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IrinaK [193]
2 years ago
12

a rectangular flower garden has area of 32 square feet. if the width of the garden is 4 feet less than the length, what is the p

erimeter, in feet, of the garden?
Mathematics
1 answer:
qaws [65]2 years ago
6 0
Let length be x feet
length= x 
width=x-4
area = 32
length * width=32
x(x-4)=32
x^2 - 4 x -32=0
(x-8)(x+4)=0
x=8 feet
length=8 feet
width=4 feet
perimeter=2(len+wid)
               =2(8+4)
                2*12=24 feet
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Find the perimeter of a quadrilateral with vertices at C (−2, 1), D (2, 4), E (5, 0), and F (1, −3). Round your answer to the ne
saveliy_v [14]

Answer: 20 units

Step-by-step explanation:

The distance between two points P(a,b) and Q(c,d) is given by :-

PQ=\sqrt{(d-b)^2+(c-a)^2}

Given : The vertices of a quadrilateral = C (−2, 1), D (2, 4), E (5, 0), and F (1, −3).

Distance between points C (−2, 1) and D (2, 4) :-

CD=\sqrt{(4-1)^2+(2-(-2))^2}\\\\\Rightarrow\ CD=\sqrt{(3)^2+(4)^2}\\\\\Rightarrow\ CD=\sqrt{9+16}=\sqrt{25}\\\\\Rightarrow\ CD=5\text{ units}

Distance between points D (2, 4) and E (5, 0) :-

DE=\sqrt{(4-0)^2+(2-5)^2}\\\\\Rightarrow\ DE=\sqrt{(4)^2+(-3)^2}\\\\\Rightarrow\ DE=\sqrt{16+9}=\sqrt{25}\\\\\Rightarrow\ DE=5\text{ units}

Distance between points E (5, 0) and F (1, −3).:-

EF=\sqrt{(-3-0)^2+(1-5)^2}\\\\\Rightarrow\ EF=\sqrt{(-3)^2+(-4)^2}\\\\\Rightarrow\ EF=\sqrt{9+16}=\sqrt{25}\\\\\Rightarrow\ EF=5\text{ units}

Distance between points C (−2, 1) and F (1, −3).:-

FC=\sqrt{(-3-1))^2+(1-(-2))^2}\\\\\Rightarrow\ FC=\sqrt{(-4)^2+(3)^2}\\\\\Rightarrow\ FC=\sqrt{16+9}=\sqrt{25}\\\\\Rightarrow\ FC=5\text{ units}

Now, the perimeter of the quadrilateral = CD+DE+EF+FC

=5+5+5+5=20\text{ units}

3 0
2 years ago
Read 2 more answers
The vertex of this parabola is at (-2,-3). When the x-value is -1, the y-value is -5. What is the coefficient of the squared exp
elena55 [62]

Answer:

Option C is correct

Step-by-step explanation:

Given: vertex of this parabola is at (-2,-3)

To find: coefficient of the squared expression in the parabola’s equation if the x-value is -1, the y-value is -5

Solution:

The equation of parabola is of the form y=a(x-h)^2+k

Here, a is the coefficient of the squared expression in the parabola’s equation.

Put (h,k)=(-2,-3)\,,\,(x,y)=(-1,-5)

-5=a(-1+2)^2-3\\-5+3=a(1)^2\\-2=a\\a=-2

So, the coefficient of the squared expression in the parabola’s equation is -2

6 0
2 years ago
6. Charlie can spend up to $8 on lunch. He wants to buy a tuna sandwich, a bottle of
PilotLPTM [1.2K]

Answer:

The maximum number of pounds of potato salad that Charlie can buy is 0.375

Step-by-step explanation:

see the attached figure to better understand the problem

Let

a ----> the cost of one tuna sandwich

b ----> the cost of a bottle of apple juice

c ----> the cost per pound of potato salad

x ----> pounds of potato salad

we have

a=\$4.25

b=\$2.25

c=\$4.00/lb

we know that

He wants to buy a tuna sandwich, a bottle of  apple juice, and x pounds of potato salad and can spend up to $8

The inequality that represent this situation is

a+b+cx \leq 8

substitute the given values

4.25+2.25+4.00x \leq 8

Solve for x

Combine like terms

6.50+4.00x \leq 8

Subtract 6.50 both sides

4.00x \leq 8-6.50

4.00x \leq 1.50

Divide by 4 both sides

x \leq 1.50/4.00

x \leq 0.375\ lbs

therefore

The maximum number of pounds of potato salad that Charlie can buy is 0.375

3 0
2 years ago
During a catered lunch, an average of 4 cups of tea are poured per minute. The lunch will last 2 hours. How many gallons of tea
EastWind [94]
<span> 4 cups of tea are poured per minute
2 hours = 2 x 60 = 120 minutes
so in 2 hours = 120 x 4 = 480 cups
</span><span>16 cups in one gallon then
</span><span>480 / 16 = 30 gallons

answer
30 gallons


</span>
5 0
2 years ago
The scale for a map says that 1 cm is equal to 25 miles. Jennifer measures the distance between two cities as 4.5 cm. How far ap
nexus9112 [7]
112.5 miles because 4x25=100 and half of 25 is 12.5 so 100+12.5= 112.5
technically 4.5x25=112.5
4 0
2 years ago
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