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Law Incorporation [45]
3 years ago
8

The standard form of the equation that represents the number of quarters, q, and the number of dimes, d, that Austin has in his

piggy bank is 5q + 2d = 270. Explain what the intercepts mean in terms of the context and how to find them.
Mathematics
2 answers:
Fynjy0 [20]3 years ago
6 0
The standard form of the equation that represents the number of quarters, q, and the number of dimes, d, that Austin has in his piggy bank is 5q + 2d = 270. This can be change to slope intercept form to see the clearer picture. By dividing the whole equation by 2, so the equation become d= -2.5q + 135.

This means that Austin has initially 135 dimes in his piggy bank and he is losing 2.5 dimes per quarter.
Hope this helps!!!



snow_lady [41]3 years ago
4 0

Answer:

Sample Response: To find one intercept, let d = 0 in the equation and solve for q. To find the other intercept, let q = 0 in the equation and solve for d. The intercepts mean that the bank could be filled with 54 quarters and no dimes, or 135 dimes and no quarters.

Step-by-step explanation:

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3 years ago
A company fills a warehouse will two types of goods A and B . they both come in tall boxes which cannot be stocked. one box of A
inessss [21]

Answer:

(1/2) * A + (1/2) * B <= 100; for A => 50; for B => 20

(5000) * A + (30000) * B <= 1500000; for A => 50; for B => 20

Step-by-step explanation:

There are two inequalities in mind, the first of the surface and the second of the price. Always bearing in mind that the minimum are 50 of A and 20 of B.

The first

A occupies 1/2 m and B occupies 1/2 m of surface, and the limit is 100 m of surface. Thus:

(1/2) * A + (1/2) * B <= 100; for A => 50; for B => 20

The second:

A costs 5,000 and B costs 30,000, and the limit is 1,500,000. Therefore:

(5000) * A + (30000) * B <= 1500000; for A => 50; for B => 20

5 0
3 years ago
Which measurements could not represent the side lengths of a right triangle?
victus00 [196]

Answer: C

Step-by-step explanation: a^2 + b^2 = c^2

A. 6^2 + 8^2 = 10^2

B. 12^2 + 35^2 = 37^2

C. 4^2 + 6^2 does not equal 10^2.....(16 + 36 = 52   10^2 = 100)

D. 10^2 + 24^2 = 26^2

5 0
3 years ago
The mean computed from ungrouped data is a more accurate measure than the mean computed from grouped data?
Rufina [12.5K]
It doesn’t make any difference whether or not the data is grouped, the mean is the same. So b. false.
4 0
3 years ago
Who can help me d e f thanks​
12345 [234]

d)

y = (2ax^2 + c)^2 (bx^2 - cx)^{-1}

Product rule:

y' = \bigg((2ax^2+c)^2\bigg)' (bx^2-cx)^{-1} + (2ax^2+c)^2 \bigg((bx^2-cx)^{-1}\bigg)'

Chain and power rules:

y' = 2(2ax^2+c)\bigg(2ax^2+c\bigg)' (bx^2-cx)^{-1} - (2ax^2+c)^2 (bx^2-cx)^{-2} \bigg(bx^2-cx\bigg)'

Power rule:

y' = 2(2ax^2+c)(4ax) (bx^2-cx)^{-1} - (2ax^2+c)^2 (bx^2-cx)^{-2} (2bx - c)

Now simplify.

y' = \dfrac{8ax (2ax^2+c)}{bx^2 - cx} - \dfrac{(2ax^2+c)^2 (2bx-c)}{(bx^2-cx)^2}

y' = \dfrac{8ax (2ax^2+c) (bx^2 - cx) - (2ax^2+c)^2 (2bx-c)}{(bx^2-cx)^2}

e)

y = \dfrac{3bx + ac}{\sqrt{ax}}

Quotient rule:

y' = \dfrac{\bigg(3bx+ac\bigg)' \sqrt{ax} - (3bx+ac) \bigg(\sqrt{ax}\bigg)'}{\left(\sqrt{ax}\right)^2}

y'= \dfrac{\bigg(3bx+ac\bigg)' \sqrt{ax} - (3bx+ac) \bigg(\sqrt{ax}\bigg)'}{ax}

Power rule:

y' = \dfrac{3b \sqrt{ax} - (3bx+ac) \left(-\frac12 \sqrt a \, x^{-1/2}\right)}{ax}

Now simplify.

y' = \dfrac{3b \sqrt a \, x^{1/2} + \frac{\sqrt a}2 (3bx+ac) x^{-1/2}}{ax}

y' = \dfrac{6bx + 3bx+ac}{2\sqrt a\, x^{3/2}}

y' = \dfrac{9bx+ac}{2\sqrt a\, x^{3/2}}

f)

y = \sin^2(ax+b)

Chain rule:

y' = 2 \sin(ax+b) \bigg(\sin(ax+b)\bigg)'

y' = 2 \sin(ax+b) \cos(ax+b) \bigg(ax+b\bigg)'

y' = 2a \sin(ax+b) \cos(ax+b)

We can further simplify this to

y' = a \sin(2(ax+b))

using the double angle identity for sine.

7 0
1 year ago
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