If x = -12, y = -3; find xy?

​

Answer:

x = 2y --------(1)

75x + 250y = 800 ---------(2)

Step-by-step explanation:

Let the number of chicken wings be x

And the number of sliders be y

x = 2y --------(1)

75x + 250y = 800 ---------(2)

The system of equation is x = 2y and 75x + 250y = 800.

x = 2y --------(1)

75x + 250y = 800 ---------(2)

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1) \(m\angle KER=m\angle MEN\) (given)

2) \(\angle 3 \cong \angle 3\) (reflexive property)

3) \(m\angle 3=m\angle 3\) (congruent angles have equal measure)

4) \(m\angle 1=m\angle 3\) (subtraction property of equality)

Answer:

The radical approximations of 7.07, 7.21, and 7.93 to the nearest whole number are:

2.65

2.68

2.82

Step-by-step explanation:

Sure, here's a step-by-step explanation of finding the approximate square root of 7.07, 7.21, and 7.93 to the nearest whole number:

Start by finding an approximate square root by making an educated guess or by using a calculator.

Use the initial guess to determine if the number is closer to the actual square root or to a smaller or larger value.

Refine the estimate by averaging the guess and the number divided by the guess.

Repeat the process of refining the estimate until a satisfactory level of accuracy is reached.

Here's an example for 7.07:

An educated guess for the square root of 7.07 could be 2.7

Dividing 7.07 by 2.7 gives an estimated value of 2.61, which is closer to the actual value.

To get a more accurate estimate, the average of 2.7 and 2.61 (2.655) is taken as the new estimate.

Repeat steps 2 and 3 until the desired level of accuracy is achieved.

After several iterations, the square root of 7.07 is approximately equal to 2.65.

Similarly, you can find the approximate square roots of 7.21 and 7.93.

Answer:

c

Step-by-step explanation:

Answer:

C) $2,975

Step-by-step explanation:

Answer:

.52 x 10^7

Step-by-step explanation:

Hey there!☺

\(Answer:\boxed{5.2\times10^{-3}}\)

\(Explanation:\)

\(0.0052\) in scientific notation would be written like this:

\(5.2\times10^{-3}\)

Hope this helps!☺

To find the estimated project completion time for the given project activities, we need to first calculate the earliest start and earliest finish times and then the latest start and latest finish times.

Using the activity times given, we can calculate the earliest start and earliest finish times for each activity as follows: Activity A: Earliest start time = 0

Earliest finish time = 1

Activity B: Earliest start time = 2

Earliest finish time = 5

Activity C: Earliest start time = 5

Earliest finish time = 11

Activity D: Earliest start time = 11

Earliest finish time = 17

Activity E: Earliest start time = 5

Earliest finish time = 8 Activity F:

Earliest start time = 8

Earliest finish time = 17

Now we can calculate the latest start and latest finish times for each activity using the backward pass.

Latest finish time = 5

Latest start time = 2

Activity A: Latest finish time = 1

Latest start time = 0

Now we can calculate the slack time for each activity as follows:Activity A:

Slack time = 0

Activity B: Slack time = 0

Activity C: Slack time = 0

Activity D: Slack time = 0

Activity E: Slack time = 3

Activity F: Slack time = 0

The critical path for this project is A -> C -> D, since these activities have zero slack time. Therefore, the estimated project completion time is 17 units of time.

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We found that the equation for the inverse function of f(x) = 7x is f^(-1)(x) = x/7. By substituting this equation into f(f^(-1)(x)) and f^(-1)(f(x)), we demonstrated that the equation holds true.

a. To find the equation for the inverse function f^(-1)(x) of f(x) = 7x, we need to interchange the roles of x and y and solve for y.

Let's start with the original function f(x) = 7x:

y = 7x

Now, we interchange x and y:

x = 7y

Next, solve for y:

y = x/7

Therefore, the equation for the inverse function is f^(-1)(x) = x/7.

b. To verify that the equation f^(-1)(x) = x/7 is correct, we need to show that f(f^(-1)(x)) = x and f^(-1)(f(x)) = x.

f(f^(-1)(x)) = x:

Substitute f^(-1)(x) = x/7 into f(x):

f(x/7) = 7(x/7) = x

This confirms that f(f^(-1)(x)) = x.

f^(-1)(f(x)) = x:

Substitute f(x) = 7x into f^(-1)(x):

f^(-1)(7x) = (7x)/7 = x

This also verifies that f^(-1)(f(x)) = x.

In both cases, we have shown that applying the inverse function f^(-1)(x) to f(x) or applying the function f(x) to f^(-1)(x) results in the original input value x. Therefore, the equation for the inverse function f^(-1)(x) = x/7 is correct.

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Answer:

800 laptops.

Step-by-step explanation:

It's basically a 3/2 fraction. 1200/3=400, and there's a 3:2 ratio. So, 400x2 is 800 laptops.

There are 800 laptops if there are 1200 students.

Given,

The ratio of students to laptops is 3:2.

The total number of students = 1200.

We need to find the total number of students.

Let the ratio of students and laptops 3:2 be:

Students = 3X

Laptops = 2X

So we have,

The total number of students = 1200.

So,

3X = 1200

X = 1200 / 3 = 400

We have X = 400 so,

Laptops = 2X = 2 x 400 = 800

The total number of laptops is 800

We can also see that,

Students: laptops

= 1200 : 800

= 12 : 8

= 3 : 2

So it is satisfied.

Thus, there are 800 laptops if there are 1200 students.

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Answer:

\(a^2+3\,a\,b-5\,a\,b-15\,b^2=(a-5\,b)\,(a+3\,b)\)

Step-by-step explanation:

Work via factoring by groups:

!) re arrange the terms as follows:

\(a^2-5ab+3ab-15b^2\)

then extract the common factor for the first two terms (a), and separately the common factors for the last two terms (3 b):

\(a^2-5ab+3ab-15b^2\\a\,(a-5\,b)+3\,b\,(a-5\,b)\)

Now notice that the binomial factor (a-5 b) is in both expressions, so extract it:

\(a\,(a-5\,b)+3\,b\,(a-5\,b)\\(a-5\,b)\,(a+3\,b)\)

which is the final factorization.

Answer:

\( \boxed{\sf (a + 3b)(a - 5b)} \)

Step-by-step explanation:

\( \sf Factor \: the \: following: \\ \sf \implies {a}^{2} + 3ab - 5ab - 15 {b}^{2} \\ \\ \sf Grouping \: like \: terms, \\ \sf {a}^{2} + 3ab - 5ab - 15 {b}^{2} = {a}^{2} + (3ab - 5ab) - 15 {b}^{2} : \\ \sf \implies {a}^{2} + (3ab - 5ab) - 15 {b}^{2} \\ \\ \sf 3ab - 5ab = - 2ab : \\ \sf \implies {a}^{2} - 2ab - 15 {b}^{2} \\ \\ \sf The \: factors \: of \: - 15 \: that \: sum \: to \: - 2 \: are \: 3 \: and \: - 5. \\ \\ \sf So, \\ \sf \implies {a}^{2} + (3 - 5)ab - 15 {b}^{2} \\ \\ \sf \implies {a}^{2} + 3ab - 5ab - 15 {b}^{2} \\ \\ \sf \implies a(a + 3b) - 5b(a + 3b) \\ \\ \sf \implies (a + 3b)(a - 5b)\)

The product of the given expression is (x²- 64)/(x² +121)

Hence,

Option C is correct.

The given expression is,

[(x - 8)/(x + 11)][(x + 8)/(x - 11)]

Now we can write the expression as,

⇒ (x-8)(x+8)/(x+11)(x-11)

Since we know the product formula

(a-b)(a+b) = a² - b²

Therefore,

The expression be,

⇒  (x²- 8²)/(x² +11²)

⇒ (x²- 64)/(x² +121)

Hence the rational expression is,

⇒  [(x - 8)/(x + 11)][(x + 8)/(x - 11)] = (x²- 64)/(x² +121)

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Answer: y = x + 2 OR f(x) = x + 2

Step-by-step explanation:

Calculating slope:

Remember rise over run; when going from one point to another point, in this case from (-3, -1) to (0,2), locate the distance moved in the x and y directions. This scenario moves 3 up and 3 right, meaning a positive slope of one. However, if the line was directed left, your slope would be negative.

Finding y-intercept:

Where does the line intersect the y-axis and have a x-value of 0? This is your y-intercept --> (0,2).

Write Equation:

y = mx +b

y = 1x + 2

y = x + 2 (your final answer)

Answer:

The yarn used by h number of hats and The yarn used by s number of scarf. hence, the system of equations which represents the situation are:

(1) h+8=20

(2) 4xh=1

Step-by-step explanation:

Given:

After 4 minutes of reading, Aaron was on page 14 of his book.

After 8 minutes he was on page 20.

To find:

The equation that models the page number, y in terms of minutes x.

Step-by-step explanation:

Let  y be the page number after x minutes of reading.

After 4 minutes of reading, Aaron was on page 14 of his book. So, the line must be passes through (4,14).

After 8 minutes he was on page 20. So, the line must be passes through (8,20).

The equation of line which passes through two points is

\(y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\)

The required line passes through (4,14) and (8,20), so the equation is

\(y-14=\dfrac{20-14}{8-4}(x-4)\)

\(y-14=\dfrac{6}{4}(x-4)\)

\(y-14=1.5(x-4)\)

\(y-14=1.5x-6\)

Add 14 on both sides.

\(y-14+14=1.5x-6+14\)

\(y=1.5x+8\)

Therefore, the correct option is B.

The given equation (4x² - y² - z² = 1) is classified under Hyperboloid of two sheets.

What is Hyperboloid equation?

When a hyperbola is rotated around one of its axes, an open surface is created that is known as a hyperboloid. The surface's general equation is written as (x²/ a²) + (y² / b²) - (z² / c²) = 1

if the surface's transverse axis is along the x axis, its centre is at the origin, and a, b, and c are its primary semi-axes.

As per question given that,

here is the equation of the quadratic surface is,

4x² - y² - z² = 1

Thus surface is a hyperboloid of two sheets.

The sketch of this quadratic surface is the sketch in the 2nd option which is shown below.

i.e. in the upper right corner.

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Answer:

The average salary is $57,500

Step-by-step explanation:

You would find the total salaries and divide that by 40 because there were 40 people: 18 + 10 +8 + 2 + 2

To find the total salaries"

18(50,000) + 10(60,000) + 8(75000) + 2(90,000) + 2(10000) = 2300000

2300000/40 = 57,500

The given series is divergent.

We can use the limit comparison test to determine the convergence or divergence of the given series:

First, note that for all n ≥ 1, we have: \(\frac{(n^9 + 1) }{ (n^10 + 1)}\) ≤ \(\frac{n^9 }{n^10} = \frac{1}{n}\)

Therefore, we can compare the given series to the harmonic series ∑ 1/n, which is a well-known divergent series. Specifically, we can apply the limit comparison test with the general term \(a_n = \frac{(n^9 + 1)}{(n^{10} + 1)}\) and the corresponding term \(b_n = \frac{1}{n}\):

lim (n → ∞) \(\frac{a_n }{ b_n}\) = lim (n → ∞) \(\frac{\frac{(n^9 + 1)}{(n^10 + 1)} }{\frac{1}{n} }\)

= lim (n → ∞) \(\frac{ n^{10} }{ (n^9 + 1)}\)

= lim (n → ∞) \(\frac{n}{1+\frac{1}{n^{9} } }\)

= ∞

Since the limit is positive and finite, the series ∑ \(\frac{(n^9 + 1) }{ (n^10 + 1) }\) behaves in the same way as the harmonic series, which is divergent. Therefore, the given series is also divergent.

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Answer: D

Step-by-step explanation:

Solve for y: y (greater than or equal to) (7-9x)/5

Slope is negative (-1.8x) so it must be A or D

Choose a test point to plug in. (0,0) works. If plugging in 0 for x and y yields a true inequality, then the area with (0,0) should be shaded. Since the result for plugging in (0,0) is 0 greater than or equal to 1.4, choose the shaded area without (0,0).

The vector z in the component form is z = < 21 , 24 , -27 >

Given data ,

A vector in component form is typically written as an ordered pair or triplet, where each component represents the magnitude of the vector along a specific coordinate axis.

Now , the vector u = < -1 , 3 , 1 >

v = < 4 , -3 , -1 >

w = < 10 , 5 , -10 >

Now , the value of vector z = < 3w - 2v + u >

z = 3w - 2v + u

z = 3w - 2 * < 4 , -3 , -1 > + < -1 , 3 , 1 >

Using scalar multiplication, we get:

z = < 30 , 15 , -30 > - < 8 , -6 , -2 > + < -1 , 3 , 1 >

Adding vectors, we get:

z = < 30 - 8 - 1 , 15 - (-6) + 3 , -30 + 2 + 1 >

z = < 21 , 24 , -27 >

Hence , the vector z in component form is z = < 21 , 24 , -27 >

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Answer:

Step-by-step explanation:

Question 1

System of equations is,

y = -6x -------(1)

y = -4x - 2 ---------(2)

Substitute the value of y from equation (1) to equation (2)

-6x = -4x - 2

-6x + 4x = -2

-2x = -2

x = 1

From equation (1)

y = -6(1)

y = -6

Question (2)

System of equations is,

-y = x --------(1)

3x + 5y = 20 ---------(2)

Substitute the value of x from equation (1) to equation (2)

3(-y) + 5y = 20

-3y + 5y = 20

2y = 20

y = 10

From equation (1)

-y = x

x = -10

Question (3)

System of the equations is,

y = -2x - 7 --------(1)

9x - 10y = 12 ----------(2)

Substitute the value of y from equation (1) to equation (2)

9x - 10(-2x - 7) = 12

9x + 20x + 70 = 12

29x = 12 - 70

29x = -58

x = -2

From equation (1)

y = -2(-2) - 7

y = 4 - 7

y = -3

Range of the value of the game played:To get the range of the value of the game played, we have to find the minimum and maximum possible scores. Minimum score of the game: The minimum score is when both teams play their strongest defense strategy.

For Letran, their strongest defense strategy is the Man-to-man defense and for Mapua, their strongest defense strategy is the Half-court Press defense.Using these defense strategies, Letran can get a score of 45 and Mapua can get a score of 30.Thus, the minimum possible score is 45 + 30 = 75.Maximum score of the game: The maximum score is when both teams play their weakest defense strategy.

For Letran, their weakest defense strategy is the Press defense and for Mapua, their weakest defense strategy is the Man-to-man defense.Using these defense strategies, Letran can get a score of 55 and Mapua can get a score of 40.Thus, the maximum possible score is 55 + 40 = 95.Therefore, the range of the value of the game played is 75 to 95.b) To find the defense strategy in which Letran is weak, we have to see which defense strategy allows Mapua to get the highest score.

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Arthur's section would measure 27.6°

A circle has 360° which means that to find out the degrees of each section, you should divide 360° by the number of sections.

= 360 / number of sections

= 360 / 26

= 13.84°

If Arthur takes up two sections, he will be seating on:

= 13.84 x 2

= 27.6 °

Arthur's section would therefore measure 27.6°.

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Answer:

4

2

+

4

+

2

Step-by-step explanation:

The perimeter are given by the sum of the expressions of the lengths of

the sides which are each equal to 4·x + 6.

Response:

Part A

Part B

Part A

Given parameters;

Perimeter of the rectangular garden = Perimeter of the triangular garden

Therefore;

Perimeter of the rectangular garden = 2 × (x + 2) + 2 × (x + 1) = 4·x + 6

Perimeter of the triangular garden = x + 3 + 2·x + 1 + x + 2 = 4·x + 6

The equation that sets the perimeters equal is therefore;

4·x + 6 = 4·x + 6

The solution of the above equation is therefore;

x = x

Part B

The values of x that make the first part of the equation true are;

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Answer:

$11.02

Step-by-step explanation:

Based on the given mean and standard deviation, we can assume that the distribution of shoe sizes of American women follows a normal distribution curve. The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation from the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.

Therefore, to find the percentage of American women with shoe sizes between 6.54 and 9.58, we need to calculate how many standard deviations away these sizes are from the mean.

First, we calculate the difference between each shoe size and the mean:

6.54 - 8.06 = -1.52

9.58 - 8.06 = 1.52

Next, we divide each difference by the standard deviation:

-1.52 ÷ 1.52 = -1

1.52 ÷ 1.52 = 1

This means that a shoe size of 6.54 is one standard deviation below the mean, and a shoe size of 9.58 is one standard deviation above the mean.

According to the empirical rule, approximately 68% of American women have shoe sizes that fall within one standard deviation from the mean. Therefore, approximately 68% of American women have shoe sizes between 6.54 and 9.58.

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As given by the question , so here the vertical and horizontal asymptotes are at x = -12 and y = 1.5.

On a function graph, a vertical asymptote represents the point at which the function is undefined. Take the formula f(x) = 1/x as an illustration. This function's graph exhibits a vertical asymptote at x = 0 since the function is undefined at this value (division by 0 is undefined).

A function's horizontal asymptote is a horizontal line on the function graph that the function approaches as the input (x-value) increases or decreases dramatically. Consider the function f(x) = x2 as an illustration. Because the y-values of the function do not converge to a fixed value as x grows very big, the graph of this function lacks a horizontal asymptote.

We must identify the values of x at which the function is undefined in order to determine the vertical asymptotes of the function 3x/(2x+24).So, to find the vertical asymptotes of the function, we need to solve the equation 2x + 24 = 0 for x. so x = -12.

Similarly, To find the horizontal asymptote in case of equal degrees of numerator and denominator i.e 1 in this case, we need to take the ratio of the first coefficients of numerator and denominator respectively which is 3/2 = 1.5.

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Answer:

Step-by-step explanation:

7(c-13)

the product of 7, and, c-13

Answer: c7-7 13

13 is smaller and is right next to the 7

Step-by-step explanation:

7(c-13)

c7-7 13

Using the distributive property 4 (3 + 4x - 2y) is equal to (12 + 16x - 8y).

The distributive property of multiplication is one of the mathematical properties.

The distributive property states that multiplying a factor by the sum of two or more numbers or addends will yield the same result as multiplying each number separately by the same factor and adding the products together.

The implication of the distributive property is that 4 (3 + 4x - 2y) is of equal value as (12 + 16x - 8y).

4 (3 + 4x - 2y)

= (3 x 4) + (4x x 4) - (2y x 4)

= (12 + 16x - 8y)

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