1. What should be done to these equations to solve the system of equations by elimination? 2+y=12 5x - 3y = -3​

Step-by-step explanation:

Let x = m² and y = 4n.

Then m⁶ - 64n³ = x³ - y³

= (x - y)(x² + xy + y²)

= (m² - 4n)(m⁴ + 4m²n + 16n²).

The period of the function represented by the sinusoidal graph has a value of 0.7

Given that we have the graph of the sinusoidal function

By definition, the period of the function is the distance between cycles

i.e. the length of a cycle

From the given graph, we have

Initial = 0

Final = 0.7

So, we have

Period = 0.7 - 0

Period = 0.7

This can also be calculated from the equation as

Period = 2π/B

From the function, we have

B = 3π

This means that

Period = 2π/3π

Evaluate

Period = 0.67

When approximated, we have

Period = 0.7

So, the period is 0.7 (approximately)

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Answer:

(x−7,y+5)

A p e x n dat

z - 9 = 10(x - 5) - 8(y - 4) this is the equation of the tangent plane at the point (5, 4, 9). (x - 5)/10 = (y - 4)/(-8) = (z - 9)/(-1). These are the symmetric equations for the normal line to the surface at the given point.

(a) To find the equation of the tangent plane to the surface z = x^2 - y^2 at the point (5, 4, 9), we first need to find the partial derivatives with respect to x and y:

∂z/∂x = 2x
∂z/∂y = -2y
Now, we evaluate these at the given points (5, 4, 9):
∂z/∂x(5, 4) = 2(5) = 10
∂z/∂y(5, 4) = -2(4) = -8
Using the tangent plane equation:
z - z₀ = ∂z/∂x (x - x₀) + ∂z/∂y (y - y₀)
Plugging in the values:
z - 9 = 10(x - 5) - 8(y - 4)
This is the equation of the tangent plane at the point (5, 4, 9).

(b) The normal vector to the surface at the given point is given by the gradient vector (∂z/∂x, ∂z/∂y, -1) = (10, -8, -1). To find the symmetric equations for the normal line, we use the point-normal form:
(x - x₀)/a = (y - y₀)/b = (z - z₀)/c
Plugging in the point (5, 4, 9) and the normal vector components (10, -8, -1):
(x - 5)/10 = (y - 4)/(-8) = (z - 9)/(-1)
These are the symmetric equations for the normal line to the surface at the given point.

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Answer:

3(x-1)

Step-by-step explanation:

Let the number be 'x'

When I take away 1 , the number is x - 1.

When I multiply 3, the number is 3(x-1).

The number is 3(x-1).

The correct option is A. The volume is 6.77 cubic units

The function and interval given are f(x) = (x - 1)^-1/4 and the x-axis on the interval (1, 6].

We want to find the volume of the solid of revolution when the region is rotated about the x-axis.

Let's consider the graph of the function: graph{(x-1)^(-1/4) [-10, 10, -5, 5]}

To set up the integral to find the volume of the solid of revolution, we can use the disk method.

We need to integrate the area of each disk perpendicular to the x-axis from x = 1 to x = 6.

The area of a disk is given by the formula: A = πr²

where r is the radius of the disk and is equal to f(x) in this case.

Therefore, the area of a disk is: A = πf(x)²

Let's substitute f(x) into this formula and integrate from x = 1 to x = 6 to get the volume of the solid.

We have The integral that should be used to find the volume of the solid is given as:

V = ∫₁⁶ πf(x)² dx

We substitute f(x) = (x - 1)^(-1/4) into this expression and integrate to get the volume.

We have: V = ∫₁⁶ π(x - 1)^(-1/2) dx

Let u = x - 1, so that du/dx = 1 and dx = du.

When x = 1, u = 0, and when x = 6, u = 5.

Therefore, we have: V = ∫₀⁵ πu^(-1/2) du= 2π[u^(1/2)]₀⁵= 2π(√5 - 1) ≈ 6.77 cubic units.

The volume of the solid of revolution when the region is rotated about the x-axis is approximately 6.77 cubic units.

Thus, the correct option is A. The volume is 6.77 cubic units.

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Answer:

-2x + (-3) = x

x = -1

Step-by-step explanation:

-2x + (-3) = x

add 2x to each side

-3 = 3x

divide each side by 3

-1 = x

Answer:

Add the product of 9 and 25 to the product of 9 and 10.

I'm confused what's being asked here...but if you're looking for someone to check it then:

The line of best fit is drawn correctly; there are about the same amount of dots on the top and bottom of the line.

And the correlation is positive

0.9  3/4  and 15/3

Hope this helps :D

and what do you mean by BOTH of there?

there is only one question

Answer:

0.90, 3/4, and im not sure about 15/3

Step-by-step explanation:

0.45 = 45% so anything above 0.45 is correct. 0.400 and 0.40 are less than 45%

3/4 would be 75% so that is greater

hope i helped a bit!!

Answer:

el que??

Step-by-step explanation:

Answer:

hola que tal amiga que haces

Hey there! I'm happy to help!

The slope is the steepness or incline of a line. From a graph, it is known as the rise over the run between two integer values. If you have a point at (1,1) and a point at (2,2), the rise (vertical difference) between them in 1 unit, and the run (horizontal difference) is 1 unit. 1/1 is 1, so the slope of a line that passes through these points is 1. This means that for every one unit to the right it goes, it goes one unit up.

The intercepts are where the line hits the x and y axes. By looking at a graph, you can find the y-intercept by seeing on what y-value the line intersects with the y-axis, and for the x-intercept you do so with the x-axis.

The slope-intercept equation is y=mx+b. This b is the y-intercept. To find the x-intercept, you plug in the value 0 for y and solve for x. This is because the x-axis is the line y=0, so you will see where the x is if y is equal to 0.

Linear equations and functions can be written in slope intercept form (y=mx+b), standard form (Ax+By=C), and point slope form \(y-y_{1} =m(x-x_{1} )\).

They can be graphed by finding the y and x intercepts from the equation and then connecting the points to draw the line!

Have a wonderful day! :D

Answer:

Exact form: -87/16

decimal from -5.4375

mixed number form -5 7/16

Step-by-step explanation:

I'ma god at math

The number of miles Eric drive the truck is 204 miles

The parameters from the question are

Base fee = $20.95

Additional charge = 74 cents or $0.74

These parameters can be represented as

Total payment = Base fee + Additional charge x The number of miles

Substitute the known values in the above equation, so, we have the following representation

20.95 + 0.74 x The number of miles = 171.91

So, we have

0.74 x The number of miles = 150.96

Evaluate the quotients

The number of miles = 204

Hence, the number of miles = 204

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The amount of the annual depreciation has been $90.

The statement provides us with the following data:

The yearly depreciation of the table saw can be calculated by subtracting the depreciated value from the original cost and dividing by the number of years.

Yearly depreciation = (Original cost - Depreciated value) / Number of years

Yearly depreciation = ($810 - $450) / 4

Yearly depreciation = $360 / 4

Yearly depreciation = $90

Therefore, the amount of yearly depreciation for the table saw is $90.

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Answer:

q = - \(\frac{2}{3}\)

Step-by-step explanation:

Given

3(q + \(\frac{4}{3}\) ) = 2 ← distribute left side

3q + 4 = 2 ( subtract 4 from both sides )

3q = - 2 ( divide both sides by 3 )

q = - \(\frac{2}{3}\)

The Answer is (x+9)^2

Answer:

-81/20

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

Out of those numbers and assuming the equation is f(x) = 6x^2=3

f(-2)= 6(-2)^2+3

Answer:

f(-6)=22

Step-by-step explanation:

f(x)=-3x+4

F(-6)=-3(-6)+4

f(-6)=18+4

f(-6)=22

Option B) If the sum of the squares of the two short sides equals the square of the longest side

Step-by-step explanation:

the average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values.

so,

(h(7) - (h(3)) / (7 - 3)

h(7) = 7² - 7×7 + 6 = 49 - 49 + 6 = 6

h(3) = 3² - 7×3 + 6 = 9 - 21 + 6 = -6

7 - 3 = 4

(6 - -6)/4 = 12/4 = 3

the average change rate in that interval is 3 (or fully 3/1).

We are 90% confident that the true difference in proportions between France and the United States falls between -0.1783 and 0.1383.

What is proportion?

The size, number, or amount of one thing or group as compared to the size, number, or amount of another. The proportion of boys to girls in our class is three to one.

The point estimate for the difference in proportions between France and the United States is:

p₁ - p₂ = (60/120) - (26/50) = 0.5 - 0.52 = -0.02

We can use the following formula to calculate the standard error of the difference in proportions:

SE = √(p₁ * (1 - p₁) / n₁ + p₂ * (1 - p₂) / n₂)

where n₁ and n₂ are the sample sizes.

SE = √((0.5 * 0.5 / 120) + (0.52 * 0.48 / 50))

SE = 0.0936

To construct a 90% confidence interval, we can use the formula:

(point estimate) ± (critical value) * (standard error)

The critical value for a two-sided 90% confidence interval with 169 degrees of freedom (calculated as df = (p₁ * n₁ + p₂ * n₂) / (p₁ + p₂)) can be found using a t-distribution table or calculator.

For a 90% confidence level, the critical value is approximately 1.656.

Using these values, the 90% confidence interval for the difference in proportions is:

-0.02 ± 1.656 * 0.0936

which simplifies to:

-0.1783 to 0.1383

Therefore, we are 90% confident that the true difference in proportions between France and the United States falls between -0.1783 and 0.1383.

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a. The probability of drawing a red ball from Box 1 is 30%.

b. If a red ball is drawn from Box 1, the probability of drawing another red ball from Box 2 on the second round is 60%.

c. If the first draw from Box 1 was black, the conditional probability of drawing a red ball from Box 3 on the second draw is 80%.

d. The probability of drawing two red balls at both draws, without any prior information, is 46%.

e. The probability of drawing a red ball at the first draw and a black ball at the second draw, without any prior information, is 21%.

a. The probability of drawing a red ball from Box 1 can be calculated by dividing the number of red balls in Box 1 by the total number of balls in Box 1. Therefore, the probability is 3/(3+7) = 3/10 = 0.3 or 30%.

b. Since a red ball was drawn from Box 1, we only consider the balls in Box 2. The probability of drawing a red ball from Box 2 is 6/(6+4) = 6/10 = 0.6 or 60%. Therefore, the probability of drawing another red ball when the first ball drawn from Box 1 is red is 60%.

c. If the first draw from Box 1 was black, we only consider the balls in Box 3. The probability of drawing a red ball from Box 3 is 8/(8+2) = 8/10 = 0.8 or 80%. Therefore, the conditional probability of drawing a red ball from Box 3 when the first ball drawn from Box 1 was black is 80%.

d. Before any draws, the probability of drawing two red balls at both draws can be calculated by multiplying the probabilities of drawing a red ball from Box 1 and a red ball from Box 2. Therefore, the probability is 0.3 * 0.6 = 0.18 or 18%. However, since there are two possible scenarios (drawing red balls from Box 1 and Box 2, or drawing red balls from Box 2 and Box 1), we double the probability to obtain 36%. Adding the individual probabilities of each scenario gives a total probability of 36% + 10% = 46%.

e. Before any draws, the probability of drawing a red ball at the first draw and a black ball at the second draw can be calculated by multiplying the probability of drawing a red ball from Box 1 and the probability of drawing a black ball from Box 2 or Box 3. The probability of drawing a red ball from Box 1 is 0.3, and the probability of drawing a black ball from Box 2 or Box 3 is (7/10) + (2/10) = 0.9. Therefore, the probability is 0.3 * 0.9 = 0.27 or 27%. However, since there are two possible scenarios (drawing a red ball from Box 1 and a black ball from Box 2 or drawing a red ball from Box 1 and a black ball from Box 3), we double the probability to obtain 54%. Adding the individual probabilities of each scenario gives a total probability of 54% + 10% = 64%.

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I hope it is right. So just learn from it and do. Thank you.

Answer:

(8,1)

Step-by-step explanation:

\(\cos^{4} x-\sin^{4} x\\\\=(\cos^{2} x+\sin^{2} x)(\cos^{2} x-\sin^{2} x)\\\\=\cos^{2} x-\sin^{2} x\\\\=\cos^{2} x-(1-\cos^{2} x)\\\\=2\cos^{2} x-1\)

In the attached diagram the perimeter of the hall way is

The perimeter of the hall way is calculated by adding all the sides of the hallway

The perimeter of the hall way  = 2x - 7 + x + 1 + 4x - 9 + x - 2 + x + 2 + 3x - 11 + x - 2 + 3x - 11 + x + 4

adding like terms results to

The perimeter of the hall way  =  17x + (-34)

Finally, the simplified expression is:

17x - 34

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The measure of angle t is 50°. therefore option are not related to answer.

An angle is defined as the intersection of two non-collinear rays with a common endpoint or the intersection of two

sides of a plane figure, sharing a common endpoint.

The given angle is coterminal with -710°. Coterminal angles have the same initial and terminal sides, i.e., the same initial

point and the same terminal point.

In order to find the measure of angle t, we must first find the equivalent angle between 0 and 360°.710° is equal to:

710° - 360° = 350°

Thus, the angle t's measure is equal to 350°.

Now, we must find the equivalent angle between 0 and 360°.350° is equal to:350° - 360° = -10° (not between 0 and 360)

Therefore, to find the equivalent angle between 0 and 360, we must add 360° to the angle that is negative.

Thus: -10° + 360° = 350°.So, the measure of angle t is 50°.Answer: 50°.

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When proving that the diagonals of a rectangle are congruent, certain elements are necessary.

To prove that the diagonals of a rectangle are congruent, we need to establish the properties and characteristics of a rectangle. The necessary elements for the proof include the definition of a rectangle, which states that it is a quadrilateral with four right angles.

Additionally, we need to consider the properties of diagonals in a rectangle, such as the fact that diagonals bisect each other and form congruent triangles. These properties are crucial in proving that the diagonals of a rectangle are congruent.

Furthermore, we may need to employ other geometric principles and theorems to support the proof. These may include the properties of parallel lines, perpendicular lines, and the congruence of corresponding angles and sides in triangles. By utilizing these principles and theorems, we can establish the necessary conditions to prove that the diagonals of a rectangle are congruent.

In conclusion, when proving that the diagonals of a rectangle are congruent, it is essential to consider the definition and properties of rectangles, as well as employ relevant geometric principles and theorems to support the proof.

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