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matrenka [14]
2 years ago
13

What are the possible values of x if (4c-5)^2= 49?

Mathematics
2 answers:
kykrilka [37]2 years ago
7 0

Answer:

c = 3                              c = -1/2

Step-by-step explanation:

(4c-5)^2= 49

Take the square root of each side

sqrt((4c-5)^2)= ±qrt(49)

4c-5 = ±7

Separate into two equations

4c-5 = 7           4c-5 = -7

Add 5 to each side

4c-5+5 = 7+5          4c-5+5 =-7+5

4c =12                         4c = -2

Divide by 4

4c/4 = 12/4                     4c/4 = -2/4

c = 3                              c = -1/2

Setler [38]2 years ago
3 0

Answer:

c = -½, 3

Step-by-step explanation:

(4c - 5)² = 49

4c - 5 = +/- 7

4c - 5 = 7

4c = 12

c = 3

4c - 5 = -7

4c = -2

c = -½

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Parker Middle School's chior needs to raise $480 for an upcoming trip they will take. At their first fundraising project, they r
harkovskaia [24]

The money does the choir still need to raise is $180.

<u>Step-by-step explanation:</u>

The money needed to be raised by the choir for an upcoming trip = $480.

It is given that, the money needed was raised in two fundraising projects.

<u>During the first fundraising project :</u>

The choir raised 25% of the money needed for the trip.

⇒ 25% of 480

⇒ (25/100) × 480

⇒ (1/4) × 480

⇒ 120

Therefore, the first fundraising project raised $120.

<u>During the second fundraising project :</u>

The choir raised 3/8 of the money needed for the trip.

⇒ 3/8 of 480

⇒ (3/8) × 480

⇒ 3 × 60

⇒ 180

Therefore, the second fundraising project raised $180.

<u>To find the money does the choir still need to raise :</u>

You need to find the remaining amount from the 480 after raising money from the two fund raising projects.

For that, find out how much you raised from those fund raising projects and subtract it from the 480.

Money needed = Total money required for the trip - Raised money

⇒ 480 - (120+180)  

⇒ 480 - 300

⇒ 180 dollars.

The money does the choir still need to raise is $180.

6 0
3 years ago
What is the product?
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8 0
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Describe the graph of the function f(x) = x3 − 11x2 + 36x − 36. Include the y-intercept, x-intercepts, and the end behavior.
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To find the x-intercepts, we need to factorize the function. A very good idea is to first try the factors of 36:

f(1)=1-11+36-36, not 0

f(2)=8-44+72-36=-36+72-36=0. Here we have our first root (2).

Now we cad divide f(x) by (x-2) which will give us a quadratic expression, which we can factorize easily (if the discriminant is non negative).

We can also try some other factors of 36. Indeed we can check that 

f(3)=27-99+108-36=135-135=0, 
and
f(6)=216-396+216-36=0.

Thus, f(x)=(x-2)(x-3)(x-6). Note that if we expanded the right hand side expression, the constant term would be the product of the constants 2, 3, 6.

This is the reason why in the first place we looked at the factors of 36 for the possible zeros of f(x).


Thus, the x-intercepts are (2, 0), (3, 0), (6, 0), or 2, 3, 6. 

The y-intercept is f(0), which is -36.


Note that f(0)<f(2) because f(0)=-36 and f(2)=0. This means that at the left side, the graph is coming from - infinity. Similarly, 

we can check that f(10)=1000-1100+360-36=224> f(6). That is, to the right of our rightmost root, the graph is getting larger.

Thus, the end behaviors are: the graph goes to + infinity as x goes to + infinity, 

and it goes to minus infinity as x goes to - infinity.
7 0
3 years ago
Javon spent %687 on pokemon cards. Energy cards cost $6 and dragon cards cost $5. If he bought a total of 127 packs then how man
pshichka [43]

Answer:

Javon purchase Energy cards = 52

Javon purchase Dragon cards = 75

Step-by-step explanation:

Given - Javon spent $687 on pokemon cards. Energy cards cost $6

             and dragon cards cost $5.

To find - If he bought a total of 127 packs then how many of each did he buy ?

Proof -

Let Javon purchase Energy cards = x

     Javon purchase Dragon cards = y

Now,

Given that he bought a total of 127 packs

⇒x + y = 127

Also,

Cost for 1 Energy card = $6

⇒Cost of x Energy cards = $ 6x

And

Cost of 1 Dragon card = $5

⇒Cost of y Dragon card = $ 5y

Now,

Given that Javon spent $687 on pokemon cards.

⇒6x + 5y = 687

∴ we get

x + y = 127                                 ..................(1)

6x + 5y = 687                            .................(2)

Multiply by 6 in equation (1) , we get

6(x + y) = 6(127)

⇒6x + 6y = 762                          .................(3)

Now,

Subtract equation (2) from equation (1) , we get

6x + 6y - (6x + 5y )= 762 - 687

⇒6x + 6y - 6x - 5y = 75

⇒y = 75

Now,

Put the value of y in equation (1), we get

x + 75 = 127

⇒x = 127 - 75

⇒x = 52

∴ we get

Javon purchase Energy cards = x = 52

Javon purchase Dragon cards = y = 75

3 0
3 years ago
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