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2 years ago

3. Solve 2log4y - log4 (5y - 12) = 1/2

Mathematics

1 answer:

Ilia_Sergeevich [38]2 years ago

4 0

Answer:

y = 4 or y = 6

Step-by-step explanation:

2log4y - log4 (5y - 12) = 1/2

2log_4(y) - log_4(5y-12) = log_4(2) apply law of logarithms

log_4(y^2) + log_4(1/(5y-12)) = log_4(/2) apply law of logarithms

log_4(y^2/(5y-12)) = log_4(2) remove logarithm

y^2/(5y-12) = 2 cross multiply

y^2 = 10y-24 rearrange and factor

y^2 - 10y + 24 = 0

(y-4)(y-6) = 0

y= 4 or y=6

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Answer:

The inequality to determine the number of days, s, Darcie can skip crocheting and still meet her goal can be given as:

$s\leq 15$

Step-by-step explanation:

The complete question is:

Darcie wants to crochet a minimum of 3 blankets to donate to a homeless shelter. Darcie crochets at a rate of 1/15 of a blanket per day. She has 60 days until when she wants to donate the blankets, but she also wants to skip crocheting some days so she can volunteer in other ways. Write an inequality to determine the number of days, s, Darcie can skip crocheting and still meet her goal.

Solution:

Given:

Darcie wants to crochet a minimum of 3 blankets to donate.

Rate at which she crochet = $\frac{1}{15}$ of a blanket per day.

Maximum number of days she has = 60.

To find the number of days Dancie can skip out of 60 days and still reach her goal.

Let $s$ represent the number of days she can skip.

Number of days left to crochet = $(60-s)$ days

At rate of $\frac{1}{15}$ of a blanket per day, number of blankets Dancie can corchet in $(60-s)$ days can be given as :

⇒ $\frac{1}{15}(60-s)$

Simplifying using distribution.

⇒ $(\frac{1}{15}.60)-(\frac{1}{15}.s)$

⇒ $4-\frac{s}{15}$

Dancie needs to crochet a minimum of 3 blankets to reach her goal.

Thus, the inequality can be given as:

$4-\frac{s}{15}\geq 3$

Solving the inequality for $s$

Subtracting 4 both sides.

$4-4-\frac{s}{15}\geq 3-4$

$-\frac{s}{15}\geq -1$

Multiplying both sides by -15.

$-15(-\frac{s}{15})\leq -15(-1)$ [On multiplying by a negative number the sign of inequality reverse]

∴ $s\leq 15$

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2 years ago

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$S=2\pi rh+2\pi r^2\\S=2\pi (3)(7.95)+2\pi3^2\\S=93.3+56.5\\S=149.8 \text{ cm}^2$

Calculate the volume.

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2 years ago

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2 years ago

A machine is supposed to mix peanuts, hazelnuts, cashews, and pecans in the ratio 5:2:2:1. A can containing 500 of these mixed n

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Answer:

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Step-by-step explanation:

Given that a machine is supposed to mix peanuts, hazelnuts, cashews, and pecans in the ratio 5:2:2:1.

A can containing 500 of these mixed nuts was found to have 269 peanuts, 112 hazelnuts, 74 cashews, and 45 pecans.

Create hypotheses as

H0: Mixture is as per the ratio 5:2:2:1

Ha: Mixture is not as per the ratio

(Two tailed chi square test)

Expected values as per ratio are calculated as 5/10 of 500 and so on

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O-E 19 -12 -26 -5 0

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square

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2 years ago

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Answer:

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After this, we decrease this to reduce the formation of the row echelon

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5 0

1 year ago

3. Solve 2log4y - log4 (5y - 12) = 1/2​

3. Solve 2log4y - log4 (5y - 12) = 1/2