Is 12n+60 equivalent to (n + 12) x 5 + 7n

The intersection points are (6, 6) and (-6, -6).

What is Intersection points?

The point at which two lines or curves intersect is referred to as the point of intersection. The point at which two curves intersect is crucial because it is the point at which the two curves take on the same value.

The given curves are the polar equations of two circles with radii 6. To find their intersection points, we can set the two equations equal to each other and solve for Ф.

6 sin(Ф) = 6 cos(Ф)

Dividing both sides by 6 and rearranging terms, we get:

tan(Ф) = 1

This equation has infinitely many solutions, but we are only interested in those that lie in the interval [0, π/2].

Ф = π/4 satisfies this condition and corresponds to the point (6, 6) in Cartesian coordinates.

Since the two curves are circles, they are symmetrical about the origin. Therefore, we can deduce that the other intersection point is (-6, -6).

Therefore, the intersection points are (6, 6) and (-6, -6).

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From the given numbers, 2.6628, 4.17183 and √9 are the rational numbers.

Rational numbers are the numbers that are in the form of p/q where q is not equal to zero that is q≠0. Rational numbers can be expressed as a fraction where both numerators and denominator are whole. When these fractions are further divided, the result will be in decimal form, which may be either terminating decimal or the repeating decimal

Irrational numbers are numbers that cannot be written as simple fractions but can be written in decimal form. It has endless non-terminating digits after the decimal point.

Now according to the question ,

i) √3300 = 57.4456…. as it has endless non-terminating digits after the decimal point. It is an irrational number.

ii) 2.6628 is a rational number as it has a terminating decimal.

iii) 4.137183 is also a rational number as it has terminating decimal.

iv) √9 = 3 is a rational number as it is a perfect square and can be written as fraction.

v) 9.327925…. is a irrational as it has endless non-terminating digits after the decimal point.

Hence 2.6628, 4.17183 and √9 are the rational numbers.

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The missing fourth vertex needed to create a rectangle is (25, 3) option D.

Vertices (singular: vertex) are the corners or points where two or more lines, edges, or curves intersect and form an angle.

Here, the width of one side of the rectangle;

⇒ +3 - (-6) = 9 unit                (left side y-coordinates)

Similarly the length of the rectangle;

⇒ 25 - (-15) = 40 unit             (up-side x-coordinates)

Since a rectangular shape has two sets of equal sides of equivalent width (y-coordinates) and length (x-coordinates), we realize that the missing fourth vertex should be 9 units and 40 units over the point (25, -6). and (-15, 3)

So, we add 9 to the y-coordinate of (25, -6) and add 40 to the x-coordinate of (-15, 3) to get the missing vertex:

⇒ (25, -6+9) = (25, 3)

⇒ (-15+40, 3) = (25, 3)

Therefore, the missing fourth vertex is (25, 3)

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Since f(x) = x^2 - 3 is not a one-to-one function, it does not have an inverse.  The graph of this function does not pass the horizontal line test.

If you tried to algebraically find the inverse, the work would look like this:

    \(\begin{aligned}y &= x^2 - 3\\[0.5em]x &= y^2 - 3 ~~~~~~ \text{swapping $x$ and $y$}\\[0.5em]x+3 &= y^2 \\[0.5em]\pm\sqrt{x+3} &= y~~~~~~\text{using the square root property}\end{aligned}\)

Because the original function is not one-to-one, when you try to find the inverse, there is no unique solution, meaning the inverse equation is not a function.  It won't pass the vertical line test.

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

\(\stackrel{f(x)}{y}~~ = ~~x^2 - 3\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~y^2 - 3} \\\\\\ x+3=y^2\implies \sqrt{x+3}\stackrel{ f^{-1}(x) }{=y}\)

now, is it a function or not?

well, is really the graph of a horizontal parabola, that has symmetry over the x-axis, so since we have a mirror image of it above and below the x-axis, it can't be a function, because a function will need to pass the vertical line test, this one doesn't pass it.

Answer:

-7 = x +6

Step-by-step explanation:

Answer:

Step-by-step explanation:si

With a scaling ratio of 5:2, the larger cylinder's volume is (C) 70m³.

A scale factor is used when a shape is enlarged and each side is multiplied by the same quantity.

This number represents the scaling factor. Map scale factors are used to show distances between locations accurately.

The new shape created by scaling the original shape is twice as big when the scale factor is 2.

Thus, calculate the larger cylinder's volume as follows:

x/5 = 28/2

2x = 28*5

2x = 140

x = 70m³

Therefore, with a scaling ratio of 5:2, the larger cylinder's volume is (C) 70m³.

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Complete question:

The scale factor of two similar cylinders is 5:2. The volume of the smaller cylinder is 28 m3. What is the volume of the larger cylinder?

Question 8 options:

A. 700 m3

B. 350 m3

C. 70 m3

D, 437.5 m3

E. 175 m3

Answer: 70m^3

Step-by-step explanation:

I took the test

The actual annual value of this job to Karla is 33000.

What are arithmetic operations?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

We have,

the job will pay 2400 per month,

if the full cost of the medical insurance is 450 a month and Karla plans to contribute the full 1500 every year tpa retirement plan,

the actual annual value of this job to Karla is:

2400 per month

annual value  = 2400 * 12 = 28,800

the medical insurance is 450 a month

half the cost of medical insurance is  225 a month

annual value  = 225  * 12 = 2700

the full 1500 every year tpa retirement plan,

So, the total value is:

= 28,800 + 2700 + 1500

= 33000

Hence,  the actual annual value of this job to Karla is 33000.

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The standard error tells us how much we can expect the sample proportion to vary from the true proportion in repeated samples of the same size. Option (d) correctly states that "In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion." This means that if we were to take many samples of 100 students from the same school and calculate the proportion of students who bring a reusable water bottle from home in each sample, about 95% of the sample proportions would fall within +/-0.048 of the true proportion.

The correct option is (d) "In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion."

The standard error of the sample proportion can be calculated using the formula:

SE = √[p*(1-p) / n]

where p is the sample proportion and n is the sample size.

In this case, the sample proportion is 37/100 = 0.37 and the sample size is 100. Plugging in these values, we get:

SE = sqrt[0.37*(1-0.37) / 100] = 0.048

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Answer:

a toxin or other foreign substance which induces an immune response in the body, especially the production of antibodies.

Answer:

0.3

Step-by-step explanation:

Let x be what you need to subtract

I hope this helps!

Answer:

3/10

Step-by-step explanation:

83/10 - 3/10 = 80/10 = 8

Answer: 11

Step-by-step explanation:

area = 121 pi  = pi r^2      Divide both sides by pi

            121 = r^2

               r= 11

Answer:

1 gallon=3.79 liters  2 liter juice bottle would hold more

Step-by-step explanation:

The expressions are simplified to;

1. 5x + 11

2. x - 11

3. x - 11y

4. 4x + 20

5. 5x² - y²

6. 5x² - 5y² - 5y

7. -12y²

8. 4x + 20

9. 4x - 20

10. 8x² - 20xy

To simply the algebraic expression, we have to expand the bracket, collect the like terms and then add or subtract them.

From the information given, we have that;

1. 3x + 5 + 2x + 6

collect and add like terms

5x + 11

2. 3x - 5 - 2x - 6

collect and add the like terms

x - 11

3. 3x - 5y - 2x - 6y

collect and add the like terms

x - 11y

4. 6x + 12 - 2x + 8

collect and add the like terms

4x + 20

5. 3x² + 5y² + 2x² - 6y²

collect and add the like terms

5x² - y²

6. 3x² - 5y² + 2x² - 6y

collect and add the like terms

5x² - 5y² - 5y

7. 6x³ - 10y³ + 4x³ - 12y²

collect and add the like terms

-12y²

8. 6(x + 2) - 2(x - 4)

expand the bracket

6x + 12 - 2x + 8

4x + 20

9. 6(x - 2) - 2(x + 4)

expand the bracket

6x - 12 - 2x - 8

4x - 20

10. 6x(x - 2y) + 2x(x - 4y)

expand the bracket

6x² - 12xy + 2x² - 8xy

8x² - 20xy

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To answer this question, we need to compare the ratios of miles traveled to gallons of gas used for car A and car B when they both use 1 gallon of gas.

For car A, we can see from the graph that 50 miles are traveled for every 2 gallons of gas used, or in other words, 25 miles are traveled for every 1 gallon of gas used. Therefore, car A can travel 25 times the distance for 1 gallon of gas.

For car B, we can see from the table that 40 miles are traveled for every 2 gallons of gas used, or in other words, 20 miles are traveled for every 1 gallon of gas used. Therefore, car B can travel 20 times the distance for 1 gallon of gas.

To compare the two ratios, we can divide the ratio of miles traveled to gallons of gas used for car A by the ratio for car B:

25/20 = 1.25

Therefore, car A can travel 1.25 times the distance car B can travel when both cars use 1 gallon of gas.

According to the given graph, we have a line with a positive slope, which means it's increasing, that is, the number of water increases while the number of minutes also increases.

To find the rate of increase, we have to use the following formula

Let's use the points (0,320) and (4, 640).

The rate is 80 liters per minute.

At last, the amount of water in the tank at 0 minutes is 320 liters because that's the initial condition.

Answer: C

Step-by-step explanation:

For box and whiskers plot the box is where the majority of the data is.  the whiskers(the lines on both sides will tell you where the range of numbers lie)

The middle line in the box is the median number.

The question is worded oddly where they want least likely to be more than 30 which means which one will have less than 30. (Double negative question)

You want the majority of the data to be less than 30, which is subway.  C

Answer:

\(0.45 - 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.419\)  

\(0.45 + 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.481\)  

And the 95% confidence interval would be given (0.419;0.481).   And the best option would be:

b. .419 to .481

Step-by-step explanation:

We know the following info:

\(n = 1000\) sample size selected

\(X= 450\) represent the number of people who favored Candidate AT

The sample proportion would be:

\(\hat p=\frac{450}{1000}=0.45\)

The confidence interval would be given by this formula  

\(\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}\)  

For the 95% confidence interval the value of \(\alpha=1-0.95=0.05\) and \(\alpha/2=0.025\), with that value we can find the quantile required for the interval in the normal standard distribution.  

\(z_{\alpha/2}=1.96\)  

And replacing into the confidence interval formula we got:  

\(0.45 - 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.419\)  

\(0.45 + 1.96 \sqrt{\frac{0.45(1-0.45)}{1000}}=0.481\)  

And the 95% confidence interval would be given (0.419;0.481).   And the best option would be:

b. .419 to .481

The strength of binding between an inhibitor and an enzyme can depend on several factors, including molecular geometry and charges.

In this case, it is likely that the structure of the inhibitor allows it to fit more snugly into the active site of the enzyme, forming more extensive hydrogen bonds and other non-covalent interactions with the amino acid residues of the enzyme. Additionally, the inhibitor may have specific charge interactions with residues in the active site that are not present with the natural substrate. These interactions can increase the binding energy between the inhibitor and the enzyme, resulting in a stronger binding affinity than that between the substrate and the enzyme.

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\(\sf\sin^2 150^\circ + \sin^2 60^\circ = 1 \\\)

Step 1: Convert degrees to radians:

\(\sf\sin^2 \left(\frac{150\pi}{180}\right) + \sin^2 \left(\frac{60\pi}{180}\right) = 1 \\\)

Step 2: Simplify the expressions using the trigonometric identity:

\(\sf\sin^2 \left(\frac{\pi}{6}\right) + \sin^2 \left(\frac{\pi}{3}\right) = 1 \\\)

Step 3: Recall the values of sine for angles \(\sf \frac{\pi}{6} \\\) and \(\sf \frac{\pi}{3} \\\):

\(\sf\left(\frac{1}{2}\right)^2 + \left(\frac{\sqrt{3}}{2}\right)^2 = 1 \\\)

Step 4: Evaluate the squares and simplify further:

\(\sf\frac{1}{4} + \frac{3}{4} = 1 \\\)

Step 5: Combine the fractions:

\(\sf\frac{4}{4} = 1 \\\)

Step 6: Simplify the fraction:

\(\sf1 = 1 \\\)

Thus, the equation \(\sf \sin^2 150^\circ + \sin^2 60^\circ = 1 \\\) is verified and true.

Answer:

\( - \frac{1}{100} \)

Step-by-step explanation:

\( - \frac{4}{5x} = 80 \\ - \frac{4}{80 } = 5x \\ x = - \frac{1}{100} \)

Answer:

a) C=31.42 units

b)  A=78.55 SQ UNITS

Step-by-step explanation:

C=2(pi)r

C=2(3.142)5

C=31.42 units

A=(Pi)r^2

A=(3.142) x 5^2

A=3.142 X 25

A=78.55 SQ UNITS

Answer:

Hope this helps ;) don't forget to rate this answer !

Step-by-step explanation:

To solve this problem, we need to perform the indicated operations in order. The first step is to simplify the expressions inside the parentheses.

(3x7 + 7x5 - 3x² + 7) + (x7 - 3x5 + 2x³ + 3)

= (21x + 35x - 3x² + 7) + (7x - 15x + 2x³ + 3)

The next step is to combine like terms within each parentheses:

= (21x + 35x - 3x² + 7) + (7x - 15x + 2x³ + 3)

= (56x - 3x² + 7) + (-8x + 2x³ + 3)

Finally, we can add the two expressions:

= (56x - 3x² + 7) + (-8x + 2x³ + 3)

= 56x - 3x² - 8x + 2x³ + 3 + 7

= 56x - 3x² - 8x + 2x³ + 10

The final answer is 56x - 3x² - 8x + 2x³ + 10.

The range of the data of temperatures remains the same at 48°

Given data ,

Let the data of temperatures be represented as A

Now , the value of A = { 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57 }

The range of the data R = highest value - lowest value

So , R = 105 - 57 = 48

So , the range is 48°

Now , when value of 80.4° is added to the data

R = highest value - lowest value

R = 48°

Hence , the range does not change

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Answer:

900

Step-by-step explanation:

Answer:

total there are 3 values of x as +5/3, -5/3 and 0

Step-by-step explanation:

the  given equation is

x(6x-10) (6x+10)=0

this equation can be solved as following

=0   using the formula (a+b)*(a-b)= (a^2-b^2)

here a=6x and b=10

from here we can write either x=0 or 36x^2= 100  

or x^2= 100/36 and x=0

or x= ±10/6 and x=0

therefore, total there are 3 values of x as +5/3, -5/3 and 0

Answer:

meter - yard

kilogram - 2 pounds

liter - quart