Apply the distributive property to create an equivalent expression. 1/3 (3j + 6) =

Jose asks his friends to guess the higher of two grades he received on his math tests. He gives them two hints. The difference o

AlekseyPX

Answer : 96

x – y = 16 --------> equation 1

$\frac{1}{8} x +\frac{1}{2} y = 52$

x is the higher grade and y is the lower grade

We solve the first equation for y

x - y = 16

-y = 16 -x ( divide each term by -1)

y = -16 + x

Now substitute y in second equation

$\frac{1}{8} x +\frac{1}{2} ( -16 + x ) = 52$

$\frac{1}{8} x - 8 + \frac{1}{2} x = 52$

$\frac{1}{8} x + \frac{1}{2} x - 8 = 52$

Take common denominator to combine fractions

$\frac{1}{8} x + \frac{4}{8} x -8 = 52$

$\frac{5}{8} x - 8 = 52$

Add 8 on both sides

$\frac{5}{8} x = 60$

Multiply both sides by $\frac{8}{5}$

x = 96

We know x is the higher grade

96 is the higher grade of Jose’s two tests.

6 0

2 years ago

Read 2 more answers

On a recent road trip, Mr. Yost drove 210 miles in 3 1/2 hours. Find both the miles driven per hour and the hours driven per mil

amid [387]

Miles driven per hour is 60 miles per hour

Hours driven per mile is 0.01667 hours per mile

<em><u>Solution:</u></em>

Given that,

On a recent road trip, Mr. Yost drove 210 miles in 3 1/2 hours

Therefore,

Miles driven = 210 miles

$Time\ taken = 3\frac{1}{2}\ hour = \frac{7}{2} = 3.5\ hour$

To find: miles driven per hour and the hours driven per mile

<h3><u>Miles driven per hour</u></h3>

$\frac{miles}{hour} = \frac{210}{3.5}\\\\\frac{miles}{hour} = 60\ miles\ per\ hour$

<h3><u>Hours driven per mile</u></h3>

$\frac{hours}{miles} = \frac{3.5}{210}\\\\\frac{hours}{miles} = 0.01667\ hours\ per\ miles$

Thus both the miles driven per hour and the hours driven per mile are found

7 0

2 years ago

Line q will be graphed on the same grid. The only solution to the system of linear equations formed by lines n and q occurs when

bija089 [108]

Answer:

$f(x) = k(x - \frac{3}{2})$

Step-by-step explanation:

Line q will be graphed on the same grid. The only solution to the system of linear equations formed by lines n and q occurs when x = $\frac{3}{2}$ and y = 0.

Now, as x = $\frac{3}{2}$ is a solution of the equation, y = f(x) = 0, so, $(x - \frac{3}{2})$ will be a factor of the linear function y = f(x).

Therefore, we can write the possible equation for the line q will be

$f(x) = k(x - \frac{3}{2})$ . (Where k is any constant} (Answer)

8 0

2 years ago

Joanne is installing weatherstripping around a 30-in. × 25-in. control box. how much weatherstripping does she need, in inches a

GrogVix [38]

<span>The control boxâ€™s dimensions are 30 inches by 25 inches. Therefore, the perimeter of the box is 30 inches + 25 inches + 30 inches + 25 inches = 110 inches. There are 12 inches per foot. 12 goes into 110 nine times, with two inches left over. Therefore, 9 feet and 2 inches of weatherstripping is needed.</span>

7 0

2 years ago

Model Exponential Growth Question :A sample of bacteria is growing at a continuously compounding rate. The sample triples in 10

Iteru [2.4K]

Answer:

The number of bacteria $B$ after $d$ days is given by