All categories

3 years ago

Which statements are true

Mathematics

1 answer:

AnnyKZ [126]3 years ago

5 0

Answer:

A, B and C (close examination)

Step-by-step explanation:

A. 15m3 - 6m = 3m(5m2 - 6m)

m = 0 or m = 1/3

B. 40m6-4=4(10m6-1)

0 = 0
All real numbers are solutions

C. 6m2+18m=6m2(1+3m)

m = 0 or m = 1 or m = -1

D. 32m4+12m3(8m+3)

128m4 + 36m3

This is tough one but I will explain this problem by close examination:

The problem is looking for an equation that have the variable m by itself

D is out of the picture because the equations does not have m by itself

Equation B's answer is that all numbers are solutions meaning any m value you put will become the same. (Similar to Infinite Solutions)

By close examination, The answer are A, B, and C.

You might be interested in

Help. Solving Multi Step Ratio Problems!

Romashka-Z-Leto [24]

Answer:

Part 1) $30\ coupons$

Part 2) $12\ sandwiches$

Part 3) $60\ push-ups$

Part 4) $96\ minutes$

Part 5) $\$95$

Part 6) $1\frac{7}{8}\ cups\ of\ pretzel$

Step-by-step explanation:

Part 1) we know that

At the Green House of Salad , you get a $1 coupon for every 3 salads you buy

Using proportion

Find out the number of salads you could buy to get $10 in coupons

$\frac{1}{3}=\frac{10}{x} \\\\x=3(10)\\\\x=30\ coupons$

Part 2) we know that

Kim orders catering for $35

She spend $5 on a large order of potato salad and the rest on turkey sandwiches

Each sandwich is $2.50

How many sandwiches does Kim buy?

step 1

Find out how many Kim spent on turkey sandwiches

Subtract $5 from $35

35-5=$30

step 2

Using proportion, find out the number of sandwiches

$\frac{1}{2.50}=\frac{x}{30}\\\\x=30/2.50\\\\x= 12\ sandwiches$

Part 3) we know that

Molly does 10 push-ups at the same time as Liza does 15 push-ups

Using proportion

Find out how many push-ups Liza does when Molly does 40 push-ups

$\frac{10}{15}=\frac{40}{x}\\\\x=15(40)/10\\\\x=60\ push-ups$

Part 4) we know that

A shark swim at a speed of 25 miles per hour

The shark rest after 40 miles

How long in minutes, does the shark swim before resting?

Using proportion

Find out how long in minutes the shark swim 40 miles

Remember that

$1\ h=60\ min$

$\frac{25}{60}\ \frac{miles}{minutes}=\frac{40}{x}\ \frac{miles}{minutes}\\\\x=60(40)/25\\\\x=96\ minutes$

Part 5) we know that

For every bar of soap that Aly sells, she earns $5

For every mug that Janet sells, she earns twice as much as Aly

Aly sells 5 bars of soap and Janet sells 7 mugs

How much money did they make altogether?

step 1

Find out the amount earned by Aly

using proportion

$\frac{1}{5}=\frac{5}{x}\\\\x=5(5)\\\\x=\$25$

step 2

Find out the amount earned by Janet

Remember that

For every mug that Janet sells, she earns twice as much as Aly

For every mug that Janet sells, she earns 2($5)=$10

using proportion

$\frac{1}{10}=\frac{7}{x}\\\\x=10(7)\\\\x=\$70$

step 3

Adds the amount earned by Aly plus the amount earned by Janet

$25+70=\$95$

Part 6) we know that

Ted is making trail mix for a party

He mixes 1 1/2 cups of nuts, 1/4 cup of rising and 1/4 cup of pretzel

How many cups of pretzel does Ted need to make 15 cups of trail mix?

Adds the quantities

$1\frac{1}{2}+\frac{1}{4} +\frac{1}{4}=2\ cups\ of \ trail\ mix$

That means

For every 2 cups of trail mix we need 1/4 cup of pretzel

using proportion

Find out how many cups of pretzel does Ted need to make 15 cups of trail mix

$\frac{2}{(1/4)}=\frac{15}{x}\\\\x=15(1/4)/2\\\\x=\frac{15}{8}\ cups\ of\ pretzel$

Convert to mixed number

$\frac{15}{8}=\frac{8}{8}+\frac{7}{8}=1\frac{7}{8}\ cups\ of\ pretzel$

6 0

4 years ago

A motel owner observes that when a room is priced at $60 per day, all 80 rooms of the motel are occupied. For every $3 rise in t

Zinaida [17]

Answer:

a) p(x) = 300 - 3

b) P(x) = -3 x² + 285 x

c) Price of per room per day = $ 157.5

when Number of rooms occupied , x = 47.5

Step-by-step explanation:

Given - A motel owner observes that when a room is priced at $60 per day, all 80 rooms of the motel are occupied. For every $3 rise in the charge per room per day, one more room is vacant. Each occupied room costs an additional $15 per day to maintain.

To find - a) Find the demand function, expressing p, the price charged for each room per day, as a function of x, the number of rooms occupied.

b) Find the profit function P(x).

c) Find the price of per room per day the motel should charge in order to maximize its profit.

Proof -

Let

(x, y) be the point

where x represents number of rooms occupied

and y represents price of room per day.

Now,

Given that,

a room is priced at $60 per day, all 80 rooms of the motel are occupied.

So, point becomes (80, 60)

And given that For every $3 rise in the charge per room per day, one more room is vacant.

So, point becomes (79, 63)

Now, we have two points (80, 60), (79, 63)

Let us assume that,

p(x) be the price charged for each room per day

Now,

By using point - slope formula , we get

p -60 = $\frac{(63 - 60}{(79 - 80)} (x - 80)$

⇒p -60 = (-3)(x-80)

⇒p-60 = 240 -3 x

⇒p(x) = 240 + 60 -3 x

⇒p(x) = 300 - 3 x

Given that,

Each occupied room costs an additional $15 per day to maintain.

Let C(x) be the cost function,

Then C(x) =15 x

now,

Revenue function,

R(x) =x*p

= x*(300 -3 x )

= 300 x - 3 x²

⇒R(x) = 300 x - 3 x²

Now,

We know

Profit function = Revenue function - Cost function

⇒P(x) = R(x)-C(x)

⇒P(x) = (300 x -3 x²) -15 x

⇒P(x) = -3 x² + 285 x

P'(x) = -6 x +285

For Maximize profit , Put P'(x) = 0

⇒-6 x+ 285 =0

⇒6 x= 285

⇒x = $\frac{285}{6}$

⇒x= 47.5

∴ we get

Maximize profit is when price, p = 300 - 3x

= 300 -3(47.5)

= $157.5

⇒Price of per room per day = $ 157.5

when Number of rooms occupied , x = 47.5

5 0

3 years ago

What is the answer to this

allochka39001 [22]

678.58 that is the surface area to this problem

5 0

3 years ago

Determine the asymptotes of the function: y=x^3-5x^2+4x-25/x^2-4x+3

igomit [66]

Answer:

Vertical A @ x=3 and x=1

Horizontal A nowhere since degree on top is higher than degree on bottom

Slant A @ y=x-1

Step-by-step explanation:

I'm going to look for vertical first:

I'm going to factor the bottom first: (x-3)(x-1)

So we have possible vertical asymptotes at x=3 and at x=1

To check I'm going to see if (x-3) is a factor of the top by plugging in 3 and seeing if I receive 0 (If I receive 0 then x=3 gives me a hole)

3^3-5(3)^2+4(3)-25=-31 so it isn't a factor of the top so you have a vertical asymptote at x=3

Let's check x=1

1^3-5(1)^2+4(1)-25=-25 so we have a vertical asymptote at x=1 also

There is no horizontal asymptote because degree of top is bigger than degree of bottom

There is a slant asympote because the degree of top is one more than degree of bottom (We can find this by doing long division)

x -1

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

x^2-4x+3 | x^3-5x^2+4x-25

- ( x^3-4x^2+3x)

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

-x^2 +x -25

- (-x^2+4x-3)

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

-3x-22

So the slant asymptote is to x-1

8 0

3 years ago

The University of Montana ski team has seven entrants in a men's downhill ski event. The coach would like the first, second, and

VikaD [51]

Answer:

210 ways

Step-by-step explanation:

given that the University of Montana ski team has seven entrants in a men's downhill ski event.

The coach would like the first, second, and third places to go to the team members.

Since one member can get only one place and order counts here we use permutation

No of ways the seven team entrants achieve first, second, and third places

= 7P3

= $7(6)(5)\\= 210$

5 0

3 years ago