Write 3+2lg a-4lg b
as a single logarithm to base 10.

The value of x for the similar triangles is 8 units.

The value of x is determined by applying the principle of similar triangles as shown below.

In the given diagram, we can assume the following for the similar triangles;

length 10 is congruent to length 10 + (3x + 1 )

length 22 is congruent to length 7x -1  + 22

So we will have the following equation;

(3x + 1  + 10 )/ 10 = (7x - 1 + 22 ) / 22

(3x + 11 ) / 10 = ( 7x + 21 ) / 22

22(3x + 11 ) = 10 (7x + 21 )

66x + 242 = 70x + 210

32 = 4x

x = 32 / 4

x = 8

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The solution for u is 36.

To solve for u using the multiplicative property of equality, we need to isolate u on one side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of the fraction that is attached to u. The reciprocal of (5/6) is (6/5), so we can multiply both sides of the equation by (6/5) to get:

(6/5) * 30 = (6/5) * (5/6) * u

Simplifying the right side of the equation gives us:

(6/5) * 30 = u

Multiplying the fraction and the whole number gives us:

(180/5) = u

Simplifying the fraction gives us:

36 = u

Therefore, the solution for u is 36.

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Answer:

78

Step-by-step explanation:

Answer:

$0.50

Step-by-step explanation:

We know

A package of 8 hot dogs is on sale for $4

What is the price per hot dog?

4 / 8 = $0.50

So, the price per hot dog is $0.50

The ratio of the surface areas to cube A to cube B is 12 : 7 .

What is known as a cube?

Six faces, eight vertices, and twelve edges make up the three-dimensional shape of a cube. An example of a prism in particular is a cube. These are the calculations for the volume of the cube formula: Amount = (side) 3.

                      The cube's face's diagonal length is equal to 2. (edge) Cube's cube's diagonal length is three (edge) 12 is the perimeter (edge). Each number multiplied by itself is a square number. The squared sign is (insert square symbol). Up to the number 100, the square numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. A number multiplied by itself three times is a cube number.

The ratio of the volumes of cube A to cube B is  =  1728 : 343

                                                                       = 12 : 7

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Answer:

To find the total surface area of a square pyramid, we need to find the sum of the areas of its base and its four triangular faces.

In this case, the base is a square with side length 11.5 inches. Therefore, its area is:

Area of base = 11.5^2 = 132.25 square inches

Each triangular face has a base length equal to the side length of the square base, which is 11.5 inches. To find the height of each triangular face, we can use the Pythagorean theorem. Since the pyramid is a square pyramid, the height of each triangular face is also the slant height of the pyramid.

The slant height of the pyramid can be found using the Pythagorean theorem:

a^2 + b^2 = c^2

where a = b = 11.5/2 = 5.75 (half the length of a diagonal of the square base) and c is the slant height. Solving for c, we get:

c = sqrt(a^2 + b^2) = sqrt(2*(5.75)^2) = 8.121 inches (rounded to 3 decimal places)

The area of each triangular face can be found using the formula:

Area of triangle = (1/2) * base * height

where the base is 11.5 inches and the height is 8.121 inches.

Area of each triangular face = (1/2) * 11.5 * 8.121 = 46.876 square inches (rounded to 3 decimal places)

So, the total surface area of the square pyramid is:

Total surface area = Area of base + 4 * Area of each triangular face

Total surface area = 132.25 + 4 * 46.876 = 330.124 square inches (rounded to 3 decimal places)

Therefore, the total surface area of the square pyramid is approximately 330.124 square inches.

Answer:

2500

Step-by-step explanation:

Total spectator 9500

Men 6375

Women and children = 9500-6375= 3125

Women X

Children 4X

If women and children = 3125

4x + X = 3125

5x = 3125

Divide both sides by 5

X = 625

Women 625

Children 625x4 = 2500

Answer:

Twenty Seven (27) cubic yards

Answer:

volume =27 cubic yards

Step-by-step explanation:

Volume = Base Area x Height

Volume= 3·3·3

Volume= 27

sin(θ + ɸ) = 17/145 and cos(θ + ɸ) = 144/145.

Suppose sin θ = -3/5, sin ɸ = 20/29. Moreover, suppose θ is in Quadrant IV and ɸ is in Quadrant l. We can find sin(θ + ɸ) and cos(θ + ɸ) by using the following formulas: sin(θ + ɸ) = sin θ cos ɸ + cos θ sin ɸ and cos(θ + ɸ) = cos θ cos ɸ - sin θ sin ɸ.

First, we need to find cos θ and cos ɸ. Since θ is in Quadrant IV, cos θ is positive. We can use the Pythagorean identity, sin² θ + cos² θ = 1, to find cos θ:

cos² θ = 1 - sin² θ
cos² θ = 1 - (-3/5)²
cos² θ = 1 - 9/25
cos² θ = 16/25
cos θ = √(16/25)
cos θ = 4/5

Similarly, since ɸ is in Quadrant l, cos ɸ is also positive. We can use the Pythagorean identity to find cos ɸ:

cos² ɸ = 1 - sin² ɸ
cos² ɸ = 1 - (20/29)²
cos² ɸ = 1 - 400/841
cos² ɸ = 441/841
cos ɸ = √(441/841)
cos ɸ = 21/29

Now we can plug in the values of sin θ, sin ɸ, cos θ, and cos ɸ into the formulas for sin(θ + ɸ) and cos(θ + ɸ):

sin(θ + ɸ) = sin θ cos ɸ + cos θ sin ɸ
sin(θ + ɸ) = (-3/5)(21/29) + (4/5)(20/29)
sin(θ + ɸ) = -63/145 + 80/145
sin(θ + ɸ) = 17/145

cos(θ + ɸ) = cos θ cos ɸ - sin θ sin ɸ
cos(θ + ɸ) = (4/5)(21/29) - (-3/5)(20/29)
cos(θ + ɸ) = 84/145 + 60/145
cos(θ + ɸ) = 144/145

Therefore, sin(θ + ɸ) = 17/145 and cos(θ + ɸ) = 144/145.

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Answer:

0.03125

Step-by-step explanation:

[tex]a_{n}[/tex] = [tex]a_{1}[/tex][tex](r)^{n-1}[/tex]  

[tex]a_{7}[/tex] = (2)[tex]\frac{1}{2} ^{(7-1)}[/tex]

[tex]a_{7}[/tex] = (2)[tex]\frac{1}{2} ^{6}[/tex]

[tex]a_{7}[/tex] = 0.03125

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

I just knew now I forgot sorry lol

Answer:

15%

Step-by-step explanation:

Subtracting -2y² from -4y² + 5d will give us -2y² + 5d.

A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, and multiplication.

To subtract the two polynomials, we first need to distribute the negative sign to the second polynomial.

So, (-4y² + 5d) - (-2y²) becomes -4y² + 5d + 2y².

Now, combine the like terms, which are the terms that contain y²:

-4y² + 5d + 2y² = (-4 + 2)y² + 5d

So, our final answer is:

-2y² + 5d.

Since our answer is in simplest terms, the final answer is -2y² + 5d.

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The domain of the piecewise function g of x is all real numbers, except for x = 2, which is the point at which the two functions overlap. Therefore, the domain is (–∞, 2) ∪ (2, ∞).

A domain is a collection of computers and devices connected to one another through a network. It is a logical grouping of computers and devices, such as a local area network (LAN) or a wide area network (WAN). Each device within the network is assigned a unique address, allowing it to communicate with other devices within the network. Domains can also be used to control access to resources, such as files, folders, printers, and databases. Domains can be used to authenticate users and set permissions, which determine the type of access a user has to the domain’s resources. This is commonly used in businesses and organizations to ensure that only authorized personnel have access to sensitive information.

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The answer in simplest form is 9/2

The division involving a whole number and a fraction can be simplified by multiplying the whole number by the reciprocal of the fraction.

The reciprocal of a fraction is obtained by flipping the numerator and denominator.

In this case, the division is 3 ÷ (2/3). The reciprocal of (2/3) is (3/2).

So, we can multiply 3 by (3/2) to simplify the division:

3 × (3/2) = (3/1) × (3/2) = (3 × 3) / (1 × 2) = 9/2

Therefore, the answer in simplest form is 9/2.

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The expression when evaluated is -5

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

6(− 2/3 ) − 1.5 + ( 1/2 )

To solve the given expression, we need to apply the order of operations, which is a set of rules that dictate the order in which mathematical operations should be performed.

Using the order of operations, we can simplify the given expression as follows:

6(− 2/3 ) − 1.5 + ( 1/2 ) = -4 − 1.5 + 0.5

Evaluate

6(− 2/3 ) − 1.5 + ( 1/2 ) = -5

Hence, the solution is (b) - 5

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a) The monthly interest rate for the $40,000 loan repaid monthly over 20 years with a monthly payment of $544.53 is 0.00153. b) The monthly interest rate for the $40,000 loan repaid monthly over 20 years with a monthly payment of $544.53 comes out as 0.00153 percent

To find the monthly payment needed to repay a $40,000 loan over 20 years with a 0.5% interest rate per month, we can use the following formula: Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^-Number of payments)

Plugging in the given values: Monthly payment = ($40,000 * 0.005) / (1 - (1 + 0.005)^-240) Monthly payment = $200 / (1 - 0.334) Monthly payment = $200 / 0.666, Monthly payment = $300.30

Therefore, the monthly payment needed to repay the $40,000 loan over 20 years with a 0.5% interest rate per month is $300.30.To find the monthly interest rate for a $40,000 loan repaid monthly over 20 years with a monthly payment of $544.53, we can use the same formula and rearrange it to solve for the monthly interest rate:

Monthly interest rate = (Monthly payment * (1 - (1 + Monthly interest rate)^-Number of payments)) / Loan amount. Plugging in the given values:

0.005 = ($544.53 * (1 - (1 + 0.005)^-240)) / $40,000

0.005 * $40,000 = $544.53 * (1 - (1 + 0.005)^-240)

$200 = $544.53 * (1 - (1 + 0.005)^-240)

$200 / $544.53 = 1 - (1 + 0.005)^-240

0.367 = 1 - (1 + 0.005)^-240

(1 + 0.005)^-240 = 0.633

1 + 0.005 = 0.633^-240

0.005 = 0.633^-240 - 1

0.005 = -0.367

Monthly interest rate = -0.367 / -240

Monthly interest rate = 0.00153

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The volume of the solid is 284π/3 cubic inches.

To find the volume of the solid, we need to break it down into simpler shapes and then calculate their volumes separately.

The solid is made up of a cylinder and a hemispherical hole cut from the top of it. Let's first calculate the volume of the cylinder. The height of the cylinder is given as 12 inches and the radius can be calculated as half of the hypotenuse of the triangle (which is 10 inches). Therefore, the radius of the cylinder is 5 inches.

The formula for the volume of a cylinder is Vcylinder = πr^2h, where r is the radius and h is the height. Substituting the values, we get:

Vcylinder = π(5^2)(12) = 300π cubic inches

Now, let's calculate the volume of the hemispherical hole. The rim of the hole is 3 inches thick, which means the radius of the hole is (5 - 3) = 2 inches. The volume of a hemisphere is given by the formula Vhemisphere = (2/3)πr^3.

Substituting the values, we get:

Vhemisphere = (2/3)π(2^3) = 16π/3 cubic inches

Now, the volume of the solid can be found by subtracting the volume of the hemispherical hole from the volume of the cylinder:

Vsolid = Vcylinder - Vhemisphere

Vsolid = 300π - 16π/3

Vsolid = 284π/3 cubic inches

Therefore, the volume of the solid is 284π/3 cubic inches.

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Answer:

The inequality that would represent the possible values for the number of hours lifeguarding, l, and the number of hours walking dogs, d, that Katherine can work in a given week is:

l + d ≤ 14

This is because the sum of the hours worked in both jobs should not exceed 14 hours.

Answer:

A. X = -4

Step-by-step explanation:

[tex]-6x-24=3x+12\\-9x=36\\x=-4[/tex]

To simplify the complex fraction ((1)/(f^(3))-(1)/(a^(3)))/((1)/(f^(2))-(1)/(a^(2))), we can use the common denominator method.

Step 1: Find the common denominator for the numerator and denominator of the complex fraction. The common denominator for the numerator is (f^(3))(a^(3)) and the common denominator for the denominator is (f^(2))(a^(2)).

Step 2: Multiply each term in the numerator and denominator by the common denominator to get rid of the fractions.

Numerator: ((1)(a^(3))-(1)(f^(3)))/(f^(3))(a^(3))

Denominator: ((1)(a^(2))-(1)(f^(2)))/(f^(2))(a^(2))

Step 3: Simplify the numerator and denominator by combining like terms.

Numerator: (a^(3)-f^(3))/(f^(3))(a^(3))

Denominator: (a^(2)-f^(2))/(f^(2))(a^(2))

Step 4: Divide the numerator and denominator by the common factor (f^(2))(a^(2)).

Simplified fraction: (a-f)/(f^(1))(a^(1))

Step 5: Simplify the final fraction by canceling out the common factors.

Final answer: (a-f)/(fa)

Therefore, the simplified complex fraction is (a-f)/(fa).

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Answer:

The area of the whole rectangle is 28 cm^2

Step-by-step explanation:

since both triangles are congruent, they have the same area. 14 x 2 = 28

The angle between \( \mathbf{u}=\langle-4,-1\rangle \) and \( \mathbf{v}=\langle-5,-2\rangle \) is approximately 12.5 degrees. To the nearest tenth of a degree, we can round this to 12.5 degrees.

To find the angle between two vectors \( \mathbf{u} \) and \( \mathbf{v} \), we can use the formula:
\[ \cos \theta = \frac{\mathbf{u} \cdot \mathbf{v}}{\| \mathbf{u} \| \| \mathbf{v} \|} \]
where \( \theta \) is the angle between the vectors, \( \mathbf{u} \cdot \mathbf{v} \) is the dot product of the vectors, and \( \| \mathbf{u} \| \) and \( \| \mathbf{v} \| \) are the magnitudes of the vectors.

First, we need to find the dot product of \( \mathbf{u} \) and \( \mathbf{v} \):
\[ \mathbf{u} \cdot \mathbf{v} = (-4)(-5) + (-1)(-2) = 20 + 2 = 22 \]

Next, we need to find the magnitudes of \( \mathbf{u} \) and \( \mathbf{v} \):
\[ \| \mathbf{u} \| = \sqrt{(-4)^2 + (-1)^2} = \sqrt{16 + 1} = \sqrt{17} \]
\[ \| \mathbf{v} \| = \sqrt{(-5)^2 + (-2)^2} = \sqrt{25 + 4} = \sqrt{29} \]

Now we can plug these values into the formula and solve for \( \theta \):
\[ \cos \theta = \frac{22}{\sqrt{17} \sqrt{29}} \]
\[ \theta = \cos^{-1} \left( \frac{22}{\sqrt{17} \sqrt{29}} \right) \]

Using a calculator, we find that \( \theta \approx 12.5 \) degrees.

Therefore, the angle between \( \mathbf{u}=\langle-4,-1\rangle \) and \( \mathbf{v}=\langle-5,-2\rangle \) is approximately 12.5 degrees. To the nearest tenth of a degree, we can round this to 12.5 degrees.

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Answer:

Elizabeth gave away 216 marbles out of a total of 360 marbles.

To find the percentage of marbles that Elizabeth gave away, we can use the formula:

percentage = (part/whole) x 100%

where "part" is the number of marbles Elizabeth gave away, and "whole" is the total number of marbles.

So, plugging in the values we have:

percentage = (216/360) x 100%

percentage = 0.6 x 100%

percentage = 60%

Therefore, Elizabeth gave away 60% of the marbles.

The measure of the central angle in the "Punk" section is 72 degrees.

The measure of the central angle in the "Punk" section can be determined by calculating the percentage of punk songs sold in relation to the total number of songs sold, and then converting that percentage to degrees.

To calculate the percentage of punk songs sold, divide the number of punk songs sold by the total number of songs sold, and multiply by 100.

For example, if 200 punk songs were sold and the total number of songs sold was 1000, the percentage of punk songs sold would be:

200/1000 * 100 = 20%

To convert this percentage to degrees, multiply the percentage by 360 (the total number of degrees in a circle).

20% * 360 = 72 degrees

Therefore, the measure of the central angle in the "Punk" section is 72 degrees.

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8×4=32

11-8=3

4×3=12

12÷2=6

32+6=38

=38inch^2

it might b wrong tho?

A double number line means the values of two different quantities are expressed in two separate lines such as corresponding values align. Here 1ml of blue water will need 3 ml of yellow water.

Here double line represents the relation between yellow water and blue water required to produce green water. 5ml of blue water needs 15ml of yellow water.

So the ratio is 5 : 15

3. One division in the line for blue water represents 1ml and 1 division in yellow water line is 3 ml.

We can also solve it using proportions

5 : 15 :: 1: x

5/15 = 1/x

x = (1×15)/5 = 3 ml

4. For 11 ml of blue water, it will require 33 ml of yellow water.

5. For 8 ml of blue water, 24 ml of yellow water is needed.

6. If we know the volume needed with 1ml of blue water, we can multiply that volume with any quantities of blue water to calculate the volume needed. For example 4 ml of blue water needs 4×3 = 12 ml of yellow water.

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The complete question is as below.

The other day, we made green water by mixing 5 ml of blue water with 15 ml of yellow water. We want to make a very small batch of the same shade of green water. We need to know how much yellow water to mix with only 1 ml of blue water.

1. On the number line for blue water, label the four tick marks shown.

2. On the number line for yellow water, draw and label tick marks to show the amount of yellow water needed for each amount of blue water.

3. How much yellow water should be used for 1 ml of blue water? Circle where you can see this on the double number line.

4. How much yellow water should be used for 11 ml of blue water?

5. How much yellow water should be used for 8 ml of blue water?

6. Why is it useful to know how much yellow water should be used with 1 ml of blue water?

Answer:

Step-by-step explanation:

18

Step-by-step explanation:

The area A of a rectangle is given by multiplying its length and width. In this case, the length is 7x - 1 units and the width is 2x + 3 units. Therefore, the area of the rectangle is:

A = (7x - 1)(2x + 3)

= 14x^2 + 19x - 3

Hence, the area of the rectangle is 14x^2 + 19x - 3 square units.

Answer:

14x^2+19x-3

Step-by-step explanation:

you have to times them together so

(7x-1)(2x+3)

14x^2+21x-2x-3

=14x^2+19x-3

so since 45000 split on a 7:10:13 ratio, so let's simply divide 45000 by (7+10+13) and distribute accordingly to each daughter.

[tex]\stackrel{Ana}{7}~~ : ~~\stackrel{Betty}{10}~~ : ~~\stackrel{Chandra}{13} \\\\\\ \stackrel{Ana}{7\cdot \frac{45000}{7+10+13}}~~ : ~~\stackrel{Betty}{10\cdot \frac{45000}{7+10+13}}~~ : ~~\stackrel{Chandra}{13\cdot \frac{45000}{7+10+13}} \\\\\\ \stackrel{Ana}{7\cdot 1500}~~ : ~~\stackrel{Betty}{10\cdot 1500}~~ : ~~\stackrel{Chandra}{13\cdot 1500} ~~ \implies~\hfill \stackrel{Ana}{10500}~~ : ~~\stackrel{Betty}{15000}~~ : ~~\stackrel{Chandra}{19500}[/tex]