To solve the inequality 18-6x > -12, first subtract 18 from both sides:
-6x > -30
Next, divide both sides by -6, remembering to flip the inequality sign when dividing by a negative number:
x < 5
So the solution to the inequality is x < 5.
We can represent this solution on the number line by plotting an open circle at 5 (since it is not included in the solution) and shading to the left to represent all values less than 5.
Number line:
-----o-->0-----o-->5-----o-->10-----o-->15-----o-->20
Shaded region: o----->5
Solve the given inequality and represent its solution on the number line.
18-6x>-12
9 answers
Clinton and Stacy decided to travel from their home near Austin, Texas, to Yellowstone National Park in their RV.
The distance from their home to Yellowstone National Park is 1,701 miles.
On average the RV gets 10.5 miles per gallon.
On average the cost of a gallon of gasoline is $3.60.
Based on the average gas mileage of their RV and the average cost of gasoline, how much will Clinton and Stacy spend on gasoline for the round trip to Yellowstone National Park and back home?
Responses
A $583.20$583.20
B $2,480.63$2,480.63
C $1,166.40$1,166.40
D $64,297.80
The distance from their home to Yellowstone National Park is 1,701 miles.
On average the RV gets 10.5 miles per gallon.
On average the cost of a gallon of gasoline is $3.60.
Based on the average gas mileage of their RV and the average cost of gasoline, how much will Clinton and Stacy spend on gasoline for the round trip to Yellowstone National Park and back home?
Responses
A $583.20$583.20
B $2,480.63$2,480.63
C $1,166.40$1,166.40
D $64,297.80
To calculate how much Clinton and Stacy will spend on gasoline for the round trip to Yellowstone National Park and back home, we need to first calculate how many gallons of gas they will need for the entire trip.
The round trip is 3402 miles (1701 miles to Yellowstone and 1701 miles back home).
Gas mileage of the RV is 10.5 miles per gallon, so the total gallons needed for the round trip is 3402 miles / 10.5 miles per gallon = 324 gallons.
Given that the cost of a gallon of gasoline is $3.60, the total cost of gasoline for the round trip is 324 gallons x $3.60 per gallon = $1166.40.
Therefore, the correct response is: C $1,166.40
The round trip is 3402 miles (1701 miles to Yellowstone and 1701 miles back home).
Gas mileage of the RV is 10.5 miles per gallon, so the total gallons needed for the round trip is 3402 miles / 10.5 miles per gallon = 324 gallons.
Given that the cost of a gallon of gasoline is $3.60, the total cost of gasoline for the round trip is 324 gallons x $3.60 per gallon = $1166.40.
Therefore, the correct response is: C $1,166.40
Danielle likes to purchase items at estate sales, clean them up, then resale them online for a profit. She recently purchased an antique dresser with a mirror at an estate sale, cleaned it up, and advertised it for 250% of her purchase price. Danielle sold the dresser for $255, which was 15% less than the advertised price.
To the nearest whole dollar, how much did Danielle purchase the antique dresser for and what was her initial advertised price?
Responses
A purchase price: $117, advertised price: $293purchase price: $117, advertised price: $293
B purchase price: $120, advertised price: $300purchase price: $120, advertised price: $300
C purchase price: $130, advertised price: $325purchase price: $130, advertised price: $325
D purchase price: $108, advertised price: $270
To the nearest whole dollar, how much did Danielle purchase the antique dresser for and what was her initial advertised price?
Responses
A purchase price: $117, advertised price: $293purchase price: $117, advertised price: $293
B purchase price: $120, advertised price: $300purchase price: $120, advertised price: $300
C purchase price: $130, advertised price: $325purchase price: $130, advertised price: $325
D purchase price: $108, advertised price: $270
Let the purchase price of the antique dresser be P.
Danielle advertised it for 250% of the purchase price, so the advertised price is 2.5P.
She sold it for 15% less than the advertised price, so she sold it for 85% of the advertised price.
It is given that she sold it for $255, so:
0.85 * 2.5P = $255
2.125P = $255
P = $255 / 2.125
P = $120
Therefore, Danielle purchased the antique dresser for $120.
The advertised price was 2.5 times the purchase price of the dresser, which is 2.5 * $120 = $300.
So, the correct response is B: purchase price: $120, advertised price: $300.
Danielle advertised it for 250% of the purchase price, so the advertised price is 2.5P.
She sold it for 15% less than the advertised price, so she sold it for 85% of the advertised price.
It is given that she sold it for $255, so:
0.85 * 2.5P = $255
2.125P = $255
P = $255 / 2.125
P = $120
Therefore, Danielle purchased the antique dresser for $120.
The advertised price was 2.5 times the purchase price of the dresser, which is 2.5 * $120 = $300.
So, the correct response is B: purchase price: $120, advertised price: $300.
Briona mixed up
pounds of homemade hot chocolate powder to give as gifts. She is going to put the hot chocolate powder in
-pound bags.
How many
-pound bags will Briona have?
bags
pounds of homemade hot chocolate powder to give as gifts. She is going to put the hot chocolate powder in
-pound bags.
How many
-pound bags will Briona have?
bags
To find out how many bags Briona will have, we need to divide the total amount of hot chocolate powder by the amount in each bag.
Let's represent the total amount of hot chocolate powder as "x" pounds and the capacity of each bag as "y" pounds.
So, she is going to put the hot chocolate powder in y-pound bags.
The number of y-pound bags she will have is given by x/y.
Therefore, Briona will have x/y bags of y-pound size.
Let's represent the total amount of hot chocolate powder as "x" pounds and the capacity of each bag as "y" pounds.
So, she is going to put the hot chocolate powder in y-pound bags.
The number of y-pound bags she will have is given by x/y.
Therefore, Briona will have x/y bags of y-pound size.
Rajindri, a physician assistant who works in an emergency room, earns $163 for every two hours that she works.
Which equation represents the relationship between
, the number of dollars Rajindri earns, and
, the amount of time Rajindri works, in hours?
Responses
A
d is equal to 163 t
B
d is equal to 81 point 5 0 t
C
d is equal to 163 plus t
D
Which equation represents the relationship between
, the number of dollars Rajindri earns, and
, the amount of time Rajindri works, in hours?
Responses
A
d is equal to 163 t
B
d is equal to 81 point 5 0 t
C
d is equal to 163 plus t
D
The number of dollars Rajindri earns, d, is directly proportional to the amount of time she works, t, in hours.
Given that she earns $163 for every two hours that she works, the equation representing this relationship is:
d = 163/2 * t
Simplifying this equation:
d = 81.50 * t
Therefore, the correct equation representing the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works in hours is:
B. d is equal to 81.50t
Given that she earns $163 for every two hours that she works, the equation representing this relationship is:
d = 163/2 * t
Simplifying this equation:
d = 81.50 * t
Therefore, the correct equation representing the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works in hours is:
B. d is equal to 81.50t
1 answer