how do i solve this​

Answer:

In the Pascal Expansion of [tex](x+3)^4[/tex] the third term is [tex]54x^2[/tex].

Step-by-step explanation:

Here, the given expression is given as [tex](x+3)^4[/tex]

Now, by the PASCAL'S TRIANGLE EXPANSION:

[tex](a + b)^4 = 1(a)^4 + 4(a)^3b + 6(a)^2b^2 + 4(a)b^3 + 1b^4\\= 1 + 4b + 6a^2 + 4b^3 + b^4.[/tex]

Substituting a  = x and b = 3, we get:

[tex](x + 3)^4 = 1(x)^4 + 4(x)^3(3) + 6(x)^2(3)^2 + 4(x)(3)^3 + 1(3)^4\\= x^4 + 12x^3 + 54x^2  + 108x+ 81[/tex]

In the given expansion, the third term is [tex]54x^2[/tex].

Hence, in the Pascal Expansion of [tex](x+3)^4[/tex] the third term is [tex]54x^2[/tex].

Final answer:

The third term is 6 times x squared times 3 squared, which simplifies to 54x².

Explanation:

To use Pascal's Triangle to determine the third term of the expansion of (x + 3)⁴, we first need to look at the row of Pascal's Triangle that corresponds to the exponent 4. This is the fifth row if we start counting from 0 and it reads 1, 4, 6, 4, 1. We use these coefficients for each term of the expansion, which follows the pattern (a + b)ⁿ = C(n,0)*aⁿ + C(n,1)*a⁽ⁿ⁻¹⁾b + C(n,2)*a⁽ⁿ⁻²⁾b² + ... + C(n,n)*bⁿ, where C(n,k) is the binomial coefficient from Pascal's Triangle.

So, the third term in the expansion is given by the third coefficient (counting from 0) from the row, which is 6, multiplied by x raised to power 4 - 2 times 3 squared. Therefore, the third term is 6x²·3², which simplifies to 54x².

Answer:

Step-by-step explanation:

10/12 divide by 2= 5/6

Answer:

-2/3 (fixed it)

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

The chemist should use 86.13 liters of the 15% solution,

47.29 liters of the 35% solution,

94.58 liters of the 65% solution to obtain a mixture of 228 liters containing 25% acid, using 2 times as much of the 65% solution as the 35% solution.

To solve this problem, we need to find how many liters of each solution should be used to obtain a mixture of 228 liters containing 25% acid, using 2 times as much of the 65% solution as the 35% solution. Here's how we can approach the problem:

Let's assume that we need to use x liters of the 15% solution, y liters of the 35% solution, and z liters of the 65% solution.

From the problem statement, we know that:

x + y + z = 228 (since we need a total of 228 liters of the mixture)

z = 2y (since we need to use 2 times as much of the 65% solution as the 35% solution)

0.15x + 0.35y + 0.65z = 0.25(228) (since we need the final mixture to contain 25% acid)

We can use these equations to solve for x, y, and z. Here's how:

Substitute z = 2y into the first equation to get x + y + 2y = 228, which simplifies to x + 3y = 228.

Rearrange this equation to get x = 228 - 3y.

Substitute z = 2y into the second equation to get 0.15x + 0.35y + 0.65(2y) = 0.25(228), which simplifies to 0.15x + 1.15y = 74.4.

Substitute x = 228 - 3y into this equation to get 0.15(228 - 3y) + 1.15y = 74.4, which simplifies to 34.2 - 0.3y = 74.4 - 1.15y.

Rearrange this equation to get 0.85y = 40.2, which simplifies to y = 47.29.

Substitute y = 47.29 into z = 2y to get z = 94.58.

Substitute y = 47.29 and z = 94.58 into x + 3y = 228 to get x = 86.13.

Therefore, the chemist should use 86.13 liters of the 15% solution, 47.29 liters of the 35% solution, and 94.58 liters of the 65% solution to obtain a mixture of 228 liters containing 25% acid, using 2 times as much of the 65% solution as the 35% solution.

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The second graph, on the right side is a straight line without any gap or break so it is a graph of continuous data.

Step-by-step explanation:

A continuous data s the type of data which contains real values also. the continuous data is measured.

The graph of a continuous data is a continuous line without any breaks. The graph starts and ends only on one note. Not having any breaks or gaps.

In the given diagram, we can observe the both graphs.

The first graph is a scatter plot which only shows points on the graph. It is graph of some discrete data.

The second graph, on the right side is a straight line without any gap or break so it is a graph of continuous data.

Keywords: Discrete data, continuous data

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Answer:

The explicit rule is Ak = 1 + 2 * (k - 1)

Step-by-step explanation:

1. Let's review the information provided to us for finding the explicit rule for the sequence.

The arithmetic sequence 1, 3, 5, 7, 9, . . . represents the set of odd natural numbers.

2. Let's find the solution:

Ak = 1 + 2 * (k - 1)

For k = 1 ⇒ Ak = 1 + 2 * (1 - 1) = 1 + 2 * 0 = 1 + 0 = 1

For k = 2 ⇒ Ak = 1 + 2 * (2 - 1) = 1 + 2 * 1 = 1 + 2 = 3

For k = 3 ⇒ Ak = 1 + 2 * (3 - 1) = 1 + 2 * 2 = 1 + 4 = 5

For k = 4 ⇒ Ak = 1 + 2 * (4 - 1) = 1 + 2 * 3 = 1 + 6 = 7

For k = 5 ⇒ Ak = 1 + 2 * (5 - 1) = 1 + 2 * 4 = 1 + 8 = 9

For k = 6 ⇒ Ak = 1 + 2 * (6 - 1) = 1 + 2 * 5 = 1 + 10 = 11

For k = 7 ⇒ Ak = 1 + 2 * (7 - 1) = 1 + 2 * 6 = 1 + 12 = 13

Answer:

1st: 1+(k-1)2

2nd: 399

3rd: C

4th: 40,000

explanation:

just did it :)

Answer:

54 cm on the blueprint represents actual distance of 27 m.

Step-by-step explanation:

Scale on the blue print drawing of a house show 6 cm represents 3 m.

So, the proportion is [tex]\frac{6}{300} = \frac{1}{50}[/tex] {Since, 3 m = 300 cm.}

Hence, the original dimensions of the house is reduced in the ratio [tex]\frac{1}{50}[/tex] in the blue print drawing.

Then, 27 m i.e. 2700 cm will be represented in the drawing by [tex]2700 \times \frac{1}{50} = 54[/tex] cm.

Therefore, 54 cm on the blueprint represents actual distance of 27 m. (Answer)

Answer:

41

Step-by-step explanation:

Given that 15 people gather for a hot dog eating contest. in the past, eight of these contestants have eaten 37 hot dog during the competition. three at 43, three ate 47 and one ate 49.

From the information given we prepare table as follows

No of hot dogs eaten  X      Frequency f       X*f

                37                                8                 296

                43                                3                 129

                47                                3                 141

                49                                1                  49    

Total                                            15                615

Expected value of X

= Mean value one person can take = [tex]\frac{615}{15} \\=41[/tex]

the expected number of hot dogs eaten by a randomly chosen contestant today is 41

Answer:

See explanation

Step-by-step explanation:

Consider triangles ACM and BCM. In these triangles,

So,

[tex]\triangle ACM\cong \triangle BCM[/tex] by ASA postulate (if one side and two angles adjacent to this side of one triangle are congruent to one side and two angles adjacent to this side of another triangle, then two triangles are congruent).

Two-column proof:

      Statement                                 Reason

1. [tex]m\angle 3=m\angle 4[/tex]                          Given

2. [tex]CM\perp AB[/tex]                        Given

3. [tex]m\angle 1=m\angle 2=90^{\circ}[/tex]       Definition of perpendicular lines CM and AB

4. [tex]\overline{CM}\cong \overline{CM}[/tex]          Reflexive property

5. [tex]\triangle ACM\cong \triangle BCM[/tex]                       ASA postulate

Answer:

[tex]y = 5[/tex]

Step-by-step explanation:

Subtract the 4 from 9

Answer:

step by step explanation:64^3x=512^2x+12

64^3x-512^2x=12

2^18x-2^18x=12

0=12

There is no solution for x in the given quadratic equation.

The equation which is of 2nd degree is known as quadratic equation.

Example: ax^2 + bx + c = 0 (quadratic equation)

               Here a, b, c are known quantities and x is variable.

               Here a can't be 0.

The equation given in the question is:

  64^3x =512^2x+12

 (8^2)^3x = (8^3)^2x + 12

 (8)^6x = (8)^6x + 12

There is no value of x, which will satisfy the equation hence it has no solution.

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Answer:

The diameter of the circle is B) 24 inches.

Step-by-step explanation:

The value given (12 inches) is the radius of the circle. The diameter of a circle is equal to 2 * radius. 2 * 12 = 24.

The diameter of the circle is 24 inches.

Option B is the correct answer.

We have,

The diameter of a circle is a line segment that passes through the center of the circle and connects two points on its circumference.

It is the longest chord of the circle and divides the circle into two equal halves.

The diameter is commonly denoted by the symbol "d" and is related to the radius of the circle (denoted by "r") by the equation:

d = 2r

Now,

r = 12 inches

So,

d = 2r = 2 x 12 inches

d = 24 inches

d = 24 inches

Thus,

The diameter of the circle is 24 inches.

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To find the sum of 3.14 and 4.83, simply add the two numbers together: 3.14 + 4.83 equals 7.97.

The sum of 3.14 and 4.83 can be calculated by performing a simple addition of the two numbers:

3.14

+ 4.83

-------

 7.97

So, the sum of 3.14 and 4.83 is 7.97.

Answer:

36

Step-by-step explanation:

171/(4+0.75) =36

you want it to be in minutes, so calculate the 45 seconds over 60 seconds, which is 0.75. Add that to the 4 minutes, and divide the total number of copies over the time used, and you have speed/minute.

To find how many copies the machine makes per minute, we convert the total time to minutes (4 minutes and 45 seconds equals 4.75 minutes) and then divide the number of copies (171) by this time, resulting in 36 copies per minute.

To calculate how many copies the machine makes per minute, we need to convert 4 minutes and 45 seconds into minutes. Since there are 60 seconds in a minute, 45 seconds is the same as 0.75 minutes (45/60). Adding this to 4 minutes gives us a total time of 4.75 minutes for the machine to make 171 copies. Now, to find the copies made per minute, we divide the number of copies by the number of minutes:

Copies per minute = Total copies / Total time in minutes

= 171 copies / 4.75 minutes

= 36 copies per minute.

Answer:

j=-37

Step-by-step explanation:

step 1

Find the slope of the given line

we have

[tex]2x+3y=21[/tex]

Convert to slope intercept form

Isolate the variable y

subtract 2x both sides

[tex]3y=-2x+21[/tex]

divide by 3 both sides

[tex]y=-\frac{2}{3}x+7[/tex]

The slope is

[tex]m=-\frac{2}{3}[/tex]

step 2

we have the points

(2,-9) and (j,17)

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{17+9}{j-2}[/tex]

[tex]m=\frac{26}{j-2}[/tex]

Remember that

If two lines are parallel then their slope are equal

therefore

[tex]\frac{26}{j-2}=-\frac{2}{3}[/tex]

[tex]26(3)=-2(j-2)\\78=-2j+4\\2j=4-78\\2j=-74\\j=-37[/tex]

Answer:

0.09259259

Step-by-step explanation:

The value of expression 25/18 divided by 5/3 would be; 0.09259259

Since Division can be interpreted as equally dividing the number that is being divided into total x parts, x is the number of parts the given number is divided.

We need to find the expression of  25/18 divided by 5/3.

A negative divided by a negative is positive, then;

25/18  ÷ 5/3

25/18   x 3/5

75/ 90

Therefore, The value of expression 25/18 divided by 5/3 would be; 0.09259259

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Answer:

$40

Step-by-step explanation:

3 hours x 10= 30 hours

$4 x 10= $40

Answer:

Measure of arc LM is 116

Measure of angle MBL is 58

Measure of angle MNL is 64

Step-by-step explanation:

took the test

Answer:

The answers are:  116, 58, 64

Step-by-step explanation:

Answer:

1104 miles

Step-by-step explanation:

Say he lives in a place in Mexico which is at a distance of a miles from the Mexico-America border point and the reunion is at b miles from the same border point, in America.

So the total distance travelled is ( a + b ) miles

( this is just sum of distance travelled in Mexico + that in America )

Given , a=747 and a+b=1851

that implies:

747 + b = 1851

So, b = 1104 miles.

Therefore he has travelled 1104 miles in America,

Answer:

-2.96 , -2 11/12, 2.95

Step-by-step explanation:

Answer:

x = - [tex]\frac{7}{8}[/tex]

Step-by-step explanation:

Given

x + [tex]\frac{3}{4}[/tex] = - [tex]\frac{1}{8}[/tex]

Multiply through by 8 to clear the fractions

8x + 6 = - 1 ( subtract 6 from both sides )

8x = - 7 ( divide both sides by 8 )

x = - [tex]\frac{7}{8}[/tex]

Answer:

x = -7/8

Step-by-step explanation:

x + 3/4 = - 1/8

Subtract both sides:

x + 3/4 - 3/4 = -1/8 - 3/4

x = -1/8 - 3/4

x = -7/8

Answer: 450574.7126 which rounds up to 450575

Step-by-step explanation: Do cross multiplication

100        X  

----- x  ---------

8.7     39200

100 x 39200 = 3920000/ 8.7 = 450574.7

TO CHECK ANSWER

450574.7216 x 8.7% ( convert to decimal .087) = 39200

Answer:

Time left for Madison for other activities is [tex]\frac{5x}{12}[/tex] h .

Step-by-step explanation:

Given as :

The time reserved by Madison for activities = x hours

The time uses for basketball = [tex]\frac{1}{4}[/tex] of x = [tex]\frac{x}{4}[/tex] h

The time uses for playing saxophone = [tex]\frac{1}{3}[/tex] of x = [tex]\frac{x}{3}[/tex] h

So , The total time used by him = [tex]\frac{x}{4}[/tex] h +  [tex]\frac{x}{3}[/tex] h

I.e The total time used by him =  [tex]\frac{7x}{12}[/tex] h

Now, The time left for other activities = x h -   [tex]\frac{7x}{12}[/tex] h

I.e  The time left for other activities =  [tex]\frac{12x - 7x}{12}[/tex] h

or,  The time left for other activities =  [tex]\frac{5x}{12}[/tex] h

Hence Time left for Madison for other activities is [tex]\frac{5x}{12}[/tex] h . Answer

Number of adult tickets sold = 17

Number of student tickets sold =32

Number of senior citizen tickets sold = 51

Given that a certain school sells:

adult tickets = $ 8 ; student tickets = $ 5 and senior citizen tickets = $ 6

Let the number of adult tickets sold be "a"

Let the number of student tickets sold be "b"

Let the number of senior citizen tickets sold be "c"

For one game 100 tickets were sold for $ 600

Number of adult tickets sold + number of student tickets sold + number of senior citizen tickets sold = 100

a + b + c = 100 ------ eqn 1

Number of adult tickets sold  x price of one adult ticket +  number of student tickets sold x  price of one student tickets +  number of senior citizen tickets sold x price of one senior citizen tickets = 600

8a + 5b + 6c = 600  ----- eqn 2

There are 3 times as many adult tickets sold as senior citizen tickets

Hence we get,

3a = c  -------- eqn 3

Put eqn 3 in eqn 1 we get,

a + b + 3a = 100

4a + b = 100

b = 100 - 4a  ----- eqn 4

Substitute eqn 3 and eqn 4 in eqn 2, we get

8a + 5(100 - 4a) + 6(3a) = 600

8a + 500 - 20a + 18a = 600

6a = 600 - 500

a = 16.67 that is approximately 17

a = 17

Substitute a = 17 in eqn 3,

3(17) = c

c = 51

Substitute a = 17 in eqn 4,

b = 100 - 4(17) = 100 - 68 = 32

b = 32

Thus we get:

number of adult tickets sold = a = 17

number of student tickets sold = b = 32

number of senior citizen tickets sold = c = 51

Answer:

The correct answer is A)-27,618 feet because -29,029 Subtract by -1,411 is -27,618 far from each other

The answer is D the other guy is wrong, trust me I just got that question wrong lol

Answer:

x=27°

Step-by-step explanation:

we know that

The Triangle Exterior Angle Theorem, states that: An exterior angle of a triangle is equal to the sum of the opposite interior angles

step 1

Find the measure of angle PLM

we know that

m∠PLM+m∠LPM=m∠PMN ----> by Triangle Exterior Angle Theorem

we have

m∠LPM=x°

m∠PMN=2x+72°

substitute

m∠PLM+x=2x+72°

m∠PLM=2x-x+72°

m∠PLM=x+72°

step 2

Find the measure of angle x

we know that

3x+m∠PLM=180° ----> by supplementary angles (form a linear pair)

we have

m∠PLM=x+72°  (see step 1)

substitute

3x+x+72°=180°

4x=180°-72°

4x=108°

x=27°

Answer:

By the given diagram,

PLM is a triangle,

K and N are points on line MN,

m∠KLP = 3x, m∠P = x, m∠PMN = 2x + 72°

We need to give the reasons in the steps of finding the value of x.

For this we have to know the following properties :

Linear pairs: Adjacent angles which are supplementary.

Subtraction property of equality : We can subtract a number or expression in both sides of an equation.

i.e. a = b ⇒ a + c = b + c

Exterior angle theorem : exterior angle formed by extending the side of a triangle is equal to the sum of its non-adjacent angles.

Thus, the steps of finding value of x are as follow,

1. m∠KLP+m∠PLM = 180°       ( linear pairs )

2. 3x +m∠PLM = 180°              ( Substitution)

3. m∠PLM = 180° - 3x              ( Subtraction property of equality)

4. m∠PMN=m∠P+m∠PLM      ( Exterior angle theorem )

5. 2x + 72° = x + 180° - 3x        ( Substitution)

6. 2x + 72° = 180° - 2x              ( Solving )

   2x = 180° - 2x - 72°  

   2x + 2x = 108°

   4x = 108°

   x   = 27°

Answer:

57

Step-by-step explanation:

The bottom line of the triangle is 180 degrees. Therefore, 2y + 4y - 36 has to equal 180. So, once you solve this linear equation, you will find that y equals 36. A triangle's angles always equal a total of 180 degrees. So, x + 51 + 2y has to equal 180, as well. Since we know y, substitute in 36 for 2y. Now the equation is 51 + 72 + x = 180. Solve for x. X is 57.

Answer:

57°

Step-by-step explanation:

The angles that are at the bottom middle are on a straight line, so they must add up to 180°. In order to determine y, use the equation 180 = 2y + 4y -36. After solving for y, you should be left with 36 = y. Now, we can fill in the bottom right angle in the left triangle. This would be 36 times 2, or 72. In triangles, all angles always add up to 180°, so, we can use the equation 180 = x + 51 + 72. Once solved for x, this will leave you with 57 = x, our final answer.

Answer:

Distance from point A(0,5) to y = -3 x  - 5 is √10 units units.

Step-by-step explanation:

Here, the given line equation is  y = -3x -5

Also, the point A (0,5) is the given point.

Now, a distance of a point (m,n)  from a line Ax + By + c = 0 is given as:

[tex]d = \frac{\mid Am +bn+c \mid}{\sqrt{A^2 + B^2} }[/tex]

Here, the equation is  y = -3 x -5

⇒ 3 x + y + 5 = 0  , here A  = 3, B = 1

Now, the value of line equation at (0,5) is  3(0) + 5 + 5 = 10

So, from the given distance formula,  we get:

[tex]d = \frac{\mid Am +bn+c \mid}{\sqrt{A^2 + B^2} }  = d = \frac{10}{\sqrt{(3)^2 + (1)^2} } = \frac{10}{\sqrt{(10)}}   = \sqrt{(10)}[/tex]

⇒ d  = √10 units

Hence, distance from point A(0,5) to y = -3 x  - 5 is √10 units units.

To find the distance from point A(0,5) to the line y=-3x-5, we can use the distance formula.

To find the distance from point A(0,5) to the line y=-3x-5, we can use the distance formula.

The distance formula is given by:

d = √((x2 - x1)² + (y2 - y1)²)

In this case, point A is (0,5) and the line is y = -3x - 5.

So, we can substitute the values into the formula:

d = √((x - 0)² + (y - 5)²)

d = √(x² + (y - 5)²)

To find the distance, we need to substitute the x and y values of a point on the line into the formula and solve for d.

Let's take the point (1, -8) as an example:

d = √((1)² + (-8 - 5)²)

d = √(1 + 169)

d = √170

So, the distance from point A(0,5) to the line y=-3x-5 is √170.

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Answer:

12 magazines

Step-by-step explanation:

cost over magazines

12.00    =      36.00    

   4                   ?

12*3=36      whatever you do to the numerator you do it to the denominator  

4*3=12

12 magazines

and im correct so gmany you better not delete my answer

Answer:

12 magazines

Step-by-step explanation:

12 (1/4) = 3

36 (1/3) =  12