Perdita goes to the fruit market with $9 to buy avocadoes. Each avocado costs $2. Write and solve an inequality to find the greatest number of avocadoes Perdita can buy

Answers

Answer 1

Answer: let x= number of avocadoes she can buy
let y= total cost

y= 2x

9= 2x 9/2= 4.5
4.5= x
(you cannot cut the avocado in half therefore your answer is simply 4)

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A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height and the longer base to be 7 yards greater than the height. She wants the area to be 295 square yards. The situation is modeled by the equation h^2 + 5h = 295. Use the Quadratic Formula to find the height that will give the desired area. Round to the nearest hundredth of a yard. A: 17.36 yards
B: 600 yards
C: 14.86 yards
D: 29.71 yards

Answers

Answer:

The height is 14.86 yards ⇒ answer C

Step-by-step explanation:

* Lets explain how to solve the problem

- The flower garden in the shape of a trapezoid

- The shorter base to be 3 yards greater than the height

- The longer base to be 7 yards greater than the height

- The area must be 295 square yards

- The situation is modeled by the equation h² + 5h = 295

- We want to find the height that will give the desired area by using

the quadratic formula

- The quadratic formula is $h=\frac{-b+-\sqrt{b^(2)-4ac}}{2a}$ ,

where a is the coefficient of h² and b is the coefficient of h and c

is the numerical term

- The equation of the area is h² + 5h = 295

∵ h² + 5h = 295

- Subtract 295 from both sides

∴ h² + 5h - 295 = 0

- Lets find the values of a , b and c from the equation

∵ a = 1 , b = 5 , c = -295

∴ $h=\frac{-5+-\sqrt{(5)^(2)-4(1)(-295)}}{2(1)}$

∴ $h=(-5+-√(25+1180))/(2)$

∴ $h=(-5+√(1205))/(2)=14.86$

- OR

∴ $h=(-5-√(1205))/(2)=-19.86$

- The dimensions of any figure must be positive value, then we will

neglect the negative value of h

∴ h = 14.86

* The height is 14.86 yards

Answer:

C: 14.86 yards

Step-by-step explanation:

to solve a quadratic equation we need to make it equal to zero and then use the Quadratic Formula

$x= \frac{-b + \sqrt{b^(2)-4ac}}{2a} / \frac{-b - \sqrt{b^(2)-4ac}}{2a}$

having

$h^(2) +5h-295=0$

we have

a=1

b=5

c=-295

the answers for the formula are

h=14.85 and h=-17.36

as we are looking for a distance we can only take the positive answer, then

h=14.85

The ratio of the side lengths of two regular hexagons is 3 to 7. If the area of the smaller hexagon is 18 square units, then the area of the larger hexagon is ________.

Answers

$(side_1)/(side_2)=(3)/(7)\n\n(Area_1)/(Area_2)=\left((3)/(7)\right)^2=(9)/(49)\n\n(18)/(Area_2)=(9)/(49)\n\ncross\ multiply\n\n9Area_2=18\cdot49\n\nArea_2=(18\cdot49)/(9)\n\nArea_2=2\cdot49\n\nArea_2=98$

Select the points you need to calculate the average rate of change from the beginning of the slide to when the slide has covered a horizontal distance of 15 feet. (0.80) (5.40) (10. 20) (15. 10)

Answers

Answer:

It would be the points (0,80) and (15,10)

Step-by-step explanation:

Just did it :)

Answer:

(0,80), (15,10)

Step-by-step explanation:

the second one is -14/3

edge 2022

Let x^2−12x=61 . What values make an equivalent number sentence after completing the square? Enter your answers in the boxes. HELP PLEASE

Answers

Complete the square:

x^2 - 12x + (-6)^2 - (-6)^2 = 61, or
(x-6)^2 -36 = 61, or

x-6 = plus or minus sqrt(97), or

x = 6 plus or minus sqrt(97)

A=1 , b=-12 , c=61. B^2-(4 •a•c) = d
-12^2-(4•1•61)= d
X= (-b-sqr (d) ) / 2a or x=(-b+sqr (d) )/2a

12. The square and rectangle shown below have the same perimeter length Show that the length of the rectangle (3x + 1) centimetres

Answers

Lets call the perimeter P and the length of the rectangle l. The first figure is a square with side length 2x + 2 so P = 4(2x + 2) = 8x + 8. For the rectangle, P = 2l + 2(x + 3) = 2l + 2x + 6. These values both equal P so they must equal each other. 8x + 8 = 2l + 2x + 6. Now we have to solve for l.

8x + 8 = 2l + 2x + 6
8x + 2 = 2l + 2x
6x + 2 = 2l
3x + 1 = l

Translate the following statement into a mathematical equation:Six, plus four times a number, is eighteen.

(6 + 4)n = 18
4n + 18 = 6
6 + 4n = 18
6 + 4 + n = 18