Write the following expression as a sum and/or difference of logarithms. Express exponents as factors:
log5[x^2z^9w√x^4-81]

The equation of the oblique asymptote of g(x) = x²+x+4/x-1 is y=x+1.

Synthetic division is a shorthand method for dividing polynomials. It is similar to long division, but simplified by removing all the steps except for the division, such as a linear factor with a leading coefficient of one.

To find the equation of the oblique asymptote, we need to divide the numerator (x²+x+4) by the denominator (x-1) using synthetic division.

To do this, we must first create a synthetic division setup, as shown above. The first number in the setup is the number that is being divided by the polynomial in the denominator.

In this case, it is 1. The other numbers in the setup are the coefficients of the polynomial in the numerator.

The synthetic division setup has 1 as the number being divided and 1, 1, and 4 as the coefficients of the numerator.

After dividing, the quotient is x+1 and the remainder is 0. Since the remainder is 0, the equation of the oblique asymptote is y = x+1.

This means that the line with the equation y = x+1 is the oblique asymptote of g(x) = x²+x+4/x-1.

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Answer:

y= 1+x+2

Step-by-step explanation:

The values of midline, amplitude and period are 2, 5 and 4.

What is midline, period and amplitude?

The amplitude is the separation between the midline and either the greatest or minimum. The period is defined as the separation between the midline points before the maximum value and points after the minimum value. From one peak to the next, or from any point to the following corresponding point, is the Period The height between the center line and the peak is known as the amplitude (or to the trough).

Midline = (Highest value + Lowest value)/2

y = (7 - 3)/2

y = 4/2

y = 2

Amplitude =  (Highest value - Lowest value)/2

= (7 - (-3)) / 2

= (7 + 3) /2

= 10/2

= 5

Period = difference between the two highest values

= 4.

Thus, the values of midline, amplitude and period are 2, 5 and 4.

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The least common multiple of 47 and 45 is 2,115. Therefore, at 2,115 minutes, both patients receive their medication at the same time. 

we need to find the least common multiple of 47 and 45, the smallest number that is divisible by both 47 and 45.

Start by listing the multiples of each number until you find a common multiple.

Multiples of 47:

47, 94, 141, 188, 235, 282, 329, 376, 423, 470, 517, 564, 611, 658, 705, 752, 799, 846, 893, 940, 987, 1034, 1081, 1128, 1175, 1222, 1269, 1316, 1363, 1410, 1457, 1551, 1598, 1645, 1692, 1739, 1786, 1833, 1880, 1927, 1974, 2021, 2068, 2115, 2162, 2206, 2206, 2309

Multiples of 45:

45, 90, 135, 180, 225, 270, 315, 360, 405, 450, 495, 540, 585, 630, 675, 720, 765, 810, 855, 900, 945, 990, 1035, 1080, 1125, 1170 1215 1260 1305 1350 1395 1440 1485 1530 1575 1620 1665 1710 1755 1800 1845 1890 1935 1980 2025 232070

We can see that the least common multiple of 47 and 45 is 2,115. Therefore, at 2,115 minutes, both patients will receive their medication at the same time.

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Answer: 12 years

Step-by-step explanation:

     We will substitute the given amount after the investment period and then solve for t, the number of years the period was.

     Given:

A = 10,000(1 + 0.043t)

     Substitue:

15,160 = 10,000(1 + 0.043t)

     Distribute:

15,160 = 10,000 + 430t

     Subtract 10,000 from both sides of the equation:

5,160 = 430t

     Divide both sides of the equation by 430:

t = 12 years

The unit conversion of 1200 milliliters to kilograms is: 1.2 milliliters

What the question tells us is to convert 1200 milliliters to kilograms.

Now, the conversion table shows us this conversion and it is simply expressed as:

1 milliliter = 0.001 kilograms.

We are given 1200 milliliters. Thus, converting to kilograms gives us:

1200milliliters * 0.001 kilograms/1 milliliter

= 1.2 milliliters

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The horizontal cross section of a rectangular prism will always be a rectangle. If the base is a square, the cross-section can also be a square.

The definition of a prism is that the cross-section parallel to the base will be uniform.

Therefore, the cross section of a rectangular prism that is sliced horizontally is a rectangle.

The persons weight that had the least absolute change is: Rebecca

We are given the initial and final weights of Ophelia, Aaron, Nathan and Rebecca.

Ophelia's change in weight = 157 - 145 = 12 lbs

Aaron's change in weight = 163 - 178 = -15 lbs

Nathan's change in weight = 217 - 136 = 81 lbs

Rebecca's change in weight = 128 - 136 = -8 lbs

The absolute value of a number or integer is the actual distance of the integer from zero, in a number line. Therefore, the absolute value is always a positive .

Thus, "absolute value" means to remove any negative sign in front of a number, and to think of all numbers as positive (or zero).

Therefore, the least absolute change is |-8 lbs| = 8 lbs

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[tex]\sf \dfrac{7}{24}.[/tex]

[tex]\sf \dfrac{7}{16} *\dfrac{4}{3}*\dfrac{1}{2}[/tex]

When multiplying fractions, we can always just multiply all the numerators together and the denominators aswell, like this:

[tex]\sf \dfrac{7*4*1}{16*3*2}=\dfrac{28}{96}[/tex]

We could divide both the numerator and denominator by 4 to fully simplify this answer:

[tex]\sf \dfrac{28/4}{96/4}=\dfrac{7}{24}[/tex]

Since the numerator (7) is a prime number, this fraction cannot be further simplified.

[tex]\sf \dfrac{7}{24}.[/tex]

If the profit desired is $24,000 and the revenue is $112,250, then the cost is $88,250.

To find the cost, we need to use the formula:

Revenue - Cost = Profit

We can rearrange this formula to solve for the cost:

Cost = Revenue - Profit

Substituting the given values, we get:

Cost = $112250 -$ 24000

Cost = $88250

Therefore, the cost is $88250.

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The average speed at which the canoe traveled toward the lighthouse was approximately 14.1 feet per minute.

We can solve this problem using trigonometry. Let's call the distance between the canoe and the lighthouse "x", and let's call the average speed of the canoe "s".

From the first measurement, we know that:

tan(6.5°) = (115 - 1.3) / x

x = (115 - 1.3) / tan(6.5°)

x ≈ 1012.6 feet

From the second measurement, we know that:

tan(48.7°) = (115 - 1.3) / (x - 5/60 * s)

x - 5/60 * s = (115 - 1.3) / tan(48.7°)

x ≈ 166.2 feet

Now we can use these two equations to solve for "s". We can start by solving the second equation for "x" and substituting the result into the first equation:

x = 5/60 * s + (115 - 1.3) / tan(48.7°)

x ≈ 5/60 * s + 80.2 feet

(115 - 1.3) / x = tan(6.5°)

x = (115 - 1.3) / tan(6.5°)

Substituting the first equation into the second equation and simplifying, we get:

5/60 * s + 80.2 = (115 - 1.3) / tan(6.5°)

s ≈ 14.1 feet per minute

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Answer: D

Step-by-step explanation:

Answer: 6

Step-by-step explanation: you would substitute the Z for 3 so it would be 5(3)-3². You would then do 3²= 9 because it’s 3*3 and 5*3 is 15. So you would do 15-9 which equals 6

Required two transformations are translated according to the rule (x, y) → (x + 8, y + 2) reflected across the x-axis.

How to find the two transformations applied to pentagon ABCDE to create A″B″C″D″E″?

To find the two transformations applied to pentagon ABCDE to create A″B″C″D″E″, we can compare the coordinates of corresponding vertices of both pentagons.

Starting with point A, we see that it has been translated 8 units to the right and 2 units up to become A″. Therefore, the first transformation is a translation according to the rule (x, y) → (x + 8, y + 2).

Next, we can compare the y-coordinates of point A and A″ to see if a reflection has been applied. We see that the y-coordinate of A has changed from 5 to -7 in A″, indicating that a reflection has been applied across the x-axis.

Therefore, the two transformations applied to pentagon ABCDE to create A″B″C″D″E″ are:

Translated according to the rule (x, y) → (x + 8, y + 2)

Reflected across the x-axis.

The other options can be ruled out as they do not correctly reflect the transformation that was applied.

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The perimeter of the right triangle is 41 centimetres.

The right triangle have sides 11 centimetres, and 13 centimetres. Therefore, let's find the third side before finding the perimeter of the right triangle.

Hence, let's find the third side using Pythagoras's theorem.

Therefore,

c²  = a² + b²

where

Therefore,

11² + 13² = c²

121 + 169 = c²

c = √290

c = 17.0293863659

c = 17.03 cm

Hence,

perimeter of the right triangle = 11 + 13 + 17.03

perimeter of the right triangle = 41.0293863659

perimeter of the right triangle = 41 cm

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The perimeter of the triangle is 41 cm

To calculate the perimeter of a right triangle, we must add up the lengths of all three sides.

Assuming the sides are

opposite, a = 11 cm

adjacent, b = 13 cm

hypotenuse, c = ?

we can apply the Pythagorean theorem which determines the hypotenuse's length. The hypotenuse is recognized as the third side within a right triangle.

This principle mathematical expression reads:

c^2 = a^2 + b^2

c^2 = 11^2 + 13^2

c^2 = 121 + 169

c^2 = 290

c = sqrt(290)

c = 17

Solving for perimeter

Perimeter = a + b + c

Perimeter = 11 cm + 13 cm + 17 cm

Perimeter = 41 cm

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The rate at which the depth is changing at 2 am is given as follows:

D'(2) = 0.4354 feet per hour.

The equation giving the depth of the water in t hours after midnight is given as follows:

D(t) = 2cos(πt/3 + 2π/5) + 3.

The derivative of the cosine is negative sine, while the inner derivative is of π/3, hence, applying the chain rule, the derivative is given as follows:

D'(t) = -2π/3sin(πt/3 + 2π/5)

2 am is 2 hours after midnight, hence the numeric value of the derivative is given as follows:

D'(2) = -2π/3sin(2π/3 + 2π/5)

D'(2) = 0.4354 feet per hour.

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The probability that a randomly selected product will last longer than 166 days is approximately 0.1492, οr 14.92%.

The probability οf an event οccurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn οut.

We can use the standard normal distribution to answer this question.

z = (x - μ) / σ

For x = 166, μ = 146, and σ = 19.5, we have:

z = (166 - 146) / 19.5

z = 1.03

Using a standard normal distribution table, we can find that the area to the right οf z = 1.03 is approximately 0.1492.

Therefore, the probability that a randomly selected product will last longer than 166 days is approximately 0.1492, οr 14.92%.

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Answer:

Θ = 1.5 radians

Step-by-step explanation:

arc length is calculated as

arc = circumference of circle × fraction of circle , then

10.5 = 2πr × [tex]\frac{0}{2\pi }[/tex] ( cancel 2π on numerator/ denominator )

10.5 = 7 × Θ ( divide both sides by 7 )

[tex]\frac{10.5}{7}[/tex] = Θ , then

Θ = 1.5 radians

Answer:

For the given question ,

The radius r= 7

and length of an arc  =10.5

Also ,we know that

length of an arc = θ/360*(2pie *r)

where,  θ is the angle and (2*pie*r) is the circumference of the circle.

therefore, 10.5=(θ/360)* 2*pie*7

on further calculations,

θ=85.9 degrees

or θ=86 degrees(approx).

Answer:

x = 19m

Step-by-step explanation:

to find the other two sides of the compound shape,

(2+6+6)= 14m , and (x-2)m

area of the compound shape = (2 x 14) + 2(x-2) =28 + 2x - 2 = 2x+26 m²

area of square = 8 x 8 = 64 m²

the question states that these two shapes have the same area,

2x + 26 = 64

2x = 38

x = 38/2

x= 19m

Should it be necessary, round your response to the nearest whole number. Your credit card debt increases by a factor of three in just nine months, going from $800 to $2400. It would take 34.9 months for the balance to increase by $7000 if it grows linearly.

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Answer:

Danielle will need 27 gallons of blue paint.

Step-by-step explanation:

If the shade of green paint requires 2 parts yellow and 3 parts blue, that means for every 2 gallons of yellow paint, we need 3 gallons of blue paint.

So to find how many gallons of blue paint Danielle will need, we can set up a proportion:

2/3 = 18/x

where x is the number of gallons of blue paint.

To solve for x, we can cross-multiply:

2x = 54

x = 27

Therefore, Danielle will need 27 gallons of blue paint.

Answer:  To make the special shade of green paint, Danielle needs 2 parts yellow and 3 parts blue. This means that for every 2 gallons of yellow paint, she needs 3 gallons of blue paint.

If Danielle uses 18 gallons of yellow paint, we can set up a proportion to find how many gallons of blue paint she needs:

2/3 = 18/x

where x is the number of gallons of blue paint she needs.

To solve for x, we can cross-multiply and simplify:

2x = 3 * 18

2x = 54

x = 27

Therefore, Danielle will need 27 gallons of blue paint to make the special shade of green paint.

Step-by-step explanation: Would really apreciate brainliest :D

The flag have 6.09 square feet of area that make up the red and blue portion. And the flag have 1.35 square feet more of the white portions than the red and blue portions.

The tripes can be observed to have the shape of trapezoids, the middle coloured stripe can be split into two smaller trapezoids while the top and bottom coloured are of same size.

Red and blue portions:

1/2 × (3.5 + 4.5) × 0.6 = 2.4 ft² {area of trapezoid}

top

top and bottom coloured stripe = 2 × 2.4 ft² = 4.8 ft²

1/2 × (1.9 + 2.4) × 0.3 = 0.645 ft²

middle coloured stripe = 2 × 0.645 ft² = 1.29 ft²

area of red and blue portions = 4.8 ft² + 1.29 ft² = 6.09 ft²

White portions:

area of white triangle portion = 1/2 × 3 × 2.6 = 3.9ft²

1/2 ×( 2.4 + 3.5) × 0.6 = 1.77 ft² {area of one white stripe trapezoid}

area of white stripes = 2 × 1.77 ft² = 3.54 ft²

white portions = 3.9ft² + 3.54 ft² = 7.44 ft²

In conclusion, the flag have 6.09 square feet of area that make up the red and blue portions. And the flag have 1.35 square feet more of the white portions than the red and blue portions.

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Using trigonometry we know that the measure for θ is 25.747121° respectively.

The branch of mathematics is concerned with the computation of certain angles and their functions.

There are six widely used angles-related trigonometric functions.

Their respective names and acronyms are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

So, 14.5 meters is the hypotenuse.

6.3 meters on the opposite side

Using trigonometry now:

sin θ = Opposite side / Hypotenuse

Using the provided values, we obtain:

sin θ = 6.3 / 14.5

sin θ = 63/145

sin θ = 0.4344

θ =25.747121°

Therefore, using trigonometry we know that the measure for θ is 25.747121° respectively.

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Answer:

50% chance for each

Step-by-step explanation:

if there are two option out of 2 then that means you have a 50 50 chance each for both

PLS GIVE BRAINLIST MEAN THE WORLD

Answer:

90° clockwise rotation.

Step-by-step explanation:

The diameter of the circle is 4 inches.

The diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circumference of the circle.

The area of the circle is 12.6 inches square. Let's find the diameter of the circle as follows:

area of a circle = πr²

area of a circle = π(d / 2)²

where

Therefore,

12.6 = 3.14 × d² / 4

12.6 = 0.785d²

divide both sides by 0.785

d² = 12.6 / 0.785

d = √16.050955414

d = 4.00635744786

Therefore,

diameter = 4 inches

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Answer:

90 feet

Step-by-step explanation:

To find the perimeter of the classroom, we need to calculate the distance between each pair of adjacent corners and add them up.

Using the distance formula, the distance between the first two corners is:

√[(-12 - (-12))^2 + (15 - (-9))^2] = √(0^2 + 24^2) = 24 feet

The distance between the second and third corners is:

√[(-12 - 9)^2 + (-9 - 15)^2] = √(21^2 + 24^2) ≈ 31.8 feet

The distance between the third and fourth corners is:

√[(9 - 9)^2 + (15 - (-9))^2] = √(0^2 + 24^2) = 24 feet

Finally, the distance between the fourth and first corners is:

√[(9 - (-12))^2 + (-9 - 15)^2] = √(21^2 + 24^2) ≈ 31.8 feet

Therefore, the perimeter of the classroom is:

24 + 31.8 + 24 + 31.8 = 111.6 feet ≈ 112 feet (rounded to the nearest foot)

So the closest option to this answer is 90 feet.

The value of x in the right triangle is 10.43 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in the triangle is 180 degrees. Therefore, let's find the value of x in the right triangle.

tan 41 = opposite / adjacent

opposite side = x

adjacent side = 12

Therefore,

tan 41° = x / 12

cross multiply

x = 12 tan 41°

x = 12 × 0.86928673781

x = 10.4314408538

Therefore,

x = 10.43 units

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