11. Find the solutions of x^2-x-30 = 0.
Please give a walkthrough/step by step I am trying to learn how to do it!

Answer:

125%

Step-by-step explanation:

Line A is y=2x+4

Line B is y=4x+9

The slope of line A is 2 and the slope of line B is 4.

The y-inetercept of line A is 4 and y-intercept of line B is 9.

Thus, line B is steeper than line A as slope of line B is greater than line B.

The slope is steeper and the line is shifted upwards.

Answer:

y = \(\sqrt{55}\)

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(altitude)² = product of parts of hypotenuse

then

y² = 11 × 5 = 55 ( take square root of both sides )

y = \(\sqrt{55}\)

EXPLANATION

Given the function:

We can see that it has an Absolute minimum in (3,-3) and No absolute maximum.

Answer:

  745

Step-by-step explanation:

You want the original number of books in the library if adding 298 children's books increased the fraction of children's books from 2/5 to 4/7.

We often like to work problems like this in terms of "ratio units." Here, we'll let x represent the number of books in a ratio unit. This means the number of children's books is originally 2x, and the total number of books is originally 5x. Then we have ...

  (2x +298)/(5x +298) = 4//7

Cross multiplying gives ...

  7(2x +298) = 4(5x +298)

  3(298) = 6x . . . . . . . . . . . . . subtract (14x+4(298))

  149 = x

  745 = 5x . . . . . . the original number of books in the library

There were 745 books in the library at first.

__

Additional comment

If we let x represent the original number of library books, then the arithmetic involves more fractions. You would have an equation like ...

  2/5x +298 = 4/7(x +298)

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Answer:

15%

Step-by-step explanation:

15%*40=46

Answer:

15%

Step-by-step explanation:

\(Percent of change =\frac{new -old}{ old} *100\\\)

The boy was 40 inches tall so that means 40 inches is the old value

The boy is currently 46 inches tall now, so 46 is the new value

Plug these values into the equation:

\(Percent of change =\frac{46 -40}{ 40} *100\\\)

Simplify:

\(Percent of change =\frac{6}{ 40} *100\\\)

\(Percent of change =\frac{600}{ 40} \\\)

\(Percent of change =15\)

I hope this answers your question :)

Answer:

The answer is "12".

Step-by-step explanation:

Lowest number\(=20\\\\\)

highest number\(=80\\\\\)

Number of classes\(=5\\\\\)

Range=highest number-lowest number

          \(=80-20\\\\=60\\\\\)

class width \(=\frac{Range}{\text{number of classes}}\)

                   \(=\frac{60}{5}\\\\=12\)

Answer:

A business person will use algebra to determine whether a piece of equipment does not lose its worth if it is in stock.

Step-by-step explanation:

Answer:

x+3 = 5    

x-7 = -5

Step-by-step explanation:

x+3 = 5          2+3 = 5  true  solution

x+2 = 8           2+2 =4    not a solution

x+1 =1            2+1 =3   not a solution

x-2 = 4          2-2 = 0   not a solution

x-7 = -5    2-7 = -5  true   solution

Answer:

A, and E

Step-by-step explanation:

just add 2, and if it doesnt make sense its not right

The position vector of a particle that has an acceleration, a(t) = 19t i + eᵗ j + e⁻ᵗ k, is equals to the 19 (t³/6)i + (eᵗ - t )j - (e⁻ᵗ - 2t - 2)k.

We have, The acceleration vector function of a particle is defined as, a(t)

= 19t i + eᵗ j + e⁻ᵗ k and intial velocity and position is, v(0) = k, r(0) = j + k.

We have to calculate the position vector of a particle. Now, as we know, the acceleration of a particle is equals to derivative of velocity of particle with time. In other words, velocity is integration of acceleration with respect to time.

Mathematically, v(t) = ∫a(t)dt , let C be integration constant ( vector).

v(t) = ∫a(t)dt = ∫[ (19t) i + (eᵗ) j + (e⁻ᵗ) k] dt

=> v(t) = 19(t²/2) i + eᵗ j - e⁻ᵗ k + C

At t = 0 , v(0) = k

=> k = 19(0²/2) i + e⁰j - e⁻⁰ k + C

=> k = 0 + j - k + C

=> C = 2k - j

so, v(t) = 19(t²/2) i + eᵗ j - e⁻ᵗ k + 2k - j

= 19(t²/2) i + (eᵗ - 1) j - (e⁻ᵗ - 2) k

Now, Position of a particle is determined by integrating the velocity of particle with respect to time, r(t) = ∫v(t)dt , let D be integration constant ( vector). So, r(t)

= ∫[19(t²/2) i + (eᵗ - 1) j - (e⁻ᵗ - 2) k ] dt

= 19 (t³/6) i + eᵗ j - t j - e⁻ᵗ k + 2t k + D

At t = 0, r(0) = j + k

=> j + k = 19 (0³/6) i +e⁰ j - 0j - e⁻⁰ k +2× 0k +D

=> j + k = 0 + j - k + D

=> D = 2k

so, r(t) = 19 (t³/6) i + eᵗ j - t j - e⁻ᵗ k + 2t k + 2k

= 19 (t³/6)i + (eᵗ - t )j - (e⁻ᵗ - 2t - 2)k

Hence, required position vector is 19 (t³/6)i + (eᵗ - t )j - (e⁻ᵗ - 2t - 2)k.

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Answer:

68.5

Step-by-step explanation:

u do 198 divided by 4 then add 19 to the awnser that u got

Answer:

width = 40 feet

Step-by-step explanation:

If w = width, then l = 19 + w

l = 19 + w

2l + 2w = 198

"Substitute 19 + w as l in the second equation"

2(19 + w) + 2w = 198,

38 + 2w + 2w = 198,

38 + 4w = 198,

4w = 198 - 38 = 160,

w = 160/4 = 40 feet

=> Solution: width = 40 feet

Answer:

8500

Step-by-step explanation:

When compounded continuously the future value,  FV , of your initial investment,  PV , is determined with the the equation

\(FW = PV\) ×\(e^{rxt}\)

where  r  is the norminal interest rate, expressed as a decimal, and  t  is the investment period in years.

Plugin the values in this equation gives

\(FW = $7,500\) × \(e^{0.015x8} =$8,456.23\)

Round to nearest hundred dollars = 8500

A high standard deviation indicates that the data points are spread out over a wider range of values, while a low standard deviation indicates that the data points are tightly clustered around the mean. It is commonly used in various fields such as finance, economics, engineering, and social sciences to analyze data and make informed decisions.

The standard deviation is given as 35 seconds and the mean is given as 163 seconds.

A statistical measure known as standard deviation can be used to quantify how variable or dispersed a set of data is. It gauges how far the values are from the data's mean (average).

sample mean = population mean

           + [population standard deviation / √(sample size)] × Z

where Z is the standard normal distribution variable corresponding to the desired level of probability.

Substituting the given values,

sample mean = 163 + (35 / √8 ) × 1.55   ≈  180.54

So the sample mean length of 8 randomly selected songs is expected to be around 180.54 seconds.

To find the symmetric length values around the mean, we can use the formula:

Lower value = population mean - (sample mean - population mean)

          = 2 × population mean - sample mean

Upper value = population mean + (sample mean - population mean)

          = 2 × sample mean - population mean

Substituting the given values,

Lower value = 2 × 163 - 180.54  ≈ 145.46

Upper value = 2 × 180.54 - 163  ≈ 217.08

Therefore, there is a 88% probability that the sample mean length of 8 randomly selected songs is between 145.46 and 217.08 seconds, symmetric to the mean of 163 seconds.

The standard deviation is given as 35 seconds and the mean is given as 163 seconds.

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Answer:

G

Step-by-step explanation:

It is G,

f(x) = 4.1/(42.4x-10(x-2)), x-intercept = -4.878, y-intercept = (0,-2.05), asymptotes: vertical at x=2, horizontal at y=0, and slant at y=4.1/8x.

Given: f(x) = 4.1/(42.4x-10(x-2))

To find the x-intercept, we set f(x) to zero and solve for x:

0 = 4.1/(42.4x-10(x-2))

0 = 4.1/(32.4x+20)

0 = 4.1/4.08(x+4.878)

So, the x-intercept is x = -4.878.

To find the y-intercept, we set x to zero and solve for f(x):

f(0) = 4.1/(42.4(0)-10(0-2))

f(0) = -2.05

So, the y-intercept is (0,-2.05).

To write f(x) in the form f(x) = -1/(ax + b) + q, we can simplify the expression as follows:

f(x) = 4.1/(42.4x-10(x-2))

f(x) = 4.1/(32.4x+20)

f(x) = 4.1/4.08(8x+5)

So, a = 8, b = 5, and q = 4.1/4.08.

To draw the graph of f, we plot the x- and y-intercepts and the vertical asymptote x = 2.

We can find the horizontal asymptote by noting that as x becomes very large or very small, the term 10(x-2) dominates the expression, so f(x) approaches 4.1/-10x. Thus, the horizontal asymptote is y = 0.

To find the equations of the slant asymptotes, we divide the numerator by the denominator using long division:

4.1

8x + 5 | 4.1

- 4.1

0

So, the slant asymptote is y = 4.1/8x.

Therefore, the intercepts of f are x = -4.878 and (0,-2.05), and the equation of f(x) in the form f(x) = -1/(ax + b) + q is f(x) = -1/(8x + 5) + 1.0039.

The graph of f has intercepts with the x-axis at x = -4.878 and the y-axis at (0,-2.05), a vertical asymptote at x = 2, a horizontal asymptote at y = 0, and a slant asymptote at y = 4.1/8x.

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The graph which correct shows an image and pre-image after reflecting across the line; y = -x as required in the task content is; Option 1.

It follows from the task content that the answer choice which correctly represents an image ajd pre-image after reflecting across the line; y = -x.

First it is noteworthy to know that the line; y = -x is one which passes through the origin and has a negative slope of; -1.

On this note, by observation; when the line y = -x is drawn; the graph which represents the image and pre-image after reflecting across the line; y = -x is; Option 1.

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The graph of the system of the inequalities is attached.

To graph the inequalities y < -x - 4 and y ≥ (3/5)x + 4, we can start by graphing the corresponding equations and then shade the appropriate regions based on the inequality signs.

Let's begin with the equation y = -x - 4:

Choose a range of x-values to plot.

For simplicity, let's use x-values from -10 to 10.

Substitute different x-values into the equation to find corresponding y-values.

For example:

When x = -10, y = -(-10) - 4 = 10 - 4 = 6.

When x = 0, y = -(0) - 4 = -4.

When x = 10, y = -(10) - 4 = -10 - 4 = -14.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = -x - 4.

Next, let's graph the equation y = (3/5)x + 4:

Again, choose a range of x-values to plot. Let's use the same range of -10 to 10.

Substitute different x-values into the equation to find corresponding y-values. For example:

When x = -10, y = (3/5)(-10) + 4 = -6 + 4 = -2.

When x = 0, y = (3/5)(0) + 4 = 0 + 4 = 4.

When x = 10, y = (3/5)(10) + 4 = 6 + 4 = 10.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = (3/5)x + 4.

Now, let's shade the regions based on the inequalities:

For y < -x - 4, we need to shade the region below the line y = -x - 4.

For y ≥ (3/5)x + 4, we need to shade the region above or on the line y = (3/5)x + 4.

Hence, the region where the shaded regions overlap represents the solution to both inequalities.

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Answer:

\(6,10\)

Step-by-step explanation:

Method 1:

\(\mathrm{Let\ two\ numbers\ be\ x\ and\ y\ such\ that:}\\\mathrm{x:y=3:5\ \ \ \ and\ \ \ \ x+y=16}\\\mathrm{or,\ \frac{x}{y}=\frac{3}{5}}\\\\\mathrm{or,\ 5x=3y..........(1)}\\\mathrm{Also\ we\ have}\\\mathrm{x+y=16}\\\mathrm{or,\ 5(x+y)=5(16)}\\\mathrm{or,\ 5x+5y=80}\\\mathrm{or,\ 3y+5y=80\ [From\ equation\ 1]}\\\mathrm{or,\ 8y=80}\\\mathrm{or,\ y=10}\\\mathrm{From\ equation\ 1,}\\\mathrm{5x=3y}\\\mathrm{or,\ 5x=3(10)=30}\\\mathrm{\therefore x=6}\)

\(\mathrm{So,\ the\ two\ numbers\ are\ 6\ and\ 10.}\)

Alternative method 1:

\(\mathrm{Let\ the\ two\ numbers\ be\ x\ and\ 16-x.}\\\mathrm{Then,\ we\ have}\\\mathrm{x:(16-x)=3:5}\\\\\mathrm{or,\ \frac{x}{16-x}=\frac{3}{5}}\\\\\mathrm{or,\ 5x=3(16-x)=48-3x}\\\mathrm{or,\ 5x+3x=48}\\\mathrm{or,\ 8x=48}\\\mathrm{\therefore x=6}\\\mathrm{So,\ the\ other\ number=16-x=16-6=10}\)

\(\mathrm{So,\ the\ two\ numbers\ are\ 6\ and\ 10.}\)

Alternative method 2:

\(\mathrm{Let\ the\ two\ numbers\ be\ 3x\ and\ 5x.}\\\mathrm{Then,}\\\mathrm{3x+5x=16}\\\mathrm{or,\ 8x=16}\\\mathrm{or,\ x=2}\\\mathrm{So,\ first\ number=3x=3(2)=6}\\\mathrm{Second\ number=5x=5(2)=10}\)

\(\mathrm{So,\ the\ two\ numbers\ are\ 6\ and\ 10.}\)

The slope-intercept form of a line's equation is y = mx + b, where m is the slope of the line and b is the y-intercept. We can use the given slope and point to solve for the y-intercept and write the equation in slope-intercept form.

Given: Slope (m) = -2 and point (-2, -3)

On solving the provided question we can say that, Number of students jumped greater than 8.5 but less than 11.5 is 7 students.

the frequency or reality that something occurs frequently or a great number of times within a specific time frame. The frequency of buses, for instance, has been the subject of more complaints in recent months.

Number of students jumped greater than 8.5 but less than 11.5= frequency of length of jump greater than 8.5 but less than 11.5

AND,

frequency of length of jump greater than 8.5 but less than 11.5 is -

Number of students jumped greater than  8.5 and less than  9.5 + Number of students jumped greater than 9.5 but less than 10.5 + Number of students jumped greater than 10.5 but less than 11.5=

3+3+1=7 ( since, sum of respective frequencies of the three class)

so, Number of students jumped greater than 8.5 but less than 11.5 is 7 students.

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Answer:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

Step-by-step explanation:

To solve this problem, we'll consider the velocities of the cruise ship and the Gulf Stream as vectors and calculate their components and resultant vector. Then we'll find the magnitude (resultant velocity) and direction (resultant direction) of the resultant vector.

Given:

Cruise ship velocity (south): 22 mph

Gulf Stream velocity (east): 4 mph

A) Vector component for the cruise ship:

The cruise ship is traveling south, so its velocity vector is (0, -22).

B) Vector component for the Gulf Stream:

The Gulf Stream is flowing east, so its velocity vector is (4, 0).

C) Resultant vector:

To find the resultant vector, we'll add the two velocity vectors together:

Resultant vector = Cruise ship velocity + Gulf Stream velocity

Resultant vector = (0, -22) + (4, 0)

Resultant vector = (0 + 4, -22 + 0)

Resultant vector = (4, -22)

D) Resultant velocity:

The magnitude of the resultant vector gives us the resultant velocity. We can use the Pythagorean theorem to calculate it:

Resultant velocity = sqrt((x-component)^2 + (y-component)^2)

Resultant velocity = sqrt((4)^2 + (-22)^2)

Resultant velocity = sqrt(16 + 484)

Resultant velocity = sqrt(500)

Resultant velocity ≈ 22.4 mph (rounded to the nearest tenth)

E) Resultant direction:

The direction of the resultant vector can be found using trigonometry. We'll use the inverse tangent function (arctan) to find the angle between the resultant vector and the positive x-axis.

Resultant direction = arctan(y-component / x-component)

Resultant direction = arctan(-22 / 4)

Resultant direction ≈ -1.405 radians or -80.5 degrees (rounded to the nearest tenth)

Therefore, the answers are:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

The conditional probabilty formula can be used here:

THe formula would be:

Answer:C

Step-by-step explanation: Measure stay the same when translated

The solution is Option C.

Yes; reflections and translations preserve lengths and angle measures, so the figures are congruent

What are Congruent Triangles?

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Given data ,

Let the triangle be represented as Triangle ΔJKL

Now , the triangle JKL is reflected across the line x = 0

So , the triangle is reflected along the y axis

And , when you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

So , the x coordinates of triangle JKL changes

Now , the triangle is translated 5 units up

So , the values of the y coordinates gets increased by 5 units

And the transformed triangle is ΔJ'K'L'

The transformed triangles retains the shape as well the angle measures

From the congruent theorem of triangles

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

So , the triangle ΔJKL ≅ ΔJ'K'L'

Hence , the triangles are congruent and reflections or translations preserve lengths and angle measures

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Answer:

She can spend $38 and have $5 left.

Step-by-step explanation:

$43 - $38 = $5. Therefore, she can afford the video game and have $5 left.

Answer:

$5

Step-by-step explanation:

Subtract 48 by 38

48 -  38

You are doing this because after you subtract the game cost from what she has at the moment she will have $5 so she can spend $5 and still get the video game.

Answer:

I think its A

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

3x=28

x=7

no.of total students=35

The Addition Property of Equality allows us to add EF to both sides of the equation without changing its truth, giving us AB + EF = CD + EF.

We have,

The Addition Property of Equality states that if we add the same quantity to both sides of an equation, the equation remains true.

In the given equation,

AB = CD, we can add the same quantity, EF, to both sides of the equation to obtain:

AB + EF = CD + EF

This is because if two quantities are equal, and we add the same amount to both of them, the result is still equal.

Therefore,

The Addition Property of Equality allows us to add EF to both sides of the equation without changing its truth, giving us AB + EF = CD + EF.

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Answer:

B. 17/80

Step-by-step explanation:

The decimal form is 0.2125.

To make sure if 17/80 is 21.25 percent divide 17÷80=0.2125=21.15 percent

Answer:

5x+5=10

5x=10-5

5x=5

x=5/5

x=1

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

Let's solve for x ~

therefore, value of x = 1 ~