Rational equations from algebra 2. Please provide steps. You don't have to solve all of the equations, any one of them will help. Thank you!

Using the relation between velocity, distance and time, it is found that:

a. The equation used to find the distance of the flowerbed from the​ hive is: d = 540 feet per minute x 1.6 minutes.

b. The distance of the flower bed from the hive is: 864 feet.

Velocity is given by the distance divided by the time, as follows:

v = d/t

In the context of this problem, we have that:

The times are as follows:

The sum of this times is of 22 - 18 = 4 minutes, hence:

[tex]t_1 + t_2 = 4[/tex]

During the first step, that is, from hive to flowerbed, the velocity is 1.5 times greater than during the second step, thus the second time is 1.5 times the first time, that is:

[tex]t_2 = 1.5t_1[/tex]

Then the first time is calculated as follows:

[tex]1.5t_1 + t_1 = 4[/tex]

[tex]2.5t_1 = 4[/tex]

[tex]t_1 = \frac{4}{2.5}[/tex]

[tex]t_1 = 1.6[/tex]

The velocity during this time was of 9 feet per second = 540 feet per minute, for 1.6 minutes, hence the equation is:

d = v x t

d = 540 feet per minute x 1.6 minutes.

d = 864 feet.

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The parallel between 2 highlights is called eduidistand

Point A

(-16, 20)

Point B

(-16, -14)

The Distance Formula itself is actually derived from the Pythagorean Theorem which is a

The distance would be 34 units

From the ellipse equation

the length of the major axis is equal to 2a. By comparing this equation with the given one, we can note that

Then, the length of the major axis is 2x7 = 14

The sum equivalent to 7√28x⁶+4√7x⁶ is :

18√7x⁶ .

Given ,7√28x⁶+4√7x⁶,

To find sum in simplest form ;

7√28x⁶+4√7x⁶

By splitting to factors,

= 7√(7*4)x⁶+4√7x⁶

= 7*2√7x⁶+4√7x⁶

= 14√7x⁶+4√7x⁶

By factoring out like terms,

= 2√7x⁶(7+2)

= 2√7x⁶(9)

= 18√7x⁶

Therefore  sum is =  18√7x⁶.

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Using concept of Quadratic Equation we got that best ticket price is $16, maximum income is $19,200 and the corresponding number of tickets are 1200.

A Quadratic Equation is one of the following: f(x) = ax2 + bx + c, where a, b, and c are positive integers and an is not equal to zero. A parabola is basically a curve that represents the graph of a quadratic equation. Parabolas can open up or down, and their "width" or "steepness" can vary, but they all have the same basic "U" shape.

We know that,

No. of people who will buy tickets at $4 = 600

For each 20¢ decrease, additional no. of people buying tickets = 50

Revenue = (No. of tickets sold)(Pricing)

Revenue = (600+50x)(4+x)

= 50[tex]x^{2}[/tex] + 800x + 2400

Solving the quadratic equation we got,

x = -4 or -12

Since we're dealing with real-life entities such as money, we'll take the value of x as positive.

Taking x as 12 (higher value),

No. of tickets sold = 600 + 50x = 1200

Pricing = 4 + x = 16

Revenue = 1200×16 = $19,200

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The correct solution of the expressions are;

1. (14⁴)² × 14⁻⁶ / 14² = 1

2. 14⁻⁵ (14³)² 14⁻² = 1 / 14

3. (14³)⁴ (14⁻⁷)² = 1 / 196

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The expressions are,

1. (14⁴)² × 14⁻⁶ / 14²

2. 14⁻⁵ (14³)² 14⁻²

3. (14³)⁴ (14⁻⁷)²

Now,

The solutions of the expressions are find as;

1. (14⁴)² × 14⁻⁶ / 14² = 14⁸ × 14⁻⁶ / 14²

                            = 14⁸⁻⁶ / 14²

                            = 14² / 14²

                            = 14²⁻²

                            = 14⁰

                            = 1

And,

2. 14⁻⁵ × (14³)² × 14⁻² = 14⁻⁵ × 14⁶ × 14⁻²

                               = 14⁻⁵⁺⁶⁻²

                               = 14⁻¹

                               = 1 / 14

And,

3. (14³)⁴ (14⁻⁷)² = 14¹²  14⁻¹⁴

                     = 14¹²⁻¹⁴

                     = 14⁻²

                     = 1 / 14²

                     = 1 / 196

Therefore,

The correct solution of the expressions are;

1. (14⁴)² × 14⁻⁶ / 14² = 1

2. 14⁻⁵ (14³)² 14⁻² = 1 / 14

3. (14³)⁴ (14⁻⁷)² = 1 / 196

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The probability of the marksman hitting the long-range target in 5 shots is 0.1429.

The geometric distribution is a Bernoulli experiment that predicts the likelihood of the first success after a certain number of failures. Negative-binomial and binomial distributions are two different forms of Bernoulli trials.

P = 0.268

x = 5

Use the geometric probability mass function below to calculate the probability:

P(X = x) = [tex](1 - P)^{(x-1)}[/tex]× P

P(X = x) = [tex](1 - 0.268)^{(3-1)}[/tex]× 0.268

P(X = x) = 0.1429

The probability that it takes 5 shots for the marksman to hit the long-range target is 0.1429.

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The equivalent expression for the indices is 17⁻⁷ × 17⁵ is  1/17²

Index is the power or exponent which is raised to a number or a variable e.g in number 3⁵, 5 is the index of 3. The 3 is called the base. The plural form of index is indices.

We have different  Laws of Indices, but the one applicable to this question is the product law and reciprocal law.

Product law: To multiply two variables or numbers with the same base, we need to add their powers and raise them to that base":   5² x 5³ = 5²⁺³ = 5 and  P⁴ + P⁶ = P¹⁰

Reciprocal Law: If the index is a negative value, then it can be shown as the reciprocal of the positive index raised to the same variable:

8⁻² = 1/8²   and b⁻⁶ = 1/b⁶      

Let's use the two laws to create an equivalent expression for 17⁻⁷ × 17⁵:

17⁻⁷ × 17⁵ = 17⁻⁷ ⁺ ⁵  = 17⁻²  = 1/17²

Therefore, the equivalent expression for 17⁻⁷ × 17⁵ is  1/17². The 1st option is the answer.

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Answer:

the value of 2/3 ^-2 is 18

Given:

yearly salary=28,800

Required:

To calculate adjusted monthly income

Explanation:

student loan

250 dollar

The number of copies that can be made would be: 35 copies

We would have to solve this problem through the use of cross multiplication

such that we have 20 copies = 8 dollars

unknown copies ? = 14 dollars

This can be re written to be arranged in the form

20 = 8 dollars

? = 14 dollars

we would have to cross multiply

14 x 20 = 8 x ?

280 = 8?

divide through by 14

? = 280 / 14

= 20

Hence the copies that would be made is 35 copies for 14 dollars at the local print shop

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A function is called bijective if it is one-to-one and onto.

To check one to one, let x1 = x2 , where x1, x2 belongs to R.

so, we can say that:

and

Given the condition that x1 and x2 are not equal to 2. So, the above equation implies that

So, it is a one-to-one function.

For onto function, let y= (3x + 4) / (x-2). Now, interchange x and y, and solve the equation fo y:

Here, the domain of the inverse of the function is R - {3}. But the function is R - {2} => R. So, it is not onto.

thus, the given function is not a bijection.

a cup of all-purpose flour as an ingredient

White sugar, 2 tablespoons

Baking powder, two teaspoons

1 salt shaker, or as desired

a cup of milk

Vegetable oil, two tablespoons

1 beaten egg

Directions

In a sizable basin, mix the flour, sugar, baking soda, and salt. Pour the milk, oil, and egg into the center well that has been created. Blend until uniform.

Over medium-high heat, preheat a griddle or frying pan with a little oil. For each pancake, pour or scoop about 1/4 cup of batter onto the griddle; cook for 1 to 2 minutes, or until bubbles form and the edges are dry. The opposite side should be browned after flipping. Use the leftover batter to repeat.

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Answer:

y = - 2x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (3, - 7 ) into the partial equation

- 7 = - 6 + c ⇒ c = - 7 + 6 = - 1

y = - 2x - 1 ← equation of line

The identified acute angles in the diagram are: D. Angle WZY and angle WXY.

An acute angle can be described as any angle that has a degree measure that is below 90 degrees, in order words, it is smaller than a right angle.

For example, an acute angle is attached below, which is 62°, and it is less than a right angle or 90 degrees. Angles 30°, 45°, 60°, 75°, etc are all regarded as acute angles because they are less than a right angle or 90 degrees.

In quadrilateral WXYZ, the acute angles that are less than a right angle, and are below 90 degrees are: D. Angle WZY and angle WXY.

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Probability that an ace is pulled from the deck = A/T=4/52=1/13

52 cards are there in all.

Four aces are found in all of the card A's.

Thirteen spades in all.

Probability that an ace is pulled from the deck = A/T=4/52=1/13

likelihood that a spade will be the next card drawn =S/T=13/52=1/4

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​

The population mean, exists even comprehended as the average or mean of all values in a population, exist determined by summing all population values and dividing that total by the number of population values.

The population mean can be determined by dividing the total number of values in the given data/population by the sum of all values in the data/population. The whole sum of the numbers is referred to as summation. The sign μ stands for the population mean.

The population mean, also known as the average or mean of all values in a population, is determined by summing all population values (represented by the symbol X) and dividing that total by the number of population values (represented by the symbol N).

Therefore, the correct answer is option a. less than the population mean.

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Quinn got paid $121,560 in his first career and on switching, he made 55% less, i.e. he made 45% of his previous career.

This is because, if in a previous career he made 100%, then a 55% reduction in salary annually would mean, he is left with only 45%.

Let us suppose, previous salary as x

then, x= $121,560

so, 45% of x= 45% of $121,560

i.e. 45% of x= 45/100 x 121560

therefore, 45% of x= $54,702

Quinn makes $54,702 now.

Therefore, a reduction in 55% of earlier salary would mean that Quinn's salary reduced from $121,560 to $54,702

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If the swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, then the time taken to travel from point Z to point Y is 1.56 hours

The speed of the swamp vehicle = 3.2 miles per hour

From the figure we can see the two triangles ΔXVM and ΔXYZ

Here we have to use the ratio of the two similar triangles

The ratio will be

VW/WX = YZ/ZX

Substitute the values in the equations

10/6 = YZ/3

We have to find the distance from point Z to point Y

YZ = (10/6)×3

= 5 Miles

We know

Speed = Distance / Time

Time = Distance / speed

= 5/3.2

= 1.56 hours

Hence, if the swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, then the time taken to travel from point Z to point Y is 1.56 hours

The complete question is

You want to go on a swamp tour. How long does it take a swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, from point Z to point Y ?

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Cutting at less than a right angle to the axis but more than the angle made by the side of the cone produces an ellipse.

Therefore, with this above statement, the statement which best describes how to slice a cone so that the resulting cross-section is an ellipse is

A plane slicing the cone diagonally without intersecting the base

The correct option, therefore, is OPTION B

We can infer that we have sufficient evidence to reject the null hypothesis and that the true mean is significantly lower than 6.7 at 10% of significance if we compare the p value and the significance level given =0.05 and observe that p'.

Hypothesis test: A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis. We can make probabilistic claims regarding population parameters thanks to hypothesis testing.

Data are provided and noted.

X=6.8 display the sample mean

σ= 0.9 show the population's standard deviation.

n= 280 samples taken

μο=6.7 the value that we wish to test should be represented

α=0.1 signify the hypothesis test's level of significance.

The stat would be represented as z. (variable of interest)

p' indicate the test's p value (variable of interest)

Name the prevailing and competing hypothesis

The system of hypothesis must be tested to see if the true mean is below the criteria.

Null hypothesis:  μ ≥ 6.7

Alternative hypothesis: μ < 6.7

Applying a z test to compare the actual mean to the reference value is preferable if the sample size is greater than 30 and we are aware of the population variation. The statistic is given by:

z=(X-μο)/σ[tex]\sqrt{n}[/tex]  ......(1)

z-test: "enables the comparison of group means. One of the most widely used tests, it is used to determine whether the mean is (higher, lower, or not equal) to a given value ".

Calculate the statistic

We can replace in formula (1) the info given like this:

z=(6.8-6.7)/0.9[tex]\sqrt{280}[/tex]

P-value

Since is a one sided test the p value would be:

p'=p(z<0.0066)

We can infer that we have sufficient evidence to reject the null hypothesis and that the true mean is considerably lower than 6.7 at 10% of significance if we compare the p value and the significance level given =0.1 and observe that p'.

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The equation of the line that is parallel to k and passes through (-1, 3) is

- x + 2y = 7

The equation of a line can be represented in different form such as point slope form, slope intercept form and standard form.

Therefore, the equation of the line is parallel to k.

Parallel line shave the same slope.

Therefore, let's find the slope of k to find the slope of the equation of the line.

Hence, using (7, 2)(1, -1)

m = -1  - 2 / 1 - 7

m = - 3 / -6

m = 1/ 2

Therefore, the slope of the line is 1 / 2. Let's find the y-intercept using the point (-1, 3)

3 = 1 / 2(-1) + b

3 = - 1 / 2 + b

b = 3 + 1 / 2

b = 7 / 2

Hence, the equation is as follows;

y = 1  /2x + 7 / 2

2y = x + 7

2y - x = 7

- x + 2y = 7

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Answer:

Explanation:

An exponential decay function is generally given in the below;

where a = initial amount

r = percentage rate of decrease in decimal

t = number of years

Given the initial value of the book(a) as $57 and the percent decrease(r) as 12% which as a decimal is 0.12 (12/100), let's go ahead and substitute these values into the above formula and we'll have;

When t = 8, let's go ahead and solve for y;

The rate of change are:

a. 3 ft/min

b. 0.5 ft/min

c. -2.2 ft/min

The formula for finding the rate of change of a relationship is given as:

Rate of change = Change in y/change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

a. (2, 8) = [tex](x_1, y_1)[/tex]

(5, 17) = [tex](x_2, y_2)[/tex]

Rate of change = (17 - 8)/(5 - 2)

Rate of change = 9/3

Rate of change = 3 ft/min

b. (3.4, 6.8) = [tex](x_1, y_1)[/tex]

(7.2, 8.7) = [tex](x_2, y_2)[/tex]

Rate of change = (8.7 - 6.8)/(7.2 - 3.4)

Rate of change = 1.9/3.8

Rate of change = 0.5 ft/min

c. (3/2, - 3/4) = [tex](x_2, y_2)[/tex]

(1/4, 2) =  [tex](x_2, y_2)[/tex]

Rate of change = (2 - (-3/4))/(1/4 - 3/2)

Rate of change = 11/4 / -5/4

Rate of change = 11/4 × -4/5

Rate of change = -11/5 = -2.2 ft/min

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Answer:

1/26

Step-by-step explanation:

If the cards are all there, you can count there are 2 red threes. And there are 52 cards. The fraction is 2/52 or 1/26

We have:

These fractions are equal because the x is found by multiplying and it is as if we have this:

And as we already know: