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labwork [276]
2 years ago
8

The archway of the main entrance of a university is modeled by the quadratic equation y = -x^2 + 6x. The university is hanging a

banner at the main entrance at an angle defined by the equation 4y = 21 − x. At what points should the banner be attached to the archway?
a. (1, 5.5) and (5.25, 6.56)
b. (1, 5) and (5.25, 3.94)
c. (1.5, 4.87) and (3.5, 4.37)
d. (1.5, 5.62) and (3.5, 6.12)
e. There is no real solution.
Mathematics
1 answer:
Zanzabum2 years ago
8 0
Find the intersection points of the two equationsÑ

1) y = - x^2 + 6x

2) 4y = 21- x => y = 21/4 - x/4

Intersection => y = y => - x^2 + 6x = 21/4 - x/4

=> x^2 - 6x - x/4 + 21/4 = 0

=> x^2 - 25x/4 + 21/4 = 0

x^2 - 6.25x + 5.25 = 0

Use the quadratic equation and you find x = 1 and x ≈ 5.25

The respective y values are: y = 5 and y ≈ 3.94

=> points (1,5) and (5.25,3.94)

Answer: option b. (1,5) and (5.25,3.94)


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2 inches wide
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648=LW2    (note, this is not LW^2 but 2 times LW)
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324=LW
legnth of base is less than 36
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we just need to find the values of legnth and width such that LW=324 and L<36 and that L or W is divisible by 3 (since each box is 3 inches long)

so lets factor 324
324=2*2*3*3*3*3
group them and find possible values for legnth and width less than 36 and divsible by 3
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(L,W,H) possible values are
(27,12,2)
(18,18,2)



the possible dimentions are
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Find the unit price of 60lbs of honey for $123.99. Round your answer to the nearest cent if necessary.
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Hailey paid \$13$13dollar sign, 13 for 1\dfrac3{7} \text{ kg}1 7 3 ​ kg1, start fraction, 3, divided by, 7, end fraction, start
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1kg of salami cost $9.1

Step-by-step explanation:

Hailey paid $13 for 1 3/7 kg of sliced salami.

What was the cost per kilogram of salami?

Cost of 1 3/7 kg of sliced salami=$13

1 3/7 kg=10/7kg

Let x=1 kg of sliced salami

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$13=10/7x

13=10/7*x

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2 years ago
The function f(x) = 1/2 x + 3/2 is used to complete this table.
Mrac [35]

Answer:

a) f(-1/2)  = -2 is NOT TRUE.

b)  f(0)  =3/2 is  TRUE.

c)   f(1)  = -1 is NOT TRUE.

d)   f(2)  = 1 is NOT TRUE.

e)   f(4)  = 7/2  is  TRUE.

Step-by-step explanation:

Here, the given function is  f(x) = (\frac{1}{2}) x+\frac{3}{2}

Now, checking for each values for the given function:

a) Putting x  = (-1/2):

 f(\frac{-1}{2} ) = (\frac{1}{2})(\frac{-1}{2} ) +\frac{3}{2}   = \frac{-1}{4}  + (\frac{3}{2} )\\\implies f(x) = \frac{-1 + 6}{4}  = (\frac{5}{4} )

and (5/4) ≠  -2

Hence, f(-1/2)  = -2 is NOT TRUE.

b)Putting x  = 0 :

f(0) = (\frac{1}{2})(0 ) +\frac{3}{2} = (\frac{3}{2} )

Hence, f(0)  =3/2 is  TRUE.

c) Putting x  = 1:

f(1 ) = (\frac{1}{2})(1 ) +\frac{3}{2}   = \frac{1}{2}  + (\frac{3}{2} )\\\implies f(x) = \frac{3 + 1}{2}  = (\frac{4}{2} )   = 2\implies 2   \neq -1

Hence, f(1)  = -1 is NOT TRUE.

d)Putting x  = 2:  

f(2 ) = (\frac{1}{2})(2 ) +\frac{3}{2}   = 1+ (\frac{3}{2} )\\\implies f(x) = \frac{2 + 3}{2}  = (\frac{5}{2} )

and (5/2) ≠  1

Hence, f(2)  = 1 is NOT TRUE.

e)Putting x  = 4:

 f(4 ) = (\frac{1}{2})(4 ) +\frac{3}{2}   = 2  + (\frac{3}{2} )\\\implies f(x) = \frac{4 + 3}{2}  = (\frac{7}{2} )

Hence, f(4)  = 7/2  is  TRUE.

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The perimeter of a rectangle is
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The length must also be "no more than", which means less than or equal to, 12 inches.
Option A satisfies both of these conditions.
5 0
2 years ago
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