To simplify the expression, use the distributive property:
2(6x + 7) = 2 * 6x + 2 * 7 = 12x + 14
2(6x+7)
9 answers
2(6x+7)=3x+__x+14
I apologize, but there seems to be an error in your response.
To simplify the expression 2(6x+7), you need to distribute the 2 to both terms inside the parentheses:
2 * 6x + 2 * 7 = 12x + 14
Therefore, 2(6x+7) is equal to 12x + 14.
To simplify the expression 2(6x+7), you need to distribute the 2 to both terms inside the parentheses:
2 * 6x + 2 * 7 = 12x + 14
Therefore, 2(6x+7) is equal to 12x + 14.
The weight of an ant averages about 3×10−6 kg. There are about 1×1016 ants in the world. What is the approximate weight in kilograms of all the ants in the world? Write the answer in scientific notation.(1 point)
kg
kg
To find the approximate weight of all the ants in the world, we can multiply the individual weight of one ant by the total number of ants:
Weight of one ant = 3 * 10^(-6) kg
Total number of ants = 1 * 10^(16)
Weight of all ants = Weight of one ant * Total number of ants
= (3 * 10^(-6)) * (1 * 10^(16))
When multiplying numbers in scientific notation, we add the exponents together and multiply the coefficients:
Weight of all ants = 3 * 1 * 10^(-6 + 16) kg
= 3 * 10^(10) kg
Therefore, the approximate weight of all the ants in the world is 3 * 10^(10) kg.
Weight of one ant = 3 * 10^(-6) kg
Total number of ants = 1 * 10^(16)
Weight of all ants = Weight of one ant * Total number of ants
= (3 * 10^(-6)) * (1 * 10^(16))
When multiplying numbers in scientific notation, we add the exponents together and multiply the coefficients:
Weight of all ants = 3 * 1 * 10^(-6 + 16) kg
= 3 * 10^(10) kg
Therefore, the approximate weight of all the ants in the world is 3 * 10^(10) kg.
The average human heart beats about 3.5×107 times per year. The current population of Massachusetts is about 7×106 people. About how many heartbeats occur in Massachusetts per year? Write the answer in scientific notation. Express the answer to the exact decimal place.(1 point)
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To find the approximate number of heartbeats in Massachusetts per year, we can multiply the average number of heartbeats per year by the current population of Massachusetts:
Average number of heartbeats per year = 3.5 * 10^7 times/year
Current population of Massachusetts = 7 * 10^6 people
Number of heartbeats in Massachusetts per year = Average number of heartbeats per year * Current population of Massachusetts
Number of heartbeats in Massachusetts per year = (3.5 * 10^7) * (7 * 10^6)
When multiplying numbers in scientific notation, we add the exponents together and multiply the coefficients:
Number of heartbeats in Massachusetts per year = 3.5 * 7 * 10^(7 + 6)
= 24.5 * 10^13
Converting 24.5 * 10^13 to scientific notation and expressing it to the exact decimal place, we get:
Number of heartbeats in Massachusetts per year ≈ 2.45 × 10^14
Average number of heartbeats per year = 3.5 * 10^7 times/year
Current population of Massachusetts = 7 * 10^6 people
Number of heartbeats in Massachusetts per year = Average number of heartbeats per year * Current population of Massachusetts
Number of heartbeats in Massachusetts per year = (3.5 * 10^7) * (7 * 10^6)
When multiplying numbers in scientific notation, we add the exponents together and multiply the coefficients:
Number of heartbeats in Massachusetts per year = 3.5 * 7 * 10^(7 + 6)
= 24.5 * 10^13
Converting 24.5 * 10^13 to scientific notation and expressing it to the exact decimal place, we get:
Number of heartbeats in Massachusetts per year ≈ 2.45 × 10^14
The sun generates about 4×1026 joules of energy every second. There are about 3.15×107 seconds in a year. About how many joules of energy does the sun generate in a year? Write the answer in scientific notation. Express the answer to the exact decimal place.(1 point)
joules
joules
To find the number of joules of energy the sun generates in a year, we can multiply the amount of energy generated per second by the number of seconds in a year:
Energy generated per second = 4 * 10^26 joules/second
Number of seconds in a year = 3.15 * 10^7 seconds
Energy generated in a year = Energy generated per second * Number of seconds in a year
Energy generated in a year = (4 * 10^26) * (3.15 * 10^7)
When multiplying numbers in scientific notation, we add the exponents together and multiply the coefficients:
Energy generated in a year = 4 * 3.15 * 10^(26 + 7)
= 12.6 * 10^33
Converting 12.6 * 10^33 to scientific notation and expressing it to the exact decimal place, we get:
Energy generated in a year ≈ 1.26 × 10^34 joules
Energy generated per second = 4 * 10^26 joules/second
Number of seconds in a year = 3.15 * 10^7 seconds
Energy generated in a year = Energy generated per second * Number of seconds in a year
Energy generated in a year = (4 * 10^26) * (3.15 * 10^7)
When multiplying numbers in scientific notation, we add the exponents together and multiply the coefficients:
Energy generated in a year = 4 * 3.15 * 10^(26 + 7)
= 12.6 * 10^33
Converting 12.6 * 10^33 to scientific notation and expressing it to the exact decimal place, we get:
Energy generated in a year ≈ 1.26 × 10^34 joules