Evaluate if t=2 and x=3: 3(2x² - £)
a.) 102
b.) 30
c.) 48
d.) 12​

Answer:

(x - 2)² + (y + 7)² = 64

(fourth option listed / option D)

Step-by-step explanation:

as you likely know, the equation of a circle (centered at origin) is x²+y²=r²

now, let's say we want to write this using the center (the origin), it could look like this:

(x - 0)² + (y - 0)² = r²

(the center is 0,0)

[we write this in parentheses when we are shifting the location of a point--similar to when we move a line on a graph]

We can use this for any center, and we write our circle equation as:

(x - h)² + (y - k)² = r²

(h, k) is the center

So, let's apply the information we know

our (h, k) is (2, -7)

so let's fill that in:

(x - h)² + (y - k)² = r²

(x - 2)² + (y - -7)² = r²          (simplify)

(x - 2)² + (y + 7)² = r²

now, we also know that our "r" (r is the radius) is 8, so let's fill that in too:

(x - 2)² + (y + 7)² = r²

(x - 2)² + (y + 7)² = 8²   (simplify)

(x - 2)² + (y + 7)² = 64

So, we have found the equation of our circle to be:

(x - 2)² + (y + 7)² = 64

hope this helps! (and hope this makes sense) have a lovely day :)

The proportion of defective corks produced by this machine through z test comes out is 0.320.

Given mean of 2 cm and standard deviation of 0.1 cm, The diameter is between 1.9 and 2.1 cm.

We have to find the proportion of defective corks that are produced by machine.

In this problem we have to first find z score and then we will be able to find the probability of defective corks produced by the machine.

Z=(X-μ)/σ

μ=2 cm and σ=0.1 cm.

Z value corresponding to X=1.9.

Z=(1.9-2)/0.1

=-0.1/0.1

=-1

Z value corresponding to X=2.1.

Z=(2.1-2)/0.1

=0.1/0.1

=1

P value of P(-1<Z<1)=2*0.3410=0.6820

Proportion of corks which are not defective=0.6820.

Proportion of corks which are defective=1-0.680.

=0.320

Hence the proportion of defective corks produced by machine is 0.320.

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Because the lines drawn are straight.

Explanation:

When the straight lines join together, the original point from where the first line started, becomes a right angle (90°)

The domain is (-2, 3) and the range is (-3, 4]

The domain

This is the possible x values

From the graph, we have the following highlights:

The endpoints at these intervals is a open circle

Hence, the domain is (-2, 3)

The range

This is the possible y values

From the graph, we have the following highlights:

The endpoint at the minimum is a open circle, while the maximum is a closed circle

Hence, the range is (-3, 4]

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The solution to the graph given is 7/16.

It should be noted that a graph is used to show the relationship between the variables illustrated.

Here, the successive approximation is used to solve equations.

This is done by the comparison to the sequence of the known quantities.

Here, the equation given is 4(-)x + 5 = 3^x + 4. solution to the graph given is 7/16. This is based on the graph given.

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For the training adaptation of maximum strength, 1 to 5 repetitions per set is recommended.

The one-repetition maximum test, also called a one-rep max or 1RM, is used to find out the heaviest weight you can lift just once.

If Maximal strength is desired, it is best achieved by performing  repetitions at  85 to 100 % of the one-repetition maximum (1RM).

Formula to find the repetition is

weight used x (reps done x 0.33 + 1) =  1RM

so,

Reps done = {{1RM/weight used} - 1}/ 0.33

By this find the no of reps are recommended for maximum strength.

The maximum strength is achieved by doing the number of reps by 85 to 100% of the value of 1 RM.

So,

For the training adaptation of maximum strength, 1 to 5 repetitions per set is recommended.

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The probability that exactly 6 out of them are women is 0.176

According to the statement

Number of selected pet owner randomly is 9. So, Here in this case n=9.(number of randomly selected owners).

Number for which have to find the probability is 6. So, Here in this case x=6.

Find the probability by a use of BINOMIAL THEOREM

So, n!/((n-x)!*x!) = 9!/((9-6)!*6!) = 84

Now, find out the probability of success p and probability of failure (1-p)=q.

From here we get p = 0.8 and q= 0.2

Now, use  p^x = (0.8)^6 = 0.2621

Then use q^(n-x) = (0.2)^(9-6) = 0.008

Now, Multiply the results obtained to get the probability is

84*0.2621*0.008 = 0.176

So, The probability that exactly 6 out of them are women is 0.176

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Answer:

a) 7

b) -1

c) 9

Step-by-step explanation:

a) Substitute -1 into the x's of the function.

f(-1) = -5(-1) + 2

f(-1) = 5 + 2

f(-1) = 7

b) f^-1(7) means: find the inverse of the function with 7 substituted as x.

Let y = f(x)

y = -5x + 2

5x = 2 - y

x = 2 - y / 5

f^-1(x) = 2 - x / 5

f^-1(7) = 2 - 7 / 5

f^-1(7) = -5/5

f^-1(7) = -1

c) We have already found the inverse of the- original function. Substitute -43 into the x's of the inverse function.

f^-1(-43) = 2 - (-43) / 5

f^-1(-43) = 2 + 43 / 5

f^-1(-43) = 45/5

f^-1(-43) = 9

Answer:

[tex]3x^{2} -2x+3x-3[/tex]

Step-by-step explanation:

This is one of the easier things to do so definitely learn how to do it.

You just start by taking the first number in each parenthesis (F) and then multiply. 2x by x is 3x^2

Then take the outer (O) number from both problems, so the leftmost and rightmost number. 2x times -1 is -2x

Then take the two inner (I) numbers, 3 and x. Multiply and get 3x

Then take the last number in each parentheses (L) which is 3 and -1, get -3

The system of equations used to find roots of the equation is y=12x³-5x and y=2x²+x+6.

Given the equation is 12x³-5x=2x²+x+6.

A set of equations containing one or more variables is called a system of equations. The variable mappings that satisfy all component equations are the solutions to systems of equations.

Firstly, separate the given equation into two parts by equating the left-hand side and right-hand side with 0, we get

12x³-5x=0

2x²+x+6=0

Now, to make a system of equations replace 0 with y as we know that system of equations contains two variables, we get

12x³-5x=y

2x²+x+6=y

Hence, the system of equations used to find the roots of the equation 12x³-5x=2x²+x+6 is y=12x³-5x and y=2x²+x+6.

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Answer:

D

Step-by-step explanation:

As you can observe from the pattern, the numerator gets multiplied by 4 every increase in the sequence.

So , clearly, the 5th term will be = [tex]\frac{64*4}{5} =\frac{256}{5}[/tex]

and the 6th term will be = [tex]\frac{256*4}{5} =\frac{1024}{5}[/tex]

Therefore , D will be the answer.

The equation in slope-intercept form of the line containing the points (3,-1) and (6, 7) is; y = ⁸/₃x - 7

We are given the coordinates of two points as;

(3,-1) and (6, 7).

Now, the formula for the equation of the line containing the two points in slope intercept form is;

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

Thus, we have;

(y + 1)/(x - 3) = (7 + 1)/(6 - 3)

(y + 1)/(x - 3) = = 8/3

y + 1 = (8/3)(x - 3)

y + 1 = ⁸/₃x - 8

y = ⁸/₃x - 7

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The proportional graph that corresponds to M = 3n is: Graph C.

The constant of proportionality, k, of a proportional graph is given as, y/x. The graph is expressed by the equation, y = kx.

The equation given, M = 3n, represents a proportional relationship where k = 3.

Using a point on graph C, (400, 1,200):

k = 1,200/400

k = 3

Therefore, the graph that corresponds to the situation is: C.

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Answer: m∡B°=38,2°.

Step-by-step explanation:

a=3,  b=5,  c=7  ∡B°=?

[tex]b^2=a^2+c^2-2*a*ccosB^0\\2*a*c*cosB^0=a^2+c^2-b^2\\cosB^0=\frac{a^2+c^2-b^2}{2*a*c} \\cosB^0=\frac{3^2+7^2-5^2}{2*3*7} \\cosB^0=\frac{9+49-25}{2*3*7} \\cosB^0=\frac{33}{42} \\cosB^0=\frac{11}{14}\\[/tex]

m∡B°=arccos[tex](\frac{11}{14})[/tex]

m∡B°≈38,2°.

Good luck!

Answer:

4230.14

Step-by-step explanation:

2040/1700=1.2

2448x1.2=2937.6

2937.6x1.2=3525.12

3525.12x1.2=4230.144

round to the nearest hundredth

4230.14

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The probability that the train will be there when Alex arrives is 5/18

If Alex arrives at any time after 1.20pm the chances that train will  be there is 1/3.

However  if alex arrives at 1.00pm exactly there is no chance the train will be arrive there.

The probability that the train will be there increase linearly to 1/3 as alex's arrival time moves from 1.00pm to 1.20pm.

By arranging the probabilities over the first 20 minutes to get a 1/6 chance the train will be there if alex arrives between 1.00pm to 1.20pm

we get the final answer by

=1/3( 1/6 + 1/3 + 1/3)

=5/18

So, the probability that the train will be there when Alex arrives is 5/18

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Answer:

The independent variables in most cases is input variable. That is a value that does not depend on any other value and it can change independently.

Step-by-step explanation:

The solutions are given below:

1. 3y- 9 = 2x

2.  2/3.

3. y/x

4.  y = (2/3)x + 3

The equation of a line with one given point (x1, y1) is (y - y1) = m(x - x1). Here m is the slope of the line.

The complete question is:

On a coordinate plane, a line goes through (0, 3) and (x, y). A triangle has a rise of 2 and run of 3. A larger triangle has a rise of 5 and run of 7.

Use similar triangles to determine the equation of the line with a slope of 2/3 that passes through the point (0, 3).

What is the ratio of the rise to the run in the smaller triangle in the diagram?

What is the ratio of the rise to the run in the larger triangle in the diagram?

What is the equation of the line in slope-intercept form?

1. slope= 2/3

coordinates= (0, 3)

y-y1 = m(x-x1)

y-3 = 2/3(x-0)

y-3 = 2/3x

3y- 9 = 2x

2. The ratio of the rise to the run in the smaller triangle in the diagram

is y/x = 2/3

3. The ratio of the rise to the run in the larger triangle = y/x

4. The equation of the line in slope-intercept form is given by:

  y = (2/3)x + 3

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Answer:

m = 2

Step-by-step explanation:

m - 2 = 2 - m

2m = 4

m = 2

Hello,

Answer: m = 2

Step-by-step explanation:

       m - 2 = 2 - m

⇔ m - 2 + m = 2 - m + m

⇔ 2m - 2 = 2

⇔ 2m - 2 + 2 = 2 + 2

⇔ 2m = 4

⇔ 2m/2 = 4/2

⇔ m = 2

Answer:

4 units to the left and 2 units up.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

→ We go up the y axis to 6 and read of the x coordinate which is 4. This is because an inverse function does the the opposite i.e.  if f ( x ) = y

f⁻¹ ( y ) = x.

Answer:

Step-by-step explanation:

15 gallons of 35% peroxide solution contains 0.35 × 15 = 5.25 gallons of hydrogen peroxide. The rest of the volume is made up of 15 - 5.25 = 9.75 gallons of water.

If we add [tex]x[/tex] gallons of water to the solution, the amount of hyrdrogen peroxide in the solution stays the same, but the volume of water increases to [tex]9.75+x[/tex] gallons, and the total volume increases to [tex]15+x[/tex] gallons.

To get a concentration of 8% in this diluted solution, we add [tex]x[/tex] gallons of water such that

[tex]\dfrac{5.25}{15+x} = 0.08[/tex]

Solve for [tex]x[/tex].

[tex]5.25 = 0.08 (15 + x)[/tex]

[tex]5.25 = 1.2 + 0.08x[/tex]

[tex]0.08x = 4.05[/tex]

[tex]x = 50.625[/tex]

To get the desired concentration, one must add 50.625 gallons of water, and one will end up with a total volume of 65.625 gallons of solution.

Answer: e= x + y = 10

Step-by-step explanation :
check out the attachment for the answer

We got the value of [tex]e=\frac{78}{7}[/tex] by solving the given equations [tex]3x+2y=26[/tex] and [tex]5x+y=26[/tex] by reduction method.

The reduction or elimination approach includes using arithmetic operations between equations to produce equivalent equations with fewer unknowns that are simpler to analyze and evaluate.

Given equations are

[tex]3x+2y=26[/tex] .........(1)

[tex]5x+y=26[/tex] ...........(2)

We need to find the value of [tex]e=x+y[/tex]

Simplifying the given equation (2) and we get

[tex]5x+y=26\\\Rightarrow y=26-5x[/tex]................(3)

Now, substitute the equation (3) in equation (1) and we get

[tex]3x+2(26-5x)=26\\\Rightarrow 3x+52-10x=26\\\Rightarrow -7x+52=26\\\Rightarrow -7x=26-52\\\Rightarrow -7x=-26\\\Rightarrow x=\frac{26}{7}[/tex]

Substitute the value of x in equation (3), we get

[tex]y=26-5\frac{26}{7} \\\Rightarrow y=26-\frac{110}{7}\\\Rightarrow y=\frac{162-110}{7}\\\Rightarrow y=\frac{52}{7}\\[/tex]

Now adding the values of x and y, we get

[tex]\therefore e=\frac{26}{7}+\frac{52}{7}\\\Rightarrow e=-{[\frac{26+52}{7}]\\\Rightarrow e={[\frac{78}{7}][/tex]

Therefore, the value of [tex]e=\frac{78}{7}[/tex].

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The material needed to make the hat is 3840 cm³.

The hat occupies the whole volume of the rectangular box. Therefore, the material needed to make the hat is the volume of the rectangular box it occupies.

Therefore,

volume of a rectangular prism = lwh

where

Therefore,

l = 16 cm

w = 16 cm

h = 15 cm

volume of a rectangular prism = 16 × 15 × 16

volume of a rectangular prism = 3840 cm³

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The question asks for the probability that a marble is NOT YELLOW

Total Marbles: orange+yellow+blue=7+3+2=12

We need to count all marbles except yellow:

orange+blue=7+2=9

Now to find the probability that is NOT YELLOW:

[tex]\frac{All Marbles Except Yellow}{Total Marbles}[/tex]= [tex]\frac{9}{12} = \frac{3}{4}[/tex]

Answer is 3/4

Hope it helps!

Answer:

I believe the answer is C

Step-by-step explanation:

Hope this helps!!!