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3 years ago

The sum of two numbers I'd 16. Three times the larger number decreased by the smaller is 72. Find the number

Mathematics

1 answer:

maksim [4K]3 years ago

4 0

Answer:

22, -6

Step-by-step explanation:

Create a system of equations.

x= the larger number

y=the smaller number

Using what you know, create the equations:

x+y=16

3x-y=72

Now add the two equations together. (elimination method)

x+y=16

+ 3x-y=72 (the y's cancel out)

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

4x = 88 Divide.

x = 22

Now plug in x=22 into one of your equations to solve for y.

x+y=16

22+y=16

y=-6

The numbers are 22 and -6.

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Find the quotient: (x2−5x+8)÷(x+2)

Aneli [31]

Answer:

Quotient = x - 7

Step-by-step explanation:

We are dividing x^2 - 5x +8 by x + 2

x + 2√x^2 - 5x + 8

Starting with dividing by x

x - 7

x + 2√ x^2 - 5x + 8

Multiplying x by x + 2

x + 2√ x^2 - 5x + 8

x^2 + 2x

= -7x + 8

Step ii, pick -7 for division

-7x + 8

-7x - 14

= +8 -(-14)

= 8+14

= 22

The answer is

( x - 7) remainder 22

(x - 7) is the quointent

22 is the remainder

3 0

3 years ago

Use series to verify that<br><br> <img src="https://tex.z-dn.net/?f=y%3De%5E%7Bx%7D" id="TexFormula1" title="y=e^{x}" alt="y=e^{

SVETLANKA909090 [29]

$y = e^x\\\\\displaystyle y = \sum_{k=1}^{\infty}\frac{x^k}{k!}\\\\\displaystyle y= 1+x+\frac{x^2}{2!} + \frac{x^3}{3!}+\ldots\\\\\displaystyle y' = \frac{d}{dx}\left( 1+x+\frac{x^2}{2!} + \frac{x^3}{3!}+\frac{x^4}{4!}+\ldots\right)\\\\$

$\displaystyle y' = \frac{d}{dx}\left(1\right)+\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(\frac{x^2}{2!}\right) + \frac{d}{dx}\left(\frac{x^3}{3!}\right) + \frac{d}{dx}\left(\frac{x^4}{4!}\right)+\ldots\\\\\displaystyle y' = 0+1+\frac{2x^1}{2*1} + \frac{3x^2}{3*2!} + \frac{4x^3}{4*3!}+\ldots\\\\\displaystyle y' = 1 + x + \frac{x^2}{2!}+ \frac{x^3}{3!}+\ldots\\\\\displaystyle y' = \sum_{k=1}^{\infty}\frac{x^k}{k!}\\\\\displaystyle y' = e^{x}\\\\$

This shows that $y' = y$ is true when $y = e^x$

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

Note 1: A more general solution is $y = Ce^x$ for some constant C.
Note 2: It might be tempting to say the general solution is $y = e^x+C$ , but that is not the case because $y = e^x+C \to y' = e^x+0 = e^x$ and we can see that $y' = y$ would only be true for C = 0, so that is why $y = e^x+C$ does not work.

6 0

3 years ago

Surveyors wished to know the distance across a lake between A and B. They measured the distance from B to C as 100 m and the ang

kherson [118]

Answer:

Step-by-step explanation:

Check the attachment for the diagram.

You can see from the diagram that it is a right angled triangle with opposite side AB and adjacent side BC. Using SOH, CAH, TOA trig identity to get the length of AB. According to TOA;

tan 35° = opposite/adjacent

tan 35° = AB/BC

tan 35° = AB/100

AB = 100tan35°

AB = 100 * 0.7002

AB = 70.02m

Hence the distance across a lake between A and B is approximately 70m

5 0

3 years ago

Find the value of Angle X

jarptica [38.1K]

<u>The angle based on the diameter is always right</u>

Then <ABC=90 and ∠BAC=∠ACB=45° ; and ∠BCD=180-45=135 then x=(180-135):2=22,5°

3 0

3 years ago

According to the same report, the 28.5 million passengers in 2018 represented a 6.7% increase in cruise passengers since 2017. h

Alisiya [41]

The number of cruise passengers must there have been in 2017 is 26.7 million.

<h3>What is percentage?</h3>

The term "percentage" comes from the Latin phrase "per centum," meaning "by the hundred." Percentages represent fractions with a denominator of 100. In other terms, it is the relationship between portion and whole in which the value of the whole is always assumed to be 100.

Now according to the question;

Let x represent the total number for cruise passengers during 2017.

In 2018, a 6.7% rise in x results in 28.5 million cruise passengers.

So, 106.7 % of x = 28.5

$\begin{aligned}&\frac{106.7}{100} * x=28.5 \\&\frac{106.7 x}{100}=28.5\end{aligned}$