Slot method 20 options 3 slots First slot: 20 options Second slot: 19 options (one used up for 1st slot) Third slot: 18 (one less than last) Multiply them 20 times 19 times 18=6840 Answer is 6840 ways

3 0

3 years ago

Read 2 more answers

10.5 divided by 1.25

zepelin [54]

Answer:

8.4

Step-by-step explanation:

8 0

3 years ago

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If measure KL=136 and measure LH= 113. find measure angle KJH

notka56 [123]

Answer:

D) 111

Step-by-step explanation:

In order to find ∠KJH we must find the measure of arc KH

Note that ∠KJH is a central angle and arc KH is the arc it intercepts

Because ∠KJH is a central angle it equal the measure of its intercepted arc

Thus, ∠KJH = arc KH

J is a circle that is made up of 3 arc; KL, LH and KH

If you didn't know the sum of the arcs in a circle = 360°

Which means that arc KL + arc LH + arc KH = 360

If arc KL = 136 and arc LH = 113

Then 136 + 113 + arc KH = 360

^ ( note that we just created an equation that we can use to

solve for arc KH )

We now solve for arc KH

136 + 113 + arc KH = 360

* combine like terms *

136 + 113 = 249

we now have 249 + arc KH = 360

* subtract 249 from each side *

249 - 249 cancels out

360 - 249 = 111

We're left with arc KH = 111°

Like stated previously arc KH = ∠KJH

Hence, ∠KJH = 111°

8 0

2 years ago

Which of the following represent the values of x, y, and z.

Paraphin [41]

Answer:

Part 1) $z=4\sqrt{3}\ units$

Part 2) $y=4\sqrt{2}\ units$

Part 3) $x=4\sqrt{6}\ units$

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

<em>Find the value of z</em>

In the right triangle DBC

$cos(C)=\frac{4}{z}$ ----> equation A

In the right triangle ABC

$cos(C)=\frac{z}{12}$ ----> equation B

equate equation A and equation B

$\frac{4}{z}=\frac{z}{12}$

$z^{2}=48$

$z=4\sqrt{3}\ units$

step 2

In the right triangle DBC

Applying the Pythagoras Theorem

$z^{2}=y^{2}+4^{2}$

we have

$z=4\sqrt{3}\ units$

substitute

$(4\sqrt{3})^{2}=y^{2}+4^{2}$

$48=y^{2}+16$

$y^{2}=48-16$

$y^{2}=32$

$y=4\sqrt{2}\ units$

step 3

Find the value of x

In the right triangle ABC

Applying the Pythagoras Theorem

$12^{2}=x^{2}+z^{2}$

we have

$z=4\sqrt{3}\ units$

substitute

$12^{2}=x^{2}+(4\sqrt{3})^{2}$

$144=x^{2}+48$

$x^{2}=144-48$

$x^{2}=96$

$x=4\sqrt{6}\ units$

6 0

3 years ago