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3 years ago

The third term of an arithmetic sequence is 21, and the eighth term is 56. The first term is

1 answer:

5 0

$a_3=21;\ a_8=56\\\\a_8-a_3=5d\\\\5d=56-21\\5d=35\ \ \ |divide\ both\ sides\ by\ 5\\d=7\\\\a_1=a_3-2d\\\\a_1=21-2\cdot7\\a_1=21-14\\a_1=7\\\\Answer:\boxed{a_1=7}$

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a ladder 6m long leans against the wall of house if the foot of the ladder makes an angle 58 degree with tye ground how far is t

Vedmedyk [2.9K]

Answer:

The base of the ladder is 3.2 meters far from the wall.

Step-by-step explanation:

We need to calculate the base of a right triangle. The given information is:

h: hypotenuse = length of the ladder = 6 m

b: is the base =?

θ: is the angle between the hypotenuse and the base = 58°

To find the base we can use the following trigonometric equation:

$cos(\theta) = \frac{b}{h}$

$b = cos(\theta)*h = cos(58)*6 = 3.2 m$

Therefore, the base of the ladder is 3.2 meters far from the wall.

I hope it helps you!

4 0

3 years ago

Find the value or measure. Assume all lines that appear to be tangent are tangent. X=

aev [14]

According to the secant-tangent theorem, we have the following expression:

$(x+3)^2=10.8(19.2+10.8)$

Now, we solve for x.

$\begin{gathered} x^2+6x+9=10.8(30) \\ x^2+6x+9=324 \\ x^2+6x+9-324=0 \\ x^2+6x-315=0 \end{gathered}$

Then, we use the quadratic formula:

$x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

Where a = 1, b = 6, and c = -315.

$\begin{gathered} x_{1,2}=\frac{-6\pm\sqrt[]{6^2-4\cdot1\cdot(-315)}}{2\cdot1} \\ x_{1,2}=\frac{-6\pm\sqrt[]{36+1260}}{2}=\frac{-6\pm\sqrt[]{1296}}{2} \\ x_{1,2}=\frac{-6\pm36}{2} \\ x_1=\frac{-6+36}{2}=\frac{30}{2}=15 \\ x_2=\frac{-6-36}{2}=\frac{-42}{2}=-21 \end{gathered}$ <h2>Hence, the answer is 15 because lengths can't be negative.</h2>

7 0

1 year ago

Help plsssssssssssssssss

Helen [10]

Answer: A .0115

Step-by-step explanation:

There are 1000 mg in a gram. So to convert to grams, you would divide by 1000

8 0

3 years ago

Read 2 more answers

U = kx+y solve for x

zhuklara [117]

Step-by-step explanation:

Kx = u - y

Divide both sides by k

X = u - y

I think that's the answer

Hope it helps:)

6 0

3 years ago

For } (x) = 4x+1 and g(x) = x2 -5, find (f/g)(x)

matrenka [14]

Answer:

Step-by-step explanation:

4x + 1

The quotient (f/g)(x) is (f/g)(x) = ---------------

x^2 - 5

Note that x^2 means "square of x," whereas "x2" is ambiguous.

7 0

2 years ago