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andrezito [222]
3 years ago
7

For what value of x do the expressions 2/3x + 2 and 4/3x -6 have the same value

Mathematics
1 answer:
Masteriza [31]3 years ago
5 0
<h2>The value of x = - \dfrac{10}{3}</h2>

Step-by-step explanation:

The given expressiona are:

\dfrac{2}{3x+2} and \dfrac{4}{3x-6}

To find, the value of x = ?

∴  \dfrac{2}{3x+2}=\dfrac{4}{3x-6}

By crossmultiplication, we get

4(3x + 2) = 2(3x - 6)

⇒ 12x + 8 = 6x - 12

⇒ 12x - 6x =  - 12 - 8

⇒ 6x = - 20

⇒ 3x = - 10

⇒ x = - \dfrac{10}{3}

∴ The value of x = - \dfrac{10}{3}

Thus, the value of x is equal to - \dfrac{10}{3}.

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The difference of two numbers is 42. the larger number is three less than six times the smaller number. find the numbers.
IgorLugansk [536]
X and y are the numbers
x>y

diffference is 42
x-y=42

larger is 3 less than 6 times smaller
x=-3+6y

subsitute -3+6y for x

x-y=42
-3+6y-y=42
-3+5y=42
add3 to both sides
5y=45
divide both sides by 5
y=9

sub back

x=-3+6y
x=-3+6(9)
x=-3+54
x=51

the numbers are 51 and 9
5 0
3 years ago
Which of the following shows the factors of 5x2 + 17x + 6? A. (5x + 1)(x + 6) B. (5x + 2)(x + 3) C. (5x + 3)(x + 2) D. (5x + 6)(
zysi [14]

Answer:

B. (x+3)(5x+2)

Step-by-step explanation:

The given quadratic trinomial is;

5x^2+17x+6

Comparing this to ax^2+bx+c, we have a=5,b=17,c=6.

ac=5\times6=30

Two factors of 30 that add up to 17 is 15  and 2.

We split the middle term to obtain;

5x^2+15x+2x+6

We factor by grouping;

5x(x+3)+2(x+3)

Factor further

(x+3)(5x+2)

The correct answer is B.

5 0
3 years ago
Read 2 more answers
How do i solve this?
vazorg [7]
Usually I would use my head, but you can use whatever you want.
3 0
2 years ago
Consider the given function and the given interval. f\(x\) = (x - 7)**2 text(, ) [5 text(, ) 11] (a) Find the average value fave
Jet001 [13]

a. f has an average value on [5, 11] of

f_{\rm ave}=\displaystyle\frac1{11-5}\int_5^{11}(x-7)^2\,\mathrm dx=\frac{(x-7)^3}{18}\bigg|_5^{11}=\frac{4^3-(-2)^3}{18}=4

b. The mean value theorem guarantees the existence of c\in(5,11) such that f(c)=f_{\rm ave}. This happens for

(c-7)^2=4\implies c-7=\pm2\implies c=9\text{ or }c=5

8 0
3 years ago
Select all that apply. Which of the following are proportions? 25/10=5/2,3/4=8/10,2/8=3/12,3/4=15/20
8_murik_8 [283]

Answer:

\frac{25}{10} = \frac{5}{2} is in proportion.

\frac{3}{4} = \frac{8}{10} is not in proportion.

\frac{2}{8} = \frac{3}{12} is in proportion.

\frac{3}{4} = \frac{15}{20} is in proportion.

Step-by-step explanation:

The first example is \frac{25}{10} = \frac{5}{2} and it is in proportion.

This is because, you will get the same simplest fraction (\frac{5}{2}) from the fraction \frac{25}{10} by dividing its numerator and denominator by 5.

The second example is \frac{3}{4} = \frac{8}{10} and it is not in proportion.

This is because, you can not  get the simplest fraction (\frac{3}{4}) from the fraction \frac{8}{10} after simplification.

The third example is \frac{2}{8} = \frac{3}{12} and it is in proportion.

This is because, you will get the same simplest fraction (\frac{1}{4}) from the fraction \frac{2}{8} by dividing its numerator and denominator by 2 and from the fraction \frac{3}{12} by dividing its numerator and denominator by 3.

The fourth example is \frac{3}{4} = \frac{15}{20} and it is in proportion.

This is because, you will get the same simplest fraction (\frac{3}{4}) from the fraction \frac{15}{20} by dividing its numerator and denominator by 5. (Answer)

3 0
2 years ago
Read 2 more answers
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