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3 years ago

Find the first term, a1, of an arithmetic sequence if a12 = 38 and a45 = 170.

1 answer:

8 0

Standard formula for arithmetic sequence:
an = a0 + d(n-1)

if we use the two terms given, setting a12 as starting term and a45 as the end term an.

170 = 38 + 33d
170 - 38 = 33d
132 = 33d

132/33 = d
This is the common difference, use it to find the first term.

38 = a0 + (132/33)(12-1)
38 = a0 + (132/33)(11)
38 = a0 + 132/3
38 - 132/3 = a0
38 - 44 = a0
-6 = a0

The starting term is -6

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(4,?) is in line y=2/7x-3. Find the other half of the coordinate

olga2289 [7]

$y = \dfrac{2}{7} x - 3$

When x = 4,

$y = \dfrac{2}{7} (4) - 3$

$y = \dfrac{8}{7} - 3$

$y = -\dfrac{13}{7}$

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Answer: (4 , -13/7)
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3 years ago

A 25-foot ladder is placed against a building. The bottom of the ladder is 7 feet from the building. If the top of the ladder sl

algol [13]

Answer:

As per the statement:

A 25-foot ladder is placed against a building. The bottom of the ladder is 7 feet from the building.

⇒Length of the ladder against a building = 25 foot

and Length of the bottom of the ladder from the building= 7 feet.

You had Before the slip.

Let x be the height of the building where ladder hits the building

By Pythagoras theorem:

$\text{Hypotenuse side}^2=\text{Perpendicular}^2+\text{Base}^2$

Here, Perpendicular side = Height of the building = x , Base = Length of the bottom of the ladder from the building = 7 foot and Hypotenuse side = 25 foot

Substitute the value to solve for x;

$25^2=x^2+7^2$

$625=x^2+49$

$x^2 = 625-49 = 576$

$x = \sqrt{576} = 24$ foot.

⇒Height of the building = 24 foot

Now, if the ladder slips down 4 feet.

You had after slip

⇒Now, the height of the building becomes = 24-4 = 20 foot.

Let y be the distance from the building wall

then by Pythagoras theorem;

$y^2+20^2 = 25^2$

$y^2+400 =625$

$y^2 = 625-400 = 225$

$y=\sqrt{225} = 15$ foot.

We have to find how many feet will the bottom slide out.

Since, Originally the distance of the bottom from the building = 7 foot

And now, the distance is = 15 foot.

The bottom slide out will be = 15 - 7 =8 foot

Therefore, 8 feet will the bottom slide out

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3 years ago

You have a rectangular Box whose dimensions are 5cm X 4 Cm X 4 Cm that holds 32 jelly beans, and another rectangular Box whose d

Marizza181 [45]

Answer:

.4 Jelly beans per cubic Centimeter

Step-by-step explanation:

Volume = 4*4*5 = 80 cm^3

Ratio = 32beans/80cm^3 = .4beans/cm^3

3 0

3 years ago

Read 2 more answers

Find the value of x. log 2 x = 3 A. 5 B. 6 C. 8 D. 9

Nataly_w [17]

Answer: Option C

$x =8$

Step-by-step explanation:

To solve this problem use the properties of the logarithms.

We know that the inverse function of $y = log_2 (x)$ is $y = 2 ^ x$ .

So when composing the function with its inverse function we have to:

$2 ^ {log_2 (x)} = x$ .

Now apply this property on both sides of the equation

$log_2(x) = 3\\\\2^{log_2(x)}=2^3\\\\x = 2^3\\\\x = 8$

the answer is the option C

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3 years ago

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Given that f(x) = 2x + 1 and g(x) = the quantity of 3x minus 1, divided by 2, solve for g(f(3)). 5 7 9 10

AlladinOne [14]

The correct answer is 10.

In order to evaluate any composite function, you need to first put the value in for the inside function. In this case f(x) is on the inside along with the number 3. So, we input 3 in for x in f(x).

f(x) = 2x + 1

f(3) = 2(3) + 1

f(3) = 6 + 1

f(3) = 7

Now that we have the value of f(3), we can stick the answer in for the outside function, which is g(x).

g(x) = (3x - 1)/2

g(7) = (3(7) - 1)/ 2

g(7) = (21 - 1)/2

g(7) = 20/2

g(f(3)) = 10

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3 years ago