Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If (20 y+5)(4y-30)=80y^(2)+by-150 for all values of y where b is a constant, then which of the following is the value of b ? Choose 1 answer: (A) -580 (B) -40 (C) 0 (D) 620

If (20y+5)(4y−30)=80y2+by−150(20y+5)(4y-30)=80y^{2}+by-150 for all values of yy where bb is a constant, then which of the following is the value of bb?\newlineChoose 11 answer:\newline(A) −580-580\newline(B) −40-40\newline(C) 00\newline(D) 620620

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 8right chevron icon
Identify equivalent linear expressions: word problemsright chevron icon

Full solution

Q. If (20y+5)(4y−30)=80y2+by−150(20y+5)(4y-30)=80y^{2}+by-150 for all values of yy where bb is a constant, then which of the following is the value of bb?\newlineChoose 11 answer:\newline(A) −580-580\newline(B) −40-40\newline(C) 00\newline(D) 620620
  1. Expand Equation: Expand the left side of the equation using the distributive property (FOIL method). \newline(20y+5)(4y−30)=20y(4y)+20y(−30)+5(4y)−5(30)(20y+5)(4y-30) = 20y(4y) + 20y(-30) + 5(4y) - 5(30)
  2. Simplify Expanded Form: Simplify the expanded form. 80y2−600y+20y−15080y^2 - 600y + 20y - 150
  3. Combine Like Terms: Combine like terms. 80y2−580y−15080y^2 - 580y - 150
  4. Compare with Right Side: Compare the simplified form with the right side of the given equation.\newline80y2−580y−150=80y2+by−15080y^2 - 580y - 150 = 80y^2 + by - 150
  5. Match Coefficients: Match the coefficients of the corresponding terms to find the value of bb.−580y=by-580y = by
  6. Conclude Value of b: Conclude that b=−580b = -580.

More problems from Identify equivalent linear expressions: word problems

Question
Simplify the expression:\newline7z2+3z27z^2 + 3z^2 \newline ______
Get tutor helpright-arrow

Posted 7 months ago

Question
Simplify the expression:\newline10f+8f−9f−6f10f + 8f - 9f - 6f\newline____
Get tutor helpright-arrow

Posted 7 months ago

Question
Subtract.\newline(3h+6)−(3h+2)(3h + 6) - (3h + 2)\newline____
Get tutor helpright-arrow

Posted 7 months ago

Question
Simplify the expression:\newline2p−p2p - p \newline______
Get tutor helpright-arrow

Posted 8 months ago

Question
A school charges $6\$6 per ticket to a dance. They spend $300\$300 on music and decorations. The expression 6n−3006n-300 describes the amount of profit the school makes from the dance if nn students buy tickets. What does 6n6n represent in this context?\newlineChoices:\newline(A)The amount of money the school charges for all `\n` tickets\newline(B)The amount of money the school spends on the dance\newline(C)The number of students who buy tickets\newline(D)The profit the school earns per ticket
Get tutor helpright-arrow

Posted 8 months ago

Question
Which is equal to cos⁡60∘ \cos 60^\circ ? \newlineChoices:\newline(A) sin⁡30∘ \sin 30^\circ \newline(B) sin⁡60∘ \sin 60^\circ \newline(C) cos⁡30∘ \cos 30^\circ \newline(D) cos⁡60∘ \cos 60^\circ
Get tutor helpright-arrow

Posted 9 months ago

Question
Which is equal to sin⁡45∘\sin 45^\circ? \newlineChoices:\newline(A) cos⁡45∘\cos 45^\circ\newline(B) cos⁡55∘\cos 55^\circ\newline(C) sin⁡55∘\sin 55^\circ\newline(D) sin⁡35∘\sin 35^\circ
Get tutor helpright-arrow

Posted 7 months ago

Question
Which is equal to cos⁡75∘\cos 75^\circ? \newlineChoices:\newline(A) sin⁡15∘\sin 15^\circ\newline(B) sin⁡75∘\sin 75^\circ\newline(C) cos⁡15∘\cos 15^\circ\newline(D) cos⁡25∘\cos 25^\circ
Get tutor helpright-arrow

Posted 7 months ago

Question
Which is equal to sin⁡30∘ \sin 30^\circ ? \newlineChoices:\newline(A) cos⁡60∘ \cos 60^\circ \newline(B) cos⁡30∘ \cos 30^\circ \newline(C) sin⁡60∘ \sin 60^\circ \newline(D) sin⁡30∘ \sin 30^\circ
Get tutor helpright-arrow

Posted 7 months ago

Question
Which is equal to cos⁡45∘ \cos 45^\circ ? \newlineChoices:\newline(A) sin⁡45∘ \sin 45^\circ \newline(B) sin⁡55∘ \sin 55^\circ \newline(C) cos⁡55∘ \cos 55^\circ \newline(D) cos⁡35∘ \cos 35^\circ
Get tutor helpright-arrow

Posted 7 months ago

View all (34)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant