Find the x and y intercepts for 3x-3y=12

The equation that best suits the sinusoidal function model in this situation is the option:
(C) y = -12cos(1/12x)+ 12.

What is the sinusoidal funtion?

A sine-based function is one that smoothly oscillates between high and low values on a periodic basis. This type of function is known as a sinusoidal function. The cosine function, which is merely a horizontal shift of the sine function, can also be used as the foundation for sinusoidal functions.

A sine wave, also known as a sinusoidal wave or simply a sinusoid, is a mathematical curve that can be described in terms of the sine trigonometric function, whose graph it is. It is a particular kind of smooth periodic function and continuous wave.

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For the given xy-plane where point C coordinates are (6,9) then equation of the line containing point O and C is given by y = ( 3/2)x.

As given in the question,

Given xy -plane,

Coordinates of the point C are (6, 9)

Coordinates of the point O are (0, 0)

Let ( x₁ , y₁) = ( 0, 0)

(x₂ , y₂) = (6, 9)

Equation of the line containing point O and C are :

( y - y₁)/(x - x₁ ) = ( y₂ - y₁)/(x₂ - x₁)

⇒ ( y -0)/(x - 0) = ( 9 - 0)/( 6 - 0)

⇒ y / x = 9 /6

⇒ y = (3/2)x

Therefore, for the given xy-plane where point C coordinates are (6,9) then equation of the line containing point O and C is given by y = ( 3/2)x.

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No , they do not form a proportion because 77 and 60 are not equal

Hence , not form proportion

Set up a proportion as 4/7 = 11/15

Cross multiply:

7×11

4×15

You should get 77 and 60 for the products. Since the products don't equal each other, they are not proportional.

complete question is

use cross products to determine whether the ratios 4/7 and 11/15 form a proportion. Do they form a proportion? Explain your steps and your conclusion

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3. Surface area of cone is 678.24 in²

  Volume of cone is 1017.4 in³

4. Surface area of Cuboid is  1534  sq meters

  Volume of Cuboid is 4080 cubic meters

5. Surface area of cylinder is 376.8 sq centimeters

  Volume of cylinder is 549.5 cubic centimeters

What are solids ?

A three-dimensional object that is closed (which may, according to some terminology conventions, be self-intersecting). A solid is any constrained area of space that is bounded by surfaces, according to Kern and Bland (1948, p. 18). The sphere, cube, cone, and cylinder, as well as the polyhedra more broadly, are some of the most basic solids.

Cone radius r = 9 in

h height = 12 in

Slant height, l² =9²+12² = 81+144 => l=15 in

Volume = (1/3)πr²h   = (1/3)*3.14*9²*12 = 1017.4 in³

Surface area = πr² + πrl  

                      = 3.14*9²+3.14*9*15

                      =254.34 + 423.9 = 678.24 in²

Cuboid volume =17*16*15  = 4080 cubic meters

Surface area = 2 ( 17*16 + 16*15 + 15*17)  = 1534  sq meters

cylinder Volume = πr²h  = π(5)²  * 7 =   549.5 cubic centimeters

cylinder Surface area= 2πr(r + h )   = 2*3.14*5(5+7) = 376.8 sq centimeters

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Answer:

Multiple

Step-by-step explanation:

A multiple of 5 is anything that it can multiply into. For example: 5, 10, 15, 20, 25 and so on.

A factor is a number that divides into your number and leaves no remainder. An example of this is 2 is a factor of 4.  15 is not a factor of 5 because it cannot divide evenly. The only factors of 5 are 1 and 5.

The slope of the given function of taxi fare mean  the rate of change of the cost of the taxi ride is $3.00 per minute..

In the situation y = mx + c the worth of m is known as the slant, (or angle), of the line. It very well may be positive, negative or zero. Lines with a positive inclination slant upwards, from left to right. Lines with a negative inclination slant downwards from left to right. Lines with a zero inclination are level.

C(x) = 3x + 2

On comparing with the general equation of line. we get

slope = 3  

slope = cost/time

Which says the rate of change of the cost of the taxi ride is $3.00 per minute.

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The required height of given regular pentagonal prism is 19 millimeters.

We work out the volume of a pentagonal crystal utilizing the recipe is V = 5/2abh where this equation is additionally perceived as V = [1/2 × 5 × base length × apothem] × level of the crystal. The qualities are placed in the recipe and compose the response so got in cubic units.

We have,

Then

V = 5/2abh

2850 =( 5×12×h)×5/2

h = 19 millimeters

Thus, required height of the pentagonal prism is 19 millimeters.

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Answer:

19 millimeters

Step-by-step explanation:

i took the test and got right hope this helps :)

Answer:

i believe it is b)

the no. of days beginning with T (2)

the no. of days not starting with T (5)

The total number of cups of punch that peter makes is  13 1/6.

The sum of the values 4 1/3, 2 1/3, and 6 1/2 is required. To make adding easier, let's first turn them into improper fractions:

= 13/ 3 + 7/3 + 13/2

We can now simplify it because two of a fractions use the same denominator, resulting in the following:

= 30/3 + 13/2

Next, we must determine which of the two fractions has the lowest common denominator.

We may modify our denominator to 6 because that is the smallest number so both 2 and 3 can fit in:

= 23/3 x (2/2) + 13/2 x (3/3)

= 40/6 + 39/6

= 79/6

We should change this back into such a mixed number for our response:

= 79/6

= 13 1/6

Thus, the total number of cups of punch that Peter makes is  13 1/6.

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The correct question is-

Peter mixes 4 1/3 cups of orange juice, 2 1/3 cups of ginger ale, and 6 1/2 cups of strawberry lemonade to make some punch. What is the total number of cups of punch that Peter makes?

When two of a triangle's angles and one of its included sides are congruent with the equivalent portion of another triangle, the two triangles are said to be in AAS or ASA congruency.

AAS Congruency:

Therefore, when two of a triangle's angles and one of its included sides are congruent with the equivalent portion of another triangle, the two triangles are said to be in ASA or AAS congruency.

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let's start by grouping the terms with the variable first, so that'd be

(x² - x) -3 = 0

(x² - x + []²) = 3

now, the middle term in a perfect square trinomial is simply the product of "2" and the root of the terms on the left and right sides, so whatever that product is, we know it must yield "x" because that's our middle term above skipping its sign, so hmmm let's check around

[tex]\qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2 \\\\[-0.35em] ~\dotfill\\\\ (x^2 - x +\square^2)=3 \\\\\\ 2\sqrt{\square^2}\sqrt{x^2}~~ = ~~x\implies 2\square x=x\implies \square=\cfrac{x}{2x}\implies \square=\cfrac{1}{2}[/tex]

so that's our missing value, now ( 1/2 )² is 1/4, however, let's recall that, all we're doing is borrowing from our very good friend Mr. Zero, 0, so if we add 1/4 we also have to subtract 1/4

[tex]\left(x^2-x+\cfrac{1}{4}-\cfrac{1}{4} \right)=3\implies \left(x^2-x+\cfrac{1}{4} \right)-\cfrac{1}{4}=3 \\\\\\ \left(x^2-x+\left( \cfrac{1}{2} \right)^2 \right)=3+\cfrac{1}{4}\implies \left(x-\cfrac{1}{2} \right)^2=\cfrac{13}{4}\implies x-\cfrac{1}{2}=\pm\sqrt{\cfrac{13}{4}} \\\\\\ x-\cfrac{1}{2}=\pm\cfrac{\sqrt{13}}{2}\implies x=\pm\cfrac{\sqrt{13}}{2}+\cfrac{1}{2}\implies \boxed{x=\pm\cfrac{\sqrt{13}+1}{2}}[/tex]

The kind of line is used when the inequality symbol is ≥ or ≤ is solid line

If the original inequality is ≤ or ≥, the boundary line is drawn as a solid line, since the points on the line will make the original inequality true.

The kind of line is used when the inequality symbol is ≥ or ≤ is solid line

But in case of < or > symbol, the line used is dotted line.

A solution of an inequality is a number which when substituted for the variable makes the inequality a true statement.

Therefore, The kind of line is used when the inequality symbol is ≥ or ≤ is solid line

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The time taken to get to work from home with a speed of 30mph will be 40 minutes, 40mph in 30 minutes, and 50mph in 24 minutes.

Velocity is the rate of distance covered per time. Velocity could be average or instantaneous.

Average velocity can be given as;

Average velocity = total distance / total time taken

Units of velocity are given by ⇒ meter/second

As per the given,

Time = distance/speed

Distance = 20 miles

With a speed of 30 mph

Time = 20/30 = 2/3 hour or 40 minutes

With a speed of 40 mph

Time = 20/40 = 1/2 hour or 30 minutes

With a speed of 50 mph

Time = 20/50 = 2/5 hour or 24 minutes

Hence "The time taken to get to work from home with a speed of 30mph will be 40 minutes, 40mph in 30 minutes, and 50mph in 24 minutes".

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Answer:

---------------------------

Find the area between x = 85 and x = 125.

The matching choice is A

Answer:

0.7938

Step-by-step explanation:

The given graph is a normal distribution curve.

If a continuous random variable X is normally distributed with mean μ and variance σ²:

[tex]\boxed{X \sim \textsf{N}(\mu,\sigma^2)}[/tex]

Given:

[tex]\text{If \; $X \sim \textsf{N}(100,15^2)$,\;\;find\;\;P$(85\leq X\leq 125)$\;\;to\;3\;s.f.}[/tex]

Therefore, we need to find the area to the left of x = 125 and subtract the area to the left of x = 85.

Method 1

Using a calculator:

[tex]\begin{aligned}\implies \text{P}(85\leq X\leq 125)&= \text{P}(X\leq 125)-\text{P}(X < 85)\\&=0.9522096477-0.1586552539 \\&=0.7935543938\\&\approx0.7938\end{aligned}[/tex]

Method 2

Converting to the z-distribution.

[tex]\boxed{\text{If\;\;$X \sim$N$(\mu,\sigma^2)$\;\;then\;\;$\dfrac{X-\mu}{\sigma}=Z$, \quad where $Z \sim$N$(0,1)$}}[/tex]

[tex]x=85 \implies Z_1=\dfrac{85-100}{15}=-1[/tex]

[tex]x=125 \implies Z_2=\dfrac{125-100}{15}=1.67[/tex]

Using the z-tables to find the corresponding probabilities (see attachments).

[tex]\begin{aligned}\implies \text{P}(-1\leq Z\leq 1.67)&= \text{P}(Z\leq 1.67)-\text{P}(Z < -1)\\&=0.9525-0.1587\\&=0.7938\end{aligned}[/tex]

In the 1980s and 1990s, many urban area kids in New York turned to "Selling Drugs" as a means of supplemental income as a means of escape.

The crack epidemic that ravaged New York City with in 1980s was beginning to fade by the early 1990s, and crime rates were also declining.

Thus, during the 1980s and 1990s, many urban area kids in New York turned to "Selling Drugs" as a means of supplemental income as a means of escape.

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The value of the car after 10 years is 4668.9 dollars

Depreciation is the reduction in the value of an asset or commodity over time and such valued reductions are reflected in the balance sheet at the year ended.

According to the given information:

Prize of the new car purchased P = 23700 dollars

the rate at which the value of a car depreciates R = 15% per year

Now, the value of the car after 10 years could be determined by the formula

Amount        =    P[tex](1-r)^{t}[/tex]

P = 23700 dollars        R = 15% per year           t = 10 years

Substituting all the values in the above formula:

Amount       =   [tex]23700(1-0.15)^{10}[/tex]

                    =    [tex]23700(0.85)^{10}[/tex]

                    =    23700×0.197

                    =     4668.9 dollars

The value of the car after 10 years is 4668.9 dollars

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If the density at any place is inversely proportional to its distance from the origin, locate the center of mass as (0,4.5).

Given that,

The area inside the circle where x² + y² = 18y and outside the circle where x² + y² = 81 is occupied by a lamina.

We have to find if the density at any place is inversely proportional to its distance from the origin, locate the center of mass.

We know that,

Take the equation

x² + y² = 18y

x² + y² - 18y=0

Adding and subtracting 9².

x² + y² - 18y+ 9²-9²=0

x² + y² - 18y+ 9²=9²

x² + (y-9)²=9²

Which is a circle of radius 9 and center (0,9), And now the second equation

Now,

x²+y²=81

Which is a circle with radius 9 and center (0,0).

We can plot the curves in the picture we can see.

The density will be evenly distributed around the lines x=0 and y=4.5, which are the lines of symmetry, in a more complicated scenario where we would need to utilize integration to identify the Center of Mass.

Therefore, if the density at any place is inversely proportional to its distance from the origin, locate the center of mass as (0,4.5).

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The solution of equation is y = -15, x = 1 .The equation used to obtain the value of y and x is y = -15x.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right   sides.

We have LHS = RHS (left hand side = right hand side) in every   mathematical equation. To determine the value of an unknown variable  that represents an unknown quantity, equations can be solved. A   statement is not an equation if it has no "equal to" sign. It will be regarded as a phrase.

The given equation is: y= -5x3

or        y= -15x

or      y\x=-15

Divide with 1 both side

    y/x = -15/1

Then  y = -15 , x = 1

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Answer: (5,28)

Step-by-step explanation:

Answer:

Here it is :)

Step-by-step explanation:

if this is incorrect, correct me and explain why so you won’t make this mistake I made when you do this on you own!

Answer:

[tex]\huge\boxed{\sf r = 1/4}[/tex]

Step-by-step explanation:

y = rx -------------------(1)

From the table,

x = 8 when y = 2

Put in the above equation.

2 = r(8)

Divide 8 to both sides

2/8 = r

r = 2/8

r = 1/4

[tex]\rule[225]{225}{2}[/tex]

Answer: 4 deliveries per hour

Step-by-step explanation:

16 divided by 4 = 4 deliveries

Aubrey has practiced piano at the rate of 54 minutes per day.

What is a unit conversion in mathematics?

Unit conversion is a multi-step process that includes multiplying or dividing by a numerical factor, determining the appropriate number of significant digits, and rounding.

Aubrey practices the piano for 1890 minutes in 5 weeks.

In one week there are 7 days.

So the total number of days will be = 5 * 7

                                                          = 35 days.

So Aubrey has practiced piano at the rate of = 1890/35 minutes per day

                                                                = 54 minutes per day.

Hence, Aubrey has practiced piano at the rate of 54 minutes per day.

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In order for the two-sample z statistic to be valid we need that the following assumptions hold samples must be random

data has to be continuous

each sample and population must be independent from each other

each population must be normally distributed

the population standard deviations must be known or the sample sizes must be ≥ 30

samples must be random

data has to be continuous

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The probability density function f(x) represents the probability at a given value of x.

In a distribution, the notation f(x) is the equivalent to the probability of event x, that is:

[tex]f(x) = P(X = x)[/tex]

The area under the curve is given by the cumulative distribution, which is given by:

[tex]P(X\leq x) = \int\limits^x_0f(x)dx[/tex]

Thus it is not f(x).

And f(x) can also be the height of the relative frequency function, but not of the function itself.

Hence the answer is the probability density function f(x) represents the probability at a given value of x.

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Step-by-step explanation:

x = the number

15x + x/2 = 62

30x + x = 124

31x = 124

x = 4

If the one factor is the gcf and the other is the sum of two numbers that do not have a common factor, then the expression will be 8(7 + 12)

The expression is given by

56 + 96

First we have to find the GCF of the numbers

Prime factorization

56 = 2×2×2×7

96 = 2×2×2×2×2×3

The GCF(56, 96) = 8

Write the expression using the GCF

56 + 96 = 8(7) + 8(12)

Here we have to apply the distributive property

AB + AC = A(B + C)

Then,

8(7) + 8(12) = 8 (7 + 12)

Hence, if the one factor is the gcf and the other is the sum of two numbers that do not have a common factor, then the expression will be 8(7 + 12)

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Mitochondria use proteins to break down sugars and produce cellular energy in the form of ATP.

Answer:

y = -1/3 x + 5

Step-by-step explanation:

To write the equation, you need the slope and the y-intercept to write the equation in the slope intercept form.  You did not state what form, so this is the form that I will use.

y = mx + b  M is the slope and b is the y intercept.

The slope is the change in y over the change in x.  For the two points we can find the change in y by using the numbers 6 and 7.  We can find the change in x by using the numbers - and -6,

[tex]\frac{6-7}{-3 - -3}[/tex] = [tex]\frac{-1}{-3+6}[/tex] = [tex]\frac{-1}{3}[/tex]  This is the slope.

To find the y intercept (b) we will use one point and the slope.  It does not matter which point that you use.  I am going to use the point (-3,6).

slope (m) = [tex]\frac{-1}{3}[/tex]

x = -3

y = 6  Plug these into the equation and solve for b.

y = mx + b

6 = ([tex]\frac{-1}{3}[/tex]) (-3) + b

6 = 1 + b  Subtract 1 from both sides.

5 = b

y = [tex]\frac{-1}{3}[/tex]x + 5

To figure how many paths there are from (0,0) to (50,50) on a Cartesian coordinate system is using the legal moves, move up and move right. The formula that can be used is ((x+y)¦x). Here the steps;

Each path from point (0,0) to (50,50) will contain 50 rightward steps (i.e. progressive along the x-axis) and 50 upward steps (progressive along y-axis), resulting in a total of 100 steps, therefore we have ((x+y)¦x)= ((50+50)¦50) = (100¦50) ways of creating such a path.

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For solving the inequalities, there are more than four steps.

The step to solve given inequalities, the first step is to add the same number to both sides, the second step is to  Subtract the same number from both sides and the third step is to  Multiply both sides by the same positive number, and the fourth step is to  Divide both sides by the same positive number, and the fifth step is to Multiply both sides by the same negative number and reverse the sign and the last step is to Divide both sides by the same negative number and reverse the sign. Out of which steps 2,3,4 and 5 are the most important steps.

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