What is the slope of the line through ( 10, 1) and (0,4)?

khan Academy ​

Answer:

Nice job dude

Step-by-step explanation:

The rectangular coordinates (in simplest radical form) are (2, -2√3).

To convert polar coordinates (r, θ) into rectangular or Cartesian form (x, y), we can use the following formulas:

x = r * cos(θ)

y = r * sin(θ)

In this case, the polar coordinates are (4, 5π/3). Therefore, we have:

r = 4

θ = 5π/3

Using the formulas, we can calculate the rectangular coordinates as follows:

x = 4 * cos(5π/3)

y = 4 * sin(5π/3)

To evaluate cos(5π/3) and sin(5π/3), we can use the unit circle or trigonometric identities.

In the unit circle, we know that cos(5π/3) = cos(π/3) = 1/2, and sin(5π/3) = -sin(π/3) = -√3/2.

Substituting these values into the formulas:

x = 4 * (1/2) = 2

y = 4 * (-√3/2) = -2√3

Therefore, the rectangular coordinates (in simplest radical form) are (2, -2√3).

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Given question is incomplete, the complete question is below:

Convert the polar coordinates (4, 5π/3) into rectangular form. Express your answer in simplest radical form.

\(\left(\dfrac x5 \right)^2 = \dfrac{x^2}{5^2} = \dfrac{x^2}{25}\)

Answer:

the amount of alex's monthly payment.

Step-by-step explanation:

he will need to pay each new month the same amount after a while.

The meaning of the slope in this equation will be ''the monthly payment pay by Alex for a new cell phone''.

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Alex bought a new cell phone.

And, The amount that he will have to pay the cell phone company, C, is described by the equation;

⇒ C=24m+75

Where, m represents the number of months during which Alex will make payments.

Now,

Since,  The amount that he will have to pay the cell phone company, C, is described by the equation;

⇒ C = 24m+75

Where, m represents the number of months during which Alex will make payments.

Here, The value of slope = 24

Clearly, This represents the monthly payment pay by Alex for a new cell phone.

Thus, The meaning of the slope in this equation will be ''the monthly payment pay by Alex for a new cell phone''.

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a. Time-invariant (no time-variable terms)

b. Time-variable (t² is time-variable)

c. Time-invariant (no time-variable terms)

d. Time-invariant (no time-variable terms)

e. Time-invariant (no time-variable terms)

A linear differential equation is one that involves only linear combinations of the dependent variable and its derivatives, as well as any coefficients that are functions of the independent variable (time in this case).

In the first equation, +2y=0, there are no terms that involve the independent variable, so this is a time-invariant equation.

In the second equation, (t²y)'=0, there is a term involving the independent variable t, specifically t². Therefore, this equation is time-variable.

In the third equation, y''+y'=-t+1, there are two terms involving the independent variable, namely -t and 1. Therefore, this equation is time-variable.

In the fourth equation, (cos(t)y)'=0, there is a term involving the independent variable t, specifically cos(t). Therefore, this equation is time-variable.

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Answer:

200 students must agree to attend in order for the school to have the festival.

Step-by-step explanation:

200 is 40% of 500. We can also use fractions to figure this out.

\(\frac{40}{100} =\frac{x}{500}\)

For 100 to become 500 it must be multiplied by 5. And whatever we do to the denominator we have to do to the numerator. So we multiply 40 × 5 = x

x = 200

\(\frac{40*5}{100*5} = \frac{x}{500}\)      

\(\frac{40}{100} =\frac{200}{500}\)

The maximum area of the rectangle inside the ellipse is 2ab.

Given that,

Ellipse = x2 / a2 + y2 / b2 = 1

we know the general coordinates of any point in an ellipse of the equation

x2 / a2 + y2 / b2 = 1 is (acosθ,bsinθ)

So, we take general vertices of rectangles as

(acosθ,bsinθ), (acosθ,-bsinθ), (-acosθ,bsinθ), and (-acosθ,-bsinθ)

So, we can see that length and breadth of the rectangle is 2acosθ and 2bsinθ

So, its area will be ab4sinθcosθ (Length x Breadth)

Applying trigonometric formula 2sinθcosθ=sin2θ, let area equals to A

Now A=2absin2θ

Now as the area is the maximum given in the question, we have to differentiate it with respect to θ

dA/dθ=2abcos2θ×2 (using dsin2θ / dθ=2cos2θ)

Equating dA / dθ=2abcos2θ×2=0, it means cos2θ=0 , which means 2θ =  π / 2 and θ=π / 4

So now we to put θ=π / 4 in the equation of area which is A=2absin2θ

We get as A=2absin2π / 4=2absinπ / 2=2ab

Hence the max area of the rectangle inside the ellipse is 2ab.

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Answer: do 8 x 12

Step-by-step explanation:

Answer:

48cm^2

Step-by-step explanation:

(b*h)/2 -> (8*12)/2 -> 96/2 = 48 cm^2

Answer:

1 = B, 2 = B, 3 = C

Step-by-step explanation:

1) When there are same digits with exponents being multiplied, you add the exponents

2) When an exponent is being distributed through a parenthesis, you multiply

3) When there are same digits with exponents being divided, you subtract the exponents

3×4 + ½ ×3×4 + 1×4 + ½×3×4

12 + 6 + 4 + 6

18+ 10

28units²

Answer: y= 3/2x - 6

Step-by-step explanation:

The equation is y=mx + b

The y-intercept is when x = 0, so on the table y-intercept = -6

The slope is rise/run, we see that y increase by three and x increase by 2, so the slope is 3/2

to get the slope of any straight line, we simply need two points off of it, let's use those ones in the picture below.

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}} \implies \cfrac{3 +3}{4} \implies \cfrac{ 6 }{ 4 } \implies {\Large \begin{array}{llll} \cfrac{3 }{ 2 } \end{array}}\)

now, the y-intercept occurs when x = 0, recheck the picture below.

Answer: 11/3 (fraction) 11 goes on top 3 bottom

​

Step-by-step explanation:

Answer:

\(x\approx136.143\)

Step-by-step explanation:

\(ln(3x-5)=6\)

\(3x-5=e^{6}\)

\(3x=e^6+5\)

\(x=\frac{e^6+5}{3}\)

\(x=136.1429312\)

\(x\approx136.143\)

Answer:

Step-by-step explanation:

Answer:

The first option. "If lines on a coordinate plane have opposite reciprocal slopes, then they are perpendicular."

Step-by-step explanation:

It is the only one that makes sense, tbh. But, it includes the proper "if-then" form like the question requests it have. It also incorporates all aspects of the original statement-

a.) lines on a coordinate plane

b.) perpendicular

c.) opposite reciprocal slopes.

You're welcome. :D

Answer:

Its A

Step-by-step explanation:

edge 2021

Answer:

Step-by-step explanation:

Given :-

To Find :-

Solution :-

We know that,

Substituting the values, we get:

↠ Perimeter = 2(9 + 7)

↠ Perimeter = 2(16)

↠ Perimeter = 32 feet

Now,

Substituting the values, we get:

↠ Area = 9 × 7

↠ Area = 56 ft²

Hence,

The correct answer of the operation is option B: 4x^2 - 9.

To perform the operation (2x-3)(2x+3), we can use the FOIL method, which stands for First, Outer, Inner, Last. Let's go through the steps:

First: Multiply the first terms of each binomial.

(2x)(2x) = 4x^2

Outer: Multiply the outer terms of each binomial.

(2x)(3) = 6x

Inner: Multiply the inner terms of each binomial.

(-3)(2x) = -6x

Last: Multiply the last terms of each binomial.

(-3)(3) = -9

A binomial is a two-term algebraic expression that contains variable, coefficient, exponents and constant, a binomial is an expression that has two unlike terms connected through an addition or subtraction operator in between.  

Now, let's combine the like terms:

4x^2 + 6x - 6x - 9

Notice that the terms 6x and -6x cancel each other out.

Simplifying further, we have:

4x^2 - 9

The correct answer is option B: 4x^2 - 9.

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Statement (c) is correct for a simple graph. Every trail is a path, and every path is a trail.

In graph theory, a simple graph is an undirected graph with no loops or multiple edges between the same pair of vertices. A path in a graph is a sequence of vertices where each consecutive pair is connected by an edge. A trail in a graph is a path that allows for repeated vertices and edges.

Statement (a) is not correct because not every path is a trail. A path does not allow for repeated vertices or edges, whereas a trail does.

Statement (b) is not correct because not every trail is necessarily a path. A trail may contain repeated vertices or edges, but a path does not.

Statement (d) is not correct because paths and trails do have a relation. A trail is a more general concept that encompasses paths by allowing for repetition of vertices and edges.

Therefore, statement (c) is the correct statement. In a simple graph, every trail is a path, and every path is a trail.

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Answer:

Step-by-step explanation:

The function f(w) is the difference of c(w) and a(w):

Correct choice is C

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path. This is formalized by using the →(if-then) and ∧(logical and) operators.

Given information and corresponding atomic propositions:

We need to formalize the given statements in terms of atomic propositions r, b, and w, which are defined as follows:

r: Rabbits have been seen in the area.

b: Berries are ripe along the path.

w: Walking on the path is safe.

Now, let us formalize each of the given statements in terms of these atomic propositions:

a) Berries are ripe along the path, but rabbits have not been seen in the area.

b: Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.

c: If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.

d: It is not safe to walk along the path, but rabbits have not been seen in the area, and the berries along the path are ripe.

e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path.

The formalizations in terms of atomic propositions are:

a) b ∧ ¬r.b) ¬r ∧ w ∧

b.c) (b → w) ∧ (¬r → w).

d) ¬w ∧ ¬r ∧

b.e) (¬r ∧ ¬b) → w.b ∧

Berries are ripe along the path, but rabbits have not been seen in the area.

This is formalized by using the ∧(logical and) operator.

(¬r ∧ ¬b) → w: It means For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

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Complete Question

The reading speed of second grade students in a large city is approximately normal, with a mean of 90 words per minute (wpm) and a standard deviation of 10 wpm.

What is the probability that a random sample of 12 second grade students from the city in a mean reading rate of more than 96 words per minute?

Answer:

\(P(\=x >96 )=0.01884\)

Step-by-step explanation:

From the question we are told that:

Sample size \(n=12\)

Sample mean \(\=x =90\)

Standard Deviation \(\sigma=10\)

Generally

\(\sigma_x=\frac{\sigma}{\sqrt{10}}\)

\(\sigma_x=\frac{10}{\sqrt{12}}\)

\(\sigma_x=2.887\)

Generally the equation for P(\=x >96 ) is mathematically given by

\(P(\=x >96 )=P(Z>\frac{\=x-\mu_x}{\sigma_x})\)

\(P(\=x >96 )=P*(Z>\frac{90-96}{2.887})\)

\(P(\=x >96 )=1-P(Z<2.08)\)

\(P(\=x >96 )=1-0.98116\)

\(P(\=x >96 )=0.01884\)

The farmer would need to weigh the tomatoes before packing them into packages of 10. She would need to ensure that each tomato weighs close to 0.5 ounces or 5 ounces per package.

This could be done using a weighing scale that is accurate to at least one decimal place.The farmer could also sort the tomatoes by size to ensure that they are all of similar size. This could be done by using a sorting machine or by manually sorting them by size.

The farmer could also visually inspect the tomatoes to ensure that they are all of similar size. This would ensure that each package contains tomatoes of similar size.

To ensure that the tomatoes are of similar size, the farmer could sort the tomatoes by size. This could be done by using a sorting machine or by manually sorting them by size. Once the tomatoes have been sorted, the farmer would need to weigh them to ensure that each package contains tomatoes of similar weight. This could be done using a weighing scale that is accurate to at least one decimal place.

The farmer could also visually inspect the tomatoes to ensure that they are all of similar size. This could be done by comparing them to a standard size. The standard size could be a tomato of known weight or a template of the desired size. Once the tomatoes have been sorted and weighed, they can be packed into packages of 10.

The farmer would need to ensure that each package contains tomatoes of similar weight. This would ensure that the customers receive packages of tomatoes of similar size and weight.

To ensure that the tomatoes are of similar size and weight, the farmer would need to sort them by size and weigh them before packing them into packages of 10. The farmer could use a sorting machine or manually sort them by size. The tomatoes could be weighed using a weighing scale that is accurate to at least one decimal place.

The farmer could also visually inspect the tomatoes to ensure that they are all of similar size. This would ensure that the customers receive packages of tomatoes of similar size and weight.

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The distance travelled from Buffalo to Cleveland if the total cost of the move is $724.85 is  479.97

The base cost of the rental is said to be 49.95 dollars + 1.19 per mile

The cost of the gas is $3.89. The mileage of the truck is 18 miles

There would be an extra cost of

$3.89/18 per mile.

= 0.216111

In x miles we would have the equation that is written as:

C(x) = 49.95 + (1.19 + 0.21611)x

C(X) = $724.85 this is the total cost. Hence we would have

$724.85 =  49.95 + 1.19x + 0.21611x

$724.85 -   49.95 = 1.40611x

674.9 = 1.40611x

divide through by 1.40611

674.9 / 1.40611 = x

x = 479.97

The distance traveled is  479.97

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Therefore, the measure of angle SQR is.   \(156-6y=26\)   degrees.

A triangle is a three-sided polygon, which means it is a flat shape with straight sides. Triangles are one of the basic shapes in geometry and can be identified by their three sides and three angles. The sum of the interior angles of a triangle is always 180 degrees, and there are various types of triangles based on their side lengths and angle measurements, including equilateral, isosceles, scalene, acute, obtuse, and right triangles. Triangles are used in many areas of mathematics and science, as well as in everyday life, such as in construction and design.

To find the measure of angle SQR, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Therefore:

Angle QRS + Angle RSQ + Angle SQR = 180

Substituting the given values, we get:

\((2y + 16) + (4y + 8) + Angle SQR = 180\)

Simplifying and solving for Angle SQR, we get:

\(Angle SQR = 180 - (2y + 16) - (4y + 8)\)

\(= 180 - 6y - 24\)

\(= 156 - 6y\)

\(= 26\)

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Work Shown:

cot(theta) = cos(theta)/sin(theta)

cot(theta) = x/y

cot(theta) = -4/(-2)

cot(theta) = 2

Answer: x = 14

Step-by-step explanation: 14 minus 12 is 2

Answer:

the line starts on (0,3) then you go down 7 points then you go 3 to the right that's thew answer

Step-by-step explanation:

Answer: the y axis is 3 and the x axis is 1

Step-by-step explanation:

The null hypothesis (H0) and the alternative hypothesis (Ha) for the given situation are H0: The distribution of the number of people who choose each day of week for quality family time is uniform.

Ha: The distribution of the number of people who choose each day of the week for quality family time is not uniform. The test statistic is x² = 1558.896.

The critical value for the test can be determined by using the chi-square distribution table with degrees of freedom df = (Num Categories - 1) = 6. Using the chi-square distribution table with df = 6 and a significance level of α = 0.05, the critical value is 12.592. As x² > 12.592, we can reject the null hypothesis. Hence, we can conclude that there is sufficient evidence to suggest that the distribution of the number of people who choose each day of the week for quality family time is not uniform.

We are given that a random sample of 765 subjects was asked to identify the day of the week that is best for quality family time. We need to test the claim that the days of the week are selected with a uniform distribution. The null and alternative hypotheses for the given situation are H0: The distribution of the number of people who choose each day of the week for quality family time is uniform. Ha: The distribution of the number of people who choose each day of the week for quality family time is not uniform.

We are also given that Num Categories = 7, Test statistic, x² = 1558.896, Critical x² = 12.592, P-Value = 0.0000, Degrees of freedom = 6, and Expected Freq = 109.2857.The test statistic is x² = 1558.896. This value measures the difference between the observed and expected frequencies, and a large value indicates that the null hypothesis is unlikely to be true. The critical value for the test can be determined by using the chi-square distribution table with degrees of freedom df = (Num Categories - 1) = 6.

Using the chi-square distribution table with df = 6 and a significance level of α = 0.05, the critical value is 12.592. As x² > 12.592, we can reject the null hypothesis. This means there is sufficient evidence to suggest that the distribution of the number of people who choose each day of the week for quality family time is not uniform. Therefore, we can conclude that the claim that the days of the week are selected with a uniform distribution is not supported by the data.

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The length of the springboard, x is  28.2. The correct option is (4).

We can say that the length of the springboard (x) is the hypotenuse of a right triangle, where the opposite side is the height of the spring (8 inches) and the angle opposite the height is 16.5 degrees.

Using trigonometry, we can write:

sin(16.5) = 8 / x

Multiplying both sides by x, we get:

x * sin(16.5) = 8

Dividing both sides by sin(16.5), we get:

x = 8 / sin(16.5)

Using a calculator, we can evaluate this expression to the nearest tenth of an inch as:

x ≈ 28.2

Therefore, the length of the springboard to the nearest tenth of an inch is approximately 28.2 inches. The answer is option (4).

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Answer:

-2

Step-by-step explanation:

Answer:

(see below)

Step-by-step explanation:

You can also solve this algebraically:

–5 – (–3)

–5 + 3

–2

Since it can't be negative units between two points on a number line, you can multiply it by –1 to make it a positive number:

–2 (–1)

2 units

Or, you can use a number line. I have screenshotted a number line attached below for you.

Hopefully this helps!