Question
5. At what point does the graph of \( 4 x-6 y=-1 \) intersect the \( x \)-axis? (A) 4 (B) 6 (C) \( \frac{2}{3} \) (D) \( \frac{1}{6} \) (E) \( -\frac{1}{4} \) 6. If \( 4 x^{3}=-64 \), then \( x= \) (A) -1 (B) 1 (C) \( -2 \sqrt[3]{2} \) (D) \( 2 \sqrt[3]{2} \) (E) 4
Ask by Harper Mcdonald. in the United Arab Emirates
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
**第5题答案：**
当 \( y = 0 \) 时，\( x = -\frac{1}{4} \)。
**答案：E**
**第6题答案：**
\( x = -2 \sqrt[3]{2} \)。
**答案：C**
Solution
**第5题解答：**
要找到 \( 4x - 6y = -1 \) 与 \( x \)-轴的交点，设 \( y = 0 \)。
\[
4x - 6(0) = -1 \implies 4x = -1 \implies x = -\frac{1}{4}
\]
因此，正确答案是 **（E）\(-\frac{1}{4}\)**。
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**第6题解答：**
给定方程 \( 4x^3 = -64 \)，求 \( x \)。
首先，除以4：
\[
x^3 = -16
\]
取立方根：
\[
x = \sqrt[3]{-16} = -\sqrt[3]{16} = -2\sqrt[3]{2}
\]
因此，正确答案是 **（C）\(-2 \sqrt[3]{2}\)**。
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find the intersection of the graph \( 4x - 6y = -1 \) with the \( x \)-axis, we set \( y = 0 \). Plugging in, we get \( 4x - 6(0) = -1 \), which simplifies to \( 4x = -1 \). Thus, \( x = -\frac{1}{4} \) is the point of intersection. So, the answer is (E) \( -\frac{1}{4} \). For the equation \( 4x^{3} = -64 \), we can isolate \( x^{3} \) by dividing both sides by 4, resulting in \( x^{3} = -16 \). Taking the cube root of both sides gives us \( x = -2 \sqrt[3]{2} \). Therefore, the answer is (C) \( -2 \sqrt[3]{2} \).
