Solve |-x+ 5| = |3x – 3| by graphing.

The two polygons triangle RST = triangle VWU are similar by the scale factor of 6/5. Option C is the correct answer.

Shapes in various dimensions can be scaled using the Scale Factor. In geometry, we study many geometrical forms that exist in both two- and three-dimensions. The scale factor is a way to compare figures with similar appearances but differing scales or measurements. Consider two circles that resemble one another but may have different radii.

The scale factor is given by:

Scale factor = length of segment of figure A / Length of segment of figure B

SF = 12/10 = 6/5

For the second segment:

SF = 18/15 = 6/5

Also, the angle WUF = angle TRS.

Hence, the two polygons triangle RST = triangle VWU are similar by the scale factor of 6/5. Option C is the correct answer.

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Answer:

1. Ali makes three straight long cuts along the diameter of the pizza.

2. Ali makes two straight long cuts along the diameter of the pizza.

Step-by-step explanation:

Answer:

(x-2)(x - 3)(x - 5)

(x - 2)(x-3)(x - 5)(x + 5)

(x + 2)(x + 3)(x + 5)

(x + 2)(x+3)(x - 5)

Answer:

first option

Step-by-step explanation:

(x-2)(x-3)(x-5)

Answer:

A.) 6π/5

B.) 756°

Step-by-step explanation:

A.) \(216*\frac{\pi }{180} = \frac{6\pi }{5}\)

B.) \(\frac{21\pi }{5} *\frac{180}{\pi } = 756 ^{0}\)

Hope this helps!

Answer:

i will help in a sec

Step-by-step explanation:

Answer:

ans is S=1

Step-by-step explanation:

7s=7

s=7/7

s=1

The balance in the fund at the end of 23 years, with monthly deposits of $1,150 and a 3.25% annual interest rate, is approximately $449,069.51. The amount of interest earned over the period is approximately $420,630.49.

a. The balance in the fund at the end of the 23-year period, considering a monthly deposit of $1,150 and an annual interest rate of 3.25% compounded annually, is approximately $449,069.51.

To calculate the balance, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the accumulated balance, P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have monthly deposits, so we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = (1 + 0.0325)^(1/12) - 1 = 0.002683

Using this monthly interest rate, we can calculate the accumulated balance over the 23-year period:

A = 1150 * [(1 + 0.002683)^(12*23) - 1] / 0.002683 = $449,069.51

Therefore, the balance in the fund at the end of the 23-year period is approximately $449,069.51.

b. The amount of interest earned over the 23-year period can be calculated by subtracting the total deposits from the accumulated balance:

Interest earned = (Monthly deposit * Number of months * Number of years) - Accumulated balance

Interest earned = (1150 * 12 * 23) - 449069.51 = $420,630.49

Therefore, the amount of interest earned over the 23-year period is approximately $420,630.49.

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Answer:

  D. 13.2

Step-by-step explanation:

The law of sines tells you side lengths are proportional to the sines of their opposite angles.

From the law of sines, we have ...

  b/a = sin(B)/sin(A) = sin(49°)/sin(16°)

You know the sine function is concave downward, so the sine of 49° cannot be more than 49/16 = 3 1/16 times the sine of 16°. That means ...

  b/a < 3 1/16   ⇒   b < (4)(3 1/16) = 12 1/4

The triangle inequality tells you ...

  c < a +b

  c < 4 + 12 1/4 = 16 1/4

Of the possible answer choices, the only sensible choice is 13.2.

If you actually want to work the problem in detail, you need to find angle C:

  C = 180° -A -B

  C = 180° -16° -49° = 115°

Then the law of sines tells you ...

  c/a = sin(C)/sin(A)

  c = a·sin(C)/sin(A) = 4·sin(115°)/sin(16°)

  c ≈ 13.2

__

Additional comment

We can revisit the estimating process using the actual value of angle C.

  C = 180° -16° -49° = 115°

  sin(C) = sin(115°) = sin(65°) . . . . . . sine identity

Again, ...

  c/a < C/A

  c < a(C/A) = 4(65°/16°) = 16 1/4 . . . . same as above.

The linear approximating polynomial for the function f(x) = 32x^3/2 centered at a is:32a^3/2 + 48a^(1/2)(x-a)sample.

This can be obtained using the formula for the linear approximation of a function:f(x) ≈ f(a) + f'(a)(x-a)where f'(a) is the derivative of f(x) evaluated at a.To find the derivative of f(x), we use the power rule, which states that the derivative of x^n is n*x^(n-1).

Therefore, the derivative of f(x) = 32x^3/2 is:f'(x) = 3*32*x^(3/2-1) = 96x^(1/2)Evaluating this at x=a, we have:f'(a) = 96a^(1/2)Finally, substituting into the linear approximation formula, we get:f(x) ≈ f(a) + f'(a)(x-a)f(x) ≈ 32a^3/2 + 96a^(1/2)(x-a)f(x) ≈ 32a^3/2 + 48a^(1/2)(x-a) * 2 / 2f(x) ≈ 32a^3/2 + 48a^(1/2)(x-a)

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Answer:

Arc Length = θ × (π/180) × r, where θ is in degree.

The Arc length of the given partial circle is 4π units or 12.56 units .

Step-by-step explanation:

Answer:

4π

Step-by-step explanation:

Hope this helps!

Answer:

1. Equation: x/-9=-16

solution: x=144

2. Equation:15*x=-75

solution: x=-5

3.Equation:0.75n=36

solution: n=48

Step-by-step explanation:

Answer:

The exam was out of 75.

Step-by-step explanation:

You know that he earned 65% so more than half his answers were correct.

Then, you would guess and check try 49/60, 49/70, and go up by 10s or 5s. You will then realize that 49÷75 equals 65.333. This rounds up to 65.

Answer:

Step-by-step explanation:

By using mid point formula ,

(X,Y) =( X1+X2/2) , Y1 +Y2/2

(-2+2/2) , (-4-10/2)

or, (0/2), (-7)

If the standard deviation of a set of data is 6, then the value of variance is 36

The formula for determining variance is variance = √Standard deviation

Variance of a set of data is equal to square of the standard deviation.

If the standard deviation of a set of data is 6 then we get variance by putting the value of standard deviation in the formula

variance = √Standard deviation

Take square root on both sides

Standard deviation² = 6²

Standard deviation= 36

Hence,  standard deviation of a set of data is 6, then the value of variance is 36

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Answer:

3 1/3 = 10/3

0.3 = 3/10

a * 1/a =1

then 1/a is multiplicative inverse of a

0.3* 3 1/3 = 3/10 * 10/3 =1

0.3 is multiplicative inverse of 3 1/3

Step-by-step explanation:

Answer:

3 1/3 = 10/3

10.3 = 0.3 = 3 1/3

x * 1/x = 1

∴ yes, the multiplicative reverse of 3 1/3 is 0.3

hope this answer helps you.....

Answer:

If \(p\) is people and \(h\) is hot dogs, the equation is \(3h=4p\).

The  relation among people who attend and hot dog sold is 4x = 3y.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

At the Football game they expect that for every 4 people that attend 3 hot dogs will be sold.

let the are total x people and y number of hot dogs will be sold.

So, the relation among people who attend and hot dog sold is

4x = 3y

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Answer:

160-128=32

Step-by-step explanation:

distribute what is in the parentheses

Answer:

you use the distance formula: square root of (x2-x1)^2 + (y2-y1)^2. it is a little hard to type the equation out so I reccomend you look up the distance formula and plug the given coordinates into it

When dealing with the problem of non-constant variance, the log transformation means using b. LogX as the independent variable instead of X.

A log transformation is a type of data transformation that is often used to address the problem of non-constant variance, also known as heteroscedasticity. This type of transformation involves taking the natural logarithm of the independent variable, X, and using LogX as the independent variable instead of X.

This transformation can help to stabilize the variance of the data and make the relationship between the independent variable and the dependent variable more linear. It is important to note that a log transformation may not always be appropriate, and it is important to carefully consider the characteristics of the data before applying this type of transformation.

In conclusion, when dealing with the problem of non-constant variance, the log transformation means using LogX as the independent variable instead of X. This can help to stabilize the variance and make the relationship between the independent and dependent variables more linear.

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Answer:

Step-by-step explanation:

Use the formula x-x1/x1-x2 = y-y1/y1-y2

Answer:

2.5hrs apart.

Step-by-step explanation:

150÷60= 2.5

150÷60=5

therefore 5-2.5 =2.5

The confidence interval for Restaurant A is (0.186, 0.266).

The two intervals are statistically different.

B. The lower confidence limit of the interval for Restaurant B is higher than the lower confidence limit of the interval for Restaurant A, and the upper confidence limit of the interval for Restaurant B is also higher than the upper confidence limit of the interval for Restaurant A. Therefore, Restaurant B has a significantly higher percentage of orders that are not accurate.

a. To construct a 95% confidence interval estimate of the percentage of orders that are not accurate at Restaurant A, we can use the following formula:

CI = p ± Z √(p(1-p)) / n)

Where:

p = (70/309 = 0.226),

Z is the z-score corresponding to a 95% confidence level (standard value is approximately 1.96),

n is the total number of orders (309).

Plugging in the values, we get:

CI = 0.226 ± 1.96 √((0.226 (1 - 0.226)) / 309)

CI = 0.226 ± 0.040

The confidence interval for Restaurant A is (0.186, 0.266).

b. To compare the results from part (a) to the 95% confidence interval for the percentage of orders that are not accurate at Restaurant B (0.209), we need to check if the confidence intervals overlap.

The confidence interval for Restaurant A is (0.186, 0.266), and the percentage for Restaurant B is 0.209. Since the confidence interval for Restaurant A does not overlap with the percentage for Restaurant B, we can conclude that the two intervals are statistically different.

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The sum of the lengths of the two longest altitudes in a triangle with sides 8, 12, and 14 would be \(12 + 14 = 26\) units.

In a triangle, the lengths of the two longest altitudes are equal to the lengths of the corresponding sides.

The sides in two different forms or polygons that are in the same position are said to have corresponding sides.

The two polygons have the same size and shape if they are congruent.

Congruence exists between the corresponding sides and angles.

So, the sum of the lengths of the two longest altitudes in a triangle with sides 8, 12, and 14 would be \(12 + 14 = 26\) units.

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The sum of the lengths of the two longest altitudes in the triangle with sides 8, 12, and 14 is 17 units.

The sum of the lengths of the two longest altitudes in a triangle can be found using the formula:

Sum of altitudes = (a + b + c) / 2

In this case, the sides of the triangle are given as 8, 12, and 14 units.

The longest altitude in a triangle is the altitude drawn from the longest side. So, we need to find the longest side in the given triangle.

To do that, we can arrange the sides in descending order: 14, 12, 8.

Now, we can use the formula to find the sum of the lengths of the two longest altitudes:

Sum of altitudes = (14 + 12 + 8) / 2 = 34 / 2 = 17 units

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Answer:

6x+4

Step-by-step explanation:

Answer:

Step-by-step explanation:

The area of a rectangle is the product of its side lengths. In this case

\(A=(2x+6)(3x-2)\\ \\ A=2x(3x)+2x(-2)+6(3x)+6(-2)\\ \\ A=6x^2-4x+18x-12\\ \\ A=6x^2+14x-12\)

B. Your initial explanation is mostly accurate, but these additional details provide a clearer understanding of the problem-solving process.

A. The process you described is commonly known as problem-solving or decision-making. Here's a breakdown of the steps involved: Identify the problem, Generate alternative solutions, Evaluate alternatives, Select the best solution, Implement the solution.

Identify the problem: The first step is to clearly identify and define the problem at hand. This involves understanding the nature of the problem, its causes, and its consequences or effects. Without a clear understanding of the problem, it would be difficult to find an appropriate solution.

Generate alternative solutions: Once the problem is identified, the next step is to brainstorm and generate multiple possible solutions or approaches to address the problem. This step encourages creativity and exploration of different options.

Evaluate alternatives: After generating alternative solutions, each option should be evaluated carefully. Factors such as feasibility, cost, time, resources required, and potential risks or benefits should be considered. This evaluation helps in narrowing down the options to those that are most viable.

Select the best solution: Based on the evaluation, one or more solutions may stand out as being the most effective or suitable for solving the problem. The best solution is selected based on its ability to address the problem efficiently and meet the desired objectives.

Implement the solution: Once the best solution is chosen, it is put into action. Implementation may involve planning, executing tasks, allocating resources, and managing the necessary steps to bring the solution to fruition.

It's important to note that the order of the steps may vary depending on the context and the complexity of the problem. While it's generally logical to evaluate and select the best solution before implementing it, sometimes it may be necessary to iterate through the steps, re-evaluate options, or make adjustments during the implementation phase.

Regarding the other options you mentioned:

A. This option suggests starting with identifying the best solution without understanding the nature of the problem or considering other possible solutions. As you correctly pointed out, this approach is flawed because it skips important steps in the problem-solving process.

C. This option implies evaluating and selecting the best solution before understanding the problem or considering other alternatives. Again, this is incorrect because a thorough understanding of the problem and exploration of multiple solutions should precede the evaluation and selection stage.

D. This option suggests implementing the solution before evaluating and selecting the best one. However, it's generally more effective to assess the potential effectiveness of different solutions before committing to their implementation.

In summary, your initial explanation is mostly accurate, but these additional details provide a clearer understanding of the problem-solving process.

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After Jonah Benavides deposits his paycheck, bonus check, and a check from his grandma, the total amount added to his account is $943.98. Adding this amount to his original balance of $476.2, the total amount in his account after the deposit will be $1,420.18.

To calculate the total amount in Jonah's account after the deposit, we need to sum up the amounts of his paycheck, bonus check, and the check from his grandma and then add it to his original balance.

Paycheck amount = $865.98

Bonus check amount = $60

Check from grandma = $18

Original balance = $476.2

Total deposit amount = Paycheck amount + Bonus check amount + Check from grandma

Total deposit amount = $865.98 + $60 + $18 = $943.98

Total amount in Jonah's account after the deposit = Original balance + Total deposit amount

Total amount in Jonah's account = $476.2 + $943.98 = $1,420.18

Therefore, Jonah will have $1,420.18 in his account after the deposit is made, assuming the checks clear.

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Answer: 12 & 15

Step-by-step explanation:

The sum of the two Must be 27

12+15=27 satisfies the given condition

Given that product must be 180

12×15=180

This also satisfies the conditions given in the question.

Answer:

15

Step-by-step explanation:

a * b = 180      Ec. 1

a + b = 27        Ec. 2

From Ec. 2:

a = 27 - b         Ec. 3

Replacing Ec. 3 in Ec. 1:

(27-b)b = 180

27*b + b*-b = 180

-b² + 27b - 180 = 0

b = {-27±√((27²)-(4*-1*-180))} / (2*-1)

b = {-27±√(729-720)} / - 2

b = {-27±√9} / - 2

b = {-27±3} / - 2

b ₁ = {-27-3} / -2 = -30/-2 = 15

b₂ = {-27+3} / -2 = -24/-2 = 12

Check:

15*12 = 180

15 + 12 = 27

Answer:

15 > 12

Then

the larger of the numbers is:

15

The integral ∫∫s xyz ds, over the given surface s, is equal to √2 ∫∫r ρ^3cosθsinθ(4-y) dρdθ, where r is the region in the xy-plane bounded by the cylinder x^2+y^2=4.

To evaluate the given integral ∫∫s xyz ds, where s is the part of the plane z=4−y that lies in the cylinder x^2+y^2=4, we can use the method of our choice. Let's use the method of cylindrical coordinates.

1. Set up the surface integral for the given function over the given surface s as a double integral over a region r in the xy-plane.
  ∫∫s xyz ds = ∫∫r xyz √(1 + (∂z/∂x)^2 + (∂z/∂y)^2) dA

2. To find the region r, we need to determine the bounds for the cylindrical coordinates. Since the cylinder has radius 2, we have 0 ≤ ρ ≤ 2. The z-coordinate ranges from the plane z = 4-y to the plane z = 0. Thus, the bounds for z are 0 ≤ z ≤ 4-y.

3. Convert the integral into cylindrical coordinates by substituting x = ρcosθ and y = ρsinθ.
  ∫∫r xyz √(1 + (∂z/∂x)^2 + (∂z/∂y)^2) dA
  = ∫∫r ρ^3cosθsinθ(4-y) √(1 + (-sinθ)^2 + (-cosθ)^2) dρdθ

4. Evaluate the double integral by integrating with respect to ρ first and then θ.
  ∫∫r ρ^3cosθsinθ(4-y) √2 dρdθ
  = √2 ∫∫r ρ^3cosθsinθ(4-y) dρdθ

Therefore, the integral ∫∫s xyz ds, over the given surface s, is equal to √2 ∫∫r ρ^3cosθsinθ(4-y) dρdθ, where r is the region in the xy-plane bounded by the cylinder x^2+y^2=4.

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Answer:

00000

Step-by-step explanation: