A line segment joins points P(-1, -7) and Q (7, 3) Determine the length of PQ to 1 decimal place?

This unit is square roots and Pythagorean Therorum. ​

Answer:

X2 - X1 = 7 - 1 = 6

Y2 - Y1 = 8 - 3 = 5

L = (6^2 + 5^2)^1/2 = 7.81

2/3 L = 5.21      length of segment

Tan θ = 5 / 6 = .833    slope of line

θ = 39.8 deg

5.21 * sin 39.8 = 3.34

5.21 * cos = 39.8 = 4.00        gives length of line segments

x2 = 1 + 4 = 5      

y2 = 3 + 3.34 = 6.34

(5, 6.34) = point 2/3 up the line

Check (length of line)

[(5 - 1)^2 + (6.34 - 3)^2]^1/2 =

l = 5.21      correct length for line segmet

Answer:

3×4-8=b

Step-by-step explanation:

The total number of batteries fatima has is :

3×4= 12

She has 12 batteries but she gave her brother 8

12-8=4

And batteries represent b

So the equation is

3×4-8=b

The domain of the quotient function (f/g)(x) consists of all numbers that belong to both the domain of f and the domain of g which is false.

A statement, opinion, or rule that forms a linking of two variables is characterized as a function. Mathematics has functions, which are necessary for the design of meaningful relationships.

The range refers to all potential values of y, and the domain refers to all conceivable values of x.

The denominator of the rational function shouldn't be 0. The function is not defined if the denominator is 0.

Thus, the given statement is false.

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To convert the hexadecimal value of the EAX register (37e11449) into binary and obtain the values of AL, AH, and EAX, we can break it down as follows:

EAX: 0011 0111 1110 0001 0001 0100 0100 1001

AH:   0011 0111

AL:    0100 1001

So, the binary representation of AL, AH, and EAX is as follows:

EAX: 0011 0111 1110 0001 0001 0100 0100 1001

AH:   0011 0111

AL:    0100 1001

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The distance that Ellie ran each afternoon is 5.5 miles for a whole week.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the distance that Ellie ran each afternoon, since she ran 24 miles, hence:

3(2.5 + x) = 24

7.5 + 3x = 24

x = 5.5 miles

The distance that Ellie ran each afternoon is 5.5 miles for a whole week.

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The percent of Hispanics that prefer to read catalogs in Spanish is equal or higher than 30%

What is percentage ?

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

%, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.

The percent of Hispanics that prefer to read catalogs in Spanish is equal or higher than 30%

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To find the velocity as a function of time (v = v(t)), we need to differentiate the position function x(t) with respect to time (t).

Given: x(t) = t^3 - 6t^2 + 9t

a. Velocity as a function of time (v = v(t)):

v(t) = dx(t)/dt

Taking the derivative of x(t) with respect to t:

v(t) = d/dt(t^3) - d/dt(6t^2) + d/dt(9t)

v(t) = 3t^2 - 12t + 9

b. Initial velocity (t = 0):

v(0) = 3(0)^2 - 12(0) + 9

v(0) = 9 m/s

Velocity after 1 second (t = 1):

v(1) = 3(1)^2 - 12(1) + 9

v(1) = 3 m/s

Velocity after 2 seconds (t = 2):

v(2) = 3(2)^2 - 12(2) + 9

v(2) = 9 m/s

Velocity after 3 seconds (t = 3):

v(3) = 3(3)^2 - 12(3) + 9

v(3) = 18 m/s

Velocity after 4 seconds (t = 4):

v(4) = 3(4)^2 - 12(4) + 9

v(4) = 33 m/s

c. Average velocity between 0 and 2 seconds:

Average velocity = (v(2) - v(0)) / (2 - 0)

Average velocity = (9 - 9) / 2

Average velocity = 0 m/s

d. Average velocity between 1 and 3 seconds:

Average velocity = (v(3) - v(1)) / (3 - 1)

Average velocity = (18 - 3) / 2

Average velocity = 7.5 m/s

e. Average velocity between 2 and 4 seconds:

Average velocity = (v(4) - v(2)) / (4 - 2)

Average velocity = (33 - 9) / 2

Average velocity = 12 m/s

f. The particle is at rest when the velocity is equal to zero:

0 = 3t^2 - 12t + 9

Solving this quadratic equation, we find two solutions:

t = 1 second and t = 3 seconds

Therefore, the particle is at rest at t = 1 second and t = 3 seconds.

g. The particle is moving in the positive x-direction when the velocity is positive.

From the velocity equation, we can see that when t > 2, v(t) is positive.

Therefore, the particle is moving in the positive x-direction when t > 2 seconds.

h. Diagram representing the motion of the particle:

```

    ^

    |

    |

    |

-----|-------------->

    |

    |

    |

```

The particle moves to the right along the x-axis.

i. Total distance traveled by the particle during the first five seconds:

To find the total distance traveled, we need to consider both the positive and negative displacements.

Distance traveled = ∫(|v(t)|) dt (from t = 0 to t = 5)

Substituting the velocity function:

Distance traveled = ∫(|3t^2 - 12t + 9|) dt (from t = 0 to t =

5)

To calculate this integral, we need to break it into intervals where the velocity function changes sign.

For t in the interval [0, 1]:

Distance traveled = ∫(3t^2 - 12t + 9) dt (from t = 0 to t = 1)

For t in the interval [1, 3]:

Distance traveled = ∫(-(3t^2 - 12t + 9)) dt (from t = 1 to t = 3)

For t in the interval [3, 5]:

Distance traveled = ∫(3t^2 - 12t + 9) dt (from t = 3 to t = 5)

Evaluating these integrals will give us the total distance traveled by the particle.

j. Displacement of the particle during the first five seconds:

Displacement = x(5) - x(0)

Displacement = (5^3 - 6(5)^2 + 9(5)) - (0^3 - 6(0)^2 + 9(0))

k. Acceleration as a function of time (a = a(t)):

Acceleration is the derivative of velocity with respect to time.

a(t) = dv(t)/dt

Taking the derivative of v(t) = 3t^2 - 12t + 9:

a(t) = d/dt(3t^2) - d/dt(12t) + d/dt(9)

a(t) = 6t - 12

1. To determine if the particle is moving with constant acceleration as a function of time, we need to check if the acceleration is constant (independent of time).

From the equation a(t) = 6t - 12, we can see that the acceleration is not constant since it depends on the value of time (t). Therefore, the particle is not moving with constant acceleration as a function of time.

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An expression that looks like Sarah's expression but is not equivalent is:

10(5j + j + 3).

A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, or variables. Let's examine the writing style of expressions. A number is 6 times larger than the other number, x, by a factor of 2. This statement is represented mathematically by the expression x/2 + 6. Using mathematical expressions, complex puzzles can be solved.

now in the question,

We can write a look alike expression which is not equivalent is:

10(5j + j + 3).

Now translating the new expression into verbal:

Sarah gets paid $10 for every shark tooth she finds. After finding 3, she asked Jhon for help. When Jhon finds a tooth, by that time Sarah finds 5 of them.

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(a) The acceleration (in m/s²) the cat requires to catch the mouse in 10 seconds can be calculated by using the formula given below:

v = u + at

Where, v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.

Substituting the given values in the above formula, we get:

0 = 4.2 + a(10)

a = -0.42

Hence, the acceleration (in m/s²) the cat requires to catch the mouse in 10 seconds is -0.42 m/s².

(b) The distance the mouse gets from x=0 before being caught by the cat can be calculated by using the formula given below:

s = ut + 1/2at²

Where, s is the distance, u is the initial velocity, a is the acceleration, and t is the time taken by the cat to catch the mouse. Here, u = 4.2 m/s, a = -0.42 m/s², and t = 10 s.

Substituting these values in the above formula, we get:

s = 4.2(10) + 1/2(-0.42)(10)²

s = 42 - 21

s = 21 m

Hence, the mouse gets 21 m from x=0 before being caught by the cat.

(c) The velocity (in m/s) of the cat with respect to the mouse at the time it catches the mouse can be calculated by using the formula given below:

v = u + at

Where, v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.

Substituting the given values in the above formula, we get:

v = 0 + (-0.42)(10)

v = -4.2

Hence, the velocity (in m/s) of the cat with respect to the mouse at the time it catches the mouse is -4.2 m/s.

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The probability of this specific sequence occurring is calculated to be 0.0078.

The probability that the first marble is blue, the second marble is red, the third marble is blue, and the fourth marble is green can be calculated by multiplying the probabilities of each event occurring.

In the explanation, we'll provide a step-by-step calculation of the probability using the concept of probability with replacement.

To find the probability, we consider that each marble selection is independent, and the probability of selecting a specific marble remains the same for each draw.

The probability of the first marble being blue is 19/59 since there are 19 blue marbles out of a total of 59 marbles remaining.

For the second marble to be red, we consider that we replace the marble back into the bag, so the total number of marbles remains the same. The probability of selecting a red marble is 13/59.

For the third marble to be blue again, the probability remains 19/59, considering that we replace the marble back into the bag.

Lastly, for the fourth marble to be green, the probability is 16/59, with the same reasoning of replacement.

To find the probability of the entire sequence, we multiply the probabilities of each event together:

(19/59) * (13/59) * (19/59) * (16/59) = 0.0078.

Therefore, the probability that the first marble is blue, the second marble is red, the third marble is blue, and the fourth marble is green is 0.0078.

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The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)

\(\mu=e^{\int p(t)dt}\)

\(\mu=e^{\frac{t}{400}}\)

So, S(t) = \(\frac{\int\mu q(t)dt+C}{\mu}\)

S(t) = \(\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}\)

S(t) = \(e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)\)

Now solving the bracket

S(t) = 4000 + \(e^{\frac{-t}{400}}\)C.....(1)

At S(0) = 100

100 = 4000 + \(e^{\frac{-0}{400}}\) C

100 = 4000 + \(e^{0}\) C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

Order of Operations: BPEMDAS

We are given the coordinates \((12 ,\ -2)\) and \((4 ,\ -6)\). Recall from our definition that they are in the format of \((x ,\ y)\). Therefore, we can set \(x_1 = 12 ,\ y_1 = -2 ,\ x_2 = 4 ,\ y_2 = -6\).

∴ the slope m of the coordinates \((12 ,\ -2)\) and \((4 ,\ -6)\) is equal to \(\displaystyle \frac{1}{2}\), or 0.5.

___

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Topic: Algebra I
Unit: Linear Equations

Answer:

\(2^{3}\)×5×3×\(x^{2}\)×\(y^{4}\)

Step-by-step explanation:

\(8xy^{4}\)= \(2^{3}\)×\(x\)×\(y^{4}\)

6\(x^{2} y\)= 2×3×\(x^{2}\)×\(y^{}\)

10\(x^{2} y^{2}\) = 2×5×\(x^{2}\)×\(y^{2}\)

\(2^{3}\)×5×3×\(x^{2}\)×\(y^{4}\)

Answer:

Step-by-step explanation:

You can start by rewriting the top equation.

\(6a^2b - 12ab^2 = - 2ab (3a + 6b)\)

Therefore,

\(\frac{6a^2b - 12ab^2}{-2ab} = \frac{-2ab(-3a+6b)}{-2ab} = -3a + 6b\)

Answer:

\(3a^{-1} b^{-1}\) would be my best answer

Answer:

x = 5 ± \(\sqrt{17}\)

Step-by-step explanation:

Given

x² - 10x + 25 = 17 ← left side is a perfect square, thus

(x - 5)² = 17 ( take the square root of both sides )

x - 5 = ± \(\sqrt{17}\) ( add 5 to both sides )

x = 5 ± \(\sqrt{17}\)

Thus

x = 5 - \(\sqrt{17}\)

x = 5 + \(\sqrt{17}\)

Step-by-step explanation:

You have to substitute the value of the letters in all the expressions:

7.

(6-8)⁵/6-2(-8)² = 16/61

8.

5(-1)² -(-4)² +3/2(-1)-4(-4) = 4/33

9.

-9² -(-6)² +3(-20) = -117

10.

3 |3 -5|² -(3•(-5))² = -213

11.

2(-3)² -5(-3•(-2) -(-2)³ = -4

12.

-(-4)² +7(-2)⁴ -2(-3)³ = 150

Answer: 13?

Step-by-step explanation:

I need help under standing

Answer:

-7/32

Step-by-step explanation:

Multiply,Simplify

Answer:

-1 1/3

Step-by-step explanation:

cross multiply

-3×12=-36

-8×7=-56

simplify

-4/-3

simplify

-1 1/3

Answer:

- Yes, They agree

Step-by-step explanation:

Do Rachel and Dylan argree?

- Yes, They agree

Prove your answer using the values of the ratio.

100 of your friends listen to it

- Total Number = 100

Rachel said the ratio of the number of the people who liked the playlist to the number of people who did not like the playlist is 75:25.

The ratio can be simplifies further by diving all through by 25;

75/25  : 25/25

3 : 1

Dylan said that for every three people who liked the playlist, one person did not.

This simplifies to 3 : 1.

Same thing with what rachel said, so they both agree

The next proportion must be satisfied

Replacing with data,

Using quadratic formula,

The negative answer has no sense in this problem, then the length of TG is 3.

Answer:

y = 1/2x - 3

Step-by-step explanation:

The -3 is where the line is positioned vertically on the graph on the Y axis.

The 1/2x is the slope:

Go up 1, over 2 to plot points on the line, starting from y = -3

Answer: The graph of y = 3/4 is a horizontal line with y-intercept at 3/4. When this graph is translated, its y-intercept changes, while its slope remains the same.

Since the new graph has asymptotes at x = -5 and y = 14, the new equation must be of the form y = m(x + 5) + 14, where m is the slope of the original line, which is 3/4. Substituting the values, we get:

y = (3/4)(x + 5) + 14

So the equation of the translated graph is y = (3/4)(x + 5) + 14.

Step-by-step explanation:

Step-by-step explanation:

2x + 4(7-x)

= 2x + 28 -4x

= 28 - 2x

The actual ground speed = 2856.19 mph

And direction of the plane = -37.452 degree.

In navigation the angle of the course (on a compass) is counted clockwise from the North

So, the direction to the North is 0 degree, to the East is 90 degree,

to the South is 180 degree and to the West is 270 degree.

The North on most maps is a vertically up direction.

Angles are measured anticlockwise from the positive direction of the horizontal X-axis (the East on most maps) in coordinate Geometry and Trigonometry, which we will utilise.

Let us perform a basic transformation into Trigonometric standard, with the direction to the East serving as an X-axis:

310 degree on a compass is 90 degree + (360 - 310) = 140 degree

Now, counterclockwise from the X-axis:

330 degree on a compass is 90 + (360 −290) = 160

counterclockwise from the X-axis.

This is a two-vector addition issue. The amplitude and angle of direction of each are used to characterize it:

airplane (vector A) has amplitude 330 mph and angle 140 degree;

wind (vector W ) has amplitude 40 (mph) and angle 290 degree.

To add these two vectors, we describe them as sums of their X and Y components:

AX = 330 cos(140 degree)

AY = 330 sin (140 degree)

WX = 40 cos ( 290 degree)

WY = 40 sin(290 degree)

Both X-components behave in the same direction, as do both Y-components. As a result, we can add X-components to obtain an X-component of the resulting movement, and we can add Y-components to obtain a Y-component of the resulting movement..

(A+W)X =A X + WX= 330 cos(140 degree)+40 cos ( 290 degree)

                               = -227.22

(A+W)Y = AY+WY= 330 sin (140 degree) + 40 sin(290 degree)

                            = 174.66

Knowing two components of the resulting vector of movement, we can simply calculate its amplitude |A+W| and direction (A+W):

|A+W| = √[(A+W)² of x +(A+W)² of y]

          = 2856.19

∠(A+W) = arctan [ (A+W)y/(A+W)x]

            = arctan[-0.766]

            = -37.452 degree.

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Answer:

Step-by-step explanation:

9x2+23x

The perimeter of the triangle is 24.3 units.

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,

Triangle vertices:

(1,5), (1,-4), (-4,-4)

Now,

Using the distance formula,

The distance between (1, 5) and (1, -4).

D(1) = √(1 - 1)² + (5 + 4)²

D(1) = √9²

D(1) = 9

The distance between (1, -4) and (-4, -4) is:

D(2) = √(1 + 4)² + (-4 + 4)²

D(2) = √(5²

D(2) = 5

The distance between (-4, -4) and (1, 5) is:

D(3) = √(-4 - 1)² + (-4 - 5)²

D(3) = √(25 + 81)

D(3) = √106

Now,

The perimeter of the triangle.

P = d(1) + d(2) + d(3)

P = 9 + 5 + √106

P = 9 + 5 + 10.30

P = 24.3

Thus,

The perimeter of the triangle with vertices (1,5),(1,-4),(-4,-4) is 24.3 units.

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Answer:

Step-by-step explanation:

You don't need the Law of Cosines, the Law of sines if what you need. You can't use the Law of Cosines because in order to find side a, you would need the length of side c and you don't have it. Using the Law of Sines is appropriate, knowing that angle B = 55:

\(\frac{sin55}{175}=\frac{sin42}{a}\) and solving for a:

\(a=\frac{175sin42}{sin55}\) so

a = 143.0

a. Decision rule: Reject the null hypothesis if the calculated z-value is less than or equal to -1.28. b. Calculated z-value: -1.8892. c. Conclusion: Reject the null hypothesis, indicating evidence that the population mean is less than 128.

To complete parts (a) through (c), we need to perform a hypothesis test for the given hypotheses

H0: μ = 128 (null hypothesis)

HA: μ ≤ 128 (alternative hypothesis)

Given: X= 119 (sample mean)

σ = 27 (population standard deviation)

n = 46 (sample size)

α = 0.10 (significance level)

a. The decision rule is to reject the null hypothesis if the calculated value of the test statistic is less than or equal to the critical value(s) of the test statistic. Since the alternative hypothesis is one-sided (μ ≤ 128), we will use a one-sample z-test and compare the calculated z-value with the critical z-value.

To find the critical z-value, we need to determine the z-value corresponding to the significance level α = 0.10. Looking up the critical value in the standard normal distribution table, we find that the critical z-value is -1.28 (rounded to two decimal places).

b. The calculated value of the test statistic, in this case, is the z-value. We can calculate the z-value using the formula

z = (X - μ) / (σ / √n)

Substituting the given values:

z = (119 - 128) / (27 / √46) ≈ -1.8892 (rounded to two decimal places)

c. The conclusion is based on comparing the calculated value of the test statistic with the critical value. Since the calculated z-value of -1.8892 is less than the critical z-value of -1.28, we have enough evidence to reject the null hypothesis. Therefore, we conclude that the population mean is less than 128.

The conclusion statement in part (c) is inconsistent with the given alternative hypothesis and should be revised accordingly.

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