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nataly862011 [7]
3 years ago
5

the length of rope P is three times the length of rope Q. After 10cm of rope is cut from rope P and rope Q respectively, the len

gth of rope P is four times the length of Q. Calculate the original length, in cm, of rope P before it is cut.
Mathematics
1 answer:
Leona [35]3 years ago
7 0

Answer:

150 cm

Step-by-step explanation:

The information in the question includes;

The length of rope P = 3 × The length of rope Q

The length of rope P - 10 cm  = 4 × (The length of rope Q - 10 cm)

Let <em>p</em> represent the original length of rope P and let <em>q</em> represent the original length of rope Q, we have;

p = 3·q...(1)

p - 10 = 4·(q - 10)...(2)

Expanding equation (2) gives;

p - 10 = 4·q - 40

∴ p = 4·q - 40 + 10 = 4·q - 50

p = 4·q - 50...(3)

Equating the values of <em>p</em> in equation (1) and equation (3) gives;

p = 3·q, and p = 4·q - 50, therefore, by the substitution property of equality, we have;

3·q = 4·q - 50

50 = 4·q - 3·q = q

q = 50

p = 3·q

∴ p = 3 × 50 = 150

The original length of P before it was cut, p = 150 cm.

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Suppose that you have $1400 in a savings account. The bank pays 1.5% annual simple interest. What would be the interest paid aft
ICE Princess25 [194]

Answer:

You should have $1,463.95

Step-by-step explanation:

The formula for this is A=P(1+r)^x

P being the initial amount, r being the percentage, and x being the time passing.

<u>1. Write out the equation:</u> A=1400(1+0.015)^3

REMEMBER- writing percentages into decimals is moving the decimal point two times to the left--or dividing by 100!

<u>2. Parentheses:</u> 1400(1.015)^3

At this point, you're going to want to do exponents first (PEMDAS). If you're typing this into a calculator it should just give you the answer right away with the full equation.

<u>3. Answer:</u> 1463.95 (rounded to the nearest hundredth).

**I apologize if this is wrong; I haven't done it in a while so I don't know if I did 3 years or 3 months.. lol. That's probably not helping with the confidence level, but good luck!

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6 0
3 years ago
How do you find the vertex and axis of symmetry for this function, <br><br> F(x)=3(x+1)^2
Andrews [41]
Answers:
Vertex is (-1,0)
Axis of symmetry is x = -1

============================================

Explanation:

F(x) = 3(x+1)^2
is the same as
y = 3(x-(-1))^2 + 0
which is in the form
y = a(x-h)^2 + k

We can see that
a = 3
h = -1
k = 0

Therefore the vertex is (h,k) = (-1,0)
The axis of symmetry is x = h = -1 which is the equation x = -1

The axis of symmetry in this case is a vertical line through the vertex. 
3 0
3 years ago
The graphs of functions f(x) and g(x) = f(x) + k are shown in the picture.
-Dominant- [34]

Answer:

Step-by-step explanation:

g(x) = f(x) -2

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At a pet store, the ratio of female birds to male birds was 7:4. Write a sentence explaining what this means.
cluponka [151]
For every 7 female birds, there are 4 male birds.
8 0
3 years ago
I need help can someone please help me
ExtremeBDS [4]

Answer:

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Step-by-step explanation:


6 0
4 years ago
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