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2 years ago

The explicit formula for a sequence is

Mathematics

1 answer:

Alexandra [31]2 years ago

3 0

Answer:

Step-by-step explanation:

Let n = 21, and evaluate the expression.

$a_n = -2 + \dfrac{3}{2}(n - 1)$

$a_{21} = -2 + \dfrac{3}{2}(21 - 1)$

$a_{21} = -2 + \dfrac{3}{2}(20)$

$a_{21} = -2 + \dfrac{3}{1}(10)$

$a_{21} = -2 + 30$

$a_{21} = 28$

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Suppose a and b are the solutions to the quadratic equation 2x^2-3x-6=0. Find the value of (a+2)(b+2).

KonstantinChe [14]

Answer:

(a+2)(b+2) = 4

Step-by-step explanation:

We are given the following quadratic equation:

$2x^2-3x-6=0$

Let a a and b be the solution of the given quadratic equation.

Solving the equation:

$2x^2-3x-6=0\\\text{Using the quadratic formula}\\\\x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{Comparing the equation to }ax^2 + bx + c = 0\\\text{We have}\\a = 2\\b = -3\\c = -6\\x = \dfrac{3\pm \sqrt{9-4(2)(-6)}}{4} = \dfrac{3\pm \sqrt{57}}{4}\\\\a = \dfrac{3+\sqrt{57}}{4}, b = \dfrac{3-\sqrt{57}}{4}$

We have to find the value of (a+2)(b+2).

Putting the values:

$(a+2)(b+2)\\\\=\bigg(\dfrac{3+\sqrt{57}}{4}+2\bigg)\bigg(\dfrac{3-\sqrt{57}}{4}+2\bigg)\\\\=\bigg(\dfrac{11+\sqrt{57}}{4}\bigg)\bigg(\dfrac{11-\sqrt{57}}{4}\bigg)\\\\=\dfrac{121-57}{156} = \dfrac{64}{16} = 4$

3 0

2 years ago

Line with a slope 6 passes through the points (2,-10) and (5,g)

Irina-Kira [14]

Answer:

8 =g

Step-by-step explanation:

We have two points so we can use the slope formula

m = ( y2 -y1)/(x2-x1)

6 = ( g - -10)/(5-2)

6 = (g+10)/(5-2)

6 = (g+10)/3

Multiply each side by 3

6*3 = g+10

18 = g+10

Subtract 10

18-10 =g

8 =g

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2 years ago

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sammy [17]

Answer:

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Step-by-step explanation:

As sum of angles of the triangle is 180°

therefore the third angle will be 180 -( 75 + 65)=40°

x=40°= vertically opposite angle

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3 years ago

Read 2 more answers

Mr. Voelz estimates that he will spend $10 on concessions at the basketball game. He actually spends $15. What is the percent er

irina [24]

Answer:

I am not sure but if you divide those 2 numbers such as dividing 10 by 15 you will get 0.666666666667 but if you round it you will have 67%

Step-by-step explanation:

Plz mark Brainliest

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2 years ago

You have $5,000 to invest for ten years. The Bank pays simple interest at an annual rate of 5%. Calculate your balance after 10

Mazyrski [523]

Answer: $7,500

Step-by-step explanation:

Use the formula: SI = P(1 + rt)

SI = 5000(1 + 0.05[10])

SI = 5000 + 2500

SI = $7,500

After 10 years, your balance should be $7,500

3 0

1 year ago