Which of the following describes what it means when subjects and verbs agree?(1 point)
Responses
They describe the same things.
They describe the same things.
They are not separated by interrupting words.
They are not separated by interrupting words.
They have the same ending.
They have the same ending.
They are both singular or both plural.
They are both singular or both plural.
Which sentence uses correct subject-verb agreement?(1 point)
Responses
The clouds swiftly moves across the sky.
The clouds swiftly moves across the sky.
My brother always want to cook dinner.
My brother always want to cook dinner.
My teachers often gives homework on the weekend.
My teachers often gives homework on the weekend.
The cat carefully steps across the fence.
The cat carefully steps across the fence.
Use the sentence to answer the question.
The sailboat with the yellow stripes on its sails drifted across the lake.
Which of the following is the subject of the sentence?
(1 point)
Responses
sailboat
sailboat
lake
lake
sails
sails
stripes
sailboat
Which sentence displays correct subject-verb agreement?(1 point)
Responses
The dialogue spoken by the actors make the crowd roar with laughter.
The dialogue spoken by the actors make the crowd roar with laughter.
The helpers working behind the stage comes out, too!
The helpers working behind the stage comes out, too!
The people in the audience stand as the show ends.
The people in the audience stand as the show ends.
The actors in the play returns to take another bow.
The people in the audience stand as the show ends.
Use the properties of integer exponents to simplify the expression (3y)0
According to the properties of integer exponents, any number raised to the power of 0 equals 1. Therefore, (3y)^0 simplifies to 1.
Is Option A or Option B the correct simplified expression of (4x3)3 using the properties of integer exponents?
Option A: 4x9
Option B: 64x9
Enter 1 for Option A or 2 for Option B
Enter 2 for Option B
Use the properties of integer exponents to simplify the expression (−3b4)(6b7).(1 point)
Responses
−18b11
negative 18 b superscript 11 baseline
18b11
18 b superscript 11 baseline
−18b28
negative 18 b superscript 28 baseline
−18b−3
To simplify the expression (−3b^4)(6b^7), you can multiply the coefficients and add the exponents when multiplying like bases.
So, (-3)(6) = -18, and (b^4)(b^7) = b^(4+7) = b^11.
Therefore, the simplified expression is -18b^11.
Apply the properties of integer exponents to generate an equivalent algebraic expression to (−2x−3)04x0
.
To generate an equivalent algebraic expression, we can use the property that any number raised to the power of 0 is equal to 1.
Thus, (-2x^(-3))^0 * 4x^0 is equivalent to 1 * 4.
Therefore, an equivalent algebraic expression is simply 4.
Expand the properties of exponents to involve monomial bases with integer exponents to simplify the expression −25x85x.(1 point)
Responses
−5x8
negative 5 x superscript 8 baseline
−5x9
negative 5 x superscript 9 baseline
5x7
5 x superscript 7 baseline
−5x7
To simplify the expression -25x^8 * 5x, we can multiply the coefficients and add the exponents for the same base.
So, -25 * 5 = -125, and (x^8)(x^1) = x^(8+1) = x^9.
Therefore, the simplified expression is -125x^9.
Use the properties of integer exponents to simplify the expression (−4a4)(−2a2).(1 point)
Responses
8a2
8 a superscript 2 baseline
−8a6
negative 8 a superscript 6 baseline
8a6
8 a superscript 6 baseline
8a8
To simplify the expression (-4a^4)(-2a^2), we can multiply the coefficients and add the exponents for the same base.
So, (-4)(-2) = 8, and (a^4)(a^2) = 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 3x3y−412x7y4.(1 point)
Responses
4x4y8
4 x superscript 4 baseline y superscript 8 baseline
312x4y8
Start Fraction 3 over 12 x superscript 4 baseline y superscript 8 baseline
14x4y8
Start Fraction 1 over 4 x superscript 4 baseline y superscript 8 baseline
14x12
Start Fraction 1 over 4 x superscript 12 baseline
To generate an equivalent algebraic expression, we can use the property that when raising a monomial to a negative exponent, we can rewrite it as the reciprocal of the base raised to the positive exponent.
Thus, 3x^3y^(-4) * 12x^7y^4 is equivalent to (3/12)x^3/(y^4)(x^7y^4).
Simplifying further, we have (1/4)x^(3-7)y^(-4+4) = (1/4)x^(-4).
Therefore, an equivalent algebraic expression is (1/4)x^(-4).
Apply the properties of integer exponents to simplify the algebraic expression (2xy3)4⋅(x2y)3.(1 point)
Responses
x10y15
x superscript 10 baseline y superscript 15 baseline
32x10y11
32 x superscript 10 baseline y superscript 11 baseline
16x25
16 x superscript 25 baseline
16x10y15
To simplify the expression, (2xy^3)^4 · (x^2y)^3, we can apply the properties of exponents. We raise each base to the power outside the parentheses and multiply the exponents inside the parentheses.
For the first term, (2xy^3)^4, we have (2^4)(x^4)(y^3*4) = 16x^4y^12.
For the second term, (x^2y)^3, we have (x^2*3)(y^3) = x^6y^3.
Now, we multiply the two simplified terms together: 16x^4y^12 * x^6y^3 = 16x^(4+6)y^(12+3) = 16x^10y^15.
Therefore, the simplified expression is 16x^10y^15.
Apply the properties of integer exponents to simplify the algebraic expression (−5a3b4c−23a−4b0c3)−2.(1 point)
Responses
c10a14b8
Start Fraction c superscript 10 baseline over a superscript 14 baseline b superscript 8 baseline End Fraction
−5c103a14b8
Start Fraction negative 5 c superscript 10 baseline over 3 a superscript 14 baseline b superscript 8 baseline End Fraction
925a12
Start Fraction 9 over 25 a superscript 12 baseline End Fraction
9c1025a14b8
To simplify the expression, we can apply the properties of exponents. When raising a power to a negative exponent, we can rewrite it as the reciprocal of the base raised to the positive exponent.
First, let's simplify the expression inside the parentheses.
(-5a^3b^4c^-2)(a^-4b^0c^3) = (-5a^(3-4)b^(4+0)c^(-2+3)) = (-5a^-1b^4c^1) = -5(a^-1)(b^4)(c^1) = -5(1/a)(b^4)(c).
Now, let's raise the expression to the power -2.
(-5(a^-1)(b^4)(c))^(-2) = (-5)^(-2)((a^-1)^(-2))((b^4)^(-2))((c)^(-2))
Now, when raising a power to a negative exponent, we can rewrite it in fraction form.
(-5)^(-2)((a^-1)^(-2))((b^4)^(-2))((c)^(-2)) = (1/(-5)^2)((1/a)^(-2))((1/b^4)^(-2))(1/c^2) = (1/25)(a^(-2))(b^(-8))(1/c^2) = (1/25)(1/a^2)(1/b^8)(1/c^2) = c^(-2)/25a^2b^8
So, the simplified algebraic expression is c^(-2)/25a^2b^8.