Write a​ slope-intercept equation for a line passing(3,-2) through the point that is parallel to the line 3X+4Y= 9. Then write a second equation for a line passing through the point (3,-2) that is perpendicular to the line 3X+4Y= 9.

______________________________

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Answer:Answer and Explanation: An algebraic expression for the phrase '6 more than the product of 8 and n' is '8n + 6.

Step-by-step explanation:

The given slope of the graph is explaining about the swimmer's lap completion throughout the time of 10 minutes.

In the given graph on the x-axis, we can find the time (in minutes) of 10 minutes.

On the y-axis, the graph represents the number of laps the swimmer is completing.

When we observe closely, the slope is giving very important information. At initial time=0, the no. of laps remaining for swimmer is 30. We can show this data clearly as below:

Number of laps remaining----------Time (in minutes)

30 --- 0

27 --- 1

24 --- 2

21 --- 3

18 --- 4

15 --- 5

12 --- 6

9 --- 7

6 --- 8

3 --- 9

0 --- 10

From the above slope data, we can conclude that for every 1 minute of time elapsing, the swimmer is completing 3 laps.  

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The calculated length of XY in the right triangle XYZ is 6

From the question, we have the following parameters that can be used in our computation:

The right triangle

The value of XY in the right triangle can be calculated using the following sine ratio

sin(30) = XY/XZ

So, we have

sin(30) = XY/12

Cross multiply the equation

So, we have

XY = 12 * sin(30)

Evaluate the products

XY = 6

Hence, the length of XY in the right triangle is 6

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Answer:

1 out of 6

Step-by-step explanation:

Each roll of the die is an independent event. This means that the second roll does not rely on the first roll. The probability of rolling a six is one out of six. The probability of rolling a two is also one out of six. Since the two events are independent of each other, you would take the average of the two probabilities, which since they are both one out of six, the probability of rolling a six and then a two is one out of six.

There are 25% chance of 5 more people in the party.

Hence option (a) is correct.

Relative frequency = (number of times of occurrence of an event )/ (number of trials)

For the given table

relative frequency for 1 people = 0.05 = 5%

relative frequency for 2 people = 0.46 = 46%

relative frequency for 3 people = 0.18 = 18%

relative frequency for 4 people = 0.22 = 22%

relative frequency for 5 people = 0.06 = 6%

relative frequency for 6 people = 0.03 = 3%

Since relative frequency for 1 people is 5%

Therefore,

Relative frequency for 5 people is = 5x5%

                                                         = 25 %

Hence,

Relative frequency of 5 more people 25%.

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The area of the similar triangle B is derived to be equal to 1.8 which makes option B correct.

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

We shall represent the hight of triangle B with the letter h so that;

h/2 = 3/5

h = (2 × 3)/5 {cross multiplication}

h = 1.2

area of triangle B = 1/2 × 3 × 1.2

area of triangle B = 1.8

Therefore, the area of the similar triangle B is derived to be equal to 1.8

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Simplifying further, you can move any negative exponents to the denominator by changing their sign:

t⁻² u⁻⁶ v⁴ = v⁴ / (t² u⁶)

what is denominator  ?

In a fraction, the denominator is the bottom number that represents the total number of equal parts into which the whole is divided. For example, in the fraction 3/4, the denominator is 4, which indicates that the whole has been divided into four equal parts.

In the given question,

When multiplying two terms with the same base, you can add their exponents, so:

t⁻¹ u v⁴* t⁻¹ u⁻⁷ v⁰ = t⁻² u⁻⁶ v⁴

Simplifying further, you can move any negative exponents to the denominator by changing their sign:

t⁻² u⁻⁶ v⁴ = v⁴ / (t² u⁶)

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The polynomial function of degree 3 with leading coefficient 1 and zeros at -5, 0, and 6 is f(x) = x³ - x² - 30x.

To find a polynomial function of degree 3 with leading coefficient 1 and zeros at -5, 0, and 6, we start by using the factor theorem. This theorem tells us that if a polynomial function has a zero at some value c, then it is divisible by the linear factor (x - c).

Therefore, the polynomial with zeros at -5, 0, and 6 can be written as:

f(x) = a(x + 5)(x - 0)(x - 6)

where a is a constant coefficient that we need to determine. Since the leading coefficient of the polynomial is 1, we set a = 1.

Multiplying out the factors, we get:

f(x) = (x + 5)(x)(x - 6)

= x³ - x² - 30x

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Answer:

The discriminant is:

(-3)^2 - 4(1)(18) = 9 - 72 = -63

Since this discriminant is negative, f(x) does not have any real number solutions.

Answer:

6

Step-by-step explanation:

To find the highest price Jenny can charge to earn $125 in profit, first write an equation.

total profit = profit per card * number of cards

You want to know when Jenny will earn $125 in profit, and the price per card, x, is the variable. The expression 0.7x represents the profit per card.

125=0.7x(–15x+120)

Now, solve for x. Start by writing the equation in standard form

125=0.7x(–15x+120)

125= –10.5x2+84x

0= –10.5x2+84x–125

Now to solve for x, you can use the quadratic formula with a= – 10.5, b=84, and

So, to the nearest dollar, the highest price Jenny can charge per card to earn $125 in profit is $6.0236 or $6.

A.15/22 is the correct answer.

The correct answer is:

A. 15/22, represents a proper fraction.

Here, we have,

A proper fraction is a fraction where the numerator (the top number) is smaller than the denominator (the bottom number).

Out of the given options, only option A,

15/22, represents a proper fraction because 15 is smaller than 22.

Therefore, the correct answer is:

A. 15/22, represents a proper fraction.

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Answer: The odds against selecting a diamond are 3:1 (or 3/4)

Step-by-step explanation: Which means that there are 3 ways to not select a diamond and only 1 way to select a diamond. The odds in favor of selecting a diamond are 1:3 (or 1/4), which means that there is only 1 way to select a diamond and 3 ways to not select a diamond.

The journal entry to record the transaction is given:

Account Debit Credit

Cash $464,000

Common Stock, $3 par value $87,000

Paid-in capital in excess of par  $377,000

A journal entry is used to record a business transaction in the accounting records of a business.

A journal entry is usually recorded in the general ledger. Alternatively, it may be recorded in a subsidiary ledger that is then summarized and rolled forward into the general ledger

Assuming the shares have a $3 par value and sell for $16 cash per share:

Cash reeived from issuance of 29,000 common shares = 29,000 x $16 = $464,000

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The perimeter and area of the square are 24√2 units and 12 units² respectively

To determine the perimeter and area of the square, we have to find the lengths of the sides.

But since we have the midpoints of all the sides, we can assume they're equidistant from one another since the figure is a square.

SQ = √(x₂ - x₁)² + (y₂ - y₁)²

SQ = √(2 - (-4)² + (5 - 11)²

SQ = 6√2

Let's find for QU

QU = √(-4 - 2)² + (-1 - 5)²

QU = 6√2

Let's find for UA ;

UA = √(-10 - (-4))² - (5 - (-1)²

UA = 6√2

And the distance from AS = 6√2

The perimeter of the square = 4 * (6√2)

Perimeter = 24√2 units

The area of the square is l²

Area of the square = (6√2)²

Area of square = 12 units²

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The model rocket will have a height of 30 meters at a time of 0.523 seconds and 11.477 seconds, respectively.

In this problem we have the case of a model rocket being launched, the height of the rocket in time is described by the following quadratic equation:

h(t) = 60 · t - 5 · t²

Where:

We need to determine the time associated to a given height of 30 meters above the ground. If we know that h(t) = 30, then the times are, respectively:

30 = 60 · t - 5 · t²

6 = 12 · t - t²

t² - 12 · t + 6 = 0

(t - 11.477) · (t - 0.523) = 0

t = 11.477 s. or t = 0.523 s.

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The side that corresponds to uv is LK

The scale factor is 3 : 1

To solve for the scale factor between two geometric figures, follow these steps:

Identify corresponding sides or corresponding lengths between the two figures.

Choose one pair of corresponding sides and write a proportion using the lengths of those sides.

Solve for the scale factor by simplifying the proportion.

The shape in UV occupies the space of 6 boxes

The space in LK is made of 2 boxes

Hence we have 6 : 2

= 3 : 1

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The answer

4.16666667 yards

a. The equation whose solutions are the points of intersection of the graphs is y = -0.14x + 0.80.

b. The points of intersection are (-0.827, 0.918) and (0.951, 0.675).

The solution has been obtained using the slope - intercept form.

What is the slope - intercept form?

When you are aware of the slope of the line being investigated and the given point is also the y intercept, use the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is represented by the symbol b in the equation.

a. From the graph, we have two points of intersection.

Using this, we get the slope as;

m = -0.14

Now, using the slope intercept form, we get the intercept as

b = 0.80

So, the equation comes out to be

y = -0.14x + 0.80

b. The graph of the equations have been attached below.

From the graph, we get the points of intersection as (-0.827, 0.918) and (0.951, 0.675). Both the points have their x-coordinate within the interval [0, 2).

Hence, the required solutions have been obtained.

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The function f(x,y) = x² + y² has a minimum value of 0 at the point (0,0) and has no maximum value.

What is a function?

A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.

The function f(x,y) = x² + y² represents the sum of the squares of the variables x and y. To find the extreme values of this function, we need to take the partial derivatives with respect to x and y and set them equal to zero.

∂f/∂x = 2x = 0

∂f/∂y = 2y = 0

From these equations, we can see that the critical point occurs at (x,y) = (0,0).

To determine whether this is the maximum or minimum, we can use the second partial derivative test. The second partial derivatives are:

∂²f/∂x² = 2

∂²f/∂y² = 2

∂²f/∂x∂y = 0

At (0,0), ∂²f/∂x² > 0 and ∂²f/∂y² > 0, so the critical point is a minimum.

Therefore, the function f(x,y) = x² + y² has a minimum value of 0 at the point (0,0) and has no maximum value.

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Applying the intersecting secants and chords theorem, the indicated measures in the circle is: HW = 35 units;   MN = 49.5 units.

To find the measures indicated, we will apply the intersecting secants and chords theorem to form an equation, then solve.

a. HZ * HW = HX * HY [based on the intersecting secants theorem]

Plug in the values:

16.8 * HW = 14 * 42

HW = 588/16.8

HW = 35 units

b. VK * VJ = VM * VN [based on the intersecting chords theorem]

Plug in the values:

27 * 18 = 36 * VN

VN = 486/36

VN = 13.5 units

MN = VM + VN = 36 + 13.5

MN = 49.5 units

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The equation of the circle in this problem is given as follows:

x² + y² = 90000

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.

The center for this problem is given as follows:

(0,0).

The radius is given as follows:

300 ft.

Hence the equation is of:

x² + y² = 90000

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Chebyshev's inequality is a statistical tool that provides a bound on the probability that a random variable deviates from its mean by a certain amount. It can be used to determine whether there is statistical evidence to support a hypothesis based on sample data.

Suppose we have a random variable D that represents the proportion of defective lightbulbs in a population. We want to test the hypothesis that the average proportion of defective lightbulbs in the population is greater than 0.10, i.e., H₀: D ≤ 0.10 vs H₁: D > 0.10. Let's assume that we have a sample of n lightbulbs and that the sample proportion of defective lightbulbs is W.

Chebyshev's inequality states that for any random variable X, the probability that X deviates from its mean by k standard deviations is at most 1/k². In other words,

P(|X - μ| ≥ kσ) ≤ 1/k²,

where μ and σ are the mean and standard deviation of X, respectively.

Now, let's apply Chebyshev's inequality to our sample proportion W. Since we don't know the true mean and standard deviation of D, we can use the sample mean and sample standard deviation as estimates. The sample mean is W/n and the sample standard deviation is √[W(1-W)/n]. We want to find the probability that D is greater than 0.10, which is equivalent to finding the probability that W/n is greater than 0.10.

Let k = (0.10 - W/n)/(√[W(1-W)/n]). Then,

P(D > 0.10) = P(W/n > 0.10) = P(W - 0.10n > 0) = P(W - μ ≥ (0.10 - μ)n) ≤ σ²/[(0.10 - μ)n]²,

where μ = E(W) = D and σ² = Var(W) = D(1-D)/n. Thus,

P(D > 0.10) ≤ D(1-D)/n[(0.10 - D)n]².

To decide whether there is statistical evidence to support the hypothesis H₁, we need to compare this upper bound on the probability of D being greater than 0.10 to the significance level α = 0.05. If the upper bound is less than α, then we reject the null hypothesis H₀ in favor of the alternative hypothesis H₁.

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The square cake can be distributed in such a way that each person out of 15 guest may get 8  , with the least amount left over .

The Correct option is (1).

What is Volume of any shape?

The volume of an object is the amount of space occupied by the object or shape, which is in three-dimensional space. It is usually measured in terms ofof cubic units.

First find the volume of square cake,

Volume = l x b x h

= 8 x 8 x 2

=128

Now there are total 15 guests, Each of get

=

=  8.533

2.Volume of round cake (d= 6 inch, r=3 inch, h= 3 inch)

Volume=

=

=

=28.26  

Now there are total 15 guests, Each of get

=

= 1.884

3.Volume of round cake (d= 8 inch, r=4inch, h= 3 inch)

Volume=

=

=

=50.24  

Now there are total 15 guests, Each of get

=

=  3.349

4. Volume = l x b x h

= 6 x 9 x 2

=108

Now there are total 15 guests, Each of get

=

=  7.2

According to question each person may get 8 .

Only the square cake can be distributed in such a way that each person may get 8 , with the least amount left over .

Harriet ate a total of 3/4 of the total pizza

Given data ,

On Monday Harriet ate 1/4 of a 8 slice of pizza

And , on Tuesday she ate 1/2 of the same pizza

Now , If the pizza has 8 slices, then Harriet ate 1/4 of 8 slices on Monday, which is 2 slices.

On Tuesday, Harriet ate 1/2 of the same pizza, which is 4 slices.

So, in total, Harriet ate 2 + 4 = 6 slices of pizza

On simplifying the equation , we get

The whole pizza has 8 slices, so Harriet ate 6/8 of the pizza, which simplifies to 3/4.

Hence , Harriet ate 3/4 of the whole pizza

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Answer: The volume of the prism is 4200 cubic units.

Explanation:

The volume of a prism is given by the formula V = Bh, where B is the area of the base and h is the height. For a hexagonal base with a side length of 10, we can divide it into six equilateral triangles with side lengths of 10. Each equilateral triangle has an area of (1/2)bh, where b is the base and h is the height. Since the base of each equilateral triangle is also 10, we have:

Area of one equilateral triangle = (1/2)(10)(10√3/2) = 50√3

Area of the hexagonal base = 6 times the area of one equilateral triangle = 6(50√3) = 300√3

Now we can use the formula for the volume of a prism:

V = Bh = (300√3)(14) = 4200 cubic units.

Therefore, the volume of the prism is 4200 cubic units.

Answer:

  a) 10:30 a.m.

  b) 75 km/h

Step-by-step explanation:

You want to know the leaving time and speed of a car from Woodlands to Muar if it left half an hour later and arrived half an hour earlier than a coach that traveled the 150 km distance at a speed of 50 km/h and arrived at 1 p.m..

The travel time of the coach is found from the relation ...

  time = distance/speed

  time = (150 km)/(50 km/h) = (150/50) h = 3 h

Then the coach left Woodlands at ...

  1 pm -3 h = 10 am

The car left half an hour later than the coach, so left at 10:30 a.m..

The car arrived at Muar at 12:30 p.m. so had a travel time of ...

  12:30 -10:30 = 2 h

The speed over the 150 km distance is given by ...

  speed = distance/time

  speed = (150 km)/(2 h) = (150/2) km/h = 75 km/h

The average speed of the car was 75 km/h.

__

Additional comment

The car passed the coach at 11:30 a.m., when both had covered half the distance.

The correct answers for the quadratic equation are:

Roots of a quadratic equation are the points where y = 0.

Abscissa of a quadratic equation are the points where x = 0.

If the equation of a quadratic equation is in the vertex form,

         y = a(x - h)² + k

         Vertex of the U-shaped curve will be (h, k)

Given in the question, where the equation of the u-shaped curve is
y = 2x(x - 11)

Convert the equation in the vertex form,

y = 2x² - 22x

y = 2(x² - 11x)

y = 2 *  (x² - 2 ( 5.5x) + (5.5)² - (5.5)²)

y = 2[(x - 5.5)² - 30.25]

y = 2(x - 5.5)² - 60.5

Hence, the vertex of the U-shaped curve will be (5.5, -60.5).

For x-intercepts,

Substitute y = 0,

0 = 2x(x - 11)

⇒ x = 0, 11

   Therefore, roots of the parabola will be (0, 0) and (11, 0).

and the  ordinate of the vertex is x = 5.5

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The resulting function is given as follows:

[tex]y = \frac{e^{2x}}{3} - 2[/tex]

The parent function in the context of this problem is given as follows:

[tex]y = e^{-2x}[/tex]

When the function is vertically compressed by a factor of 3, we have that it is divided by three on the range, hence:

[tex]y = \frac{e^{-2x}}{3}[/tex]

When the function is reflected across the x-axis, we multiply by -1 on the domain, hence:

[tex]y = \frac{e^{2x}}{3}[/tex], as -2x x -1 = 2x.

When it is shifted down two units, we subtract by two on the range, hence:

[tex]y = \frac{e^{2x}}{3} - 2[/tex]

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The distance between the zeros of the equation [tex](2x-8)^{2}[/tex] - 4 = 12 is 4 units.

First, we can simplify the equation  [tex](2x-8)^{2}[/tex] - 4 = 12 by adding 4 to both sides:

[tex](2x-8)^{2}[/tex] = 16

Next, we can take the square root of both sides:

2x-8 = ±4

Solving for x in each case, we get:

2x-8 = 4: 2x = 12 → x = 6

2x-8 = -4: 2x = 4 → x = 2

So the zeros of the equation are x=6 and x=2. The distance between them is:

distance = |6 - 2| = 4

As a result, there are 4 units between zeros of the equation [tex](2x-8)^{2}[/tex] - 4 = 12.

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