9x/4y=1 and y= 18, what is the value of x​

Ada is incorrect, as the length of diagonal SQ is not two times the length of diagonal OM. The theorem used is the Pythagoras Theorem.

For Rectangle PQRS:-

By Pythagoras Theorem, in right triangle PQS,

SQ² = PQ² + PS²,

or, SQ² = 8² + 16² sq. inches,

or, SQ² = 64 + 256 sq. inches,

or, SQ = √320 sq. inches,

or, SQ = 8√5 inches.

Thus, the length of diagonal SQ, of rectangle PQRS is 8√5 inches.

For Square LMNO:-

By Pythagoras Theorem, in right triangle LMO,

OM² = LM² + LO²,

or, OM² = 8² + 8² sq. inches,

or, OM² = 64 + 64 sq. inches,

or, OM = √128 sq. inches,

or, OM = 8√2 inches.

Thus, the length of diagonal OM, of square LMNO is 8√2 inches.

We know that 2*OM ≠ SQ, as 2*8√2 ≈ 8√5.

Thus, Ada is incorrect, as the length of diagonal SQ is not two times the length of diagonal OM. The theorem used is the Pythagoras Theorem.

Learn more about the diagonal of square and rectangle at

https://brainly.com/question/22078692

#SPJ4

Rewrite the second expression as

[tex]\dfrac1{1+x^m + x^{-n}} = \dfrac{x^{\ell+n}}{x^{\ell+n} + x^{\ell+m+n}+x^\ell} = \dfrac{x^{-m}}{x^{-m} + 1 + x^\ell}[/tex]

and the third expression as

[tex]\dfrac1{1 + x^n + x^{-\ell}} = \dfrac{x^\ell}{x^\ell + x^{\ell+n} + 1} = \dfrac{x^\ell}{x^\ell + x^{-m} + 1}[/tex]

so the fractions all have the same denominator.

Then combining the fractions gives the desired result,

[tex]\dfrac1{1+x^\ell+x^{-m}} + \dfrac1{1+x^m+x^{-n}} + \dfrac1{1+x^n+x^{-\ell}} = \dfrac{1+ x^\ell + x^{-m}}{1+x^\ell+x^{-m}} = \boxed{1}[/tex]

Based on the information provided in the first table, we have the following angle and trigonometric function:

Based on the information provided in the first table, we have the following trigonometric function:

tanθ = √3

θ = tan⁻¹(√3)

θ = 60°.

In radians, we have:

θ = 60 × π/180

θ = 1.0472 radian.

sin60 = √3/2

cos60 = 1/2

csc60 = 2/√3

sec60 = 2

cot60 = 1/√3

Based on the information provided in the second table, we have the following trigonometric function:

θ = 30 × π/180

θ = 0.5236 radian.

sin30 = 1/2

cos30 = √3/2

tan30 = 1/√3

csc30 = 2

sec30 = 2/√3

cot30 = √3

Based on the information provided in the third table, we have the following trigonometric functions:

sinθ = √2/2                                   tanθ = 1

θ = sin⁻¹(√2/2)                               θ = tan⁻¹(1)

θ = 45°.                                          θ = 45°.

In radians, we have:

θ = 45 × π/180

θ = 0.7854 radian.

cos45 = √2/2

csc45 = √2

sec45 = √2

cot45 = 1

Based on the information provided in the fourth table, we have the following trigonometric function:

sinθ = 1                                

θ = sin⁻¹(1)                      

θ = 90°.

θ = 90 × π/180

θ = 1.5708 radian.

cos90 = 0

tan90 = not defined

csc90 = 1

sec90 = not defined

cot90 = 0

Read more on trigonometry here: https://brainly.com/question/20519838

#SPJ1

The area under the curve between the two values is (d) 0.0750

From the table, we have:

P(z = -0.45) = 0.3264

P(z = -0.67) = 0.2514

The area under the curve is calculated as:

Area = P(z = -0.45) - P(z = -0.67)

So, we have:

Area = 0.3264 - 0.2514

Evaluate the difference

Area = 0.0750

Hence, the area under the curve between the two values is (d) 0.0750

Read more about curve areas at:

https://brainly.com/question/24075649

#SPJ1

Answer:

M = 4.5

N = 2.1

Step-by-step explanation:

angle p would be 25.  180 - 155 = 25

M = 5cos25 =4.5 rounded to the tenths place.

M = 5sin25 = 2.1 rounded.

The value of f(-2) is 0

The graph of the function is added as an attachment

The graph is given as:

y = f(x)

When x =-2. we have

y = f(-2)

From the graph, we have:

x = -2 and y = 0

So, we have

f(-2) = 0

Hence, the value of f(-2) is 0

Read more about functions at;

https://brainly.com/question/2456547

#SPJ1

The correct labels are matched to their appropriate locations on the graph as shown in the image attached below.

A graph refers to a type of chart that's used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate, which are the x-axis and y-axis.

In this exercise, you're required to drag the correct labels to their appropriate locations on the graph as shown in the image attached below.

Read more on graphs here: brainly.com/question/25875680

#SPJ1

Part A:

According to a life cycle analysis of the U.S. food system conducted by the University of Michigan, the U.S. consumes 13.9 quads of mostly fossil fuel energy to produce 1.75 quads of food energy annually. A quad is a unit of energy equal to 1 quadrillion (10¹⁵) British thermal units (BTUs). One quad is equal to the energy of 183 million barrels of petroleum.

Answer:

  (d)  1 unit

Step-by-step explanation:

The length of the dilated line segment is the product of the dilation factor and the length of the original line segment. It can also be computed as the length of the segment between the dilated coordinates.

The length of the original horizontal line segment BC is the difference of its x-coordinates:

  BC = 6 -4 = 2 . . . . units

(We know the segment is horizontal because the y-coordinates of the end points are the same.)

Multiplying the length of the original segment by the dilation factor, we find the length of B'C':

  B'C' = dilation factor × BC

  B'C' = 0.5×(2 units)

  B'C' = 1 unit

The dilation factor multiplies each coordinate value:

  B' = 0.5B = 0.5(4, 3) = (2, 1.5)

  C' = 0.5C = 0.5(6, 3) = (3, 1.5)

The length of B'C' is the difference of x-coordinates: 3 -2 = 1 unit.

The surface area of the composite figure is equal to 233.6 square centimeters.

The surface area is the area of all faces of a solid. Since the surface area of the figure is a combination of triangles and quadrilaterals, we must sum all the areas to determine the surface area of the figure. Now we proceed to determine this:

A = 4 · (1/2) · (3 cm) · (2 cm) + 2 · (6 cm) · (3 cm) + 2 · (8 cm) · (6 cm) + 2 · (8 cm) · (2 cm) + 2 · (8 cm) · (3.6 cm)

A = 233.6 cm²

To learn more on surface areas: https://brainly.com/question/2835293

#SPJ1

Answer:

The chance of the committee being all boys is 28.57% or 29%

The length of the missing length in the triangle is 53.6 units

The given triangle is a right triangle.

Right triangles are triangles that have a measure of angle that is 90 degrees.

The missing side is x, and the value of x is calculated using the following sine rule

We have

sin(angle) = opposite/hypotenuse

This gives

sin(66) = 49/x

Divide both sides by sin(66)

1 = 49/x sin(66)

Multiply both sides by x

x = 49/sin(66)

Divide the expression

x = 53.6

Hence, the length of the missing length is 53.6 units

Read more about right triangles at

https://brainly.com/question/2437195

#SPJ1

As the value of x increases and the function of f(x) also increases since it is moving in the upward direction. The x-intercept is (-3,0)

A function is a set of input values into a program that produces the desired output. In mathematical terms, we can say a function is a set of x values that maps to a set of y values.

Functions can also be represented on the graph called graphical representation.

From the given graphical information, as the value of x increases, the function of f(x) also increases since it is moving in the upward direction.

The x-intercept is the value where the line cuts the horizontal x-axis when y is zero, therefore the x-intercept is (-3,0)

Learn more about what is a function here:

https://brainly.com/question/17043948

#SPJ1

Using the relation between velocity, distance and time, it is found that a reasonable estimation of the current is of 1 mph.

Velocity is distance divided by time, hence:

[tex]v = \frac{d}{t}[/tex]

Upstream, against the current, he traveled 3 miles in t hours, hence the equation is:

[tex]2 - c = \frac{3}{t}[/tex]

[tex]c = 2 - \frac{3}{t}[/tex]

Downstream, with the current, he traveled 3 miles in 4 - t hours, hence the equation is:

[tex]2 + c = \frac{3}{4 - t}[/tex]

Hence:

[tex]c = \frac{3}{4 - t} - 2[/tex]

Then, taking the two equal equations:

[tex]2 - \frac{3}{t} = \frac{3}{4 - t} - 2[/tex]

[tex]\frac{3}{4 - t} + \frac{3}{t} = 4[/tex]

[tex]\frac{3t + 12 - 3t}{t(4 - t)} = 4[/tex]

12 = -4t² + 16t

4t² - 16t + 12 = 0

t² - 4t + 3 = 0

(t - 3)(t - 1) = 0.

The current is positive, hence:

[tex]c = 2 - \frac{3}{3}[/tex]

c = 2 - 1

c = 1 mph.

More can be learned about the relation between velocity, distance and time at https://brainly.com/question/24316569

#SPJ1

If the graph of the line falls from left to right the slope is negative.

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

---> y = -2x + 3

Step-by-step explanation:

18z+10z+40z+5+1=360

68z+6=360

68z=360-6

68z=364

z≈5.353

Using Percentage, the eighth graders voted for Luke is of 72 percentage or 72%.

According to the question,

They are 450 eighth graders at Wilson Middle School. In the class president, 324 students voted for Luke, 81 students voted for Alice, and 45 students voted for Chris.

In order to find the percentage of eighth graders voted for Luke only if 252 divided by 350.

[tex]\frac{252}{350} = 0.72[/tex]

To convert decimal into Percentage multiply 0.72 into 100.

0.72*100 = 72%.

Hence, the percentage of the eighth graders voted for Luke is of 72 percentage or 72%.

Learn more about Percentage here

https://brainly.com/question/18149932

#SPJ4

The proportional relationship that represents the market that sells their carrots at a lower rate per pound is: y = 1.6x.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

From the table, the rate is:

k = $8.8/4.4 = 2.

From the market, the rate is:

k = $4.8/3 = $1.6.

Hence the equation is y = 1.6x.

More can be learned about proportional relationships at https://brainly.com/question/10424180

#SPJ1

Answer:

C

Step-by-step explanation:

cosecΘ = [tex]\frac{1}{sin0}[/tex] = [tex]\frac{2}{\sqrt{3} }[/tex] ( cross- multiply )

2sinΘ = [tex]\sqrt{3}[/tex] ( divide both sides by 2 )

sinΘ = [tex]\frac{\sqrt{3} }{2}[/tex] , then

Θ = [tex]sin^{-1}[/tex] ( [tex]\frac{\sqrt{3} }{2}[/tex] ) = 60°

Answer:

C.  60°

Step-by-step explanation:

by definition,  cosec(θ) is the reciprocal of sin(θ)

In other words ,

[tex]\text{cosec} \left( \theta \right) =\frac{1}{\sin \theta }[/tex]

Then

[tex]\text{cosec} \left( \theta \right) =\frac{2}{\sqrt{3} }[/tex]

[tex]\Longleftrightarrow \frac{1}{sin \left( \theta \right) } =\frac{2}{\sqrt{3} }[/tex]

[tex]\Longleftrightarrow sin \left( \theta \right) =\frac{\sqrt{3} } {2}[/tex]

Then

θ = 60°

Answer:

f(2) = 3

Step-by-step explanation:

Plug in 2 for x

Answer:

I have wrote just answer.

The equation of a parabola whose vertex is (0, 0) and focus is (1 / 8, 0) is equal to x = 2 · y².

Herein we have the case of a parabola whose axis of symmetry is parallel to the x-axis. The standard form of the equation of this parabola is shown below:

(x - h) = [1 / (4 · p)] · (y - k)²     (1)

Where:

The distance from the vertex to the focus is 1 / 8. If we know that the location of the vertex is (0, 0), then the standard form of the equation of the parabola is:

x = 2 · y²     (1)

The equation of a parabola whose vertex is (0, 0) and focus is (1 / 8, 0) is equal to x = 2 · y².

To learn more on parabolae: https://brainly.com/question/4074088

#SPJ1

The correct answer is (40, 35) because by plugging in,  40 +35 = 75 and

(40 x 5) + (35 x 3) > 300

Word problem can be solved by interpreting the problem into its best fit equation. The equation may be linear, quadratic or simultaneous equations.

Given that

5x + 3y > 300

x + y = 75

Let us first assume that 5x + 3y = 300. That is,

5x + 3y = 300

x + y = 75

Eliminate y by multiplying equation 2 by 3

5x + 3y = 300

3x + 3y = 225

2x = 75

x = 75/2

x = 37.5

Substitute x in equation 2

37.5 + y = 75

y = 75 - 37.5

y = 37.5

The correct answer is (40, 35) because 40 +35 = 75 and

(40 x 5) + (35 x 3) > 300

Therefore,  the solution to the system is (40, 35)

Learn more about Simultaneous Equation here: https://brainly.com/question/16863577

#SPJ1

The wavelength of X-rays for the given frequency is [tex]$1 \times 10^{-10} \mathrm{~m}$[/tex].

The distance between the two crests or troughs of the light wave is known as the wavelength of light.

The color of light is determined by its wavelength, and the pitch of sound is determined by its wavelength. The visible spectrum of light has wavelengths between around 700 nm (red) to 400 nm (violet). The range of audible sound wavelengths is roughly 17 mm to 17 m.

To calculate the wavelength of light, we use the equation:

[tex]$\lambda=\frac{c}{\nu}$[/tex]

where,

λ = wavelength of the light  

c = speed of light = [tex]$3 \times 10^{8} \mathrm{~m} / \mathrm{s}$[/tex]

ν= frequency of light = [tex]$3 \times 10^{18} s^{-1}$[/tex]

Putting the above value in equation,

[tex]$\lambda=\frac{3 \times 10^{8} \mathrm{~m} / \mathrm{s}}{3 \times 10^{19} \mathrm{~s}-1}=1 \times 10^{-10} \mathrm{~m}$[/tex]

Hence, the wavelength of X-rays for the given frequency is [tex]$1 \times 10^{-10} \mathrm{~m}$[/tex].

To know more about Wavelength of light visit:

https://brainly.com/question/14673590

#SPJ4

Answer:

[tex]y = -x^{2} +4x-10[/tex]

Step-by-step explanation:

I used a graphing calculator to calculate the points so I'm not sure how to do it without, but I hope this helped!

The function given can be classified as a function. That is option C.

Function can be defined as the expression that has both an x domain value and a y range value and it's being classified based on the quality of these values.

A function can be represented based on their roster forms.

Using the function equation given, f(X) = 10.2^2

Here, the first element is the domain or the x value and the second element is the range or the f(x) value of the function.

Learn more about arithmetic function here:

https://brainly.com/question/10439235

#SPJ1

Step-by-step explanation:

Therefore,the answer is [tex] \cfrac{3}{y} - x[/tex].

Answer:

2 hours 46 minutes and 40 seconds

Step-by-step explanation:

First we divide by 60 to find how many minutes are in 10000 seconds :

10000÷60 = 166 minutes with remainder 40 seconds

If 166 minutes and 40 seconds is 100000 seconds then we change 166 minutes into hours and minutes :

We do this by dividing 166 by 60 :

166 ÷ 60 :

2 hours Remainder 46 minutes

So our final answer is :

2 hours 46 minutes and 40 seconds

Hope this helped and have a good day

Answer:

1.2

2.4√3÷3

3. x=45, y=15

Step-by-step explanation:

OK,

1. So the first part requires the Pythagoreanism formula which is: b²=a²+c²:

AC²=AB²+BC²====> AC²=(1)²+(√3)²===> AC²=4===> AC=2

2.The second part requires the formula of tan:

tan A=BC÷AB===> tan A=√3÷1===> tan A=√3

tan C=AB÷BC===> tan C=1÷√3===> tan C=√3/3

tan A+tan C=√3+√3/3===> 4√3÷3

3.And the last part requires the equation of angles:

A+B+C=180===>

x+y+x-y+90=180===> 2x=90===> x=45, y=15

Answer: [tex]y-8=-2(x+3)[/tex]

Step-by-step explanation:

See attached image, it's direct formula substitution.