Which of the diagrams A-D shows the locus of points inside the rectangle PQRS that are 5 m away from the edge QR? A с S P₁ S 5m 5m E 1Q R 7Q R B P S P₁ S 5m 5m 1Q R 1Q R​

The solution to the given system of equations y = x² + 10x + 11, y = x² + x - 7 is x = -2, y = -5.

The given set of equations

y = x² + 10x + 11 --- eqn(1)

y = x² + x - 7 --- eqn(2)

Solving the equations by elimination method

⇒ Subtracting eqn 2 from eqn 1, we get

⇒ y - y = x² + 10x + 11 - (x² + x - 7)

⇒ 0 = x² + 10x + 11 - x² - x + 7

⇒ 0 = 9x + 18

⇒ 9x = -18

⇒ x = -2

Put the value of x in eqn 1, and we get

⇒ y = (-2)² + 10(-2) + 11

⇒ y = 4 - 20 + 11

⇒ y = -5

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The percentage of his income that he pays in taxes would be = 32%

Taxes is defined as the amount that is paid to the government by working class individuals as a way of generating internal revenue for the country.

The total amount of money made by Mr. Sullivan = $24,000

The amount of tax paid for the wedges = $7,700

The percentage of the income paid as tax would be calculated as;

= 7700/24000 × 100

= 770000/24000

= 32.01

= 32%

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The number of meters that he travel farther will be 2,000 meters.

The distance covered by the particle or the body in an hour is called the average speed. It is a scalar quantity. It is the ratio of the total distance to the total time.

We know that the average speed formula is given as,

Average speed = Total distance / Total time

Shawn take 2 minutes to cycle 800 m. Then the average speed is calculated as,

Average speed = 800 / 2

Average speed = 400 meters per minute

If he continues to cycle for another 5 minutes at the same average speed. Then the total distance is calculated as,

400 = Total distance / 5

Total distance = 400 x 5

Total distance = 2,000 meters

The number of meters that he travel farther will be 2,000 meters.

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The average speed is 400 m/ min and the distance covered in 5 minutes is 2000 m.

Given:

Time= 2 min

Distance = 800 m

So, speed= Distance / time

speed = 800/ 2

speed = 400 m/ min

Now, fir time= 5 min

Distance= speed x time

D = 400 x 5

D= 2000m

Hence, the distance covered is 2000m.

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Answer:

17°

Step-by-step explanation:

m∠1 = m∠2.

Set the expressions for 1 and 2 equal to each other.

6x + 5 = 9x - 46

Separate x's on one side.

3x = 51

x = 17

The Area of a triangle whose height is 8 feet and has a base length of t feet is; 20 ft².

It follows from the task content that the area of the triangle whose height is 8 feet and base length is 5 feet be determined.

Since the area of a triangle is given by;

A = 1/2 × b × h

Therefore, the area of the triangle in discuss can be determined as follows;

Area, A = 1/2 × 8 × 5

Area, A = 20 ft².

On this note, it follows that the area of the triangle is; 20 ft².

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Answer:

20 square feet

Step-by-step explanation:

The formula for the area of a triangle is:

[tex]\boxed{A=\dfrac{1}{2}bh}[/tex]

where:

Given the base of the triangle is 5 feet, and the height is 8 feet, substitute b = 5 and h = 8 into the formula and solve for A:

[tex]\begin{aligned}\implies A&=\dfrac{1}{2} \cdot 5 \cdot 8\\\\&=\dfrac{5}{2} \cdot 8\\\\&=\dfrac{5 \cdot 8}{2}\\\\&=\dfrac{40}{2}\\\\&=20\; \sf ft^2\end{aligned}[/tex]

Therefore, the area of a triangle that has a height of 8 feet and a base length of 5 feet is 20 square feet.

The relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”.

Now, According to the question:

What is inequality?

A statement involving the symbols '>', '<', ' ≥', '≤' is called an inequality. For example 5 > 3, x ≤ 4, x + y ≥ 9.

(i) Inequalities which do not involve variables are called numerical inequalities. For example 3 < 8, 5 ≥ 2.

We use the equal sign "=" to say that two things are the same. However, sometimes we just want to show that something is bigger or smaller than something else. Or maybe we just want to say that two things are not equal. These cases are called inequalities.

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The value of integral is [tex]\frac{1}{2 \sqrt{5}} \tan ^{-1}\left(\frac{t^2}{\sqrt{5}}\right)+C$$[/tex]

The Integral is [tex]$$\int \frac{t}{t^4+5} d t$$[/tex]

Indefinite integrals are not defined using the upper and lower limits. The indefinite integrals represent the family of the given function whose derivatives are f, and it returns a function of the independent variable.

Let [tex]$t^2=u= > t d t=\frac{d u}{2}$[/tex]

The above Integral becomes

[tex]$\frac{1}{2} \int \frac{1}{u^2+(\sqrt{5})^2} d u=\frac{1}{2 \sqrt{5}} \tan ^{-1}\left(\frac{u}{\sqrt{5}}\right)+C$$[/tex]

Substitute u In terms of t

[tex]$$\int \frac{t}{t^4+5} d t=\frac{1}{2 \sqrt{5}} \tan ^{-1}\left(\frac{t^2}{\sqrt{5}}\right)+C$$[/tex]

Therefore, the value of integral is [tex]\frac{1}{2 \sqrt{5}} \tan ^{-1}\left(\frac{t^2}{\sqrt{5}}\right)+C$$[/tex].

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The solutions for the given equation are (0, 0), (1, 2.5), (2, 5) and (3, 7.5).

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is y=5/2 x.

Substitute x=0, 1, 2, 3, 4,......

When x=0

y=0

When x=1

y=5/2=2.5

When x=2

y=5

When x=3

y=7.5

Therefore, the solutions for the given equation are (0, 0), (1, 2.5), (2, 5) and (3, 7.5).

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

Use the equation y=5/2 x to complete the table. Is y proportional to x? Explain why or why not.

The cost of 1 water canteen will be $12.6 using the equation 54+10w=182.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations.

When performing calculations but unsure of the precise amount, algebra is used.

So, we have:

Subtotal of $182.

Each lantern costs $5.40 and each water canteen costs w dollars.

Now, an equation that will determine total cost using w will be:

Let C be the total cost, then calculate as the cost of 1 water canteen:

10*5.40 + 10w = 182

54+10w=182

10w = 180 - 54

10w = 126

w = 126/10

w = $12.6

Therefore, the cost of 1 water canteen will be $12.6 using the equation 54+10w=182.

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The definite integral is [tex]$$\left(r^{\wedge} 3\right) /\left(\text { sqrt }\left(4+r^{\wedge} 2\right)\right) d r$$[/tex] [tex]=0.116[/tex].

As per given data,

Definite Integral helps to find the area of a curve in a graph. It has limits, which are the start and the endpoints, within which the area under a curve is calculated. The limit points can be taken as [a, b], to find the area of the curve f(x), with respect to the x-axis.

Here,

∫ = Integration symbol

a = Lower limit

b = Upper limit

f(x) = Integrand

dx = Integrating agent

Thus, ∫ab f(x) dx is read as the definite integral of f(x) with respect to dx from a to b.

Indefinite integrals are implemented when the boundaries of the integrand are not specified.

Consider the following integral:

[tex]$$\int_0^1 \frac{r^3}{\sqrt{4+r^2}} d r$$[/tex]

The objective is to evaluate the integral, using substitution method.

Let [tex]$u=4+r^2 \rightarrow r^2=u-4$[/tex]

[tex]$$\begin{aligned}& d u=2 r d r \\& r d r=\frac{d u}{2}\end{aligned}$$[/tex]

when [tex]$r=0$[/tex], then [tex]$u=4$[/tex]

When [tex]r =1[/tex], then [tex]u=5[/tex]

Use the above details to evaluate the integral.

[tex]& =\frac{1}{2}\left[\frac{2 u^{\frac{3}{2}}}{3}-8 \sqrt{u}\right]_4^5 \\& =\left[\frac{u^{\frac{3}{2}}}{3}-4 \sqrt{u}\right]_4^5 \\& =0.116 \\& =\frac{5^{\frac{3}{2}}}{3}-4 \sqrt{5}-\frac{4^{\frac{3}{2}}}{3}+8 \\& =0.11585 \\& \left.=\left[\frac{5^{\frac{3}{2}}}{3}-4 \sqrt{5}\right]^{-}\left(\frac{4^{\frac{3}{2}}}{3}-4 \sqrt{4}\right)\right][/tex]

[tex]$$& \int_0^1 \frac{r^3}{\sqrt{4+r^2}} d r=\int_0^1 \frac{r^2}{\sqrt{4+r^2}}(r d r) \\& =\int_4^5 \frac{(u-4)}{\sqrt{u}}\left(\frac{d u}{2}\right) \\& =\frac{1}{2} \int_4^5 \frac{(u-4)}{\sqrt{u}} d u \\& =\frac{1}{2} \int_4^5\left(\sqrt{u}-\frac{4}{\sqrt{u}}\right)^{d u} \\[/tex]

[tex]& =\left[\frac{u^{\frac{3}{2}}}{3}-4 \sqrt{u}\right]_4^5 \\& =0.116 \\& =\frac{5^{\frac{3}{2}}}{3}-4 \sqrt{5}-\frac{4^{\frac{3}{2}}}{3}+8 \\& =0.11585 \\& \left.=\left[\frac{5^{\frac{3}{2}}}{3}-4 \sqrt{5}\right]^{-}\left(\frac{4^{\frac{3}{2}}}{3}-4 \sqrt{4}\right)\right][/tex]

Therefore, the evaluated integral is 0.116.

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The perimeter of the rectangle is 19.93 meter and the area of the rectangle is 22.22 sq. meter.

Here one side of the rectangle is 3( 3/10 ) and the other side is 6 (2/3 ) meter respectively.

Perimeter of the rectangle is 2 ( l + w ) and the Area of the rectangle is (l)*(w), where l is the length and w is the width of the rectangle.

Perimeter = 2(3 3/10 + 6 2/3) = 2(3.3 + 6.666667) = 2(9.96667) = 19.93334 meters

To find the area of a rectangle, we multiply the length by the width. The area of a rectangle with side lengths of 3 3/10 meters and 6 2/3 meters is:

Area = (3 3/10) * (6 2/3) = 3.3 * 6.666667 = 22.222222 square meters

Note that you can convert the mixed numbers to decimals, since it's more convenient to work with decimals when solving arithmetic problems.

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Answer:

To find the final balance of an account earning interest compounded continuously, you can use the formula:

A = Pe^(rt)

where A is the final account balance, P is the initial principal (or starting) amount, r is the interest rate, and t is the time (in years) for which the interest is being calculated.

Substituting in the given values:

A = 500 * e^(0.07 * 20)

An open box is to be constructed from a square area piece of sheet metal, then the dimension of the sheet​ metal is,

[tex]l = 5 feet[/tex] , [tex]b = 5 feet[/tex] , [tex]h = 24.2 feet[/tex]

Given that,

An open box length [tex]l[/tex] = 5 feet

An open box breadth b = 5 feet

An open box height = h

An open box area = 605 cubic feet

A square is a four-sided polygon which has it's all sides equal in length and the measure of the angles are 90 degrees. The shape of the square is such as, if it is cut by a plane from the center, then both the halves are symmetrical. Each half of the square then looks like a rectangle with opposite sides equal.

Area = [tex]l * b * h[/tex]    (Equation - 1)

So,

We can substitute l , b , h values in the equation - 1,

605 = 5 * 5 * h

605 = 25 * h

605/25 = h

24.2 = h

Therefore,

An open box is to be constructed from a square area piece of sheet metal, then the dimension of the sheet​ metal is,

[tex]l = 5 feet[/tex] , [tex]b = 5 feet[/tex] , [tex]h = 24.2 feet[/tex]

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Calculation for the videorecorder:

A) Hire Purchase Price: $2700

B) Monthly Instalment: $233.33

C) Difference between the hire purchase price and the cash price: $540

D) Difference as a percentage of the cash price: 20%

Solution:

A) The hire purchase price is the total cost of the item, which in this case is $2700.

B) The monthly instalment is calculated by taking the total cost of the item and subtracting the initial deposit (20% of the cash price), which is $540, and then dividing this amount by 12 (the number of months). Therefore, the monthly instalment is $233.33.

C) The difference between the hire purchase price and the cash price is calculated by taking the hire purchase price of $2700 and subtracting the cash price of $2160 (which is 80% of the hire purchase price). Therefore, the difference is $540.

D) The difference as a percentage of the cash price is calculated by taking the difference between the hire purchase price and the cash price ($540) and dividing it by the cash price ($2160). Therefore, the difference is 20%.

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Longitudes: The vertical lines running north-south, join the two poles. They are called the meridians of longitude. They are spaced farthest apart at the equator and converge at a point at each pole.

Horizontal lines called latitudes are used to measure distances north or south of the equator. Vertical lines known as longitudes are used to determine the west or east of the meridian in Greenwich, England. Latitude and longitude work together to help cartographers, geographers, and others find specific locations on the globe.

What is the uses of latitude?

Any location's distance from the equator may be determined using its latitude, which is based on its degree. We can locate any point on Earth using longitude and latitude. The GPS or Global Positioning System uses these coordinates.

The grid system that enables us to locate absolute or precise places on the surface of the Earth is made up of latitude and longitude. Latitude and longitude can be used to pinpoint certain locations. Landmark identification also benefits from knowledge of latitude and longitude.

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Answer:

2x^7

Step-by-step explanation:

To simplify this expression, there are two steps. You have to act as though the exponents are whole numbers and add them together to combine like terms.

[tex]2x^4 \times x^3\\= 2x^{4+3}\\= 2x^7[/tex]

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Using the quadratic function for the company to break even the company should charge at least $ 15 for it's product but no more than $ 50.

A quadratic function is an equation in which the highest power of the unknown is 2.

Since we have the function f(x) = -0.5x² + 32.5x - 375, to determine the value of x at which the company breaks even, we equate f(x) to zero and solve for x.

So, f(x) = 0

⇒ -0.5x² + 32.5x - 375 = 0

So, using the quadratic formula, we solve for x

so, [tex]x = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]

where

So, substituting the values of the variables into the equation, we have that

[tex]x = \frac{-32.5 +/- \sqrt{(32.5)^{2} - 4\times(-0.5)\times(-375)} }{2\times(-0.5)}\\= \frac{-32.5 +/- \sqrt{1056.25 - 750} }{-1}\\= \frac{-32.5 +/- \sqrt{306.25} }{-1}\\= \frac{-32.5 +/- 17.5 }{-1} \\x = \frac{-32.5 - 17.5 }{-1} or x = = \frac{-32.5 + 17.5 }{-1} \\x = \frac{-50}{-1} or x = \frac{-15}{-1} \\x = 50 or x = 15[/tex]

So, for the company to break even the company should charge at least $ 15 for it's product but no more than $ 50.

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Answer: Value of p= 28

Step-by-step explanation:

Use remainder theorem to find the value of p

K(x) = 2x^3+4x^2+px-12  is take f(x)

           (x + 3)  

 f(3)  = 21

f(3)    = 2*3^3+4*3^2+p*3-12

           = 2*27+4*9+3p-12

           = 54+36+3p-12= -6

           =  90-12+3p = -6

           =78+3p = -6

           = 3p = 78--6

                     =78+6

              3p  = 84

              p = 84/3

                 = 28

The value of p is 28

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Sound decibel are not additive because humans listen to sound logarithmically and LaTrenda is correct

Osman is not correct in his claim that 88 + 75 decibels would be 163 decibels. The decibel unit is not an additive unit, meaning that when you add the decibel levels of two different sound sources, you do not simply add the decibel levels.

Instead, adding the decibel levels of two different sound sources together would give you the total sound pressure level (SPL) of the combined sound.

To calculate the SPL of the combined sound, you would need to add the intensities of the two sounds and then calculate the decibel level of the combined sound using the formula:

SPL (dB) = 10 log10 (I1/I0) + 10 log10 (I2/I0)

Where I1 and I2 are the intensities of the two sound sources and I0 is the reference intensity, which is the threshold of human hearing.

It would make more sense to add the intensities of the two sounds and then calculate the number of decibels, because the human ear perceives loudness of sounds logarithmically, not linearly.

So, LaTrenda would be correct in this scenario.

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There is percent decrease of 30%

50 pounds to 35 pounds

Original amount = 50 pounds

New amount= 35 pounds

Since, New amount is less than the original amount, this is a percentage of decrease.

Change in amount = 35 -50

Change in amount = -15 pounds

Substitute the given values we have;

% change = (change/original value) x 100

% change = -(15/50) x 100

% change = - 30%

Therefore, there is percent of decrease which is 30%.

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yes there is no work show below

Answer:

  4y

Step-by-step explanation:

You want to simplify the expression (12x²y)/(3x²).

When reducing any fractions, common factors in the numerator and denominator are cancelled. Here, the factor 3x² in the numerator is cancelled by the same factor in the denominator.

  [tex]\dfrac{12x^2y}{3x^2}=\dfrac{(3x^2)(4y)}{(3x^2)}=\boxed{4y}[/tex]

The amplitude of a sine or cosine function is the vertical stretch or compression factor of the function. In this case, the function f(x) = sin(x) has been stretched vertically by a factor of 3. Therefore, the amplitude of the function g(x) is A = 3.

The function g(x) = 3sin(12x) + (-5)

Answer:

Three lines of symmetry.

Step-by-step explanation:

A figure is symmetrical when it is made up of exactly similar parts facing each other or around an axis.

See the attached photo.

There are 3 symmetrical lines:

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The range of the given constant function y = -5 is {-5}.

The range of a function is the set of all possible output values (y-values) that the function can produce for any input value (x-value).

y = -5 is a constant function, which means that the output value is always equal to -5 for any input value, the range of this function would be the set of real numbers that contain only the value -5.

So the range of y = -5 is {-5}.

A constant function is a special kind of function that always returns the same output value regardless of the input value.

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The color of Everett's jumpsuit is given as follows:

Pink.

The color of Everett's jumpsuit is obtained considering the patterns in this problem, which are given by each of the sentences.

The jumper who wears the yellow suit started skydiving 1 year after Everett, which means that Everett does not wear yellow.

The jumper who wears the aquamarine suit started skydiving sometime before Gordon, which means that Everett could have worn the aquamarine suit.

Francisco started skydiving 2 years after Everett, which means that Everett jumped either in 1982 or in 1983.

Rodney started skydiving sometime after the skydiver who wears the pink suit, hence the order is given as follows:

Everett - Rodney - Francisco - Gordon.

From 4, we have that Everett wore the pink suit.

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To enlarge a shape by a scale factor of 1/3, you would need to reduce its size by multiplying the dimensions of the shape by 1/3. This can be done by dividing the length and width of the shape by 3.

when we say "enlarge a shape by a scale factor" it means to change the size of the shape by a certain percentage. A scale factor of 1/3 means that the new shape will be 1/3 the size of the original.

To accomplish this, you would need to multiply the length and width of each side of the shape by 1/3.

For example, If a shape has a length of 6 and a width of 4, to reduce it by 1/3, the new shape will have a length of 61/3=2 and a width of 41/3=1.3(approximately).

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What graph are you talking about?

Answer:

Exact Form:

r=√143.36346562,    −√143.36346562

Decimal Form:

r

=

11.97344835

…

,

−

11.97344835

…

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer: B

Step-by-step explanation: You are adding the shirts times the amount, hence X the variable plus the money already spent to then be less then the 200 dollar maximum.