complete the problems using synthetic division

The value of the given logarithm ln(x²y⁵) in terms of u and v will be 2u + 5v thus option (D) is correct.

The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.

In another word, a logarithm is a different way to denote any number.

As per the given expressions,

u = ln x and v = ln y

Take anti-log as

x = [tex]e^{u}[/tex] and y = [tex]e^{v}[/tex]

Thus, x² = [tex]e^{2u}[/tex] and y⁵ = [tex]e^{5v}[/tex].

Multiply both as

x²y⁵ =  [tex]e^{2u}[/tex][tex]e^{5v}[/tex]

Take logarithms on both sides,

ln(x²y⁵) = ln( [tex]e^{2u}[/tex][tex]e^{5v}[/tex])

By log property that ln(A x B) = lnA + lnB

ln(x²y⁵) = ln  ([tex]e^{2u}[/tex]) + ln([tex]e^{5v}[/tex])

ln(x²y⁵) = 2u ln e + 5v ln e

ln(x²y⁵) = 2u + 5v



Hence "In terms of u and v, the value of the given logarithm ln(x²y⁵) will be 2u + 5v.".

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Answer:

D. y ≤ -1/4x - 3

A. y < 2/3x + 3

Step-by-step explanation:

For the first question, the answer would obviously be either B or D because the y-intercept is -3. The slope of the graph is -1/4 so the answer is D.

For the second question, the answer would be A or B because its a dashed line. Next, the slope is 2/3 so the answer is A.

Answer:

V=whl=3·7·4=84

Step-by-step explanation:

By understanding the property of circles, it can be concluded that the measurement of dimension A is 1 1/4".

Circle is a geometric shape in which all the constituent points are at a certain distance from the center point. A circle has a diameter that shows the maximum distance between any two points of the circle. Whilst the radius is half the diameter.

Now we take a look at the picture thoroughly.

The width of the manufactured part =

the diameter of the circle on the far left = 2 * the radius

                                                                  = 2 * 1"

                                                                  = 2"

This value is equal to the sum of A, the radius of the circle at the very bottom (1/2"), and the space between this circle and the edge (1/4"). We write it down mathematically:

2" = A + 1/2'' + 1/4''

2" = A + 3/4"

A = 2" - 3/4"

  = 1 1/4"

Thus the measurement of dimension A is 1 1/4".

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The slope of the line is -6/5

It is important to note that the formula for the equation of a line is given as;

y = mx + c

Where;

The formula for slope of a line is expressed as;

Slope, m = y₂ - y₁/x₂ - x₁

Given the points,

A(-2. 4)

B (3, -2)

Substitute the values

Slope, m = -2 - (4)/3 - (-2)

simply the values

Slope, m = -2- 4/3 + 2

Add or subtract the values

Slope, m = -6/5

Hence, the value is -6/5

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Answer:

5x+3y=10

subtract both sides by 5x

divide everything by 3

y= -5/3x +10/3

hopes this helps

Answer:

slope: 1/2

Step-by-step explanation:

(2,7) and (4,6) are the points

the formula for finding slope when there are two points is

y2-y1/x2-x1

6-7/4-2=1/2

The value of the the angle tanPQS is 24.65⁰

You should understand that a cuboid is a polygon with six faces, the four opposite sides form a quadrilateral and diagonals make right triangles.

The image is a cuboid that has similar sides

From the cuboid, the length of PS=QR=5cm

Also, the length PQ = 12 cm

Using Pythagoras rule,

12²-5²=SQ

This means that 144-25 = SQ

Then SQ=√19 = 10.9

Also, from trigonometric ratio,

TanPQS= opposite/adjacent

Tan PQS= 5/10.5

Tan PQS= 0.4587

PQS = tan⁻¹0.4587

In conclusion <PQS=24.65⁰

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The position value, r(t) is equals to the (t³/6)k + 2j and velocity value, v(t) is equals to ( t²/2 )k + 4i , for a(t) = tk, v(0) = 4i, r(0) = 2j.

Acceleration is defined as the rate of change of the velocity of an object with respect to time. Accelerations are vector quanty.

a = dv/dt

We have the following informations are available,

Initial velocity, v(0) = 4i

Initial position, r(0) = 2j

Acceleration at any time "t",

a(t) = tk

we have to determine the value of v(t) and r(t).

As we know, a(t) = dv(t)/dt = tk

integrating the above equation ,

v(t) = ∫tk dt = ( t²/2 )k + c

at t = 0 , v(0) = 0 + c = 4i ( since, v(0) = 4i

=> c = 4i

So, v(t) = ( t²/2 )k + 4i

Also, velocity is calculated by derivative of postion (r) with respect to time.

=> v(t) = dr(t) /dt

=> r(t) = ∫ v(t) dt

=> r(t) = ∫ ( t²/2 )k dt

integrating value of the right hand side,

r(t) = ( t³/2×3 )k +d

= (t³/6)k + d

At t = 0, r(0) = (0/6)k + d

=> r(0) = d = 2j

so, r(t) = (t³/6)k + 2j

Hence, the required position and velocity are

(t³/6)k + 2j and ( t²/2 )k + 4i.

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If variation in a process results from common causes alone, the process is said to be in statistical control.

When talking about control charts, being in-control means your process is exhibiting common cause variation and is predictable.

Variation due to the inherent variability in a system of operation is called. special or assignable causes.

Industrial control systems are used by a discipline known as industrial process control in continuous manufacturing processes to produce at a level of consistency, economy, and safety that is impossible to achieve exclusively through manual human control. Process control systems make guarantee that industrial activities are carried out efficiently, dependably, and with as little fluctuation as is practical. They are installed in industrial settings to guarantee throughput, quality, yield, and energy efficiency. Ensure that work is done profitably and safely according to established procedures.

Therefore,

If variation in a process results from common causes alone, the process is said to be in statistical control.

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Peter will need approximately 169169 centimetres of red ribbon to make the "x" on his flag. Rounded to the nearest centimetre, this is 169200 centimetres.

To find the length of the red ribbon needed to make the "x" on the flag, we need to find the length of the diagonal of the square. The diagonal of a square is a line segment that connects two opposite corners of the square and passes through the centre of the square.

The diagonal of a square can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In the case of a square, the two shorter sides of the right triangle are equal in length to the sides of the square, so the Pythagorean theorem can be written as:

[tex]a^2 + a^2 = c^2[/tex]

Where "a" is the length of a side of the square and "c" is the length of the diagonal.

To find the length of the diagonal of Peter's flag, we can substitute 121212 for "a" in the equation above:

[tex](121212)^2 + (121212)^2 = c^2[/tex]

Solving for "c" gives us:

c = 169169 centimetres

Therefore, Peter will need approximately 169169 centimetres of red ribbon to make the "x" on his flag. Rounded to the nearest centimetre, this is 169200 centimetres.

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Answer:

Step-by-step explanation:

144 días

Option(C) represents the function.

What is a function?

A function is a relation between a set of inputs (also called the domain) and a set of outputs (also called the range) such that for each input, there is exactly one output. A graph of a function is a visual representation of the relationship between the inputs and outputs, with the inputs represented on the x-axis and the outputs represented on the y-axis.

A curve can be a function if it meets the definition of a function, which states that for each input (x value), there is exactly one output (y value). In other words, no two points on the curve have the same x-coordinate but different y-coordinates.

Hence, Option(C) represents the function.

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The logarithmic expression [tex]\log {750}[/tex]  is the lograrithm with base 10 of 750 and it's value is approximately equal to 2.8751


Logarithms are expressed mathematically as [tex]\log_{x}b=y[/tex] where [tex]x[/tex] denotes the base of the logarithm, [tex]b[/tex] denotes a number and [tex]y[/tex] denotes the exponent. The above expression can also be written as [tex]x^{y}=b[/tex]
We will be using two logarithmic properties in this question:

The first one is, [tex]log(mn) = logm + logn[/tex]

And the second one is, [tex]log(m^{n}) = n*logm[/tex]

Whenever the base in the question is not shown then it is assumed to be 10 in mathematics.

∵ This is a base 10 logarithm, we must determine a value of [tex]y[/tex] for expression [tex]10^{y} = 750[/tex]
Since there is no other value of log given we have to use the calculator.

If the value of [tex]log_{}3[/tex] and [tex]log5[/tex] is given then we can solve the question:

[tex]log750 = log_{10} 750[/tex]

⇒[tex]log_{10}(3*5^{2} * 10)[/tex]  

⇒[tex]log 3 + 2log 5 + log 10[/tex]

⇒[tex](0.47712) + 2(0.69897) + 1[/tex]

⇒[tex](0.47712) + (1.39794) + 1[/tex]

≈ [tex]2.8751[/tex]

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4 and 1/2 ft taller is the giraffe at the end of month 11 than at the end of month 2.

The function h(m) = (1/2)*m + (6 + 1/2) represents the height (on feet) of the giraffe as a function of the number of months, m.

We want to find the difference in the height between month 11 and month 2, then we need to find:

difference = h(11) - h(2)

We can directly calculate this:

difference = [ (1/2)*11 + (6 + 1/2)] - [(1/2)*2 + (6 + 1/2)]

difference = (1/2)*11 - (1/2)*2 = (1/2)*(11 - 2) = (1/2)*(9) = 9/2

And we can write 9 = 9 + 1, then:

difference=9/2 = (8 + 1)/2 = 8/2 + 1/2

difference= 4 + 1/2

Therefore, the giraffe is (4 and 1/2) ft taller in month 11 than in month 2.

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The expression is a polynomial expression that has 3 terms

The constant is 1/10

the leading coefficient is 1

A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc., that only uses non-negative integer powers or only positive integer exponents of a variable.

A polynomial with an exponent of 1 is, for instance, 2x + 5.

The given polynomial is written as -x + 1/10 + x⁴

x⁴ - x + 1/10

the number of terms are 3

the constant term is 1/10

the leading coefficient is the coefficient of x⁴ which is 1

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Answer: the answer is £12.

Step-by-step explanation:

To solve this problem, we can set up an equation to represent the information given in the problem. Let's call the amount of money Hasim had at the beginning of the day x.

We know that Hasim gave his brother 1/3 of his money, so we can represent that with the equation:

x / 3 = y

Where y is the amount of money Hasim gave to his brother.

We also know that Hasim spent £12 on a present for his sister, so we can subtract that amount from x to find the amount of money he had left:

x - 12 = z

Where z is the amount of money Hasim had left after buying the present.

Finally, we are told that the amount of money Hasim had left is half of what he had at the beginning of the day, so we can represent that with the equation:

x / 2 = z

Now we have three equations that all involve the variable x. We can solve for x by substituting the first equation into the second and third equations:

x / 3 = x - 12

x / 2 = x / 3

Solving these equations, we find that x = 36.

This means that Hasim had £36 at the beginning of the day, and gave his brother £36 / 3 = £<<36/3=12>>12.

Answer:

No its not but each time a car come you need to move to your side of the lane

Answer

third choice

Step-by-step explanation:

Answer:

it would be the 3rd answer

The rate of increase of the radius of the balloon at the instant when the radius is 30 cm is 0.0167 cm/min and when the radius is 60 cm, it is 0.0021 cm/min.

(a) At the instant when the radius of the balloon is 30 cm, the rate of increase of the radius of the balloon is

Rate of Increase of radius = (Change in Volume/ Change in Time) / (4/3 × π × (radius)^3)

= (800 cm3/min) / (4/3 × π × (30 cm)^3)

= 0.0167 cm/min

(b) At the instant when the radius of the balloon is 60 cm, the rate of increase of the radius of the balloon is

Rate of Increase of radius = (Change in Volume/ Change in Time) / (4/3 × π × (radius)^3)

= (800 cm3/min) / (4/3 × π × (60 cm)^3)

= 0.0021 cm/min

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The best sampling method, among these four, will be ¹²C₂ × ¹⁰C₁.

A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.

Three pupils will be chosen from a class of 12 girls and 10 males to sit on a school advisory council. Here are four distinct approaches to choosing.

The total number of students is given as,

Total = 12 + 10 = 22

Then the best sampling method, among these four will be given as,

¹²C₃ × ¹⁰C₀, ¹²C₂ × ¹⁰C₁, ¹²C₁ × ¹⁰C₂, ¹²C₀ × ¹⁰C₃

The best sampling method, among these four, will be ¹²C₂ × ¹⁰C₁.

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3x√5 and 3(³√5x) are like radicals because they both have the same radicand (the number or expression inside the radical symbol) of 5 and the same index (the number that indicates the root being taken) of 3. The only difference is the coefficient (the number multiplying the radical) of 3 in front of the radical symbol, which is a factor that does not affect the radical itself.

x(³√5) and y √√5 are not like radicals to 3x√5 because they have different radicands.

√5y is not a like radical to 3x√5 because it has a different index.

g(2) is -1/4 for function g(x)= 1-x/x².

A relation is a function if it has only One y-value for each x-value.

The given function is  g(x)= 1-x/x²

g of x equal to one minus x divided by x square

g(x)= 1-x/x²

Now we need to find the value of g(2).

Replace the x with 2

g(2)=1-2/2²

When two is subtracted from one we get minus one and two square is four

g(2)=-1/4

Hence, g(2) is -1/4 for function g(x)= 1-x/x².

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Answer:

x = -4

y = -3

Step-by-step explanation:

-4x + 4y = 4          Eq.  1

y = 3x + 9             Eq. 2

Replacing Eq. 2 in Eq. 1:

-4x + 4(3x+9) = 4

-4x + (4*3x + 4*9) = 4

-4x + (12x+ 36) = 4

8x + 36 = 4

8x = 4 - 36

8x = -32

x = -32/8

x = -4

From Eq. 2

y = 3*-4 + 9

y = -12 + 9

y = -3

Check:

From Eq. 1

-4x + 4y = 4

-4*-4 + 4*-3 = 4

16 - 12 = 4

The graph of the parabola is drawn below. And all the intersection points are shown in the diagram.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The equation is given below.

y = -4(x - 5)² + 125

Where y is the height of the rocket and x is the number of seconds since launch.

The vertex of the parabola is at (5, 125).

The graph of the parabola is drawn below. And all the intersection points are shown in the diagram.

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Using Pythagoras theorem, the hypothenuse is equal 4 units

Pythagoras theorem states that in a right triangle, the square of the length of the longest side (the hypotenuse) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, it can be expressed as a²+ b² = c², where a and b are the lengths of the two shorter sides, and c is the length of the hypotenuse.

The length of the third side is the hypothenuse and we can use Pythagoras theorem to find that.

a²+ b² = c²

3² + (√7)² = c²

9 + 7 = c²

c² = 16

Taking the square root of both sides;

c = √16

c = 4

The third side is 4 units

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The third side which is a hypotenuse of the right angle triangle have the length equal to 4.

We shall represent the length of the third side with x, so that by Pythagoras rule we evaluate for the hypotenuse as follows:

x² = 3² + (√7)² {note that: (√7)² = √7 × √7 = 7}

x² = 9 + 7

x² = 16 {square root of both sides}

x = √16

x = 4.

Hence the length of the hypotenuse is equal to 4 by proper application of the Pythagoras rule.

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Answer:

m= slope - - = +. formula is m=y2-y1

Answer:(-5/0) (y,x) (rise/run)

Step-by-step explanation:

Assuming that those are two points, the slope is -5/0.

(y1-y2)       Rise

over         over

(x1-x2)       Run

Use identity:

Modify it as follows:

Substitute a = p, b = 1/p and evaluate:

Proved

Answer:
$33.64

If this help please set brainliest.

Step-by-step explanation:

The total cost of all the items before the discount is $42.05. The discount Joseph receives is 20% of this amount, so the discount he receives is $42.05 * 20% = $8.41.

The total cost after the discount is applied is $42.05 - $8.41 = $33.64. This is the total cost in dollars and cents, before tax, rounded to the nearest cent.

Answer:

21 cm

Step-by-step explanation:

The perimeter of a triangle is the sum of the lengths of the 3 sides. We already know all 3 lengths. The base is 6 cm, and the other two sides are 7 cm and 8 cm. 6+7+8 = 21. The perimeter is 21 cm.

perimeter of the triangle when base=6cm , height=6cm and side=7cm:

perimeter =6+6+7= 19cm.

perimeter of the triangle when base=6cm , height=6cm and side=8cm:

perimeter =6+6+8= 20cm.

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