Question

3 fill in the blank 1 point round 3.9467 to the nearest hundredths place answer type your answer... 4 fill in the blank 1 point solve. $-29 = 5(1 - 6x) + 3(7 + 5x)$ answer x= type your answer...

Explanation:

Question 3

Step1: Identify the hundredths place

In the number \( 3.9467 \), the digit in the hundredths place is \( 4 \), and the digit to the right (thousandths place) is \( 6 \).

Step2: Apply rounding rule

Since \( 6 \geq 5 \), we round up the hundredths place digit. So \( 4 \) becomes \( 4 + 1 = 5 \), and the digits after the hundredths place are dropped.

Step1: Expand the equation

First, expand \( 5(1 - 6x) + 3(7 + 5x) \). Using the distributive property (\( a(b + c)=ab + ac \)):
\( 5(1 - 6x)=5\times1 - 5\times6x = 5 - 30x \)
\( 3(7 + 5x)=3\times7 + 3\times5x = 21 + 15x \)
So the equation becomes \( -29 = 5 - 30x + 21 + 15x \).

Step2: Combine like terms

Combine the constant terms (\( 5 + 21 = 26 \)) and the \( x \)-terms (\( -30x + 15x=-15x \)):
\( -29 = 26 - 15x \)

Step3: Isolate the \( x \)-term

Subtract \( 26 \) from both sides:
\( -29 - 26 = -15x \)
\( -55 = -15x \)

Step4: Solve for \( x \)

Divide both sides by \( -15 \):
\( x=\frac{-55}{-15}=\frac{11}{3}\approx 3.666\cdots \) (or as an improper fraction \( \frac{11}{3} \), or a mixed number \( 3\frac{2}{3} \))

Answer:

\( 3.95 \)

Question 4