Can someone solve this for me?

Please I really need this fast<br><br> Find the values of a and b in the kite below.

Marina CMI [18]

Answer:

a=5, b=15

Step-by-step explanation:

we know that

The figure MNLO is a Kite

so

LO=NO and MN=LM

we have

LO=7a-14, NO=b+6

7a-14=b+6 -----> equation A

MN=b, LM=3a

b=3a -----> equation B

Solve the system of equations by substitution

Substitute equation B in equation A and solve for a

7a-14=(3a)+6

7a-3a=6+14

4a=20

a=5

Find the value of b

b=3a ----> b=3(5)=15

therefore

a=5, b=15

5 0

3 years ago

the sum of the measures of the interior angels of a convex polygon is 3240 classify the polygon by the number of sides

Ipatiy [6.2K]

Answer:

20-gon

Step-by-step explanation:

First we start with the formula to find what the sum of angles will be if we know the number of sides.

S=(n-2)*180 where S is the sum of angles and n is the number of sides.

Normally you'd plug in n to find S, but you can do the opposite too.

3240=(n-2)*180

Let me know if you need help working it from here.

5 0

3 years ago

What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?

Trava [24]

Answer:

$\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}$

Step-by-step explanation:

The explicit formula for a geometric sequence:

$a_n=a_1r^{n-1}$

$a_n$ - n-th term

$a_1$ - first term

$r$ - common ratio

$r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}$

We have

$a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...$

The common ratio:

$r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}$

<h2>It's not a geometric sequence.</h2>

If $a_3=-\dfrac{1}{16}$ then the common ratio is $r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}$

Put to the explicit formula:

$a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}$

Put $a_n=\dfrac{1}{1024}$ and solve for <em>n </em>:

$-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1$