All categories

2 years ago

Plz help............

Mathematics

1 answer:

yuradex [85]2 years ago

3 0

Hi there!

$\large\boxed{x < 2}$

$\frac{4x + 6}{7} < 2$

Begin by multiplying both sides by 7:

$4x + 6 < 2 * 7 \\\\4x + 6 < 14$

Subtract 6 from both sides to isolate for x:

$4x + 6 - 6 < 14 - 6\\\\4x < 8$

Divide both sides by 4 to solve for x:

$4x/4 < 8/4\\\\x < 2$

You might be interested in

How do the arrows for +1 and -1 show both distance and direction?

Fofino [41]

By the way the arrow is pointing?

3 0

3 years ago

find two positive real numbers such that they sum to 108 and the product of the first times the square of the second is a maximu

topjm [15]

The two positive numbers are 36 and 72 which gives a sum equal to 108 and the product of 36 and the square of 72 is a maximum.

Any integer greater than zero is considered a positive number. A positive number can either be written as a number or with the "+" symbol in front of it.

Let us consider the two positive real numbers as x and y. Then, their sum is written as,

x+y=108

Then, y=108-x

And the product is written as,

P=xy²

Substitute value of y in the above equation, we get,

$\begin{aligned}P&=x(108-x)^2\\&=x(11664-216x+x^2)\\&=11664x-216x^2+x^3\\&=x^3-216x^2+11664x\end{aligned}$

Now, differentiate P with respect to x, and we get,

$\begin{aligned}\frac{dP}{dx}&=3x^2-432x+11664\\&=x^2-144x+3888\end{aligned}$

Solving the above equation to zero, we get,

$\begin{aligned}x^2-144x+3888&=0\\x^2-36x-108x+3888&=0\\x(x-36)-108(x-36)&=0\\(x-108)(x-36)&=0\\x&=\text{108 or 36}\end{aligned}$

Substitute values of x in y=108-x, to get values of y.

If we substitute x=108, we get the y value as zero which doesn't give the required solution.

But, if we substitute x=36, we get,

$\begin{aligned}y&=108-36\\y&=72\end{aligned}$

Thus, the two positive numbers are 36 and 72.

To know more about positive numbers:

brainly.com/question/1635103

#SPJ4

4 0

1 year ago

7 times as much as the sum of 1/3 and 4/5

Jet001 [13]

First of all, you add 1/3 and 4/5, so you get:
$\frac{1}{3} + \frac{4}{5}$

To add 2 fractions, they need to have the same denominator. Since 3 and 5 don't have a common factor, so you multiply 1/3 by 5, and 4/5 by 3, so you get:
$\frac{1*5}{3*5} + \frac{4*3}{5*3}$
$\frac{5}{15} + \frac{12}{15}$

Now, the two fractions got the same denominator, and you can add them by adding the numerators over the same denominator. (You don't add denominators in addition) so you get:
$\frac{5+12}{15}$
$\frac{17}{15}$

That's the sum of 1/3 + 4/5.

Now, they want the sum of the 2 fractions 7 times. So you multiply 17/15 by 7. And as you know, 7 = 7/1. So you get:
$\frac{17}{15} * \frac{7}{1}$

In multiplication no need to have the same denominator. You multiply nominators by nominators and denominators by denominators. So you get:
$\frac{17*7}{15*1}$
$\frac{119}{15}$

Since 119 and 15 don't have a common factor, so they can't be simplified.
So, the answer is 119/15.

Hope this Helps! :D

7 0

3 years ago

Read 2 more answers

Amount of sugar in a sugar bowl is 0.75 cups

Mariana [72]

I equals 70 grams cup because

4 0

3 years ago

which numbers are irrational? check all that apply. square root of 196, square root of 80, square root of 16, pi, square root of

Vilka [71]

Answer: $\sqrt{80}$ , $\pi$ , $\sqrt{12}$