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Volgvan
4 days ago
13

John bought 24 pens and pencils. There were 6 more pens than pencils. How many pens were bought by John?

Mathematics
1 answer:
tester [12K]4 days ago
7 0
Let x denote the number of pens and y represent the pencils. From the information given, we have x + y = 24, indicating there are 24 pens and pencils combined. Additionally, the equation x = y + 6 has been established, as there are 6 more pens than pencils. We can substitute the second expression into the first: x + y = 24, so (y + 6) + y = 24. When we consolidate the terms, we have 2y + 6 = 24. By rearranging, we find 2y = 18, leading to y = 9. This means there are 9 pencils; thus, there are 6 more pens than that, which gives us 15 pens. Therefore, John purchased 15 pens and 9 pencils.
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Which equation represents a proportional relationship with a constant of proportionality of 14? y = x + 14 y = 14x 14y = x y = x
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The equation that demonstrates a proportional relationship, maintaining a constant of proportionality equal to 14, is: Here,  and are proportional with a constant of proportionality of 14.
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22 days ago
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Would $3.99$ million flies or $47,000,000$ ants have a greater mass? Approximately how much greater, in grams, would the greater
zzz [11969]

Answer:

Ants weigh approximately 118,615,000mg more.

Step-by-step explanation:

Based on a quick search, the average housefly weighs around 11.5mg, while an ant averages at 3.5mg. With these average weights, we can calculate the total weight of each species.

Flies: 3,990,000 * 11.5mg = 45,885,000mg

Ants: 47,000,000 * 3.5mg = 164,500,000mg

Consequently, it's clear that the 47 million ants possess a greater mass, specifically

164,500,000 - 45,885,000 = 118,615,000mg more

3 0
11 days ago
The diagonals of the figure below represent the support beams for a patio covering.
Svet_ta [12410]
The response is B: 5 and 5 square root 3.
3 0
23 days ago
1. A certain ceiling is made up of tiles. Every square meter of ceiling requires 10.75 tiles.
Svet_ta [12410]
Every square meter of ceiling needs 10.75 tiles. To calculate the number of tiles needed for various ceiling areas: For a ceiling area of 1, it requires 10.75 tiles. For a ceiling area of 10, it requires 10.75 × 10, which equals 107.5 tiles. For an area of 100, it needs 10.75 × 100, totaling 1075 tiles. Consequently, that represents the necessary solution.
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6 days ago
Initially 5 grams of salt are dissolved into 10 liters of water. Brine with concentration of salt 5 grams per liter is added at
Svet_ta [12410]

The salt enters at a rate of (5 g/L)*(3 L/min) = 15 g/min.

The salt exits at a rate of (x/10 g/L)*(3 L/min) = 3x/10 g/min.

Thus, the total rate of salt flow, represented by x(t) in grams, is defined by the differential equation,

x'(t)=15-\dfrac{3x(t)}{10}

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e^{3t/10}x'+\dfrac{3e^{t/10}}{10}x=15e^{3t/10}

\implies\left(e^{3t/10}x\right)'=15e^{3t/10}

Next, integrate both sides and solve for x:

e^{3t/10}x=50e^{3t/10}+C

\implies x(t)=50+Ce^{-3t/10}

Initially, the tank contains 5 g of salt at time t=0, so we have

5=50+C\implies C=-45

\implies\boxed{x(t)=50-45e^{-3t/10}}

The duration required for the tank to contain 20 g of salt is t, such that

20=50-45e^{-3t/10}\implies t=\dfrac{20}3\ln\dfrac32\approx2.7031\,\mathrm{min}

3 0
1 month ago
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