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nekit [7.7K]
3 years ago
9

Triangle ABC and Triangle DEF are similar. For triangle ABC, AB = 2x , AC = 24 inches and BC = 20. For triangle DEF, EF = 5 and

DF = x - 2 . What is the value of x?
Mathematics
1 answer:
Norma-Jean [14]3 years ago
8 0
X=8.

Following the similarity statement, we know that AC is to DF as BC is to EF.  The ratio would be:

24/(x-2) = 20/5

Cross multiply:
24*5 = 20(x-2)

Use the distributive property:
120 = 20x - 40

Add 40 to both sides:
120+40 = 20x - 40 + 40
160 = 20x

Divide both sides by 20:
160/20 = 20x/20
8 = x
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Leno4ka [110]

Answer:

21x

Step-by-step explanation:

In the parentheses, 3 * x is the same thing as 3x.  Distribute 7 into 3x to get 21x as your final answer.

8 0
3 years ago
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MAJORR HELP!!!
WINSTONCH [101]

Answer:

a)$1628.90

b)$1647.00

c)$1648.72

Step-by-step explanation:

The question is on compound interest.

The formula to apply here is;

A=P(1+\frac{r}{n} )^{nt}

where

  • P=principal /beginning amount
  • r=interest rate as a decimal
  • n=number of compoundings a year
  • t=total number of years

a) If compounded annually, n=1

p=$1000, r=5%=0.05 t=10

Amount will be;

A=1000(1+\frac{0.05}{1} )^{10} \\\\\\A=1000(1.05)^{10} \\\\\\A=1000*1.6289=1628.90

Amount=$1628.90

b) If compounded monthly, n=12

p=$1000, r=5%=0.05, t=10, n=12

A=1000(1+\frac{0.05}{12} )^{12*10} \\\\\\A=1000(1.0042)^{120} \\\\\\A=1000*1.647=1647

Amount=$1647.00

c)If interest compounded continuously, it means the principal is earning interest constantly and the interest keeps earning on the interest earned.Here the formula to apply is;

A=Pe^rt where e is the mathematical constant e=2.71828182846

Hence the amount will be;

A=Pe^{rt} \\\\\\A=1000*e^{0.05*10} \\\\\\A=1000*2.71828182846^{0.5} \\\\\\A=1648.72

Amount=$1648.72

8 0
3 years ago
Using the distributive property simplify the expression<br> -2(5y + 6) + 3 - 5y
vivado [14]

Answer:

\Huge \boxed{-15y-9}

Step-by-step explanation:

To solve this problem, first you have to use the distributive property of \displaystyle a(b+c)=ab+ac.

First, expand.

\displaystyle -2(5y+6)

-2*5=-10

\displaystyle -2*6=-12

\displaystyle -10y-12

\displaystyle -10y-12+3-5y

Next, solve.

\displaystyle -10-12+3-5=\boxed{-15y-9}

In conclusion, the correct answer is -15y-9.

5 0
4 years ago
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Anyone know how to do this one?<br> 2x+7y=-1<br> 4x-3y=-19
nlexa [21]
<span>2x+7y=-1  (1)
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multiply equation (1) by 2
4x + 14y = -2 (1')
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---------------------subtract
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answer
(-4, 1)
7 0
4 years ago
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