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:

Solve the system of equations.\newliney=x2+40x−20y = x^2 + 40x - 20\newliney=40x−4y = 40x - 4\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Solve a system of linear and quadratic equationsright chevron icon

Full solution

Q. Solve the system of equations.\newliney=x2+40x−20y = x^2 + 40x - 20\newliney=40x−4y = 40x - 4\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Set Equations Equal: We have the system of equations:\newliney=x2+40x−20y = x^2 + 40x - 20\newliney=40x−4y = 40x - 4\newlineTo find the intersection points, set the two equations equal to each other.\newlinex2+40x−20=40x−4x^2 + 40x - 20 = 40x - 4
  2. Simplify and Rearrange: Simplify the equation by subtracting 40x40x from both sides and adding 44 to both sides.\newlinex2+40x−20−40x+4=40x−4−40x+4x^2 + 40x - 20 - 40x + 4 = 40x - 4 - 40x + 4\newlinex2−16=0x^2 - 16 = 0
  3. Solve Quadratic Equation: Solve the quadratic equation for xx.x2−16=0x^2 - 16 = 0Factor the left side of the equation.(x−4)(x+4)=0(x - 4)(x + 4) = 0
  4. Factor and Solve: Set each factor equal to zero and solve for xx.(x−4)=0 or (x+4)=0(x - 4) = 0 \text{ or } (x + 4) = 0x=4 or x=−4x = 4 \text{ or } x = -4
  5. Find y-Values: Find the corresponding y-values for each x-value by substituting back into either of the original equations. We'll use y=40x−4y = 40x - 4.\newlineFor x=4x = 4:\newliney=40(4)−4y = 40(4) - 4\newliney=160−4y = 160 - 4\newliney=156y = 156
  6. Coordinate Calculation: For x=−4x = -4:y=40(−4)−4y = 40(-4) - 4y=−160−4y = -160 - 4y=−164y = -164
  7. Coordinate Calculation: For x=−4x = -4:y=40(−4)−4y = 40(-4) - 4y=−160−4y = -160 - 4y=−164y = -164Write the coordinates in exact form.First Coordinate:(4,156)\text{First Coordinate}: (4, 156)Second Coordinate:(−4,−164)\text{Second Coordinate}: (-4, -164)

More problems from Solve a system of linear and quadratic equations

Question
The function h(t)=−16t2+144h(t) = -16t^{2} + 144 represents the height, h(t)h(t), in feet, of an object from the ground at tt seconds after it is dropped. A realistic domain (for time) for this function is:\newline(A)(A) −3≤t≤3-3 \leq t \leq 3\newline(B)(B) 0≤t≤30 \leq t \leq 3\newline(C)(C) 0≤h≤1440 \leq h \leq 144\newline(D)(D) all real numbers
Get tutor helpright-arrow

Posted 2 months ago

Question
Деление с остатком
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve the system of equations.\newliney=−36x+26y = -36x + 26\newliney=x2−46x−13y = x^2 - 46x - 13\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve the system of equations.\newliney=32x2+32x−23y = 32x^2 + 32x - 23\newliney=32x+9y = 32x + 9\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve the system of equations.\newliney=x2+12x−41y = x^2 + 12x - 41\newliney=17x+9y = 17x + 9\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve the system of equations.\newliney=x2−43x−14y = x^2 - 43x - 14\newliney=−45x+34y = -45x + 34\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve the system of equations.\newliney=14x−26y = 14x - 26\newliney=2x2+14x−34y = 2x^2 + 14x - 34\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the discriminant.\newline3u2−8u+4=03u^2 - 8u + 4 = 0
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the discriminant.\newline7w2+5w+8=07w^2 + 5w + 8 = 0
Get tutor helpright-arrow

Posted 2 months ago

Question
Answer the questions below about the quadratic function.\newlinef(x)=−3x2+6x−5 f(x)=-3 x^{2}+6 x-5 \newlineDoes the function have a minimum or maximum value?\newlineMinimum\newlineMaximum\newlineWhat is the function's minimum or maximum value?\newline□ \square \newlineWhere does the minimum or maximum value occur?\newlinex= x= \newline□ \square
Get tutor helpright-arrow

Posted 5 hours ago

View all (6)