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3 years ago

48 ÷ [(5 + 16) − 13]

Mathematics

1 answer:

Salsk061 [2.6K]3 years ago

3 0

Answer:

Step-by-step explanation:

48 ÷ [(5 + 16) − 13]

PEMDAS work from the inside out

48 ÷ [21 − 13]

48 ÷ [8]

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Two people together can do a certain job in twenty minutes.If one of them can do the job alone in forty-five minutes, how long w

OlgaM077 [116]

<h2>Answer:</h2>

36 minutes

<h2>Step-by-step explanation:</h2>

Going through the question in bits:

i. <em>Two people together can do a certain job in 20 minutes.</em>

This implies that the time taken to finish the job is 20 minutes.

This also means that in 1 minute, they will do $\frac{1}{20}$ of the job i.e the rate at which the job is done by the two of them is $\frac{1}{20}$

ii. <em>If one of them can do the job in 45 minutes.</em>

This implies that the time taken by one of them to finish the job is 45 minutes.

This also means that in 1 minute, he will do $\frac{1}{45}$ of the job. i.e the rate at which the job is done by one of them is $\frac{1}{45}$

iii. <em>let the other person do the job in x minutes.</em>

This implies that the time take by the other person to finish the job is x minutes.

This also means that in 1 minute, he will do $\frac{1}{x}$ of the job. i.e the rate at which the job is done by the other person is $\frac{1}{x}$

Now,

The rate by which the job will be done by the two of them combined is the sum of the individual rates.

i.e

$\frac{1}{20}$ = $\frac{1}{45}$ + $\frac{1}{x}$

Multiply through by 90x and solve

(90x * $\frac{1}{20}$ ) = (90x * $\frac{1}{45}$ ) + (90x * $\frac{1}{x}$ )

4.5x = 2x + 90

4.5x - 2x = 90

2.5x = 90

x = $\frac{90}{2.5}$

x = 36

Therefore it will take the other person 36 minutes to finish the job.

3 0

3 years ago

Find the length of each side of the triangle determined by the three points P1,P2, and P3. State whether the triangle is an isos

Tanya [424]

Answer:

The triangle is both an Isosceles triangle and a right triangle.

Step-by-step explanation:

Given the vertices of a triangle.

$P_{1} = (- 1, 4)$

$P_{2} = (6, 2)$ and

$P_{3} = (4, - 5)$

We find the distance between all the points to determine the length of each side of the triangle.

Distance between any two points, say, $(x_1, y_1)$ and $(x_2, y_2)$ is:

$\sqrt{\bigg ( \textbf{x}_{\textbf{2}} \hspace{1mm} \textbf{- x}_{\textbf{1}} \bigg )^{\textbf{2}} \textbf{+} \bigg( \textbf{y}_{\textbf{2}} \hspace{1mm} \textbf{- y}_{\textbf{1}} \bigg)^ {\textbf{2}}$

Length between $P_1$ and $P_{2}$ , (Side 1) :

$(x_1, y_1) = (- 1, 4)$ and

$(x_2, y_2) = (6, 2)$

Distance = $\sqrt{\bigg(6 - (-1) \bigg)^{2} \hspace{1mm} + \hspace{1mm} \bigg( 2 - 4 \bigg )^2$

$= \sqrt{7^2 + 2^2}$

$= \sqrt{49 + 4}$

$= \sqrt{\textbf{53}}$

Length of Side 1 = $\sqrt{\textbf{53}}$ units.

Distance between $P_1$ and $P_2$ , (Side 2):

$(x_1, y_1) = (-1, 4)$

$(x_2, y_2) = (4, - 5)$

Distance = $\sqrt{ \bigg( 4 + 1 \bigg)^2 \hspace{1mm} + \bigg( - 5 - 4 \bigg ) ^2$

$= \sqrt{ 25 + 81 }$

$= \sqrt{\textbf{106}}$

Length of Side 2 = $\sqrt{\textbf{106}}$ units.

Distance between $P_2$ and $P_3$ , Side 3 :

$(x_1, y_1) = (4, 5)$

$(x_2, y_2) = (6, 2)$

Distance = $\sqrt{ 2^2 \hspace{1mm} + \hspace{1mm} 7^2}$

$= \sqrt{49 + 4}$

$= \sqrt{\textbf{53}$

Length of Side 3 = $\sqrt{\textbf{53}}$ units.

Note that the length of Side 1 = Length of Side 3.

That means the triangle is Isosceles.

Also, For a triangle to be right angle triangle, using Pythagoras theorem we have:

(Side 1)² + (Side 3)² = (Side 2)²

$\bigg( \sqrt{53} \bigg )^2 \hspace{1mm} + \hspace{1mm} \bigg( \sqrt{53} \bigg)^2 \hspace{1mm} = \hspace{1mm} \bigg ( \sqrt{106} \bigg ) ^2$

i.e, 53 + 53 = 106

Hence, the triangle is a right - angled triangle as well.

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4 years ago

How to write 4,703.601 in expanded form

BigorU [14]

4,000+700+3+0.6+0.001

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3 years ago

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PLEASE HELP Evaluate the limit, if it exists. Show work. lim_(x->5)((x^(2)-3x-10)/(2x-10))

gayaneshka [121]

Answer:

$lim \: x \: —>5 \: \: \frac{ {x}^{2} - 3x - 10 }{2x - 10} \\ \\ lim \: x \: —>5 \: \: \: \frac{(x - 5)(x + 2)}{2(x - 5)} \\ \\ lim \: x \: —>5 \: \: \frac{(x + 2)}{2} = \frac{5 + 2}{2} = \frac{7}{2} \\ \\ \\ = \frac{7}{2} = 3.5$

I hope I helped you^_^

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3 years ago

3z-4=6z-17 how do solve

Maru [420]

3z-4=6z-17
-3z-4=-17 (subtracted the 6z from both sides)
-3z=-13 (added the 4 to both sides)
z= $\frac{-13}{-3z}$ (divided both sides by -3z)
z= $\frac{13}{3}$

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4 years ago

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