b) A different sequence has this expression for the nth term: 1 (n + 1)² Work out the first four terms in the sequence. b ) A different sequence has this expression for the nth term : 1 ( n + 1 ) ² Work out the first four terms in the sequence.
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The System of Equations 1, 2, 3, and 4 have solutions corresponding to the option B, A, C, and D.

A system of equations is a set of equations that have a common solution.

The first system of equations is

y+12 = x² +x

x+y = 3

To determine the solution, the equations are plotted on the graph and the intersection of the equations gives the solution.

The solution is (-5,8) (3,0)

The second system of equation is

y-15 = -x² +4x

x+y = 1

The solution to the system is (7,-6) (-2,3)

The third system of equation is

y+5 = x²-3x

2x+y = 1

The solution to the system is (3,-5) (-2,5)

The fourth system of equation is

y-17 = x²-9x

-x+y =1

The solution to the system is (2,3) , (8,9)

Therefore, the System of Equations 1, 2, 3, and 4 have solutions corresponding to the option B, A, C, and D.

The graphs are attached with the answer.

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Based on the calculations, the equation for the locus of these points is equal to x² + y² = 9.

First of all, we would determine the distance between points A and B as follows:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(-3 - 3)² + (0 - 0)²]

Distance = √[-9² + 0]

Distance = √81

Distance = 9.

Four (4) times the distance between points A and B​ is given by:

Distance = 9 × 4

Distance = 36.

Translating the word problem into a mathematical expression, we have:

a² + b² = 36

Also, from the distance formula we have:

a = √[(h + 3)² + (k - 0)²]

a² = h² + 6h + 9 + k²    

Similarly, b² is given by:

b = √[(h - 3)² + (k - 0)²]

b² = h² - 6h + 9 + k²

Equating the equations, we have:

a² + b² = 36

h² + 6h + 9 + k² + h² - 6h + 9 + k² = 36

2h² + 2k² = 36 - 18

2h² + 2k² = 18

Dividing both sides by 2, we have:

h² + k² = 9   ⇒ x² + y² = 9.

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Answer:

  $83,802

Step-by-step explanation:

The description is of an annuity due. Payments at the beginning of the period earn interest for the period, unlike those made at the end of the period.

The future value of an annuity due is given by the formula ...

  FV = P(1 +r)((1 +r)^t -1)/r

where P is the annual payment, r is the annual interest rate, and t is the number of years.

This is essentially the sum of t terms of a geometric series with first term P(1+r) and common ratio (1+r).

For P=$1000, r = 0.06, and t = 30, the future value is ...

  FV = $1000(1.06)(1.06^30 -1)/0.06 ≈ $83,801.68

To the nearest dollar, the account value will be $83,802.

__

Additional comment

Spreadsheets and many graphing calculators have time-value-of-money (TVM) formulas built in. You need to make sure to choose the option that gives an annuity due, rather than an ordinary annuity. In the attached TVM picture, this setting is accomplished by PmtMode=1.

Answer:

#of advanced tickets (x) = 30

#of same-day tickets (y) = 20

Step-by-step explanation:

x-#of advanced tickets

y-#of same-day tickets

[tex]x+y=50,\\35x+30y=1650[/tex]

5x+30(x+y)=1650

5x+30(50)=1650

5x=150

x=30

y=20

[tex]2x - 7x + 2 + 1 - 2[/tex]

[tex]2x - 7x + 3 - 2[/tex]

[tex] - 5x + 1[/tex]

Answer:

2304 inches

Step-by-step explanation:

please mark brainiest

Answer:

2304

Step-by-step explanation:

If you would like a step-by-step explanation, please just let me know. I sincerely hope this helps.

The distance between the ships is 26.65.

Based on the information given, after 3 hours, the distance of ship B will be:

= 20 + (17 × 3)

= 71.

A = 21 × 3 = 63

Well calculate the square root which will be:

A² + B² = 71² + 63²

= 5041 + 3969

= 9010

Therefore, ✓9010 = 94.92

Finally, the distance will be:

= (63 × 21) + (71 × 17) / 94.92

= (1323 + 1207)/94.92

= 26.65

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Answer:

(1,5)

Step-by-step explanation:

The solution to the system of equations is where the two graphs intersect.

The two lines intersect at x=1 and y =5

The point of intersection is (1,5)

Answer: (1, 5)

Step-by-step explanation: Over to the right one, up five; I hope this helps!

Key: (xGraph, yGraph) If a number is positive on the x axis, go right, if negative, go left. The same applies to the y graph, if the number is positve, go up, if negative go down. Your solution is where the two lines meet.

The graph of the solution set for the inequality can be seen below.

Here we have the inequality:

3x - 2y < -12

If we isolate y, we get:

3x + 12 < 2y

(3x + 12)/2 < y

(3/2)x + 6 < y

Now, we just need to graph the line y = (3/2)x + 6 with a dashed line (because the points on the line are not solutions).

And then we need to shade the region above the line.

The graph of the solution set can be seen below.

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The height of the flagpole with an angle of elevation to the top of the pole of 31° is 60.086 feet

An equation is an expression that shows the relationship between two or more numbers and variables.

Trigonometric ratio is used to show the relationship between the sides and angles of a triangle.

Let h represent the height of the flagpole, hence:

tan(31) = h/100

h = 60.086 feet

The height of the flagpole with an angle of elevation to the top of the pole of 31° is 60.086 feet

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The equation of the line going through (-6, 0) and (0, -3) is y = -(1/2)x - 3

The equation of the line going through (0, 3) and (-4, -5) is y = 2x + 3

An equation is an expression that shows the relationship between two or more variables and numbers.

The equation of the line going through (-6, 0) and (0, -3) is:

y - 0 = [(-3 - 0) / (0- (-6)](x - (-6))

y = -(1/2)x - 3

The equation of the line going through (0, 3) and (-4, -5) is:

y - 3 = [(-5 - 3) / (-4 - 0)](x - 0)

y = 2x + 3

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Answer:

2

-1/2

Step-by-step explanation:

Answer:

shorter side: 5 km

longer side: 27 km

Step-by-step explanation:

So you're already given the formula for the area of a rectangle, the next thing to do is assign length and width in terms of some unknown variable, which for convenience, I'll just say is x. So let's say one of the sides is x, the one that's the shorter side, since the longer side can be related to the shorted side, which is x. The longer side is 12km longer than 3 times the other side, so since the other side is x, it's length is (3x+12). So we simply multiply this by x, to get the area which is 135

"Known" Values: one side=x, other side=3x+12, area=135 km^2

[tex]135=x(3x+12)[/tex]

Distribute the x

[tex]135=3x^2+12x[/tex]

Subtract 135 from both sides

[tex]0=3x^2+12x-135[/tex]

Now since the equation is equal to zero, we can use the quadratic equation. In this case a=3, b=12, and c=-135

[tex]x=\frac{-12\pm\sqrt{12^2-4(3)(-135)}}{2(3)}[/tex]

Simplify denominator and multiply inside of the radical

[tex]x=\frac{-12\pm\sqrt{144+1,620}}{6}[/tex]

If you're confused where the negative went in the radical, it canceled out when multiply -4 by -135. Now add the stuff in the radical

[tex]x=\frac{-12\pm\sqrt{1,764}}{6}[/tex]

Simplify the radical

[tex]x=\frac{-12\pm 42}{6}[/tex]

Now you might think there are two solutions to this equation, but the thing is that one of the sides simply cannot have a "negative length", because in this context, x must be positive. So it's easy to see you have to use the positive sign, since using the negative sign would result in -12-42 over 6 which is certainly negative. So we can ignore that solution as it doesn't mean anything in this context. We only need the positive solution

[tex]x=\frac{-12+42}{6}[/tex]

Add values

[tex]x=\frac{30}{6}[/tex]

Divide

[tex]x=5[/tex]

Since the shorter side was 5, that's the solution to the shorter side, now to find the longer side we plug in 5 into the equation: [tex]3x+12[/tex] which becomes 3(5) + 12 = 15+12 = 27. This means the two lengths are 5 and 27

Step-by-step explanation:

let x = length of shorter side

[tex](3x + 12)(x)= 135[/tex]    This is the equation

[tex]3x^2+12x=135[/tex]        use distributive property to multiply out

[tex]3x^2+12x-135=0[/tex]   subtract 135 from both sides to get in position to factor

[tex]3(x^2+4x-45)[/tex]           factor out a 3

[tex]3(x-5)(x-9)[/tex]           factor the resulting expression

[tex]x=5,9[/tex]                       two answers (we want one so see which one works)

Check both values of x

[tex]5*3+12=27[/tex]

[tex]27*5=135[/tex]

Therefore, we know the shorter side is 5 km and the longer side is 27 km.

At this point, we do not even need to check x=9

The correct expansion is the one in option b:

[tex]Log_9(\frac{6}{11}) = Log_9(6) - Log_9(11)[/tex]

Here we must use the logarithmic property:

[tex]Log(a) -Log(b) = Log(\frac{a}{b})[/tex]

Our expression in this case is:

[tex]Log_9(\frac{6}{11})[/tex]

Using the above property, we can rewrite the expression as:

[tex]Log_9(\frac{6}{11}) = Log_9(6) - Log_9(11)[/tex]

From this, we conclude that the correct option is B.

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Answer:

35mph

Step-by-step explanation:

divide 140/4=35

Answer: x-axis

Step-by-step explanation:

If you visualize the line of reflection, it must be vertical. Option A is the only option that has a vertical line.

Answer: [tex]20x^2 + 47x+24[/tex]

Step-by-step explanation:

We just multiply the values on the edges like we are finding the area of a square, L * L = area.

4x * 5x = 20x^2

4x * 8 = 32x

3 * 8 = 24

3 * 5x = 15x

Next add the answers together

20x^2 + 47x + 24

Answer:

option 3

Step-by-step explanation:

you need to times (4x+3) by (5x+8)

so you basically need to expand the brackets and collect like terms

The expression that is equivalent to the given expression is 16⁴

From the question, we are to determine the expression that is equivalent to the given expression

The given expression is

[tex](\frac{1}{16} )^{-4}[/tex]

Evaluating

[tex](\frac{1}{16} )^{-4}[/tex]

[tex]= (16^{-1} )^{-4}[/tex]

[tex]= 16^{-1 \times -4}[/tex]

[tex]= 16^{4}[/tex]

Hence, the expression that is equivalent to the given expression is 16⁴

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Answer:

84π m^3

Step-by-step explanation:

1. The formula of a cone is: (1/3) · π · r^2 · h

2. The radius is 6m. (Diameter / 2)

3. (1/3) * π * (6^2) * 7

4. Multiply all numbers besides pi to get the answer in terms of pi

5. (36 / 3 ) = 12 * 7 = 84

6. 84π

[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{Given...}}}}} \: [/tex]

[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{To \: Find ...}}}}} \: [/tex]

[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{Formula \: Using ...}}}}} \: [/tex]

[tex]\Large❏ \: \Large\begin{gathered} {\underline{\boxed{ \sf {{\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{3}\pi {r}^{2} h}}}}}\end{gathered}[/tex]

Where,

[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{Solution ...}}}}} \: [/tex]

Substituting the given values in formula.

[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{3}\pi {r}^{2} h[/tex]

[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{3}\pi {(6)}^{2} \: \times \: 7[/tex]

[tex] \large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{ \cancel3}\pi \: \times \: \cancel{ 36} \: \: ^{ \pink{12}} \: \times \: 7 \\ [/tex]

[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \:\pi \: \times \: 12 \: \times \: 7 \\ [/tex]

[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: 84 \pi \: {m}^{3} [/tex]

Hence , option b is the correct answer

Answer:

162, 163, and 164.

Step-by-step explanation:

Here we will use algebra to find three consecutive integers whose sum is 489. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 489. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) = 489

To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 489

3X + 3 = 489

3X + 3 - 3 = 489 - 3

3X = 486

3X/3 = 486/3

X = 162

Which means that the first number is 162, the second number is 162 + 1 and the third number is 162 + 2. Therefore, three consecutive integers that add up to 489 are 162, 163, and 164.

162 + 163 + 164 = 489

We know our answer is correct because 162 + 163 + 164 equals 489 as displayed above.

Answer:

161, 163, 165

Step-by-step explanation:

x + x+2 + x +4 =489.

This is how we calculate three consecutive odd integers!

Combine like terms:

3x+6=489

3x=483

x=161

Three numbers are:

161, 161+2, 161+4.

161, 163, 165

Answer:

(30+30) +(7+1) = 68

Step-by-step explanation:

hope this helps you (ʘᴗʘ✿)

Answer: AB = 90.7 meter

Given following:

Find angle A :

⇒ 180° - (104.6° + 14.4°)

⇒ 61°

Now, use sine rule:

[tex]\sf \dfrac{AB}{BC} = \dfrac{sin(C^{\circ })}{sin(A^{\circ \:})}[/tex]

[tex]\sf \dfrac{AB}{319} = \dfrac{sin(14.4) } {sin(61)}[/tex]

[tex]\sf AB = \dfrac{319 \ sin(14.4) } {sin(61)}[/tex]

[tex]\sf AB = 90.70464953 \quad \approx \quad 90.7 \ m \ (rounded \: to \: nearest \ tenth)[/tex]

Answer:

Is there a graph related to this question?

The percentage composition of salt in the solution is; 84.2%.

Since, it follows that there are 16 ounces in 1 pound. Then the 3 lb of salt is equivalent to; 3×16 = 48ounces.

Consequently, the percentage of salt in the solution as described is;

{48/57} × 100%

Percentage composition of salt is therefore;

= 84.2%.

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The equations of the transformed graphs are [tex]f(x) = \frac 23\sqrt{x - 3}[/tex], [tex]f(x) = 8\sqrt{x }-3[/tex], [tex]f(x) = \sqrt{\frac x7} + 5[/tex] and [tex]f(x) = \sqrt{-x} - 10[/tex]

The function #1

The function is given as::

[tex]f(x) = \sqrt{x}[/tex]

It is shifted right by 3 units.

So, we have:

[tex]f(x) = \sqrt{x - 3}[/tex]

It is shrunk vertically by a factor of 2/3

[tex]f(x) = \frac 23\sqrt{x - 3}[/tex]

Hence, the equation of the transformed graph is [tex]f(x) = \frac 23\sqrt{x - 3}[/tex]

The function #2

The function is given as::

[tex]f(x) = \sqrt{x}[/tex]

It is stretched vertically by a factor of 8

[tex]f(x) = 8\sqrt{x }[/tex]

It is shifted down by 3 units.

So, we have:

[tex]f(x) = 8\sqrt{x }-3[/tex]

Hence, the equation of the transformed graph is [tex]f(x) = 8\sqrt{x }-3[/tex]

The function #3

The function is given as::

[tex]f(x) = \sqrt{x}[/tex]

It is stretched horizontally by a factor of 7

[tex]f(x) = \sqrt{\frac x7}[/tex]

It is shifted up by 5 units.

So, we have:

[tex]f(x) = \sqrt{\frac x7} + 5[/tex]

Hence, the equation of the transformed graph is [tex]f(x) = \sqrt{\frac x7} + 5[/tex]

The function #4

The function is given as::

[tex]f(x) = \sqrt{x}[/tex]

It is reflected across the y-axis

[tex]f(x) = \sqrt{-x}[/tex]

It is shifted down by 10 units.

So, we have:

[tex]f(x) = \sqrt{-x} - 10[/tex]

Hence, the equation of the transformed graph is [tex]f(x) = \sqrt{-x} - 10[/tex]

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The addition is one of the four fundamental mathematical operations. Jenny can have dinner at 7 pm and 7.5 mins.

The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

The time can be calculated as,

Flight lands at 4 pm

Jenny has bought a 2.4kg chicken. It takes 35-45 minutes per kg plus an additional 30 minutes to cook the chicken. Time needed for cooking the chicken = (2.5×45 + 30) = 142.5 min

⇒ 15+25+5+142.5 min

Thus, the total time it takes for Jenny to cook the food starting when the flight lands are ⇒ 187.5 mins = 3 hours 7.5 mins

Since the flight lands at 4 pm

⇒ 4 pm + 3 hours 7.5 mins

⇒ 7 pm and 7.5 mins

Hence, Jenny can have dinner at 7 pm and 7.5 mins.

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Answer:

The last option

Step-by-step explanation:

When you plug in 1 for the x and 2 for y, the answer is -5 for the first equation and is 12 for the second equation. I hope that helps!

Step-by-step explanation:

general form of a parabola :

y = ax² + bx + c

we have 3 points of the parabola to calculate the 3 variables :

the 2 intercepts are actually

(-2, 0)

(6, 0)

and then

(8, 6)

so, we get the 3 equations

0 = a(-2)² + b×-2 + c = 4a - 2b + c

0 = a×6² + b×6 + c = 36a + 6b + c

6 = a×8² + b×8 + c = 64a + 8b + c

from the 1st equation we get

c = -4a + 2b

using that in the 2nd equation we get

0 = 36a + 6b - 4a + 2b = 32a + 8b = 4a + b

b = -4a

therefore,

c = -4a + 2b = -4a + 2×-4a = -4a - 8a = -12a

using all that in the 3rd equation we get

6 = 64a + 8×-4a + -12a = 64a - 32a - 12a = 20a

a = 6/20 = 3/10 = 0.3

b = -4a = -4×3/10 = -12/10 = -1.2

c = -12a = -12×3/10 = -36/10 = -3.6

so, we have

y = 3/10 x² - 12/10 x - 36/10 = 3/10 × (x² - 4x - 12)