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:

{:[7y^(2)=50 x-150],[y=(3-x)/(2)]:} If (x_(1),y_(1)) and (x_(2),y_(2)) are distinct solutions to the system of equations shown, what is the product of the y_(1) and y_(2) ? ◻

7y2=50x−1507y^2 = 50x-150\newliney=y =3−x2\frac{3-x}{2}\newlineIf x1,y1x_{1},y_{1} and x2,y2x_{2},y_{2} are distinct solutions to the system of equations shown, what is the product of the y1y_{1} and y2y_{2} ?\newline◻

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Write a quadratic function from its x-intercepts and another pointright chevron icon

Full solution

Q. 7y2=50x−1507y^2 = 50x-150\newliney=y =3−x2\frac{3-x}{2}\newlineIf x1,y1x_{1},y_{1} and x2,y2x_{2},y_{2} are distinct solutions to the system of equations shown, what is the product of the y1y_{1} and y2y_{2} ?\newline◻
  1. Substitute and solve for x: Substitute yy from the second equation into the first equation to eliminate yy and solve for xx.7y2=50x−1507y^2 = 50x - 150 becomes 7((3−x)/2)2=50x−1507((3-x)/2)^2 = 50x - 150.
  2. Expand and simplify: Expand and simplify the equation. 7(9−6x+x2)4=50x−150\frac{7(9 - 6x + x^2)}{4} = 50x - 150.
  3. Clear the fraction: Multiply both sides by 44 to clear the fraction.7(9−6x+x2)=200x−6007(9 - 6x + x^2) = 200x - 600.
  4. Distribute and simplify: Distribute the 77 on the left side.63−42x+7x2=200x−60063 - 42x + 7x^2 = 200x - 600.
  5. Move terms and set to zero: Move all terms to one side to set the equation to zero.\newline7x2−42x−200x+63+600=07x^2 - 42x - 200x + 63 + 600 = 0.
  6. Combine like terms: Combine like terms. 7x2−242x+663=07x^2 - 242x + 663 = 0.
  7. Factor the quadratic equation: Factor the quadratic equation.\newline(7x−221)(x−3)=0(7x - 221)(x - 3) = 0.

More problems from Write a quadratic function from its x-intercepts and another point

Question
Solve by completing the square.\newlinem2−10m−29=0m^2 - 10m - 29 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`m` = ____ or `m` = _____
Get tutor helpright-arrow

Posted 2 months ago

Question
Find g(x) g(x) , where g(x) g(x) is the translation 5 5 units up of f(x)=x2 f(x)=x^2 .\newlineWrite your answer in the form a(x–h)2+k a(x–h)^2+k , where a a , h h , and k k are integers.\newlineg(x)= g(x)= ____
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the range of this quadratic function?\newliney=x2−4x+4y = x^2 - 4x + 4\newlineChoices:\newline{y∣y≥2}\left\{y \mid y \geq 2\right\}\newline{y∣y≤0}\left\{y \mid y \leq 0\right\}\newline{y∣y≥0}\left\{y \mid y \geq 0\right\}\newlineall real numbers\text{all real numbers}
Get tutor helpright-arrow

Posted 2 months ago

Question
Write the equation of the parabola that passes through the points (1,0)(1,0), (2,0)(2,0), and (3,–16)(3,\text{–}16). Write your answer in the form y=a(x–p)(x–q)y = a(x – p)(x – q), where aa, pp, and qq are integers, decimals, or simplified fractions.\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinef2+8f+_____f^2 + 8f + \_\_\_\_\_
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve for h h .\newlineh2+39h=0 h^2 + 39h = 0 \newline\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlineh= h = ____\newline
Get tutor helpright-arrow

Posted 2 months ago

Question
Write a quadratic function with zeros −9-9 and −7-7.\newlineWrite your answer using the variable xx and in standard form with a leading coefficient of 11.\newlinef(x)=_____f(x) = \_\_\_\_\_
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the equation of the axis of symmetry for the parabola y=x2y = x^2. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline‾\underline{\hspace{3cm}}
Get tutor helpright-arrow

Posted 3 months ago

Question
Find g(x)g(x), where g(x)g(x) is the translation 88 units up of f(x)=x2f(x) = x^2.\newlineWrite your answer in the form a(x–h)2+ka(x – h)^2 + k, where aa, hh, and kk are integers.\newlineg(x)=g(x) = ______\newline
Get tutor helpright-arrow

Posted 3 months ago

Question
Solve for xx.\newlinex2=1x^2 = 1\newline\newlineWrite your answer in simplified, rationalized form.\newlinex=x = ______ or x=x = ______\newline
Get tutor helpright-arrow

Posted 3 months ago

View all (161)