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3 years ago

9

See the picture below!!

1 answer:

Darya [45]3 years ago

7 0

Answer:

Q1) x = 17.3

y = 8.7

Q2) d = 19

Step-by-step explanation:

Question 1

Angle = 60°

Hypotenuse = x

Adjacent = y

Opposite = 15

<u>Step 1: Find x</u>

Sin (angle) = opposite/hypotenuse

Sin (60°) = 15/x

x = 10√3 = 17.3

<u>Step 2: Find y</u>

Tan (angle) = opposite/adjacent

Tan (60°) = 15/y

y = 5√3 = 8.7

Question 2

<u>Step 1: Find the diagonal of the base</u>

c² = a²+b²

c² = 6² + 10²

c = 2√34 = 11.7

<u>Step 2: Find diagonal d</u>

c² = a² + b²

d² = 11.7² + 15²

d = 19

!!

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Find the indicated nth partial sum of the arithmetic sequence.<br> −7, −3, 1, 5, . . ., n = 30

TiliK225 [7]

Step-by-step explanation:

Given the Arithmetic sequence

$-7, -3, 1, 5, . . .$

An arithmetic sequence has a constant difference d and is defined by

$a_n=a_1+\left(n-1\right)d$

$\mathrm{Compute\:the\:differences\:of\:all\:the\:adjacent\:terms}:\quad \:d=a_{n+1}-a_n$

$-3-\left(-7\right)=4,\:\quad \:1-\left(-3\right)=4$

$\mathrm{The\:difference\:between\:all\:of\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}$

$d=4$

$\mathrm{The\:first\:element\:of\:the\:sequence\:is}$

$a_1=-7$

as

$a_n=a_1+\left(n-1\right)d$

$\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:$

$a_n=4\left(n-1\right)-7$ ∵ $d=4$

$\mathrm{Arithmetic\:sequence\:sum\:formula:}$

$n\left(a_1+\frac{d\left(n-1\right)}{2}\right)$

$\mathrm{Plug\:in\:the\:values:}$

$n=30,\:\space a_1=-7,\:\spaced=4$

$=30\left(-7+\frac{4\left(30-1\right)}{2}\right)$

$=30\left(58-7\right)$ ∵ $\frac{4\left(30-1\right)}{2}=58$

$=30\cdot \:51$

$=1530$ ∵ $\mathrm{Multiply\:the\:numbers:}\:30\cdot \:51=1530$

Therefore, the indicated nth partial sum of the arithmetic sequence is 1530.

ANOTHER METHOD

as

$a_n=4\left(n-1\right)-7$

n = 30

$\sum _{n=1}^{30}\:4\left(n-1\right)-7$

$=\sum _{n=1}^{30}4n-11$

$\mathrm{Apply\:the\:Sum\:Rule}:\quad \sum a_n+b_n=\sum a_n+\sum b_n$

$=\sum _{n=1}^{30}4n-\sum _{n=1}^{30}11$

as

$\sum _{n=1}^{30}4n=1860$

and

$\sum _{n=1}^{30}11=330$

so

$=1860-330$

$=1530$

7 0

4 years ago

Nth term of this sequence -5 -2 3 10 19

Georgia [21]

Answer:

3

Step-by-step explanation:

5 0

3 years ago

Which of the following is equivalent to x+1/y divided by g+1/h

Vikki [24]

Answer:

B) x + 1/y times h/g+1

Step-by-step explanation:

We need to divide $\frac{x+1}{y}$ by $\frac{g+1}{h}$ then match with given choices to find the correct equivalent result.

where given choices are:

A) x/y times h/g

B) x + 1/y times h/g+1

C) x+ 1/y divided h/g+1

D) y/x+1 divided g+1/h

So let's divide $\frac{x+1}{y}$ by $\frac{g+1}{h}$

$\frac{\left(\frac{x+1}{y}\right)}{\left(\frac{g+1}{h}\right)}$

we are allowed to flip the bottom fraction and change division sign into multiplication. So we get:

$=\left(\frac{x+1}{y}\right)\cdot\left(\frac{h}{g+1}\right)$

Hence correct choice is: B) x + 1/y times h/g+1

3 0

3 years ago

Help me solve this pleaseee

Drupady [299]

Since they are equal to 90 degrees. (complimentary angles)

6x-11+7x+10= 90

Combine like terms.

13x-1= 90

Add one to both sides.

13x= 91

x= 7

Plug that into the b.

7(7)+10

49+10

59

I hope this helps!
~kaikers

3 0

4 years ago

What are two consecutive even integers that has a sum of -42?

Dafna1 [17]

Answer:

<h2>-22 and -20</h2>

Step-by-step explanation:

$n,\ n+2-\text{two consecutive even integers}\\\\\text{The equation:}\\\\n+(n+2)=-42\\\\n+n+2=-42\qquad\text{subtract 2 from both sides}\\\\2n=-44\qquad\text{divide both sides by 2}\\\\n=-22\\\\n+2=-22+2=-20$

8 0

4 years ago