Three fourths of X added to twice of X is more than eleven

Answers

Answer 1
3/4x + 2x > 11

Is the answer

Related Questions

What is the mode of 1,1,2,2,3,3,4,4​

Answers

Answer: There is no mode.

Step-by-step explanation:

The mode is the number that appears the most in a given set of data. Each number in this data set is repeated twice. Therefore, there is no mode.

I hope this helped!! :)

Answer:

1, 2, 3, 4

or none

Step-by-step explanation:

Mode is the value or values in the data set that occurs most frequently.

example:

For the data set 1, 1, 2, 5, 6, 6, 9 the mode is 1 and also 6.

in 1, 1, 2, 2, 3, 3, 4, 4 all numbers occur the same amount of times, therefore they all (or none) are the mode

hope this helps:)

What is the value of h?

Answers

Answer:

h=-2

Step-by-step explanation:

the graph was shifted 2 units left

Select the correct answer. Which set of vertices forms a parallelogram? OA A2,4), B(3, 3), C6, 4), D(5, 6) OB. A(-1, 1), B(2, 2), C(5, 1), D(4, 1) OC. A(-5, -2), B(-3, 3), C3, 5), D(1, 0) OD. A(-1, 2), B(1, 3), C5, 3), D(1, 1).​

Answers

Answer:

(6,4)

Step-by-step explanation:

^^^

In a random sample of 250 students, 150 were in favor of longer hours at the school library. At 98% level of confidence, what is the margin of error?

Select one:

0.051


0.080


0.065


0.072


0.078


0.061

Answers

0.072 is the margin of error.

What is standard error?

The standard error (SE) of a statistic is the standard deviation of its sampling distribution or an estimate of that standard deviation.

According to the question,

In a random sample of 250 students,

p= 0.98 (or 98%) were in favor of longer hours at the school library.

The standard error of p(the sample proportion) is (approximately)

The standard error of p =   [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

p = 0.98

1 - p = 1 - 0.98 = 0.02

Here,

n = 250

The standard error of p =   [tex]\sqrt{ \frac{0.98 (0.02) }{250}[/tex]

The standard error of p ≈   0.072

Therefore,

The margin of error is 0.072.

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If P(n) and Q(n) are polynomials of degree j and k, respectively, then the series
Infinite
Σ P(n)/Q(n)
n=1
converges if j < k − 1 and diverges if j ≥ k – 1.
Use the polynomial test given above to determine whether the series converges or diverges.
Infinite
Σ 1/(n)^8 +7
n=1
O converges
Odiverges

Answers

Answer:

converges

Step-by-step explanation:

well the two polynomials in the series are 1 and n^8 (I'm assuming the +7 is not in the decimal but it seems to not matter). The degree of the polynomial 1 is 0 which can be represented by 1x^0. The second polynomial in the denominator has a degree of 8. So j = 0  and k = 8. Since 0 < (8-1)

0 < 7 the series converges

If “a” is a non zero constant, what is the maximum number of turns for the graph of
y = x³ + ax² - 7x+10

Answers

The maximum number of turns for the graph given by the function is; 2.

What is the maximum number of turns for the graph?

It follows from the task content that the graph given is that of a cubic function. On this note, it follows that the graph has 2 turning points.

This follows from the fact that the degree of the polynomial is 3 and hence, the maximum number of turns on the graph is 2.

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The perimeter of an equilateral triangle is 9x + 3, this is greater than the perimeter of a
regular pentagon which is 10x - 5.
Write down an inequality to represent this information.

Answers

Answer:

x < 8

Step-by-step explanation:

9x + 3 > 10x - 5

9x - 10x > -5 - 3

-x > -8

x < 8

Which functions have a vertex with a x-value of 0? Select three options.

f(x) = |x|
f(x) = |x| + 3
f(x) = |x + 3|
f(x) = |x| − 6
f(x) = |x + 3| – 6

Answers

Answer:

f(x) = |x|f(x) = |x| + 3f(x) = |x| − 6

Answer:

A,B,D

Step-by-step explanation:

A ​20-ft by ​the 40-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 256 ft2​, how wide is the​ walkway?

Answers

Answer:  2 feet

========================================================

Explanation:

x = width of the walkway in feet

This is some positive real number.

The dimension of 20 feet bumps up to 20+2x when adding on x from both directions. Similarly, the 40 ft dimension becomes 40+2x

Refer to the diagram below.

The 20 ft by 40 ft pool is surrounded by a larger rectangle that is 20+2x ft by 40+2x ft

The pool itself is 20*40 = 800 sq ft. Add on the walkway area to get 800+256 = 1056 sq ft.

-----------

Area = length*width

1056 = (20+2x)*(40+2x)

1056 = 20*40 + 20*2x + 2x*40 + 2x*2x ... FOIL rule

1056 = 800 + 40x + 80x + 4x^2

0 = 4x^2 + 40x + 80x + 800 - 1056

0 = 4x^2 + 120x - 256

4x^2 + 120x -  256 = 0

4(x^2 + 30x - 64) = 0

x^2 + 30x - 64 = 0

Let's use the quadratic formula to finish solving for x.

Plug in a = 1, b = 30, c = -64

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-30\pm\sqrt{(30)^2-4(1)(-64)}}{2(1)}\\\\x = \frac{-30\pm\sqrt{1156}}{2}\\\\x = \frac{-30\pm34}{2}\\\\x = \frac{-30+34}{2} \ \text{ or } \ x = \frac{-30-34}{2}\\\\x = \frac{4}{2} \ \text{ or } \ x = \frac{-64}{2}\\\\x = 2 \ \text{ or } \ x = -32\\\\[/tex]

Recall we made x be positive. This is because a negative walkway width does not make sense. This means we'll ignore x = -32.

The only practical solution is x = 2

Therefore, the walkway is 2 feet wide

A water sprinkler sends water out in a circular pattern. How large is the watered area if the radius of the watering pattern is 3 feet?

Use 3.14 for pi.

Answers

Answer:

28.26 feet squared

Explanation:

Area of circle is determined by : π(radius)²

Here given:

π = 3.14radius = 3 feet

Solve for area:

π(radius)²3.14(3)²28.26 feet²

Answer:

28.26 feet squared

Step-by-step explanation:

Radius of the watering pattern = 3 feet

Area = π r²

= 3.14 × 3²

= 28.26 feet squared

Which is the graph of f,(x) = 0.5(4)*

Answers

I assume you meant [tex]f(x)=0.5(4)^{x}[/tex]. The graph is shown below.

The linear function that is represented by which table has the same slope as the graph? On a coordinate plane, a line goes through points (0, negative 3) and (2, 1). a A 2-column table with 5 rows. Column 1 is labeled x with entries negative 25, negative 21, negative 17, negative 13, negative 9. Column 2 is labeled y with entries negative 9, negative 7, negative 5, negative 3, negative 1. b A 2-column table with 5 rows. Column 1 is labeled x with entries negative 25, negative 21, negative 17, negative 13, negative 9. Column 2 is labeled y with entries 9, 7, 5, 3, 1. c A 2-column table with 5 rows. Column 1 is labeled x with entries negative 9, negative 7, negative 5, negative 3, negative 1. Column 2 is labeled y with entries negative 25, negative 21, negative 17, negative 13, negative 9. d A 2-column table with 5 rows. Column 1 is labeled x with entries 1, 3, 5, 7, 9. Column 2 is labeled y with entries negative 9, negative 13, negative 17, negative 21, negative 25.

Answers

Option C. A 2-column table with 5 rows. Column 1 is labeled x with entries negative 9, negative 7, negative 5, negative 3, negative 1. Column 2 is labeled y with entries negative 25, negative 21, negative 17, negative 13, negative 9.  This labeled is correct.

According to the linear function,
Every linear function is characterized by a constant rate of change; the slope. The slope of a linear function is a measure of the “steepness” of the line. We use the symbols Δx and Δy which mean respectively the “change in x ” and the “change in y ”.

So Option C is correct after all assumptions.

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Michael went to the game store there was so much games he wanted and if one of them was $42.29 and the other one was $87.99 and he had $142 how much would he have left ​

Answers

Answer:

$11.72

Step-by-step explanation:

Add: $42.29 + $87.99 = $130.28

Subtract: $142 - $130.28 = $11.72

Answer:

he would have spent 131.08 dollars meaning he has 11.72 dollars left.

Step-by-step explanation:

Need help, can't figure this one out:

Find the perimeter of the following rectilinear figure.

Answers

The perimeter of the following rectilinear figure is 54 units.

What is Perimeter ?

Perimeter of a figure is the distance covered when a person walk one round across its edges .

The given figure is in the form of a rectangle ,

The perimeter is equal to the sum of all sides ,

The bottom base is 13 includes (base of the small extended figure )

The left side is 14(includes left side of the small extended figure)

The right side is 10+5+4 (includes right side of the small extended figure)

The top is 8

Therefore the perimeter is 13+14+10+5+4+8 = 54 units

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The United States Postal Service reports that 90% of first-class mail within the same city is delivered in two days of the time of mailing. Ten letters are randomly sent to different locations. a. What is the probability that all 10 will arrive within two days? b. What is the probability that exactly 8 will arrive within two days? c. What is the probability that 5 or fewer will arrive within two days? d. What is the mean number of letters that will arrive within two days? e. What is the standard deviation of the number of letters that will arrive within two days?

Answers

a)The probability that all 10 will arrive within two days is 0.3486.

b)  P(x = 8) = 0.1937

c)  P(x=5)= 0.0014

d)  mean = 9

e) Standard deviation = √0.90 = 0.9486

What is Binomial Probability?

The binomial distribution model allows us to compute the probability of observing a specified number of "successes" when the process is repeated a specific number of times and the outcome for a given patient is either a success or a failure.

Given:

p = 90/100 = 0.90

q(probability of success) = 1 - p = 1 - 0.90 = 0.10

n = 10

a)The probability that all 10 will arrive within two days

P(x = 10) = 0.3486

b) P(x = 8) = 0.1937

c) P(x=5)= 0.0014

d) mean = np = 10 × 0.90 = 9

e) Variance = npq = 10 × 0.90 × 0.10 = 0.90

Standard deviation = √0.90 = 0.9486

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1. A water tank measuring 80 cm by 40 cm by 30 cm is completely filled with water. Water flows out of the tank at a rate of 4 per minute. At this rate, how long will the tank be completely drained out of water? 80 cm 40 cm 30 cm 1. A water tank measuring 80 cm by 40 cm by 30 cm is completely filled with water . Water flows out of the tank at a rate of 4 per minute . At this rate , how long will the tank be completely drained out of water ? 80 cm 40 cm 30 cm​

Answers

Answer:

6.34 min to empty

Step-by-step explanation:

80 cm x 40 cm x 30 cm = 96000 cm^3

  this volume represents  25.36 gallons of water (US)

25.36 gal / 4 gal/min = 6.34 min  to empty

the perimeter of a rectangle is 70 cm . if the ratio of the width to the length is 2:5 what is the width ?

Answers

Answer:

width = 10 cm

Step-by-step explanation:

the ratio of width to length is 2 : 5 = 2x : 5x ( x is a multiplier )

the perimeter (P) of a rectangle is calculated as

P = 2 × width + 2 × length

given P = 70 then

2(2x) + 2(5x) = 70

4x + 10x = 70

14x = 70 ( divide both sides by 14 )

x = 5

Then

width = 2x = 2 × 5 = 10 cm and length = 5x = 5 × 5 = 25 cm

Above is right thinkso



Thanks

Math: Evaluating a piece wise function...help!

Answers

The values of the functions are g(-0.5) = -1, g(0.3) = 0 and g(0.5) = 1

How to evaluate the piece wise function?

The function is given as:

[tex]g(x) = \left[\begin{array}{cc}-2&-2.5 < x \le -1.5\\-1&-1.5 < x \le -0.5\\0&-0.5 < x < 0.5&1&0.5 \le x < 1.5\end{array}\right[/tex]

To calculate g(-0.5), we make use of the domain -1.5 < x ≤ -0.5

At this domain;

g(x) = -1

So, the value of g(-0.5) is

g(-0.5) = -1

To calculate g(0.3), we make use of the domain -0.5 < x  0.5

At this domain;

g(x) = 0

So, the value of g(0.3) is

g(0.3) = 0

To calculate g(0.5), we make use of the domain 0.5 ≤ x  1.5

At this domain;

g(x) = 1

So, the value of g(0.5) is

g(0.5) = 1

Hence, the values of the functions are g(-0.5) = -1, g(0.3) = 0 and g(0.5) = 1

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Consider the following loan. Complete parts (a)-(c) below
An individual borrowed $88,000 at an APR of 6%, which will be paid off with monthly payments of $667 for 18 years.
a. Identify the amount borrowed, the annual interest rate, the number of payments per year, the loan term, and the payment amount.
The amount borrowed is $, the annual interest rate is%, the number of payments per year is the loan term is years, and the payment amount is $

Answers

The complete statements are mathematically given as

the amount borrowed= 88000the annual interest rate= 6%the number of payments per year= 12The loan term= 18the payment amount.=8004

What is the amount borrowed, the annual interest rate, the number of payments per year, the loan term, and the payment amount.?

Generally,  The transfer of money, products, or services in return for other goods and services in proportions that have been previously agreed upon and deemed acceptable is what is meant by the term "payment."

In conclusion, the amount borrowed= 88000

the annual interest rate= 6%

the number of payments per year= 12

The loan term= 18

the payment amount.=667*12

the payment amount.=8004

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Which of the following expressions are equal to -8/11 - 3/4 - 1/4

Answers

In the expressions that we are given, we can note that there is a negative in all of them. This means that we can factor out the negative.

With the negative factored out, it will look like this: [tex]-(\frac{8}{11} + \frac{3}{4} + \frac{1}{4} )[/tex]
The reasoning for this is because you distribute the negative to each term. For example 8/11 is a term, and so is 3/4, and 1/4. So our first answer is D.

Another way we can do this is by combining like terms. We see that in the denominator for -3/4 and -1/4 they both share 4. We can combine it so it becomes -4/4 or -1. It would be E.

The third way
we can do this is by rewriting it. Answer A rewrites it so that it is + -, effectively just -. This allows us to treat the equation as if it were the original one.

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HELP THIS IS URGENT WILL GIVE BRANLIEST ANSWER 3 AND 6

Answers

awnser is c because i just did it

One person ran 4 miles in 24 minutes. At this rate, how long would it take to run 26 miles?

Answers

The answer is 156 minutes.

If it takes them 24 minutes to run 4 miles, to find the minutes it takes to run 1 mile divide 4 by 24. This comes out to 6 minutes to run 1 mile. Then just multiple 6 minutes by 26 miles to get 156 minutes.

8(w-5)=16 solve for w please give working out

Answers

The answer is 7 according

Construct a polynomial function with the following properties fifth degree, 3 is a zero of multiplicity 3, - 4 is the only other zero, leading coefficient is 3

Answers

The polynomial function with the given properties is; y = 2(x - 3)³(x + 4)²

How to construct polynomial functions?

Polynomials are defined as algebraic expressions that consist of variables, coefficients, and constants. The standard form of polynomials has mathematical operations such as addition, subtraction, and multiplication.

We need to form a polynomial expression with the following properties;

fifth-degree, 3 is a zero of multiplicity 3, −4 is the only other zero and ,the leading coefficient is 3. Thus, the polynomial will be;

y = 2(x - 3)³(x + 4)²

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3z^2-4z+11 -(12z^2+2z-11 find the difference . polynomials functions

Answers

Answer:

−135z

2

−2z
The 2 is representing Square

Step-by-step explanation:

(3z)
2

−4z+11−(12z)
2

+2z−11

Expand (3z)

2

.

3

2

z

2

−4z+11−(12z)

2

+2z−11

Calculate 3 to the power of 2 and get 9.

9z

2

−4z+11−(12z)

2

+2z−11

Expand (12z)

2

.

9z

2

−4z+11−12

2

z

2

+2z−11

Calculate 12 to the power of 2 and get 144.

9z

2

−4z+11−144z

2

+2z−11

Combine 9z

2

 and −144z

2

 to get −135z

2

.

−135z

2

−4z+11+2z−11

Combine −4z and 2z to get −2z.

−135z

2

−2z+11−11

Subtract 11 from 11 to get 0.

−135z

2

−2z

x=7-3y
2(7-3y)+4y=8
14-6y +4y=8
14-2y=8
-2y = -6
y=3
x + 3(3) = 7

Answers

Answer:

(-2,7)

Step-by-step explanation:

x=7-3y

2(7-3y)+4y=8

14-6y +4y=8

14-2y=8

-2y = -6

y=3

x + 3(3) = 7

x + 9 = 7

x = -2

(-2,7)

Answer: -2,3

Step-by-step explanation:

determine whether each pair of lines is perpendicular parallel or neither

Answers

Answer:

1st set of equations - parallel

2nd set - perpendicular

3rd set - neither

Step-by-step explanation:

First set:

simplify the equation for line 1  by dividing by -4: y = 0.5x + 1

simplify the equation for line 1  by dividing by -6: y = 0.5x - 1.5

Both have the same slope: 0.5 so the lines are parallel.

Second set:

simplify the equation for line 1  by dividing by 3: y = -2/3x + 4

simplify the equation for line 1  by dividing by -4: y = 3/2x - 7/4

-2/3 * 3/2 = -1, so the lines are perpendicular

Third set

simplify the equation for line 1  by dividing by 1/2: y = -2x+4

simplify the equation for line 1  by dividing by 2: y = -1/4x +2

-2x+4=-0.25x+2

-2x+0.25x=2-4

-1.75x=-2

x=1.14

y=-2(1.14)+4 = 1.7143. So there is an intersection point

The pair of lines 2x - 4y = -4 & 3x - 6y = 9, 2x + 3y = 12 & and 6x - 4y = 7, and x + (1/2)y = 2 & (1/2)x + 2y = 4 will be parallel lines, perpendicular lines, and neither parallel nor perpendicular, respectively.

What is a linear equation?

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The pair of lines is given as,

2x - 4y = -4     ⇒        y = (1/2)x + 1

3x - 6y = 9      ⇒        y = (1/2)x - 3/2

The pair of lines are parallel to each other because the slope is equal.

2x + 3y = 12     ⇒        y = -(2/3)x + 4

6x - 4y = 7       ⇒        y = (3/2) x - 7/4

The pair of lines are parallel to each other because the product of slopes is -1.

x + (1/2)y = 2        ⇒        2x + y = 4

(1/2)x + 2y = 4      ⇒        2x + 4y = 8

The pair of lines are neither parallel nor perpendicular to each other.

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Can someone check whether its correct or no? this is supposed to be the steps in integration by parts​

Answers

Answer:

[tex]\displaystyle - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given integral:

[tex]\displaystyle -\int \dfrac{\sin(2x)}{e^{2x}}\:\text{d}x[/tex]

[tex]\textsf{Rewrite }\dfrac{1}{e^{2x}} \textsf{ as }e^{-2x} \textsf{ and bring the negative inside the integral}:[/tex]

[tex]\implies \displaystyle \int -e^{-2x}\sin(2x)\:\text{d}x[/tex]

Use integration by parts.

[tex]\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}[/tex]

[tex]\textsf{Let }\:u=\sin (2x) \implies \dfrac{\text{d}u}{\text{d}x}=2 \cos (2x)[/tex]

[tex]\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}[/tex]

Substituting the defined parts into the formula:

[tex]\begin{aligned}\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\sin (2x)- \int \dfrac{1}{2}e^{-2x} \cdot 2 \cos (2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\sin (2x)- \int e^{-2x} \cos (2x)\:\text{d}x\end{aligned}[/tex]

[tex]\displaystyle \textsf{For }\:-\int e^{-2x} \cos (2x)\:\text{d}x \quad \textsf{integrate by parts}:[/tex]

[tex]\textsf{Let }\:u=\cos(2x) \implies \dfrac{\text{d}u}{\text{d}x}=-2 \sin(2x)[/tex]

[tex]\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}[/tex]

[tex]\begin{aligned}\implies \displaystyle -\int e^{-2x}\cos(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\cos(2x)- \int \dfrac{1}{2}e^{-2x} \cdot -2 \sin(2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x\end{aligned}[/tex]

Therefore:

[tex]\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x[/tex]

[tex]\textsf{Subtract }\: \displaystyle \int e^{-2x}\sin(2x)\:\text{d}x \quad \textsf{from both sides and add the constant C}:[/tex]

[tex]\implies \displaystyle -2\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+\text{C}[/tex]

Divide both sides by 2:

[tex]\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{4}e^{-2x}\sin (2x) +\dfrac{1}{4}e^{-2x}\cos(2x)+\text{C}[/tex]

Rewrite in the same format as the given integral:

[tex]\displaystyle \implies - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}[/tex]

Differentiation Rules used:

[tex]\boxed{\begin{minipage}{5.7 cm}\underline{Differentiating $\sin(k)$}\\\\If $y=\sin(kx)$, then $\dfrac{\text{d}y}{\text{d}x}=k\cos(kx)$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{5.7 cm}\underline{Differentiating $\cos(k)$}\\\\If $y=\cos(kx)$, then $\dfrac{\text{d}y}{\text{d}x}=-k\sin(kx)$\\\end{minipage}}[/tex]

Integration Rules used:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $e^{kx}$}\\\\$\displaystyle \int e^{kx}\:\text{d}x=\dfrac{1}{k}e^{kx}+\text{C}$\end{minipage}}[/tex]

What would the following figure look like after a reflection in a horizontal mirror, followed by a rotation 90 degrees counterclockwise?

Answers

Answer:

Step-by-step explanation:

To rotate any figure we have to have the CENTER of rotation!!!!

You did not provide us (your helpers) with that point, so I chose point on the horizontal mirror.

Consider a triangle ABC like the one below. Suppose that B=129°, a=7, and c=42. (The figure is not drawn to scale.) Solve the triangle.
Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".
4-C-b-0
DOD
X
No
solution
5
?

Answers

The angles are: A =24.7° ; B = 40.6° ; C =114.7°.

What is Cosine law?

The law of cosine helps in establishing a relationship between the lengths of sides of a triangle and the cosine of its angles. The cosine law in trigonometry generalizes the Pythagoras theorem, which applies to a right triangle.

Cosine Law

a² = b²+c²-2bc cos A

b² = c²+a² -2ca cos B

Sum of three angles of a triangle is 180°.

a = 34 ; b= 53; c = 74

Substituting the given values in the cosine law, we have

34² = 53² + 74² - 2*53 *74 * cos A

7844 cos A = 2809 + 5476 - 1156 = 7129

cos A = 7129/7844 = 0.9088

A = cos⁻¹ (0.9088) = 24.6600° = 24.7°

53² = 74² + 34² - 2 (74)(34) cos B

5032 cos B = 5476 + 1156 - 2809 = 3823

cos B = 3823/5032 = 0.7597

B = cos⁻¹ (0.7597) = 40.5622° = 40.6°

Also, A + B + C = 180°

24.7 + 40.6 + C =180

C =180 -  65.3 = 114.7°

Thus, the angles are: A =24.7° ; B = 40.6° ; C =114.7°

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