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zlopas [31]
2 years ago
9

What is n -8+4(1+5n)=-6n-14

Mathematics
1 answer:
jeka942 years ago
4 0

Answer:

n = (-5)/13

Step-by-step explanation:

Solve for n:

4 (5 n + 1) - 8 = -6 n - 14

4 (5 n + 1) = 20 n + 4:

20 n + 4 - 8 = -6 n - 14

Add like terms. 4 - 8 = -4:

20 n - 4 = -6 n - 14

Add 6 n to both sides:

20 n + 6 n - 4 = (6 n - 6 n) - 14

6 n - 6 n = 0:

20 n + 6 n - 4 = -14

20 n + 6 n = 26 n:

26 n - 4 = -14

Add 4 to both sides:

26 n + (4 - 4) = 4 - 14

4 - 4 = 0:

26 n = 4 - 14

4 - 14 = -10:

26 n = -10

Divide both sides of 26 n = -10 by 26:

(26 n)/26 = (-10)/26

26/26 = 1:

n = (-10)/26

The gcd of -10 and 26 is 2, so (-10)/26 = (2 (-5))/(2×13) = 2/2×(-5)/13 = (-5)/13:

Answer: n = (-5)/13

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2 years ago
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Y=2x+1<br> y=4x-1<br> SHOW YOUR WORK PLEASE
Tanya [424]

Let's solve your system by substitution.

y=2x+1;y=4x−1

Step: Solve y=2x+1for y:

y=2x+1

Step: Substitute2x+1foryiny=4x−1:

y=4x−1

2x+1=4x−1

2x+1+−4x=4x−1+−4x(Add -4x to both sides)

−2x+1=−1

−2x+1+−1=−1+−1(Add -1 to both sides)

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−2x

−2

=

−2

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(Divide both sides by -2)

x=1

Step: Substitute1forxiny=2x+1:

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y=(2)(1)+1

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3 0
2 years ago
Mrs. Gilbert is interested in determining how many students spend 4 or more hours doing homework each week. She asks every stude
docker41 [41]

Answer:

C. Biased, because she only asked students on honor roll.

Step-by-step explanation:

Since Mrs. Gilbert's goal was to find how many students that spent >4 hours and not how many students that earned Honor Roll that spent >4 hours, the data is biased. Choose C.

4 0
2 years ago
Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈ R if and only if ad = bc. Ar
Veseljchak [2.6K]

Answer:

The given relation R is equivalence relation.

Step-by-step explanation:

Given that:

((a, b), (c, d))\in R

Where R is the relation on the set of ordered pairs of positive integers.

To prove, a relation R to be equivalence relation we need to prove that the relation is reflexive, symmetric and transitive.

1. First of all, let us check reflexive property:

Reflexive property means:

\forall a \in A \Rightarrow (a,a) \in R

Here we need to prove:

\forall (a, b) \in A \Rightarrow ((a,b), (a,b)) \in R

As per the given relation:

((a,b), (a,b) ) \Rightarrow ab =ab which is true.

\therefore R is reflexive.

2. Now, let us check symmetric property:

Symmetric property means:

\forall \{a,b\} \in A\ if\ (a,b) \in R \Rightarrow (b,a) \in R

Here we need to prove:

\forall {(a, b),(c,d)} \in A \ if\ ((a,b),(c,d)) \in R \Rightarrow ((c,d),(a,b)) \in R

As per the given relation:

((a,b),(c,d)) \in R means ad = bc

((c,d),(a,b)) \in R means cb = da\ or\ ad =bc

Hence true.

\therefore R is symmetric.

3. R to be transitive, we need to prove:

if ((a,b),(c,d)),((c,d),(e,f)) \in R \Rightarrow ((a,b),(e,f)) \in R

((a,b),(c,d)) \in R means ad = cb.... (1)

((c,d), (e,f)) \in R means fc = ed ...... (2)

To prove:

To be ((a,b), (e,f)) \in R we need to prove: fa = be

Multiply (1) with (2):

adcf = bcde\\\Rightarrow fa = be

So, R is transitive as well.

Hence proved that R is an equivalence relation.

8 0
3 years ago
What is the value of b(10) when b(x)=|3-x|+1 ?
vredina [299]
B(x) = |3-x|+1

b(10) means that we need to replace x by 10:
b(10) = |3-10|+1
As you can notice, 3-10 is between the lines of the absolute power. So if the answer is positive, you keep positive. If the answer is negative, you transform it to positive. |a| = a and |-a| = a. So |a|=|-a|.
So |3-10| = |-7| = |7| = 7.

b(10) = |3-10|+1 = 7 + 1 = 8.

So the value of b(10) when b(x)=|3-x|+1 is 8.

Hope this Helps! :)
7 0
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