Click and drag like terms onto each other to simplify fully.
-2y−2y+1+1+6y+6y+4+4-7−7

DeltaMath

A node or event with a duration of 0 days is a b. milestone

A milestone refers to an important event in a project that has a duration of zero days. It signifies the completion of a significant phase or task within the project. Milestones are numbers placed on roads, such as roads, railroads, canals, or borders. They can show distances to cities, towns, and other places or regions; or they can set their work on track with respect to a reference point.

They are found on the road, often by the roadside or in a warehouse area. They are also called mile markers (sometimes abbreviated MM), milestones, or mileposts (sometimes abbreviated MP). "mile point" is the term used for the medical field where distance is usually measured in kilometers rather than miles. "Distance marking" is a general term that has nothing to do with units.

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The formula for the volume of a cone is:

V = (1/3)πr²h

where r is the radius of the base, h is the height of the cone, and π is pi.

In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:

h² = s² - r²

h² = 17² - 8²

h² = 225

h = 15

Now that we have the height, we can plug in the values for r and h into the formula for the volume:

V = (1/3)π(8²)(15)

V = (1/3)π(64)(15)

V = (1/3)(960π)

V = 320π

Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.

The large integer is 60.

Let x be the small integer.

Then the large integer would be 5x.

According to the problem, the difference between the large integer and the small integer is 48.

This can be expressed as:5x - x = 48

Simplifying,4x = 48

Dividing both sides by 4,x = 12

Therefore, the small integer is 12 and the large integer is 5x = 5(12) = 60.

Hence, the large integer is 60.

Zero, a positive natural number, or a negative integer with a minus sign are all examples of integers. The additive inverses of the positive numbers are the negative numbers.

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Step-by-step explanation:

floor = 12*10= 120 sq ft

rug = r² = 9 Пr2

120-9π = 91.74 sq ft

The common difference of the arithmetic sequence 2, 7, 12, 17, ... is 5. The fifth term is 22. The nth term is given by the formula an = 2 + 4(n - 1). The 100th term is 497.

The common difference is calculated by subtracting the first term from the second term. In this case, 7 - 2 = 5. The fifth term is calculated by using the formula an = a1 + (n - 1)d, where a1 is the first term, n is the term number, and d is the common difference. In this case, a5 = 2 + (5 - 1)5 = 22. The nth term is also calculated using the same formula. In this case, an = 2 + 4(n - 1). The 100th term is calculated by plugging in n = 100 into the formula, which gives an = 497.

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Answer:

96

Step-by-step explanation:

We simply need to plug in a = 4 so 6a² = 6 * 4² = 6 * 16 = 96.

Answer:

14.91

Step-by-step explanation:

Have a good day :)

Answer:

The answer is 14.91

Step-by-step explanation:

To find the answer we must first see how many times 5 can go into 74.55.  Since 5 x 14.91 = 74.55, then it means that our answer is 14.91.  

The characteristic polynomial of a matrix A is p(λ)= (λ−1)(λ−3) 2(λ−4) 3. The size of A is 6 x 6. A is invertible. A has a total of three eigenspaces.

Given the characteristic polynomial of a matrix A is p(λ)= (λ−1)(λ−3) 2(λ−4) 3. We need to determine the following three parts:a) Size of A b) Invertibility of Ac) Number of eigenspaces of Aa) Size of AThe size of A is given by the degree of the characteristic polynomial of A. The degree of the characteristic polynomial of A is given by the total number of factors. In this case, the degree of p(λ) is the total number of factors i.e., (1 + 2 + 3) = 6. Therefore, the size of A is 6 x 6.

b) Invertibility of AFor a matrix A, A is invertible if and only if det(A) ≠ 0. The determinant of a matrix is given by the product of the eigenvalues. From the given characteristic polynomial, we can see that A has eigenvalues of 1, 3, and 4, and these are the only eigenvalues. Therefore, det(A) = (1 * 3^2 * 4^3) ≠ 0. Thus, A is invertible.

c) Number of eigenspaces of AThe eigenvalue 1 has only one corresponding factor in the characteristic polynomial. Therefore, 1 has a geometric multiplicity of one. The eigenvalue 3 has two corresponding factors in the characteristic polynomial. Therefore, 3 has a geometric multiplicity of two. The eigenvalue 4 has three corresponding factors in the characteristic polynomial. Therefore, 4 has a geometric multiplicity of three. Thus, A has a total of three eigenspaces.

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Answer:

x = 0 or x = 1/4

Step-by-step explanation:

You are able to factor out 3x² from 12x³ - 3x² to get 3x²(4x-1).

Set everything to zero and solve.

1.  x² - 5x - 16 can be written as (x - 8)(x + 2).

2. 6an² - 3b²n² = n²(6a - 3b²).

3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².

4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

5. 17x³y⁴z⁶ = (x²y²z³)².

6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Let's simplify the given expressions:

Simplifying x² - 5x - 16:

To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.

Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).

Simplifying 6an² - 3b²n²:

To simplify this expression, we can factor out the common term n² from both terms:

6an² - 3b²n² = n²(6a - 3b²).

Simplifying 4x² - 4xy + y²:

This expression represents a perfect square trinomial, which can be factored as (2x - y)².

Simplifying n + 1 - n³ - n²:

Rearranging the terms, we have -n³ - n² + n + 1.

Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

Simplifying 17x³y⁴z⁶:

To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:

17x³y⁴z⁶ = (x²y²z³)².

Simplifying 12a²b³:

To simplify this expression, we can multiply the exponents of a and b with the given expression:

12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

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Answer:

72

Step-by-step explanation:

Let the number be \(xy\)

Value of number = \(10x+y\)

\(10x+y=8(x+y)\)

\(10x+y=8x+8y\)

\(2x-7y+0........(1)\)

\(10x+y-45=10y+x\)

\(9x-9y=45\)

\(x-y=5............(2)\)

Multiply by \(-2\)

\(-2x+2y=-10\)

Add to \((1)\)

\(-5y=-10\)

\(y=2\)

\(x-y=5\)

\(x-(2)=5\)

\(x=7\)

Number = 72

hope this helps...

Step-by-step explanation:

make 2 triangles ABO and ACO

compare them

AB=AC

AO is the same in both

and BO=CO

opposite equal sides are equal angles so angleAbBO=angleACO

theres a fact that says that opposite to equal angles are equal sides and conversely so because AO is equal to both triangles angle ABO and angle ACO are equal

\(12^2+9^2=x^2\\144+81=x^2\\x^2=225\\x=15\)

Answer:

it is a concave octagon

Step-by-step explanation:

A convex octagon has no angles pointing inward so in other words, the angles cant be acute. A concave octagon has angles pointing inward therefor it is a concave octagon.

Answer: C

Step-by-step explanation:

A p e x

The graph of the function shown in option (C) is one to one function option (C) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The graph of the function is shown in the picture.

As we know, the one-to-one function follows a horizontal line test.

If the horizontal line touches more than one point in the graph of the function then the function will not be a one-to-one function.

The one-to-one function should have only one cross-point if the horizontal line draws on the graph paper or coordinate plane.

Graph C passes the horizontal line test.

Thus, the graph of the function shown in option (C) is one to one function option (C) is correct.

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Answer:

The graph is linear and increasing from x = -6 to x = -2.

The graph is nonlinear and decreasing from x = -2 to x = 0.

Step-by-step explanation:

Linear means it has a constant slope, or a constant rate of change. That makes a straight line on a graph. On the given graph, you can see the straight line increasing from x = -6 to x = -2.

Non-linear is just anything that isn't a constant slope, and makes a curve on a graph. On the given graph, the curve decreases from x = -2 until x = 0, where it reaches its lowest point and starts heading upwards again.

Answer: Below :p

Step-by-step explanation:

-10 - (-3) is -7.

The opposite of -3 is 3 since there were parentheses around -3.

Tom might have added the negatives wrong to get -13 or he thought the subtraction symbol was an addition symbol.

The true statements about the arcs and angles in circle C are:

In Geometry, the sum of the measures of the interior angles in a quadrilateral is equal to 360°. Thus, we have:

m∠G + m∠GDC + m∠DCE + m∠GEC = 360°

60 + 90 + m∠DCE + 90 = 360

240 + m∠DCE = 360

m∠DCE = 360 - 240

m∠DCE = 120°.

Since ∠DFE is an inscribed angle that is subtended by arc DE, we have:

m∠DFE =  m∠DCE

m∠DFE =  120

m∠DFE = 1/2 × 120

m∠DFE = 60°.

Therefore, ∠EFD ≅ ∠EGD.

From circle C, we can deduce that side ED is subtended by arc ED and side FD is subtended by arc FD (side ED ≅ side FD). Thus, arc ED ≅ arc FD and m arc FD is equal to 120°.

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Answer:

A C E

took quiz

The given function is f(x) = 15(1.02)^x, where x is the number of years from the date at which money is initially deposited.

This means that $15 were initially deposited into the account, and the amount grows at an annual rate of 2% (which is represented by 1.02 being raised to the power of x).

Therefore, the correct answer is: $15 were initially deposited into the account, which grows at an annual rate of 2%.

Hope I helped you...

Answer:

Step-by-step explanation:

diameter of each circle = 20/2 = 10 cm

rectangle is 20 cm by 10 cm

area of rectangle = 20×10 = 200 cm²

radius of each circle = 10/2 = 5 cm

area  of each circle = πr² = 25π cm²

shaded area = 200  - 2(25π) = 200 - 50π =42.92 cm²

Answer:

f(x) = 3x - 14

Step-by-step explanation:

note that y = f(x), thus rearrange the equation making y the subject.

Given

y - 3x = - 14 ( add 3x to both sides )

y = 3x - 14 , that is

f(x) = 3x - 14 ← in functional notation

The triangle similarity can be proven by three methods, and the AA similarity postulate states that two triangles are similar if and only if their corresponding angles are congruent.

If they have the same shape but different sizes. This is what is known as similarity. In mathematics, there are three ways to prove that two triangles are similar: AA, SAS, and SSS.

In the case of AA similarity postulate, two triangles are similar if and only if two corresponding angles are congruent, meaning they have the same degree measure.

Similarly, if triangle ABC is similar to triangle JKL by AA similarity postulate, it means that the corresponding angles of both triangles are congruent.

Therefore, it is possible that triangle ABC is similar to one or more of the triangles given, but it is not possible to say without further information such as the angles and lengths of the sides.

Complete Question:

Define triangle is ​△ABC​ similar to Similarity property and why?

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Answer:

Alex has 3x dollars and an extra 15 dollars in his coat pocket. He buys a new Nike shoe for 84 dollars. How much money did Alex spend that was not in his pocket.

Step-by-step explanation:

Answer:

Part A: Word problem

Maria went to the store and purchased some books for her book club. Each book cost $3, and she also bought some bookmarks at $15 each. Maria's total purchase, including tax, amounted to $84. If Maria bought x books, write an equation to represent the situation.

Part B: Solution

To solve the equation 3x + 15 = 84, we need to isolate the variable x on one side of the equation.

Step 1: Subtract 15 from both sides of the equation to eliminate the constant term on the left side:

3x + 15 - 15 = 84 - 15

3x = 69

Step 2: Divide both sides of the equation by 3 to isolate x:

3x/3 = 69/3

x = 23

So, the solution to the equation is x = 23.

Part C: Explanation

In the given equation 3x + 15 = 84, the variable x represents the number of books Maria purchased. The equation states that the cost of x books at $3 each, represented by 3x, plus the cost of $15 for bookmarks, totals to $84. Thus, the value of x represents the number of books Maria bought in this scenario. In the solution, x = 23, it means Maria purchased 23 books for her book club.

Step-by-step explanation:

Answer:

50.2 inches

Step-by-step explanation:

circumference =2pir

2(3.14)8

6.28(8)

50.24 inches roused to the tenth place so 20.2

Answer:

50.27 or 16pi

Step-by-step explanation:

C = 2πr = 2·π·8 ≈ 50.26548 or 16pi

The cost of a whisky is GHC 0.85.

A linear equation is defined as an equation in which the highest power of the variable is always one.

Let x be the cost of brandy and y be the cost of a whisky.

As per the question, we have:

x = y + 0.10 (Brandy is 10p more expensive than whisky)

3x + 5y = 7.10 (A round of three Brandies and 5 whiskies cost GHC 7.10)

Substituting the value of x from the first equation into the second equation, we get:

3(y + 0.10) + 5y = 7.10

Expanding and simplifying, we get:

3y + 0.30 + 5y = 7.10

8y + 0.30 = 7.10

8y = 6.80

y = 0.85

Therefore, the cost of a whisky is GHC 0.85.

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Worker 11: Basic rate = $6.35 per hour
Worker 12: Basic rate = $8.75 per hour

To calculate the basic rate for each factory worker, we need to divide the total weekly wage by the number of hours worked.

For worker 11, the basic wage is $254 for a 40-hour week. To find the basic rate per hour, we divide $254 by 40.

$254 ÷ 40 = $6.35

So, the basic rate for worker 11 is $6.35 per hour.

For worker 12, the basic wage is $306.25 for a 35-hour week. To find the basic rate per hour, we divide $306.25 by 35.

$306.25 ÷ 35 = $8.75

So, the basic rate for worker 12 is $8.75 per hour.

In summary:
- Worker 11: Basic rate = $6.35 per hour
- Worker 12: Basic rate = $8.75 per hour

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Answer:

You will end up with more money when you need it.

To find σg(X)^2, we need to calculate the variance of the function g(X) = 4X^2 + 2, where X is a random variable with a given density function. The density function is defined as f(x) = (3/2)(x + 1) for 0 ≤ x and 0 elsewhere. By calculating the variance of g(X), we can determine the value of σg(X)^2.

To calculate the variance of g(X), we first need to find the mean of g(X), denoted as E[g(X)]. For a continuous random variable, the mean is calculated as the integral of the function multiplied by the density function. In this case, we have:

E[g(X)] = ∫(4X^2 + 2) * f(x) dx

Substituting the given density function, we have:

E[g(X)] = ∫(4X^2 + 2) * (3/2)(X + 1) dx

After simplifying and evaluating the integral, we can find the value of E[g(X)].

Next, we calculate the variance of g(X), denoted as Var[g(X)]. The variance is calculated as the expectation of the squared difference between g(X) and its mean, E[g(X)]^2. In mathematical terms:

Var[g(X)] = E[(g(X) - E[g(X)])^2]

By substituting the values of g(X) and E[g(X)], we can evaluate this expression and find the value of Var[g(X)].

Finally, to find σg(X)^2, we take the square root of Var[g(X)], i.e., σg(X) = √Var[g(X)]. After calculating Var[g(X)], we can determine the value of σg(X) to three decimal places as needed.

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Answer:

The cost of admission to a festival was $112 for 9 children and 3 adults. The admission was $108 for 8 children and 3 adults in another festival. How much was the admission for each child and adult?

Step-by-step explanation:

(a) By plugging in different values for x1, we can plot the indifference curves passing through the given points (2, 2), (1, 2), and (4, 2).

(b) The shape of the indifference curves shows convexity.

(c) The property used to determine this is the non-satiation property of preferences.

(d) The Walrasian demand may not always be single-valued.

(e) Receiving the voucher makes the consumer better-off .

(f) The cash payment allows the consumer to maximize utility by making trade-offs

For 4x1 + x2 = x1 + 2x2, rearranging the equation gives x2 = 3x1, representing the linear part of the indifference curves.

For x1 + 2x2 = 4x1 + x2, rearranging the equation gives x2 = 3x1, representing the kink in the indifference curves.

By substituting different values for x1, we can plot the indifference curves. They will be upward sloping straight lines with a kink at x2 = 3x1.

(b) Properties of the preferences deduced from the shape of indifference curves and utility function:

Diminishing Marginal Rate of Substitution (MRS): Indifference curves are convex, indicating diminishing MRS. The consumer is willing to give up less of one good as they consume more of it, holding the other good constant.

Non-Satiation: Indifference curves slope upwards, showing that the consumer prefers more of both goods. They always prefer bundles with higher quantities.

Convex Preferences: The kink in the indifference curves indicates convexity, implying risk aversion. The consumer is willing to trade goods at different rates depending on the initial allocation.

(c) UMP does not have a solution when Pk = 0 and X -> R2+. This violates the assumption of finite resources and prices required for utility maximization. The property used is non-satiation, as a consumer will always choose an infinite quantity of goods when they are available at zero price.

(d) Walrasian demand depends on relative prices:

If p1 = p2 > 4, the maximizing bundle lies on the linear portion of indifference curves, where x2 = 3x1.

If 4 < p1 = p2 < 1/2, the maximizing bundle lies on the linear portion of indifference curves but at lower x1 and x2.

If p1 = p2 < 1/2, the maximizing bundle lies at the kink point where x1 = x2.

Walrasian demand may not be single-valued due to the shape of indifference curves and the kink point, allowing for multiple optimal solutions based on relative prices.

(e) Given p1 = p2 = 1 and w = $60, the initial budget set is x1 + x2 = 60. With a $10 voucher for good 1, the new budget set becomes x1 + x2 = 70. Since p1 = 1, the consumer spends the voucher on good 1, resulting in x1 = 20 and x2 = 40. Receiving the voucher improves the consumer's welfare by allowing more consumption of good 1 without reducing good 2.

(f) If given the choice between a $10 cash payment and a $10 voucher for good 1 only, the consumer would choose the cash payment. It provides flexibility to allocate the funds based on individual preferences. The answer remains the same even if the assistance were $30, as the cash payment still allows optimal allocation based on preferences. Cash payment offers greater utility-maximizing options compared to the voucher, which restricts choices.

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