The nth term of a sequence is given by 3n²
What is the position of the term in the sequence that is the first one with a value greater than 1000? ​

Answer:

48

Step-by-step explanation:

The mean of a number is the sum of all the numbers divided by how many numbers there are. We can set up this formula: [tex]mean = \frac{sum}{amountnumbers}[/tex].

When we plug our values into this equation, we get: [tex]6 = \frac{sum}{8}[/tex]. Solving this equation gets us sum = 6 * 8 = 48

Answer:

24 ft.

Step-by-step explanation:

Radius = 4 ft

Central angle = 6°

Arc length = radius × central angle

= 4 × 6°

= 24 ft.

Answer:

ASA

Step-by-step explanation:

by ASA congruence theorem

Answer:

The square root of 36/196 is 3/7.

The square root of 36/169 is 6/13.

Answer:

2.4 × 10⁶

Step-by-step explanation:

Given:

To calculate the value of R, substitute the given values into the given formula:

[tex]\begin{aligned}\sf R & = \sf \dfrac{x^2}{y}\\\\ \implies \sf R& = \sf \dfrac{(3.8 \times 10^5)^2}{5.9 \times 10^4}\\\\& = \sf \dfrac{3.8^2 \times (10^5)^2}{5.9 \times 10^4}\\\\& = \sf \dfrac{14.44 \times 10^{10}}{5.9 \times 10^4}\\\\& = \sf \dfrac{14.44}{5.9} \times \dfrac{10^{10}}{10^4}\\\\& = \sf 2.4474... \times 10^{(10-4)}\\\\& = \sf 2.4474... \times 10^6\\\\\end{aligned}[/tex]

Therefore, the value of R to 1 decimal place is 2.4 × 10⁶

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

Exponent Rules used

[tex](a^b)^c=a^{bc}[/tex]

[tex]{a^b}{a^c}=a^{b-c}[/tex]

[tex]R = \frac{ {x}^{2} }{ y} \\ \\ R = \frac{ {(3.8 \times {10}^{5})}^{2} }{5.9 \times {10}^{4} } \\ \\ R = \frac{ ({3.8})^{2} \times ( { {10}^{5} )}^{2} }{5.9 \times {10}^{4} } \\ \\ R = \frac{14.44 \times {10}^{10} }{5.9 \times {10}^{4} } \\ \\ R = \frac{14.44 \times {10}^{10 - 4} }{5.9} \\ \\ R = 2.45 \times {10}^{6} [/tex]

Answer:

Tara can make 60 bracelets.

Step-by-step explanation:

908 / 15 = 60.5

Answer:

A wave period is the measure of the time it takes for the wave cycle to complete.

The period of the wave is 2 seconds.

The angles are p=67°, q=15°, x=82°, y=81°, s=28° and m=72.5°.

For the given figures we need to find the unknown angles.

In the first figure to find angle p first apply the angle sum property to the triangle.

That is, 82°+31°+p=180° (∵ Sum of interior angles of a triangle is 180°)

⇒p=67°.

p=67° is a vertically opposite angle to the other triangle.

To find q:

67°+98°+q=180°

⇒q=15°.

In the second figure to find angles x and y apply the angle sum property to the triangle.

That is, 28°+(53°+x)+17°=180°

⇒98°+x=180°

⇒x=82°.

To find y:

x+y+17°=180°

⇒82°+y+17°=180°

⇒y=81°

In the third figure to find angles x and y apply the angle sum property to the triangle.

That is, 100-x+30+4x+7x=180°

⇒10x=80°⇒x=10°.

Now the angles of the triangle are 100-10=90°, 30+4x=70°

y=90°+70°=160° (∵Exterior angle is equal to the sum of two opposite interior angles).

In the 4th figure, to find angle 's' use the isosceles triangle concept.

That is, s+76°+76°=180° (∵In isosceles triangle base angles are equal)

⇒s=28°

In the 5th figure, to find angle 'm' use the isosceles triangle concept.

That is, 35°+m+m=180° (∵In isosceles triangle base angles are equal)

⇒2m=145°

⇒m=72.5°

Hence, the angles are p=67°, q=15°, x=82°, y=81°, s=28° and m=72.5°.

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The green-colored area of the graph attached below shows the solution set to 3eˣ>(-1/2)x.

Inequality is the relationship between two expressions showing the relationships like greater than, lesser than, lesser than equals to, and greater than equals to.

Here assume f is a function which is given by f(x)=3eˣ

and g be another function which is given by g(x)= (-1/2)x

Here we have to find the solution graph showing the relationship

f(x) > g(x)

Let at point (a,b) the f(x) and g(x) meet each other.

After that intersection point, g(x) will decrease as g(x) is a decreasing function. and f(x) will increase.

So in the solution set will contain the area where g(x) is larger than f(x).

Therefore the solution graph of this inequality is the green-colored area as shown below,

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To find the maxima and minima of the function, we need to calculate the derivative of the function. Note, before the denominator is a perfect square trinomial, so the function can be simplified as

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f(x) = \frac{x^2 - x - 2}{(x - 3)^2}} \end{gathered}$}[/tex]

So the derivative is:

  [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f'(x) = \frac{(2x - 1)(x - 3)^2 - 2(x - 3)(x^2 - x - 2)}{(x - 3)^4} } \end{gathered}$}[/tex]

Simplifying the numerator, we get:

                 [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f'(x) = \frac{(x - 3)(-5x + 7)}{(x - 3)^4} = \frac{-5x + 7}{(x - 3)^3} } \end{gathered}$}[/tex]

The function will have a maximum or minimum when f'(x) = 0, that is,

                  [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f'(x) = \frac{-5x + 7}{(x - 3)^3} = 0 } \end{gathered}$}[/tex]

which is true if -5x + 7 = 0. Then x = 7/5.

To determine whether x = 7/5 is a maximum, we can use the second derivative test or the first derivative test. In this case, it is easier to use the first derivative test to avoid calculating the second derivative. For this, we evaluate f'(x) at a point to the left of x = 7/5 and at a point to the right of it (as long as it is not greater than 3). Since 1 is to the left of 7/5, we evaluate:

                    [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f(1) = \frac{-5 + 7}{(1 - 3)^3} = \frac{2}{-8} < 0} \end{gathered}$}[/tex]

Likewise, since 2 is to the right of 7/5, then we evaluate:

                                   [tex]\large\displaystyle\text{$\begin{gathered}\sf \displaystyle \bf{\frac{-10 + 7}{(2 - 3)^3} = \frac{-3}{-1} > 0} \end{gathered}$}[/tex]

Note that to the left of 7/5 the derivative is negative (the function decreases) and to the right of 7/5 the derivative is positive (the function increases).

The value of f(x) at 7/5 is:

                               [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f\left(\tfrac{7}{5}\right) = \frac{\tfrac{49}{25} - \tfrac{7}{5} - 2}{\tfrac{49}{25} - 6 \cdot \tfrac{7}{5} + 9} = -\frac{9}{16} } \end{gathered}$}[/tex]

This means that [tex]\bf{\left( \frac{7}{5}, -\frac{9}{16} \right)}[/tex] is a minimum (and the only extreme value of f(x)).

[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

Answer:

[tex]\text{Minimum at }\left(\dfrac{7}{5},-\dfrac{9}{16}\right)[/tex]

Step-by-step explanation:

The local maximum and minimum points of a function are stationary points (turning points).  Stationary points occur when the gradient of the function is zero.  Differentiation is an algebraic process that finds the gradient of a curve.

To find the stationary points of a function:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $y=\dfrac{u}{v}$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{v \dfrac{\text{d}u}{\text{d}x}-u\dfrac{\text{d}v}{\text{d}x}}{v^2}$\\\end{minipage}}[/tex]

[tex]\text{Given function}: \quad \text{f}(x)=\dfrac{x^2-x-2}{x^2-6x+9}[/tex]

Differentiate the function using the Quotient Rule:

[tex]\text{Let }u=x^2-x-2 \implies \dfrac{\text{d}u}{\text{d}x}=2x-1[/tex]

[tex]\text{Let }v=x^2-6x+9 \implies \dfrac{\text{d}v}{\text{d}x}=2x-6[/tex]

[tex]\begin{aligned}\implies \dfrac{\text{d}y}{\text{d}x} & =\dfrac{(x^2-6x+9)(2x-1)-(x^2-x-2)(2x-6)}{(x^2-6x+9)^2}\\\\& =\dfrac{(2x^3-13x^2+24x-9)-(2x^3-8x^2+2x+12)}{(x^2-6x+9)^2}\\\\\implies \text{f}\:'(x)& =\dfrac{-5x^2+22x-21}{(x^2-6x+9)^2}\\\\\end{aligned}[/tex]

Set the differentiated function to zero and solve for x:

[tex]\begin{aligned}\implies \text{f}\:'(x)& =0\\\\\implies \dfrac{-5x^2+22x-21}{(x^2-6x+9)^2} & = 0\\\\-5x^2+22x-21 & = 0\\\\-(5x-7)(x-3) & = 0\\\\\implies 5x-7 & = 0 \implies x=\dfrac{7}{5}\\\\\implies x-3 & = 0 \implies x=3\end{aligned}[/tex]

Put the x-values back into the original equation to find the y-values:

[tex]\implies \text{f}\left(\frac{7}{5}\right)=\dfrac{\left(\frac{7}{5}\right)^2-\left(\frac{7}{5}\right)-2}{\left(\frac{7}{5}\right)^2-6\left(\frac{7}{5}\right)+9}=-\dfrac{9}{16}[/tex]

[tex]\implies \text{f}(3)=\dfrac{\left(3\right)^2-\left(3\right)-2}{\left(3\right)^2-6\left(3\right)+9}=\dfrac{4}{0} \implies \text{unde}\text{fined}[/tex]

Therefore, there is a stationary point at:

[tex]\left(\dfrac{7}{5},-\dfrac{9}{16}\right)\:\text{only}[/tex]

To determine if it's a minimum or a maximum, find the second derivative of the function then input the x-value of the stationary point.

Differentiate f'(x) using the Quotient Rule:

Simplify f'(x) before differentiating:

[tex]\begin{aligned}\text{f}\:'(x) & =\dfrac{-5x^2+22x-21}{(x^2-6x+9)^2}\\\\& = \dfrac{-(5x-7)(x-3)}{\left((x-3)^2\right)^2}\\\\& = \dfrac{-(5x-7)(x-3)}{(x-3)^4}\\\\& = -\dfrac{(5x-7)}{(x-3)^3}\\\\\end{aligned}[/tex]

[tex]\text{Let }u=-(5x-7) \implies \dfrac{\text{d}u}{\text{d}x}=-5[/tex]

[tex]\text{Let }v=(x-3)^3 \implies \dfrac{\text{d}v}{\text{d}x}=3(x-3)^2[/tex]

[tex]\begin{aligned}\implies \dfrac{\text{d}^2y}{\text{d}x^2} & =\dfrac{-5(x-3)^3+3(5x-7)(x-3)^2}{(x-3)^6}\\\\& =\dfrac{-5(x-3)+3(5x-7)}{(x-3)^4}\\\\\implies \text{f}\:''(x)& =\dfrac{10x-6}{(x-3)^4}\end{aligned}[/tex]

Therefore:

[tex]\text{f}\:''\left(\dfrac{7}{5}\right)=\dfrac{625}{512} > 0 \implies \text{minimum}[/tex]

Answer:

113 degrees

Step-by-step explanation:

Two angles are called supplementary when they add up to 180 degrees

[tex]180 = x + y \\ 180 = 67 + y \\ y = 180 - 67 \\ y = 113 \\ therefore \: mB \: = 113[/tex]

The remainder represented by synthetic division is -5.

Synthetic division can be defined as a simplified way of dividing a polynomial with another polynomial equation of degree 1.

Given

A vertical line and a horizontal line combine to make an L shape.

There are two rows of entries within the shape.

Row 1 has entries 2, 10, 1, 5.

Row 2 has entries blank, -10, 0, -5.

Entry -5 is on the outside to the left of the shape. The entry represents the zero of the divisor. This entry to the variable (assume the variable is x) is;

x + 5 = 0

x = -5

Hence, the divisor of the synthetic division is -5.

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Answer:

its a) -5

Step-by-step explanation:

The ordered pair of the equation 3x +2y = 6 will be ( 0,3) and ( 2 , 0).

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

We have an equation 3x + 2y = 6 now the ordered pair of the equation will be found by the graph will be ( 0,3) and ( 2, 0). The graph is also attached with the answer below.

Therefore the ordered pair of the equation 3x +2y = 6 will be ( 0,3) and ( 2 , 0).

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The number of matchsticks that each side of the biggest triangle contains is; 137 matchsticks

We know that for a diagram to be a triangle, then two smallest sides must not be greater than the third side.

Now, if there are 273 matchsticks, then the greatest side of the triangle must not be less than 273/2 = 136.5 ≈ 137

Thus, the largest side will have at least 137 matchsticks

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Hey there!

2(2y - 12) = 0
2(2y) + 2(-12) = 0

4y - 24 = 0

ADD 24 to BOTH SIDES

4y - 24 + 24 = 0 + 24

SIMPLIFY IT!

4y = 0 + 24

4y = 24

4y/4 = 24/4

SIMPLIFY IT!

y = 24/4

y = 6

Therefore, your answer should be:

y = 06 (Option B.)

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

y=6 (06) should be your answer

Step-by-step explanation:

4y-24=0

After you simply the first equation in the parenthesis, you then move the 24 to the 0,

4y=24

The answer becomes positive 24 because when you move things across the equal sign you switch the sign

y=6

Then divide 24 by 4 to isolate y, which then gives you the answer 6.

Answer:

x° = 75

(x + 30)° = 105°

Step-by-step explanation:

supplementary angle is two angles that sum is 180°

x° + (x + 30)° = 180°

2x + 30 = 180°

2x + 30 - 30 = 180 - 30

2x = 150

2x / 2 = 150 / 2

x° = 75

plug in 75,

75 + 30 = 105

check: 75 + 105 = 180

Answer: 75 degrees

Step-by-step explanation:

Do you see how both sides of the angle come together to form the straight line seen at the bottom? This means that these are supplementary angles.

Supplementary Angles: Both sides have to add up to a total of 180 degrees.

With this, form an equation: x+(x+30)= 180

Get rid of the parenthesis:

x+x+30= 180

Combine like terms.

2x+30= 180

2x= 180-30

2x= 150

x= 150÷2

x= 75

Checks:

x+x+30= 180

75+75+30= 180

You can also check using the equation in its simplified form: 2x+30= 180.

2x+30=180

2(75)+30=180

150+30=180

Hence x=75

Answer:

[tex]C=23\pi[/tex] inches

or as a decimal

72.26 inches

Step-by-step explanation:

Formula for circumference: [tex]C=2\pi r[/tex]

Radius = [tex]\frac{d}{2}[/tex]

Altogether we get: [tex]C=2*\pi*\frac{d}{2}[/tex]

Which simplifies to: [tex]C=\pi d[/tex]

So now we can plug in 23 for [tex]d[/tex].

[tex]C=\pi*23[/tex]

Our final answer is:

[tex]C=23\pi[/tex] inches

or as a decimal

72.26 inches

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: length = 11 \: \: in[/tex]

[tex]\qquad \tt \rightarrow \: width = 4 \: \: in[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Let the measures be :

[tex] \textsf{\large Area of rectangle :} [/tex]

[tex]\qquad \tt \rightarrow \: Area = length \sdot width [/tex]

[tex]\qquad \tt \rightarrow \: 44 = x \sdot(x + 7)[/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + 7x = 44[/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + 7x - 44 = 0[/tex]

[tex]\qquad \tt \rightarrow \: {x}^{2} + 11x - 4x - 44 = 0[/tex]

[tex]\qquad \tt \rightarrow \: x(x + 11) - 4(x + 11) = 0[/tex]

[tex]\qquad \tt \rightarrow \: (x + 11)(x - 4) = 0[/tex]

possible values of x = -11 and 4

[tex] \textsf{But the acceptable value of x = 4} [/tex]

[ length or width of rectangle can't be negative ]

[tex]\qquad \tt \rightarrow \: length = x + 7 = 4 + 7 = 11 \: \: in[/tex]

[tex]\qquad \tt \rightarrow \: width = x = 4 \: \: in[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

yes

Step-by-step explanation:

2 bases 3 rectangles, folds properly.

Answer:

52=x-15(being vertically opposite angle)

52+15=x

x=67

Answer:

184.73

Step-by-step explanation:

1 yard = 0.91m

203 yard=?

(203x0.91)/1=184.73.

+1(415) 450-6164

Answer: 40/21

Step-by-step explanation:

[tex]3 \times 105=315\\\\6 \times 10^{2}=600\\\\\implies \frac{6 \times 10^{2}}{3 \times 105}=\frac{600}{305}=\boxed{\frac{40}{21}}[/tex]

Reason:

I'm assuming that the swimmer travels along the 50 meter side

Divide 1500 over 50 to get 1500/50 = 30, which tells us that the swimmer must make 30 trips.

The value of FY in the triangle will be 30.11

From the information given, the value of BE will be:

= [tex]\sqrt{64.2}[/tex]² - [tex]\sqrt{51.2}[/tex]²

= 38.7

From the triangle, DY will be

= [tex]\sqrt{64.22}[/tex]² - [tex]\sqrt{61.7}[/tex]²

= 17.7

AY will be:

= [tex]\sqrt{61.7}[/tex]² + [tex]\sqrt{17.7}[/tex]²

= 64.2

FY will now be:

= [tex]\sqrt{64.2 - 56.7}[/tex]²

= 30.11

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Answer:

1936

Step-by-step explanation:

We can start by removing the center tile, because all four diagonals over lap on that tile. We'll add it back later. 88/4=22. which means there are 22 tiles per half, 44+1(the center tile) total tiles per side, which means there are a total of 1936 tiles.

AOPS ANSWER:

Suppose that we have a square with dimensions [tex]$e \times e$[/tex]. The diagonals each have [tex]$e$\\[/tex] tiles. If [tex]$e$\\[/tex] is even, the number of yellow tiles is [tex]$2e$[/tex], because the [tex]2[/tex] diagonals don't intersect. If [tex]$e$[/tex] is odd, then the number of yellow tiles is [tex]$e+e-1=2e-1$[/tex]. (We have to subtract [tex]1[/tex] because the center tile is counted [tex]2[/tex] times). We know that there are [tex]89[/tex] yellow tiles, which is an odd number, so [tex]$89=2e-1$[/tex]. This implies that [tex]$e = 45$[/tex]. So the dimensions of the floor are [tex]$45 \times 45$[/tex], or [tex]2025\\[/tex] square units. Since all of the other tiles are gray, there are [tex]$2025-89=\boxed{1936}$[/tex] gray tiles.

The algebraic expression that represents the number of new accounts that he will add in m months is x ≥ 7m.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Every month, a salesperson adds 7 new accounts.

Let m be the number of the month and x be the number of the accounts.

Then the inequality equation will be

x ≥ 7m

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The solution is 1756.69

A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner.

We have to find the 18.5% of 2155.45.

So,

2155.45 * 0.185 = 398.75825

Now, subtract

21.55.45 - 398.75825

= 1756.69175

Hence, the value is 1756.69

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Step-by-step explanation:

z = 4√3

y = ?

Z° = 90° - 30° = 60°

Y° = 30°

• Find y.

y/sin(Y) = z/sin(Z)

y/sin(30°) = 4√3/sin(60°)

y/(1/2) = 4√3/(1/2 √3)

y . 1/2 √3 = 4√3 . 1/2

y . 1/2 √3 = 2√3

y = 2√3 . 2/√3

y = 4√3/√3

y = 4

The answer is A.