George Washington was an officer in the British army during the French and Indian War. He later used what he learned to lead the Revolutionary army.
Give one example of what Washington learned about different styles or methods of fighting that would help him lead the Americans to victory against the British in the Revolutionary War.
(2 points)
One example of what Washington learned about different styles or methods of fighting that would help him lead the Americans to victory against the British in the Revolutionary War was the importance of guerrilla warfare. During the French and Indian War, Washington observed Native American warriors and frontier settlers using guerrilla tactics effectively against the British forces. These tactics involved ambushing enemy forces, using natural cover to their advantage, and quickly retreating after an attack. Washington incorporated these strategies into the American Revolutionary army's warfare, allowing them to effectively target and weaken the larger and more traditional British forces.
Expand the properties of exponents to involve monomial bases with integer exponents to simplify the expression −25x85x
.(1 point)
Responses
−5x^7
negative 5 x superscript 7 baseline
−5x^8
negative 5 x superscript 8 baseline
−5x^9
negative 5 x superscript 9 baseline
5x^7
None of the provided responses are correct.
To simplify the expression −25x^8⋅5x^7, you need to multiply the coefficients and add the exponents with the same base.
When multiplying the coefficients, -25 and 5, you get -125.
When multiplying the variables with the same base, x^8 and x^7, you add the exponents, which gives you x^(8+7) = x^15.
Therefore, the simplified expression is -125x^15.
Expand the properties of exponents to involve monomial bases with integer exponents to simplify the expression −25x^8/5x
.(1 point)
Responses
−5x^7
negative 5 x superscript 7 baseline
−5x^8
negative 5 x superscript 8 baseline
−5x^9
negative 5 x superscript 9 baseline
5x^7
To simplify the expression −25x^8/5x, we can divide the coefficients and subtract the exponents with the same base.
When dividing the coefficients, -25 and 5, we get -5.
When subtracting the exponents with the same base, x^8 and x^1, we have (x^8)/(x^1) = x^(8-1) = x^7.
Therefore, the simplified expression is -5x^7.
Use the properties of integer exponents to simplify the expression (−4a^4)(−2a^2)
.(1 point)
Responses
8a^8
8 a superscript 8 baseline
8a^2
8 a superscript 2 baseline
−8a^6
negative 8 a superscript 6 baseline
8a^6
8 a superscript 6 baseline
To simplify the expression (−4a^4)(−2a^2), we can multiply the coefficients and add the exponents with the same base.
When multiplying the coefficients, -4 and -2, we get 8.
When multiplying the variables with the same base, a^4 and a^2, we add the exponents, which gives us a^(4+2) = a^6.
Therefore, the simplified expression is 8a^6.
Apply the properties of integer exponents to generate an equivalent algebraic expression to 3x^3y^−4/12x^7y^4
.(1 point)
Responses
1/4x^4y^8
Start Fraction 1 over 4 x superscript 4 baseline y superscript 8 baseline
4x^4y^8
4 x superscript 4 baseline y superscript 8 baseline
1/4x^12
Start Fraction 1 over 4 x superscript 12 baseline
3/12x^4y^8
To generate an equivalent algebraic expression for 3x^3y^−4/12x^7y^4, we can simplify the expression by applying the properties of integer exponents.
When simplifying the coefficients, 3 and 12, we can divide them both by their greatest common divisor, which is 3. Dividing 3 by 3 gives us 1, and dividing 12 by 3 gives us 4.
When dividing the variables with the same base, x^3 and x^7, we subtract the exponents, which gives us x^(7-3) = x^4.
Similarly, when dividing the variables with the same base, y^(-4) and y^4, we subtract the exponents, which gives us y^(-4+4) = y^0 = 1.
Therefore, the simplified expression is (1/4)x^4.