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2 years ago

Are 4(a - 3) and 4a - 7 equivalent expressions?

Mathematics

2 answers:

Anarel [89]2 years ago

7 0

Answer:

Yes

Step-by-step explanation:

Given expression: 3x+9

Take 3 outside from the expression, we get,

= 3(x+3), which is called the equivalent expression

spin [16.1K]2 years ago

4 0

Answer:

Step-by-step

We have to multiply the 4 by both the a and the 3 since there a parenthesis around them. This would of course be distributive property. Since you don't know what a is, it would just be 4a and since we can multiply 4 and 3 that would be 12. So, 4(a - 3) is equivalent to 4a - 12.

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What is the domain of the absolute value function below?

vovikov84 [41]

The domain is all real numbers. (-infinity, infinity)
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3 years ago

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Grace is three times as old as Hans, but in 5 years she will be twice as old as Hans is then. How old are they now? Set up an th

frosja888 [35]

Answer:

3x - y = 0; 2x - y = -5

Step-by-step explanation:

Let x be the present age of Hans and y be the present age of Grace,

Since, in present Grace is three times as old as Hans,

⇒ y = 3x

⇒ 3x - y = 0

Now, after 5 years,

The age of Hans = x + 5,

And, the age of Grace = y + 5

Also, in 5 years Grace will be twice as old as Hans is then,

⇒ y + 5 = 2 ( x + 5 )

⇒ y + 5 = 2x + 10

⇒ 2x - y = -5

Hence, the required system of linear equations is,

3x - y = 0; 2x - y = -5

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3 years ago

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r-ruslan [8.4K]

Answer is in the file below

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3 years ago

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Which of the following is equivalent to <br><br> 3x−4y=18?

sammy [17]

The equation which is equivalent to the equation as given in the task content is; 6x -8y = 36.

<h3>Which equation is equivalent to the equation as given in the task content?</h3>

According to the task content, it follows that the equation which is given in the task content is;

3x -4y = 18.

Hence, upon multiplication of the whole equation by 2; the resulting equation from the multiplication is;

6x -8y = 36

Ultimately, the equivalent equation is; 6x -8y = 36.

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1 year ago

f(x) = 3 cos(x) 0 ≤ x ≤ 3π/4 evaluate the Riemann sum with n = 6, taking the sample points to be left endpoints. (Round your ans

Kruka [31]

Answer:

$\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx\approx 3.099558$

Step-by-step explanation:

We want to find the Riemann sum for $\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx$ with n = 6, using left endpoints.

The Left Riemann Sum uses the left endpoints of a sub-interval:

$\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_0)+f(x_1)+2f(x_2)+...+f(x_{n-2})+f(x_{n-1})\right)$

where $\Delta{x}=\frac{b-a}{n}$ .

Step 1: Find $\Delta{x}$

We have that $a=0, b=\frac{3\pi }{4}, n=6$

Therefore, $\Delta{x}=\frac{\frac{3 \pi}{4}-0}{6}=\frac{\pi}{8}$

Step 2: Divide the interval $\left[0,\frac{3 \pi}{4}\right]$ into n = 6 sub-intervals of length $\Delta{x}=\frac{\pi}{8}$

$a=\left[0, \frac{\pi}{8}\right], \left[\frac{\pi}{8}, \frac{\pi}{4}\right], \left[\frac{\pi}{4}, \frac{3 \pi}{8}\right], \left[\frac{3 \pi}{8}, \frac{\pi}{2}\right], \left[\frac{\pi}{2}, \frac{5 \pi}{8}\right], \left[\frac{5 \pi}{8}, \frac{3 \pi}{4}\right]=b$

Step 3: Evaluate the function at the left endpoints

$f\left(x_{0}\right)=f(a)=f\left(0\right)=3=3$

$f\left(x_{1}\right)=f\left(\frac{\pi}{8}\right)=3 \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}=2.77163859753386$

$f\left(x_{2}\right)=f\left(\frac{\pi}{4}\right)=\frac{3 \sqrt{2}}{2}=2.12132034355964$

$f\left(x_{3}\right)=f\left(\frac{3 \pi}{8}\right)=3 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}=1.14805029709527$

$f\left(x_{4}\right)=f\left(\frac{\pi}{2}\right)=0=0$

$f\left(x_{5}\right)=f\left(\frac{5 \pi}{8}\right)=- 3 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}=-1.14805029709527$

Step 4: Apply the Left Riemann Sum formula

$\frac{\pi}{8}(3+2.77163859753386+2.12132034355964+1.14805029709527+0-1.14805029709527)=3.09955772805315$

$\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx\approx 3.099558$

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3 years ago