Question

find the value of y that makes the equation true. y^2 - 5 = 4. what is the value of angle x in the figure below? (7.g.5) thursday 9.18.2025 you must show your work. no work = no credit. (7.rp.3) an ice - cream recipe requires 1/2 cup of sugar for every 1/2 gallon of how many cups of sugar are needed per gallon of milk?

Explanation:

Step1: Solve the equation for $y$

Add 5 to both sides of $y^{2}-5 = 4$. We get $y^{2}=4 + 5$, so $y^{2}=9$.

Step2: Find the value of $y$

Take the square - root of both sides. Since $y^{2}=9$, then $y=\pm\sqrt{9}$, so $y=\pm3$.

Step3: Solve for angle $x$

Vertical angles are equal. The angle vertical to the $51^{\circ}$ angle is $51^{\circ}$. The angle $x$ and the $51^{\circ}$ angle are complementary (they form a right - angle, $90^{\circ}$). So $x=90 - 51$, and $x = 39^{\circ}$.

Step4: Solve the ratio problem

If $\frac{1}{2}$ cup of sugar is required for every $\frac{1}{4}$ gallon of milk, to find the cups of sugar per gallon of milk, we set up a proportion. Let $s$ be the cups of sugar per gallon of milk. We have $\frac{\frac{1}{2}}{\frac{1}{4}}=\frac{s}{1}$. Cross - multiply: $\frac{1}{4}s=\frac{1}{2}\times1$. Then $s=\frac{1/2}{1/4}=\frac{1}{2}\times4 = 2$ cups of sugar per gallon of milk.

Answer:

$y=\pm3$
$x = 39^{\circ}$
2 cups of sugar per gallon of milk