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3 years ago

Solve the equation 7/z-1 = 9/z+4

Mathematics

1 answer:

algol [13]3 years ago

3 0

Answer:

z is equal to 18.5

Step-by-step explanation:

When an equation is in the format a/b = c/d, the quickest way to simplify it is to cross multiply. Each side is multiplied by the other sides denominator, eliminating the division:

$\frac{7}{z-1} = \frac{9}{z + 4}\\7(z + 4) = 9(z - 1)\\7z + 28 = 9z - 9\\7z - 9z = -9 - 28\\-2z = -37\\z = 37/2\\z = 18.5$

So z is equal to 18.5

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A custodian plans to repaint some classrooms. He has 5 = gallons of paint. All of

dlinn [17]

Answer: 2 bookcases.

Step-by-step explanation:

Let be "x" the number of bookcases that the custodian will be able to repaint completly with 5 gallons of paint.

According to the data given, the custodian needs 2 gallons of paint to repaint one bookcase. Since all the bookcases are equal, you can set up the following proportion:

$\frac{2}{1}=\frac{5}{x}$

Now you must solve for "x" in order to find its value:

$(x)(\frac{2}{1})=5\\\\2x=5\\\\x=\frac{5}{2}\\\\x=2.5$

Notice that the custodian will be able to repaint 2 bookcases completely, then you can say that:

$x\approx2$

5 0

4 years ago

1. The flowers are supposed to get 1.5 cups of water per plant. You have a 3-quart water pail. How many flowers can you water be

kramer

Answer: 8

Step-by-step explanation:

4 0

3 years ago

Which is better having a stock that goes up by 30% on Monday than drops 30% on Tuesday

AURORKA [14]

Answer:

<u>Both stocks will have a net loss of 9%</u>

Complete statement and question:

Which is better: having a stock that goes up 30% on Monday than drops 30% on Tuesday, or a stock drops 30% on Monday and goes up 30% on Tuesday? In each case, what is the net percent gain or loss?

Source:

Previous question that can be found at brainly

Step-by-step explanation:

Four our analysis, let's assume a initial price of $ 10 for both stocks

Stock A

Price on Monday when stock market opens = $ 10

Price on Monday when stock market closes = 10 + 0.3 * 10 = 10 + 3 = $ 13

Price on Tuesday when stock market opens = $ 13

Price on Tuesday when stock market closes = 13 - 0.3 * 13 = 13 -3.9 = $ 9.10

<u>The stock had a net loss of $ 0.90 or 9%</u>

Stock B

Price on Monday when stock market opens = $ 10

Price on Monday when stock market closes = 10 - 0.3 * 10 = 10 - 3 = $ 7

Price on Tuesday when stock market opens = $ 7

Price on Tuesday when stock market closes = 7 + 0.3 * 7 = 7 + 2.10 = $ 9.10

<u>The stock had a net loss of $ 0.90 or 9%</u>

4 0

3 years ago

Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) x4 18x2 4 x5

loris [4]

Your integrand is missing some symbols. My best interpretation is the following integral:

$I=\displaystyle\int\frac{x^4+18x^2+4}{x^5+30x^3+20x}\,\mathrm dx$

Decompose into partial fractions; we're looking for an expansion of the form

$\dfrac{x^4+18x^2+4}{x^5+30x^3+20x}=\dfrac ax+\dfrac{bx^3+cx^2+dx+e}{x^4+30x^2+20}$

Now:

$x^4+18x^2+4=a(x^4+30x^2+20)+(bx^3+cx^2+dx+e)x$

$=(a+b)x^4+cx^3+(30a+d)x^2+ex+20a$

Matching up coefficients tells us that

$\begin{cases}a+b=1\\c=0\\30a+d=18\\e=0\\20a=4\end{cases}\implies a=\dfrac15,b=\dfrac45,d=12$

so that

$I=\displaystyle\frac15\int\frac{\mathrm dx}x+\frac45\int\frac{x^3+15x}{x^4+30x^2+20}\,\mathrm dx$

The integral is trivial:

$\displaystyle\frac15\int\frac{\mathrm dx}x=\frac15\ln|x|+C$

For the second integral, notice that

$\mathrm d(x^4+30x^2+20)=(4x^3+60x)\,\mathrm dx$

Distribute the 4 over the numerator, then substitute $u=x^4+30x^2+20$ and $\mathrm du=(4x^3+60x)\,\mathrm dx$ :

$\displaystyle\frac15\int\frac{4x^3+60x}{x^4+30x^2+20}\,\mathrm dx=\frac15\int\frac{\mathrm du}u=\frac15\ln|u|+C=\frac15\ln(x^4+30x^2+20)+C$

So we have

$I=\dfrac15\ln|x|+\dfrac15\ln(x^4+30x^2+20)+C$

and with some simplification,

$I=\boxed{\ln\sqrt[5]{|x^5+30x^3+20x|}+C}$

4 0

3 years ago

Is 23 a prime number

Gekata [30.6K]

Answer:

Step-by-step explanation:

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not prime is called a composite number.

3 0

3 years ago