Functions can be defined using graphs, tables, and ordered pairs. What is the domain of a function?
The domain is any y-value.
The domain is all numbers.
The domain is the input.
The domain is the output.

Answer:

There are 50 calories per cup of popcorn.

Step-by-step explanation:

The common denominator for 3/5 and 3/3 is 15.

3/5 = 9/15

3/3 = 15/15

Answer:

Try this

so u look for the common denominator for both which will be 15 the u convert both

3/5=  9/15

3/3=15/15

T test is used to compute the confidence interval, when the mean and standard deviation is given.

What is Standard Deviation?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be very close to the set mean. The lower case Greek letter (sigma), again for population standard deviation, or even the Latin letter s, again for sample standard deviation, are most frequently used in mathematical texts and equations to represent standard deviation. Standard deviation may be abbreviated as SD. A random variable, specimen, statistical population, data set, as well as probability distribution's standard deviation is equal to the square root of its variance. When the number in a sample, sample mean and sample standard deviation is given, the test statistic that should be used when computing a confidence interval is t test

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The derivative formula for the function g(x) = 15 - 8ln(x) is g'(x) = -8/x.

To find the derivative of g(x), we can use the power rule and the chain rule. The power rule states that the derivative of x^n is n*x^(n-1), and the chain rule allows us to differentiate composite functions.

In this case, g(x) is a combination of a constant function (15) and the natural logarithm function (ln(x)). The derivative of the constant term (15) is 0 since it does not depend on x.

The derivative of the natural logarithm function, ln(x), is 1/x. Therefore, using the chain rule, the derivative of -8ln(x) is -8 * (1/x), which simplifies to -8/x.

Hence, the derivative of g(x) = 15 - 8ln(x) is g'(x) = -8/x.

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When h=9 and j=1/2 the q value is 1152.

Given that:

q is directly proportional to the square root of h and inversely proportional to the cube of​ j, and q=24 when h= 16 and j=2.

q ∝ \(\sqrt{h}\)/\(j^{3}\)

q = k \(\sqrt{h}\)/\(j^{3}\)

24 = k \(\sqrt{16}\)/\(2^{3}\)

24 = k 4/8

k = 24 *2

k = 48

q = 48 \(\sqrt{h}\)/\(j^{3}\)

substitute h = 9 and j = 1/2

q = 48\(\sqrt{9\)/\(1/2^{3}\)

q = 48 * 3/1/8

q = 48 * 3 * 8

q = 48 * 24

q = 1152

Therefore when h=9 and j=1/2 the q value is 1152.

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Answer: See explanation

Step-by-step explanation:

Slope intercept formula: y = mx + b

5 = 10x - 5y

Add 5y to both sides

5y + 5 = 10x

Subtract 5 from both sides

5y = 10x - 5

Divide both sides by 5

y = 2x - 1

The y-intercept is -1

Hope I helped!

The y-intercept of the line 5 = 10x - 5y is b = - 5.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, an equation of line  5 = 10x - 5y.

In slope-intercept form it is 5y = 10x - 5 (y = mx + b).

So, the y-intercept of this line is - 5.

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One possibility could be :

y = x - 3

wherein:

x : number of apples on Monday

y : number of apples on Tuesday, the day after

Hope I helped you! :)

Have a great day/night!!

The derivative of H(z) is H'(z) = -2zd^2/[(d^2-z^2)(d^2+z^2)].

To differentiate the function H(z) = ln[(d^2-z^2)/(d^2+z^2)]^(1/2), we will use the chain rule and the power rule of differentiation.

First, we can simplify the expression inside the natural logarithm using the laws of exponents:

[(d^2-z^2)/(d^2+z^2)]^(1/2) = [(d^2-z^2)^(1/2)/(d^2+z^2)^(1/2)]

Now we can differentiate H(z) as follows:

H'(z) = d/dz [ln[(d^2-z^2)/(d^2+z^2)]^(1/2)]

= (1/2)[(d^2+z^2)^(1/2)/(d^2-z^2)^(1/2)] * d/dz [(d^2-z^2)/(d^2+z^2)]

Using the quotient rule, we can simplify the derivative:

d/dz [(d^2-z^2)/(d^2+z^2)] = [(2z)(d^2+z^2) - (d^2-z^2)(2z)]/(d^2+z^2)^2

= -4zd^2/(d^2+z^2)^2

Substituting this back into H'(z), we get:

H'(z) = (1/2)[(d^2+z^2)^(1/2)/(d^2-z^2)^(1/2)] * (-4zd^2/(d^2+z^2)^2)

= -2zd^2/[(d^2-z^2)(d^2+z^2)]

Therefore, the derivative of H(z) is:

H'(z) = -2zd^2/[(d^2-z^2)(d^2+z^2)]

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Answer:

nxkankankxnalmzlamzlamzo

Answer:

width = 40 cm

Step-by-step explanation:

Since the pentagons are similar then the ratios of corresponding sides are equal, that is

\(\frac{4x}{x}\) = \(\frac{48}{x+2}\) ( cross- multiply )

4x(x + 2) = 48x ← distribute left side

4x² + 8x = 48x ( subtract 48x from both sides )

4x² - 40x = 0 ← factor out 4x from each term on left side

4x(x - 10) = 0

Equate each factor to zero and solve for x

4x = 0 ⇒ x = 0

x - 10 = 0 ⇒ x = 10

However, x > 0 then x = 10

Thus width = 4x = 4 × 10 = 40 cm

The surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder \(\frac{x^2}{25} +\frac{y^2}{9}\) is 15π√150 and this can be determined by using the given data.

We are given the two equations are:

10x + 7y + z = 4---------(1)

\(\frac{x^2}{25} +\frac{y^2}{9} =1-------------(2)\)

equation(1) is written as

z = 4 - 10x - 7y-----------(3)

The surface area is given by the equation:

A(S) = ∫∫√[(∂f/∂x)² + (∂f/∂y)² + 1]dA------------(4)

compare equation(4) with equation(3) we get the values of ∂f/∂x and

∂f/∂y

∂f/∂x = -10

∂f/∂y = -7

substitute these values in equation(4)

A(S) = ∫∫√[(-10)² + (-7)² + 1]dA

A(S) = ∫∫√[100 + 49 + 1]dA

A(S) = ∫∫√[150]dA

A(S) = √150 ∫∫dA

Where ∫∫dA is the elliptical cylinder

From the general form of an area enclosed by an ellipse with the formula;

comparing x²/a² + y²/b² = 1  with x²/25 + y²/9 = 1, from that we get the values of a and b

a = 5 and b = 3

So, the area of the elliptical cylinder = πab

Thus;

A(S) = √150 × π(5 × 3)

A(S) = 15π√150

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Answer:

a. x = 9 + 4y

b. x = (7y-2)/6

c. x = (17 + k)/4

d. x = (9-c)/k

Step-by-step explanation:

In each of the equations, we want to make x the formula subject

a) 3x-12y = 27

3x = 27 + 12y

3x = 3(9 + 4y)

x = 9 + 4y

b) 6x-7y = -2

6x = 7y-2

x = (7y-2)/6

c) 4x - k = 17

4x = 17 + k

x = (17 + k)/4

d) kx + c = 9

kx = 9-c

x = (9-c)/k

Answer:

103 & 77 degrees

Step-by-step explanation:

Supplements add up to 180 degrees.

I started at 90 & did:

90 + 13 = 103

(Because 13 * 2 is 26, but if you subtract 26 then the supplement will be 52 away & not 26)

180 - 103 = 77

103 - 77 = 26

Hope this helped. :)

Answer:

true

Step-by-step explanation:

they cancel each other out.

Answer:

True

Step-by-step explanation:

The numbers 2.3 and -2.3 are opposites or additive inverses. They add to zero.

Answer: True

Answer:

a_48000cm^3

b_48000000mm^3

Step-by-step explanation:

first of all, let's find the base area:

Ab=((b+B)h)/2=((10cm+30cm)20cm)/2=400cm^2

then, to find the volume, we need to multiplicate the base area to the height of the prism:

V=Ab*H=400cm^2*120cm=48000cm^3=48000000mm^3

Answer:

answer=14π

units=cm

Step-by-step explanation:

GIVEN

diameter (d) = 14 cm

radius (r) = d / 2 = 14 / 2 = 7

Now

Circumference (c)

= 2πr

= 2 * π * 7

= 14π cm

do eat popcorn in a tub

:)

poopy face

If line AB and BC are intersecting at point B and ray BD bisect the angle ABC, then the value of x is 23

The line AB and BC are intersecting at point B.

Ray BD bisect the  angle ABC

∠ABD = x+8 degrees

∠ABD=∠DBC = x+8

Because the ray BD bisect the ∠ABC, so ∠ABD and ∠DBC will be equal

∠ABD+∠DBC= 4x-30 degrees

Because both are vertically opposite angles

Substitute the values in the equation

x+8 + x+8 = 4x-30

2x+16 = 4x-30

2x-4x = -30-16

-2x = -46

x = 23

Hence, if line AB and BC are intersecting at point B and ray BD bisect  the angle ABC, then the value of x is 23

The complete question is

Line AB and BC are intersecting at point B and ray BD bisect the angle ABC. What is the value of x?

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That is a question about spatial geometry.

In our problem, we have to calculate lateral surface area of a triangular prism. Let's see how to solve this.

A triangular prism has 5 faces: 3 equals rectangles and 2 equals triangles. If we can find a way to calculate those areas, we can solve the problem.

The first thing that we should note is that we know the dimensions of the rectangular faces. The dimesions of the rectangular are 5cm and 8cm. To calculate the are of a rectangle, we multiplicate the dimensios of it. Therefore, each rectangle (in our problem) has \(5 \times 8 = 40cm^2\) of area. There are 3 rectangles, so, the sum of the 3 rectangular area is \(40 + 40 + 40 = 120cm^2\).

Now, we need to know the area of the triangular areas. To calculate the area of a triangle, we need to know the value of the base and the value of the height.

In the image, we know the value of the base, but we do not know the value of the height. To calculate the height, we can use the Pythagorean Theorem because we have a right triangle. (Please find attached the document.)

The Pythagorean theorem says that:

\(\boxed{a^2 = b^2 + c^2}\)

a is the hypotenuse and b and c are cathetus.

In this right triangle, the value of the hypotenuse is 5cm and the value of one cathetus is the half of 6cm (that is 3cm). Let's replace the values in the expression:

\(a^2=b^2+c^2\\5^2= 3^2 +c^2\\25 = 9 + c^2\\c^2 = 25 - 9\\c^2 = 16\\c = \sqrt{16} \\c = 4cm\)

Now, we know the bases and the height of the triangular areas. To calculate the area of a triangle, we multiply the base and the height and we divided the result by 2. See the expression:

\(\boxed{A_t=\frac{b\times h} {2}}\)

b is the base and h is the height. Let's replace the values in the expression:

\(A_t = \frac{b\times h}{2} \\A_t = \frac{6\times4}{2} \\A_t = \frac{24}{2} \\A_t = 12cm^2\)

So, each triangular area has 12cm² of area. Therefore, the sum of the triangular areas is \(12 + 12 = 24cm^2\).

Finally, we know that the sum of the rectangular area is 120cm², and the sum of the triangular area is 24cm², so, the lateral surface area is \(120 + 24 = 144cm^2\).

In other words, they didn't choose the correct answer because the correct answer is J) 144 cm².

I hope I've helped. :D

Enjoy your studies. \o/

Answer:

Step-by-step explanation:

If you have a variable like 4x the coefficient would be the 4 because it is being multiplied by the x or the variable. it is usually a number, but it could also be an expression.

I hope this helps

The intercept of the line is 10,985.00.

Given,  Y=5X+10,985.00

We can write the equation in the form of y = mx + c

Where y is the dependent variable, x is the independent variable, m is the slope and c is the intercept.

So, y = 5x + 10,985.00

So, the intercept of the line is 10,985.00.

The intercept of the line is 10,985.00.

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Answer:

Slope of the line 'm' = 5

Step-by-step explanation:

Step(i):-

Given that the straight line

              5 x - y = 20

          ⇒ 5x - 20 = y

               y = 5 x - 20

Step(ii):-

The equation of the straight line having to slope 'm'

               y = m x + c

given that the straight line

              y = 5x +20

comparing   y = m x + c

Slope of the line 'm' = 5

Answer:

i had the exact same question as this, dm me on discord so i can screenshare my answer

Step-by-step explanation:

jey0001 is my discord

Answer:

False

Step-by-step explanation:

5x+3y =-4

Substitute the point into the equation and see if it is true

5(4) +3(6) = -4

20 +18 = -4

38 = -4

This is false so the point is not a solution

Answer:

No.

Step-by-step explanation:

5x + 3y = -4

For (4, 6) to be a solution, 4 must be put in for x and 6 for y and the solution must be -4.

(5 * 4) + (3 * 6) = 20 + 18 = 38

Since 38 is NOT equal to -4, (4, 6) is not a solution.

Hope this helps!

Answer:

this graph is a non linear function

the y intercept of the graph is the function value y=0

the smallest positive x intercept of the graph is located at x= pi/2

the greatest value of y is y=2

for x between x=-pi and, the function value y>0

Step-by-step explanation:

its on khan i hope this is right for your test

The complete sentences are as follows:

This is the graph of a non  linear function.

This is a nonlinear function's graph.

The function value y=1 is the graph's y-intercept.

The graph's smallest positive x-intercept is found at x=π.

When x=0, the value of y that is greatest is y=1.

The function value for x between x=pi and x=2π is y0.

What are the various intercept forms?

The location where the graph and axes cross is known as an intercept. Typically, we operate in two dimensions, which means that the x-axis (abscissa) and y-axis exist (ordinate). There are two sorts of intercepts: x-intercept and y-intercept, which correspond to axes. The point where the graph intersects the x-axis is known as the x-intercept if the graph crosses the x-axis. The point at which a graph contacts the y-axis is referred to as the y-intercept.

Solution:

The graph does not represent a straight line which means it is a non linear function.

To find y-intercept make the value of x as 0 and solve for y.Hence we got the value for y-intercept as 1.

The x intercept is the point where the line on the graph crosses the x-axis.so we get the smallest x intercept as π.

Next to the greatest y intercept form is 1.

Finally through the graph we can make out that the relation between x= π and x=2π is a function of y0.

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Answer: around 2.6 cm because I rounded to the tenth.

Step-by-step explanation:

r^2=170/8.1×3.14

r^2=170/25.434

r^2≈6.68

Next square root both sides so r^2 becomes r and 6.68 square rooted is about 2.6 cm is the radius.

R≈2.6cm

Carlo's trip home took 40 minutes.

To calculate the total time it took for Carlo to complete his trip home, we need to consider the time he spent biking and walking separately.

First, let's calculate the time he spent biking. We know that Carlo's speed while biking was 12 miles per hour, and he rode for 20 minutes. We can convert the time to hours by dividing 20 minutes by 60 (since there are 60 minutes in an hour):

Time biking = 20 minutes ÷ 60 = 1/3 hour

Next, let's calculate the time he spent walking. Carlo's speed while walking was 3 miles per hour, and he walked the remaining distance after getting a flat tire. Since the total distance from school to home is 5 miles and he already biked a portion of it, the remaining distance he walked can be calculated as:

Remaining distance = Total distance - Distance biked

Remaining distance = 5 miles - 12 miles/hour × 1/3 hour

Remaining distance = 5 miles - 4 miles

Remaining distance = 1 mile

To calculate the time spent walking, we can divide the remaining distance by Carlo's walking speed:

Time walking = Remaining distance ÷ Walking speed

Time walking = 1 mile ÷ 3 miles/hour

Time walking = 1/3 hour

Finally, to find the total time of Carlo's trip home, we add the time spent biking and walking:

Total time = Time biking + Time walking

Total time = 1/3 hour + 1/3 hour

Total time = 2/3 hour

Since 2/3 hour is equivalent to 40 minutes, Carlo's trip home took a total of 40 minutes.

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Answer:

Add to eliminate X that way it will be much easier to solve the system of equations.

Step-by-step explanation:

-9x + 4y = 17

9x + 7y = 5

11y = 22

Last step is to divide both sides by 11 and your answer should come to 2!

Answer:

y= 9x -4

Step-by-step explanation:

Please see attached picture for full solution.

The integers here are 9 and -4.

There isnt a need to use fractions in this case and hence I did not write the integers into a fraction (e.g. -4 into \( \frac{ - 4}{1} \)) since the question requires them to be in the simplest form.

Answer:

I'm pretty sure that it's exponential but I'm still going over this topic in class.