Triangle LMN has coordinates L (0, 0), M (0, -2), and N (2, 0). If ΔLMN ≅ ΔXYZ, what is the measure of XZ?

Can u help me ASAP. i need to know how to do it step by step

12345 [234]

Answer:

Step-by-step explanation:

$f(x) =4x^3-8x^2+ax+b$ has a factor $2x-1$ and

when divided by $x+2$ , remainder is 20.

To find:Remainder when divided by (x-1) ?

Solution:

$2x-1$ is a factor

$2x - 1 = 0 \Rightarrow x = \frac{1}{2}$ when we put this value of x to the function, it will become 0.

i.e.

$\Rightarrow f(\dfrac{1}{2}) =0 =4\times (\dfrac{1}2)^3-8(\dfrac{1}2)^2+\dfrac{a}{2}+b=0\\\Rightarrow \dfrac{1}{2}-2+\dfrac{a}{2}+b=0\\\Rightarrow 1-4+a+2b=0\\\Rightarrow a +2b=3 ......(1)$

Remainder is 20 when f(x) is divided by $x+2$

i.e.

$f(-2) =20$

$\Rightarrow f(-2) =20 =4\times (-2)^3-8(-2)^2-2a+b=20\\\Rightarrow -32-32-2a+b=20\\\Rightarrow -2a+b=84 ...... (2)$

Solving (1) and (2), Multiply equation (1) by 2 and adding to (2):

$5b=6+84\\\Rightarrow b = \dfrac{90}{5} = \bold{18}$

By equation (1):

$a+2(18) = 3\\\Rightarrow a = -33$

So, the equation becomes:

$f(x) =4x^3-8x^2-33x+18$

$\Rightarrow f(1) = 4(1) -8 (1) -33(1) +18 = \bold{19}$

So, when divided by (x-1), remainder will be <em>19</em>.

4 0

3 years ago

Can anyone help me?

natali 33 [55]

answer is c ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

6 0

3 years ago

Solve this problem please

djyliett [7]

The formula for depreciation is:

$y=x(1-r)^t$

Where x = Initial value,

y= Amount after depreciation.

r= Rate of depreciation,

t = time (in years)

According to given problem,

x = 1040, y= 944 and t = 12 months =1 year.

So, first step is to plug in these values in the above formula, So,

$944 = 1040(1-r)^1$

944 = 1040 (1 -r)

$\frac{944}{1040} =1-r$ Divide each sides by 1040.

0.907692308 =1 - r

0.907692308 - 1 = -r Subtract 1 from each sides.

-0.092307692 = -r

So, r = 0.09 or 9%.

Now plug in 0.09 in the above equation to get the depreciation equation. So,

$y = x (1- 0.09)^t$

So, $y = 0.91x^t$

b) To find the value of the bike after 5 months,

plug in t = 5 months= 5/12 = 0.41667 years in the above equation of depreciation.

So, $y= 1040 *(0.91)^{0.41667}$

y = 1040 * 0.961465659

y = 999.9242852

y = 1000 (Rounded to nearest integer).

Hence, the value of the bike after 5 months is $1000.

7 0

3 years ago

Use the Law of Cosines to find the missing angle. In triangle JKL, j=3in., k=4in., and l=2.89., find mJ

slega [8]

Using the law of cosine for Triangle KJL, we can write:

$j^{2} = k^{2} + l^{2}-2(k)(l)cos(J) \\ \\ 
2(k)(l)cos(J)=k^{2} + l^{2}- j^{2} \\ \\ 
cos(J)= \frac{k^{2} + l^{2}- j^{2}}{2(k)(l)}$

Using the values of k,j and l, we can write:

$cos(J)= \frac{ 4^{2} + (2.89)^{2} - 3^{2} }{2(4)(2.89)} \\ \\ 
cos(J)= 0.664 \\ \\ 
J= cos^{-1}(0.664) \\ \\ 
J=48.39$

Rounding to nearest integer, the measure of angle J will be 48 degrees.
So option B gives the correct answer

8 0

3 years ago

Read 2 more answers

How do you verify the identity?

rodikova [14]

Their both the answer hope this helps

5 0

3 years ago