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2 years ago

15

Which expression is equivalent to the given expression? 8^6

1 answer:

Rasek [7]2 years ago

4 0

I don’t know what the possible answers are, but it could be any of the following.

8x8x8x8x8x8
(8^3)*(8^3)

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In the △ABC, the height AN = 24 in, BN = 18 in, AC = 40 in. Find AB and BC. Consider all possible cases. Case 1 : N∈BC, AB = __,

aivan3 [116]

Answer:

Case 1:

$AB = 30$

$BC = 50$

Case 2:

$AB = 15.9$

$BC = 36.7$

Case 3: Not possible

Step-by-step explanation:

Given

See attachment for illustration of each case

Required

Find AB and BC

Case 1:

Using Pythagoras theorem in ANB, we have:

$AB^2 = AN^2 + BN^2$

This gives:

$AB^2 = 24^2 + 18^2$

$AB^2 = 576 + 324$

$AB^2 = 900$

Take square roots of both sides

$AB = \sqrt{900$

$AB = 30$

To calculate BC, we consider ANC, where:

$AC^2 = AN^2 + NC^2$

$40^2 = 24^2 + NC^2$

$1600 = 576 + NC^2$

Collect like terms

$NC^2 = 1600 - 576$

$NC^2 = 1024$

Take square roots

$NC = \sqrt{1024$

$NC = 32$

So:

$BC = NC + BN$

$BC = 32 + 18$

$BC = 50$

Case 2:

Using Pythagoras theorem in ANB, we have:

$AN^2 = AB^2 + BN^2$

This gives:

$24^2 = AB^2 + 18^2$

$576 = AB^2 + 324$

Collect like terms

$AB^2 = 576 - 324$

$AB^2 = 252$

Take square roots of both sides

$AB = \sqrt{252$

$AB = 15.9$

To calculate BC, we consider ABC, where:

$AC^2 = AB^2 + BC^2$

$40^2 = 252 + BC^2$

$1600 = 252 + BC^2$

Collect like terms

$BC^2 = 1600 - 252$

$BC^2 = 1348$

Take square roots

$BC = \sqrt{1348$

$BC = 36.7$

Case 3:

This is not possible because in ANC

The hypotenuse AN (24) is less than AC (40)

3 0

2 years ago

The quotient of a number and -7 decreased by 2 is 10 find the number

yarga [219]

X/-7 -2 =10
x/-7 = 12
x = -84

7 0

2 years ago

At the gas station, each liter of gas costs $ 3 $3dollar sign, 3, but there's a promotion that for every beverage you purchase y

IgorC [24]

Answer:

Yes! Our total savings on gas proportional to the number of beverages you purchase.

Step-by-step explanation:

Here, each liter of gas costs $3.

Every beverage you purchase you save $0.20.

So, if you purchase for $9, you will save 3*$0.20 = $0.60

So, this is proportional because when increase in purchase, there is proportional increase in savings.

6 0

3 years ago

g If a snowball melts so that its surface area decreases at a rate of 4 cm2/min, find the rate (in cm/min) at which the diameter

maks197457 [2]

Answer:

Rate of change of the diameter is equal to 0.053cm/min

Step-by-step explanation:

A snowball is of the shape of a sphere

Surface area of Sphere (S)= $4*pi*R^2$

Rate of change of surface area

dS/dt = -4 $cm^2/min$

the negative sign indicates the surface area is decreasing.

Radius = d/2 where d represents diameter

using this is the surface area equation

S = $4*pi*(d/2)^2$

= $pi*d^2$

dS/dt = 2*pi*d*d(d)/dt

4 = 2*pi*d*(d)/dt

d(d)/dt = 2/12*pi= $\frac{1}{6pi}$ cm/min

so the rate of change of the diameter is equal to 0.053cm/min

5 0

2 years ago

Mr Reid needs 5 1/2 yards of fabric to make a costume. He already has 2 1/4 yards. How many yards of fabric does he need?

KiRa [710]

He needs 3 1/4 more yards of fabric because 5.5 - 2.25 = 3.25

8 0

2 years ago