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:

Bjorn is making aush, and he does not have enough of all the ingredients. He decides to make (5)/(6) of a whole recipe, which means he uses 1(1)/(4)L of water. How much water is in a whole recipe? L

Bjorn is making aush, and he does not have enough of all the ingredients. He decides to make 56 \frac{5}{6} of a whole recipe, which means he uses 114 L 1 \frac{1}{4} \mathrm{~L} of water.\newlineHow much water is in a whole recipe?\newlineL

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Interpret parts of quadratic expressions: word problemsright chevron icon

Full solution

Q. Bjorn is making aush, and he does not have enough of all the ingredients. He decides to make 56 \frac{5}{6} of a whole recipe, which means he uses 114 L 1 \frac{1}{4} \mathrm{~L} of water.\newlineHow much water is in a whole recipe?\newlineL
  1. Convert to Improper Fraction: Bjorn uses 1(14)L1\left(\frac{1}{4}\right)L of water for (56)\left(\frac{5}{6}\right) of the recipe. We need to find out how much water is needed for the whole recipe. We can set up a proportion to solve for the total amount of water needed.
  2. Set Up Proportion: First, we convert the mixed number 1(14)L1\left(\frac{1}{4}\right)L to an improper fraction. 1(14)L1\left(\frac{1}{4}\right)L is the same as (54)L\left(\frac{5}{4}\right)L because 1L1L is the same as (44)L\left(\frac{4}{4}\right)L, and we add (14)L\left(\frac{1}{4}\right)L to it.\newlineCalculation: $\(1\)L + \left(\frac{\(1\)}{\(4\)}\right)L = \left(\frac{\(4\)}{\(4\)}\right)L + \left(\frac{\(1\)}{\(4\)}\right)L = \left(\frac{\(5\)}{\(4\)}\right)L
  3. Cross-Multiply: Now we set up the proportion. If \((\frac{5}{6})\) of the recipe requires \((\frac{5}{4})L\) of water, then the whole recipe (which is \(1\) or \((\frac{6}{6})\) of the recipe) requires \(X\) liters of water.\(\newline\)Proportion: \(\frac{(\frac{5}{6}) \text{ recipe}}{(\frac{5}{4})L} = \frac{(\frac{6}{6}) \text{ recipe}}{X L}\)
  4. Simplify Equation: We can solve for \(X\) by cross-multiplying.\(\frac{5}{6} \times X = \frac{6}{6} \times \frac{5}{4}\)
  5. Divide by Reciprocal: Simplify the equation.\(\newline\)\(X = \left(\frac{6}{6}\right) \times \left(\frac{5}{4}\right) / \left(\frac{5}{6}\right)\)
  6. Cancel Common Factors: Since \((\frac{6}{6})\) is equal to \(1\), the equation simplifies to: \(X = \frac{\frac{5}{4}}{\frac{5}{6}}\)
  7. Multiply Fractions: To divide by a fraction, we multiply by its reciprocal. \(X = \frac{5}{4} \times \frac{6}{5}\)
  8. Simplify Fraction: We can cancel out the common factors of \(5\) in the numerator and denominator.\[X = \left(\frac{1}{4}\right) * \left(\frac{6}{1}\right)\]
  9. Convert to Mixed Number: Now we multiply the remaining fractions. \(X = \frac{6}{4}\)
  10. Convert to Mixed Number: Now we multiply the remaining fractions.\(\newline\)\(X = \frac{6}{4}\)Simplify the fraction \(\frac{6}{4}\) by dividing both the numerator and the denominator by their greatest common divisor, which is \(2\).\(\newline\)\(X = \frac{6}{4} / 2\)\(\newline\)\(X = \frac{3}{2}\)
  11. Convert to Mixed Number: Now we multiply the remaining fractions. \(\newline\)\(X = \frac{6}{4}\) Simplify the fraction \(\frac{6}{4}\) by dividing both the numerator and the denominator by their greatest common divisor, which is \(2\). \(\newline\)\(X = \frac{6}{4} / 2\) \(\newline\)\(X = \frac{3}{2}\) Convert the improper fraction \(\frac{3}{2}\) back to a mixed number to find the total liters of water needed for the whole recipe. \(\newline\)\(X = 1\frac{1}{2}\)L

More problems from Interpret parts of quadratic expressions: word problems

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 8 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 7 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 5 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 5 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 5 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 5 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 5 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 4 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 4 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 5 months ago

View all (97)

Related topics

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