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3 years ago

Can you show the working out as well please?

Mathematics

2 answers:

Airida [17]3 years ago

6 0

Answer:

BC = 60

Step-by-step explanation:

3X + X = 80 <---- X = BC

3X + X = 4X

4X = 80 <---- DIVIDE BOTH SIDES BY 4

4X ÷ 4 = X

80 ÷ 4 = 20

20 × 3 = 60

irinina [24]3 years ago

4 0

Answer:

AB = 20 m

BC = 60 m

Step-by-step explanation:

Let AB be x

So BC becomes 3x

AC is 80 metres

So,

x+3x = 80

4x = 80

Dividing both sides by 4

x = 20

So,

AB = 20 metres

While

BC = 3(20) = 60 metres

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Which of the following functions is not linear?

Marrrta [24]

Answer:

Step-by-step explanation:

The equation of a linear function is in form:

$y=mx+b$

We have:

$\bold{A.}\\\\y=8(x+8)+4(x+8)\qquad\text{use the distributive property}\\\\y=8x+64+4x+32\qquad\text{combine like terms}\\\\y=12x+86\to m=12,\ b=86\\\\\bold{linear\ function}$

$\bold{B.}\\\\y=\dfrac{\sqrt8}{8}x-4\to m=\dfrac{\sqrt8}{8},\ b=-4\\\\\bold{linear\ function}$

$\bold{C.}\\\\y=\dfrac{1}{8}x+8\to m=\dfrac{1}{8},\ b=8\\\\\bold{linear\ function}$

$\bold{D.}\\\\y=8x^2+8x+4\\\\\bold{not\ linear\ function}\\\\\text{because is}\ x^2\\\\\text{It's a quadratic function}$

3 0

3 years ago

Which number is farther from 0 on a number line -9 or 6

Dafna11 [192]

-9 is farther from 0 on the number line.

3 0

3 years ago

There are 9 red marbles and 5 blue marbles in a bag. What is the ratio of blue marbles to all marbles

LenKa [72]

Answer:

9:5

Step-by-step explanation:

I think it's 9:5 sorry if I'm wrong.

4 0

2 years ago

(6x10^2)/(3x10-5) help what is this in standard form?

Tasya [4]

<u>Answer: </u>

The standard form of $\frac{6 \times 10^{2}}{3 \times 10^{-5}}$ is 20,00,0000

<u>Solution: </u>

Given that $\frac{6 \times 10^{2}}{3 \times 10^{-5}}$ ---- eqn 1

To write $\frac{6 \times 10^{2}}{3 \times 10^{-5}}$ in standard form,

We know that $\bold{\frac{1}{a^{-m}} = a^{m}}$ .So $\frac{1}{10^{-5}}$ becomes $10^{5}$ .

Now eqn 1 becomes,

$= \frac{6 \times 10^{2}}{3} \times 10^{5}$ ----- eqn 2

We know that $\bold{a^{m} \times a^{n}=a^{m+n}}$ , so $10^{2} \times 10^{5} = 10^{7}$

Now eqn 2 becomes,

$= \frac{6}{3} \times 10^{7}$

$= 2 \times 10^{7}$ ---- eqn 3

Expanding $10^{7}$ :

Here 10 is the base term and 7 is the exponent value. So base term 10 is multiplied by itself 7 times.

$10^{7} = 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10$

Now eqn 3 becomes,

$= 2 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10$

= 20,00,0000

Hence the standard form of $\frac{6 \times 10^{2}}{3 \times 10^{-5}}$ is 20,00,0000

6 0

3 years ago

Show in each case that the series converges or diverges

Montano1993 [528]

I can't make out the summand in (d), and I addressed (c) in your other question.

(a) $\displaystyle\sum_{n\ge1}\frac{\cos n\pi}{n\sqrt n}$

We have for positive integers $n$ that $\cos n\pi=(-1)^n$ . We also are aware that the series

$\displaystyle\sum_{n\ge1}\frac1{n^{3/2}}$

converges, since it is a $p$ -series with $p=\dfrac32>1$ . Since the $p$ -series converges in absolute value, the alternating series must also converge by comparison.

- - -

(b) $\displaystyle\sum_{n\ge1}(-1)^n\frac{\ln n}n$

By the alternating series test, this series will converge if the absolute value of the summand is increasing for some large enough $N$ and approaches zero.

We have

$\left|(-1)^n\dfrac{\ln n}n\right|=\dfrac{\ln n}n>0$

for all $n\ge1$ , and we also have that

$\displaystyle\lim_{n\to\infty}\frac{\ln n}n=\lim_{m\to\infty}\frac m{e^m}=0$

(where we substituted $m=\ln n$ , so that $e^m=n$ ).

Therefore (b) also converges.

4 0

3 years ago

Can you show the working out as well please?​

Can you show the working out as well please?