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cluponka [151]
3 years ago
9

One positive number is three more than twice another. If their product is 629, find the numbers.

Mathematics
1 answer:
sineoko [7]3 years ago
5 0

Answer:

x = 17 and y = 37

Step-by-step explanation:

Let the numbers be x and y.

y = 3 + 2x

xy = 629

substituting y in the second equation we get

x(3+2x) = 629

3x + 2x^{2} = 629

2x^{2} + 3x - 629 = 0

Solving a quadratic equation by using its formula:

x = [-3 ±√(9-4(2)(-629)] / 4

x = [-3 ± √5041] / 4

x = [-3 ± 71] / 4

x = 17 and \frac{-37}{2}

Ignore the negative number in x and just use x = 17 in the first equation we get

y = 3 + 2(17) = 37

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. For each of these intervals, list all its elements or explain why it is empty. a) [a, a] b) [a, a) c) (a, a] d) (a, a) e) (a,
Eva8 [605]

Answer:

Elements are of the form

 (i) [a,a]=\{[x,y] : a\leq x\leq a, a\leq y\leq a; a\in \mathbb R\}

(ii) [a,b)=\{[x,y) :a\leq x

(iii)(a,a]=\{(x,y] :a

(iv)(a,a)=\{(x,y): a

(v) (a,b) where a>b=\{(x,y) : a>x>b,a>y>b;a>b,a,b \in \mathbb R\}

(vi) [a,b] where a>b=\{[x,y] : a\geq x\geq b,a\geq y\geq b;a>b,a,b \in \mathbb R\}

Step-by-step explanation:

Given intervals are,

(i) [a,a] (ii) [a,a) (iii) (a,a] (iv) (a,a) (v) (a,b) where a>b (vi)  [a,b] where a>b.

To show all its elements,

(i) [a,a]

Imply the set including aa from left as well as right side.

Its elements are of the form.

\{[a,a] : a\in \mathbb R\}=\{[0,0],[1, 1],[-1,-1],[2,2],[-2,-2],[3,3],[-3,-3],........\}

Since there is a singleton element a of real numbers, this set is empty.

Because there is no increment so if a\in \mathbb R then the set  [a,a] represents singleton sets, and singleton sets are empty so is [a,a].

(ii) [a,a)

This means given interval containing a by left and exclude a by right.

Its elements are of the form.

[ 1, 1),[-1,-1),[2,2),[-2,-2),[3,3),[-3,-3),........

Since there is a singleton element a of real numbers withis the set, this set is empty.

Because there is no increment so if a\in \mathbb R then the set  [a,a) represents singleton sets, and singleton sets are empty so is [a.a).

(iii) (a,a]

It means the interval not taking a by left and include a by right.

Its elements are of the form.

( 1, 1],(-1,-1],(2,2],(-2,-2],(3,3],(-3,-3],........

Since there is a singleton element a of real numbers, this set is empty.

Because there is no increment so if a\in \mathbb R then the set  (a,a] represents singleton sets, and singleton sets are empty so is (a,a].

(iv) (a,a)

Means given set excluding a by left as well as right.

Since there is a singleton element a of real numbers, this set is empty.

Its elements are of the form.

( 1, 1),(-1,-1],(2,2],(-2,-2],(3,3],(-3,-3],........

Because there is no increment so if a\in \mathbb R then the set  (a,a) represents singleton sets, and singleton sets are empty, so is (a,a).

(v) (a,b) where a>b.

Which indicate the interval containing a, b such that increment of x is always greater than increment of y which not take x and y by any side of the interval.

That is the graph is bounded by value of a and it contains elements like it we fixed a=5 then,

(a,b)=\{(5,0),(5,1),(5,2).....\} e.t.c

So this set is connected and we know singletons are connected in \mathbb R. Hence given set is empty.

(vi) [a,b] where a\leq b.

Which indicate the interval containing a, b such that increment of x is always greater than increment of y which include both x and y.

That is the graph is bounded by value of a and it contains elements like it we fixed a=5 then,

[a,b]=\{[5,0],[5,1],[5,2].....\} e.t.c

So this set is connected and we know singletons are connected in \mathbb R. Hence given set is empty.

8 0
3 years ago
Negative solution for Multi-step equations
nydimaria [60]

Answer:

\frac{1}{2}(4x+6)+3x=7x+9

\frac{1}{2}(4x+8)+3x=7x+9

Step-by-step explanation:

By putting the numbers in the given equation,

\frac{1}{2}(4x+6)+3x=7x+9

2x + 3 + 3x = 7x + 9

5x + 3 = 7x + 9

(5x + 3) - 7x = (7x + 9) - 7x

(5x - 7x) + 3 = 9

-2x + 3 = 9

(-2x + 3) - 3 = 9 - 3

-2x = 6

-\frac{2x}{2}=\frac{6}{2}

-x = 3

x = -3

Therefore, our equation is correct which has a negative result.

In place of 6 if we use 8, value of x will be negative again.

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3 years ago
a cylindrical oil drum has a diameter of 2 feet and a height of 3 feet what is the volume of the oil drum​
Nesterboy [21]

Answer:

9.42 Ft³

Step-by-step explanation:

I did the work.

6 0
2 years ago
Evaluate 4x3 + 2 for x = -1
Darina [25.2K]
4 {x}^{3} + 2

Plug in -1 for x

and you'll get this:
4 {( - 1)}^{3} + 2

Solve it further and you'll get:
4( - 1) + 2 \\ = - 4 + 2 \\ = - 2

Therefore,
4 {x}^{3} + 2
where x = -1
8 0
3 years ago
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liq [111]

Answer:

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Step-by-step explanation:

I was just trying to help but ok..... :)

4 0
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