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2 years ago

Three is subtracted from a number, and then the difference is divided by eleven. The result is twelve. What is the

Mathematics

1 answer:

Nostrana [21]2 years ago

8 0

Answer:

The number is 135.

Step-by-step explanation:

1) Form an equation

Three is subtracted from a number

⇒ $x-3$ (where x is "the number")

The difference is divided by 11

⇒ $\displaystyle \frac{x-3}{11}$

The result is 12

⇒ $\displaystyle \frac{x-3}{11}=12$

2) Solve the equation

$\displaystyle \frac{x-3}{11}=12$

Multiply both sides by 11

$\displaystyle \frac{x-3}{11}*11=12*11\\\\x-3=132$

Add 3 to both sides

$x-3+3=132+3\\x=135$

Therefore, the number is 135.

I hope this helps!

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creativ13 [48]

Answer:

f(x)=x(x-5)(x+2)

Step-by-step explanation:

Since the steps of the factorization of the polynomial f(x) is not given, I will proceed to give the correct factorization of f(x).

f(x)=x³-3x²-10x

First, we factor out x since it is a common term.

f(x)=x(x²-3x-10)

Next, we factorize the quadratic expression x²-3x-10.

f(x)=x(x²-5x+2x-10)

f(x)=x(x(x-5)+2(x-5))

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The correct factorization of the polynomial f(x)=x³-3x²-10x is: f(x)=x(x-5)(x+2)

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3 years ago

-(1+7x)-6(-7-x)=36 what is x equal to

Katyanochek1 [597]

Answer:

x = 5

Step-by-step explanation:

Step 1: Write equation

-(1 + 7x) - 6(-7 - x) = 36

Step 2: Solve for x

Distribute: -1 - 7x + 42 + 6x = 36
Combine like terms: -x + 41 = 36
Subtract 41 on both sides: -x = -5
Divide both sides: x = 5

Step 3: Check

Plug in x to verify it's a solution.

-(1 + 7(5)) - 6(-7 - 5) = 36

-(1 + 35) - 6(-12) = 36

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-36 + 72 = 36

36 = 36

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3 years ago

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jenyasd209 [6]

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3 years ago

Tim mixed 2 parts vinegar and 5 parts water to make a cleaning liquid. How many parts of vinegar did Tim mix with each part of w

Leviafan [203]

5 parts of water plus 2 parts of vinegar.

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3 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.

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3 years ago