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2 years ago

Solve the following equation. Then place the correct number in the box provided.

Mathematics

2 answers:

raketka [301]2 years ago

7 0

The answer is:

z ≥ − 6

melisa1 [442]2 years ago

4 0

Your answer should be z ≥ − 6

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Find the missing lengths: LK=15 and KH=9, find KI and HI.

Luda [366]

Answer:

KI=11.25 and HI=6.75

Step-by-step explanation:

Consider the below figure attached with this question.

According to Pythagoras Theorem:

$base^2+perpendicular^2=hypotenuse^2$

Use Pythagoras in triangle HKL

$LH^2+KH^2=LK^2$

$(LH)^2+9^2=15^2$

$(LH)^2+81=225$

$(LH)^2=144$

Taking square root on both sides.

$LH=12$

Let length of HI be x.

LI = 12+x

Use Pythagoras theorem in ΔKLI,

$(KI)^2+15^2=(12+x)^2$

$(KI)^2+225=x^2+24x+144$

$(KI)^2=x^2+24x+144-225$

$(KI)^2=x^2+24x-81...(1)$

Use Pythagoras theorem in ΔHKI,

$(KI)^2=x^2+9^2$

$(KI)^2=x^2+81...(2)$

From (1) and (2) we get

$x^2+81=x^2+24x-81$

$24x=162$

$x=\dfrac{162}{24}=6.75$

Hence, the measure of HI is 6.75 units.

Substitute x=6.75 in equation (2).

$(KI)^2=(6.75)^2+81$

$(KI)^2=126.5625$

Taking square root on both sides.

$KI=\sqrt{126.5625}$

$KI=11.25$

Hence, the measure of KI is 11.25 units.

3 0

2 years ago

The United states has 12,383 miles of coastline. If 0.8%of the coastline is located in george, about how many miles of boasting

Vladimir [108]

The answer is that there is a proximity 10 miles of coast 9.904... it be exact

6 0

3 years ago

Solve the following systems of equations. 2= 2y + 5 | 3y - 3x = -12

ivanzaharov [21]

Answer:

x=5/2, y=-3/2. (5/2, -3/2).

Step-by-step explanation:

2=2y+5

3y-3x=-12

--------------

2-5=2y

2y=-3

y=-3/2

3(-3/2)-3x=-12

-9/2-3x=-12

3x=-9/2-(-12)

3x=-9/2+12

3x=-9/2+24/2

3x=15/2

x=(15/2)/3

x=(15/2)(1/3)

x=15/6=5/2

7 0

3 years ago

Can someone pls help me solve this question!!!!!!!

KiRa [710]

Total of 90 fish:

c + p = 90

Charlie gave 1/4 c to Peter. Now

Charlie has c - (1/4) c

Peter has p + (1/4) c

Peter gave 2/5 of his to Charlie. Now

Peter has p + (1/4) c - 2/5( p + (1/4) c )

Charlie has c - (1/4) c + 2/5( p + (1/4) c )

And then they had equal number:

c - (1/4) c + 2/5( p + (1/4) c ) = p + (1/4) c - 2/5( p + (1/4) c )

Let's do the easy subtractions then multiply by 20 to clear the fractions,

(3/4) c + 2/5( p + (1/4) c ) = 3/5( p + (1/4) c )

15c + 8p + 2c = 12p + 3c

14c = 4p

7c = 2p

c + p = 90

2c + 2p = 180

2c + 7c = 180

9c = 180

c = 20

p = 70

Answer: Charlie started with 20, Peter with 70

Check:

Initially C:20, P:70

1/4(20)=5 to P

C:15, P:75

(2/5) 75 = 30 to C

C:45, P45

Good

3 0

2 years ago

F(-1) if f(x)= 4x^2 Help solve please

nasty-shy [4]

Answer:

Option C, $f(-1) = 4\\$

Step-by-step explanation:

Step 1: Set x to -1

$f(x)=4x^2$

$f(-1)=4(-1)^2$

$f(-1)= 4(1)$

$f(-1) = 4\\$

Answer: Option C, $f(-1) = 4\\$

5 0

2 years ago

Read 2 more answers