write down in trems of n an expression for the nth term in the following sequences 1 8 15 22 29

The first rational expression is 63m²+20m−32. To rewrite this with a common denominator of (3m−4)(m+8)(m−7), first we need to find the LCD (Lowest Common Denominator) of both terms. So, we need to multiply each numerator and denominator of the first rational expression by (3m−4)(m+8)(m−7).

In the numerator, we need to multiply 63m² by (3m−4)(m+8)(m−7):

63m² × (3m−4)(m+8)(m−7) = 63m³ - 224m² + 784m - 504

In the denominator, we need to multiply 1 by (3m−4)(m+8)(m−7):

1 × (3m−4)(m+8)(m−7) = 3m³ - 12m² + 24m - 16

Therefore, the rewritten rational expression is:

63m³ - 224m² + 784m - 504/3m³ - 12m² + 24m - 16

The second rational expression is 3m³m²−25m+28. To rewrite this with a common denominator of (3m−4)(m+8)(m−7), we first need to find

The value of the variable "x" is 11.

We have a triangle. The vertices of the triangle are K, L, and M. The side KM is extended from point M to point N. The measures of the angles MKL, LMN, and KLM are (3x + 19)°, (7x + 5)°, and (2x + 8)°, respectively. We need to find out the value of the variable "x".

The angles LMK and LMN form a linear pair. It means they are supplementary angles. The sum of the angles is 180°.

∠LMK + ∠LMN = 180°

∠LMK + (7x + 5)° = 180°

∠LMK = 180° - (7x + 5)°

In the triangle KLM, we will use the angle sum property of a triangle. The sum of all the angles in a triangle is equal to 180°.

∠K + ∠L + ∠M = 180°

(3x +19)° + (2x + 8)° + [180° - (7x + 5)°] = 180°

3x +19 + 2x + 8 + 180 - 7x - 5 = 180

-2x + 22 = 0

2x = 22

x = 11

Hence, the value of the variable "x" is 11.

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Step-by-step explanation:

7

not equivalent

8

6.11 $

Answer:

The perimeter of the square is 32x + 20 inches, and the perimeter of the rectangle is (4x - 5) + (4x - 5) + (12x + 15) + (12x + 15) = 32x + 20 inches.

So, to find the value of x that makes the perimeters the same, we set 32x + 20 = 32x + 20 and solve for x.

x = 0

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

x = 90

Step-by-step explanation:

The given diagram shows a circle with intersecting chords, KM and JL.

To find the value of x, we can use the Angles of Intersecting Chords Theorem.

According to the Angles of Intersecting Chords Theorem, if two chords intersect within a circle, the angle formed at the intersection point is equal to half the sum of the measures of the arcs intercepted by the angle and its corresponding vertical angle.

Let the point of intersection of chords KM and JL be point P.

As the chords are straight lines, angle x° forms a linear pair with angle JPM.

Note: We cannot use the Angles of Intersecting Chords Theorem to find the value of x directly, since we have not been given the measures of the arcs KJ and ML. Therefore, we need to use the theorem to find m∠JPM first.

From inspection of the given diagram:

Using the Angles of Intersecting Chords Theorem, we can calculate the measure of angle JPM (shown in orange on the attached diagram):

\(\begin{aligned}m \angle JPM &=\dfrac{1}{2}\left(m\overset\frown{JM}+m\overset\frown{LK}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+(2x-30)^{\circ}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+2x^{\circ}-30^{\circ}\right)\\\\&=\dfrac{1}{2}\left(2x^{\circ}\right)\\\\&=x^{\circ}\end{aligned}\)

As angle JPM forms a linear pair with angle x°, the sum of the two angles equals 180°:

\(\begin{aligned}m \angle JPM+x^{\circ}&=180^{\circ}\\\\x^{\circ}+x^{\circ}&=180^{\circ}\\\\2x^{\circ}&=180^{\circ}\\\\\dfrac{2x^{\circ}}{2}&=\dfrac{180^{\circ}}{2}\\\\x^{\circ}&=90^{\circ}\\\\x&=90\end{aligned}\)

Therefore, the value of x is 90, which means that the two chords intersect at right angles.

Answer:

a=0.2 b=86

Step-by-step explanation:

in this equation, a is the coefficient (what the base is multiplied by) and b is the base (what you start out with).  because isabella started off with $86 so that is her base and because her sales increased by 20% so that is her coefficient

Answer:

89.8ft

Step-by-step explanation:

678-672=6, the value for line ZW

Using Pythagoras theorem, then t²+6²=90²

t²=90²-6²

t²=8100-36

√t²=√8064

t=89.8ft

Answer:the answer is 5 and 8 i guess

Step-by-step explanation: For example, angles 1 and 2 are both facing in the same direction, to the upper right. Such angles are called corresponding angles. Similarly we have angles 3 and 6, angles 4 and 7, and angles 8 and 5 as corresponding angles.

Answer:

The base of the triangle is 4cm and the height is 6cm

Answer:

\(\dfrac{5e^2}{2}\)

Step-by-step explanation:

Differentiation is an algebraic process that finds the slope of a curve. At a point, the slope of a curve is the same as the slope of the tangent line to the curve at that point. Therefore, to find the slope of the line tangent to the given function, differentiate the given function.

Given function:

\(y=x^2\ln(2x)\)

Differentiate the given function using the product rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let\;$u=x^2}\)\(\textsf{Let\;$u=x^2$}\implies \dfrac{\text{d}u}{\text{d}x}=2x\)

\(\textsf{Let\;$v=\ln(2x)$}\implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{2}{2x}=\dfrac{1}{x}\)

Input the values into the product rule to differentiate the function:

\(\begin{aligned}\dfrac{\text{d}y}{\text{d}x}&=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}\\\\&=x^2 \cdot \dfrac{1}{x}+\ln(2x) \cdot 2x\\\\&=x+2x\ln(2x)\end{aligned}\)

To find the slope of the tangent line at x = e²/2, substitute x = e²/2 into the differentiated function:

\(\begin{aligned}x=\dfrac{e^2}{2}\implies \dfrac{\text{d}y}{\text{d}x}&=\dfrac{e^2}{2}+2\left(\dfrac{e^2}{2}\right)\ln\left(2 \cdot \dfrac{e^2}{2}\right)\\\\&=\dfrac{e^2}{2}+e^2\ln\left(e^2\right)\\\\&=\dfrac{e^2}{2}+2e^2\\\\&=\dfrac{5e^2}{2}\end{aligned}\)

Therefore, the slope of the line tangent to the graph of y = x²ln(2x) at the point where x = e²/2 is:

\(\boxed{\dfrac{5e^2}{2}}\)

Therefore, on dividing 6216 by 21 we get 126

Given 6216 / 21

21 ) 6216 ( 296

      42

(-)...................     (By subtracting these two numbers we get )

      201            

       189

(-)..................    

          126

          126

.(-)..........................

            0

Therefore 6216 / 21 = 126

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Answer: 1.6

Step-by-step explanation:

each golf is 1.6 ounces and you 20 golf balls in order to reach 32 ounces

Answer:

shown below

Step-by-step explanation:

golf balls per ounce = 5/8 or 0.625

ounces per gold ball = 8/5 or 1.6

Answer: Endpoint = (-4,6)

Step-by-step explanation:

To find any endpoint use the formula \(\frac{x_1+x_2}{2} = Xmp\)    \(\frac{y_1+y_2}{2} =Ymp\)

\(\frac{6+x_2}{2} = 1\)          \(\frac{-2+y_2}{2} =2\)    

multiply each by 2  to simplify

\(\frac{6+x_2}{2*2} = 1*2 = {6+x_2}= 2\)    \(\frac{-2+y_2}{2*2} =2*2 = -2+y_2=4\) take the equations and simplify

6+\(x_{2}\) = 2                          -2+\(y_{2}\) = 4  =  

-6       -6                          +2       +2

   \(x_{2}\) = -4                               \(y_{2}\) =  6

To check use the Midpoint formula

\(\frac{-4+6}{2} , \frac{6-2}{2} = \frac{2}{2} , \frac{4}{2} = (1,2)\)

Answer:

The sample size is    \(n = 68 \)

Step-by-step explanation:

From the question we are told that

    The margin of error is  \(E = 5 \ years\)

     The standard deviation is  \(\sigma = 22\)

From the question we are told the confidence level is  94% , hence the level of significance is    

      \(\alpha = (100 - 94 ) \%\)

=>   \(\alpha = 0.06\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  1.881\)

Generally the sample size is mathematically represented as  

   \(n = [\frac{Z_{\frac{\alpha }{2} } *  \sigma }{E} ] ^2\)

=>  \(n = [\frac{1.881 } *  22 }{5} ] ^2\)

=>  \(n = 68 \)

Answer:

7 inches..............

Answer:

8

Step-by-step explanation:

Volume = Length * Width * Height

512 = 8*8*Height

Height = 512/64=8

Answer:

X _> 3

Step-by-step explanation:

6/2 = 2x/2

3 = x

x = 3

The common number in both sets will be 18. And the row labeled 6 is the multiplication of the row labeled 3 with 2.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

A multiplication table.

In the row labeled 3, the numbers 9, 12, 15, 18, and 21 are highlighted.

In the row labeled 6, the numbers 18, 24, 30, 36, and 42 are highlighted.

Look at the highlighted portions in rows 3 and 6.

The common number in both sets will be 18.

The row labeled 6 is the multiplication of the row labeled 3 with 2.

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Answer: the person above is wrong

its 3, 4, 5, 6, and 7

Answer:

(-6, -3) (-3,-3) (-3,-6)

Step-by-step explanation:

Multiple all of the vertices by 1.5.

(-6, -3) (-3,-3) (-3,-6)

Hope I helped!

[enlargment will still be a triangle]

Answer:

For acute angles, remember what sine means: opposite over hypotenuse. If we increase the angle, then the opposite side gets larger. That means "opposite/hypotenuse" gets larger or increases.

Step by Step:

Keep this in mind >>

Consider the unit circle > The sine and cosine ratios are the only ratios that have 1 (the radius or hypotenuse) as the denominator. The numerators (sides) vary between 0 and 1, thus determining that the sine and cosine do the same.

All of the other ratios (tangent, cotangent, secant, cosecant) have a side as the denominator, varying between 0 and 1. As any denominator approaches 0, the value of the ratio approaches infinity.

Answer:

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Subtract 6 to 7 then add that to the 7.

Answer:

M = 4pi²a³ / GT²

Step-by-step explanation:

Cross multiply: T² × GM = GMT²

1 × 4pi²a³ = 4pi²a³

It becomes: GMT² = 4pi²a³

Divide both sides by GT² to solve for M

We have : M = 4pi²a³ / GT²

Answer:

e is 63 degrees

d is 31 degrees

Answer:

(3,7)

Step-by-step explanation:

(7,4)

Moving left and right relates to x

Moving up and down relates to y

When you move to the left, you subtract

When you move to the right, you add

When moving up, you add

When moving down you subtract

X= 7-4 = 3

x=3

Y= 4+3 = 7

y = 7

(3,7)

Answer:

237

Step-by-step explanation:

This is a system of equations.

The theater sold 364 adult and child tickets, so a + c = 364

They made a total of $1930. Each adult ticket was $6 & child tickets were $4. The second equation is 6a + 4c = 1930.

Let's line them up

a  +  c = 364

6a + 4c = 1930

Since we need to solve for the number of adult tickets, we want to get rid of the c variable. I'm going to multiply the entire first equation by -4 to do this. The second equation stays the same. Now, I have:

-4a - 4c = -1456

6a + 4c = 1930            Add them together

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

2a = 474                      Divide by 2 to solve for a

a = 237

There were 237 adult tickets sold

Answer:

74.7

Step-by-step explanation:

To adjust the recipe to make 30 rolls instead of 12, we need to multiply the amount of each ingredient by a factor of 30/12 = 2.5.

A factor is a number or expression that divides another number or expression evenly without a remainder.

To adjust the recipe to make 30 rolls instead of 12, we need to multiply the amount of each ingredient by a factor of 30/12 = 2.5.

To determine this factor, we divide the desired number of rolls (30) by the original number of rolls (12):

2.5 = 30/12

To find the amounts of each ingredient needed to make 30 rolls, we multiply the original amounts by 2.5:

Yeast: 1/4 oz x 2.5 = 0.625 oz (or about 0.63 oz)

Warm water: 1 cup x 2.5 = 2.5 cups

Molasses: 3 tbsp x 2.5 = 7.5 tbsp (or about 1/2 cup + 1 tbsp)

Powdered milk: 1/3 cup x 2.5 = 0.83 cups (or about 3/4 cup + 1 tbsp)

Egg yolk: 1 beaten yolk x 2.5 = 2.5 beaten yolks (or about 2 yolks)

Egg white: 1 beaten white x 2.5 = 2.5 beaten whites (or about 2 whites)

Bread flour: 3 1/2 cups x 2.5 = 8.75 cups (or about 8 3/4 cups)

Butter: 6 tbsp x 2.5 = 15 tbsp (or about 1 cup - 1 tbsp)

Salt: 1 tsp x 2.5 = 2.5 tsp (or about 2 1/2 tsp)

Whole wheat flour: 1/2 cup x 2.5 = 1.25 cups (or about 1 1/4 cups)

Raisins: 1/3 cup x 2.5 = 0.83 cups (or about 3/4 cup + 1 tbsp)

To make 30 rolls, you will need 0.625 oz (or about 0.63 oz) of yeast.

To make 30 rolls, you will need 0.83 cups (or about 3/4 cup + 1 tbsp) of powdered milk.

To make 30 rolls, you will need 15 tbsp (or about 1 cup - 1 tbsp) of butter.

To make 30 rolls, you will need 8.75 cups (or about 8 3/4 cups) of bread flour, which is 8.75 - 1.25 = 7.5 cups more than the 1.25 cups of whole wheat flour needed.

If you put in 3/8 cup of water instead of the 1/4 cup called for in the original recipe, you have added an extra 3/8 - 1/4 = 1/8 cup of water, or 2 tablespoons of water.

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Answer: \(w=\frac{12}{13}\)

Step-by-step explanation:

To solve for w, we want to isolate the variable.

\(\frac{1}{3}w +\frac{5}{6}w-2=-w\)        [add both sides by 2 and w]

\(\frac{1}{3}w +\frac{5}{6}w+w=2\)           [convert to same denominator]

\(\frac{2}{6}w +\frac{5}{6}w+\frac{6}{6} w=2\)         [add]

\(\frac{13}{6} w=2\)                          [multiply both sides by 6/13]

\(w=\frac{12}{13}\)

Now we know that \(w=\frac{12}{13}\).

Answer:

Step-by-step explanation:

1/3w + 5/6w - 2 = -w    Collect like terms on the left.

Before I do, I'm going to assume the question is (1/3)w + (5/6)w - 2 = - w

(1/3)w + (5/6)w - 2 = - w

1/3 + 5/6 = 2/6 + 5/6 = 7/6

(7/6)w - 2 = -w             Add w to both sides

(7/6)w + w - 2 = 0        Combine the left

(7/6)w + 6/6 w - 2 = 0

(13 / 6) w - 2 = 0          Add 2 to both sides

(13/ 6) w = 2                 Divide by 13/6

w = (2/1 ) ÷ (13/6)          Invert the denominator and multiply

w = 2/1 * 6/13

w = 12/13    

Part a; compounded semiannually (n = 2); CI =  $6,390.

Part b: compounded quarterly ( n = 4) ; CI =  $6,425

Part c: compounded monthly (n = 12): CI =  $6,450

Part d: compounded continuously; CI =  $6,467.

The compound interest is calumniated by formula.

A = P(1 + r/100n)∧nt

In which,

A  = amount after compounding

P = principal amount  ($20,000 )

n = number of time principal amount compounded in a year.

t = total time in years (7 years)

r= rate of interest (4%)

Part a; compounded semiannually (n = 2)

A = P(1 + r/100n)∧nt

A = 20,000(1 + 4/200)∧(2x7)

A = 26390

CI = A - P

CI =  26,390 -  20,000

CI =  $6,390.

Part b: compounded quarterly ( n = 4)

A = 20,000(1 + 4/400)∧(4x7)

A = 26425

CI = A - P

CI =  26,425 -  20,000

CI =  $6,425

Part c: compounded monthly (n = 12)

A = 20,000(1 + 4/1200)∧(12x7)

A = 26450

CI = A - P

CI =  26,450-  20,000

CI =  $6,450

Part d: compounded continuously.

P = P₀e∧rt

P = (20,000)(2.72)∧(0.04 x 7)

P = 20,000 x 1.32

P = 26,467

CI =  26,467 - 20, 000

CI =  $6,467.

Thus, the for compounded continuously is $6,467.

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