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2 years ago

(2x +0.5y = 3(x + 2y = 8.5

Mathematics

1 answer:

lora16 [44]2 years ago

8 0

Answer:

x=0.5 y=4

Step-by-step explanation:

Let's solve your system by substitution.

2x+0.5y=3;x+2y=8.5

Rewrite equations:

x+2y=8.5;2x+0.5y=3

Step: Solvex+2y=8.5for x:

x+2y=8.5

x+2y+−2y=8.5+−2y(Add -2y to both sides)

x=−2y+8.5

Step: Substitute−2y+8.5forxin2x+0.5y=3:

2x+0.5y=3

2(−2y+8.5)+0.5y=3

−3.5y+17=3(Simplify both sides of the equation)

−3.5y+17+−17=3+−17(Add -17 to both sides)

−3.5y=−14

−3.5y

−3.5

−14

−3.5

(Divide both sides by -3.5)

y=4

Step: Substitute4foryinx=−2y+8.5:

x=−2y+8.5

x=(−2)(4)+8.5

x=0.5(Simplify both sides of the equation)

Answer:

x=0.5 and y=4

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the doctor recommended that Matt increase the number of calories you consume from 2000 to 2800 by what percent did the number of

nikdorinn [45]

Answer:

40% number of calories have increased

Step-by-step explanation:

Old Value ( Calories consume before) = 2000

New Value (increase in Calories consumed) = 2800

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To find percent increase, the formula used is:

$Percent\: increase=\frac{New\:Value-Old\:Value}{Old\:Value}\times 100%$

Putting values in formula and finding percent increase

$Percent\: increase=\frac{New\:Value-Old\:Value}{Old\:Value}\times 100\%\:\\Percent\: increase=\frac{2800-2000}{2000}\times 100\%\: \\Percent\: increase=\frac{800}{2000}\times 100\%\: \\Percent\: increase=0.4\times 100\%\: \\Percent\: increase=40\%$

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2 years ago

Seventeen is three times the difference between four times a number and five

expeople1 [14]

17 = 3(4x - 5)

Distributive property.

17 = 12x - 15

Add 15 to both sides.

32 = 12x

Divide both sides by 12.

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Let me know if you have any questions.

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2 years ago

Prove the following by induction. In each case, n is apositive integer. 2^n ≤ 2^n+1 - 2^n-1 -1.

frutty [35]

<h2>Answer with explanation:</h2>

We are asked to prove by the method of mathematical induction that:

$2^n\leq 2^{n+1}-2^{n-1}-1$

where n is a positive integer.

Let us take n=1

then we have:

$2^1\leq 2^{1+1}-2^{1-1}-1\\\\i.e.\\\\2\leq 2^2-2^{0}-1\\\\i.e.\\2\leq 4-1-1\\\\i.e.\\\\2\leq 4-2\\\\i.e.\\\\2\leq 2$

Hence, the result is true for n=1.

Let us assume that the result is true for n=k

i.e.

$2^k\leq 2^{k+1}-2^{k-1}-1$

Now, we have to prove the result for n=k+1

i.e.

To prove: $2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1$

Let us take n=k+1

Hence, we have:

$2^{k+1}=2^k\cdot 2\\\\i.e.\\\\2^{k+1}\leq 2\cdot (2^{k+1}-2^{k-1}-1)$

( Since, the result was true for n=k )

Hence, we have:

$2^{k+1}\leq 2^{k+1}\cdot 2-2^{k-1}\cdot 2-2\cdot 1\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{k-1+1}-2\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-2$

Also, we know that:

$-2$

(

Since, for n=k+1 being a positive integer we have:

$2^{(k+1)+1}-2^{(k+1)-1}>0$ )

Hence, we have finally,

$2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1$

Hence, the result holds true for n=k+1

Hence, we may infer that the result is true for all n belonging to positive integer.

i.e.

$2^n\leq 2^{n+1}-2^{n-1}-1$ where n is a positive integer.

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3 years ago

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ASHA 777 [7]

What type of diagram?

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3 years ago

I don’t understand what i can do

alexandr402 [8]

Answer:

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Step-by-step explanation:

$3^{-3} +5+9\\$

0.037+5+9

14.037

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2 years ago

(2x +0.5y = 3(x + 2y = 8.5​

(2x +0.5y = 3(x + 2y = 8.5