Solve the logarithmic equation. loga​(x−2)−loga​(x+9)=loga​(x−3)−loga​(x+4) Determine the equation to be solved after removing the logarithm. (Type an equation. Do not simplify.) What is the exact solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Simplify your answer. Type an exact answer. Use a comma to separate answers as needed.) B. There is no solution.

The values of a, b and c are given as follows:

a = 9, b = 15, c = 25.

The law of cosines states that we can find the side c opposite to an Angle C of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which the parameters are listed as follows:

The parameters for this problem are given as follows:

a = 3x, b = x + 5, c = y, C = θ.

Hence the expression is given as follows:

y² = (3x)² + (x + 5)² - 2(x + 5)(3x)(1/6)

y² = 9x² + x² + 10x + 25 - x² + 5x

y² = 9x² + 15x + 25.

Hence the values of a, b and c are given as follows:

a = 9, b = 15, c = 25.

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Answer: If Francesca's pedometer underestimates her step count by 4%, then the actual number of steps she walked can be found by dividing the pedometer reading by 0.96 (100% - 4% underestimation).

So, actual number of steps = 8,256 / 0.96 = 8,600.

Therefore, Francesca actually walked 8,600 steps.

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Answer:

(5, -1) or x = 5, y = -1

Step-by-step explanation:

[tex]\mathrm{Substitute\:}y=2x-11[/tex]

[tex]\begin{bmatrix}2x+3\left(2x-11\right)=7\end{bmatrix}[/tex]

[tex]8x-33=7[/tex]

[tex]\mathrm{Isolate}\:x\:\mathrm{for}\:8x-33=7[/tex]

[tex]8x=40[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}8[/tex]

[tex]\frac{8x}{8}=\frac{40}{8}[/tex]

[tex]x=5[/tex]

[tex]y= 2x-11 \\ \mathrm{Substitute\:}x=5[/tex]

[tex]y=2\cdot \:5-11[/tex]

[tex]y=-1[/tex]

Answer:

(5, - 1 )

Step-by-step explanation:

2x + 3y = 7 → (1)

y = 2x - 11 → (2)

substitute y = 2x - 11 into (1)

2x + 3(2x - 11) = 7

2x + 6x - 33 = 7

8x - 33 = 7 ( add 33 to both sides )

8x = 40 ( divide both sides by 8 )

x = 5

substitute x = 5 into (2)

y = 2(5) - 11 = 10 - 11 = - 1

solution is (5, - 1 )

Answer:

(1, 2 )

Step-by-step explanation:

y = - 2x + 4 → (1)

y = 3x - 1 → (2)

substitute y = 3x - 1 into (1)

3x - 1 = - 2x + 4 ( add 2x to both sides )

5x - 1 = 4 ( add 1 to both sides )

5x = 5 ( divide both sides by 5 )

x = 1

substitute x = 1 into either of the 2 equations and solve for y

substituting into (2)

y = 3(1) - 1 = 3 - 1 = 2

solution is (1, 2 )

Answer:

16cups

Step-by-step explanation:

1 pint of milk is 2cups

1.5pint of milk is 3cups

If 1 bottle contained 3 cups of milk,

8 ounces of strawberry is 1 cup

1 bottle contained 3cups of milk and 1 cup of strawberry syrup

1 bottle has 4 cups of milkshake

4 bottles have (4x4) cups of milkshake

Ans 16

Answer: it is 13

Step-by-step explanation:

it is 13 if you are on study island

The probability of having an older son is 1/2 in families with two children and The proportion of all sons who are eldest sons = 1/3, when each family has three children.

If each family has two children, then the two possible situations are that the family has two sons or a son and a daughter. So the chance of having an older son is 1/2 in families with two children. Thus, the proportion of all sons who are older sons is 1/2.

If each family has three children, then the possible situations are having three sons, two sons and one daughter, or two daughters and one son. If two sons and one daughter are there in the family, then the older one will be the eldest son. If two daughters and one son are there in the family, then the only son will be the eldest son.

Therefore, there is only one eldest son among three children in the second case. If the family has three sons, then the probability that the eldest son is responsible for taking care of their parents is 1. Hence, if each family has three children, the proportion of all sons who are eldest sons is 1/3.The following is the step-by-step answer to this question:

Probability of having an older son = 1/2 in families with two children. Probability of having an eldest son = 1/3 in families with three children. The proportion of all sons who are older sons = 1/2, when each family has two children. The proportion of all sons who are eldest sons = 1/3, when each family has three children.

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Answer:

y = 2x - 6

Step-by-step explanation:

Using the 'y=mx+c' form,

Since m = 2,

y = 2x + c

Substituting (1, -4) into the above equation:

-4 = 2 + c

c = -6

Hence,

y = 2x - 6

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In unit form, 1.6 x 0.7 equals 1.12 square meters.

The terms millimeter (mm), centimeter (cm), meter (m), and kilometer (km) are used to describe length (km). The weight is measured in kilograms (kg) and grammes (g). Milliliter (ml) and liter are used to measure volume (L).

We must identify the units of measurement that have been employed for each of the numbers in order to express 1.6 x 0.7 in unit form.

By calculating the length by the width and assuming that 1.6 meters represents the length, and 0.7 meters represents the width, we can determine the surface area of a rectangle with these measurement techniques:

1.12 square meters is equal to 1.6 x 0.7 meters.

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complete question is:

Write the expression 1.6 x 0.7 in unit form.

In unit form, 1.6 x 0.7 equals 1.12 square meters.

What kind of unit would that be?

The terms millimeter (mm), centimeter (cm), meter (m), and kilometer (km) are used to describe length (km). The weight is measured in kilograms (kg) and grammes (g). Milliliter (ml) and liter are used to measure volume (L).

We must identify the units of measurement that have been employed for each of the numbers in order to express 1.6 x 0.7 in unit form.

By calculating the length by the width and assuming that 1.6 meters represents the length, and 0.7 meters represents the width, we can determine the surface area of a rectangle with these measurement techniques:

1.12 square meters is equal to 1.6 x 0.7 meters.

Therefore, In unit form, 1.6 x 0.7 equals 1.12 square meters.

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After 45 blue counters are removed, the remaining number of blue counters is 63 more than yellow counters. Setting up an equation, we find that there were 162 blue counters to start with.

Let's start by assigning variables to the unknowns:

Let x be the number of yellow counters.

Then, the number of blue counters is 3x.

After 45 blue counters are removed, the number of blue counters is 3x - 45.

Finally, there are 63 more blue counters than yellow, so we can set up the equation:

3x - 45 = x + 63

Solving for x, we get:

2x = 108

x = 54

Therefore, there were 3x = 3(54) = 162 blue counters to start with.

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Answer:

Step-by-step explanation:

If a square has a perimeter of 100 feet, then each side of the square must be 25 feet long, since all four sides of a square are equal.

The area of a square is given by the formula A = s^2, where s is the length of one side of the square. Substituting s = 25 feet, we get:

A = (25 feet)^2

A = 625 square feet

Therefore, the area of the playground is 625 square feet.

Answer:

625 ft^2

Step-by-step explanation:

A square will have all 4 sides equal to each other.  Let x be the length of 1 side.  The perimeter, P, of such a square would be:

  P = 4x

We are told that p = 100 feet

 100 feet = 4x

 x = 25 feet

Each side has a length of 25 feet.

The area of this square wuld be (25')*(25') = 625 ft^2

The equation to calculate the probability that this coin is gold is (X / (X + Y)) x (R / (R + S)) x (T / (T + U))

Let's assume that after the first transfer, there are M gold coins and N silver coins in pot A, and R gold coins and S silver coins in pot B. The probability of selecting a gold coin from pot B after the first transfer is R / (R + S).

After the second transfer, the number of gold and silver coins in each pot changes again. Let's assume that there are T gold coins and U silver coins in pot A, and V gold coins and W silver coins in pot B. The probability of selecting a gold coin from pot A after the second transfer is T / (T + U).

To find the probability that a gold coin is selected from pot A after all transfers are complete, we need to multiply the individual probabilities together. That is:

Probability of selecting a gold coin from pot A after all transfers = (X / (X + Y)) x (R / (R + S)) x (T / (T + U))

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Answer:

x = 15/4

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 4x - 10 = 5

Then the value of x will be,

→ 4x - 10 = 5

→ 4x = 5 + 10

→ 4x = 15

→ [ x = 15/4 ]

Hence, the value of x is 15/4.

Answer:

[tex]9.9[/tex]

Step-by-step explanation:

Interpreted:

[tex]3^2-(4\div5\div8)+1[/tex]

1) Simplify 4 ÷ 5 to 0.8.

[tex]3^2-0.8\div8+1[/tex]

2) Simplify 3² to 9.

[tex]9-0.8\div8+1[/tex]

3) Simplify 0.8 ÷ 8 to 0.1.

[tex]9-0.1+1[/tex]

4) Simplify 9 - 0.1 to 8.9.

[tex]8.9+1[/tex]

5) Simplify.

[tex]9.9[/tex]

The time it will take to fill the tank is 1.256 hours and this it will take longer than an hour to fill the tank

A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces.

The volume of the cylinder needs to be calculated first. Volume of a cylinder is expressed as ;

V = πr²h, where r is the radius and h is the height of the cylinder.

V = 3.14 × 30² × 160

V = 452160 cm³

Since 1litres = 1000cm³

452160cm³ = 452160/1000 = 452.16litres

The rate at which it is filled is 0.1 litres per second

therefore for a volume of 452.16litres

= 452.16/0.1 = 4521.6 sec

3600sec = 1 hour

therefore 4521.6 sec = 4521.6/3600 = 1.256hours.

Therefore it takes longer than 1 hour to fill the tank.

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Answer:

Geometric sequences and exponential functions are alike in that they both involve repeated multiplication by a constant factor. In a geometric sequence, each term is found by multiplying the previous term by the same constant factor. In an exponential function, the value of the function is found by raising a constant base to an exponent that increases by a constant amount.

However, they differ in the way they are expressed. In a geometric sequence, each term is written as a discrete value in the sequence, while in an exponential function, the value of the function is written as a continuous function of the input variable. Additionally, geometric sequences are often used to model discrete phenomena, while exponential functions are often used to model continuous phenomena.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The sample proportion of encounters where a whale came within 985 feet of the bow is given by p-hat = 0.03, and the sample size is n = 85.

The mean of a sample proportion can be calculated using the formula:

μ = p

where p is the population proportion.

In this case, we do not have the population proportion, but we can use the sample proportion as an estimate of the population proportion. Therefore, the mean of the sample proportion is:

μ = p = p-hat = 0.03

So the mean of the sample proportion is 0.03.

Answer:

We can use the expression 2x = y , where 'x' is the amount she saves yesterday and y being the amount she saves this day.

Table = if x = 0 , y = 0
            if x = 1 , y = 2
            if x = 2 , y =4
            if x = 4 , y= 8

Answer:

x=3
y=4

Step-by-step explanation:

y=3x-9
5x+4y=32

You substitute what y is into the equation:
5x + 4(3x - 9) = 32
5x + 12x - 36 = 32
17x - 36 = 32
17x = 68
x = 4
Now you substitute x into y:
y = 3x - 9
12 - 9 = 3
y = 3

Answer:

? = 7.2

Step-by-step explanation:

The given equation is comprised of two ratios.

Using the given ratio 5.4 : 3, we can reduce it and see the ratio is 1.8 : 1

Now, using the same idea for the unknown value, we must multiply 1.8 by 4, giving 7.2.

The length of the whole movie was 130 minutes.

Let's call the length of the whole movie "x". According to the problem, Newton and his friends watch 50% of the movie before taking a break. This means they watched 0.5x minutes of the movie.

After the break, they watch the remaining 65 minutes of the movie. So the total time they watched the movie is:

0.5x + 65

But we know that the total time they watched the movie is the same as the length of the whole movie "x". So we can set these two expressions equal to each other and solve for "x":

0.5x + 65 = x

Subtracting 0.5x from both sides, we get:

65 = 0.5x

Dividing both sides by 0.5, we get:

x = 130

Therefore, the length of the whole movie was 130 minutes.

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Answer: [tex]x=24[/tex]

Step-by-step explanation: Since the ratio of 6:3 is a 2:1 ratio simplified, you know that x will need to double the value on the other side. Therefore, you can just multiply 12 by 2 to get the x-value which is 24. Another method is to see that the 3 on the other side of the ratio is 1/4 the value of 12. This means that the 6 is 1/4 the value of x. if you multiply 4 on both sides x=24. Those are the two methods I recommend you use to solve these ratio problems.

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{Equation:}\\\\\large\boxed{\mathsf{6:3}}\\\\\large\textsf{Simplifying for:}\\\\\large\boxed{\rightarrow \mathsf{x:12}}\\\\\large\textsf{Simplifying:}\\\\\large\boxed{\mathsf{\rightarrow 6\times 4: 3\times4}}\\\\\large\boxed{\mathsf{\rightarrow{24:12}}}\\\\\\\huge\text{Therefore your answer should be: }\\\huge\boxed{\mathsf{\bold{24}:12}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

x=50

Step-by-step explanation:

2x=100

divided both sides by 2

x=50

answer: x=50

Answer:

50

Step-by-step explanation:

2x = 100, divide 2 from 2x and also 100, you will be left with x = 50

Using the law of sines, the length of the other side of the sail, which is the third side of the isosceles formed, is calculated as about 32.5 feet.

An isosceles triangle is a triangle with at least two sides of equal length.

Let's call the length of the other side of the sail "x". Since the sail is an isosceles triangle, the other two angles opposite the two equal sides are also equal, each measuring (180 - 54)/2 = 63 degrees.

We can use the law of cosines to find x:

x² = 23² + 23² - 2(23)(23)cos(63)

x² = 1054.75

x ≈ 32.5

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Answer: 7

Step-by-step explanation:

To find the median, we need to first put the data points in order from least to greatest:

2, 3, 5, 9, 12, 21

There are six data points, so the median is the middle value. In this case, the middle two values are 5 and 9. To find the median, we take the average of these two numbers:

(5 + 9) / 2 = 7

Therefore, the median number of songs written by the members of Python Sunboat is 7.

Differential equation of the total quantity Q of dead leaves at time t= dt/dQ = -0.65Q + 5. and 7.69 grams per square centimeter is the equilibrium level.

The differential equation for the total quantity Q of dead leaves (per square centimeter) at time t is given by:dt/dQ = -0.65Q + 5.B.

Assuming that there are no leaves on the ground initially, t = 0.  

Q(0) = 0.

Qeq = 7.69 grams per square centimeter.

The solution to the differential equation is given by: Q(t) = (20/13) + Ce^(-0.65t) where C is an arbitrary constant. At equilibrium, dQ/dt = 0, or -0.65Q + 5 = 0.Qeq = 7.69 grams per square centimeter is the equilibrium level.

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There are now 29 business majors enrolled in both business calculus and elementary statistics based on Venn Diagram.

To find the number of students who are currently enrolled in both Elementary Statistics and Business Calculus, we need to use the information given in the problem and draw a Venn diagram. Let's assume that the set of students who are enrolled in Elementary Statistics is E, and the set of students who are enrolled in Business Calculus is C. We want to find the size of the intersection of these two sets, denoted by E ∩ C.

From the problem, we know that the total number of Business majors who are currently enrolled in at least one of the two courses is 100. This means that the size of the union of the sets E and C is 100. We also know that 77 students are enrolled in Elementary Statistics and 52 students are enrolled in Business Calculus.

Using this information, we can set up an equation that relates the sizes of the sets E, C, and E ∩ C:

E + C - E ∩ C = 100

77 + 52 - E ∩ C = 100

E ∩ C = 29

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To measure length ABAC=3.5 cm, open the compass,=3.5cm is a positive value because. Hence, BD will be higher than BC. Cut an arc on ray BX using point B as the center. Let D be where the arc crosses BX.

A point where two lines meet produces an angle.

The breadth of the "opening" between these two rays is referred to as a "angle". It is depicted by the figure.

Radians, a unit of circularity or rotation, and degrees are two common units used to describe angles.

By connecting two rays at their ends, one can make an angle in geometry. The sides or limbs of the angle are what are meant by these rays.

The limbs and the vertex are the two main parts of an angle.

The common terminal of the two beams is the shared vertex.

According to our question-

draw perpendicular bisector of CD

A where perpendicular bisector intersects BD

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By secant line formula, the slopes corresponding to the lines are listed below:

In this problem we have nine representations of lines, whose slopes must be determined. A line is represented by equations of the form:

y = m · x + b

Where:

According to analytic geometry, slope can be found by knowning the location of two points (initial, final) set on Cartesian plane and secant line formula:

m = (y₂ - y₁) / (x₂ - x₁)

Where:

Case 1: (x₁, y₁) = (0, - 3), (x₂, y₂) = (2, 1)

m = (2 - 0) / [1 - (- 3)]

m = 2 / 4

m = 1 / 2

Case 2: (x₁, y₁) = (- 3, 2), (x₂, y₂) = (1, - 3)

m = (- 3 - 2) / [1 - (- 3)]

m = - 5 / 4

Case 3: (x₁, y₁) = (- 3, - 4), (x₂, y₂) = (2, 3)

m = [3 - (- 4)] / [2 - (- 3)]

m = 7 / 5

Case 4: (x₁, y₁) = (0, 3), (x₂, y₂) = (3, - 3)

m = (- 3 - 3) / (3 - 0)

m = - 6 / 3

m = - 2

Case 5: (x₁, y₁) = (- 2, 1), (x₂, y₂) = (3, 2)

m = (2 - 1) / [3 - (- 2)]

m = 1 / 5

Case 6: (x₁, y₁) = (- 4, 3), (x₂, y₂) = (4, 1)

m = (1 - 3) / [4 - (- 4)]

m = - 2 / 8

m = - 1 / 4

Case 7: (x₁, y₁) = (2, - 4), (x₂, y₂) = (4, 2)

m = [2 - (- 4)] / (4 - 2)

m = 6 / 2

m = 3

Case 8: (x₁, y₁) = (- 4, - 1), (x₂, y₂) = (0, - 3)

m = [- 3 - (- 1)] / [0 - (- 4)]

m = - 2 / 4

m = - 1 / 2

Case 9: (x₁, y₁) = (- 2, 0), (x₂, y₂) = (4, 1)

m = (1 - 0) / [4 - (- 2)]

m = 1 / 6

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It will take approximately 4.4 years to earn enough money to go on the trip if we invest our 2200 in a savings account with a 1.55% interest rate compounded annually.

First, we need to calculate the amount of money that we need to save in order to cover the cost of the trip. This can be done by subtracting the amount we have already saved from the total cost of the trip:

Total cost of trip = 2500

Amount already saved = 2200

Amount to save = 2500 - 2200 = 300

Next, we can use the compound interest formula to calculate how long it will take to earn 300 with an interest rate of 1.55% compounded annually. We can set up the formula as follows:

A = P(1 + i)n

where:

A = accumulated amount = 300 + 2200 = 2500 (the total cost of the trip)

P = principal = 2200

i = interest rate per year = 1.55%

n = number of years we need to save for

We can now solve for n:

2500 = 2200(1 + 0.0155)n

Divide both sides by 2200:

1.13636 = 1.0155n

Take the natural logarithm of both sides:

ln(1.13636) = n ln(1.0155)

Divide both sides by ln(1.0155):

n = ln(1.13636)/ln(1.0155) ≈ 4.4 years

Therefore, it will take approximately 4.4 years to earn enough money to go on the trip if we invest our 2200 in a savings account with a 1.55% interest rate compounded annually.that we rounded our final answer to the nearest tenth as instructed.

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Answer: $4496

Step-by-step explanation:

Since we know that one pack of croissanwich costs $562, multiply $562 by 8 to get $4496.