3x+4=6

Step-by-step explanation:

The total number of miles Ahmad drove the truck is given by the equation A = 238.988 miles ≈ 240 miles

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The base fee of the truck = $ 20.95

The cost for each mile driven = $ 0.84

The total amount Ahmad paid = $ 221.7

Let the total number of miles be A

Now , the equation will be

The total amount Ahmad paid = base fee of the truck + cost for each mile driven x total number of miles

Substituting the values in the equation , we get

221.7 = 20.95 + ( 0.84 )A

Subtracting 20.95 on both sides of the equation , we get

0.84A = 200.75

Divide by 0.84 on both sides of the equation , we get

A = 238.988 miles

Hence , the equation is A = 238.988 miles

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The points where the curve intersect the paraboloid is (2, 0, 4).

To find the points of intersection, we set the two equations equal to each other and solve for x, y, and z.

Now, to find the point where the curve r(t) intersects the paraboloid z = x² + y², we can substitute the given value of t into the parametric equations of the curve.

The curve is defined as:

r(t) = t i + (2t - t²) k

where i and k are unit vectors in the x and y directions, respectively.

value of t is given.

Setting t = 2, we have:

x = 2

y = 2(2) - (2)² = 0

z = x² + y² = 4 + 0 = 4

So, the point of intersection is (2, 0, 4).

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_____The given question is incorrect, the correct question is given below:

At what point does the curve r(t)=ti+(2t−t2)k, where t= 2

intersect the paraboloid z=x²+y².

The angle 'b' measure 120 degrees from the diagram.

The given diagram is a circle geometry. Given the following parameters

x= 44° and;

a = 32°

In order to determine the measure of angles 'b'. we will use the expression below;

x = 1/2(b + a)

44 = 1/2 (b- 32)
88 = b - 32

b = 88 + 32

b = 120 degrees

Hence the measure of the angle 'b' from the diagram is 120 degrees.

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The zeroes of the equation is  0, 1 and 9.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

w³ -w² + 9w= 9

Now. solving for 'w'

w(w² - w + 9)=9

so, either w= 9 or w² - w + 9 = 9

w= 9 or w² - w = 0

w= 9 or w(w-1) = 0

w= 9 or w= 0, w= 1

So, the zeroes are 0, 1 and 9.

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Answer:123 degrees west

Step-by-step explanation: ngl i need them points but the degrees add up to 123 sine the is a prime number

If you are told that a 20 kilogram object is raised by 10 meters, you know that (b) the mass of the object is 20 kilograms.

The force of gravity, also known as gravitational force, is the force that attracts two objects with mass towards each other.

AS we all know that Mass refers to the amount of matter an object contains, and is measured in kilograms. Weight, on the other hand, refers to the force of gravity on an object, and is measured in newtons.

Now, let's look at the options provided.

Option b states that the mass of the object is 20 kilograms, which is correct. This means that the object contains 20 kilograms of matter, regardless of its location or gravitational force acting on it.

In conclusion, we can determine from the given information that the mass of the object is 20 kilograms. However, we cannot determine the force of gravity acting on the object without additional information.

To calculate the force of gravity on an object, we can use the formula

Fg = mg,

where Fg is the force of gravity, m is the mass of the object, and g is the acceleration due to gravity (approximately 9.81 m/s² on Earth).

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The area of the triangle is given by Heron's formula A = 269.99 units² which is approximately 270 units²

Heron's formula is used to calculate the area of a triangle in terms of the lengths of its sides. If a, b, and c are the lengths of the sides, then the area of the triangle is

Area of Triangle A = √ [ s(s - a) (s - b) (s - c) ]

where s is half the perimeter, or (a + b + c) / 2

Given data ,

Let the triangle be represented as ΔKLM

Now , the measure of side KL , a = 30

The measure of side KM , b = 25

The measure of side LM , c = 22

From Heron's formula , the half the perimeter s = (a + b + c) / 2

Substituting the values in the equation , we get

s = ( 30 + 25 + 22 ) / 2

s = 38.5

Now , Area of Triangle A = √ [ s(s - a) (s - b) (s - c) ]

Substituting the values in the equation , we get

Area of Triangle A = √ [ 38.5 ( 38.5 - 30 ) ( 38.5 - 25 ) ( 38.5 - 22 ) ]

On simplifying the equation , we get

Area of Triangle A = √ [ 38.5 ( 8.5 ) ( 13.5 ) ( 16.5 ) ]

Area of Triangle A = √ ( 72,894.9375 )

On further simplification , we get

Area of Triangle A = 269.99 units² ≈ 270 units²

Hence , the area of triangle is 270 units²

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Expressing the given percentage as a fraction is; 1/10

To change a percent to a fraction, put the percentage over 100 (after removing the % sign) and simplify if necessary. For example, to convert 17% to a fraction, put 17 over 100, like this: 17/100.

Now, we are told that the largest Hmong population per capita in the United States is in St. Paul, Minnesota, where about 10% are Hmong Americans.

Thus, expressing this as a fraction gives us;

10/100 = 1/10

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After multiplying and adding given equations, new equations are
3x² + 2xy - 8y² = -273 and 4x - 2y = -32 respectively.

Solutions of the equations are x = -5 and y = 6.

A linear equation is an equation in which the greatest power of a variable is always 1. Also called the 1 degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. where x is a variable, A is a coefficient, and B is a constant.  

Given equations,

a) x + 2y = 7

b) 3x - 4y = -39

Multiplying both equations

(x + 2y)(3x - 4y) = (7)(-39)

Using Foil method (a+b)(c+d) = ac + ad + bc + bd

3x² - 4xy + 6xy - 8y² = -273

3x² + 2xy - 8y² = -273

Which is a new equation.

Adding both equations

(x + 2y)+(3x - 4y) = (7)+(-39)

Adding like terms, we get

4x - 2y = -32

Solving the equations (a) and (b)

a) x + 2y = 7

x = 7 - 2y

Substituting x in terms of y in equation (b)

b) 3x - 4y = -39

3(7 - 2y) - 4y = -39

21 - 6y - 4y = -39

-10y = -60

y = 6

then x = 7 - 2(6)

⇒ x = - 5

Hence, x = -5 and y = 6 are solutions of given equations.

3x² + 2xy - 8y² = -273 is the equation, after multiplying both equations.

4x - 2y = -32 is equation after both equations are added.

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The probability that the number is either even or a perfect square is [tex]\frac{3}{5}[/tex]

Probability refers to potential.This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability is a concept in mathematics that helps predict the likelihood of certain events. Probability generally refers to the degree to which something is likely to occur..we will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a certain event will occur.

Total Number of Outcome = 100

Number of even numbers = 50

Number of perfect square = 10

[tex]Probability \:=\:\frac{Number\: of\: favourable\:outcome\:}{Number\: of\: total\:outcome\:}[/tex]

[tex]Probability=\frac{50}{100} +\frac{10}{100} = \frac{60}{100} =\frac{3}{5}[/tex]

Therefore,  the probability that the number is either even or a perfect square is [tex]\frac{3}{5}[/tex]

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Monica's age is 20 years and her father's age is 52

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.

Represent Monica's age by x and her father's age by y

y -x = 32 equation 1

y-16= 9(x-16)

= y-16 = 9x -144

y-9x = -144+16

y - 9x = -128 equation 2

subtract equation 2 from 1

-x-( -9x )= 32-(-128)

8x = 160

x = 160/8

x = 20

substitute 20 for x in equation 1

y = 32+x

y = 32+20

y = 52

Therefore Monica's age is 20 and her father's age is 52

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Using the cosine ratio, the value of x, to the nearest tenth, is: 39.3°.

The cosine ratio is part of the trigonometric ratios, which is given as:

cos ∅ = length of adjacent side / length of hypotenuse.

Given the following:

Length of adjacent side = 6.5

Length of hypotenuse = 8.4

Reference angle (∅) = x

Plug in the values:

cos x = 6.5/8.4

x = cos^(-1)(6.5/8.4)

x = 39.3°

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Answer:

y ≥ 9

Step-by-step explanation:

−2(4y+4)+5y ≤ −35

-8y - 8 + 5y ≤ -35

-3y - 8 ≤ -35

-3y ≤ -27

y ≥ 9

The required probability of the randomly selected households either having internet access or cable television is equal to 0.85.

Let us consider 'A' represents the number of house hold has internet access.

And 'B' represents the number of house hold has cable television.

P(A) = 75%

      = 0.75

P(B) = 80%

       = 0.80

Number of household has both internet access and cable television

= P( A∩B)

= 70%

= 0.70

Probability of randomly selected household either with internet access or cable are P( A∪B) :

P( A∪B) = P(A) + P(B) - P( A∩B)

Substitute the value we get,

⇒  P( A∪B) = 0.75 + 0.80 - 0.70

⇒  P( A∪B) =  0.85

Therefore, the probability of household having either internet access or cable television is equal to 0.85.

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The pair of measurements that is not equivalent is 25 g and 25,000 kg. Option A.

Unit of measurement is defined as every entity having its measures in dimensions, weight, and time. Such as for length we have a meter, for liquid we have liters, and so on.

Here,

The pair of measurements that is not equivalent is 25 g and 25,000 kg.
25 g is a relatively small amount of mass, while 25,000 kg is a very large amount of mass. Therefore, these two measurements are not equivalent.

The other pairs of measurements are equivalent because they involve conversions between different units of the same base unit. For example:

16 g and 16,000 mg,  1 g = 1,000 mg, so 16 g = 16,000 mg

140 mg and 0.14 g, 1 g = 1,000 mg, so 0.14 g = 140 mg

5 kg and 5,000 g,  1 kg = 1,000 g, so 5 kg = 5,000 g

Thus, the pair of measurements that is not equivalent is 25 g and 25,000 kg. Option A.

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Answer:

Step-by-step explanation:

The equation h = -0.0159d² + 290 models the curve of the natural stone bridge, where h is the height of the curve in feet and d is the width of the curve in feet.

To find the vertex of the curve, we need to use the formula x = -b / 2a, where x represents the x-coordinate of the vertex and a and b are coefficients of the quadratic equation. In this case, the quadratic equation is h = -0.0159d² + 290, so a = -0.0159 and b = 0. To find the vertex, we plug these values into the formula:

x = -b / 2a = 0 / (2 * (-0.0159)) = 0

So the x-coordinate of the vertex is 0, which means the vertex is at the point (0, 290).

The vertex tells us that the highest point of the bridge (the vertex) is at a width of 0 feet. This means that the bridge is tallest at its center, and the height decreases as the width increases in either direction. Additionally, since the coefficient of the squared term is negative, the parabolic curve is downward-facing, which indicates that the bridge curves downward as it extends outward.

To find the span of the rainbow bridge, we need to find the width of the bridge where the height is 0. This represents the point where the bridge intersects with the river. To do this, we set h = 0 and solve for d:

0 = -0.0159d² + 290

0.0159d² = 290

d² = 290 / 0.0159

d ≈ 77.36

So the width of the bridge where the height is 0 is approximately 77.36 feet. Therefore, the span of the rainbow bridge is approximately 154.72 feet (twice the width at the point where the height is 0).

Answer:

44 ft

Step-by-step explanation:

To find the height of the tree, h, model the given scenario as a two right triangles and solve using the tan trigonometric ratio.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Tan trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\end{minipage}}[/tex]

See attached for a diagram modelling the given information.

Create two tan ratios using the given information, and rearrange each equation to isolate x.

Equation 1

Given:

Therefore:

[tex]\begin{aligned}\implies \tan 42^{\circ}&=\dfrac{h}{x+12}\\\\ x+12&=\dfrac{h}{\tan 42^{\circ}}\\\\ x&=\dfrac{h}{\tan 42^{\circ}}-12\end{aligned}[/tex]

Equation 2

Given:

[tex]\begin{aligned}\implies \tan 50^{\circ}&=\dfrac{h}{x}\\\\ x&=\dfrac{h}{\tan 50^{\circ}}\end{aligned}[/tex]

To find the value of h, substitute equation 2 into equation 1 to eliminate x and solve for h:

[tex]\implies \dfrac{h}{\tan 50^{\circ}}=\dfrac{h}{\tan 42^{\circ}}-12[/tex]

[tex]\implies \dfrac{h}{\tan 50^{\circ}}-\dfrac{h}{\tan 42^{\circ}}=-12[/tex]

[tex]\implies \dfrac{h\tan 42^{\circ}-h\tan 50^{\circ}}{\tan 50^{\circ}\tan 42^{\circ}}=-12[/tex]

[tex]\implies \left(\dfrac{\tan 42^{\circ}-\tan 50^{\circ}}{\tan 50^{\circ}\tan 42^{\circ}}\right)h=-12[/tex]

[tex]\implies h=\dfrac{-12\tan 50^{\circ}\tan 42^{\circ}}{\tan 42^{\circ}-\tan 50^{\circ}}[/tex]

[tex]\implies h=44.1967977...[/tex]

Therefore, the approximate height of the tree to the nearest foot is 44 ft.

The total cost of wax to cover the floor is

The area for of the floor is calculated and multiplied by the unit cost $1.38 to get the total cost

The floor is segmented and the area calculated and added together at last

1. Area of rectangle joining the right triangle

= 15 * (30 - 20)

= 150 square feet

2. Area of right triangle

= 1/2 * 15 * (35 - 10)

= 187.5 square feet

3. Area of the large rectangle

= 40 * 20

= 800 square feet

total area = 800 + 187.5 + 150 = 1137.5

cost of wax to cover the floor

= total area * unit cost

= 1137.5 * 1.35

= $1569.75

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complete question: image is attached

Answer:

The correct answer is B.

Step-by-step explanation:

I literally just took the test.

The term that describes a group of statements that executes as a single unit is a "block". A block of code is a program that is grouped together and treated as a single unit. So, the correct option is D.

In computer programming, a block is a group of statements or declarations that are enclosed within a set of curly braces ({ }). The block serves as a single unit that is executed together. Blocks are used to organize code and to apply control structures, such as loops and conditional statements, to multiple statements.

A block can contain any number of statements, which can include variable declarations, function calls, loops, conditional statements, and other constructs. The statements within a block are executed in sequence, one after another, unless a control statement is encountered that alters the normal sequence of execution.

For example, a while loop in Java consists of a block of code that is executed repeatedly while a certain condition is true:

while (condition) {

   // block of code to be executed while condition is true

}

In this example, the block of code inside the curly braces will be executed repeatedly while the condition specified in the while statement is true. The block can contain any number of statements, and these statements will be executed each time the loop iterates.

Another common use of blocks is to define functions or methods. A function or method is a block of code that can be called from other parts of the program, and can take inputs (arguments) and return outputs. For example, in Python, a function can be defined as follows:

def function(argument1, argument2):

   # block of code to be executed in the function

   return result

In this example, the block of code enclosed within the function definition is executed when the function is called. The function can take inputs (argument1 and argument2), which can be used within the function, and it can return a result using the return statement.

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Answer:

Step-by-step explanation:

There are several ways to find the center of a triangle:

The Centroid: The centroid is a point that divides each median of the triangle into two equal parts. It is the average of the vertices of the triangle. To find the centroid, you simply average the x-coordinates and the y-coordinates of the vertices:

G = (x1 + x2 + x3)/3, (y1 + y2 + y3)/3

where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices of the triangle.

The Circumcenter: The circumcenter is the center of the circle that passes through all three vertices of the triangle. To find the circumcenter, you need to find the midpoint of each side of the triangle and then draw perpendicular bisectors to each side. The point where the perpendicular bisectors intersect is the circumcenter.

The Orthocenter: The orthocenter is the point where the altitudes of the triangle intersect. The altitudes are the perpendicular lines from each vertex to the line that contains the opposite side. To find the orthocenter, you need to find the equations of the altitudes and then solve for the point where they intersect.

Note: If the triangle is an equilateral triangle, then the circumcenter and the centroid are the same. If the triangle is a right triangle, then the orthocenter and the circumcenter are the same.

The equivalent fraction to the given fraction is 1/2. Therefore, option C is the correct answer.

Equivalent fractions are two or more fractions that are all equal even though they different numerators and denominators.

On the number line, the fraction marked is 3/6.

Here, divide both numerator and denominator by 3

We get (3÷3)/(6÷3)

= 1/2

Therefore, option C is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

Johnny found a fraction equivalent to the one shown by the point on the number line.  Which fraction could he have found?

A) 1/4

B) 1/3

C) 1/2

D) 2/3

The Domain is 0 ≤ x ≤ 4 and Range is 0 ≤ y ≤ 80.

The range of values that we are permitted to enter into our function is known as the domain of a function.  A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given:

We know that the domain of a function is the set of values that we are allowed to plug into our function.

From the Graph the x values ranges from 0 to 4.

So, domain is 0 ≤ x ≤ 4.

and, the range is the corresponding output for the input

From the Graph the y values ranges from 0 to 80.

So, Range is 0 ≤ y ≤ 80.

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The difference of the numbers of cookies produced by production lines A and B in a day is 280 cookies.

When two algebraic expressions are equated, a mathematical statement is called an algebraic equation. P = 0 or P = Q, where P and Q are polynomials, are the generic forms of algebraic equations. One variable only algebraic equations are referred to as univariate equations, while multiple variable algebraic equations are referred to as multivariate equations. A balanced equation in algebra is a given. Because of this, the right side of the equation will equal the left side.

Let the cookies produced by production line A = x.

Let the cookies produced by production line B = y.

Given that, the two production lines produce 7280 cookies in total each day.

x + y = 7280

Also, production line A produces 8% more cookies than production line B.

x = y + y(8/100)

x = y + 0.08y

x = 1.08y

The system of equations thus are:

x = 1.08y

x + y = 7280

Substitute the value of x in equation 2:

x + y = 7280

1.08y + y = 7280

2.08y = 7280

y = 3500

Substitute the value of y in equation 2:

x + y = 7280

x + 3500 = 7280

x = 3780

The difference between the cookies produced is:

D = x - y

D = 3780 - 3500

D = 280

Hence, the difference of the numbers of cookies produced by production lines A and B in a day is 280 cookies.

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