Differentiate the function:
f(x)=5x times ln(7x)-5x

The given points  P, Q, R are not collinear

To determine whether the given points (0,0), (3,7), and (-3,-7) are collinear, we can calculate the distances between the points and check if they satisfy the condition: d(P,Q) + d(Q,R) = d(P,R).

Let's calculate the distances:

d(P,Q) = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(3 - 0)² + (7 - 0)²]

= √(3² + 7²)

= √(9 + 49)

= √58

≈ 7.62

d(Q,R) = √[(x₃ - x₂)² + (y₃ - y₂)²]

= √[(-3 - 3)² + (-7 - 7)²]

= √((-6)² + (-14)²)

= √(36 + 196)

= √232

≈ 15.23

d(P,R) = √[(x₃ - x₁)² + (y₃ - y₁)²]

= √[(-3 - 0)² + (-7 - 0)²]

= √((-3)² + (-7)²)

= √(9 + 49)

= √58

≈ 7.62

Now, let's check if d(P,Q) + d(Q,R) = d(P,R):

√58 + √232 ≈ 7.62 + 15.23 ≈ 22.85

Since d(P,Q) + d(Q,R) is not equal to d(P,R), the given points (0,0), (3,7), and (-3,-7) are not collinear.

Therefore, the points are not collinear.

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Answer:

the quotient of 4 and n

Step-by-step explanation:

or 4 divided by n

Answer: I'd say a broad audience made up of all kinds of people

It had different parts and concepts that could entertain any age group

Answer:

A broad audience made up of all kinds of people

Step-by-step explanation:

x + y = -4 ----------------(1)

x -

The 3x3 matrix after composite transformation of scaling by 2, a rotation of 90° about origin is \(\left[\begin{array}{ccc}2c&2d&2i\\2b&2e&2h\\2a&2d&2g\end{array}\right]\).

Let A=\(\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right]\) be a 3x3 matrix

scaling the matrix A by 2 then  the result will be

\(2A=2\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right]\\\\=\left[\begin{array}{ccc}2a&2b&2c\\2d&2e&2f\\2g&2h&2i\end{array}\right]\)

now, rotating the resultant matrix by 90° in counterclockwise direction about the origin, we get

\(=\left[\begin{array}{ccc}2c&2d&2i\\2b&2e&2h\\2a&2d&2g\end{array}\right]\)

Thus, a 3x3 matrix after composite transformation of scaling by 2, a rotation of 90° about origin is \(\left[\begin{array}{ccc}2c&2d&2i\\2b&2e&2h\\2a&2d&2g\end{array}\right]\)

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To find the polar equation for the given Cartesian equation x^2 + y^2 = 8y, we can use the following relationships between Cartesian and polar coordinates:

x = rcos(θ)

y = rsin(θ)

Let's substitute these equations into the Cartesian equation:

(x^2) + (y^2) = 8y

(rcos(θ))^2 + (rsin(θ))^2 = 8(rsin(θ))

Expanding and simplifying:

r^2(cos^2(θ) + sin^2(θ)) = 8rsin(θ)

r^2 = 8rsin(θ)

Dividing both sides by r and rearranging:

r = 8sin(θ)

Therefore, the polar equation for the curve represented by the given Cartesian equation x^2 + y^2 = 8y is r = 8sin(θ).

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Complete question:

Anty was riding his bike to school at a speed of 12 mph. When he was half of the way there, he got a flat tire. His mother drove him the rest of the way at a speed of 48 mph. What was his average speed?

Answer:

His average speed is 19.2 mph

Step-by-step explanation:

Given;

speed of Anty to school half of the way, v₁ = 12 mph

speed of Anty when his mother drove him half of the way, v₂ = 48 mph

The average speed of Anty is calculated as;

\(V_{average} = \frac{Total \ distance }{Total \ time }\)

The value of the average speed is closer to 12 mph than 48 mph because Anty spent more time moving at 12 mph than at 48 mph.

Let the equal distance travel at each speed = 96 miles

Time taken at 12 mph = \(\frac{96 \ mile}{12 \ m/h} = 8 \ hours\)

Time taken at 12 mph = \(\frac{96 \ mile}{48 \ m/h} = 2 \ hours\)

Average speed = \(\frac{Total \ distance}{Total \ time } = \frac{96 \ mile \ + \ 96 \ mile}{2\ hr \ + \ 8\ hr} = \frac{192 \ miles}{10 \ hrs} = 19.2 \ mph\)

Also, you can assume any other equal distance traveled at each speed, the average speed will still be 19.2 mph.

Check: let the equal distance traveled at each speed = 480 miles

Time taken at 12 mph = 480/12 = 40 hours

Time taken at 48 mph = 480/ 48 = 10 hours

Average speed = (480 + 480) / (40 + 10)

                          = 19.2 mph

Answer:

3x3 should be the maximum dimensions of a rectangle with a perimeter of 12.

Simplify implies to reduce a mathematical expression to it lowest form. The 4th root of the given question is 6x.

Simplification is a process which requires showing a given equation in its most simple form. Such that it can not be simplified further i.e complete simplification.

To simplify the given question completely, convert all the terms to the power of 4. Because we are to simplify the 4th root of the given expression.

So that,

\(\sqrt[4]{1296x^{2} }\)  =  \(\sqrt[4]{(6^{4})(x^{4}) }\)

              = \(((6^{4})*(x^{4}) ^{\frac{1}{4} }\)

expand as follows;

\(((6^{4})*(x^{4}) ^{\frac{1}{4} }\) = \((6)^{\frac{4}{4} } (x)^{\frac{4}{4} }\)

                    = 6*x

                    = 6x

Therefore, the simplified form of the given question is 6x.

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Answer: Because it's winter therefore he can't enjoy the gift. or he can't walk

Step-by-step explanation:

The estimated length of the diagonal of a square with area 100 cm square is 14 cm.

The length of the diagonal of a square with area 100 cm square can be estimated using the formula d = 1.4x2, where d is the length of the diagonal and x is the area of the square. Substituting x with 100 cm square, we get:

d = 1.4(100)^(1/2)

d = 1.4(10)

d = 14 cm

Therefore, the estimated length of the diagonal of a square with area 100 cm square is 14 cm.

The formula d = 1.4x2 can be derived using the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In a square, the diagonal is the hypotenuse of two right-angled triangles formed by the sides of the square. If we let s be the length of the sides of the square, then we can write the Pythagorean theorem as: s^2 + s^2 = d^2

Simplifying this equation, we get: 2s^2 = d^2

Taking the square root of both sides, we get: d = (2s^2)^(1/2)

Since the area of the square is x = s^2, we can substitute s^2 with x to get: d = (2x)^(1/2)

Simplifying this equation, we get:

d = x^(1/2) * 2^(1/2)

To estimate the value of d, we can substitute 1.4 for 2^(1/2) and get:

d = 1.4x^(1/2)

This formula allows us to estimate the length of the diagonal of a square when we know its area.

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Answer:

the answer is b 4-n. Hope this helps

Answer:

the second one (4-n).

Step-by-step explanation:

lol

Answer:

1/4 cup of flour and 1/8 cup of sugar

Step-by-step explanation:

1 1/2=3/2, 3/2/6=3/2*1/6=3/12 or 1/4

3/4/6=3/4*1/6, 3/24, 1/8

Answer:

sorry ima need to use your page

Step-by-step explanation:

Answer:

sorry ima need to use ur page

Step-by-step explanation:

Answer:

$17.96

Step-by-step explanation:

4.49 for 5

5 times 4 = 20

4.49 times 4 = 17.96

Therefore the solution to this equation is imaginary given by x = \(\rm \dfrac { 3 \pm \sqrt{-3}}{2}\)

A Quadratic equation is an equation that can be written in the form of

ax² +bx+c = 0

The solution of the given quadratic equation

x² -3x +3 = 0

the roots of the equation is given by

\(\dfrac { -b \pm \sqrt{b^2 -4ac}}{2a}\)

here a = 1 , b = -3 , c = 3

Substituting the values

The solution is

\(\rm \dfrac { 3 \pm \sqrt{(-3)^2 -4*1 *3}}{2}\)

Therefore the solution to this equation is imaginary

given by

x = \(\rm \dfrac { 3 \pm \sqrt{-3}}{2}\)

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So, the simpler form of the radical expression 4 sqrt 1296 x^16y^12 is 144x^14y^14 sqrt (x) sqrt (y).

To simplify the radical expression 4 sqrt 1296 x^16y^12, we need to first factor the number inside the radical. 1296 can be factored into 36 x 36, which simplifies to 6^4. So, the expression becomes 4 sqrt (6^4 x^16y^12).
Next, we can simplify the expression further by using the property of exponents that says a^m x a^n = a^(m+n). This means that we can combine the exponents of x and y, which gives us 4 sqrt (6^4 x^(16+12) y^(12+16)). Simplifying this, we get 4 sqrt (6^4 x^28 y^28).
Now, we can simplify the radical expression even further by using the property that says sqrt (a x b) = sqrt (a) x sqrt (b). Applying this to our expression, we get 4 x 6^2 x sqrt (x^28) x sqrt (y^28). Simplifying this further, we get 144x^14y^14 sqrt (x) sqrt (y).
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I Agree With person up  

:p

The rectangle with the given properties is added as an attachment

From the question, we have the following parameters that can be used in our computation:

We start by calculating the side lengths using

Perimeter = 2 * (Length + Width)

So, we have

2 * (Length + Width) = 28

Divide by 2

Length + Width = 14

Because the y-axis is a line of symmetry, then it means that the rectangle is divided into equal segments by the y-axis

Here, we can assume that

Length = Width (this is so because a square is a type of rectangle)

So, we have

Length = Width = 7

The above computations also mean that the vertices are equidistant from the axes and the origin

So, we have

Vertices = (3.5, 3.5), (3.5, -3.5), (-3.5, 3.5) and (-3.5, -3.5)

See attachment for the rectangle

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We have derived the following equations:

(10) Y = 7,000 - 200r - 1,000ε
(11) 10 = r + 5ε
(12) NX = 500 - 500r - 2,500ε
(13) CF = -50,000 + 50,000r + 250,000ε

To solve the given equations for the equilibrium values of C, NX, CF, r, and ε, let's go step by step.

First, we'll substitute equations (2), (3), (4), (5), (6), (7), (8), and (9) into equation (2) to eliminate the variables C, I, G, NX, CF, and T.

Equation (2) becomes:
Y = (1/2)(Y - T) + (2,000 - 100r) + 1,500 + (500 - 500ε)

Next, let's simplify the equation:

Y = (1/2)(Y - 1,000) + 2,000 - 100r + 1,500 + 500 - 500ε

Distribute (1/2) to the terms inside the parentheses:

Y = (1/2)Y - 500 + 2,000 - 100r + 1,500 + 500 - 500ε

Combine like terms:

Y = (1/2)Y + 3,500 - 100r - 500ε

Now, let's isolate Y by subtracting (1/2)Y from both sides:

(1/2)Y = 3,500 - 100r - 500ε

Multiply both sides by 2 to get rid of the fraction:

Y = 7,000 - 200r - 1,000ε

We now have one equation (10) in terms of Y, r, and ε.

Next, let's substitute equation (1) into equation (10) to solve for Y:

5,000 = 7,000 - 200r - 1,000ε

Subtract 7,000 from both sides:

-2,000 = -200r - 1,000ε

Divide both sides by -200:

10 = r + 5ε

This gives us equation (11) in terms of r and ε.

Now, let's substitute equation (11) into equation (5) to solve for NX:

NX = 500 - 500ε

Substitute r + 5ε for ε:

NX = 500 - 500(r + 5ε)

Simplify:

NX = 500 - 500r - 2,500ε

This gives us equation (12) in terms of NX, r, and ε.

Finally, let's substitute equation (12) into equation (6) to solve for CF:

CF = -100r

Substitute 500 - 500r - 2,500ε for NX:

CF = -100(500 - 500r - 2,500ε)

Simplify:

CF = -50,000 + 50,000r + 250,000ε

This gives us equation (13) in terms of CF, r, and ε.

To summarize, we have derived the following equations:

(10) Y = 7,000 - 200r - 1,000ε
(11) 10 = r + 5ε
(12) NX = 500 - 500r - 2,500ε
(13) CF = -50,000 + 50,000r + 250,000ε

These equations represent the equilibrium values of Y, r, ε, NX, and CF in the given open economy.

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Answer:

J

Step-by-step explanation:

Using the cofunction identity

cosθ = sin(\(\frac{\pi }{2}\) - θ )

Then

\(\frac{1}{sin(\frac{\pi }{2}-0) }\)

= \(\frac{1}{cos0}\)

= \(\frac{1}{0.8}\)

= 1.25 → J

The value of 1/sin(\(\frac{\pi }{2}\) - θ) is 1.25.

The coordinate axes divide the plane into four quadrants, labelled first, second, third and fourth as shown. Angles in the third quadrant, for example, lie between 180 degrees and 270 degrees.

Given

1/cosθ = 0.8

1/sin(\(\frac{\pi }{2}\) - θ) =?

By using quadrants in trigonometry

we know that sin(\(\frac{\pi }{2}\) - θ) = cosθ

= 1/sin(\(\frac{\pi }{2}\) - θ)

= 1/cosθ

= 1/0.8

= 1.25

1/sin(\(\frac{\pi }{2}\) - θ) = 1.25

Hence, the value of 1/sin(\(\frac{\pi }{2}\) - θ) is 1.25.

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Looking at the triangles, the information needed to prove that ABC∼△DEF is AC = 10

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

Examining the figure shows that pair of equivalent sides are

AB and DE, BC and FE, then AC and DF

The solution is worked out using sides BC and FE, then AC and DF

BC / AC = FE / DF

8 / AC = 16 / 20

reducing the fraction 16/20 gives

8 / AC = 8 / 10

hence  AC = 10

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The 15 and 9 units side lengths of the parallelogram ABCD, and the 36° measure of the acute interior angle, A indicates the values of the ratios are;

1. AB:BC = 5:3

2. AB:CD = 1:1

3. m∠A : m∠C= 1 : 4

4. m∠B:m∠C = 4:1

5. AD: Perimeter ABCD = 3:16

A ratio is a representation of the number of times one quantity is contained in another quantity.

The shape of the quadrilateral ABCD in the question = A parallelogram

Length of AB = 15

Length of BC = 9

Measure of angle m∠A = 36°

Therefore;

1. AB:BC = 15:9 = 5:3

2. AB ≅ CD (Opposite sides of a parallelogram are congruent)

AB = CD (Definition of congruency)

AB = 15, therefore, CD = 15 transitive property

AB:CD = 15:15 = 1:1

3. ∠A ≅ ∠C (Opposite interior angles of a parallelogram are congruent)

Therefore; m∠A = m∠C = 36°

∠A and ∠D are supplementary angles (Same side interior angles formed between parallel lines)

Therefore; ∠A + ∠D = 180°

36° + ∠D = 180°

∠D = 180° - 36° = 144°

∠D = 144°

m∠A : m∠C = 36°:144° =1:4

m∠A : m∠C = 1:4

4. ∠B = ∠D = 144° (properties of a parallelogram)

m∠B : m∠C = 144° : 36° = 4:1

5. AD ≅ BC (opposite sides of a parallelogram)

AD = BC = 9 (definition of congruency)

The perimeter of the parallelogram ABCD = AB + BC + CD + DA

Therefore;

Perimeter of parallelogram ABCD = 15 + 9 + 15 + 9 = 48

AD:Perimeter of the ABCD  = 9 : 48  = 3 : 16

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Answer:

1464.84375

Step-by-step explanation:

The n th term of a geometric sequence is

\(a_{n}\) = a₁ \((r)^{n-1}\)

where a₁ is the first term and r the common ratio

Here a₁ = 6 and r = 15 ÷ 6 = 2.5, thus

\(a_{7}\) = 6 × \((2.5)^{6}\) = 6 × 244.140625 = 1464.84375

The seventh term of the geometric progression will be 1464.84375

When there is a constant between the two successive numbers in the series then it is called a geometric series.

The nth term of a geometric sequence is

\(a_n =a_1(r)^{n-1}\)

where a₁ is the first term and r is the common ratio

Here a₁ = 6 and r = 15 ÷ 6 = 2.5, thus

\(a_7=6\times (2.5)^{6}\)  = 6 × 244.140625 = 1464.84375

Therefore the seventh term of the geometric progression will be 1464.84375

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The equation of the line is y = 2/3x + 2

What is equation ?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

When two expressions are joined by an equal sign, a mathematical statement is called an equation. An equation is something like 3x - 5 = 16. By solving for x, we discover that x equals 7, which is the value for the variable.

Slope between two points

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

   = (2 - (-2)) / (-3 - (-6))

   = 4 / 6

   = 2/3

y - y1 = m (x - x1)

y - (-2) = 2/3 (x - (-6))  

y + 2 = 2/3(x+6)

y = 2/3x +4 - 2

y = 2/3x + 2

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The way we can decompose the composite figure to determine its area is given by: Option D: as a semicircle, a trapezoid, and two rectangles.

Surface area are derived for some standard shapes like circle, triangle, parallelogram, rectangle, trapezoid, etc.

When some shape comes which isn't standard figure, then we find its area by slicing it (virtually, like by drawing lines) in standard shapes. Then we calculate those composing shapes' area and sum them all.

Thus, we have:

\(\text{Area of composite figure} = \sum (\text{Area of composing figures})\)

That ∑ sign shows "sum"

Since the considered composite figure consists of a semicircle, trapezoid, and 2 rectangles, so we can find its area by their use.

Thus, the way we can decompose the composite figure to determine its area is given by: Option D: as a semicircle, a trapezoid, and two rectangles.

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Answer:

d

Step-by-step explanation:

i just finished the test

The three friends spent:Jan spent $30.5, Danetta spent $18.5, and Elaine spent $37.

Let's denote the amount Jan spent as J. Danetta spent $12 less than Jan, so her expenditure is J - $12. Elaine spent twice as much as Danetta, so her expenditure is 2(J - $12). The total expenditure of the three friends is $86. By setting up an equation using these values, we can find the individual expenditures of each friend.

Let's denote the amount Jan spent as J. According to the given information, Danetta spent $12 less than Jan, so her expenditure can be expressed as J - $12. Similarly, Elaine spent twice as much as Danetta, so her expenditure can be expressed as 2(J - $12).

The total expenditure of the three friends is stated as $86. We can set up the equation J + (J - $12) + 2(J - $12) = $86 to represent the sum of their expenditures. Simplifying this equation, we have 4J - $36 = $86.

By rearranging the equation, we find 4J = $122, which implies J = $30.5. Therefore, Jan spent $30.5.

Using this value, we can calculate the expenditures of the other two friends. Danetta spent J - $12, which is $30.5 - $12 = $18.5. Elaine spent twice as much as Danetta, so she spent 2($18.5) = $37.

In summary, Jan spent $30.5, Danetta spent $18.5, and Elaine spent $37.

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Answer:

hi I am new here ☺ ✨ ☺ ✨ ☺

Answer:

12 goles

Step-by-step explanation:

5 goles/25 min = x goles/60 min (multiplicación cruzada)

(60 * 5)/25 = x

300/25 = 12