what is the condensed form of the following logarithm: 2log w + 5log v

Both the angles are supplementary angles hence the value of x is 8°.

To solve for the value of x in the given scenario, we can use the fact that the interior angles between two parallel lines are supplementary, meaning they add up to 180 degrees.

Given:

Angle 1: (8x + 1)

Angle 2: 115°

Since these two angles are supplementary, we can set up the equation:

(8x + 1) + 115 = 180

Now we can solve for x by simplifying and isolating the variable:

8x + 1 + 115 = 180

8x + 116 = 180

8x = 180 - 116

8x = 64

To isolate x, we divide both sides of the equation by 8:

8x/8 = 64/8

x = 8

Therefore, the value of x is 8.

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The Triangle Inequality Theorem holds for these values, and only one triangle is possible with these side lengths. Lucas' claim is false.

According to the Triangle Inequality Theorem, any two triangle sides' sums must be greater than the length of the third side. In other words, the following three inequalities must hold for any three positive numbers, a, b, and c:

a+b>c

a+c>b

b+c>a

In this case, a=9, b=13, and c=15. Let's check if the Triangle Inequality Theorem holds for these values:

9+13>15 (true)

9+15>13 (true)

13+15>9 (true)

Therefore, the Triangle Inequality Theorem holds for these values, and only one triangle is possible with these side lengths.

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The solutions of the quadratic equation are: x = 1

The x-intercept is x = 1

The formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

The y-intercept is the point at which the graph crosses the y-axis and in this case it is: y = 1

The x-intercepts are where the graph touches the x-axis and in this case, it is x = 1

The zeros of the quadratic equation are the x-intercepts and since the curve does not cross, then we can say that the zeros are x = 1 and x = 1 which signifies double root and as such the solution is x = 1

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Answer:

Step-by-step explanation:

$15 for one pizza it's simple

The amount of juice served this year is given as follows:

513 gallons.

The amount of juice served this year is obtained applying the proportions in the context of the problem.

The amount last year was given as follows:

540 gallons.

The percentage of this year's amount relative to last year's amount is given as follows:

95%, due to the decay of 5%, 100 - 5 = 95%.

Hence the amount of juice served this year is given as follows:

0.95 x 540 = 513 gallons.

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If Jeremy wants to try to prove ∠3 ≅ ∠6, then the statement that Jeremy can write is ∠1 ≅ ∠4

That's it :)

This equation represents the value of the stock, V(t), in dollars, t years after 1940, taking into account the 7% annual Growth rate V(t) = $1.25 * (1 + 0.07)^t.

The value of the stock, V(t), in dollars, t years after 1940, we can use an exponential growth equation since the stock's value grows by 7% each year after 1940.

formulate the equation step by step:

1. We know that the initial value of the stock in 1940 is $1.25. This initial value serves as the starting point for our equation.

2.We are given that the value of the stock grows by 7% each year. This means that for every year that passes, the stock's value increases by 7% of its previous value.

3. In mathematical terms, if V(0) represents the initial value in 1940 ($1.25), then the value of the stock after t years can be represented as:

V(t) = V(0) * (1 + r)^t,

where r is the growth rate expressed as a decimal (in this case, 7% = 0.07).

4. Plugging in the given values, our equation becomes:

V(t) = $1.25 * (1 + 0.07)^t.

This equation represents the value of the stock, V(t), in dollars, t years after 1940, taking into account the 7% annual growth rate.

For example, if we wanted to find the value of the stock 10 years after 1940, we would substitute t = 10 into the equation:

V(10) = $1.25 * (1 + 0.07)^10.

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The value of x is 8 units.

Given that a right triangle, with an altitude dividing the hypotenuse into 4 and 16 units,

The measure of the altitude is x we need to find the measure of the x,

So, according to the definition of similarity,

Their corresponding sides are proportional,

We get,

x / 4 = 16 / x

x² = 4 × 16

x² = 64

x = 8

Hence the value of x is 8 units.

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The number in the green box is 31.78° .

Given,

Triangle with sides 11 , 12 , 20.

From Cosine Law.

Let △ABC have sides a, b,  c.

Here,

a = 11

b = 20

c = 12

Length of the side opposite vertex A is called a.

Length of the side opposite vertex B is called c.

Length of the side opposite vertex C is called c.

Let θ = ∠C

Then, the Cosine Law says that

c²=a²+b²−2abcosθ.

Substitute the values of a , b , c .

12²  = 11² + 20² - 2 × 11× 20 cosθ

θ = 31.78°

Hence the angle can be found out from cosine law.

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Answer:

f(x) has the most x intercepts

The error in the problem is given by the equation in step(3). and the value is given by g ( x ) = 2x² + 4x - 4

Given data ,

Let the equation be represented as g ( x )

Now , the value of g ( x ) is

g ( x ) = 2 ( x + 1 )² - 6

On simplifying the equation , we get

From the distributive law of multiplication , we get

g ( x ) = 2 ( x + 1 ) ( x + 1 ) - 6

g ( x ) = 2 ( x² + 2x + 1 ) - 6

On further simplification , we get

g ( x ) = 2x² + 4x + 2 - 6

g ( x ) = 2x² + 4x - 4

Therefore, the value of g ( x ) is g ( x ) = 2x² + 4x - 4

Hence , the equation is g ( x ) = 2x² + 4x - 4

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A truck is being filled with cube-shaped packages that have side lengths of foot, the volume of the part of the truck that is being filled is 34,808 cubic feet.

To discover the finest range of applications that may in shape in the truck, we want to calculate the volume of the truck and divide it by using the quantity of every cube-formed bundle.

The quantity of the truck is given with the aid of the method:

Volume = Length x Width x Height

Volume = 8 ft x 61 ft x 71 ft

Volume = 34,808 cubic toes

The volume of every cube-shaped bundle is given with the aid of the method:

Volume = Side [tex]Length^3[/tex]

Volume = 1 [tex]ft^3[/tex]

Number of packages = Volume of truck / Volume of each package

Number of packages = 34,808 ft^3 / 1 ft^3

Number of packages = 34,808

Thus, the greatest number of packages that can fit in the truck is 34,808.

Volume of the part of the truck being filled = Number of packages x Volume of each package

Volume of the part of the truck being filled = 34,808 x 1 ft^3

Volume of the part of the truck being filled = 34,808 ft^3

Thus, the volume of the part of the truck that is being filled is 34,808 cubic feet.

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The volume of the sphere, given that the sphere has a diameter of 14.6 mm is 1628.7 mm³

The following data were obtained from the question:

The volume of a sphere is giving by the following formula

Volume of sphere = 4/3πr³

Inputting the given parameters, we can obtain the volume of the sphere as follow:

Volume of sphere = (4/3) × 3.14 × 7.3³

Volume of sphere = (4/3) × 3.14 × 389.017

Volume of sphere = 1628.7 mm³

Thus, we can conclude from the above calculation that the volume of the sphere is 1628.7 mm³

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The area of the slice of pizza is 25.1 inches squared.

The circular pizza has a diameter of 16 inches. Each slice of pizza have a angle of 45 degrees.

Therefore, the area of the slice of pizza can be calculated as follows:

area of the slice of pizza = ∅ / 360 × πr²

where

Therefore,

r = 16  /2

r = 8 inches

area of the slice of pizza = 45 / 360 × 3.14 × 8²

area of the slice of pizza = 45 / 360 × 3.14 × 64

area of the slice of pizza = 9043.2 / 360

area of the slice of pizza = 25.12 inches²

area of the slice of pizza = 25.1 inches²

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6.56 × [tex]10^{-7}[/tex] by 4.86×[tex]10^{-7}[/tex] is 3.18816 × [tex]10^{-13}[/tex] is factorize.

To find the product of 6.56 × [tex]10^{-7}[/tex] by 4.86×[tex]10^{-7}[/tex]. The conventions of scientific notation can be applied. To get 31.8816, we must first multiply the coefficients, which are 6.56 and 4.86. The exponents, which are -7 and -7, are then added to provide -14.

The product of 6.56 × [tex]10^{-7}[/tex] by 4.86 × [tex]10^{-7}[/tex] is 3.18816 × [tex]10^{-13}[/tex] This, according to the conventions of scientific notation, can be calculated by multiplying the coefficients and adding the exponents.

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Answer:

[tex]a_{n}[/tex] = 6n

Step-by-step explanation:

there is a common difference between consecutive terms, that is

12 - 6 = 18 - 12 = 6

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = 6 and d = 6 , then

[tex]a_{n}[/tex] = 6 + 6(n - 1) = 6 + 6n - 6 = 6n

Area of the given heptagon = 364 square unit.

The given figure is regular heptagon,

length of each side = 10

Distance between Centre and edge = 10.4

Since we know that,

A seven-sided polygon with seven angles, seven vertices, and seven edges is known as a heptagon. They may have the same or different length dimensions. It is a closed figure, and a regular heptagon is one with all equal seven sides.

Now,

Perimeter of the given heptagon = 7x10

                                                       = 70

Area of heptagon = perimeter x 10.4/2

                              = 70 x 5.2

                              = 364

Hence,

Area = 364 square unit.

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Answer:

x = 8 units

Step-by-step explanation:

Because this is a right triangle, we can find x using the Pythagorean theorem, which is given by:

a^2 + b^2 = c^2, where

In the triangle, the 6 unit side and the x unit sides are the legs while the 10 unit side is the hypotenuse.

Thus, we can solve for x by plugging in 6 for a and 10 for c in the theorem and solving for a (aka x, simply a in the theorem):

a^2 + 6^2 = 10^2

a^2 + 36 = 100

a^2 = 64

a = 8

x = 8

Thus, x is 8 units.

The mathematical statement that represents "17 more than a number n is 26" can be written as: n + 17 = 26

Given that a statement we need to convert it into a mathematical statement,

The mathematical statement that represents "17 more than a number n is 26" can be written as:

n + 17 = 26

To solve for n, we can subtract 17 from both sides of the equation:

n + 17 - 17 = 26 - 17

Simplifying the equation gives:

n = 9

Therefore, the number n is 9.

Hence the mathematical statement that represents "17 more than a number n is 26" can be written as: n + 17 = 26

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Any three lengths that satisfy the triangle inequality theorem can form the sides of a triangle. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In order for three lengths to form a triangle, they must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's consider three lengths: a, b, and c.

To determine if they can form a triangle, we need to check the following conditions:

a + b > c

a + c > b

b + c > a

If all three conditions are true, then the lengths a, b, and c can form a triangle.

For example, let's consider the lengths 3, 4, and 5.

3 + 4 > 5 (True)

3 + 5 > 4 (True)

4 + 5 > 3 (True)

Since all three conditions are true, the lengths 3, 4, and 5 can form a triangle.

Therefore, any three lengths that satisfy the triangle inequality theorem can be the lengths of the sides of a triangle.

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The triangles are similar because they are both right triangles, so they both have an angle that is equals to 90º. They both share a common vertex, <C. So they are similar by the Angle-Angle criterion.

Two triangles are defined as similar triangles when they share these two features listed as follows:

For this problem, they have two equal angle measures, the right angle and < C, hence the third angle also must be equal, and they are similar by the Angle-Angle criterion.

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The value of the expression [tex]n^2 - 11n + 10[/tex] is equivalent to (n - 1)(n - 10).

To find the value of the expression [tex]n^2 - 11n + 10[/tex], we can follow these steps:

Start with the given expression: [tex]n^2 - 11n + 10.[/tex]

Look for any like terms that can be combined. In this case, there are no like terms.

Since there are no like terms, we can simplify further by factoring the expression. We need to find two numbers that multiply to give 10 (the constant term) and add up to -11 (the coefficient of the middle term, which is -11n).

The numbers that satisfy these conditions are -1 and -10, because

(-1) × (-10) = 10 and (-1) + (-10) = -11.

Now we can rewrite the expression using these numbers:

[tex]n^2 - 11n + 10 = (n - 1)(n - 10).[/tex]

So the factored form of the expression is (n - 1)(n - 10).

Therefore, the value of the expression [tex]n^2 - 11n + 10[/tex] is equivalent to (n - 1)(n - 10).

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The number of degrees the Figure A must be rotated counterclockwise around the origin to line up with Figure B is = 270°

Given data ,

Let the number of degrees the Figure A must be rotated counterclockwise around the origin to line up with Figure B be represented as A

Now , the triangle is represented by the figure A with coordinates as

A ( -2 , 3 )

And , the coordinates of the rotated triangle is A' ( 3 , 2 )

270° clockwise rotation: (x,y) becomes (-y,x)

270° counterclockwise rotation: (x,y) becomes (y,-x)

So , the triangle is rotated 270° counterclockwise rotation

Hence , the rotation is 270° counterclockwise

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Answer: $561.63

Step-by-step explanation: To find the distance you subtract 500 by -61.63

You get the equation 500--61.63

The two negative signs cancel out to become a positive sign

So the new equation is 500+61.63

So the distance is $561.63

Answer:

$561.63

Step-by-step explanation:

To find out the distance between 500 and -61.63 it will be $500-$-61.63. So 500 - (-61.63) becomes 500 + 61.63 because 2 negatives in a row make a positive. So when you do 500+61.63, you'll get 561.63.

Answer:

3. Substitution because it said angle HKI = angle GKH, so we substitutioned that angle for the other one. I'm not sure about 4. If you provide us with the answer choices for that one, then I could help

Answer: i'm kind of just guessing, but i think x = 13

Step-by-step explanation:

please don't ask me how i don't know

The calculated measure of the angle 1 is 43 degrees

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

The circle

Also, we have

The line AB tangent to the circle

This means that

Angle 1 = 1/2 * the arc subtended by the line

So, we have

Angle 1 = 1/2 * 86

Evaluate

Angle 1 = 43

Hence, the measure of the angle 1 is 43 degrees

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The statistics that always corresponds to the 75th percentile in a distribution include the following: B. Third Quartile.

In Mathematics and Statistics, IQR is an abbreviation for interquartile range and it can be defined as a measure of the middle 50% of data values when they are ordered from lowest to highest.

Mathematically, interquartile range (IQR) of a data set is the difference between third quartile (Q₃) and the first quartile (Q₁):

IQR = Q₃ - Q₁ = 75th percentile - 25th percentile.

In this context, we can reasonably infer and logically deduce that the 75th percentile in a distribution is always equal to the third quartile.

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Answer: The answer is...

y = -2/3 x + 1

Step-by-step explanation:

The others would have crossed paths with y = -2/3 x + 10