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Bug Institute: 3-LS1-1, 4-LS1-2
Energy Sources and the Environment: 4-ESS3-1, 5-ESS3-1
Examining Matter: 5-PS1-3, 5-PS1-4
Objects Attracted by Magnets: 3-PS2-3, 5-PS2-1
Rock Layers: 3-LS4-1, 4-ESS1-1
School Garden: 5-LS1-1, 5-LS2-1
Simple Cardboard Invention May Help Billions: 4-ESS3-1, 5-ESS3-1
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Asteroid Belt: MS-PS2-1, MS-PS2-4
Cells Under a Microscope: MS-LS1-1, MS-LS1-3
Coral Reefs: MS-LS3-2, MS-LS4-4
Effect of Temperature on Water and Table Sugar: MS-PS1-1, MS-PS1-4
Groundwater: MS-ESS2-4, MS-ESS3-1
Maglev Trains: MS-PS2-3, MS-PS2-5
Moon Phase Activity: MS-ESS1-1, MS-ESS1-2, MS-ESS1-3
Observations of Plate Motion: MS-ESS1-4, MS-ESS2-2, MS-ESS2-3
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2025 Released Operational Items
Content CRs with Student Responses & Annotations
All MCAP Algebra I 2024 Released Items
Arithmetic with Polynomials and Rational Expressions (Algebra I)
Creating Equations (Algebra I)
Functions - Building Functions (Algebra I)
Functions - Interpreting Functions (Algebra I)
Functions - Linear, Quadratic, and Exponential Models (Algebra I)
Reasoning with Equations and Inequalities (Algebra I)
Seeing Structure in Expressions (Algebra I)
All MCAP Algebra II 2024 Released Items
Arithmetic with Polynomials & Rational Expressions (Algebra II)
Building Functions (Algebra II)
Interpreting Categorical and Quantitative Data (Algebra II)
Interpreting Functions (Algebra II)
Linear, Quadratic, & Exponential Models (Algebra II)
Reasoning with Equations and Inequalities (Algebra II)
Seeing Structure in Expressions (Algebra II)
The Complex Number System (Algebra II)
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Arctic Ice: HS-ESS2-2, HS-ESS3-5
Calvert Cliffs: HS-LS4-1, HS-ESS2-7
Earthquake Energy: HS-PS4-1, HS-ESS2-2
Fukushima Butterflies: HS-LS1-1, HS-LS3-2
Global Cooling: HS-ESS2-4, HS-PS3-3
Honeybees and Almond Trees: HS-LS2-2, HS-LS2-6
Ladybird Beetle: HS-LS4-2, HS-LS4-5
Correct Answernegative 12.
$$ -12 $$
Explanation
To find the value of b in the given problem, we'll start by expanding and simplifying the expression 2 x plus open parenthesis x minus 7 close parenthesis squared \( 2x+(x-7)^2 \) and then compare it to the expression x squared plus b x plus 49. \( x^2 + bx + 49. \) 2 x plus open parenthesis x minus 7 close parenthesis, squared
$$ 2x + (x - 7)^2 $$
equals 2 x plus x squared minus 14 x plus 49.$$ = 2x + x^2 - 14x + 49 $$
equals x squared minus 12 x plus 49.$$ = x^2 - 12x + 49 $$
This expanded expression can be compared with x squared plus b x plus 49 \( x^2 + bx + 49 \) from the problem, and we see that the coefficient of x in both expressions must be the same. The value of b is negative 12. \( -12. \)
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This is a fill in the blank question that allows you to enter only numbers.
The expression is equivalent to for all values of .
What is the value of ?
Enter your answer in the space provided.