Mariah spent $9.50 on 9 pounds of limes and pears. Limes cost $0.50 per pound and pears cost $1.50 per pound. Let l be the numbe
r of pounds of limes and let p be the number of pounds of pears. Which system of linear equations models the scenario?
l + p = 9.5 and 1.5l + 0.5p = 9
l + p = 9 and 0.5l + 1.5p = 9.5
l = p + 9 and 9.5l + 0.5p = 0.5
l + p = 9.5 and 1.5l + 0.5p = 9
l + p = 9 and 0.5l + 1.5p = 9.5
l = p + 9 and 9.5l + 0.5p = 0.5
1 answer:
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Answer:
see explanation
Step-by-step explanation:
I don't have graphing facilities but can give you the vertex and 1 other point.
Given a parabola in standard form
y = ax² + bx + c ( a ≠ 0 )
Then the x- coordinate of the vertex is
x = -
y = - x² - 2x + 8 ← is in standard form
with a = - 1 and b = - 2 , then
x = - = - 1
Substitute x = - 1 into the equation for corresponding value of y
y = - (- 1)² - 2(- 1) + 8 = - 1 + 2 + 8 = 9
vertex = (- 1, 9 )
To obtain another point substitute any value for x into the equation
x = 0 : y = 0 - 0 + 8 , then (0, 8 ) is a point on the graph
x = 2 : y = - (2)² - 2(2) + 8 = - 4 - 4 + 8 = 0 then (2, 0 ) is a point on the graph
The proportion of the recipe required to make the grocery list is obtained from the recipe for the beans soup.
The grocery list is therefore;
- <u>15 cups of honey beans</u>
- <u>9 cups carrots</u>
- <u>12 cups cherry tomato</u>
- <u>192 oz. vegetable broth</u>
- <u>10.5 cup turnips</u>
- <u>6 teaspoon salt</u>
- <u>8 cups potato onions</u>
- <u>1.25 teaspoons thyme</u>
- <u>12 teaspoons garlic</u>
Reason:
Amounts of beans soup Sam wants to make = 4 gallons
<em>The recipe for the beans soup is as follows as obtained from an online home work document are</em>;
<em>Vegetable Bean Soup that Serves 4 with volume of 0.</em><em> gallons</em>
<em>1.25 cups of honey beans</em>
<em>0.75 cup carrots</em>
<em>1 cup cherry tomato</em>
<em>16 oz. vegetable broth</em>
<em>0.875 cup turnips</em>
<em>0.5 teaspoon salt</em>
<em /><em> cup potato onions</em>
<em>0.125 teaspoon thyme</em>
<em>1 teaspoon garlic</em>
The amount of each ingredient Sam needs is given by the ratio of amount of soup Sam wants to make and the given amount of soup made by the ingredients as follows;
Therefore, Sam has to buy twelve times the amount of each ingredient as follows;
Vegetable Bean Soup that Serves 4 with volume of 0. gallons
12 × 1.25 = 15 cups of honey beans
12 × 0.75 = 9 cups of carrots
12 × 1 = 12 cups of cherry tomato
12 × 16 = 192 oz. vegetable broth
12 × 0.875 = 10.5 cup turnips
12 × 0.5 = 6 teaspoon salt
12 × = 8 cups of potato onions
12 × 0.125 = 1.25 teaspoons thyme
12 × 1 = 12 teaspoons garlic
The grocery list is therefore;
- 15 cups of honey beans
- 9 cups carrots
- 12 cups cherry tomato
- 192 oz. vegetable broth
- 10.5 cup turnips
- 6 teaspoon salt
- 8 cups potato onions
- 1.25 teaspoons thyme
- 12 teaspoons garlic
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Answer:
The value of x must be greater than 100.
Step-by-step explanation:
We need to find the value x for which the value of log(x) is greater than than 2.
According to the property of logarithm, if a is a real number.
Using the above property of logarithm, the given inequality can be rewritten as
We conclude that the value of log(x) is greater than 2 for real values of x which are greater than 100.
Therefore, the value of x must be greater than 100.