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Andru [333]
3 years ago
15

Which of the following shows the correct solution steps and solution to 3x+2=17?

Mathematics
2 answers:
Gnom [1K]3 years ago
8 0

Answer:

\huge\boxed{\sf x =  5}

Step-by-step explanation:

\sf 3x + 2= 17

Subtracting 2 to both sides

\sf 3x = 17-2\\3x = 15

Dividing both sides by 3

\sf x = 15/3\\x = 5

diamong [38]3 years ago
3 0

Answer:

x=5

Step-by-step explanation:

Subtract 2 from both sides.

3x + 2 - 2 = 17 - 23x = 15

Next, we need to divide both sides by 3.

\frac{3x}{3}=\frac{15}{3}\\x=5

The answer, as stated above, is x=5

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Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doe
ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for n\geq 78

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: \sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4

For n=1: \sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4

From this point we will assume that n\geq 2

As we can see, \sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4 and (4n)^4=256n^4. Then,

\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4

Now, we will use the formula for the sum of the first 4th powers:

\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}

Therefore:

\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0

and, because n \geq 0,

465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1

Observe that, because n \geq 2 and is an integer,

n^2(465n-6n^2-10)\geq -1 \iff 465n-6n^2-10 \geq 0 \iff n(465-6n) \geq 10\\\iff 465-6n \geq 0 \iff n \leq \frac{465}{6}=\frac{155}{2}=77.5

In concusion, the statement is true if and only if n is a non negative integer such that n\leq 77

So, 78 is the smallest value of n that does not satisfy the inequality.

Note: If you compute  (4n)^4- \sum^{n}_{i=0} (2i)^4 for 77 and 78 you will obtain:

(4n)^4- \sum^{n}_{i=0} (2i)^4=53810064

(4n)^4- \sum^{n}_{i=0} (2i)^4=-61754992

7 0
3 years ago
If you help me I’ll mark brainliest
Dafna11 [192]

Answer:

1= 2x+74

or,

or,

or

now,

1+3= being straight angle

5 0
3 years ago
3) You owe $1,842.66 on a credit card at a 14.5% APR. You pay $250.00 at the beginning of the month and put another $250.00 in a
Wittaler [7]

3. Credit Card: (1842.66 - 250) (.145/12) = $19.24

Savings: 250(0.04/12) = $0.83  

Difference = 19.24 - 0.83 = $18.41  

4. Credit Card: (1842.66 - 500) (.145/12) = $16.22

You will save $18.41 - $16.22 = $2.19 by putting all $500 toward the higher credit card rate.  

8 0
3 years ago
Read 2 more answers
I did something wrong could you help?
posledela

Answer:

Slope = 1/2

y-intercept = 30

Equation : y = 1/2x + 30

D. 150 miles

Step-by-step explanation:

We can use the two visible points you marked on the graph.

They are (0,30) which is also the y-intercept and (20,40).

Calculate change of y over change of x.

10/20 or 1/2

So the slope is 1/2 and the y-intercept is 30.

Therefore, using y = mx + b form, the equation is y = 1/2x + 30

Then, to find how many miles you drove if the cost was $105, we can plug in 105 for y in the equation.

105 = 1/2x + 30

75 = 1/2x

x = 150

8 0
3 years ago
Find the indicated angle measures. Then justify the answer. ​
ExtremeBDS [4]
Pretty sure it’s 65 since its alternate interior angles which equal 180
8 0
2 years ago
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