6) 9x - 7y = -4
18x - 14 y = 10
A) (8, -1)
C) (-8,-8)
B) (-8,-1)
D) No solution

Answer:

<

Step-by-step explanation:

If they were positive it would be square root of 50 but its a larger negative njmber

Answer:

2+

Step-by-step explanation:

Answer:

we can compare 4 x 3 and 2 x 6, equal to 12. So, we can see that both products are similar and neither is greater.

Step-by-step explanation:

We can use the commutative property of multiplication to see that 3 x 4 is the same as 4 x 3 and 6 x 2 is the same as 2 x 6. When multiplying two numbers, the order of the numbers does not affect the product. Therefore, we can compare 4 x 3 and 2 x 6, equal to 12. So, we can see that both products are similar and neither is greater.

NEED MORE EXPLANATION?

The commutative property of multiplication states that when multiplying two numbers, the order of the numbers does not affect the product. This means that 3 x 4 is the same as 4 x 3, and 6 x 2 is the same as 2 x 6. We can use this property to compare 4 x 3 and 2 x 6, equal to 12. Therefore, we can see that both products are identical and neither is greater.

Answer:

37

Step-by-step explanation:

Using balanced billing, the monthly payment is $278

Using balanced billing to determine their monthly payment, we simply need to divide their total annual payment by the total number of months in a year. This will result to dividing the entire annual bill by 12 to determine the monthly payment.

Given that the Ross family spent $3,336 for electricity last year, we can calculate their monthly payment as follows:

Monthly payment = Total cost / Number of months

Monthly payment = $3,336 / 12

Monthly payment  = $278

Therefore, the Ross family's monthly payment for balanced billing will be approximately $278.

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Answer:

Step-by-step explanation:

from the figure and the measurements it is a square, the diagonals are perpendicular and form 4 angles of 90°, so 90° is your answer.

Answer:

15

Step-by-step explanation:

Answer: The boat is approximately 357.4 feet from the base of the cliff.

Step-by-step explanation:

Let x be the horizontal distance from the base of the cliff to the boat. Using the tangent function, we can write:

tan(38) = 275 / x

Solving for x, we have:

x = 275 / tan(38)

Using a calculator, we get:

x ≈ 357.4 feet

Therefore, the boat is approximately 357.4 feet from the base of the cliff.

Answer:

352m

Step-by-step explanation:

h = 275m

a = b (alternative angles)

.: b = 38°

Let the base from the boat to the cliff be d

Tan 38° = opposite ÷ adjacent

Tan 38° ° = 275 ÷d

d = 275 ÷ Tan 38 °

d = 352m

.: The boat is 352m away from the foot of the cliff

The number of pork sliders sold is given as follows:

24 pork sliders.

The number of pork sliders sold is obtained applying the proportions in the context of the problem.

The total number of pork sliders is given as follows:

120 pork sliders.

The percentage of pork sliders sold is given as follows:

20%. (proportion of 0.2).

Hence the amount sold is given as follows:

0.2 x 120 = 24 pork sliders.

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9514 1404 393

Answer:

  19. wrong multiplier was used, and used incorrectly; x = -324

  20. wrong multiplier was used, and used incorrectly; y = 5

Step-by-step explanation:

In each case, the equation was multiplied by the coefficient of the variable, instead of divided. In each case, the square of the coefficient was evaluated incorrectly (so the error wasn't noticed).

__

19) As described above.

  (-36)(9) = (x/9)(9)

  -324 = x

__

20) In addition to the errors described above, the variable was changed from y to x.

  15/3 = (3y)/3

  5 = y

Commutativity justifies the statement, of If n is a multiple of 8, then n is even. However, n is not even. Therefore, n is not a multiple of 8.

Commutativity is used in Maths equations and describes sums that can be moved around and will still give the same answer.

'Commutative' comes from the word 'commute' which means to move and travel around, so equations that are commutative have numbers that can be moved within the equation.

commutative law, in mathematics, is either of two laws relating to number operations of addition and multiplication that are stated symbolically as a + b = b + a and ab = ba.

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The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.

Step 1: Set up hypotheses

H₀: The outcomes of the die are equally likely.

H₁: The outcomes of the die are not equally likely.

Step 2: Select the significance level

The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.

Step 3: Compute the test statistic

We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.

Expected frequencies (fair die):

1: 200/6 = 33.33

2: 200/6 = 33.33

3: 200/6 = 33.33

4: 200/6 = 33.33

5: 200/6 = 33.33

6: 200/6 = 33.33

Applying the chi-square formula, we get the test statistic:

χ² = ∑((observed - expected)² / expected)

Calculating this value, we get χ² ≈ 13.97.

Step 4: Determine the critical value

Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.

Step 5: Make a decision

The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.

The loaded die appears to behave differently from a fair die.

In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

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Answer:

Step-by-step explanation:

The perimeter of the rectangle below is 102 units. Find the length of side VY.

Write your answer without variables.

102 : 2 = 51 (semiperimeter)

3x + 4x + 2 = 51

7x = 49

x = 49 : 7

x = 7

VY = 3x

VY = 3 x 7

VY = 21

------------------------

check

find the other side

4x + 2 =

28 + 2 = 30

30 + 30 + 21 + 21 = 102

the answer is good

Answer:

f(x) on x = 4

h(x) on x = -2

Step-by-step explanation:

for h(x) the axis of symmetry is x = -2 based on the graph

for f(x) = -2(x-4)² + 2 we must find for x intercept so take f(x) = 0

0 = -2(x-4)² + 2

-2 = -2(x-4)²

-2/-2 = (x-4)²

1 = (x-4)²

x-4 = √1

x-4 = 1 and x-4 = -1

so

x - 4 = 1

x = 5

x - 4 = -1

x = 3

so x intercept occured in x = 3 and x = 5

so the symmetry axis is in the middle x =4

(actually there's an easiest way, you can find the x axis from the form of y = a(x+b)² + c. The x-axis must be -b)

The axis of symmetry for each function is f(x) on x = 4, and h(x) on x = -2, after applying the transformation.

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.

From the graph:

For f(x) = -2(x-4)² + 2 we must find for x-intercept so take f(x) = 0

For h(x) the axis of symmetry is x = -2 based on the graph

0 = -2(x-4)² + 2

After solving:

x = 5

x - 4 = -1

x = 3

Thus, the axis of symmetry for each function is f(x) on x = 4, and h(x) on x = -2, after applying the transformation.

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Answer:

6

Step-by-step explanation:

Since she gave herself 3 pieces of gum, she gave 12 pieces to her friends. She gave 2 pieces to each friends. 12 pieces of gum divided by the 2 pieces given to each friend is 6

The company's advanced degree holders make up 18% of the workforce.

A percentage, which is denoted by the number 100, is a proportion, fraction, or piece of a whole. The Roman phrase per centum, which meaning "by the 100" or "per one hundred," is where the term "percent" originates. A numerical value and the percentage symbol (%) can be used to express percentages.

Part A:

The following expression sums up the amount of company employees with advanced degrees:

0.40c(0.15) + 0.60c(0.20)

Explanation: First, we multiply the overall amount of workers (c) by the proportions of male and female employees, which are, respectively, 40% and 60%. The number of male workers (0.40c) is then multiplied by the percentage of men who have advanced degrees (15%), and the number for female employees (0.60c) is multiplied by the percentage of women who have advanced degrees (20%). In order to calculate the overall number of workers with advanced degrees, we must add these two numbers.

If we condense this phrase, we get:

0.06c + 0.12c = 0.18c

Part B:

The number of staff members with advanced degrees must be divided by the total amount of employees, and the result must be multiplied by 100% to determine the percentage of the business that holds advanced degrees:

(0.18c/c) × 100% = 18%

Therefore, 18% of the company has advanced degrees.

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Answer:

The approximate length of the missing side is of 5.57 cm.

Step-by-step explanation:

Pythagorean Theorem:

In a right triangle with sides a and b and hypotenuse c, the Pythagorean theorem states that:

\(a^2 + b^2 = c^2\)

In this question:

\(a = 15, c = 16\)

We want to find b. Then

\(a^2 + b^2 = c^2\)

\(15^2 + b^2 = 16^2\)

\(b^2 = 256 - 225\)

\(b^2 = 31\)

\(b = \sqrt{31}\)

\(b = 5.57\)

The approximate length of the missing side is of 5.57 cm.

Answer:

b. -3

Step-by-step explanation:

30 - 3 = 27

27 - 3 = 24

24 - 3 = 21....

Answer:

you did it right D is right answer

Answer:

-1/2

Step-by-step explanation:

We know

The dilation of K(-2,4) equals K'(1,-2)

To get from -2 to 1, we time -1/2

To get from 4 to -2, we time -1/2

So, the scale factor used for the dilation is -1/2

Answer:

  C.  As x → –∞, y → +∞, and as x → +∞, y → +∞

Step-by-step explanation:

The leading coefficient of this even-degree function is positive, so y goes to +∞ when the magnitude of x gets large.

_____

When the function is even degree, its value for large magnitude x heads toward the infinity with the same sign as the leading coefficient.

When the function is odd degree, its value for large magnitude x will head toward the infinity with the sign that matches the product of the sign of x and the sign of the leading coefficient.

Answer:

1)  The functions are not inverses.

\(\textsf{2)} \quad g^{-1}(n)=&\dfrac{3}{8}n-\dfrac{7}{8}\)

\(\textsf{3)} \quad g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\)

Step-by-step explanation:

The inverse composition rule states that if two functions are inverses of each other, then their compositions result in the identity function.

Given functions:

\(g(x) = 4 + \dfrac{7}{2}x \qquad \qquad f(x) = 5 - \dfrac{4}{5}x\)

Find g(f(x)) and f(g(x)):

\(\begin{aligned} g(f(x))&=4+\dfrac{7}{2}f(x)\\\\&=4+\dfrac{7}{2}\left(5 - \dfrac{4}{5}x\right)\\\\&=4+\dfrac{35}{2}-\dfrac{14}{5}x\\\\&=\dfrac{43}{2}-\dfrac{14}{5}x\\\\\end{aligned}\)                 \(\begin{aligned} f(g(x))&=5 - \dfrac{4}{5}g(x)\\\\&=5 - \dfrac{4}{5}\left(4 + \dfrac{7}{2}x \right)\\\\&=5-\dfrac{16}{5}-\dfrac{14}{5}x\\\\&=\dfrac{9}{5}-\dfrac{14}{5}x\end{aligned}\)

As g(f(x)) or f(g(x)) is not equal to x, then f and g cannot be inverses.

\(\hrulefill\)

To find the inverse of a function, swap the dependent and independent variables, and solve for the new dependent variable.

Calculate the inverse of g(n):

\(\begin{aligned}y &= \dfrac{8}{3}n + \dfrac{7}{3}\\\\n &= \dfrac{8}{3}y + \dfrac{7}{3}\\\\3n &= 8y + 7\\\\3n-7 &= 8y\\\\y&=\dfrac{3}{8}n-\dfrac{7}{8}\\\\g^{-1}(n)&=\dfrac{3}{8}n-\dfrac{7}{8}\end{aligned}\)

Calculate the inverse of g(x):

\(\begin{aligned}y &= 1-2x^3\\\\x &= 1-2y^3\\\\x -1&=-2y^3\\\\2y^3&=1-x\\\\y^3&=\dfrac{1}{2}-\dfrac{1}{2}x\\\\y&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\\end{aligned}\)

Answer:

1.

If the composition of two functions is the identity function, then the two functions are inverses. In other words, if f(g(x)) = x and g(f(x)) = x, then f and g are inverses.

For\(\bold{g(x) = 4 + \frac{7}{2}x\: and \:f(x) = 5 -\frac{4}{5}x}\), we have:

\(f(g(x)) = 5 - \frac{4}{5}(4 + \frac{7}{2}x)\\ =5 - \frac{4}{5}(\frac{8+7x}{2})\\=5 - \frac{2}{5}(8+7x)\\=\frac{25-16-14x}{5}\\=\frac{9-14x}{5}\)

\(g(f(x)) = 4 + (\frac{7}{5})(5 - \frac{4}{5}x) \\=4 + (\frac{7}{5})(\frac{25-4x}{5})\\=4+ \frac{175-28x}{25}\\=\frac{100+175-28x}{25}\\=\frac{175-28x}{25}\)

As you can see, f(g(x)) does not equal x, and g(f(x)) does not equal x. Therefore, g(x) and f(x) are not inverses.

Sure, here are the inverses of the functions you provided:

2. g(n) = (8/3)n + 7/3

we can swap the roles of x and y and solve for y to find the inverse of g(n). In other words, we can write the equation as y = (8/3)n + 7/3 and solve for n.

y = (8/3)n + 7/3

n =3/8*( y-7/3)

Therefore, the inverse of g(n) is:

\(g^{-1}(n) = \frac{3}{8}(n - \frac{7}{3})=\frac{3}{8}*\frac{3n-7}{3}=\boxed{\frac{3n-7}{8}}\)

3. g(x) = 1 - 2x^3

We can use the method of substitution to find the inverse of g(x). We can substitute y for g(x) and solve for x.

\(y = 1 - 2x^3\\2x^3 = 1 - y\\x = \sqrt[3]{\frac{1 - y}{2}}\)

Therefore, the inverse of g(x) is:

\(g^{-1}(x) =\boxed{ \sqrt[3]{\frac{1 - x}{2}}}\)

Answer:

3x2+15x=18

Step 1: Subtract 18 from both sides.

3x2+15x−18=18−18

3x2+15x−18=0

Step 2: Factor left side of equation.

3(x−1)(x+6)=0

Step 3: Set factors equal to 0.

x−1=0 or x+6=0

x=1 or x=−6

Answer:

A

I worked them out myself so if their wrong uh please don't get mad I tried my best.

Step-by-step explanation:

3x (2) + 15x = 18                               3x (2) + 15x = 18

6x + 15x = 18                                     6x + 15x = 18  

-6x + -6x = 18                                            -18     -18

--------------------------                             ------------------------

0 + 9x = 18                                            6x + -3 = 0

   ------  -------                                         -3 +  -3

      18  18                                           --------------------

          x = 2                                              -3 + 0

                                                                    X = -3

The linear relationship illustrated in the provided table can be effectively described by the equation Y = -4x + 2. Option D.

To determine the equation that represents the given table with the values of x and y, we can observe the pattern and find the equation of the line that fits these points.

Given the table:

X: 2 0 4

Y: -4 3 1

We can plot these points on a graph and see that they form a straight line.

Plotting the points (2, -4), (0, 3), and (4, 1), we can see that they lie on a line that has a negative slope.

Based on the given options, we can now evaluate each equation to see which one represents the line:

Y = 1/2x + 5

When we substitute the x-values from the table into this equation, we get the following corresponding y-values: -3, 5, and 6. These values do not match the given table, so this equation does not represent the table.

Y = -1/2x + 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: 4, 3, and 2. These values also do not match the given table, so this equation does not represent the table.

Y = 2x - 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -4, -3, and 5. These values do not match the given table, so this equation does not represent the table.

Y = -4x + 2

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -6, 2, and -14. Interestingly, these values match the y-values in the given table. Therefore, the equation Y = -4x + 2 represents the table.

In conclusion, the equation Y = -4x + 2 represents the linear relationship described by the given table. So Option D is correct.

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Answer:

a^*=y

3332

Step-by-step explanation:

$2200/month

The graphs have been correctly dragged to the table to show the image of the triangle after it is reflected over the x-axis, the y-axis, and the line y = x.

By applying a reflection over the x-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (x, -y)

(1, -3)             →      (1, -(-3)) = (1, 3)

(3, -2)             →      (3, -(-2)) = (3, 2)

(4, -5)             →      (4, -(-5)) = (4, 5)

By applying a reflection over the y-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (-x, y)

(1, -3)             →        (-1, -3)

(3, -2)             →      (-3, -2)

(4, -5)             →      (-4, -5)

By applying a reflection over the line y = x to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (y, x)

(1, -3)             →        (-3, 1)

(3, -2)             →      (-2, 3)

(4, -5)             →      (-5, 4)

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Answer:

1

Step-by-step explanation:

One to the power of anything is one

Answer:

1^2+2^3+3^4

=1+8+81=90

Step-by-step explanation:

Answer:

Step-by-step explanation:

The nth term of the sequence is

A(n) = 5n + 7

To find the (n+1)st term substitute n+1 into the general equation

That's

For (n + 1)st term

A(n+1) = 5(n+ 1) + 7

A(n+1) = 5n + 5 + 7

Hope this helps you

\( n^{\text{th}} \text{ term is } 5n+7 \)

forget n for a while.

let's call it t .

The \( t^{\text{th}} \text{ term is } 5t+7 \)

agreed? I don't think there should be a problem.

you're asked what's the \((t+1)^{\text{th}}\) term.

let's call it u . so just like we did before,

\( u^{\text{th}} \text{ term is } 5u+7 \)

but we know, \(u=t+1\)

So, \(5u+7=5(t+1)+7=5t+12\)

does that answer your question?