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Ostrovityanka [42]
3 years ago
14

What value of c makes x2 − 24x + c a perfect square trinomial? −144 −48 48 144

Mathematics
1 answer:
attashe74 [19]3 years ago
8 0

Answer:

144

Step-by-step explanation:

Hello, please consider the following.

x^2-24x+c

is a perfect square means that the discriminant is 0.

\Delta = b^2-4ac=24^2-4c=0\\\\24^2-4c =0 4c=576\\\\\text{We divide by 4}\\\\c= \dfrac{576}{4}=144

Thank you

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Kimberly's family has a dinner bill of $26 and wants to leave a 15% tip for
tester [92]

5.00Answer:

Step-by-step explanation:

8 0
2 years ago
A designer is making a rectangular prism box with maximum volume, with the sum of its length, width, and height 8 in. The length
Sever21 [200]

Answer:

width = 1.8 in

length =   3.6 in

height =8-3w =8-3(1.8)= 2.6 in

Step-by-step explanation:

A designer is making a rectangular prism box with maximum volume, with the sum of its length, width, and height 8 in

Let l , w and h are the length , width and height

l +w+h=8\\l=2w

Plug it in the first equation

2w+w+h=8\\3w+h=8\\h=8-3w

volume the box is length times width times height

volume = (2w)(w)(8-3w)\\16w^2-6w^3

To get maximum volume we take derivatived

v'=32w-18w^2

set the derivative =0 and solve for w

0=32w-18w^2\\0=-2w(9w-16)\\w=0 , w= \frac{16}{9}

width = 1.8 in

length = 2w= 3.6 in

height =8-3w =8-3(1.8)= 2.6 in

6 0
3 years ago
A certain standardized test's math scores have a bell-shaped distribution with a mean of 530 and a standard deviation of 119. Co
kumpel [21]

Answer:

a) 68.2%

b) 31.8%

c) 2.3%

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 530

Standard Deviation, σ = 119

We are given that the distribution of math scores is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) P(test scores is between 411 and 649)

P(411 \leq x \leq 649)\\\\= P(\displaystyle\frac{411 - 530}{119} \leq z \leq \displaystyle\frac{649-530}{119})\\\\= P(-1 \leq z \leq 1)\\\\= P(z \leq 1) - P(z < -1)\\= 0.841 - 0.159 = 0.682 = 68.2\%

b) P(scores is less than 411 or greater than 649)

P(x < 411 < x, x > 649)\\=1 = P(411 \leq x \leq 649)\\=1 - 0.682\\=0.318 = 31.8\%

c) P(score greater than 768)

P(x > 768)

P( x > 768) = P( z > \displaystyle\frac{768 - 530}{119}) = P(z > 2)

= 1 - P(z \leq 2)

Calculation the value from standard normal z table, we have,  

P(x > 768) = 1 -0.977 = 0.023 = 2.3\%

5 0
3 years ago
-7 x - 2y = -13 <br> x - 2y = 11
VashaNatasha [74]
Well the first one would convert to
-2y= 7x-13 and the second one would be -2y=-x+11 and you solve from there (lmk if you need the steps) but your final answer would be. Y= -7/2x+ 13/2 and y=1/2x - 11/2
8 0
3 years ago
What is -(3/7) x (-1/6)?
krok68 [10]
The answer is 1/14. -3/7 x -1/6. 3 crosses 6 2 time so you are left with -1/7 x -1/2 that is 1/14
3 0
3 years ago
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