2. Use the Pythagorean Theorem to solve for c.
5 feet
18 feet

Answer:

I think like this but I not sure what format you learn

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:

x = 6, y = 2

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Distance travelled is 300 miles

The total movement of an object, independent of direction, is its distance. The amount of space that an object has traveled, regardless of where it started or ended, is referred to as distance.

According to the given information

You know the equation: D = r × t.

where D represents the distance traveled, r is the train's speed, and t denotes the amount of time (in hours) required.

Train travels for 3.75 hours at 80 miles per hour

By putting the values in the above equation

D = 80 miles in 3.75 hours per hour

  = 80 × 3.75

  = 300 miles

Distance travelled is 300 miles

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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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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.

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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x= -32.

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

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

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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The value of JG = 24,

                      FJ = 7,

                     ∠EFH = 74°,

                     ∠HGE = 16°

What are the properties of a diagonal of rhombus?

In a rhombus, diagonals bisect each other at right angles. Diagonals bisect the angles of a rhombus. The sum of two adjacent angles is equal to 180 degrees. You will get a rectangle when you join the midpoint of the sides.

Solution:

Given :

EJ = 24

∴ GJ = 24

∠FHG = 74°

∴ ∠EFH = 74° by alternate angle properties

Now, we know

FG² =FJ² + GJ² - 2FJ × GJ × cos(90) ------ diagonals of the rhombus are perpendicular to each other

Substitute FG = 25, GJ = 24, we get

25² = FJ² + 24² - 2FJ × GJ × cos(90)

FJ² = 49

∴FJ = 7

180 =∠GHJ  +∠HGJ + ∠GJH ------ sum of all angles of a triangle is 180°

∴ ∠HGE = ∠HGJ = 180 - 90 - 74

∴ ∠HGE = 16°

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2. The value of JL = 14

                         ML = 7√2

                         ∠KNL = 90°

                          ∠MKJ = 45°

What are the properties of diagonals of a square?

The diagonals of the square bisect each other at 90°.The two diagonals of the square are equal to each other. The diagonal of the square divide it into two similar isosceles triangles.

Solution:

Given; NM = 7

We know that diagonals of the square are equal

∴ NM = NL = NK = NJ = 7

∵ JL = JN + NL

∴ JL = 7 + 7

∴JL = 14

∠KNL = 90° ----- as we know that diagonals bisect each other at 90°

For ∠MKJ

we know that KM = KN + NM = 14

KJ = JM = 7√2------- property of isosceles triangle

∠KJM = 90° ----- all angles of square are 90°

We know that diagonals of a square dissects the square into two equal isosceles triangle.

∴ ∠MKJ = JMK = ∠KJM/2

∴ ∠MKJ = 90/2

∴ ∠MKJ = 45°

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The value of JG = 24 ,   FJ = 7,   ∠EFH = 74°,   ∠HGE = 16°

What are the properties of a diagonal of rhombus?

In a rhombus, diagonals bisect each other at right angles. Diagonals bisect the angles of a rhombus. The sum of two adjacent angles is equal to 180 degrees. You will get a rectangle when you join the midpoint of the sides.

Given :

EJ = 24

∴ GJ = 24

∠FHG = 74°

∴ ∠EFH = 74° by alternate angle properties

Now, we know

FG² =FJ² + GJ² - 2FJ × GJ × cos(90) ------ diagonals of the rhombus are perpendicular to each other

Substitute FG = 25, GJ = 24, we get

25² = FJ² + 24² - 2FJ × GJ × cos(90)

FJ² = 49

∴FJ = 7

180 =∠GHJ  +∠HGJ + ∠GJH ------ sum of all angles of a triangle is 180°

∴ ∠HGE = ∠HGJ = 180 - 90 - 74

∴ ∠HGE = 16°

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2. The value of JL = 14

              ML = 7√2

                        ∠KNL = 90°

                         ∠MKJ = 45°

The diagonals of the square bisect each other at 90°.The two diagonals of the square are equal to each other. The diagonal of the square divide it into two similar isosceles triangles.

Given; NM = 7

We know that diagonals of the square are equal

∴ NM = NL = NK = NJ = 7

∵ JL = JN + NL

∴ JL = 7 + 7

∴JL = 14

∠KNL = 90° ----- as we know that diagonals bisect each other at 90°

For ∠MKJ

we know that KM = KN + NM = 14

KJ = JM = 7√2------- property of isosceles triangle

∠KJM = 90° ----- all angles of square are 90°

We know that diagonals of a square dissects the square into two equal isosceles triangle.

∴ ∠MKJ = JMK = ∠KJM/2

∴ ∠MKJ = 90/2

∴ ∠MKJ = 45°

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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 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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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 volume of the box is 858 cube inches.

A cuboid is a three-dimensional solid shape that has 6 faces, 8 vertices, and 12 edges. It is one of the most commonly seen shapes around us which has three dimensions: length, width, and height

length of box = 13 inches

Width of box = 11 inches

height of box = 6 inches

Volume of cuboid = length x width x height

volume of cuboid = 13 x 11 x 6 which is 858 cube inches

In conclusion the volume of the box is 858 cube inches

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Answer:

5/1

Step-by-step explanation:

I think?

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:

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

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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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

Step-by-step explanation:

x - 7y = -45

-x +8y = 51

the X's cancel out

-7y + 8y = -45 + 51

y = 6

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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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 correct postulate is the Linear Pair postulate. It can be find out by the concept of supplementary angles.

What is supplementary angles?

Two angles are said to be supplementary if their sums total 180 degrees.

Linear Pair postulate: When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.

Segment Addition Postulate: According to the segment addition postulate, if two points on a line segment, A and C, are given, a third point, B, will only be found on line segment AC if and only if the distances between the points satisfy the conditions of the equation AB + BC = AC. This option is not correct.

Vertical Angles: When two lines intersect each other then the angles made on the opposite sides of the intersection point is known as vertical angles and they give equal measurment. This option is not correct.

Addition Postulate states: The measure of an angle formed by two angles side by side is the sum of the measures of the two angles. This option is not correct.

Hence, the correction postulate is the Linear Pair postulate. It can be find out by the concept of supplementary angles.

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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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It is to be noted that the volume of Emma's storage tank is: 785.3cubic feet.

Start by calculating the area of the base of the storage tank. The area of a circle is calculated by: A = π*r², where r is the radius of the circle.

Where:

π = 22/7

r = radius of the circular base

Recall that for Emma’s cylindrical storage tank, the radius of the base is 5 feet.

So we replace this value in the formula and calculate the area of the base, which is equal to:

A = π*5²

A = 22/7 * 5²

= 78.5714285714

[tex]\approx[/tex] 78.54 square feet.

Now we need to compute the volume of the cylindrical storage tank. The volume of a cylinder is calculated by:

V = π*r²*h,

where r is the radius of the circle and h is the height of the cylinder.

Recall that for Emma’s tank, the height is 10 feet. Hence,

We substitute these values in the formula and calculate the volume, which is equal to:

V = π*5²*10 = 785.4 cubic feet.

Therefore, Emma’s cylindrical storage tank has a capacity of 785.4 cubic feet.

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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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