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2 years ago

What is the solution to 5a-15+9a=3a+29

Mathematics

2 answers:

mart [117]2 years ago

5 0

Combine like terms:

5a + 9a - 15 = 3a + 29

14a - 15 = 3a + 29

Subtract 3 from both sides and add 15 to both sides to get constants on one side of the equal side and variables on the other.

14a - 3a = 29 + 15

Combine like terms again:

11a = 44

Divide by 11 on both sides to isolate the variable:

a = 44/11

a = 4

pogonyaev2 years ago

3 0

5a-15+9a=3a+29

We simplify the equation to the form, which is simple to understand

5a-15+9a=3a+29

We move all terms containing a to the left and all other terms to the right.

+5a+9a-3a=+29+15

We simplify left and right side of the equation.

+11a=+44

We divide both sides of the equation by 11 to get a.

a=4

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2. 3.913 kg (3 dp)

3. light cream

4. 240 CoffeeStops

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6. 2,861 cups of coffee each day

Step-by-step explanation:

Given:

Skim milk density at 20 °C = 1.033 kg/l
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$\begin{aligned}\textsf{1 gallon} & = \sf \dfrac{1}{0.264}\:liters\\\\\implies \textsf{Mass (1 gallon of skim milk)} & = \sf Density \times Volume\\& = \sf 1.033\:kg/l \times \dfrac{1}{0.264}\:l\\& = \sf 3.913\:kg\:(3\:dp)\end{aligned}$

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Question 3

Given:

Volume of liquid = 9 liters
Mass of liquid = 9.108 kg

$\begin{aligned}\implies \sf Density & = \sf \dfrac{Mass}{Volume}\\\\& = \sf \dfrac{9.108\:kg}{9\:l}\\\\& = \sf 1.012\:kg/l \end{alilgned}$

Therefore, the container holds light cream.

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Question 4

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$\begin{aligned}\implies \textsf{Number of Coffeestops} & = \sf \dfrac{population}{density}\\\\& = \sf \dfrac{1,602,000}{100,000/15}\\\\& = \sf \dfrac{1,602,000}{100,000} \times 15\\\\& = \sf 240.3\end{aligned}$

Therefore, there are 240 CoffeeStops.

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Question 5

Given

Manhattan ≈ 34 square miles

$\begin{aligned}\implies \textsf{CoffeeStops density} & = \sf \dfrac{number\:of\:stores}{land\:area}\\\\& = \sf \dfrac{240}{34}\\\\& \approx \sf 7 \: \textsf{CoffeeStops per square mile}\end{aligned}$

Therefore, the density of CoffeeStops is 7 per square mile.

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Question 6

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Each person buys 3 cups of coffee per week

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