For the following word problems, first write a system of equations then solve for full marks.

3. The perimeter of a rectangle is 64 cm. Twice the width is 4 cm more than the length.
Find the dimensions of the rectangle.

The series of transformation that would map the quadrilateral in figure G to the quadrilateral in figure H are;

A geometric transformation involves either a change in location, size, or orientation or a combination of changes of a geometric figure.

The possible polygon with vertices in the question obtained from a similar question online and drawn using MS Excel is attached;

The vertices of the polygon are;

The coordinates of the vertices of Figure G; (-2, 7), (-6, 3), (-1, 5), (-1, 1)

The coordinates of the corresponding vertices of Figure H; (5, 7), (9, 3), (4, 5), (4, 1)

The y-values of figure G and figure H are the same, while the x-values changes both value and sign.

The coordinates of the point (x, y), following a reflection about the y-axis is the point (-x, y)

Therefore, the possible transformation that maps figure G unto figure H includes a reflection across the y-axis;

The coordinates of the vertices of figure G following a reflection about the y-axis are;

Image of figure G following a reflection about the y-axis; (2, 7), (6, 3), (1, 5), and (1, 1)

The transformation that maps the image produced by the reflection and figure H are;

Transformation (5 - 3, 7 - 7) = (3, 0)

(9 - 6, 3 - 3) = (3, 0)

(4 - 1, 5 - 5) = (3, 0)

(4 - 1, 1 - 1) = (3, 0)

The transformation that maps the image of figure G to figure H is therefore T₍₃, ₀₎, which is a translation of 3 units to the right.

The series of transformation that maps figure G to figure H are therefore;

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Speed of rocket travelling at 150 m/h into feet per second is 0.1367 feet per second

3.28084 feet is about equal to one meter. Multiply 3.28084 feet to the given meter value to convert

According to the given information

Speed of rocket in meter per hour is 150 m/h

To know the speed of rocket in feet per second

1 meter = 3.280 feet

15o meter = 150 × 3.280

                 = 492 feet

1 hour = 60 × 60

          = 3600 second

So,

speed of rocket in feet per second = [tex]\frac{492}{3600}[/tex]

                                                          = 0.1367 feet per second

Speed of rocket travelling at 150 m/h into feet per second is 0.1367 feet per second

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Monthly payment option 1 = $300,000 / 166.79161 = $1,798.65 and the monthly payment option 2 = $300,000 / 130.7201 = $2,294.98.

The numbers are missing, so I looked for similar questions to fill in the blanks:

You need a ​$300,000 loan. Option​ 1: a​ 30-year loan at an APR of 6​%. Option​ 2: a​ 15-year loan at an APR of ​4.5%.

We can use the present value of an annuity formula to calculate monthly payments.

Present value = monthly payment x PV annuity factor

Monthly payment = present value / PV annuity factor

Present value = $300,000

Option 1: PV annuity factor, 0.5%, 360 periods = 166.79161

Option 2: PV annuity factor, 0.375%, 180 periods = 130.7201

Monthly payment option 1 = $300,000 / 166.79161 = $1,798.65

Monthly payment option 2 = $300,000 / 130.7201 = $2,294.98

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The two quadrilaterals JKLQ and LMNP are congruent.

What is congruent quadrilaterals?

You will always have two opposite pairs of parallel sides if the two pairs of opposite sides in a quadrilateral are congruent. They must measure similarly to be considered congruent. Consider this: two congruent sides must always maintain the same separation between the opposing lines to maintain the other pair of opposite sides.

To prove that all corresponding pairs of sides and angles are congruent, you must put the interior angles and sides of one quadrilateral in correspondence with those of another.

For the given quadrilaterals JKLQ and LMNP it is given that,

JK ≅ MN, JQ ≅ NP, QL ≅ PL and  KL ≅ ML

Also,

∠J ≅ ∠N, ∠Q ≅ ∠P, ∠K ≅ ∠M, and ∠L is the common for both quadrilaterals.

Here the corresponding sides and angles of the quadrilaterals are congruent.

Hence, the two quadrilaterals JKLQ and LMNP are congruent.

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The critical points of the given function are p = 2 ± √13.

A relation between a collection of inputs and outputs is known as a function.

A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Each function has a range, codomain, and domain.

Critical function:

The key points are locations inside the function's domain where the function's nature changes.

The function stops increasing or decreasing at these places.

The function is: [tex]h(p)=\frac{p-2}{p^2+9}[/tex]

The derivative test will be applied here:

[tex]\begin{aligned}& \therefore h^{\prime}(p)=0 \\& \Rightarrow \frac{d}{d p}\left(\frac{p-2}{p^2+9}\right)=0 \\& \Rightarrow \frac{\frac{d}{d p}(p-2)\left(p^2+9\right)-\frac{d}{d p}\left(p^2+9\right)(p-2)}{\left(p^2+9\right)^2}=0 \\& \Rightarrow \frac{1 \cdot\left(p^2+9\right)-2 p(p-2)}{\left(p^2+9\right)^2}=0 \\& \Rightarrow \frac{-p^2+4 p+9}{\left(p^2+9\right)^2}=0 \\& \Rightarrow-p^2+4 p+9=0\end{aligned}[/tex]

Then,

[tex]\begin{aligned}& \Rightarrow p_{1,2}=\frac{-4 \pm \sqrt{4^2-4(-1) 9}}{2(-1)} \\& \Rightarrow p_{1,2}=\frac{-4 \pm \sqrt{52}}{-2} \\& \Rightarrow p_{1,2}=-\frac{-4 \pm \sqrt{52}}{2} \\& \Rightarrow p_{1,2}=-\frac{-4 \pm 2 \sqrt{13}}{2} \\& \Rightarrow p_{1,2}=2 \pm \sqrt{13}\end{aligned}[/tex]

Therefore, the critical points of the given function are p = 2 ± √13.

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The values of sin 2θ, cos 2θ, and tan 2θ are:

a) sin 2θ = √(3)/2

b) cos 2θ = 1/2

c) tan 2θ = √(3)

Generally, If sin θ = 1/2 and θ is in quadrant I, then θ is equal to 30 degrees.

To evaluate each expression, we can use the trigonometric identities:

a) sin 2θ = 2 * sin θ * cos θ

= 2 * (1/2) * (√(3)/2)

= √(3)/2

b) cos 2θ = cos^2 θ - sin^2 θ

= (√(3)/2)^2 - (1/2)^2

= (3-1)/4 = 1/2

c) tan 2θ = (2 * tan θ) / (1 - tan^2 θ)

= (2 * (√(3)/3)) / (1 - (√(3)/3)^2)

= 2 * √(3) / (4 - 3)

= √(3)

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The circle which shows the distribution of the money has been attached.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

In our daily life, we always see circular objects for example our bike wheel.

As per the given,

The team used 60% of the money for uniforms,10% for equipment, and 30% for travel.

60% of the area of the circle is used for uniforms.

10% of the area of the circle is used for equipment.

30% of the area of the circle is used for travel.

Hence "The attached circle depicts how the funds were distributed.".

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The system of equation is dependent because both equation has same slope.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given a system of equation as;

-3x + y = 4

x-1/3y = 1

Therefore, we need to write as straight line equation.

-3x + y = 4

y = 3x + 4

Thus, the slope is 3 and the y intercept is 4

Now x-1/3y = 1

x= 1 + 1/3y

y = 3x - 3

Thus, the slope is 3 and the y intercept is -3

The system of equation is dependent.

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Answer:

please add screenshots of the question and/or illustrations

The roots of the given quadratic equation are 4.56 and 0.439.

The roots of an equation are the solution of that equation, since an equation consists of hidden values of the variable so to determine them by different processes and then the resultant is called roots.

As per the given quadratic equation,

x² - 5x + 2 = 0

The roots will be as,

x = [+5 ± √(5² - 4 × 1 × 2)]/(2 × 1)

x = [5 ± 4.1232]/2

x = 4.56,0.439

Hence "The roots of the given quadratic equation are 4.56 and 0.439".

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Answer:

170,100 milligrams

Step-by-step explanation:

1 ounce = 28.35 grams

6 ounces = ?

6*28.35 = 171.10 grams

1 gram - 1000 milligrams

171.10 grams = ?

171.10*1000 =

171,100 milligrams

Answer:

A recipe calls for 170,100 milligrams of raisins.

Step-by-step explanation:

I took the exam and got it right

The linear equation for the first scenario is y = 500 while for the second scenario is y = 20x

The equation of a straight line is given by:

y = mx + b;

where y,x are variables, m is the slope of the line and b is the y intercept.

let x represent the number of sales and y represent the total salary for a weeks.

For scenario 1, there is a constant salary of $500. The linear equation becomes:

y = 500

For scenario 2, there is a commission of $20 per sale. The linear equation becomes:

y = 20x

The graph that shows the proportional relationship between the number of liters of water (y) supplied after some time (x), is shown below.

A proportional relationship can be defined as a relationship between two variables, say x and y, in such a way that the equation, y = kx, models their relationship, where k is the constant of proportionality.

Given that the faucet supplies 12 liters of water after 3 minutes, where:

y = liters of water

x = number of minutes

Constant of proportionality, k = y/x = 12/3 = 4

The equation that describes the relationship would therefore be written by substituting the value of k = 4 into y = kx:

y = 4x

Thus, the graph that shows this proportional relationship is attached below.

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Step-by-step explanation:

x - 7y = -45

-x +8y = 51

the X's cancel out

-7y + 8y = -45 + 51

y = 6

At [tex]$5 \mathrm{pm}$[/tex] the distance between the ships is changing at the speed of [tex]$\mathbf{3 0 . 2 1}$[/tex] knots

Firstly we need to an equation to represent both ships and the distance between each. A is moving [tex]$25 \mathrm{knots}$[/tex] west and [tex]$B$[/tex] is moving [tex]$17 \mathrm{knot}$[/tex] north. [tex]$D$[/tex]will be the distance between the two. Drawing it, you'll notice that it creates a right triangle.

So we use the Pythagorean Theorem:

[tex]$$D^{\wedge} 2=A^{\wedge} 2+B^{\wedge} 2$$[/tex]

Differentiate in relation to time:

[tex]$$2 \mathrm{D}(\mathrm{dD} / \mathrm{dt})=2 \mathrm{~A}(\mathrm{dA} / \mathrm{dt})+2 \mathrm{~B}(\mathrm{~dB} / \mathrm{dt})$$[/tex]

Now we must find all of our variables.

[tex]& A=\text { time(speed })+\text { original distance }=5(25)+10=135 \\[/tex]

[tex]& B=5(17)+0=85 \\[/tex]

[tex]& D=V\left(A^{\wedge} 2+B^{\wedge} 2\right)=159.53 \\[/tex]

[tex]& d A / d t=25 \\[/tex]

[tex]& d B / d t=17[/tex]

Plug in all your variables and solve for

[tex]$(\mathrm{dD} / \mathrm{dt})$ :[/tex]

[tex]& 2 \mathrm{D}(\mathrm{dD} / \mathrm{dt})=2 \mathrm{~A}(\mathrm{dA} / \mathrm{dt})+2 \mathrm{~B}(\mathrm{~dB} / \mathrm{dt}) \\[/tex]

[tex]& 2(159.53)(\mathrm{dD} / \mathrm{dt})=2(135)(25)+2(85)(17) \\[/tex]

[tex]& 319.061(\mathrm{dD} / \mathrm{dt})=9640 \\[/tex]

[tex]& \mathrm{dD} / \mathrm{dt}=9640 / 319.061 \\[/tex]

[tex]& \mathrm{dD} / \mathrm{dt}=30.21 \text { knots }\end{aligned}[/tex]

At [tex]$5 \mathrm{pm}$[/tex] the distance between the ships is changing at the speed of [tex]$\mathbf{3 0 . 2 1}$[/tex] knots

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The result of the given mathematical expression is 8459.46

What is Mathematical expression and decimal

Mathematical expression consist of combination of numbers along with addition, subtraction, multiplication and division.

Decimal numbers are those numbers which have an integer part and a fractional part.

Decimal can be terminating as well as non terminating.

Terminating decimals are those numbers which have finite number of digits after decimal point.

Non terminating decimals are those numbers which have infinite number of digits after decimal point.

Mathematical expression to be solved

[tex]31520 \times 0.029 \times \frac{(1+0.029)^4}{(1+0.029)^4-1}[/tex]

Decimal number is present in the above expression.

The given expression is to be simplified to get a solution

Now,

[tex]31520 \times 0.029 \times \frac{(1+0.029)^4}{(1+0.029)^4-1}\\\\31520 \times 0.029 \times \frac{(1.029)^4}{(1.029)^4-1}\\\\31520 \times 0.029 \times \frac{1.1211442633}{0.1211442633}[/tex]

8459.46

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The width of the piece of metal will be 21 inches while the length will be 26 inches.

What is a rectangle?

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Main body:

Area of rectangle = length × width.

Perimeter of rectangle = 2( length + width).

Let's say the width of metal w then the length will be w + 5

Now if we cut 1 inch square from the corner of the metal and then fold then the resultant cuboid will have;

Length = w+5 - 2 -= w + 3

Width = w - 2

Height = 1

So,

Volume = (w+3)(w-2)1

456 = w² - 2w + 3w - 6

w² + w - 462 = 0

By solving this

w = 21 so width will be 21 and length will be 21 + 5 = 26.

Hence "The width of the piece of metal will be 21 inches while the length will be 26 inches".

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Answer:

71 mph

Step-by-step explanation:

Lets call the speed of the eastbound train E and the speed of the westbound train W.

E = W - 18

distance travelled  = speed * time

thus

Wt + Et = 320

Wt + (W - 18)t = 320

factor out t

t * (2W - 18) = 320

t = 2 hours

2 * (2W - 18) = 320

2W - 18 = 160

2W = 178

W = 89

Then, E = (89) - 18 = 71 mph

Answer:

i) 960  ,    ii) 10 cm

Step-by-step explanation:

V of rectangular carton = 80 · 60 · 40 = 192 000

V of a packet of soap = 10 · 5 · 4 = 200

192 000 / 200

1920/2

960

ii)

960 : 1200 = 192 000 : x

x = 192 000 · 1200 / 960

x = 192 000 · 120 / 96

x = 240 000

80 · 60 · x = 240 000

4800 · x = 240 000

x = 240 000/4800

x = 2400/48

x = 200/4

x = 50

50 - 40 = 10

Answer:

i) 960 packets of soap

ii) 10 cm

Step-by-step explanation:

volume of cuboid = l*w*h

volume of carton = 80*60*40 = 192000 cm³

i)

volume of a packet of soap = 10*5*4 = 200 cm³

192000/200 = 960 packets of soaps

ii)

I am assuming the height is 40 cm

volume of carton/volume of a packet of soap = number of soap

x = volume of carton

x/200 = 1200

x = 1200*200 = 240000 cm³

80*60*h = 240000

4800h = 240000

h = 240000/4800 = 50 cm

50cm (desired height) - 40cm (current height) = 10cm

Answer:

Step-by-step explanation:

To convert the amount of water in gallons to liters, we need to first convert the number of gallons to quarts and then convert the number of quarts to liters.We know that 1 gallon is equal to 4 quarts, so 4.7 gallons is equal to 4.7 gallons * 4 quarts/gallon = 4.7*4=18.8 quarts.We also know that 1 liter is equal to 1.057 quarts, so to convert the number of quarts to liters, we can divide the number of quarts by 1.057 quarts/liter: 18.8 quarts / 1.057 quarts/liter = 18.8/1.057=17.8 liters.Therefore, 4.7 gallons is equal to 17.8 liters.

x= -32.

[tex]-128 = 4x[/tex]

[tex]\frac{-128}{4} = \frac{4x}{4} \\\\-32=x\\ \\x=-32[/tex]

The difference in temperature is currently six degrees Celsius. Therefore, the appropriate reaction is six degrees Celsius.

When two independent temperature readings are subtracted, or when calculating the amount of temperature rise or fall, the result is a temperature difference, also referred to as a delta temperature (T).

Simply subtract the smaller amount from the larger one to determine the difference in temperature, in this case 19 degrees Celsius from 25 degrees Celsius. We now have a six-degree Celsius temperature difference as a result. Therefore, six degrees Celsius, is the appropriate response.

Due to the varied amounts of radiation the Earth receives from the Sun at various periods of the year, there are variations in climate all over the world. The equator receives more heat from the Sun than the north and south poles, where the angle of the Sun's beams is lower.

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Answer:

original price is 26 dollars

Step-by-step explanation:

19.50/0.75=26

The expected value of the number of cups of coffee Alex drinks each day is 00.805 cups.

the mean/ average is gotten by dividing the sum of the values in the set by their number.

The concept of mean/average is used in this ques to calculate the expected value of the number of cups of coffee Alex drinks each day.

Mean/ Average=     sum of values

                              number of values

Mean/ Average= 00.200 cups +00.163 cups+ 00.976 cups+ 01.881 cups

                                                                 4

Mean/ Average= 00.805 cups

Hence, The expected value of the number of cups of coffee Alex drinks each day is 00.805 cups.

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The given points form an equation for a line that has a value of 14.

Explanation:

m =( -5 - -7)(0 - -7)

   = 2*7

   = 14.

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As we can solve the square root 80 or [tex]\sqrt{80\\}[/tex] = [tex]\sqrt{2^4}.\sqrt{5}[/tex]

so [tex]\sqrt{2^4}.\sqrt{5}[/tex] is the correct answer for square root 80

What is Square root?

The component of a number that, when multiplied by itself, yields the original number is known as the square root of the number. Special exponents include squares and square roots. Think about the number 9. When the number 3 is multiplied by itself, the result is 9. This can be expressed as either 32 or 3 3. We refer to this as a square since there is a 2 exponent. When the exponent is now 1/2, the square root of the integer is being discussed. For instance, when n is a positive integer, n = n1/2

The value of a number's power 1/2 is the number's square root. It is the number whose product by itself yields the original number, to put it another way. It is symbolised by the character "." The number behind the square root sign is referred to as the radicand, whereas the square root symbol itself is known as a radical.

1)

[tex]\sqrt[4]{2} .\sqrt{5}[/tex] =[tex]2^{\frac{1}{4} } .\sqrt{5}[/tex]

which is not equal to [tex]\sqrt{80\\}[/tex]

2)

[tex]\sqrt{2^4}.\sqrt{5}[/tex] = [tex]2^{4.\frac{1}{2} } .\sqrt{5}[/tex]

=[tex]4\sqrt{5}[/tex] or[tex]\sqrt{16 * 5} =\sqrt{80}[/tex]

3)

[tex]\sqrt{2}. \sqrt{2}. \sqrt{5} =2\sqrt{5}[/tex]

which is not equal to [tex]\sqrt{80\\}[/tex]

4)

[tex]\sqrt{2^{2} } .\sqrt{2^{2} } .\sqrt{5^{2} } = 2.2.5 \\\\\4.5 = 20[/tex]

which is not equal to [tex]\sqrt{80\\}[/tex]

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Answer:

So there are 32/4= 8 such groups. In each group, every team plays once against every other team

Step-by-step explanation: