The boundary line shown is
$2x+3y=6$ . Write the inequality shown by the graph.
The line
$2x+3y=6$ is the boundary line. On one side of the line are the points with
$2x+3y>6$ and on the other side of the line are the points with
$2x+3y<6$ .
Let’s test the point
$\left(0,0\right)$ and see which inequality describes its side of the boundary line.
What if the boundary line goes through the origin? Then we won’t be able to use
$\left(0,0\right)$ as a test point. No problem—we’ll just choose some other point that is not on the boundary line.
Graph the linear inequality
$y\le \mathrm{-4}x$ .
Solution
First we graph the boundary line
$y=\mathrm{-4}x$ . It is in slope–intercept form, with
$m=\mathrm{-4}\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}b=0$ . The inequality is
$\le $ so we draw a solid line.
Now, we need a test point. We can see that the point
$\left(1,0\right)$ is not on the boundary line.
Is
$\left(1,0\right)$ a solution of
$y\le \mathrm{-4}x$ ?
The point
$\left(1,0\right)$ is not a solution to
$y\le \mathrm{-4}x$ , so we shade in the opposite side of the boundary line. See
[link] .
Some linear inequalities have only one variable. They may have an
x but no
y , or a
y but no
x . In these cases, the boundary line will be either a vertical or a horizontal line. Do you remember?
Washing his dad’s car alone, eight-year-old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour. How long does it take the Levi’s dad to wash the car by himself?
Ethan and Leo start riding their bikes at the opposite ends of a 65-mile bike path. After Ethan has ridden 1.5 hours and Leo has ridden 2 hours, they meet on the path. Ethan’s speed is 6 miles per hour faster than Leo’s speed. Find the speed of the two bikers.
Nathan walked on an asphalt pathway for 12 miles. He walked the 12 miles back to his car on a gravel road through the forest. On the asphalt he walked 2 miles per hour faster than on the gravel. The walk on the gravel took one hour longer than the walk on the asphalt. How fast did he walk on the gravel?
Mckenzie
Nancy took a 3 hour drive. She went 50 miles before she got caught in a storm. Then she drove 68 miles at 9 mph less than she had driven when the weather was good. What was her speed driving in the storm?
Mr Hernaez runs his car at a regular speed of 50 kph and Mr Ranola at 36 kph. They started at the same place at 5:30 am and took opposite directions. At what time were they 129 km apart?
Melody wants to sell bags of mixed candy at her lemonade stand. She will mix chocolate pieces that cost $4.89 per bag with peanut butter pieces that cost $3.79 per bag to get a total of twenty-five bags of mixed candy. Melody wants the bags of mixed candy to cost her $4.23 a bag to make. How many bags of chocolate pieces and how many bags of peanut butter pieces should she use?
enrique borrowed $23,500 to buy a car he pays his uncle 2% interest on the $4,500 he borrowed from him and he pays the bank 11.5% interest on the rest. what average interest rate does he pay on the total $23,500
Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 square feet of tiles. She will use basic tiles that cost $8 per square foot and decorator tiles that cost $20 per square foot. How many square feet of each tile should she use so that the overall cost of the backsplash will be $10 per square foot?
The equation P=28+2.54w models the relation between the amount of Randy’s monthly water bill payment, P, in dollars, and the number of units of water, w, used. Find the payment for a month when Randy used 15 units of water.
From Google: The quadratic formula, , is used in algebra to solve quadratic equations (polynomial equations of the second degree). The general form of a quadratic equation is , where x represents a variable, and a, b, and c are constants, with . A quadratic equation has two solutions, called roots.
w = 10.15
You add 2.6 to both sides and then solve for w (-2.6 zeros out on the left and leaves you with w= 7.55 + 2.6)
Korin
Nataly is considering two job offers. The first job would pay her $83,000 per year. The second would pay her $66,500 plus 15% of her total sales. What would her total sales need to be for her salary on the second offer be higher than the first?
Estelle is making 30 pounds of fruit salad from strawberries and blueberries. Strawberries cost $1.80 per pound, and blueberries cost $4.50 per pound. If Estelle wants the fruit salad to cost her $2.52 per pound, how many pounds of each berry should she use?
$1.38 worth of strawberries + $1.14 worth of blueberries which= $2.52
Leitha
how
Zaione
is it right😊
Leitha
lol maybe
Robinson
8 pound of blueberries and 22 pounds of strawberries
Melissa
8 pounds x 4.5 = 36
22 pounds x 1.80 = 39.60
36 + 39.60 = 75.60
75.60 / 30 = average 2.52 per pound
Melissa
8 pounds x 4.5 equal 36
22 pounds x 1.80 equal 39.60
36 + 39.60 equal 75.60
75.60 / 30 equal average 2.52 per pound
Melissa
hmmmm...... ?
Robinson
8 pounds x 4.5 = 36
22 pounds x 1.80 = 39.60
36 + 39.60 = 75.60
75.60 / 30 = average 2.52 per pound
Melissa
The question asks how many pounds of each in order for her to have an average cost of $2.52. She needs 30 lb in all so 30 pounds times $2.52 equals $75.60. that's how much money she is spending on the fruit. That means she would need 8 pounds of blueberries and 22 lbs of strawberries to equal 75.60