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2 years ago

Simplify the expression

Mathematics

2 answers:

Dafna11 [192]2 years ago

7 0

$\bf \left( \cfrac{2}{5m^5} \right)^{-4}\implies \left( \cfrac{5m^5}{2} \right)^{4}\implies \cfrac{5^4m^{5\cdot 4}}{2^4}\implies \cfrac{625m^{20}}{16}$

BaLLatris [955]2 years ago

6 0

The answer is 625m^20/16

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An airline offers daily flights between Chicago and Denver. The total monthly cost C (in millions of dollars) of these flights c

Ira Lisetskai [31]

Answer:

6250

Step-by-step explanation:

Fill in the given number and solve for x. The answer is 1000x, rounded.

$C=\sqrt{0.2x+1}\\\\1.5=\sqrt{0.2x+1} \quad\text{use given value for C}\\\\2.25=0.2x+1 \quad\text{square both sides}\\\\1.25=0.2x \quad\text{subtract 1}\\\\6.25=x \quad\text{multiply by 5}$

x is in thousands, so 6.25×1000 = 6,250 passengers flew in June.

8 0

3 years ago

The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm^2/

VARVARA [1.3K]

Answer:

The base is decreasing at 2 cm/min.

Step-by-step explanation:

The area (A) of a triangle is given by:

$A = \frac{1}{2}bh$ (1)

Where:

b: is the base

h: is the altitude = 10 cm

If we take the derivative of equation (1) as a function of time we have:

$\frac{dA}{dt} = \frac{1}{2}(\frac{db}{dt}h + \frac{dh}{dt}b)$

We can find the base by solving equation (1) for b:

$b = \frac{2A}{h} = \frac{2*120 cm^{2}}{10 cm} = 24 cm$

Now, having that dh/dt = 1 cm/min, dA/dt = 2 cm²/min we can find db/dt:

$2 cm^{2}/min = \frac{1}{2}(\frac{db}{dt}*10 cm + 1 cm/min*24 cm)$

$\frac{db}{dt} = \frac{2*2 cm^{2}/min - 1 cm/min*24 cm}{10 cm} = -2 cm/min$

Therefore, the base is decreasing at 2 cm/min.

I hope it helps you!

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2 years ago

Which expressions are equivalent to the one below? Check all that apply. 21^x/3^x

satela [25.4K]

Answer:

<em>options: A,C,E </em>are correct.

Step-by-step explanation:

We have to find the expression equivalent to the expression:

$\dfrac{21^x}{3^x}$

we know that: $21^x=(3\times7)^x\\\\21^x=3^x\times7^x$

Hence,

$\dfrac{21^x}{3^x}=\dfrac{3^x\times7^x}{3^x}=7^x$ -----(1)

A) $(\dfrac{21}{3})^x= 7^x$ (same as(1))

Hence, option A is correct.

B) 7 ; which is a different expression from (1)

Option B is incorrect.

C) $7^x$ (Same as (1))

Option C is correct.

D) $(21-3)^x=18^x$ which is a different expression from (1)

Hence, option D is incorrect.

E) $\dfrac{7^x\times3^x}{3^x}=7^x$ ; which is same as (1)

Hence, Option E is correct.

F) $3^x$ ; which is not same as expression (1)

Hence, option F is incorrect.

5 0

3 years ago

Read 2 more answers

Help with these 2 please !!

stiks02 [169]

The answer is A and B

3 0

2 years ago

What are the coordinates of the vertices of the triangle under the translation (x y) (x − 1 y − 3)

Vsevolod [243]

Answer:

A: (-9,-3)(-2,-4)(-5,-8)

B: (-5,2)(-1,-3)(3,2)

C: (4,-7)(-1,-3)(4,1)

D: (-1,-11)(-2,-4)(-6,-7)

Step-by-step explanation:

So of the transformations, translations are pretty much the easiest. x-1 just means move all coordinates left 1 and y-3 means move all coordinates down 3. So for the first one the x coordinate gets 1 subtracted from it and the y value gets 3 subtracted from it.

(-8,0) => (-8-1, 0-3) = (-9,-3)

I do recommend double checking though, for practice and in case I flubbed a calculation.

7 0

3 years ago