Solve:
x²-14x + 58=0

Answer: \(x=\frac{3}{5}+i\frac{4}{5},\:x=\frac{3}{5}-i\frac{4}{5}\)

Step-by-step explanation:

\(25x^2-30x+25=0\)

\(x_{1,\:2}=\frac{-\left(-30\right)\pm \sqrt{\left(-30\right)^2-4\cdot \:25\cdot \:25}}{2\cdot \:25}\)

\(\sqrt{\left(-30\right)^2-4\cdot \:25\cdot \:25}\)

\(=\sqrt{30^2-4\cdot \:25\cdot \:25}\)

\(=\sqrt{30^2-2500}\)

\(=i\sqrt{2500-30^2}\)

\(=40i\)

\(x_{1,\:2}=\frac{-\left(-30\right)\pm \:40i}{2\cdot \:25}\)

\(x_1=\frac{-\left(-30\right)+40i}{2\cdot \:25},\:x_2=\frac{-\left(-30\right)-40i}{2\cdot \:25}\)

\(x=\frac{3}{5}+i\frac{4}{5},\:x=\frac{3}{5}-i\frac{4}{5}\)

Answer:

See explanation below

Step-by-step explanation:

We have t as a real number.

The reference number associated with t is the shortest distance along the unit circle between the terminal point determined by t and the x-axis.

c. look at the attachment

π = 90° => 2π = 180°

π = 3.14 => 2π = 6.28

so t = 6 is less than 2π

so t' = 2π - t = 2π - 6

d. same principle but direction will go clockwise rather than counterclockwise in (+) number

π = 90° => 2π = 180°

π = 3.14 => 2π = 6.28

so we ignore the (-) since it is the direction

t = 7 which is more than 2π

so t' = -7 - 2π

you have -7 because the difference will be negative which points to direction of clockwise

Give me brainliest if this helps you.

Answer: 9 shirts I think

Step-by-step explanation: 54/6=9

Answer:

its 10

Step-by-step explanation:

'of' means multiply

1/4 of (1/4 times ) the opposite of (-) difference of 5 and a number (5-n) is lesss than 20 (<20)

1/4 times -(5-n)<20

multiply both sides by 1/4

-(5-n)<5

multiply both sides by -1 remember to flip sign

5-n>-5

add n

5>n-5

add 5

10>n

n<10

the number is any number less than 10

Answer:

\(\mathrm{5\ and\ 1}\)

Given: 18 27 24 22 29 21 23 25 25 31 19 21

The median is the middle number of the numbers given.

Lets arrange the numbers from smallet to largest:

18 19 21 27 21 22 23 24 25 25 29 31

From there we find the middle number by crossing out the numbers on both ends:

18 19 21 21 22 23 24 25 25 27 29 31

As you can see the number in the middle are 23 and 24 but we need one so we just find the number between 23 and 24 which is 23.5

Answer: Median is 23.5

The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.

The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.

Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).

The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.

The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.

The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).

Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

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If the data were transformed and points with the coordinates

(x, log(y)) were plotted then the points (1, 1.079), (2, 1.919), (3, 2.763) were plotted.

To plot the points with the coordinates (x, log(y)), we need to take the logarithm of the y-values.

Let's calculate the logarithms for the given data:

x     y            log(y)

1     12          log(12) = 1.079

2     83        log(83) = 1.919

3     580      log(580) = 2.763

Therefore, the points that would be plotted are (1, 1.079), (2, 1.919), (3, 2.763)

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The values of x for which f(x) = 7 are x = 61 and x = 21.

To find the values of x for which f(x) = 7, we can set up the equation and solve for x.

The given function is f(x) = 0.5|x - 41| - 3.

Setting f(x) equal to 7, we have:

0.5|x - 41| - 3 = 7.

First, let's isolate the absolute value term:

0.5|x - 41| = 7 + 3.

0.5|x - 41| = 10.

To remove the absolute value, we can consider two cases:

Case: (x - 41) is positive or zero:

0.5(x - 41) = 10.

Multiplying both sides by 2 to get rid of the fraction:

x - 41 = 20.

Adding 41 to both sides:

x = 61.

So x = 61 is a solution for this case.

Case: (x - 41) is negative:

0.5(-x + 41) = 10.

Multiplying both sides by 2:

-x + 41 = 20.

Subtracting 41 from both sides:

-x = -21.

Multiplying both sides by -1 to solve for x:

x = 21.

So x = 21 is a solution for this case.

Therefore, the values of x for which f(x) = 7 are x = 61 and x = 21.

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Answer:

1/4

Step-by-step explanation:

Divide the area by the length and you will find the width.

Answer:

1) Antonio's statement

2) <A = 123

Step-by-step explanation:

1) Antonio's statement is incorrect. This is because the opposite angles of a quadrilateral add up to 180°. Erin was incorrect because the opposite angles of this quadrilateral are unequal.

2) 2x+7+5x-2 = 180° (opposite angles of quadrilateral)

Now

7x+5 = 180

7x = 175

x = 25

<A = 5x-2

= 5(25)-2

= 125-2

= 123

Based on the given polynomial function, as x approaches positive or negative infinity, the function f(x) = 2x³ - 3x - 4x⁴ + 1 approaches negative infinity.

The end behavior of a polynomial function is determined as follows:

Examine the leading term of the function f(x) = -4x⁴ + 2x³ - 3x + 1

The leading term of the function is -4x⁴.

For large positive values of x, as x approaches positive infinity, the leading term -4x⁴ becomes increasingly negative since x⁴ grows faster than any positive constant.

Therefore, the end behavior of the function as x approaches positive infinity is that f(x) approaches negative infinity.

Similarly, for large negative values of x, as x approaches negative infinity, the leading term -4x⁴ becomes increasingly negative since x⁴ grows faster than any positive constant.

Therefore, the end behavior of the function as x approaches negative infinity is that f(x) approaches negative infinity.

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Answer:

The answer is <-2

Step-by-step explanation:

Answer: I'm late but here you go

Step-by-step explanation:

Answer:

x= -3

x= 2.

Step-by-step explanation:

x^2 + x - 6 = 0

(x+3)(x-2)=0

x= -3

x= 2

x={2, -3}.

Answer:

The price would go down as people would be more willing to buy cheaper potatoes and the producers would want to sell them for a lower price to get rid of them easy and fast.

Step-by-step explanation:

Hope this helps you :)

The length of v to the nearest 10th of an inch is 2.0 inches.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

We can use the Law of Sines,

Which states that for any triangle ABC:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides of the triangle opposite the angles A, B, and C.

Now,

a = UV = u = 3.4 inches

A = ∠TUV

  = 180° - m∠U - m∠V

  = 180° - 144° - 35°

  = 1°

B = ∠UTV

   = m∠U

   = 144°

C = ∠TVU

  = m∠V

  = 35°

Using the Law of Sines,

v/sin(C) = u/sin(B)

Substituting in the values.

v/sin(35°) = 3.4/sin(144°)

Solving for v.

v = (3.4 × sin(35°)) / sin(144°)

v = 1.97 inches

Therefore,

The length of v to the nearest 10th of an inch is 2.0 inches.

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Answer:

y = 6

x = 0.2

Step-by-step explanation:

5x + y =7

20x + 2 = y

5x(4) + y(4) = 7(4)

20x + 4y = 28

(20x = 28 - 4y) = (20x = y - 2)

28 - 4y = y - 2

30 - 4y = y

30 = 5y

y = 6

5x + y =7

20x + 2 = y

y = 7 - 5x

7 - 5x = 20x + 2

5 - 5x = 20x

5 = 25x

x = 0.2

Answer:

40000, 20000

Step-by-step explanation:

Let the amount a grandchild receives be \(x\). Then, the amount a child receives is \(2x\).

Thus, \(220000=2(2x)+7x=11x \implies x=20000\).

This means each grandchild gets $20,000 and each child gets $40,000.

Hey there! :)

Answer:

A. x + 4

D. x + 2

Step-by-step explanation:

Starting with:

x² + 6x + 8

Find numbers that add up to 6 and multiply to 8. We get:

2, 4.

Put these into the factors:

(x + 2)(x + 4)

Therefore, the correct answers are:

A. x + 4

D. x + 2

To simplify the expression \(\displaystyle\sf 5x-3(-5y+6x)+4y\), we can follow the order of operations, which involves simplifying the expressions within parentheses, applying the distributive property, and combining like terms.

Using \(\displaystyle\sf \) tags for formatting, the expression becomes:

\(\displaystyle\sf 5x-3(-5y+6x)+4y\)

First, we simplify the expression within the parentheses:

\(\displaystyle\sf 5x-3(-5y+6x)+4y\)

\(\displaystyle\sf 5x+15y-18x+4y\)

Next, we can combine the like terms:

\(\displaystyle\sf 5x-18x+15y+4y\)

\(\displaystyle\sf -13x+19y\)

Therefore, the simplified expression is \(\displaystyle\sf -13x+19y\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:

Amount remaining = Initial amount × (1/2)^(number of half-lives)

In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.

So, the equation becomes:

Amount remaining = Initial amount × (1/2)^4

Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.

Simplifying the equation:

Amount remaining = Initial amount × (1/16)

Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

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Answer: $1,634.62

Step-by-step explanation:

There are 52 weeks in a year. However, Sean does not get paid every week, he gets paid every other week. 52/2 = 26, thus he gets paid 26 times a year.

His annual salary is 42,500. To figure out his salary in each paycheck, divide the net salary by the number of pay periods per year. In this case 42,500/26.

42500/26 = 1,634.62 (rounded to the nearest cent)

Answer:

the perimeter of the shape is 13cm

Step-by-step explanation:

Perimeter is the distance round a shape. As for polygons perimeter is the sum of all the sides. In this polygon, the sum of all the sides is 5cm + 1cm + 1cm + 2cm + 4cm which is equal to 13cm

4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.

5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.

In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;

RU ║ ST

Slope of side RU = Slope of side ST

Slope of RU = (y₂ - y₁)/(x₂ - x₁)

Slope of RU = (1 + 3)/(5 + 3)

Slope of RU = 4/8

Slope of RU = 0.5.

Slope of RS = (y₂ - y₁)/(x₂ - x₁)

Slope of RS = (-9 + 3)/(-4 + 3)

Slope of RS = -6/-1

Slope of RS = 6.

Slope of ST = (y₂ - y₁)/(x₂ - x₁)

Slope of ST = (-2 - 1)/(10 - 5)

Slope of ST = -3/5

Slope of ST = -0.6.

Slope of UT = (y₂ - y₁)/(x₂ - x₁)

Slope of UT = (-2 + 9)/(10 + 4)

Slope of UT = 7/14

Slope of UT = 0.5.

Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.

Question 5.

In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance RT = √[(-2 + 3)² + (10 + 3)²]

Distance RT = √170 units.

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance US = √[(5 + 4)² + (1 + 9)²]

Distance US = √181 units.

Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.

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Answer:

23009.87

Step-by-step explanation:

I think it has to be compounded monthly because that's how they got the 647.74

The remaining loan balance on a loan at a given period is just the present value of the remaining payments. The original loan was 5*12= 60 payments, and we have paid 22. This means that there are 60-22= 38 payments remaining. Thus, the remaining balance at this time is the present value of the 38 payments.

\(647.74*\frac{1-(1+.042/12)^{-38}}{.042/12}=23009.87048\)

Answer:

23009.87

Step-by-step explanation:

Answer:

friction is what helps you to walk

Step-by-step explanation:

your foot rubbing against the floor cause friction

Answer:

Friction helps you: Brakes us friction to stop a wheel like on cars, bikes, etc.

Friction hurts you: It can hurt you like when you fall it creates friction and can scrape yourself