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3 years ago

What is the length of segment LP?

Mathematics

1 answer:

Mariana [72]3 years ago

8 0

In the image, as denoted by similar sides OP and MN, we can conclude that the 2 triangles are similar triangles. To look for the value of x (which we can substitute later to find the length of segment LP), we relate the relations of segments LO and LP to segments LM and LN. This relation is shown below:

LO/LP = LM/LN

22 / x+12 = 30 / x+12 + 5
22 / x+12 = 30 / x+17

Cross-multiplying:
30x + 360 = 22x + 374

Isolating x to one side of the equation by subtracting 22x and 360 from both sides:

30x + 360 - 360 - 22x = 22x + 374 - 360 - 22x
8x = 14
x = 1.75

Since we now have the value of x, we substitute this to the equation of LP:
LP = x + 12
LP = 1.75 + 12
LP = 13.75

Therefore the value of LP is 13.75 in.

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X=3/5
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Given f(x) = | – 5 – 4x| ,find the following:

jasenka [17]

Answer:

$f(10) = 35 \\ \\ f( - 11) = 39 \\ \\ f(12) = 53 \\ \\ f(2) = 13$

Step-by-step explanation:

$f(x) = | - 5 - 4x|$

To solve for the following substitute the value of x in the brackets into the above formula and solve for the value of x

NB:  Absolute value of a negative number is the same number but positive.

So we have

$f( - 10) = | - 5 - 4( - 10)| \\ = | - 5 + 40| = 35 \\ \\ f( - 11) = | - 5 - 4( - 11)| \\ = | - 5 + 44| = 39 \\ \\ f(12) = | - 5 - 4(12)| \\ = | - 5 - 48| \\ = | - 53| = 53 \\ \\ f(2) = | - 5 - 4(2)| \\ = | - 5 - 8| = | - 13| \\ = 13$

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3 years ago

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Please help me with part b of number 16.

natka813 [3]

You want to find the time (x) when the distance from desitnation is 0:

d = 0,

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3 years ago

<img src="https://tex.z-dn.net/?f=%20-%203%20%2B%205i%20%20%5Cdiv%20%20-%203%20-%204i" id="TexFormula1" title=" - 3 + 5i \div

Likurg_2 [28]

Answer:

$\frac{-11}{25}+\frac{-27}{25}i$ given you are asked to simplify

$\frac{-3+5i}{-3-4i}$

Step-by-step explanation:

You have to multiply the numerator and denominator by the denominator's conjugate.

The conjugate of a+bi is a-bi.

When you multiply conjugates, you just have to multiply first and last.

(a+bi)(a-bi)

a^2-abi+abi-b^2i^2

a^2+0 -b^2(-1)

a^2+-b^2(-1)

a^2+b^2

See no need to use the whole foil method; the middle terms cancel.

So we are multiplying top and bottom of your fraction by (-3+4i):

$\frac{-3+5i}{-3-4i} \cdot \frac{-3+4i}{-3+4i}=\frac{(-3+5i)(-3-4i)}{(-3-4i)(-3+4i)}$

So you will have to use the complete foil method for the numerator. Let's do that:

(-3+5i)(-3+4i)

First: (-3)(-3)=9

Outer:: (-3)(4i)=-12i

Inner: (5i)(-3)=-15i

Last: (5i)(4i)=20i^2=20(-1)=-20

--------------------------------------------Combine like terms:

9-20-12i-15i

Simplify:

-11-27i

Now the bottom (-3-4i)(-3+4i):

F(OI)L (we are skipping OI)

First:-3(-3)=9

Last: -4i(4i)=-16i^2=-16(-1)=16

---------------------------------------------Combine like terms:

9+16=25

So our answer is $\frac{-11-27i}{25}{/tex] unless you want to seprate the fraction too:[tex]\frac{-11}{25}+\frac{-27}{25}i$

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lora16 [44]

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