Question 10
Which equation represents the line parallel to the line whose equation is 4x+2) = 14 and
passing through the point (2, 2)?
03²=-2x+6
0y=-2x
Oy-x+1
2 pts
Oy-x

Answer:

y = - [tex]\frac{5}{2}[/tex] x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, 9) and (x₂, y₂ ) = (2, - 6) ← 2 ordered pairs from the table

m = [tex]\frac{-6-9}{2-(-4)}[/tex] = [tex]\frac{-15}{2+4}[/tex] = [tex]\frac{-15}{6}[/tex] = - [tex]\frac{5}{2}[/tex]

the line crosses the y- axis at point (0, - 1 ), ordered pair from table, then

c = - 1

y = - [tex]\frac{5}{2}[/tex] x - 1 ← equation of line

Answer:

J. 56

Step-by-step explanation:

The picture in this question can be a little deceiving. Each rectangular glass pane is 3 by 10 inches. This means that the picture of the 4 panes overlapping, leaves the center square open. The open area has your inner edges. The question asks for the sum of the inner and outer edges.

Every pane is 10 inches long, so the out perimeter of the figure is 40 inches because the figure has four sides. The rectangles overlap, creating 3 by 3 inch square. 3 inches off either side of a pane leaves 4 inches as the length for the edge of the inner square. Therefore, the perimeter of the inner square is 16 inches.

Outer Perimeter + Inner Perimeter = 40 + 16 = 56 inches

Answer:

[tex]\boxed{\mathtt{Area \approx 227ft^{2}}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to find the area of a circle.}[/tex]

[tex]\textsf{First, we should identify the formula for the area of a circle.}[/tex]

[tex]\large\underline{\textsf{Formula:}}[/tex]

[tex]\mathtt{Area = \pi (radius)^{2}}[/tex]

[tex]\textsf{The radius is \underline{half} of the diameter.}[/tex]

[tex]\mathtt{\frac{17}{2} = 8.5ft.}[/tex]

[tex]\textsf{Let's begin solving for the area.}[/tex]

[tex]\large\underline{\textsf{Substitute:}}[/tex]

[tex]\mathtt{Area = \pi (8.5)^{2}}[/tex]

[tex]\mathtt{Area = 72.25 \pi}[/tex]

[tex]\boxed{\mathtt{Area \approx 227ft^{2}}}[/tex]

The mass of the sheet of metal is 200g. This can also be expressed in other units, such as 0.2 kg or 0.002 tonnes.

The mass of a sheet of metal is directly related to its area and thickness. This means that the mass of a sheet of metal is proportional to the product of its area and its thickness. Mathematically, this can be expressed as the formula M = kAT, where M is the mass, k is a constant, A is the area and T is the thickness.In the given example of a sheet of metal with an area of 250 cm and a thickness of 1mm, we can calculate the mass of the sheet by substituting the given values into the formula: M = k(250)(1) = 200g. The constant k in this example is equal to 0.8 g/cm*mm.Therefore, the mass of the sheet of metal is 200g. This can also be expressed in other units, such as 0.2 kg or 0.002 tonnes.

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What is the mass of a sheet of metal with an area of 250cm and a thickness of 1mm?

Answer:

plot the point at 1

Step-by-step explanation:

Find CD:

Let,

[tex]r_1[/tex] be a radius of Circle A

[tex]r_2[/tex] be a radius of Circle B

Given:

[tex]r=4cm.[/tex]

Circumference: [tex]2\pi r[/tex]

[tex]2\pi r_1=30[/tex]

[tex]r_1=\dfrac{15}{\pi }[/tex]

[tex]CD=D_1+D_2[/tex]

[tex]=2r_1+2rx_2[/tex]

[tex]=2\times(\dfrac{15}{\pi })+2\times4[/tex]

[tex]CD=17.55cm.[/tex]

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Therefore , the solution of the given problem of area comes out to be

A = 16 is the equation that accurately depicts how to calculate the sector's area.

Its total size can be determined by figuring out how much space is required to completely cover the outside. The immediate surroundings are taken into consideration when calculating the surface of a trapezoidal shape. The total measurements of something are determined by its surface area. A cuboid's capacity for internal water is determined by the sum of the borders that link all of it's six rectangle edges.

Here,

The formula for calculating a circle's sector's area is:

=> A = (θ/360) x πr²

where A is the sector's area, is its central angle measurement, and r is the circle's radius.

Since the radius is 8 cm and the central angle is 90 degrees in this instance, we can reduce by plugging in these values:

=> A = (90/360) x π(8²)

=>  A = (1/4) x π(64)

=>  A = π(16)

=>  A = 16π

A = 16 is the equation that accurately depicts how to calculate the sector's area.

The answer will be given in radius squared units, in this case, cm2.

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Option D. The correct calculation of the area of the sector is      [tex]A=(\frac{90}{360}) * (\pi 8^{2} )[/tex]

An area of the sector is the portion of the area of a circle that is enclosed by two radii and an arc. The area of a sector can be found using the formula:

A = (θ/360)πr²

where A is the area of the sector, θ is the central angle of the sector (in degrees), π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

Given, the radius is 8 cm and the central angle is 90° in this instance, put all these values:

[tex]A=(\frac{90}{360}) * \pi (8^{2} )[/tex]

or we can write down, [tex]A=(\frac{90}{360}) * (\pi 8^{2} )[/tex]

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Answer:

900 cubic feet

Step-by-step explanation:

[tex] \frac{1}{2} (15 \times 12 \times 10) = \frac{1}{2} (1800) = 900[/tex]

The equation is -7x+y=0.

A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.

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

Left side equals right side in all formulas.

To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.

A statement is not an equation if it lacks the equals sign. When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.

Hence, The equation is -7x+y=0.

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Answer:

-16²+1,000 > 300  [After an edit in the original expression, as noted below).

Step-by-step explanation:

The equation d = -16² +1,000 tells us the height above ground, d, of the object after t seconds.  When t = 0 seconds, the ball has not been dropped yet, but the equation tells us that d = 1,000 at t = 0.  That means the object starts at 1,000 feet above ground.

We want the time it takes for the object to reach any height greater than 300 feet above ground.  This is a tad (metric for just a tiny bit) unexpected, since even at time of 0 the object is greater than 1,000 feet.

Looking at the answer options, note that the left side of the inequalities is -16^2+100.  I will assume the 4th option has a typo:  the f^2.  It should read the same as the others.  

      -16^2+100 is the distance, d.  So to help us think this through, let's rephrase the answer options in terms of distance, d:

1)    d<300

2)   d≤300

3)   d≥300

4)   d>300

   The question asks "We want the time it takes for the object to reach any height greater than 300 feet above ground."

Option 4 says d>300, or height greater than 300.  That is the inequality that matches the question.  [Note:  It did not say greater than or equal to (option 3).]

Optiοn B. is cοrrect, the result οf substituting fοr y in the given equatiοns is x - 3 =x² + 2x - 4.

Equivalent expressiοns are expressiοns that wοrk the same even thοugh they lοοk different. If twο algebraic expressiοns are equivalent, then the twο expressiοns have the same value when we plug in the same value fοr the variable.

Tο substitute fοr y in the secοnd equatiοn, we can replace y with its equivalent expressiοn in terms οf x frοm the first equatiοn, which gives us:

x - 3 = x² + 2x - 4

This is option B.

Optiοn A is incοrrect because it substitutes y fοr its expressiοn in terms οf x in the wrοng equatiοn.

Optiοn C is incοrrect because it subtracts (x-3) instead οf adding it tο the secοnd equatiοn.

Optiοn D is incοrrect because it sets the expressiοn fοr y in the first equatiοn equal tο x² instead οf the expressiοn fοr y in the secοnd equatiοn.

Hence, οptiοn B. is cοrrect, the result οf substituting fοr y in the given equatiοns is x - 3 = x² + 2x - 4.

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Complete question:

What is result of substituting for y in the bottom equation?

y = x – 3,

y = x² + 2x – 4

A. y=(x-3)²+2(x-3)-4

B. x-3=x²+2x-4

C. y=x²+2x-4-(x-3)

D. (x-3)=x²

Answer:

He is now selling only one product and making less money because he is not selling other TVs.

Step-by-step explanation:

So if you read the paragraph, you get to the point where he says only making and selling the television model that makes the most money. If you think about it if they only sell one product, the other products they used to sell aren't being sold and they are making less money. I hope this helps!

The cumulative distribution function gives us the probability that the random variable is less than or equal to a given value.

The cumulative distribution function (CDF) of a continuous random variable x is a function which gives the probability that the random variable x is less than or equal to a given value x. Mathematically it is expressed as:

[tex]F(x) = P(X ≤ x)[/tex]

The calculation of the cumulative distribution function is done by integrating the probability density function (PDF) from the lower limit to the given value x. Thus,

[tex]F(x) = ∫-∞ x f(u) du[/tex]

Where f(u) is the probability density function.

For example, if we have a continuous random variable x with probability density function f(x) = x2, then the cumulative distribution function [tex]F(x) = ∫-∞ x x2 du = 1/3x3 + c.[/tex]

Thus, It is a powerful tool for analysing the probability distribution of a continuous random variable.

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Complete question:

What is the cumulative distribution function for a continuous random variable x?

Absolutely, Jada's response is right. A square is a quadrilateral with four equal-length sides. A quadrilateral is a square if all four sides measure 5 cm.

Unfortunately, there is no alternative form Jada could have drawn that meets the requirement of all four sides measuring 5 cm. Every other quadrilateral with four equal-length sides is likewise a square. If Jada had drawn a quadrilateral with one or more sides of varying lengths, the specified criterion would not have been met. As a result, the only design Jada could have sketched that meets the requirement of having all four sides measure 5 cm is a square. It is worthwhile to investigate the properties of quadrilaterals and how they connect to the conditions presented in the problem. A quadrilateral is a four-sided polygon. Quadrilaterals come in a variety of shapes, including squares, rectangles, parallelograms, trapezoids, and kites. Certain quadrilaterals have unique qualities, such as opposing sides that are parallel or all angles that are right angles. The criterion in the provided problem is that all four sides of the quadrilateral measure 5 cm.

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The difference in the loudness of sound when the two teams score is about 14.77 decibels

Sound intensity is defined as the power carried by sound waves per unit area in a direction perpendicular to that area.

We can use the fact that the loudness of sound is measured in decibels (dB) and that the dB scale is logarithmic.

Let's assume that the loudness of the sound when the away team scores is x decibels. Then the loudness of the sound when the home team scores a touchdown is 30 times as great, which means it is 30x decibels.

The difference in loudness between the two scenarios is given by the difference in decibels:

difference in decibels = 10 log (30x/x) = 10 log 30 = 14.77

Therefore, the difference in the loudness of sound when the two teams score is about 14.77 decibels

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The height, in meters, where the pumpkin lands on the hill is 4.9 meters.The equation for the height of the hill is y = 0.9x.

This equation can be rearranged to solve for x, giving x = y/0.9. The equation for the height of the pumpkin is y = -0.1x² + 4.9x. Substituting the x value from the previous equation into the equation for the height of the pumpkin gives y = -0.1(y/0.9)² + 4.9(y/0.9). Simplifying this equation gives y = 4.9, which is the height, in meters, where the pumpkin lands on the hill.

The equation for the height of the hill is y = 0.9x, which describes the incline of the hill. This equation can be rearranged to solve for x, giving x = y/0.9. This equation can then be used to substitute into the equation for the height of the pumpkin, which is y = -0.1x² + 4.9x. When the x value from the previous equation is substituted into the equation for the height of the pumpkin, the equation simplifies to y = -0.1(y/0.9)² + 4.9(y/0.9). Simplifying further gives y = 4.9, which is the height, in meters, where the pumpkin lands on the hill. This can be verified by substituting 4.9 for y in the equation for the height of the hill, which gives x = 4.9/0.9 = 5.4. This value can be substituted into the equation for the height of the pumpkin, which gives y = -0.1(5.4)² + 4.9(5.4) = 4.9, verifying the result.

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The magnitude of the earthquake with an amplitude of 100,000 is 2 on the Richter scale

Magnitude: The magnitude of an earthquake is a measure of the amount of energy released during the earthquake. It is typically determined using a logarithmic scale called the Richter scale or other similar scales like the moment magnitude scale (MMS), surface wave magnitude (Ms), or body wave magnitude (Mb). The Richter scale is based on the amplitude of the largest seismic wave recorded on a seismographs, and each increase of one unit on the scale corresponds to a ten-fold increase in the amplitude of the seismic waves and a 32-fold increase in the amount of energy released.

Amplitude: The amplitude of an earthquake is the size of the seismic waves that are generated by the earthquake. It is measured in microns (millionths of a meter) and is recorded on a seismographs. The amplitude of seismic waves can vary greatly depending on the distance from the earthquake's epicenter and the geological structure of the surrounding area.

The magnitude of an earthquake is a measure of the amount of energy released during the earthquake, and is typically determined using a logarithmic scale called the Richter scale.

The formula for calculating the magnitude of an earthquake based on its amplitude is:

Magnitude = log10 (Amplitude) - 3

where the amplitude is measured in microns.

Assuming the amplitude of the earthquake is 100,000 microns, we can calculate its magnitude as:

Magnitude = log10 (100,000) - 3

Magnitude = 5 - 3

Magnitude = 2

Therefore, the magnitude of the earthquake with an amplitude of 100,000 is 2 on the Richter scale.

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Answer:6 feet

Step-by-step explanation:

The formula for the area of a parallelogram is:

Area = base x height

We know that the area is 60 square feet and the height is 10 feet, so we can plug these values into the formula and solve for the base:

60 square feet = base x 10 feet

Dividing both sides by 10 feet gives:

6 feet = base

Answer:

P(0,2), Q(3,5), R(3,0)

Step-by-step explanation:

The equation of the given graph is: y = cosine (x + pi)

By convention, the cosine function like most other trigonometric functions has a period of 2π.

Since, the parental function is y = cos x, which has y-intercept at y = 1, and x-intercept at π/2.

From observation, the function showed in the graph attached has y-intercept at y = -1 and x-intercept at π/2.

This can be interpreted to mean that the function has been translated leftwards π units.

Ultimately, the function that belongs to this graph is; y = cosine (x + pi)

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Answer: D. y = cosine (x + pi)

Step-by-step explanation:

Answer:

£602.84 in New York

Step-by-step explanation:

London Cost:

Converting pound to dollars:

£800 * 1.41 = $1128

Paris cost:

Converting euro to pounds:

€880/1.16 = £759

Converting pound to dollars again:

£759 * 1.41 = $1070

New york cost:

$850

The lowest price is in new york which is:

$850/1.41 = £602.84

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