Can someone help me please

The slope of the line that goes through the origin and the point (6, -4) is -2/3.

To find the slope of a line that goes through two given points (x₁, y₁) and (x₂, y₂), you can use the formula:

slope = (y₂ - y₁) / (x₂ - x₁)

In this case, one of the points is the origin, which has coordinates (0, 0), so x₁ = 0 and y₂ = 0. The other point is (6, -4), so x₂ = 6 and y₂ = -4. Substituting these values into the slope formula gives:

slope = (-4 - 0) / (6 - 0) = -4/6 = -2/3

To learn more about slope click on,

https://brainly.com/question/27924340

#SPJ1

Answer:

9

Step-by-step explanation:

First, write the equation.

C(n) = 4 + 3n

We know that C(n) = 31, so we can substitute it.

31 = 4 + 3n

Subtract 4 from both sides to isolate the term with the variable.

27 = 3n

Divide both sides by 3 to get the variable by itself.

9 = n

The value of n such that C(n) = 31 is true is 9

Given the cost in dollars, of a cafeteria meal plan as a function of the number of meals  purchased, n as:

If the cost value C(n) is 31, hence;

31 = 4 + 3n

3n = 31 - 4

3n = 27

n = 27/3

n = 9

Hence the value of n such that C(n) = 31 is true is 9

Learn more on equations here: https://brainly.com/question/2972832

To find the point on the surface 6x = y^2 + z^2 where its tangent plane is parallel to a given plane, we need to find a point on the surface and determine the normal vector of the surface at that point.

Then, we can compare the normal vector of the surface to the normal vector of the given plane to check if they are parallel.

Let's first find a point on the surface by substituting a value for either y or z and solving for x. Let's choose y = 0:

6x = 0^2 + z^2

6x = z^2

x = z^2/6

So, one point on the surface is (z^2/6, 0, z).

To find the normal vector of the surface at this point, we can calculate the partial derivatives with respect to x, y, and z:

∂/∂x (6x) = 6

∂/∂y (y^2 + z^2) = 0

∂/∂z (y^2 + z^2) = 2z

The normal vector is then N = (6, 0, 2z) = (6, 0, 2z) / ||(6, 0, 2z)||, where ||N|| represents the magnitude of N.

To determine if the tangent plane is parallel to a given plane, we compare the normal vector of the surface to the normal vector of the given plane. If they are parallel, their direction vectors should be proportional.

If the given plane is parallel to the xy-plane and has a normal vector N_1 = (0, 0, 1), we can compare it to the normal vector of the surface. In this case, we see that the z-component of N (2z) is not proportional to the z-component of N_1 (1). Therefore, the tangent plane of the surface at the chosen point is not parallel to the given plane.

To find a point on the surface where its tangent plane is parallel to the given plane, we would need to choose a different point on the surface such that the normal vector of the surface at that point is parallel to the given plane's normal vector.

Learn more about Tangent here -: brainly.com/question/26153770

#SPJ11

Work Shown:

y = 15.6 - 3.8x

y = 15.6 - 3.8*3

y = 4.2

Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

The product of the slopes of two non-vertical perpendicular lines is always -1.

It is NOT possible for two perpendicular lines to both have a positive slope because the product of two positives is positive. So for the product of the slopes to be -1, one of the slopes must be positive and the other negative.

The definition of perpendicular lines is lines that intersect and at the point of intersection they form a right angle of 90°.

In determining the gradient of two mutually perpendicular when multiplied it will produce the number -1. So the formula used is:

y = mx + c

Meanwhile, the gradient formula is m1 = -1/m2.

Learn more about Perpendicular lines at

https://brainly.com/question/18271653

#SPJ4

Answer:

175.259 cm

Step-by-step explanation:

(A) The length that beats 80 seconds is 256 cm.

(B) The time of a pendulum with length 36 cm is 30 seconds.

(A) According to the given information, the time of a pendulum varies as the square root of its length. Let's denote time as T and length as L. Therefore, T ∝ √L. To find the constant of proportionality, we can use the provided data: T1 = 15 seconds and L1 = 9 cm. So, we have T1 / √L1 = k, where k is the constant. Now, let's find k: k = 15 / √9 = 15 / 3 = 5.

Now, we want to find the length (L2) of a pendulum that beats 80 seconds (T2). We can use the formula T2 = k * √L2. Substituting the values, we get 80 = 5 * √L2. To find L2, we can rearrange and solve for it: L2 = (80 / 5)² = 16² = 256 cm.

(B) To find the time (T3) of a pendulum with a length of 36 cm (L3), we can use the same formula with the known constant k: T3 = k * √L3. Substituting the values, we get T3 = 5 * √36 = 5 * 6 = 30 seconds.

In conclusion, the length of a pendulum that beats 80 seconds is 256 cm, and the time of a pendulum with a length of 36 cm is 30 seconds.

To know more about pendulum, refer to the link below:

https://brainly.com/question/29268528#

#SPJ11

Answer:

b

Step-by-step explanation:

Answer:

B. $1.30

Step-by-step explanation:

The value of sin(θ) is approximately 0.921 and the value of cos(θ) is approximately 0.391.

To find the value of each variable using sine and cosine, we need to set up a right triangle with the given information. Let's label the sides of the triangle as follows:

Using the Pythagorean theorem, we can find the length of the hypotenuse:

h2 = s2 + t2

h2 = 31.32 + 13.32

h2 = 979.69 + 176.89

h2 = 1156.58

h = √1156.58

h ≈ 34.0

Now that we know the length of the hypotenuse, we can use sine and cosine to find the values of the variables:

sin(θ) = s / h

sin(θ) = 31.3 / 34.0

sin(θ) ≈ 0.921

cos(θ) = t / h

cos(θ) = 13.3 / 34.0

cos(θ) ≈ 0.391

About value here:

https://brainly.com/question/30145972

#SPJ11

Answer:

x=1.7320508075688...... equal to 1.73

Step-by-step explanation:

equation is: y=x*x+1

so put 4 instead of y

4=x*x+1

so x*x=3

x=1.7320508075688......

Answer:

A=2m⁴+17m³+11m²+24m

Step-by-step explanation:

The area of rectangle is length × width

A=LW

A=(m+8)(2m³+m²+3m)

A= 2m⁴+m³+3m²+16m³+8m²+24m

A=2m⁴+m³+16m³+3m²+8m²+24m

A=2m⁴+17m³+11m²+24m

Recall that the inequality x>b in interval notation is:

Subtracting 3 to the given inequality we get:

Which in interval notation is:

Answer:

Answer: D

Step-by-step explanation:

We will try it to determine how much the need to save using the exponential function. In an exponential function,we need the start up amount and the common difference.

We know that the common difference is is 1.085  because if they will earn 8.5% interest plus 100% .

So  1.085 raised to the number of years times a number has to equal 250,000

x * 1.085^14 = 250,000   now solve for x

3.13340357495x = 250,000

x = 79785.44544 Rounded to the nearest cent is $79785.45

It's important to know that reciprocals are the multiplicative inverse of a numbers, for example, the reciprocal of 7 is 1/7.

As you can observe, using reciprocals would help to solve equations when we have to get rid off a factor. For example, if we have the equations 4x = 8, we would use the reciprocal of 4 to isolate the variable x: (4x)/4 = 8/4 then x = 2.

Answer:

The slope is -10, and the y-intercept is 1.

Step-by-step explanation:

Assuming that the equation is y = -10x+1, the easiest way to identify slope and the y-intercept is by knowing the equation for slope-intercept (y = mx+b)

Equation for slope-intercept (y = mx+b) explained:

The equation is y = mx+b, let's break it down.

y = The line

m = The slope

b = The y-intercept

Now that we know the equation and broke it down you can identify them in your equation

Slope (m)= -10

y-intercept = 1

Conclusion: The slope is -10, and the y-intercept is 1.

The probability that the airline will lose at least 10 suitcases in a week is 0.1723 or about 17.23%.

Given information:

µ = 6.7 (mean)

σ = 3.5 (standard deviation)

We need to find the probability of losing at least 10 suitcases in a week. We can use the normal distribution formula to solve this problem:

P(X ≥ 10) = 1 - P(X < 10)

To use this formula, we need to standardize the variable X to the standard normal distribution with mean 0 and standard deviation 1. We can do this using the following formula:

Z = (X - µ) / σ

Substituting the given values, we get:

Z = (10 - 6.7) / 3.5

Z = 0.943

Now, we can use a standard normal distribution table or calculator to find the probability of Z being greater than or equal to 0.943. The table or calculator will give us the probability of Z being less than 0.943, which we can then subtract from 1 to get the desired probability.

Using a standard normal distribution table, we find that P(Z < 0.943) = 0.8277.

Therefore, P(X ≥ 10) = 1 - P(X < 10) = 1 - P(Z < 0.943) = 1 - 0.8277 = 0.1723.

So, the probability that the airline will lose at least 10 suitcases in a week is 0.1723 or about 17.23%.

To learn more about probability visit:

https://brainly.com/question/15124899

#SPJ11

Answer:

Part A)

\(\displaystyle \frac{dy}{dx}=\frac{2xy}{y-x^2}\)

Part B)

\(y=x-2\)

Part C)

\((0, \sqrt{3})\text{ and } (0, -\sqrt3)\)

Part D)

\(\displaystyle \frac{d^2y}{dx^2}_{(1, -1)}=-\frac{1}{2}\)

Step-by-step explanation:

We have the equation:

\(y^2-2x^2y=3\)

Part A)

We want to find the derivative of the equation. So, dy/dx.

Let’s take the derivative of both sides with respect to x. Therefore:

\(\displaystyle \frac{d}{dx}\Big[y^2-2x^2y\Big]=\frac{d}{dx}[3]\)

Differentiate. We will need to implicitly different on the left. The second term will also require the product rule. Therefore:

\(\displaystyle 2y\frac{dy}{dx}-4xy-2x^2\frac{dy}{dx}=0\)

Rearranging gives:

\(\displaystyle \frac{dy}{dx}\Big(2y-2x^2\Big)=4xy\)

Therefore:

\(\displaystyle \frac{dy}{dx}=\frac{4xy}{2y-2x^2}\)

And, finally, simplifying:

\(\displaystyle \frac{dy}{dx}=\frac{2xy}{y-x^2}\)

Part B)

We want to write the equation for the line tangent to the curve at the point (1, -1).

So, we will require the slope of the tangent line at (1, -1). Substitute these values into our derivative. So:

\(\displaystyle \frac{dy}{dx}_{(1, -1)}=\frac{2(1)(-1)}{(-1)-(1)^2}=1\)

Now, we can use the point-slope form:

\(y-y_1=m(x-x_1)\)

Substitute:

\(y-(-1)=1(x-1)\)

Simplify:

\(y+1=x-1\)

So:

\(y=x-2\)

Part C)

If the line tangent to the curve is horizontal, this means that dy/dx=0. Hence:

\(\displaystyle 0=\frac{2xy}{y-x^2}\)

Multiplying both sides by the denominator gives:

\(0=2xy\)

Assuming y is not 0, we can divide both sides by y. Hence:

\(2x=0\)

Then it follows that:

\(x=0\)

Going back to our original equation, we have:

\(y^2-2x^2y=3\)

Substituting 0 for x yields:

\(y^2=3\)

So:

\(y=\pm\sqrt{3}\)

Therefore, two points where the derivative equals 0 is:

\((0, \sqrt{3})\text{ and } (0, -\sqrt3)\)

However, we still have to test for y. Let’s go back. We have:

\(0=2xy\)

Assuming x is not 0, we can divide both sides by x. So:

\(0=2y\)

Therefore:

\(y=0\)

And going back to our original equation and substituting 0 for y yields:

\((0)^2-2x^2(0)=0\neq3\)

Since this is not true, we can disregard this case.

So, our only points where the derivative equals 0 is at:

\((0, \sqrt{3})\text{ and } (0, -\sqrt3)\)

Part D)

Our first derivative is:

\(\displaystyle \frac{dy}{dx}=\frac{2xy}{y-x^2}\)

Let’s take the derivative of both sides again. Hence:

\(\displaystyle \frac{d^2y}{dx^2}=\frac{d}{dx}\Big[\frac{2xy}{y-x^2}\Big]\)

Utilize the quotient and product rules and differentiate:

\(\displaystyle \frac{d^2y}{dx^2}=\frac{(2y+2x\frac{dy}{dx})(y-x^2)-2xy(\frac{dy}{dx}-2x)}{(y-x^2)^2}\)

Let dy/dx=y’. Therefore:

\(\displaystyle \frac{d^2y}{dx^2}=\frac{(2y+2xy^\prime)(y-x^2)-2xy(y^\prime-2x)}{(y-x^2)^2}\)

For (1, -1), we already know that y’ is 1 at (1, -1). Therefore:

\(\displaystyle \frac{d^2y}{dx^2}_{(1, -1)}=\frac{(2(-1)+2(1)(1))((-1)-(1)^2)-2(1)(-1)((1)-2(1))}{((-1)-(1)^2)^2}\)

Evaluate:

\(\displaystyle \frac{d^2y}{dx^2}_{(1, -1)}=-\frac{1}{2}\)

Answer:

Step-by-step explanation:

the percetnage is 45%

Answer:

anong grade po yan?

baka alam ko po

Answer:

a) 12

Step-by-step explanation:

Given that,

→ p = -24

→ q = 4

The equation is,

→ 2p/-q

Let's solve the problem,

→ 2p/-q

→ 2(-24)/-4

→ -48/-4

→ 48/4 = 12

Hence, the answer is 12.

The given sequence is [ a_{n}=\left(\frac{1}{2}\right)^{n}(5 n-4) ]

To find the first four terms of the sequence, we need to substitute the values of n from 1 to 4 one by one.

When n=1, we have [ a_{1}=\left(\frac{1}{2}\right)^{1}(5(1)-4)=\frac{1}{2} ]

When n=2, we have [ a_{2}=\left(\frac{1}{2}\right)^{2}(5(2)-4)=\frac{3}{4} ]

When n=3, we have [ a_{3}=\left(\frac{1}{2}\right)^{3}(5(3)-4)=\frac{7}{8} ]

When n=4, we have [ a_{4}=\left(\frac{1}{2}\right)^{4}(5(4)-4)=\frac{9}{16} ]

Hence, the first four terms of the sequence are

\(1221​ , 3443​ , 7887​ , and 916169​ .\)

Learn more about sequence here:

https://brainly.com/question/23857849

#SPJ11

Answer:

−xy−y2+2y+30 is the answer simplified

Answer:

i think more than is the answer

The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

For more such questions on lengths

https://brainly.com/question/28322552

#SPJ8

The equation of line that passes a point (–3, 7) and has slope of 4, in the point-slope form is y - 7 = 4 (x + 3)

A linear equation can be expressed in three forms:

- slope intercept form : y = mx + c

- point-slope form: y - y₁ = m (x - x₁)

- standard form: Ax + By + C = 0

Where:

m = slope

(x₁, y₁) = point on the line

A, B, C are constant

In this problem, the point is (–3, 7) and the slope is 4. Hence,

x₁ = –3

y₁ = 7

m = 4

Plug these parameters into the equation:

y - y₁ = m (x - x₁)

y - 7 = 4 (x - (-3))

y - 7 = 4 (x + 3)

Learn more about point-slope form here:

https://brainly.com/question/24907633

#SPJ4

Answer:

x = -45

Step-by-step explanation:

Please refer to the image for answer to your question the answer is explained in detail.

Triangulation is the method of finding the location of an object based on the measurements made from the two other locations. The above statement is true statement.

Triangulation is the division of a face or plane polygon into a series of triangles, usually with the limitation that each side of a triangle is fully shared by two adjacent triangles. In geometry, triangulation is the division of planar objects into triangles, or more broadly, the division of high-dimensional geometric objects into simplifications. Triangulation of a 3D volume involves subdivision into packed tetrahedra that directly measure distances to points. It is a method for finding the location of the object.

Learn more about triangulation in

https://brainly.com/question/16782270

#SPJ4