If the point (3,-4) is dilated by a scale factor of 74 , what are the new coordinates?
Now take the new points and rotated them 180°. What are the new coordinates?

Answer:

II and III

THATS IIITTT WHY SO MANY QUESTION!!!???

The coefficient of \(\(x_{1}^{3} x_{2}^{2} x_{3}^{2}\)\) in \(\((x_{1}+2x_{2}+3x_{3})^{7}\)\) is 2,520. This can be obtained by using the multinomial theorem and considering the power of each term in the expansion.

To determine the coefficient of \(\( x_{1}^{3} x_{2}^{2} x_{3}^{2} \)\) in the expansion of \(\( \left(x_{1}+2 x_{2}+3 x_{3}\right)^{7} \)\), we need to apply the multinomial theorem. According to the theorem, the coefficient can be calculated using the following formula:

\(\[\frac{{7!}}{{3! \cdot 2! \cdot 2!}} \cdot 1^{3} \cdot 2^{2} \cdot 3^{2} = 2,520\]\)

In this case, the multinomial coefficient represents the number of ways we can choose the powers of \(\( x_{1} \), \( x_{2} \), and \( x_{3} \)\) in the term. The factorials in the denominator account for the repetitions of the powers. The powers themselves are determined by the exponents in the term \(\( x_{1}^{3} x_{2}^{2} x_{3}^{2} \)\). Finally, multiplying all these values together gives us the coefficient of the term.

In the given problem, the coefficient is calculated as\(\( \frac{{7!}}{{3! \cdot 2! \cdot 2!}} \cdot 1^{3} \cdot 2^{2} \cdot 3^{2} = 2,520 \).\)

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Answer:

C. 1/2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (2, -1)

Point (-2, -3)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

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Answer:

x = 7, y = 16

Step-by-step explanation:

Looking at the image we can conclude the following
Sides with measurements y - 4 and x + 5 are equal

So we get the equation y - 4 = x + 5

The sides with measurements 2x + 5 and x + 12 are equal\

We get another equation 2x + 5 = x + 12

Let's take the second equation which is in terms of x only and solve for x

2x + 5 = x + 12

Subtract x from both sides

2x - x + 5 = x - x + 12

==> x + 5 = 12  

Subtract 5 from both sides:
x + 5 - 5 = 12 - 5

x = 7

Now that we know the value of x, we can substitute this value into the first equation y - 4 = x + 5

==> y - 4 = 7 + 5

y - 4 = 12

Add 4 to both sides:

y - 4 + 4 = 12 + 4

y = 16

Answer:

Step-by-step explanation:

Substitute and calculate:

Expressions can be expressed in logarithmic forms, and in exponential forms

The two equations are \(\ln(10) = y\) and \(10 = e^y\)

The statement is given as "the natural logarithm of 10 is y".

The logarithmic expression of the above statement is:

\(\ln(10) = y\)

Rewrite the above expression, as an exponential equation

\(10 = e^y\)

Hence, the two equations are \(\ln(10) = y\) and \(10 = e^y\)

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Answer:

  (X_1, X_2) = (2, 4)

  Z = 110

Step-by-step explanation:

You want a graphical solution to ...

  minimize Z = 15 X_1 +20 X_2

  subject to ...

A graph of the reverse of the inequalities is attached. This makes the feasible solution region be white (rather than shaded multiple times), so its vertices are easier to see. (The dashed lines are part of the solution space.)

The vertex of the solution space that minimized the objective function is (X_1, X_2) = (2, 4). The minimum value of Z is 110.

Answer:

1

Step-by-step explanation:

I used DESMOS and to find this answer

Hope this Helped

Answer:

20%

Step-by-step explanation:

Answer:

Answer is equation C

Step-by-step explanation:

They are converting Celsius temperature to Fahrenheit temperature.

F = 1.8C + 32

F = 1.8(0) + 32 = 32 Fahrenheit

F = 1.8(30) + 32 = 86 Fahrenheit

F = 1.8(100) + 32 = 212 Fahrenheit

Answer:

C) F = 1.8C + 32

Step-by-step explanation:

Hello! The easiest way to do this is to substitute the numbers from your table into your possible answer choices until you find numbers that make a true/correct statement.

For A:

F = 32C + 1.8 <== substitute any number for F and C from your table

32 = 32(0) + 1.8 <== multiply

32 = 0 + 1.8 <== add

32 = 1.8

This statement is false/incorrect

For B:

C = 1.8F + 32 <== substitute any number for F and C from your table

0 = 1.8(32) + 32 <== multiply

0 = 57.6 + 32

0 = 89.6

This statement is false/incorrect

For C:

F = 1.8C + 32 <== substitute any number for F and C from your table

32 = 1.8(0) + 32 <== multiply

32 = 0 + 32 <== add

32 = 32

This statement is true/correct

For D:

C = 32F + 1.8 <== substitute any number for F and C from your table

0 = 32(32) + 1.8 <== multiply

0 = 1024 + 1.8 <== add

0 = 1025.8

This statement is false/incorrect

As we can see, the only equation that makes a true statement is C.

Therefore, the correct answer is C.

Hope this helps!

Answer:

80 lemons

Step-by-step explanation:

Let x represent the amount of lemons that were on the tree.

We can use this to set up an equation:

\(40\%x=32\)

Note that percentages can also be written as that number over 100.

\(\frac{40}{100}x=32\)

Simplify the fraction.

\(\frac{2}{5}x=32\)

Multiply both sides by 5

\(2x=160\)

Divide both sides by 2

\(x=80\)

There were 80 lemons on the tree before he picked the lemons.

Answer: mandatory and discretionary.

Q:    Which of the following equations is equivalent to S = pi r squared h?

A:     B  (CC ALGEBRA 2A, ED20)

The equations is equivalent to S = pi r squared h would be; B. h=S/πr²

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

To know the equation equivalent to πr²h, we will make h the subject of the formula from the one given in equation.

S = πr²h

To get h, we needd to divide both sides by the coefficient of h (i.e πr²)

S/πr² = πr²h/πr²

S/πr² = h

h = S/πr²

This equation shows that h = S/πr² is equivalent to S = πr²h

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Answer:

The x-coordinate of point A is: 6

The y-coordinate of point D is: 3

The point that is on the x-axis is: Point E

The point that is on the y-axis is: Point B

Step-by-step explanation:

Hope this helps :)

Answer:

6 = x-coordinate of Point A

3 = y-coordinate of point D

E is on the x-axis

B is on the y-axis

Step-by-step explanation:

The linear equations for cost price and selling price are c = 3x + 35 and  y = 5x.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Let Max make x cups of lemonade cup.

According to given conditions,

Cost of 1 cup of lemonade = $3.

Also, Max pay for renters fee = $35.

The cost of x cups of lemonade = 3x

The total cost c = 3x + 35

Since, Max sells lemonade for $5 per cup.

Let the selling price is represented by y,

Then selling price y = 5x

Hence, linear equations for cost price and selling price are c = 3x + 35 and  y = 5x.

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Answer:

a. not a triangle

Step-by-step explanation:

Well the two small sides of a triangle should always add up to be greater than or equal to the greatest side.

a + b ≥ c

Thus,

the answer is a. not a triangle.

Hope this helps :)

Answer:

Step-by-step explanation:

Writing Algebraic Expressions

Writing Algebraic Expressions

Group workProblem: Ms. Jensen likes to divide her class into groups of 2. Use mathematical symbols to represent all the students in her class.

Solution: Let g represent the number of groups in Ms. Jensen's class.

Then 2 · g, or 2g can represent "g groups of 2 students".

In the problem above, the variable g represents the number of groups in Ms. Jensen's class. A variable is a symbol used to represent a number in an expression or an equation. The value of this number can vary (change). Let's look at an example in which we use a variable.

Example 1: Write each phrase as a mathematical expression.

Phrase Expression

the sum of nine and eight 9 + 8

the sum of nine and a number x 9 + x

The expression 9 + 8 represents a single number (17). This expression is a numerical expression, (also called an arithmetic expression). The expression 9 + x represents a value that can change. If x is 2, then the expression 9 + x has a value of 11. If x is 6, then the expression has a value of 15. So 9 + x is an algebraic expression. In the next few examples, we will be working solely with algebraic expressions.

Example 2: Write each phrase as an algebraic expression.

Phrase Expression

nine increased by a number x 9 + x

fourteen decreased by a number p 14 - p

seven less than a number t t - 7

the product of 9 and a number n 9 · n   or   9n

thirty-two divided by a number y 32 ÷ y   or    

In Example 2, each algebraic expression consisted of one number, one operation and one variable. Let's look at an example in which the expression consists of more than one number and/or operation.

Example 3: Write each phrase as an algebraic expression using the variable n.

Phrase Expression

five more than twice a number 2n + 5

the product of a number and 6 6n

seven divided by twice a number 7 ÷ 2n   or    

three times a number decreased by 11 3n - 11

bonusExample 4: A small company has $1000 to distribute to its employees as a bonus. How much money will each employee get?

Solution: Let e represent the number of employees in the company. The amount of money each employee will get is represented by the following algebraic expression:

electricianExample 5: An electrician charges $45 per hour and spends $20 a day on gasoline. Write an algebraic expression to represent his earnings for one day.

Solution: Let x represent the number of hours the electrician works in one day. The electrician's earnings can be represented by the following algebraic expression:

Solution: 45x - 20

The industrial designer fails to support the hypothesis that the average time to assemble the "easy to assemble" toy is 22 minutes. The sample evidence suggests that the average assembly time is significantly higher than the hypothesized value.

The industrial designer's hypothesis states that the average time it takes an adult to assemble an "easy to assemble" toy is 22 minutes. However, based on a sample of 400 assembly times, the average time was found to be 23 minutes with a variance of 2 minutes. To determine if the hypothesis holds or if it fails, we need to perform a hypothesis test.

Using the sample data, we can calculate the standard deviation (σ) by taking the square root of the variance, which is \(\sqrt{2} \approx 1.41\) minutes. Since the sample size (n) is large (n = 400) and we assume normality of assembly times, we can use a z-test.

The test statistic (z-score) is calculated as:

\(z = (\bar X - \mu ) / (\sigma / \sqrt {n})\)

where \(\bar X\) is the sample mean, μ is the hypothesized population mean, σ is the standard deviation, and n is the sample size.

Plugging in the values, we get:

z = (23 - 22) / (1.41 / \(\sqrt{400}\))

z = 1 / (1.41 / 20)

z ≈ 14.18

By comparing the z-score to the critical value at a chosen significance level (e.g., \(\alpha\) = 0.05), we can determine if the null hypothesis is rejected or not. Since the calculated z-score (14.18) is far beyond the critical value, we can reject the null hypothesis.

Therefore, based on the given sample data, the industrial designer fails to support the hypothesis that the average time to assemble the "easy to assemble" toy is 22 minutes. The sample evidence suggests that the average assembly time is significantly higher than the hypothesized value.

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a. Noah will have money in the account after 9 yrs is $4900.

b. Noah has earned interest from this account after 9 years is 22.5%.

What is compound interest?

Compound interest is when interest on a loan, investment, or savings account grows exponentially over time rather than linearly.

Formula to calculate simple interest

I = Prt

Where, I = Simple interest

t = time

r = earned interest

P = Compound interest

Here, we have

P = $4000, r = 2.5%, t = 9 years

By applying the compound interest formula, we get

I = 4000×0.025×9

= 900

The total amount after 9 years is 4000+900= 4900

Hence,

a. Noah will have money in the account after 9 yrs is $4900.

b. Noah has earned interest from this account after 9 years is 22.5%.

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The probability exactly two of the appeals were successful is 0.9536

We are given that 40% of first-round appeals were successful (The Wall Street Journal, October 22, 2012), and suppose ten first-round appeals have just been received by a Medicare appeals office.

This situation can be represented through Binomial distribution as;

\(P(X=r)={}^{n}C_{r}(p)^r(1-p)^r\) where \(x=0,1,2,3.....\)

where,  n = number of trials (samples) taken = 10

            r = number of success

            p = probability of success which in our question is % of first-round

                  appeals that were successful, i.e.; 40%

So, here X ~ Binom(n=10 , p=0.40

Probability that at least two of the appeals will be successful = P(X>=2)

   P(X >= 2) = 1 - P(X = 0) - P(X = 1)

                    = 1 - \(^{10}C_{0}(0.40)^0(1-0.40)^{10-0}-^{10}C_{1}(0.40)^1(1-0.40)^{10-1}\)

                     = 1 - 0.00605 - 0.0403

                     = 0.9536

Hence, the probability exactly two of the appeals were successful is 0.9536

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The solution of the expression 2(4+9)-(3 x 2) will be 20.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given expression is 2 x (4+9)-(3 x 2). The solution to the expression is given below:-

E = 2 x (4+9)-(3 x 2)

E = 2x 13 - 6

E = 26 - 6

E = 20

Therefore, the solution of the expression 2(4+9)-(3 x 2) will be 20.

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the partial fraction decomposition of the rational function is 3/(x - 2) - 1/(x + 2)

the integral ∫ (4x³ + 2x² - 11x - 10)/(x²-4) dx is  3 ln| x - 2 | - ln| x + 2 | + C, where C is the constant of integration.

To find the partial fraction decomposition of the rational function (4x³ + 2x² - 11x - 10)/(x²-4), we first factor the denominator:

x² - 4 = (x - 2)(x + 2)

The denominator has two distinct linear factors, (x - 2) and (x + 2).

Now, let's express the given rational function as the sum of two fractions with the following form:

(4x³ + 2x² - 11x - 10)/(x²-4) = A/(x - 2) + B/(x + 2)

To find the values of A and B, we need to determine the numerator for the right-hand side. By multiplying through by the common denominator (x² - 4), we have:

(4x³ + 2x² - 11x - 10) = A(x + 2) + B(x - 2)

Expanding and collecting like terms, we get:

4x³ + 2x² - 11x - 10 = (A + B)x + (2A - 2B)

Now, we can equate the coefficients of the corresponding powers of x:

For the x³ term: 4 = 0 (since there is no x³ term on the right-hand side)

For the x² term: 2 = A + B

For the x term: -11 = 2A - 2B

For the constant term: -10 = 0 (since there is no constant term on the right-hand side)

From the constant term equation, we get A + B = 2. From the x term equation, we get 2A - 2B = -11. Solving these two equations simultaneously, we find A = 3 and B = -1.

Therefore, the partial fraction decomposition of the rational function is:

(4x³ + 2x² - 11x - 10)/(x²-4) = 3/(x - 2) - 1/(x + 2)

Now, to evaluate the integral:

∫ (4x³ + 2x² - 11x - 10)/(x²-4) dx

We can rewrite it as:

∫ (3/(x - 2) - 1/(x + 2)) dx

Using the properties of integrals, we can evaluate each term separately:

∫ (3/(x - 2)) dx = 3 ln| x - 2 |

∫ (-1/(x + 2)) dx = - ln| x + 2 |

Therefore, the integral ∫ (4x³ + 2x² - 11x - 10)/(x²-4) dx is:

∫ (4x³ + 2x² - 11x - 10)/(x²-4) dx = 3 ln| x - 2 | - ln| x + 2 | + C, where C is the constant of integration.

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complete question is below

Determine the partial fraction decomposition of (4x³ + 2x² - 11x - 10)/(x²-4)

Use this decomposition to evaluate the integral ∫ (4x³ + 2x² - 11x - 10)/(x²-4) dx

answer:

$0.75

Step-by-step explanation:

the function can be represented as:

f(x)=0.25x+3.5

the function produces the following values for years 1, 2, and 3 respectively:

f(1)=0.25(1)+3.5=3.75

f(2)=0.25(2)+3.5=4.00

f(3)=0.25(3)+3.5=4.25

therefore, 

there is a $0.75 increase per year

Answer:

8

Step-by-step explanation:

10/3 divided by 5/12

10/3 multiple 12/5

So the 3 and 12 will cross out same as 10 and 5 then we will get 8 as an answer

Answer:

I love algebra anyways  

the ans is in the picture with the steps  

(hope it helps can i plz have brainlist :D hehe)

Step-by-step explanation:

The dot product of vectors a and b  || a |= 6,|| b ||= 4 and the angle between the vectors θ = π/3 is (c) 12.

The dot product of two vectors, we can use the formula:

a · b = ||a|| ||b|| cos(theta)

where ||a|| and ||b|| represent the magnitudes of vectors a and b, respectively, and theta is the angle between the vectors.

In this case, we are given that ||a|| = 6, ||b|| = 4, and the angle between the vectors is theta = π/3.

Substituting these values into the formula, we have:

a · b = 6 × 4 × cos(π/3)

To evaluate cos(π/3), we can use the fact that it is equal to 1/2. So we have:

a · b = 6 × 4 × 1/2

= 12

Therefore, the dot product of vectors a and b is 12.

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To find the speed of the movement of the spotlight along the shore, we need to determine the rate at which the distance between the light and the point where the beam meets the shore is changing.

Let's consider a right triangle formed by the light, the point where the beam meets the shore, and the shoreline. The hypotenuse of the triangle represents the distance between the light and the point on the shore where the beam meets. The angle between the hypotenuse and the shoreline is 60°.

Using trigonometry, we can relate the distance between the light and the shore to the angle of the beam. The distance is given by the formula:

distance = hypotenuse = 4 km

The rate of change of the distance is given by the derivative of the distance with respect to time:

d(distance)/dt = d(hypotenuse)/dt

Since the light rotates at a constant angular speed of 3.5 rad/min, the rate of change of the angle is constant:

d(angle)/dt = 3.5 rad/min

Using the chain rule, we can relate the rate of change of the distance to the rate of change of the angle:

d(distance)/dt = d(distance)/d(angle) * d(angle)/dt

Since the angle is 60°, we can calculate the rate of change of the distance:

d(distance)/dt = (4 km) * (π/180 rad) * (3.5 rad/min)

Simplifying the expression, we get:

d(distance)/dt = 2π km/min

Therefore, the speed of the movement of the spotlight along the shore when the beam is at an angle of 60° with the shoreline is 2π km/min.

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Answer: 9.128 x 10^7

Step-by-step explanation:

9.1x10^7+280,000

91,000,000 + 280,000

91,280,000

9.128x10^7