Rewrite in simplest terms: (3x+7)-(-4x+7)

What is the boundary line for the linear inequality 4x + 2y < 18?

Cloud [144]

Answer:

Simplifying

x = 4.5 + -0.5y

Step-by-step explanation:

4 0

3 years ago

If GE=42 and DH=16, find GF

Sergeu [11.5K]

DGFH is a rhombus where E is the midpoint of the lines GE and GF
please look at the image

7 0

3 years ago

Margo spends 0.25 of her paycheck on a new dress, 1/8 of her paycheck on shoes, and $24 on a birthday present. If she spent $60

crimeas [40]

First, lets set up the equation.
0.25x + (1/8)x + 24 = 60
The variable x will be equal to the total amount of the paycheck. We used 0.25 of the paycheck on the first item bought, 1/8 on the second item bought, and then 24 more dollars. After assembling the equation, we merely need to solve for x to find the value of the paycheck. I'll be converting 1/8 to 0.125 at this point for simplisity's sake.

Subtract 24 from both sides.
0.25x + 0.125x = 36
Combine like terms on the left side.
0.375x = 36
Divide both sides by 0.375.
x = 96
The total is A, 96 dollars.

4 0

3 years ago

Calculus= Integrate 5^x dx please break down how answer is 1/6x^6+C

aleksley [76]

Answer:

$\int\limits {5^x} \, dx = \frac{5^x}{ln\ x} + c$

Step-by-step explanation:

Note that the integral of $5^x$ is not $\frac{1}{6}x^6 + c$

The solution is as follows:

Given

$5^x$

Required

Integrate

Represent the given expression using integral notation

$\int\limits {5^x} \, dx$

This question can't be solved directly;

We'll make use of exponential rules which states;

$\int\limits {a^x} \, dx = \frac{a^x}{ln\ x} + c$

By comparing $\int\limits {5^x} \, dx$ with $\int\limits {a^x} \, dx$ ;

we can substitute 5 for a;

Hence, the expression $\int\limits {a^x} \, dx = \frac{a^x}{ln\ x} + c$ becomes

$\int\limits {5^x} \, dx = \frac{5^x}{ln\ x} + c$

-------------------------------------------------------------------------------------

However, the integral of $x^5$ is $\frac{1}{6}x^6 + c$

This is shown below:

Given that $x^5$

Applying power rule;

Power rule states that

$\int\limits{x^n}\ dx = \frac{x^{n+1}}{n+1} + c$

In this case ( $x^5$ ), n = 5;

So, $\int\limits{x^n}\ dx= \frac{x^{n+1}}{n+1} + c$

becomes

$\int\limits{x^5}\ dx = \frac{x^{5+1}}{5+1} + c$

$\int\limits{x^5}\ dx = \frac{x^{6}}{6} + c$

$\int\limits{x^5}\ dx= \frac{x^{6}}{6} + c$

4 0

3 years ago

HELP ASAP!! GIVING 20 POINTS AND BRAINLIEST!!! Solve for x. y=7x-7z-9

svetlana [45]

We just need to see everything that is not x as a number.

if I asked
$5 = 7x - 7(2) - 9$
we would solve it by combining like terms first. but, if I tell you not to do that, we would add 9 and 7(2) to both side and end up with
$5 + 7(2) + 9 = 7x$
we would then divide both sides by 7
$\frac{5 + 7(2) + 9}{7} = x$

math is always math... it's just how we look at it. so, do the same steps!
$y = 7x - 7z - 9$
add 9 and 7z to both side
$y + 7z + 9 = 7x$
divide both sides by 7
$\frac{y + 7z + 9}{7} = x$

8 0

3 years ago