two angles are supplementary. one angle has a measure that is eight more than three times the other. what is the measure of the smaller angle?

x = 3y because of corresponding angles theorem

y = x/3

Answer:

Option A - 32 cm³

Step-by-step explanation:

Volume of a pyramid is given by the formula :

V = \(\frac{lwh}{3}\)

Substituting values given gives us :

V = (4)(4)(6)/3

V = (16)(6)/3

V = 96/3

V = 32

Units will be cm³ as this is volume

Hope this helped and have a good day

Answer:

A. 32 cm³

Step-by-step explanation:

V = (1/3)(area of base)(height)

The base is a square of side 4 cm.

area of base = side × side

V = (1/3)(4 cm × 4 cm)(6 cm)

V = 32 cm³

It will take 15 hours more to build the wall using only 5 bricklayers.

This question deals with indirect proportion. To solve it, you need to first find the product of the number of bricklayers and the number of hours it took to build the wall.

= Number of bricklayers x Number of hours taken

= 8 x 25

= 200 bricklayer hours are required to build that wall if using 8 bricklayers.

Because you are using 5 bricklayers, the number of hours they will take is:

= Number of hours taken to build by 8 bricklayers/ Number of bricklayers available

= 200 / 5

= 40 hours

Difference is:

= 40 - 25

= 15 hours

In conclusion, it will take 5 bricklayers, 15 hours more to build the wall.

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Answer:

yo whats your name i think that we are from the same class

Step-by-step explanation:

The parametric equation of the line is given by;  x(t)=-2 + 5ty(t)=2 - 3tz(t)=5 - 3t

To find the vector and parametric equations for the line through the point P(-2, 2, 5) and orthogonal to the plane 5x - 3y - 3z = -3, the following  

Write the equation of the plane.5x - 3y - 3z = -3  is the given equation

Find a vector that is orthogonal to the planeThis can be done by finding the normal vector of the plane. Using the coefficients of x, y, and z in the equation of the plane.  A normal vector of the plane is obtained and simplified:<5,-3,-3>.

Find the vector equation of the line.

Let L be the line through P(-2, 2, 5) and orthogonal to the plane. A direction vector of the line,  v is the normal vector of the plane (which is <5,-3,-3>), a point P(-2, 2, 5) on the line can be used to obtain the vector equation of the line:

Parametric form (parameter t, and passing through P when t = 0):x(t)=-2 + 5ty(t)=2 - 3tz(t)=5 - 3t

The vector form:<-2, 2, 5> + t<5,-3,-3> The parametric equation of the line is given by;  x(t)=-2 + 5ty(t)=2 - 3tz(t)=5 - 3t

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a.  y = cos 4x satisfies the differential equation.

b. The only solution is the trivial solution (C₁ = 0, C₂ = 0), the set of solutions {sin 4x, cos 4x} is linearly independent.

c. The general solution of the differential equation as a linear combination of the solutions:

y(x) = C₁(sin 4x) + C₂(cos 4x)

A function's derivative with respect to an independent variable can be used to define differentiation. Calculus differentiates to measure the function per unit change in the independent variable.

(a) To verify that each solution satisfies the differential equation y" + 16y = 0:

For y = sin 4x:

Taking the first and second derivatives of y:

y' = 4cos 4x

y" = -16sin 4x

Substituting these derivatives into the differential equation:

y" + 16y = (-16sin 4x) + 16(sin 4x) = 0

The equation holds true, so y = sin 4x satisfies the differential equation.

For y = cos 4x:

Taking the first and second derivatives of y:

y' = -4sin 4x

y" = -16cos 4x

Substituting these derivatives into the differential equation:

y" + 16y = (-16cos 4x) + 16(cos 4x) = 0

The equation holds true, so y = cos 4x satisfies the differential equation.

(b) To test the set of solutions for linear independence:

The set of solutions {sin 4x, cos 4x} can be tested for linear independence by checking if the equation C₁(sin 4x) + C₂(cos 4x) = 0 has only the trivial solution (C₁ = 0, C₂ = 0) or if there exist non-zero constants C₁ and C₂ that satisfy the equation.

In this case, we have:

C₁(sin 4x) + C₂(cos 4x) = 0

To solve for C₁ and C₂, we can compare the coefficients of sin 4x and cos 4x separately:

C₁ = 0

C₂ = 0

Since the only solution is the trivial solution (C₁ = 0, C₂ = 0), the set of solutions {sin 4x, cos 4x} is linearly independent.

(c) Since the set of solutions is linearly independent, we can write the general solution of the differential equation as a linear combination of the solutions:

y(x) = C₁(sin 4x) + C₂(cos 4x)

Here, C₁ and C₂ are arbitrary constants.

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The function g(x) = (-2 + √(1 + x)) / 2 is the inverse function of f(x) = 2x^2 + 4x, denoted as f^(-1)(x). It satisfies the composition property, meaning that (g∘f)(x) = (f∘g)(x) = x

To find the function g(x) such that (g∘f)(x) = (f∘g)(x) = x, we are looking for an inverse function of f(x) = 2x² + 4x.

To find the inverse function, let's follow the steps:

Replace f(x) with y.

y = 2x² + 4x

Swap the roles of x and y.

x = 2y² + 4y

Now solve the equation for y.

Rearranging the equation, we get:

2y² + 4y - x = 0

To solve this quadratic equation for y, we can use the quadratic formula:

y = (-4 ± √(4² - 4(2)(-x))) / (2(2))

y = (-2 ± √(1 + x)) / 2

Now, we have two potential solutions for g(x):

g(x) = (-2 - √(1 + x)) / 2

(f∘g)(x) = f(g(x))

= 2(g(x))² + 4(g(x))

= x

(g∘f)(x) = g(f(x))

= g(2x² + 4x)

≠ x

As we can see, (g∘f)(x) ≠ x, but (f∘g)(x) = x.

This means that g(x) = (-2 + √(1 + x)) / 2 is the inverse function of f(x), denoted as f⁻¹(x), but g(x) = (-2 - √(1 + x)) / 2 is not the inverse function.

So, g(x) = f⁻¹(x) is true only for g(x) = (-2 + √(1 + x)) / 2.

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Step-by-step explanation:

2x + 2y  = 28   <=====given

x * y = 40     <===given .....  re-arrange to :

           y = 40 / x    <===substitute this 'y'  into the first equation

2x + 2 ( 40/x) = 28   <=====solve for x

2x^2 -28x + 80 = 0

x^2 -14x +40 = 0

(x -10)(x-4) = 0                        shows x = 10 or 4    then y = 4 or 10

dimensions    10    and 4   inches

Answer:

4 or 10 inches

Step-by-step explanation:

I added a photo of my solution

The value of the function (f.h)(x) is 96x⁵ + 132x⁴ + 78x³ + 18x²

f(x) = 3x² + 4x³ + 8x⁴

g(x) = -3x + 12x² - 5x³

h(x) = 12x + 6

Therefore,

(f.h)(x) = f(x).h(x)

Hence,

f(x).h(x) = (3x² + 7x³ + 8x⁴)(12x + 6)

f(x).h(x) = 36x³ + 18x² + 84x⁴ + 42x³ + 96x⁵ + 48x⁴

(f.h)(x) = 96x⁵ + 84x⁴ + 48x⁴ +  36x³ + 42x³ + 18x²

(f.h)(x) =  96x⁵ + 132x⁴ + 78x³ + 18x²

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Answer:

Segment QR is the shortest

Answer:

qr

Step-by-step explanation:

The simplified expression \((3.05 * 10^-7) (8.67 * 10^4)\) in standard form to 3 decimal places is approximately 0.026

To simplify the expression\((3.05 * 10^-7) (8.67 *  10^4)\) and provide the answer in standard form to 3 decimal places.

Step 1: Multiply the coefficients (3.05 and 8.67).
3.05 * 8.67 = 26.4445

Step 2: Use the properties of exponents to multiply the powers of 10.
\(10^{-7} * 10^4 = 10^{(-7+4)} = 10^-3\)

Step 3: Multiply the results from Step 1 and Step 2.
\(26.4445 * 10^-3 = 0.0264445\)

Step 4: Round the result to 3 decimal places.
0.0264445 ≈ 0.026

So, the simplified expression (3.05 x 10^-7) (8.67 x 10^4) in standard form to 3 decimal places is approximately 0.026.

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Answer:

A=3

Step-by-step explanation:

-7a+28=7

subtract 28 from both sides to eliminate it from the first side

-7a=-21

Two negatives equals a positive

7a=21

divide both sides by 7

a=3

Answer:

7.2

Step-by-step explanation:

7.4-0.2=7.2

Considering the situation described, the classification of the elections is given as follows, according to their order of finish:

David, Greg, Victor, Mac, Bill.

We take the situation that is described, and build the classification from it. The classification has the following format:

P1 - P2 - P3 - P4 - P5

With P1 being the first placed candidate, P2 being the second placed candidate, and so on until P5 which is the fifth placed candidate.

From the text given in this problem, we have that:

Hence the classification of the election is given by:

David, Greg, Victor, Mac, Bill.

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To calculate the gain on the sale of the office furniture, we need to determine the asset's book value and compare it to the sale price.

First, let's calculate the accumulated depreciation on the furniture. The furniture was purchased on January 1, 2014, and the straight-line depreciation method is used over 10 years with a salvage value of $80,200.

Depreciation per year = (Cost - Salvage Value) / Useful Life

Depreciation per year = ($746,800 - $80,200) / 10 years

Depreciation per year = $66,160

Next, we need to calculate the accumulated depreciation for the period from January 1, 2014, to May 1, 2021 (the date of the sale). This is approximately 7.33 years.

Accumulated Depreciation = Depreciation per year × Years

Accumulated Depreciation = $66,160 × 7.33 years

Accumulated Depreciation = $484,444.80

Now, we can calculate the book value of the furniture:

Book Value = Cost - Accumulated Depreciation

Book Value = $746,800 - $484,444.80

Book Value = $262,355.20

Finally, we can calculate the gain on the sale:

Gain on Sale = Sale Price - Book Value

Gain on Sale = $300,000 - $262,355.20

Gain on Sale = $37,644.80

Therefore, the gain that should be recognized on the sale of the office furniture is approximately $37,644.80.

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The gain that should be recognized on the sale of the office furniture is $84,080.

The gain is calculated by subtracting the equipment's book value from the sale price. This gain will be reported on the company's income statement. Here is how to calculate the gain:First, find the equipment's book value using the straight-line method of depreciation.

Straight-line depreciation is calculated by taking the difference between the equipment's original cost and its salvage value, and then dividing it by the number of years the equipment is used. The annual depreciation expense is then multiplied by the number of years the equipment is used to find the equipment's book value at the end of its useful life.

For this question, the book value of the equipment at the time of sale is:Cost of equipment: $746,800Salvage value: $80,200Depreciable cost: $746,800 - $80,200 = $666,600Annual depreciation: $666,600 ÷ 10 years = $66,660Book value at the end of 2020: $666,600 - ($66,660 x 7) = $156,420

Next, subtract the equipment's book value from the sale price to find the gain:Sale price: $300,000Book value: $156,420Gain: $143,580Finally, round the gain to the nearest dollar:$143,580 ≈ $143,580.00So the gain that should be recognized on the sale of the office furniture is $84,080.

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In math, the '!' sign are used in factorial. Factorial is multiplications on numbers itself and with another numbers that less than the number itself. Example :

5! =5x4x3x2x1 or nx(n-1)x(n-2)...2x1

Answer:

Simple random sampling

Step-by-step explanation:

Luke wants to study average minutes students read each night. For that matter, he has selected a 'sample' of 25 students from entire 'population' of students in school.

He has selected the sample students randomly, for collecting data related to minutes of study each night. He also collects data from them directly ie with primary contact with them.

So, primary data collection, simple random sampling - has been used as a type of data collection.

Answer:

x = -2

Step-by-step explanation:

To solve for x always get x on one side

First add 4 on each side, 4 + 7x - 4 = -18 + 4

Next subtract 18 from 4, making it -14    7x = -14

Now divide 7 on each side, x = -2

Answer:

104 units

Step-by-step explanation:

You have the measurements you just need to add the numbers.

In the given proof, we are provided with a series of statements and axioms. We need to use the results from page 36 of the cheat sheet (excluding Theorem 11, which is the goal of the proof) to complete the proof. Let's analyze the steps and apply the appropriate results to complete the proof:

Proof:

1. (-a) -((a+b) (a-(ab)))

2. b-a-b

3. a-a (Axiom 6, Axiom 1, Theorem 1)

We start with the first statement: (-a) -((a+b) (a-(ab))). To simplify this expression, we can use one of the results from page 36 of the cheat sheet. Let's consider Result 5, which states: "(-a)-(b-(a-(ab))) = a-ab." By comparing the given expression with Result 5, we can see that we need to make a few adjustments to match the pattern.

We have (-a) -((a+b) (a-(ab))), and we can rewrite it as (-a) - ((a+b) - (a - (ab))). Now, we can apply Result 5, which gives us (-a) - ((a+b) - (a - (ab))) = a - (ab).

So, our first statement simplifies to a - (ab).

Moving on to the second statement: b-a-b. To prove this statement, we can utilize another result from page 36. Let's consider Result 2, which states: "a - (b - a) = 2a - b." By comparing the given expression with Result 2, we see that we need to rearrange the terms.

We have b - a - b, and we can rewrite it as b - (a - b). Now, we can apply Result 2, which gives us b - (a - b) = 2b - a.

So, our second statement simplifies to 2b - a.

Finally, we have the third statement: a - a. This statement is directly derived from Axiom 6, which states: "a - a = 0."

Combining the simplified forms of the first and second statements, we have a - (ab) = 0 and 2b - a = 0. Now, we can use these two equations along with Axiom 1, which states: "a - (ab) = (a - b)a," to derive the conclusion.

From a - (ab) = 0, we can multiply both sides by a to get a^2 - a(ab) = 0. Rearranging this equation, we have a^2 = a(ab).

Next, we substitute 2b - a = 0 into the equation a^2 = a(ab). This yields a^2 = (2b)(ab), which simplifies to a^2 = 2(ab)^2.

Using Theorem 1, which states: "If a^2 = b^2, then a = b or a = -b," we can conclude that a = √(2(ab)^2) or a = -√(2(ab)^2).

Therefore, by applying the results from page 36 of the cheat sheet and the given axioms, we have derived the conclusion that a = √(2(ab)^2) or a = -√(2(ab)^2) in the given proof.

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Answer: 20m i know it pro

Step-by-step explanation:

Answer:

39 acute isoceleleellsllelsls

Step-by-step explanation:

The angles of triangle always add to 180 degrees. So that angle on the bottom already takes up 102 so 180-102=78 and there are 2 angles left so both of those are 39 because 78/2=39  and 39 is an acute angle since its less than 90 degrees so ya

The correct option B. 9(5 + 8) ; is the equivalent expression to 45 + 72 using the GCF and the distributive property.

A mathematical statement made up of variables, constants, and mathematical operators is called an expression.

The formula is 45 + 72.

45 and 72 divided by one is three and nine.

The GCF is nine.

The largest number that evenly divides two or even more given numbers is known as the greatest common factor.

You can write the phrase as,

9 ( 5 + 8)

45 +72 = 9 ( 5 + 8)

Thus, the Distributive property was used to factor this.

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The correct question is-

Which correctly shows how to use the GCF and the distributive property to find an expression equivalent to 45 + 72?

A. 3(15 + 24)

B. 9(5 + 8)

C. (5)(9) + (2)(36)

D. (3)(15) + (8)(9)

Answer:

1st Answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sum: addition

Difference: subtraction

Product: multiplication

Number                    Sum                    Difference                    Product

1, 4                         1 + 4 = 5                     4 - 1 = 3                       1 * 4 = 4

2, 8                       2 + 8 = 10                   8 - 2 = 6                      2 * 8 = 16

Hope this helps!

Option (b) 2.8600 is the correct answer.

To find the number of rental trucks that a local U-Move moving truck rental company can expect to rent during a given week, we need to find the expected value of the probability distribution.

The expected value of a probability distribution is given by:

Expected Value = Sum of (Number of Rented Trucks × Probability)

Therefore, Expected Value = (0 × 0.23) + (1 × 0.18) + (4 × 0.27) + (5 × 0.32)

Expected Value = 0 + 0.18 + 1.08 + 1.6Expected Value = 2.86

Therefore, the company can expect to rent 2.86 rental trucks during a given week. Option (b) 2.8600 is the correct answer.

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Answer:

A)  10.8

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Let the three consecutive integers be;

    x , x + 1 and x + 2:

The sum of squares of the two smaller numbers:

  The two smaller numbers are x and x+ 1

Sum of their squares:

           x² + (x+1)²;

        x² + x² + 2x + 1 = 2x² + 2x + 1

It is 45 more than the square of the larger number:

    Larger number = x + 2

        (x+2)² = x² + 4x + 4

 45 more;

        x² + 4x + 4 + 45  = x² + 4x + 49

Both are equal:

 2x² + 2x + 1 =  x² + 4x + 49  

  2x² - x² + 2x - 4x + 1 - 49 = 0

      x² - 2x - 48 = 0

      x² - 6x + 8x - 48 = 0

      x(x - 6) + 8(x - 6) = 0

      (x + 8)(x-6) = 0

      x + 8 = 0 or x - 6 = 0

      x  = -8 or x = 6

We choose x = 6 because it makes the solution true as a positive integer

  Sum of the three numbers:

     x + x + 1 + x + 2 = 6 + 6 + 1 + 6 + 2 = 21

Answer:

Step 1: Lets say 'x' is the total wage. Then we subtract 1/4 from the total wages.

=> 4x/4 - x/4

=> 3x/4 = Remaining Wages Left.

Step 2: Subtract 20% from 3x/4.

3x/4 - x/5 = Remaining Wages Left.                                 [20% = 20x/100 = x/5]

=> 11x/20 = Remaining Wages Left.

Step 3: Subtract 0.15x from his remaining wages left.

=> 11x/20 - 3x/20 = Remaining Wages Left.                     [0.15 = 15/100 = 3/20]

=> 8x/20 = Remaining Wages Left.

Step 4: Simplify

8x/20 = 2x/5 = 0.40x

=> Simon has saved 2x/5 of the wages.

Please give me brainliest :)

Answer:

Step-by-step explanation:

The total is 100% or 1.

Spent:

Left: