sqrt(y^6) = -y^3
y=?

Answer:

Step-by-step explanation:

x - y² = -1     ⇒   - y² = - x - 1    ⇒    y² = x + 1   {x≥-1}

4x² + 9y² = 72

4x² + 9(x + 1)² = 72

4x² + 9(x² + 2x + 1) = 72

4x² + 9x² + 18x + 9 - 72 = 0

13x² + 18x - 63 = 0     ⇒   a = 13,  b = 18,  c = -63

\(x=\dfrac{-18\pm\sqrt{18^2-4\cdot13\cdot(-63)}}{2\cdot13}=\dfrac{-18\pm\sqrt{324+252}}{26}=\dfrac{-18\pm\sqrt{576}}{26}\\\\x=\dfrac{-18+24}{26}=\dfrac3{13}\qquad\vee\qquad x=\dfrac{-18-24}{26}=-\dfrac{21}{13}\\\\ y^2= x + 1\quad\iff\quad x\ge-1\\\\y^2=\dfrac3{13}+1\\\\ y^2=\dfrac{16}{13}\\\\y=\dfrac{4}{\sqrt{13}}=\dfrac{4\sqrt{13}}{13}\qquad\vee\qquad y=-\dfrac{4\sqrt{13}}{13}\)

Answer:

379.94

Step-by-step explanation:

Hope this helps :)

Answer:

x=14

Step-by-step explanation:

(7x - 1)° + (6x - 1)° = 180°

(13x - 2)° = 180°

13x = 182°

x = 182°/13

x = 14

Answer:

Look at the image.

Step-by-step explanation:

If 12 is 24%, then half of the percent is the actual number.

36% = 18

24% = 12

18% = 9

22% = 11

18 + 12 + 9 + 11 = 50

18 students would like to learn Spanish.

Answer:

107

Step-by-step explanation:

The statistical model is not good, and this is true for a negatively skewed curve.

It is a statistical term implies that a curve is skewed at the left side.

In a statistical data for a certain distribution, we can get a negatively skewed curve when most of the data values are located on the right side of the distribution graph. The high concentration of values on the right side of distribution curve forms a long tail in the negative direction.

In general, negatively skewed curve is not good because it expresses the tendency of left tail events. Negatively skewed curves indicate a poor return from an investment. That means a person might be earn lower or no profit from his business. In case of an exam scores, negative skewed data value implies the question was too easy to perform better than usual.

In a word, left skewed or negatively skewed curve or data values inform us to be aware about the current statistical model and inspire us to take proper steps for wellbeing.

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Answer:

2. -12, -3, 0, 36, -24

3. 0, 8, 13, 15, 9

p-by-step explanation:

The mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

Given data values are 55, 56, 70, 61, 53, 57, 50, 73, 52, 69, and 2. We need to calculate the mean, median, and mode of this sample.So, let's first arrange the data values in ascending order:2, 50, 52, 53, 55, 56, 57, 61, 69, 70, 73

Mean:The mean is the sum of all the data values divided by the total number of data values. So, we can use the following formula to calculate the mean:

Mean = (sum of all the data values) / (total number of data values)Sum of all the data values = 55 + 56 + 70 + 61 + 53 + 57 + 50 + 73 + 52 + 69 + 2 = 598Total number of data values = 11

Therefore,Mean = (sum of all the data values) / (total number of data values) = 598 / 11 = 54.36 (rounded to two decimal places)Therefore, the mean of the given data values is 54.36.

Median:The median is the middle value of a sorted data set. Since the data set has 11 data values, the median is the average of the 6th and 7th values (counting from smallest to largest).

Therefore, the median is :Median = (55 + 56) / 2 = 55.5Therefore, the median of the given data values is 55.5.

Mode:The mode is the data value that appears most frequently in the data set. In this case, there is no data value that appears more than once. So, there is no mode.

Therefore, the mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

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Answer:

16+3=y

y=19

Step-by-step explanation:

In 5 years after depositing 3500, the bank account will have 3850

It is the operation in which we calculate the profit produced by a capital loaned at a given percentage.

The formula for simple interest and procedure we will use to solve this exercise is:

S.I.= (P*R*T)/100

Where:

Information about the problem:

Applying the simple interest formula, we get:

S.I.= (P*R*T)/100

S.I.= (3500*2*5)/100

S.I.= 350

Calculating the total amount that would be in my savings account, we get:

Total amount = P + S.I.

Total amount = 3500 + 350

Total amount = 3850

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Answer:

40

Step-by-step explanation:

The serving sizes, \(x\), of 20, 80, and 120 have a required amount of meat in pounds, \(y\), of \(y=\frac{1}{10}x\) (the number of pounds of meat is equal to 1/10th the serving size)

However, for the row with a serving size of 40, the number of pounds of meat is equal to \(\frac{6}{40}=\frac{3}{20}\) the serving size. Therefore, the serving size of 40 has a different ratio of serving size to pounds of meat than the other ratios.

Answer:

47°

Step-by-step explanation:

Given that m<BOC = 6x + 29, m<AOB = 3x + 124, and m<AOC is a straight angle, therefore, m<AOC = 180°.

m<BOC +m<AOB = 180°

6x + 29 + 3x + 124 = 180

Solve for x

6x + 3x + 29 + 124 = 180

9x + 153 = 180

Subtract both sides by 153

9x = 180 - 153

9x = 27

Divide both sides by 9

x = 3

m<BOC = 6x + 29

Plug in the value of x

m<BOC = 6(3) + 29

m<BOC = 18 + 29 = 47°

Answer:

B.6

Step-by-step explanation:

You compose two functions:  f is composed of g(x).

(f o g)(x) = f(g(x)) = f(1 / x - 6) = sqrt [3(1/x-6)]

The domain is where the expression is defined, (6,∞)

Answer:

Step-by-step explanation:

Let the number of cleaners be x

Let the time taken be y

This relationship is inverse

x = k/y

If x = 3 and y = 4

3 = k/4

k = 3*4

k = 12

To get the time it will take 4 people, we will substitute k = 12 and x = 4 into the expression x = k/y

x = 12/4

x = 3

Hence it will take 4 people 3 hours at the same rate

If Lucinda used a random selection method, made an effort to ensure that the sample is representative, and the sample size is large enough, then it's possible that the sample is indeed random.

what are perpendicular lines?

Perpendicular lines are two lines that intersect at a 90-degree angle, forming four right angles at the point of intersection. In other words, if you were to draw a perpendicular line from one of the lines to the other at their point of intersection, it would form a right angle with each of the original lines.

Without having access to more information about how Lucinda selected the sample of students, it's difficult to determine whether or not the sample is truly random.

However, there are a few things that we can consider when trying to determine whether or not the sample is random. For example:

Did Lucinda use a random selection method to choose the students? If she simply surveyed her friends or classmates, for example, the sample would not be random.

Did Lucinda make any effort to ensure that the sample is representative of the larger population of students? For example, did she make sure to include students from a variety of grades, genders, and ethnic backgrounds.

Therefore, if Lucinda used a random selection method, and made an effort to ensure that the sample is representative, and the sample size is large enough, then it's possible that the sample is indeed random.

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The definition of an eigenvector of A with eigenvalue λ.

True.

By definition, an eigenvector of a matrix A is a non-zero vector x that satisfies the equation Ax = λx, where λ is a scalar called the eigenvalue corresponding to x.

So if Ax = λx for some scalar λ, then x is a non-zero vector that satisfies the definition of an eigenvector of A with eigenvalue λ.

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Answer:

x=21.1

Step-by-step explanation:

12.8=m -8.3

12.8+8.3=m

21.1=x

x=21.1

Answer:

your answer would be 21.1

Step-by-step explanation:

so first you would have to 8.3 to 12.8 which would give you 21.1 then divide it by m but m is one so it would be just 21.1

Step-by-step explanation:

5x=10 divide both sides by the coefficient of x and that will give you 2. Therefore, x=2

2x=14 divide both sides by the coefficient of x and that will give you 7. Therefore, x=7

3x=15 divide both sides by the coefficient of x and that will give you 3. Therefore, x=3

7x =21 divide both sides by the coefficient of x and that will give you 3. Therefore, x=3

5x=30 divide both sides by the coefficient of x and that will give you 6. Therefore, x=6

9p=27 divide both sides by the coefficient of p and that will give you 3. Therefore, p=3

6m=30 divide both sides by the coefficient of m and that will give you 5. Therefore, m=5

3q=24 divide both sides by the coefficient of q and that will give you 8. Therefore, q=8

8r=24 divide both sides by the coefficient of r and that will give you 3. Therefore, r=3

I will be glad to be corrected if I make any mistake

Answer:

For the chart, the missing number on top is 10. the bottom numbers are 1.5 then 9.

For the question, all of the numbers equal the ration 5:3.

Question 2: Yes. 30/x=2/4 which equals 60 (minutes) which is an hour.

Step-by-step explanation:

1A:

2.5 amount of water  - 1.5 amount of pasta

10 amount water - 6 amount pasta

15 amount water - 9 amount pasta

2.5 : 1.5

5 : 3

10 : 6

15 : 9

1B. these quantities are proportional because they can all be simplified to the same unit rate of 5 : 3.

2. Johnny is correct. The rate is 4 : 2, with a unit rate of 2 : 1. If you multiply both sides by 30 (how many inches deep the hot tub is) you get a ratio of 60 : 30, meaning it would take an hour to fill up the tub.

Answer:x=21

Step-by-step explanation:

10/14=15/x

5/7=15x^-1

(5/7)/15=ans

ans=x^-1

ans^-1=21

Answer: x=21

Step-by-step explanation:

\(\frac{10}{14} =\frac{15}{x}\)

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 14x, the least common multiple of 14,x.

x×10=14×15

Multiply 14 and 15 to get 210.

x×10=210

Divide both sides by 10.

x=

10

210

​

Divide 210 by 10 to get 21.

x=21

you can do this two ways:

1. reflect ABC on the x and y axis, then translate the points up one and three to the right.

2. translate 3 to the left and 1 down and then reflect ABC on the x and y axis.

Answer:

\(\huge\boxed{x \approx 5.4}\)

Step-by-step explanation:

We can break down this problem by first realizing different parts of the circle.

With this, we can find out if we find the radius of the circle, we have our answer.

We should also note that the angle formed by the 3.6 units long line and the chord is a right angle.

What we need is a way to find the radius of the circle. This will get us x. The radius of a circle will be the length of any line that starts from point O and ends at the circle edge.

If we draw a line connecting the end of the 3.6 line at point O to the end of the 8 unit long chord, we get a triangle! (Image attached for reference).

We can solve for the hypotenuse using the Pythagorean Theorem. This theorem states that:

Since we know one side is 3.6, we can use that as A. The second side will be 4 since the 3.6 line lies directly in the center of the chord = 8/2 = 4!

Therefore, since this is the radius of the circle (also the hypotenuse), this can be said for any line that comes from point O onto the edge of the circle.

The line X does just that. Therefore, the value of x is also 5.4.

Hope this helped!

\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \pounds 400\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &2 \end{cases} \\\\\\ I = (400)(0.05)(2) \implies I = 40\)

Answer:

Answer → 63°

Step-by-step explanation:

» m<3 and m<4 are supplementary angles.

☑ Supplementary angles are angles that measure up to 180°

\({ \tt{m \angle 3 + m \angle 4 = 180 \degree}} \\ { \tt{117 \degree + m \angle 4 = 180 \degree}} \\ { \tt{m \angle 4 = 180 \degree - 117 \degree}} \\ { \tt{m \angle 4 = 63 \degree}}\)

The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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Answer:

9.5 feet

Step-by-step explanation:

Area of square garden = side length²

⇒ 90 = l²

⇒ l = √90

⇒ l = 3√10

⇒ l = 9.5 feet (nearest tenth)

The length of one side lies between the whole numbers 9 and 10.

Answer:

9 and 10

side length = 9.5 ft (nearest tenth)

Step-by-step explanation:

Area of a square = s²  (where s is the side length)

Therefore, if the square garden measures 90 ft², the length of one side will be √90.

To find the two whole numbers that √90 lies between, find the perfect square either side of 90.

Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, ...

Therefore, 90 lies between 81 and 100:  

⇒ 81 < 90 < 100

Square root the numbers:

⇒ √81 < √90 < √100

⇒ 9 < √90 < 10

Therefore, the length of one side of Grandma's garden is between 9 and 10.

To estimate √90 to the nearest tenth, find the difference between the three numbers:

\(81 \overset{+9}{\longrightarrow} 90 \overset{+10}{\longrightarrow} 100\)

As 90 is almost in the middle of 81 and 100,

⇒ √90 = 9.5 (nearest tenth)

According to the calculator, √90 = 9.486832981... = 9.5 (nearest tenth)
which verifies the estimation.

Answer:

ya no

Step-by-step explanation:

Answer:

Step-by-step explanation:

are you showing the entire question because that actually makes no sense

Using the Factor Theorem, the quadratic functions are given as follows:

The Factor Theorem states that a polynomial function with roots \(x_1, x_2, \codts, x_n\) is given by:

\(f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)\)

In which a is the leading coefficient.

For this problem, the roots are given as follows:

\(x_1 = -3, x_2 = 8\)

Hence:

f(x) = a(x + 3)(x - 8)

f(x) = a(x² - 5x - 24).

It opens upward with a positive leading coefficient, that is, a > 0, hence one example is a = 1 as follows:

f(x) = x² - 5x - 24.

It opens downward with a negative leading coefficient, that is, a < 0, hence one example is a = -1 as follows:

f(x) = -x² + 5x + 24.

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