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4 years ago

Translate the given phrase into an algebraic expression and simplify if possible: the product of -13 and the difference of c

Mathematics

1 answer:

Musya8 [376]4 years ago

7 0

Answer: $-13c+13d$

Step-by-step explanation:

For this exercise it is important to remember the following:

1. By definition, the "Product" is the result of a multiplication.

2. The "Difference" is defined as the result of a subtraction.

3. The Distributive property states that:

$a(b+c)=ab+ac\\\\a(b-c)=ab-ac$

Keeping the above on mind, you know that:

"The difference of $c$ and $d$ " can be represented with the following expression:

$c-d$

Therefore, "The product of -13 and the difference of $c$ and $d$ " can be represented with this expression:

$-13(c-d)$

Finally, you must apply the Distributive property in order to simplify the expression. You get:

$=-13c+13d$

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4. none of the above

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Lilian says that 25% of a number will always be less than 75% of any other number. Complete one inequality to support Lillian's

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3 years ago

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3 years ago

A plan that costs $29.99 another company $19.99 and $0.35 during nights and weekends for what numbers of night and weekend does

Masja [62]

Answer:

29 minutes more

Step-by-step explanation:

Let m represent minutes

changing the statement to algebra, since the second company charges a different rate at night and weekend we have the equation below;

$19.99 + $0.35m > $29.99

Subtract 19.99 from both sides to isolate m and we have;

$19.99 -$19.99 + $0.35 > $29.99 - $19.99

= $0,35m > $10.00

Divide both side by 0.35 to obtain the value of m;

$\frac{0.35m}{0.35}$ > $\frac{10}{0.35}$

= m > 28.57

m ⩾ 29 minutes

The second company's will be twenty nine minutes or more costlier than the first company

5 0

3 years ago

Read 2 more answers

How do you do this question?

Ksivusya [100]

Answer:

V = (About) 22.2, Graph = First graph/Graph in the attachment

Step-by-step explanation:

Remember that in all these cases, we have a specified method to use, the washer method, disk method, and the cylindrical shell method. Keep in mind that the washer and disk method are one in the same, but I feel that the disk method is better as it avoids splitting the integral into two, and rewriting the curves. Here we will go with the disk method.

$\mathrm{V\:=\:\pi \int _a^b\left(r\right)^2dy\:},\\\mathrm{V\:=\:\int _1^3\:\pi \left[\left(1+\frac{2}{y}\right)^2-1\right]dy}$

The plus 1 in '1 + 2/x' is shifting this graph up from where it is rotating, but the negative 1 is subtracting the area between the y-axis and the shaded region, so that when it's flipped around, it becomes a washer.

$V\:=\:\int _1^3\:\pi \left[\left(1+\frac{2}{y}\right)^2-1\right]dy,\\\\\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx\\=\pi \cdot \int _1^3\left(1+\frac{2}{y}\right)^2-1dy\\\\\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\= \pi \left(\int _1^3\left(1+\frac{2}{y}\right)^2dy-\int _1^31dy\right)\\\\$

$\int _1^3\left(1+\frac{2}{y}\right)^2dy=4\ln \left(3\right)+\frac{14}{3}, \int _1^31dy=2\\\\=> \pi \left(4\ln \left(3\right)+\frac{14}{3}-2\right)\\=> \pi \left(4\ln \left(3\right)+\frac{8}{3}\right)$

Our exact solution will be V = π(4In(3) + 8/3). In decimal form it will be about 22.2 however. Try both solution if you like, but it would be better to use 22.2. Your graph will just be a plot under the curve y = 2/x, the first graph.

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3 years ago