What is the point-slope form of a line that has a slope of 3 and passes through point (1, 4)?
O y-4-3(x-1)
0 1-y-3(x-4)
4-4-3(1-x)
1-y, -3(4-x)

Answer:

m = -5

Step-by-step explanation:

Let the score she needs be x.

\(\frac{79+82+74+59+96+2x}{7}=80 \\ \\ 79+82+74+59+96+2x=560 \\ \\ 2x=170 \\ \\ \boxed{x=85}\)

Answer:

4/7

Step-by-step explanation:

Given:

Diameter of ball = 8 cm

To find:

The volume of the ball.

Solution:

We know that the radius of sphere is half of is diameter.

It is given that the the diameter of ball is 8 cm. So, the radius of the ball is:

\(r=\dfrac{8}{2}\)

\(r=4\)

The radius of the ball is 4 cm.

The volume of a sphere is:

\(V=\dfrac{4}{3}\pi r^3\)

Where r is the radius of the sphere.

Putting \(\pi = 3.14, r=4\) in the above formula, we get

\(V=\dfrac{4}{3}(3.14)(4)^3\)

\(V=\dfrac{4}{3}(3.14)(64)\)

\(V=267.946667\)

\(V\approx 267.95\)

Therefore, the volume of the ball is about 267.95.

A plane is a flat surface made up of points that extends infinitely in all directions.

In mathematics, a plane is a fundamental geometric concept. It is a two-dimensional flat surface that extends infinitely in all directions. A plane can be visualized as a flat sheet or a tabletop. It has length and width but no thickness.

A plane is defined by three non-collinear points or by a linear equation in three variables. The equation of a plane in three-dimensional space is typically written as Ax + By + Cz + D = 0, where A, B, C are coefficients representing the plane's orientation, and D is a constant term.

Planes are important in various branches of mathematics, such as geometry, linear algebra, and calculus. They serve as a foundation for understanding concepts like lines, angles, and shapes in two dimensions. Additionally, planes are used in vector operations, linear transformations, and solving systems of linear equations.

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One statement that is necessarily true when a quadrilateral is inscribed in a circle is that the opposite angles of the quadrilateral are supplementary. In other words, the sum of the measures of two opposite angles is always 180 degrees.

To understand why this is true, let's consider a specific example. Imagine a quadrilateral PQRS inscribed in circle A. Let's say angle PQR measures 80 degrees. Since angle PQR is an inscribed angle that intercepts arc PS, it is equal in measure to half the measure of arc PS. Therefore, arc PS measures 160 degrees.

Now, let's focus on angle PSR. Angle PSR also intercepts arc PS, so it has the same measure as half the measure of arc PS, which is 160 degrees. Therefore, angle PSR measures 160 degrees as well.

If we add the measures of angles PQR and PSR, we get 80 + 160 = 240 degrees. This violates the fact that the sum of the measures of angles in a quadrilateral is always 360 degrees. Thus, it is clear that angles PQR and PSR cannot both measure 80 degrees.

Based on this example, we can conclude that the opposite angles of a quadrilateral inscribed in a circle are supplementary. This means that their sum is always 180 degrees.

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Step-by-step explanation:

Find what 14.6 mi/hr is in f/s

14.6 mi / hr   *  1 hr / 3600 s  *  5280 ft / mi =  21.413 f/s

Then  distance / rate = time :

75 f  /  21.413 f/s = 3.5 sec

It would take Julio approximately 3.5 seconds to run from first base to second base at his top speed. Rounded to the nearest tenth of a second, it is approximately 3.5 seconds.

To calculate the time it takes for Julio to run from first base to second base, we first need to convert the distance between the bases from feet to miles.

1 mile = 5280 feet

So, 75 feet is equal to:

75 feet / 5280 feet per mile = 0.0142 miles (approximately, rounded to four decimal places)

Now, we'll use the formula for time:

Time = Distance / Speed

Time = 0.0142 miles / 14.6 miles per hour

Time ≈ 0.00097222222 hours

Now, we need to convert the time from hours to seconds:

1 hour = 3600 seconds

Time = 0.00097222222 hours * 3600 seconds per hour ≈ 3.5 seconds

So, it would take Julio approximately 3.5 seconds to run from first base to second base at his top speed. Rounded to the nearest tenth of a second, it is approximately 3.5 seconds.

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Answer:

9

Step-by-step explanation:

18/2 = 9

27/3 =9

63 = 9

I don't know how to explain this more

The maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight is 1.771 ounces.

The maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight can be calculated using the formula:

Margin of error = Z-score x (population standard deviation / square root of sample size)

Here, the Z-score for a 90% confidence level is 1.645 (obtained from a standard normal distribution table). The population standard deviation is given as 5.7 ounces, and the sample size is 28.

Plugging in these values, we get:

Margin of error = 1.645 x (5.7 / sqrt(28))
= 1.645 x (1.076)
= 1.771

Therefore, the maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight is 1.771 ounces. This means that we can be 90% confident that the true population mean turtle weight lies within the range of (60 - 1.771) to (60 + 1.771) ounces, or 58.229 to 61.771 ounces.

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Answer:

SA = 10,800 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 40

w = 60

h = 30

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 60(40) + 30(40) + 30(60) )

SA = 2 ( 2400 + 1200 + 1800 )

SA = 2 ( 5400 )

SA = 10,800 ft²

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The product in descending order with respect to the power c is cn³ + cp³ - cpn² - cp²n

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By multiplying the variables, we have the following:

c(n - p)²(n + p)

c(n - p)(n - p)(n + p)

c(n² - pn - pn + p²)(n + p)

c(n² - 2pn + p²)(n + p)

c(n³ + pn² - 2pn² - 2p²n + p²n + p³)

c(n³ - pn² - p²n + p³)

cn³ - cpn² - cp²n + cp³

cn³ + cp³ - cpn² - cp²n

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The definite integral for the area of the surface generated by revolving the curve y = 6x^3 + 2x about the x-axis, over the interval 1 ≤ x ≤ 2, can be set up and evaluated as follows:

∫[1 to 2] 2πy √(1 + (dy/dx)^2) dx

To calculate dy/dx, we differentiate the given equation:

dy/dx = 18x^2 + 2

Substituting this back into the integral, we have:

∫[1 to 2] 2π(6x^3 + 2x) √(1 + (18x^2 + 2)^2) dx

Evaluating this definite integral will provide the surface area generated by revolving the curve about the x-axis.

b) The definite integral for the area of the surface generated by revolving the curve x = 4y - 1 about the y-axis, over the interval 1 ≤ y ≤ 4, can be set up and evaluated as follows:

∫[1 to 4] 2πx √(1 + (dx/dy)^2) dy

To calculate dx/dy, we differentiate the given equation:

dx/dy = 4

Substituting this back into the integral, we have:

∫[1 to 4] 2π(4y - 1) √(1 + 4^2) dy

Evaluating this definite integral will provide the surface area generated by revolving the curve about the y-axis.

By setting up and evaluating the definite integrals for the given curves, we can find the surface areas generated by revolving them about the respective axes. The integration process involves finding the appropriate differentials and applying the fundamental principles of calculus.

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The value of x is 10.

Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.

Opposite sides are parallel, and the opposite sides and opposite angles are equal.

Parallelogram has the property that the consecutive or adjacent angles of a parallelogram are supplementary.

That is, they sum up to 180°.

Here, (6x)° and (12x)° are supplementary.

6x + 12x = 180

18x = 180

x = 10

Hence the value of x is 10.

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Answer:

5) y = -8x -4

6) y = 2x + 3

Step-by-step explanation:

Slope is rise over run. For the first problem, you went down 8 and over 1 to your next point. Going down means you have a negative slope. -8/1 is 8. Your y intercept is where the line meets the y axis. The line meets the y axis at -4.

The line meets a new point every time it goes over 1 and up 2. Rise over run means 2/1. The line goes up so the slope is positive. The line meets the y axis at 3

Answer:

B

Step-by-step explanation:

Answer:

If s = 1 over 3 unit and A = 18s² what is the value of A, in square units? ____ square unit(s).Step-by-step explanation:

Answer:

check online for more information

Answer:

awnser G

Step-by-step explanation:

Answer:

H

Step-by-step explanation:

y and x² are corresponding angles and are congruent, that is

y = x²

Then

\(\frac{y^3}{3}\) = \(\frac{(x^2)^{3} }{3}\) = \(\frac{x^6}{3}\) → H

To determine which differential equation(s) are linear, we need to examine the form of each equation. A linear differential equation is one that can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x), b(x), c(x), and g(x) are functions of x.

The differential equation 2xy" - 5xy' + y = sin(3x) is linear. It can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x) = 2x, b(x) = -5x, c(x) = 1, and g(x) = sin(3x).
The differential equation (v)² + xy = In(x) is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (v)², where v represents the derivative of y with respect to x. This term does not have a linear coefficient.
The differential equation y' + sin(y) = e^(3x) is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = sin(y), and g(x) = e^(3x).
The differential equation (x²+1)y" - 3y - 2x³y = -x - 9 is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (x²+1)y", where the coefficient is a function of x.
The differential equation y' + xy = y" is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = x, and g(x) = y".

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Answer:

1. 20

2. 86.6

3. 173.2

4. 17.32/20

5. 10/20

6. 17.32/10

Step-by-step explanation:

sin 60 = x/20 17.32

cos 60 = x/20. 10

The lengths of PR and QS are; 20 and 28.28

The area of triangle PQR is, 282.8

The area of the rectangle PQRS is, 100√3.

The sine ratio of angle PRS is , 1 / 2.

The cosine ratio of angle PRQ is, √3 / 2.

The tangent ratio of angle PQS is, √3 / 3.

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

we know that its diagonal bisects each other therefore PT=TR i.e. 10 units

PS = 20 units  

The area of triangle PQR = 1/2 x 28.28 x 20

= 282.8

Area of rectangle = PQ x PS

Area = 100√3

The angle PRS is 30°                                

The sum of interior angle of a triangle.

sin30° = PS/PR

1/2 x 20 = PS

PS= 10 units

The angle PRQ is 60°                                    

By Alternate interior angle

cosine60°=QR/PR

1/2 x 20 = QR

QR= 10 unit

cos QSR = 10/20

cosQSR=1/2

angle QSR = 60°

Thus angle PQS is 30°

tanPQS = 1/√3

PQ= 10√3

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The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:

y^2 / 25 - x^2 / a^2 = 1

where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.

Thus, the equation for the hyperbola is:

y^2 / 25 - x^2 / (400/9) = 1

or

9y^2 - 400x^2 = 900

The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.

To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.

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All you have to do is, make the operations.

Step 1

break the parenthesis and add the terms

so, the answer is -22

A rock that contains equal amounts of potassium-40 and argon-40 is old as  1.25 billion years half life.

The duration it takes for a substance's radioactivity to decrease to half of what it once was is known as half-life.

The half-life of potassium-40 is about  1.25 billion, years. it undergoes beta decay and becomes argon-40. Equal amounts would be one half-life, so the sample is also 1.25 billion years old.

A property of a specific isotope is whether or not it emits radioactive material. While some isotopes are stable for all time, others are radioactive and degrade through a distinctive sort of emission. The radioactivity level falls with time as the radioactive isotope is present in decreasing amounts. The time it takes for one-half of a radioactive isotope to decay is known as its half-life, and it is both an intriguing and practical feature of radioactive decay. A particular radioactive isotope's half-life is constant; it is unaffected by environmental factors and is unrelated to the starting concentration of that isotope.

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Answer:

Area of quadrilateral ABCD = 29.79 units² (Approx)

Step-by-step explanation:

Area of triangle ABD

s = (3.48+8.66+8.6) / 2

s = 10.37

Area of triangle ABD = √10.37(10.37-8.66)(10.37-8.6)(10.37-3.48)

Area of triangle ABD = √212.4616

Area of triangle ABD = 14.5760625 unit²

Area of triangle ACD

s = (3.54+8.84+8.6) / 2

s = 10.49

Area of triangle ACD = √10.49(10.49-8.6)(10.49-8.84)(10.49-3.54)

Area of triangle ACD = √227.3558

Area of triangle ACD = 15.0783222 unit²

Area of quadrilateral ABCD = Area of triangle ABD + Area of triangle ACD

Area of quadrilateral ABCD = 14.5760625 unit² + 15.0783222 unit²

Area of quadrilateral ABCD = 29.6542units²

Area of quadrilateral ABCD = 29.79 units² (Approx)

Answer:

less than 16

Step-by-step explanation:

Answer:

less the 16

16 multiplied by 3/4 is 12

Answer:

cold to hot hope it helps

Answer:

Therefore, the volume of the cylinder is approximately 2,262.9 cubic centimeters.

Step-by-step explanation:

The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the base and h is the height of the cylinder.

Substituting the given values, we get:

V = π(6 cm)^2(20 cm)

V = 720π cm^3

To find the volume to the nearest tenth, we can use the approximation π ≈ 3.14 and calculate:

V ≈ 720(3.14) cm^3

V ≈ 2,262.8 cm^3

Rounding to the nearest tenth, we get:

V ≈ 2,262.8 cm^3 ≈ 2,262.9 cm^3

Therefore, the volume of the cylinder is approximately 2,262.9 cubic centimeters.

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If cosA = 24/25 tanB = 4/3 and angles A and B are in Quadrant I. The value of tan(A-B) is -23/33.

We can start by using the identity: tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

From the given information, we have:

cos A = 24/25, which means sin A = sqrt(1 - cos^2 A) = 7/25 (since A is in Quadrant I)

tan B = 4/3, which means sin B = 4/sqrt(4^2 + 3^2) = 4/5 and cos B = 3/sqrt(4^2 + 3^2) = 3/5

Now, we can use the definitions of sine and cosine to find tan A:

tan A = sin A / cos A = (7/25)/(24/25) = 7/24

Substituting the values we have found into the formula for tan(A - B), we get:

tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

= [(7/24) - (4/3)]/[1 + (7/24)(4/3)]

= (-13/72)/(25/72)

= -13/25

Therefore, tan(A - B) = -13/25.

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Answer:

All values of x make the equation true.

Step-by-step explanation:

When you work on an equation, if it ends with something like 5 = 5, y = y, or 13 = 13, it means that x has infinitely many solutions and so all and any value of x makes the equation true.

Only when you have something like 5 ≠ 7 or 16 ≠ 1, then there are no solutions for the value of x.

If there is a definite solution for x like x = 5, x = 1.3, then there is only one solution.

Answer:

All values of x make the equation true.

Answer:

15^2 = 225

7^3 = 343

Step-by-step explanation: