how is multiplying and dividing fractions the same as adding and subtracting fractions.

The solutions to the quadratic equation x² = -7x - 8 are x equals  \(\frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\).

Given the quadratic equation in the question:

x² = -7x - 8

To find the solutions of the quadratic equation x² = -7x - 8, we can rearrange it into standard quadratic form, which is ax² + bx + c = 0, and apply the quadratic formula.

x² = -7x - 8

x² + 7x + 8 = 0

a = 1, b = 7 and c = 8

Plug these into the quadratic formula: ±

\(x = \frac{-b \± \sqrt{b^2 -4(ac)}}{2a} \\\\x = \frac{-7 \± \sqrt{7^2 -4(1*8)}}{2*1} \\\\x = \frac{-7 \± \sqrt{49 -4(8)}}{2} \\\\x = \frac{-7 \± \sqrt{49 - 32}}{2} \\\\x = \frac{-7 \± \sqrt{17}}{2} \\\\x = \frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\)

Therefore, the values of x are \(\frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\).

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The sum of interior angles of triangle sum up to 180°

Hence,

∠O + 70° + 65° = 180°

∠O = 180° - 65° - 70°

∠O = 45°

∴ The angle ∠O is 45 degrees.

Use cosine rule: a² = b² + c² - 2bc cos(A)

Hence,

TO² = 3² + 3² - 2(3)(3) cos(65)

TO² = 10.39287129

To = √10.4

TO = 3.22 ≈ 3 meters (rounded to nearest whole number)

∴ The length of TO is 3 meters.

Answer:

x = \(942\frac{2}{9}\)

Step-by-step explanation:

0.9 ( x - 20) = 830

0.9x - 18 = 830

0.9x = 848

9x = 8480

x = \(942\frac{2}{9}\)

Answer:

1.2 books per month

12/10

Step-by-step explanation:

Answer: £450

Step-by-step explanation:

If they bought 2 tickets, they could get an extra ticket for free. As there are three of them, they would buy 2 tickets, get one for free and then buy another ticket to make it four.

In that case they would have only paid for 3 tickets.

The total cost of 3 tickets is:

= 600 * 3

= £1,800

The 4 of them would therefore have to pay:

= 1,800 / 4

= £450

Answer:

the answer is C.815+(-97)

Step-by-step explanation:

Longwei should first recognize that implementing goals, policies, and structure is only one aspect of effective leadership. A leader's ability to motivate and inspire their employees is just as important. Therefore, Longwei should use the principles of organizational behavior (OB) to better understand his employees and their motivations.

Additionally, Longwei should take a personality assessment to become more self-aware of his own leadership style and how it may be impacting the employees. He should examine his perceptions and biases to ensure that he is making fair and objective judgments and decisions. This may involve seeking feedback from other leaders or mentors, participating in leadership development programs, or engaging in self-reflection and mindfulness practices.

By taking these steps, Longwei can better understand and address the unmotivated employees in his company. He can then develop strategies to engage and inspire them, such as offering incentives, providing opportunities for professional development, or creating a more positive and inclusive work environment. Ultimately, Longwei's success as a leader will depend not only on his ability to set and implement goals but also on his ability to motivate and engage his employees.

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Answer:

I think A

Step-by-step explanation:

I am not quite sure what this is asking, but based off of what I can tell it should be A.

Hope this helps :)

The rate of change of the length of the man's shadow on the building when he is 10 m from the building is approximately -0.278 m/s

The rate of change of the length of the man's shadow on the building when he is 10 m from the building can be found by first setting up a proportion using similar triangles.

Here are the steps:

Set up a proportion using similar triangles:
(height of man) / (distance from light to man) = (length of shadow) / (distance from light to building)

Plug in the given values:

(1.85 m) / (10 m) = (length of shadow) / (30 m)

Solve for the length of shadow:
Length of shadow = 1.85 m x 30 m / 10 m = 5.55 m

Differentiate the proportion equation with respect to time (t) to find the rate of change of the shadow length (dS/dt):
d(height of man) / d(time) / d(distance from light to man) / d(time)

= d(length of shadow) / d(time) / d(distance from light to building) / d(time)

Since the height of the man and the distance from the light to the building are constants, their derivatives with respect to time are 0.

The rate of change of the distance from the light to the man is -1.5 m/s (negative because the man is walking toward the light).

Plug in the values:
0 / (-1.5 m/s) = (dS/dt) / 0

Solve for the rate of change of the shadow length (dS/dt):
dS/dt = -1.5 m/s x (5.55 m / 30 m) = -0.2775 m/s

So, the rate of change of the length of the man's shadow on the building when he is 10 m from the building is approximately -0.278 m/s (rounded to three significant digits after the decimal point).

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6 integers that satisfy the given condition are 10,11,12,13,14,15.

Inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size

we have the number X

Of which the square root is greater than 3 and less than 4

so,

\(3 < \sqrt{X} < 4\)

on squaring both sides

\(3^2 < (\sqrt{X})^{2} < 4^2\)

\(9 < X < 16\)

so the integer that satisfies the condition is 10,11,12,13,14,15.

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Answer:

6

Step-by-step explanation:

Because 4 > √x > 3, we know that 16 > x > 9. Thus, the integers from 10 to 15 inclusive satisfy this inequality, which means 6 integers satisfy the condition in the problem.

The cost of one apple is $0.70.

Let's assume that the cost of one apple is "a" dollars and the cost of one banana is "b" dollars. We can create two equations based on the information given:

4a + 9b = 12.70 ...(1)

8a + 11b = 17.70 ...(2)

To solve for "a", we can use elimination method by multiplying equation (1) by 8 and equation (2) by -4, so that the coefficients of "a" in both equations will be equal and opposite:

32a + 72b = 101.60

-32a - 44b = -70.80

Adding these two equations, we get:

28b = 30.80

Simplifying and solving for "b", we get:

b = 1.10

Now, we can substitute the value of "b" in equation (1) and solve for "a":

4a + 9(1.10) = 12.70

4a + 9.90 = 12.70

4a = 2.80

a = 0.70

Therefore, the cost of one apple is $0.70.

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The length of the line segment with points (-5, 5) (3, -1) is 10 units

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points  (-5, 5) and (3, -1) is calculated as follows

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

d =√{(-5 - 3)² + (5 - -1)²}

d =√{64 + 36}

d = √100

d = 10 units

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One strategy that may help Emilio write more fluently is practicing speed writing or shorthand techniques.

Practicing speed writing or shorthand techniques can help Emilio increase his writing speed without sacrificing legibility. Speed writing involves using abbreviations, symbols, and shortcuts to represent words or phrases, allowing for faster transcription of thoughts onto paper.

Shorthand systems, such as Gregg shorthand or Pitman shorthand, provide structured methods for condensing words and phrases into simplified symbols.

By learning and practicing speed writing or shorthand techniques, Emilio can improve his writing efficiency and reduce the time it takes to write a few sentences. This strategy allows him to maintain neatness while increasing his writing speed, enabling him to express his thoughts more fluently.

With regular practice and familiarity, Emilio will become more comfortable with the shorthand system and experience a significant improvement in his writing speed and fluency.

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a. The amplitude of the function y = c + asin[b(x-d)] is |a| = 4.6. b. The period of the function is 2π/|b| ≈ 3.14/|b|. c. The phase shift of the function is d. d. The vertical translation (vertical shift) of the function is c.

a. The amplitude of the function y = c + asin[b(x-d)] is the absolute value of the coefficient 'a' in front of the sine function. In this case, the amplitude is |a| = 4.6.

b. The period of the function is determined by the coefficient 'b' inside the sine function. The period is given by 2π/|b|, which represents the distance between two consecutive cycles of the graph. In this case, the period is approximately 3.14/|b|.

c. The phase shift of the function is determined by the value of 'd' inside the sine function. It represents the horizontal shift of the graph. If 'd' is positive, the graph is shifted to the right, and if 'd' is negative, the graph is shifted to the left.

d. The vertical translation or vertical shift of the function is represented by the constant 'c'. It determines the amount by which the graph is shifted vertically. If 'c' is positive, the graph is shifted upward, and if 'c' is negative, the graph is shifted downward.

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Answer:

I think 83 ÷ 10 and it said that it incorrect

Step-by-step explanation:

Answer:

z=17−6x−2y

y=19−5x+6z

x=5−3y/2−3z/2

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

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

The Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

To solve the ODE using the Euler method, we divide the interval into smaller steps and approximate the derivative with a difference quotient. Given that the step size is h = 0.5, we will perform three steps to obtain the numerical solution.

we calculate the initial condition: y(0) = -2.

1. we evaluate the derivative at t = 0 and y = -2:

y' = 3(0) - 10(-2)² = -40

Next, we update the values using the Euler method:

t₁ = 0 + 0.5 = 0.5

y₁ = -2 + (-40) * 0.5 = -22

2. y' = 3(0.5) - 10(-22)² = -14,860

Updating the values:

t₂ = 0.5 + 0.5 = 1

y₂ = -22 + (-14,860) * 0.5 = -7492

3. y' = 3(1) - 10(-7492)² ≈ -2.2395 x 10^9

Updating the values:

t₃ = 1 + 0.5 = 1.5

y₃ = -7492 + (-2.2395 x 10^9) * 0.5 = -1.1198 x 10^9

Therefore, after performing three steps of the Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

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Answer:

11250 cm^3

Step-by-step explanation:

45cm × 25cm × 10cm =11250cm

Answer:

A. 2x²-13x+15 / (x-3)(x+3)(x-4)

Step-by-step explanation:

Step-by-step explanation:

=   2x / (( x+3)(x-3))     -   5 / ((x -4)(x+3))        

                multiply L term by   (x-4)/ (x-4)    and the R term by (x-3)/(x-3)

                      to get a common denominator

[ 2x (x-4)       -    5(x-3)  ] / ((x-3)(x+3)(x-4)        then simplify a bit to get

(2x^2 -13x +15 )  ((x-3)(x+3)(x-4)        Done.

Out of a whole population, a sample is a small part which is considered for any survey.  

The population in this case would be all the one-bedroom apartments available for rent near the college.

The sample would be the listings that Greg is looking at in the local newspaper and on the internet site.

Sample: listings in a local newspaper and on an Internet site              

Population: all available apartments near the college          

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Answer:

6 and 8 are corresponding.

2 and 4 is corresponding.

Step-by-step explanation:

and 2 and 7 is alternate.

3 and 6 are alternate.

The figure W has one Rotational symmetries. This can be observed by rotating the figure by 0 or 180 degrees and noting that the shape remains unchanged. so the correct option is (b).

The letter W has one vertical line of symmetry that divides it into two identical halves. However, it does not have any rotational symmetry of order 2 or higher because there is no way to rotate the letter by a certain angle and have it look the same as before the rotation. Therefore, the answer is (b) 1, as W has only one line of symmetry and no rotational symmetry of order 2 or higher. In other words, if you rotate the letter by any angle other than 0 or 180 degrees, it will look different than before the rotation.

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______The given question is incomplete, the complete question is given below:

How many rotational symmetries does W alphabet have?

a. 0

b. 1

c. 2

d. 3

Answer:

Step-by-step explanation:

The graph is widest when the coefficient of \(x^2\) has the smallest absolute value.

The graph is narrowest when the coefficient of \(x^2\) has the largest absolute value.

By comparing the graphs of the functions, function 1: y = 0.25x2 is the widest and function 4: y = -16x2 is the narrowest.

The graph is widest when the coefficient of \(x^{2}\) has the smallest absolute value.

The graph is narrowest when the coefficient of \(x^{2}\) has the largest absolute value.

The answer lies in the coefficient for the \(x^{2}\) term. When the absolute value of the coefficient gets bigger, the graph gets narrower (positive and negative simply show the direction the parabola is pointing, with positive opening up and negative opening down).

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The income plainness of demand for eatery reflections is Income plainness = 200/ 20 = 10

Chance is a way of expressing a volume as a bit of 100. It's frequently denoted using the percent symbol(), which represents" per hundred". For illustration, 25 is original to25/100 or0.25 as a numeric.

By question-

The income plainness of demand measures the responsiveness of the volume demanded of a good or service to a change in income, all other effects being equal .However, it means that the good is a normal good, and the volume demanded increases as income increases, If the income plainness is positive. However, it means that the good is an inferior good, and the volume demanded diminishments as income increases, If the income plainness is negative.

In this case, John's pay increased by 20 percent, and the average number of eatery reflections he consumed increased from one a week to three a week. We can calculate the income plainness of demand for eatery reflections as follows

Income plainness = chance change in volume demanded/ chance change in income

The chance change in volume demanded is

( 3 reflections per week- 1 mess per week)/ 1 mess per week) x 100 = 200

The chance change in income is 20

thus, the income plainness of demand for eatery reflections is

Income plainness = 200/ 20 = 10

Since the income plainness is positive and lesser than 1, we can conclude that eatery reflections are a luxury good for John. Option( b) is the correct answer.

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The answer to (c) is ||4v — 4w|| ≈ 27.07.

Given that || v || = 3, || w || = 3, and the angle between v and w is 2.8 radians. We can calculate the following:(a) v. w = ?The dot product of two vectors is defined as the product of their magnitudes and the cosine of the angle between them.

Therefore, v.w = ||v|| ||w|| cos θWhere, θ is the angle between v and w. So, v.w = 3×3 cos(2.8) ≈ -3.20 Therefore, v.w ≈ -3.20.(b) ||1v + 4w|| = ?

The magnitude of the vector ||1v + 4w|| can be calculated as follows:||1v + 4w|| = √((1v + 4w).(1v + 4w))= √(1v.1v + 8v.w + 16w.w) Substitute the value of v.w we obtained above and calculate||1v + 4w|| = √(9 + 8×(-3.20) + 16×9)≈ 9.97

Therefore, ||1v + 4w|| ≈ 9.97.(c) ||4v — 4w|| =Similarly, the magnitude of the vector ||4v — 4w|| can be calculated as follows:

||4v — 4w|| = √((4v — 4w).(4v — 4w))= √(16v.v — 32v.w + 16w.w) Substitute the values of v.w and ||v|| we obtained above and calculate||4v — 4w|| = √(16×9 — 32×(-3.20) + 16×9)≈ 27.07 Therefore, ||4v — 4w|| ≈ 27.07.

The answer to (a) is v.w ≈ -3.20. The answer to (b) is ||1v + 4w|| ≈ 9.97. The answer to (c) is ||4v — 4w|| ≈ 27.07.

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Answer:

76.5%

Step-by-step explanation:

He lost 10% of them on way to the top of the hill

10% of 10,000 men

= 0.1 * 10,000

= 1,000 men

Remaining men = 10,000 - 1,000

= 9,000 men

15% of the rest as he marched them back down the hill.

15% of 9,000 men

= 0.15 × 9000

= 1,350 men

Total men remaining = 9000 - 1,350

= 7,650 men

% remaining =

x% of 10000 men = 7,650

x/100 * 10,000 = 7,650

Cross product

10,000x =7,650 * 100

10,000x = 765,000

x = 765,000/10,000

= 76.5%

x = 76.5%

Answer:

your answer should be 3

The equation of the red graph is G(x) = 4 - x⁴

In mathematics, the parent function is the simplest function in a family of functions from which other functions are derived by suitable transformations.

For example,

the parent function in f(t) = t² - 5 is P(t) = t²

From the given graph, the parent function is x⁴ from which -x⁴ is derived and this gives the shape of the graph.

The function F(x) = 3 - x⁴ shifts the graph of -x⁴ by 3 units upward.

The function G(x) = 4 - x⁴ shifts the graph an additional 1 unit upward from F(x) = 3 - x⁴ as shown in the graph

Hence the graph in red is represented by the equation

• G(x) = 4 - x⁴

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