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The required r log a + y log c is equivalent to the expression as [tex]r log a + y log c = log (a^r c^y)[/tex].

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
The expression r log a + y log c can be simplified using logarithmic properties. Specifically, we can use the rule that says:

[tex]log a^b = blog a[/tex]

Using this rule, we can write the expression as:

[tex]r log a + y log c = log a^r + log c^y[/tex]

Now we can use the rule that says:

log a + log b = log ab

to combine the two logarithms:

[tex]log a^r + log c^y = log (a^r c^y)[/tex]

Therefore, the expression r log a + y log c simplifies to:

[tex]r log a + y log c = log (a^r c^y)[/tex]

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Answer:

Below

Step-by-step explanation:

Here is what the graph should look like ...you can see that he will have 0 fence left to paint  ( 0 = y ) when time = 3 hrs

As said, 48 model automobiles are driven by Jim at the moment, and the ratio might alter to 19:13.

An organisation of the integers a and b stated as a/b is still a ratio if b is truly not comparable to 0. Two ratio with the same value are established by the percent formula. As an illustration, you might write your ration as follows: 1:3 when there is 1 man and 3 females.

You know there's an 8:6 ratio between the grand total of model cars Jim and Terrence possess.

As a result, you can respond to the assignment as follows: Assume Jim owns x different car models.

8/6 = x/36

x = 36*8/6

x = 288/6

x = 48

The new percentage of Jim's against Terrence's model vehicles will be as follows because both Jim & Terrence sell ten of their model cars:

(48-10)/(36-10) = 38/26 = 19/13

Jim's to Terrence's miniature automobiles will now be in a 19:13 ratio.

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The given expression simplifies to sin 2x.

Option (D) is correct.

What are trigonometric ratios?

Trigonometric ratios are ratios of the sides of a right triangle that are used to define the relationships between the angles and the sides of the triangle. The three basic trigonometric ratios are sine, cosine, and tangent, which are commonly abbreviated as sin, cos, and tan, respectively.

The expression (sin 3x)(cos x) − (cos 3x)(sin x) is an example of a trigonometric identity known as the "sin of a difference" formula:

sin(A - B) = sin A cos B - cos A sin B

By comparing this formula to the given expression, we can see that:

A = 3x

B = x

Substituting these values into the formula, we get:

sin(3x - x) = sin 2x = (sin 3x)(cos x) − (cos 3x)(sin x)

Hence, the given expression simplifies to sin 2x.

Option (D) is correct.

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Answer:

x+1/x

Step-by-step explanation:

The equation of the polynomial is P(x) = -4(x + 1)(x - 1)(x - 2)^2

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

The graph

On the graph, we have the following readings:

A polynomial is represented as

P(x) = a * (x - zero)^multiplicity

Using the above as a guide, we have the following:

P(x) = a * (x + 1)(x - 1)(x - 2)^2

The y-intercept is -12

So, we have

a * (0 + 1)(0 - 1)(0 - 2)^2 = -12

This gives

a = -4

Hence, the expression is P(x) = -4(x + 1)(x - 1)(x - 2)^2

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Answer:

36.

Step-by-step explanation:

o find F'(4), we need to use the chain rule of differentiation. The chain rule states that if F(x) = f(g(x)), then F'(x) = f'(g(x)) * g'(x).

Given that f(-2) = 5, f'(-2) = 9, f'(4) = 3, g(4) = -2, and g'(4) = 4, we can calculate F'(4) as follows:

F'(4) = f'(g(4)) * g'(4) = f'(-2) * g'(4) = 9 * 4 = 36

Therefore, F'(4) = 36.

A measurement which is closest to the volume of the cylinder in cubic cm is 158.87 cubic cm.

Mathematically, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

Next, we would determine the radius of the base of the cylinder:

Circumference of a circle = 2πr

10 = 2πr

Radius, r = 1.59 cm.

Substituting the given parameters into the volume of a cylinder formula, we have the following;

Volume of a cylinder, V = 3.142 × (1.59)² × 20

Volume of a cylinder, V = 158.87 cubic cm.

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The rule A(x,y) ⇒  (-y,x) describes a transformation. The correct option is D.

The concept of rotation in mathematics has its roots in geometry. Any rotation is a movement of a certain area while maintaining at least one point. It may be used to describe, for instance, how a rigid body moves around a fixed point.

Our point A(x,y) becomes A' when a point is rotated 90 degrees counterclockwise about the origin (-y,x). To put it another way, flip x, and y, making y negative.

The transformation is described by the rule A(x,y) (-y,x). The right answer is D.

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Jade and Juliette 44.7days  more days to complete their trip.

To calculate how many more days Jade and Juliette need to ride, we can use the equation:

Total distance = Distance on first day + Distance on second day + Distance on remaining days

We know the first and second day distances, and the daily distance for the remaining days, so we can substitute those values in the equation:

2878 = 45.4 + 56.3 + 62x

where x is the number of remaining days they need to ride.

Simplifying the equation:

2878 - 101.7 = 62x

2776.3 = 62x

Dividing both sides of the equation by 62

x = 44.7

hence, Jade and Juliette need to ride for 44.7 more days to complete their trip.

The value of the variable y is 3

From the information given, we have that;

ACDF∼VWYZ

Given that the lengths are;

Since the diagrams are equivalent, then,

A/VZ = CD/YW

substitute the values, we have;

12/3y - 1 = 9/6

cross multiply

3y - 1 = 12(6)/9

divide the values

3y - 1 = 8

collect like terms

3y = 9

Make 'y' the subject

y =3

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The properties of the polynomial are

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

The graph

On the graph, we have the following readings:

Using the above as a guide, we have the following:

Degree = sum of multiplicities

Degree = 1 + 1 + 2 + 1

Degree = 5

The leading coefficient is negative

This is so because the graph opens down

There are 3 zeros with odd multiplicities and 1 zero with even multiplicity

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The condition which satisfy the congruency of the given triangle is

BC≈QR.

Two triangles are said to be congruent if all the corresponding sides are equal and all the corresponding angles are equal. The symbol of congruency is '≅'

To show that triangle ABC≈triangle PQR by SSS,

In this type of congruency, all the sides of the triangle ABC is equivalent to the all the sides of the triangle PQR.

Given, AC≅PR, AB≅PQ.

The another one condition is BC≅QR.

Hence, the condition which satisfy the congruency of the given triangle is BC≈QR.

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The given expression can be written in a single radical as q³ .   [tex]\sqrt[]{ q^{\frac{7}{6} } }[/tex]. The solution has been obtained by solving the radical expressions.

What are radical expressions?

An expression which contains a square root is referred to as a radical expression. The 'V'-shaped portion of the radical sign will have a superscript number when it is used to represent any root other than a square root.

We are given √q³ [tex]\sqrt[3]{q^{8} }[/tex].

On simplifying the expression, we get

⇒√q² . q [tex]\sqrt[3]{q^{3} . q^{3} . q^{2} }[/tex]

⇒q . √q . q² .  [tex]\sqrt[3]{ q^{2} }[/tex]

⇒q³ . √q  [tex]\sqrt[3]{ q^{2} }[/tex]

⇒q³ . [tex]\sqrt[]{ q^{\frac{1}{2} + \frac{2}{3} } }[/tex]

⇒q³ . [tex]\sqrt[]{ q^{\frac{7}{6} } }[/tex]

Hence, the given expression can be written  in a single radical as q³ . [tex]\sqrt[]{ q^{\frac{7}{6} } }[/tex].

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Let's call the tens digit "x" and the units digit "y". We know that the number is a multiple of 9, so:

x + y = 9

and the ratio of the units digit to the tens digit is 1:2, so:

y = 2x

Substituting the second equation into the first, we get:

x + 2x = 9

3x = 9

x = 3

So the tens digit is 3 and the units digit is 2 times that, or 6. The number is 36.

Answer:

63

Step-by-step explanation:

___________________

First, let's list all the 2-digit multiples of "9":

______________________________________________________

18, 27, 36, 45, 54, 63, 72, 81, 90, 99.

______________________________________________________

From this list, the only answer that has a ratio in which its "units digits to its tens digits" is "1:2" is: "63" . "3:6" = "1:2" .

The equation of the line with slope 3 that goes through the point (2, 5) is y = 3x - 1.

What is the slope-point form of the line?

The point-slope form of the equation of a line is given by:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is a point on the line.

Using the given slope of 3 and the point (2, 5), we can substitute into the point-slope form to get:

y - 5 = 3(x - 2)

Expanding the right-hand side:

y - 5 = 3x - 6

Adding 5 to both sides:

y = 3x - 1

Hence, the equation of the line with slope 3 that goes through the point (2, 5) is y = 3x - 1.

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Answer: 12.72 ft.

Step-by-step explanation:

[tex]\frac{6}{8.3} = \frac{x}{17.6} \\\\ 8.3x= 105.6\\\\x= 12.72[/tex]

The dimensions of the sticker are 11 millimeters and 3 millimeters.

Area of a two dimensional shape is the total region which is bounded by the object's shape.

Perimeter of a straight sided figures or objects is the total length of it's boundary.

Given is a sticker which is rectangular in shape.

Area of the sticker = 33 millimeters²

Perimeter of the sticker = 28 millimeters

Area of a rectangle = Length × Width

Perimeter of a rectangle = 2(Length + Width)

Let x be the length and y be the width of the rectangle.

x y = 33

2(x + y) = 28 ⇒ 2x + 2y = 28 ⇒ 2y = 28 - 2x ⇒ y = 14 - x

Substituting y = 14 - x in x y = 33,

x(14 - x) = 33

14x - x² = 33

-x² + 14x - 33 = 0

x² - 14x + 33 = 0

Factorizing the quadratic equation,

(x - 11) (x - 3) = 0

x - 11 = 0 or x - 3 = 0

x = 11 or x = 3

If x = 11, then y = 33/11 = 3

If x = 3, y = 33/3 = 11

Hence the dimensions are 11 millimeters and 3 millimeters.

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Answer: 1/2 is

Step-by-step explanation:

On solving the provided question we can say that the quadratic equation is  3x²+15x+9=0

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

the quadratic equation is 3x²+15x+9=0

by Shridhara Charya formula method, we have

x=−0.697224

x=−4.30278

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Answer:

= 9x - 1

Step-by-step explanation:

[tex] \frac{(5x - 1)}{x} + 4 \\ = x \times \frac{5x - 1}{x} + 4(x) \\ = 5x - 1 + 4x \\ = 5x + 4x - 1 \\ = 9x - 1[/tex]

The chances are that your gain will be $40 if you purchase two shares of ABC stock and no shares of XYZ stock, and if it is not $40 the gain is:

1) 50%, $0

2) 25%, $20

3) 75%, $30

4) 50%, $20

So, the option (4) 50%, $20 is the correct option.

The given question is asking what the chances are that your gain will be $40 if you purchase two shares of ABC stock and no shares of XYZ stock, and what the gain will be if it is not $40.

Mathematically, this can be broken down as follows:

There is a 50% chance that the temperature will be lower than average, in which case the stock price for ABC will increase by $20. Thus, the expected gain from investing in ABC is 50% x $20 = $10.

There is a 25% chance that the temperature will be higher than average, in which case the stock price for XYZ will increase by $20. Since you are not investing in XYZ, your expected gain from this is 0.

Therefore, the expected gain from investing in ABC and not investing in XYZ is 50% x $10 + 25% x $0 = $10 + $0 = $10.

Since you are investing in two shares of ABC stock, your expected gain is 2 x $10 = $20. Thus, there is a 50% chance that your gain will be $40, and otherwise your gain will be $20.

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Answer:

The simplified expression is a^(21/20).

Step-by-step explanation:

To simplify the expression, we can use the rule for multiplying two powers with the same base, which is to add the exponents.

a^(3/5) * a^(3/4) = a^(3/5 + 3/4) = a^(6/5 + 3/4)

We can then simplify the fractional exponent by finding a common denominator for the numerators, which is 20 in this case:

a^(6/5 + 3/4) = a^(6/20 + 15/20) = a^(21/20)

The simplified expression is a^(21/20).

Answer:

x=5 and LN= 30, MP= 40

Step-by-step explanation:

Add like terms to both sides of the equation and you will get your answer

Answer:

C) 0.24 kg

----------------------------

Find the weight of two loaves of bread:

Find the difference of weights of 2 loaves of bread and 6 muffins:

The matching choice is C.

The difference of weights of 2 loaves of bread and 6 muffins:

= 0.24 kg

We have to given that,

One loaf of bread weighs 0.68 kilogram.

And, Six muffins weigh 1.12 kilograms.

Now, We can Find the weight of two loaves of bread:

Here, One loaf of bread weighs 0.68 kilogram.

Hence, the weight of two loaves of bread:

0.68 x 2 = 1.36 kg

Hence, the difference of weights of 2 loaves of bread and 6 muffins:

= 1.36 kg - 1.12 kg

= 0.24 kg

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Answer:

Both of them are correct.

Step-by-step explanation:

Let's review both of their methods and check their validity.

This method is the most straight forward and seems to be correct as we're simply calculating the total value of each, and then subtracting the difference. We can write the expression as: [tex]2.25(4.25)-2.25(2.85)[/tex] and this should give us the difference assuming the prices and math is done correctly.

While this method is a bit difference, it actually does work! Think of this way, we first calculate the difference in the prices and then for each pound we increase it by, the difference also increases by this amount. It also helps to look at our original expression: [tex]2.25(4.25)-2.25(2.85)[/tex], notice how we have a factor of 2.25 on both sides? Well we can just factor that out to get: [tex]2.25(4.25 - 2.85)[/tex] and this is essentially what Ariel's method is. This should give us the difference in prices and is likely easier than Kaylee's method as we do less multiplication and with smaller numbers.

The domain of the real valued function as required is; [3, infinity).

The range of the function as required is; (-infinity, -3].

By observation of the given function; the domain is the set of all real numbers except those for which;

4x - 12 < 0

4x < 12

x < 3.

Hence, the domain of the function is; [3, infinity).

The range as observed in the task content has a maximum value of; -3. Hence, the range of the function as required is; (-infinity, -3].

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Answer:

Step-by-step explanation:

Since the polynomial has a root of multiplicity 2 at x = 3, it can be written as (x - 3)^2 times another polynomial Q(x). Also, since it has roots of multiplicity 1 at x = 0 and x = -4, it can be written as (x - 3)^2 * (x - 0) * (x + 4) * Q(x).

Next, we can use the fact that the polynomial goes through the point (5, 144) to find the formula for Q(x). The polynomial P(x) must satisfy P(5) = 144, so we can write:

(5 - 3)^2 * (5 - 0) * (5 + 4) * Q(5) = 144

4 * 9 * 9 * Q(5) = 144

36 * Q(5) = 144

Q(5) = 4

So, the polynomial P(x) can be written as:

P(x) = (x - 3)^2 * (x - 0) * (x + 4) * 4

  = 4 * (x - 3)^2 * (x - 0) * (x + 4)

  = 4 * (x^2 - 6x + 9) * x * (x + 4)

  = 4x^4 - 84x^3 + 378x^2 - 648x + 576

This is the formula for P(x).

The final price of Thomas Peters' new SUV  is $30,309 , can be calculated by subtracting the rebates from the initial cost.

The initial cost of the SUV was $32,984, and he received a $2,175 rebate from the car dealer and a $500 rebate from the manufacturer. So, the final price would be calculated as follows:

Final Price = $32,984 - $2,175 - $500

Final Price = $30,309

Therefore, the final price of Thomas Peters' new SUV is $30,309.

It is important to note that rebates can play a significant role in reducing the cost of a car purchase. In this case, Thomas Peters was able to receive a total of $2,675 in rebates, which reduced the cost of his new SUV by over 8%. This shows that it is often worth the time and effort to research available rebates and incentives when making a car purchase. Additionally, it is also a good idea to negotiate the price with the car dealer, as there may be room for further discounts.

By taking these steps, you may be able to save a significant amount of money on your car purchase and get a better value for your money. Ultimately, it is important to weigh the cost and benefits of each car option to determine the best choice for your needs and budget.

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