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4 years ago

What is the solution to the equation 1/3 (x - 2) = 1/5 (x + 4) + 2?

Mathematics

2 answers:

allsm [11]4 years ago

6 0

The solution is x=26

VladimirAG [237]4 years ago

5 0

Answer:

The solution is x = 26

Step-by-step explanation:

Here, the given equation is,

$\frac{1}{3}(x-2)=\frac{1}{5}(x+4)+2$

Add fractions on right side,

$\frac{1}{3}(x-2)=\frac{x+4+10}{5}$

By cross multiplication,

$5(x-2)=3(x+14)$

By distributive property,

$5x-10=3x+42$

Adding 10 on both sides,

$5x=3x+52$

Subtract 3x on both sides,

$2x=52$

Divide both sides by 2,

$x=26$

Which is the required solution,

Last option is correct.

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If $4,000 is invested in an account for 25 years. Calculate the total interest earned at the end of 25 years if the interest is:

Scrat [10]

The interest is a) $7000

b) $17709.73

c) $18672.62

d) $18901.67

What is the formula for simple and compound interest?

Simple interest = (P× r× t)

Compound interest = P(1+r/n)^nt - P

We will find the interest as shown below:

P=$4,000

t=25 years

a) r=7%=0.07

Simple interest = (P× r× t)

= (4000×0.07×25)

= $7000

b) r=7%=0.07

Compound interest = P(1+r)^t - P

= 4000(1+0.07)^25-4000

= $17709.73056

rounding to nearest cents

= $17709.73

c) r=7%=0.07

n=4

Compound interest = P(1+r/n)^nt - P

= 4000(1+0.07/4)^(25*4)-4000

= $18672.62375

rounding to nearest cent

= $18672.62

d) r=7%=0.07

n=12

Compound interest = P(1+r/n)^nt - P

= 4000(1+0.07/12)^(25*12)-4000

= $18901.6728

rounding to nearest cent

= $18901.67

Hence, the interest is a) $7000

b) $17709.73

c) $18672.62

d) $18901.67

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2 years ago

Graph the image of the given triangle under a dilation with a scale factor of –4 and center of dilation (0,0).

Dvinal [7]

Step-by-step explanation:

Hey there!

The coordinates of a triangle are;

A (1,2)
B (1,-2)
C (-2,-2)
Scale factor = -4 and centre at (0,0)

Now, We have;

P(x,y)----------- P'(kx, ky)

Keep formula;

A(1,2)---------- A'(-4×1 ,-4×2)

= A'(-4, -8)

B(1,-2)------------- B'(-4,8)

C(-2,-2)-------------C'(8,8)

[ The A' should be kept in (-4,-8). There was no place in this graph so, i kept it just below -7. Please while plotting remember to keep it on "-8".]

Hope it helps..

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3 years ago

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