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4 years ago

Is 15/7 an irrational number

Mathematics

1 answer:

kozerog [31]4 years ago

3 0

Not really because the numbers are odd and also the 15 is larger than 7. it would be better to just simplify it

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A small garden measures 9 ft by 13 ft. A uniform border around the garden increases the total area to 192 ft square. What is the

victus00 [196]

The width of border is 1.5 feet

<h3><u>Solution:</u></h3>

Given that small garden measures 9 ft by 13 ft

A uniform border around the garden increases the total area to 192 ft square

To find: width of border

Let the width of border be "x"

Then the new measures of garden are (9 + 2x) feet and (13 + 2x) feet

The total area of garden = 192 square feet

$(9 + 2x)(13 + 2x) =192$

$117 + 18x + 26x + 4x^2 = 192\\\\4x^2 + 44x - 75 = 0$

<em><u>Let us solve the above equation by quadratic formula</u></em>

$\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Using the above formula,

For $4x^2 + 44x - 75 = 0$ , we have a = 4 ; b = 44 ; c = -75

Substituting the values of a = 4 ; b = 44 ; c = -75 in above quadratic formula we get,

$\begin{aligned}&x=\frac{-44 \pm \sqrt{44^{2}-4(4)(-75)}}{2 \times 4}\\\\&x=\frac{-44 \pm \sqrt{1936-1200}}{8}\\\\&x=\frac{-44 \pm \sqrt{3136}}{8}\\\\&x=\frac{-44 \pm 56}{8}\end{aligned}$

$\begin{aligned}&x=\frac{-44+56}{8} \text { or } x=\frac{-44-56}{8}\\\\&x=\frac{12}{8} \text { or } x=\frac{-100}{8}\\\\&x=1.5 \text { or } x=-12.5\end{aligned}$

Since "x" cannot be negative,

we get x = 1.5

Thus width of border is 1.5 feet

4 0

3 years ago

Where is 50−−√+5√ located on a number line? A. between 7 and 8 B. between 8 and 9 C. between 9 and 10 D. between 10 and 11

mel-nik [20]

Answer:

between 7 and 8

Step-by-step explanation:

7 0

4 years ago

<img src="https://tex.z-dn.net/?f=%20%5Csf%20Evaluate%5Cint%20log%20%5C%3A%20x%20%5C%3A%20dx" id="TexFormula1" title=" \sf Evalu

Greeley [361]

Answer:

x(log(x) - 1) + C

Step-by-step explanation:

The formula for the derivative of a logarithm function is:

$\frac{d}{dx} log_{a}(x) = \frac{1}{xlog(a)}$

For your case, the base is 10. Now that we have the derivative, lets use integration by parts. I will be differentiating log(x) and integrating 1:

u = log(x)

du = dx/xlog(10)

dv = 1

v = x

You get:

log(x)x - integral(dx/log(10))

Therefore the answer is:

log(x)x - x/log(10) + C

x(log(x) - 1) + C

8 0

2 years ago

Read 2 more answers

The price of a holiday was decreased by 12% to £600. What was the price before

lilavasa [31]

Answer:

£672

Step-by-step explanation:

so you add 12 to 100 which is 112

then do 112 divided by 100 and multiplied by 600 on a scientific calculator.

you will get £672 I'm not sure but try it anyways.

3 0

3 years ago

Read 2 more answers

If it takes 100 minutes to complete a circuit, demand at the next work center is 5 parts per minute, and a kanban container hold

Harrizon [31]

5 times 100 = 500
500 divided by 20 = 25
25 containers

4 0

4 years ago