What is the product of the binomials (4a – 1) and (2b + 3)?
Answers
The product of the binomials (4a – 1) and (2b + 3) is 8ab + 12a - 2b - 3 the answer is 8ab + 12a - 2b - 3.
What is polynomial?
Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
We have given two binomials (4a – 1) and (2b + 3)
The product of the two binomials is:
= (4a – 1)×(2b + 3)
After applying the distributive property:
= 4a×2b + 4a×3 -1×2b - 1×3
= 8ab + 12a - 2b - 3
As we know, the expression is the combination of constants and variables with mathematical operators.
The product of the two binomials is 8ab + 12a - 2b - 3 which is a expression having four terms.
Thus, the product of the binomials (4a – 1) and (2b + 3) is 8ab + 12a - 2b - 3 the answer is 8ab + 12a - 2b - 3.
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B.
5 and 7
C.
11 and 13
D.
143 and 145
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We know the square root of 9 is 3, and the square root of 16 is 4, so the square root of 12, which is between 9 and 16, must be between 3 and 4.
Answers
rate in seconds per foot=1 / (0.5 ft/s)=2 s/ ft.
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4xs-16 or 3x + 5 2 17
Answers
The solution of the compound inequality 4x ≤ -16 or 3x + 5 ≥ 17 is x ≤ -4 or x ≥ 4 and graphed in option (B).
What is inequality?
Essentially, comparing any two values shows whether one is smaller, greater, or equal to the value on the other side of the equation. Essentially, comparing any two values shows whether one is smaller, greater, or equal to the value on the other side of the equation.
Given the first inequality,
4x ≤ -16
Dividing 4 both sides
x ≤ -4
Second inequality,
3x + 5 ≥ 17
Subtract 5 on both sides
3x ≥ 12
Divide 3 both side
x ≥ 4
So,
x ≤ -4 or x ≥ 4
Hence "The solution of the compound inequality 4x ≤ -16 or 3x + 5 ≥ 17 is x ≤ -4 or x ≥ 4".
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Answer:
B
Step-by-step explanation:
Work out the difference between the bonus Akhtar gets and the bonus Karl gets.
Answers
Answer:
Akhtar gets £12 less than the bonus Karl gets
Step-by-step explanation:
20% of £70 is £14
so, £14 - £26 = -£12
in conclusion, Akhtar gets £12 less than the bonus Karl gets
Answer:
To find the difference between the bonus Akhtar gets and the bonus Karl gets, you can follow these steps:
Calculate Akhtar's bonus:
Akhtar's bonus is 20% of £70. To find this, multiply 20% (or 0.20 as a decimal) by £70:
Akhtar's bonus = 0.20 * £70 = £14
Calculate the difference between Akhtar's bonus and Karl's bonus:
Difference = Akhtar's bonus - Karl's bonus
Difference = £14 - £26
Now, subtract £26 from £14 to find the difference:
Difference = -£12
So, the difference between the bonus Akhtar gets and the bonus Karl gets is -£12. Since Akhtar's bonus is smaller than Karl's, the difference is negative, indicating that Karl receives a higher bonus than Akhtar.
Answers
(56% divided by 100 to get the percentage and will work for any percentage
Answer:
"Provide an example of a new theorem related to triangles and describe the steps as to how this theorem can be proven."
Answer:
"Explain how to prove one of the following properties of parallelograms: opposite sides are congruent, opposite angles are congruent, diagonals bisect each other"
Answer:
Answers
Answer: One possible way to answer your question is:
To connect the ideas of congruency and rigid motion, we can use the following definition: Two figures are congruent if and only if there exists one or more rigid motions that map one figure onto the other. Rigid motions are transformations that preserve the size and shape of a figure, such as reflections, rotations, and translations. Therefore, congruency means that two figures have the same size and shape, and can be superimposed by applying one or more rigid motions.
To prove congruency, we can use the following criteria: Two triangles are congruent if they satisfy one of the following conditions:
SSS (Side-Side-Side): All three pairs of corresponding sides are equal in length.
SAS (Side-Angle-Side): Two pairs of corresponding sides are equal in length, and the included angles are equal in measure.
ASA (Angle-Side-Angle): Two pairs of corresponding angles are equal in measure, and the included sides are equal in length.
AAS (Angle-Angle-Side): Two pairs of corresponding angles are equal in measure, and a pair of corresponding sides not included between the angles are equal in length.
HL (Hypotenuse-Leg): The hypotenuses and a pair of corresponding legs of two right triangles are equal in length.
To prove one of these conditions, we can use the properties of parallel lines, isosceles triangles, midpoints, bisectors, perpendiculars, etc. For example, to prove that opposite sides of a parallelogram are congruent, we can use the following steps:
Given a parallelogram ABCD, draw a diagonal AC.
By the alternate interior angles theorem, we have ∠BAC = ∠DCA and ∠BCA = ∠DAC.
By the reflexive property, we have AC = AC.
By the ASA criterion, we have ΔABC ≅ ΔCDA.
By the CPCTC4 (Corresponding Parts of Congruent Triangles are Congruent), we have AB = CD and BC = AD.
Therefore, opposite sides of a parallelogram are congruent.