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4 years ago

Simplify each expressions: a) -72÷8+(-6)-2 b) -4+(-32)÷(-4×5)

1 answer:

3 0

$\bf -72\div 8+(-6)-2\implies \stackrel{\mathbb{PEMDAS}}{-72\div 8-6-2}\implies -9-6-2
\\\\\\
-15-2\implies -17\\\\
-------------------------------\\\\
-4+(-32)\div(-4\times 5)\implies \stackrel{\mathbb{PEMDAS}}{-4+(-32)\div(-20)}
\\\\\\
-4+1.6\implies -2.4$

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Anna has a total of 36 goldfish in her aquarium, some are orange and some are black. The number of orange goldfish is 7 more tha

andriy [413]

Answer:

x + y = 36.....Equation 1

x = 7 + 2y...... Equation 2

Step-by-step explanation:

Let the number of:

Orange goldfish = x

Black gold fish = y

Anna has a total of 36 goldfish in her aquarium, some are orange and some are black.

x + y = 36.....Equation 1

The number of orange goldfish is 7 more than twice the number of black goldfish.

x = 7 + 2y...... Equation 2

We can rewrite this as:

x - 2y = 7..... Equation 2

The system of equations below that can be used to describe the number of black and orange goldfish in Anna's aquarium is :

x + y = 36.....Equation 1

x = 7 + 2y...... Equation 2

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A particle moves with velocity vector

asambeis [7]

Answer:

$\vec{s(t)}=\frac{1}{2}t^2\hat{i}-(2t+1)\hat{j}+(\frac{1}{3}t^3+1)\hat{k}$

Step-by-step explanation:

We are given that velocity vector of a particle

$\vec{v(t)}=t\hat{i}-2\hat{j}+t^2\hat{k}$

When t=0 then the particle is at the point (0,-1,1).

We have to find the position of particle at time t.

We know that

Velocity = $\frac{Displacement }{time}=\frac{ds}{dt}$

Therefore, $\vec{v}=\frac{\vec{ds}}{dt}$

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Integrate on both sides then we get

$\vec{s(t)}=\frac{1}{2}t^2\hat{i}-2t\hat{j}+\frac{1}{3}t^3\hat{k}+C$

$\int x^n dx=\frac{x^{n+1}}{n+1}+C$

Substitute the value of point at time t=0 then we get

C= $-\hat{j}+\hat{k}$

Substitute the value of C then we get

$\vec{s(t)}=\frac{1}{2}t^2\hat{i}-2t\hat{j}+\frac{1}{3}t^3\hat{k}-\hat{j}+\hat{k}$

Therefore, the position of particle at time t

$\vec{s(t)}=\frac{1}{2}t^2\hat{i}-(2t+1)\hat{j}+(\frac{1}{3}t^3+1)\hat{k}$

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3 years ago

18. *

frozen [14]

Answer:

More than 10% of Gillway students earned honors.

Step-by-step explanation:

Step 1: Find the number of students who earned honors

43 + 17 = 60

Step 2: Find the total number of students

381 + 108 = 489

Step 3: Find the percentage of students who earned honors

Students who earned honors/Total students x 100

60/489 x 100

12.27%

Step 4: Find the correct answer

Just under 11% of Gillway students earned honors.

This is incorrect since the percentage is more than 11%.

Just over 11% of Gillway students earned honors.

This is incorrect as just over 11% would mean somewhere between 11 and 12% whereas the actual percentage is just over 12%.

More than 10% of Gillway students earned honors.

This is correct as compared to all other statements since 12.27% is more than 10%.

Almost 11% of Gillway students earned honors.

This is incorrect since almost 11% means less than 11% whereas the actual percentage is more than 11%.

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3 years ago