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Bezzdna [24]
3 years ago
14

Use the discriminant to determine the number and type of solutions the equation has.

Mathematics
2 answers:
AysviL [449]3 years ago
6 0
ax^2+bx+c=0\ \ \ \Rightarrow\ \ \ \Delta=b^2-4\cdot a\cdot c\\\\\Delta>0\ \ \ \Rightarrow\ \ \ two\ real\ solutions\\\Delta=0\ \ \ \Rightarrow\ \ \ one\ real\ solution\\\Delta0\ \ \ \ \Rightarrow\ \ \ two\ real\ solutions\ \ \ \Rightarrow\ \ \ Ans.\ C
White raven [17]3 years ago
5 0
x^2 + 8x + 12 = 0\\ \\a=1 , b= 8, c= 12 \\ \\ \Delta =b^2-4ac = 8^2 -4\cdot1\cdot12= 64-48= 16\\ \\\Delta > 0 \\ \\ Answer : \ C. \ \ two \ rational \ solutions


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Please rewrite 5x − 15y = − 60 in the slope intercept form
Margarita [4]
Basically solve for y
minus 5x fromboth sides
-15y=-5x-60
divide both sides by -15
y=1/3x+4
4 0
3 years ago
Adam is building a computer desk with a separate compartment for the computer. The compartment for the computer is a rectangular
Alik [6]

Answer:

The width of the computer compartment is 9 inches

The length of the computer compartment is 33 inches

The height of the computer compartment is 27 inches

Step-by-step explanation:

The given data on the rectangular prism compartment are;

The volume of the rectangular prism, V = 8019 cubic inches

The length of the compartment, l = 24 inches + The width, w

The height of the compartment, h = 18 inches + The width, w

Therefore, we have;

l = 24 + w

h = 18 + w

V = l × h × w

∴ V = (24 + w) × (18 + w) × w = w³ + 42·w² + 432·w = 8019

w³ + 42·w² + 432·w - 8019 = 0

By graphing the above function with MS Excel, we have one of the solution is w = 9

∴ (w - 9) is a factor of w³ + 42·w² + 432·w - 8019 = 0

Dividing, we get;

w² + 51·w + 891

w³ + 42·w² + 432·w - 8019 = 0

w³ - 9·w²

     51·w² - 459·w

                 891·w

                 891·w + 8019

                             0

Therefore,

w³ + 42·w² + 432·w - 8019 = 0

w³ + 42·w² + 432·w - 8019  = (x - 9)·(w² + 51·w + 891) = 0

The determinant of the factor, w² + 51·w + 891 = 51² - 4×1×891 = -963, therefore, the it has complex roots

Therefore, the real solution of (x - 9)·(w² + 51·w + 891) = 0 is w = 9

The width of the computer compartment, w = 9 inches

The length of the computer compartment, l = 24 inches + 9 inches = 33 inches

The height of the computer compartment, h = 18 inches + 9 inches = 27 inches.

3 0
3 years ago
The sum of two integers is 26. the sum of the squares of the two integers is 340. what is the product of the two numbers?
Phoenix [80]
Lets say that the two unknown integers are n and m.

We know the following things about n and m:

n+m=26
n^2+m^2=340

And, we want to find nm.

To solve this, we'll use the expansion of the squared of the sum of any two inegers; this is expressed as:

(n+m)^2=n^2+2nm+m^2

So, given what we know about the unknown integers, the previous can be written as:

(26)^2=340+2nm

We can easily solve for nm:

nm= \frac{(26)^2-340}{2}= \frac{676-340}{2}= \frac{336}{2}=168

The answer is 168.

Another approach to solve the problem is, from the two starting equations, compute the values of n and m, which are 12 and 14, and directly compute their product; however, the approach described is more elegant. 
5 0
3 years ago
I need the length of c in the triangle shown. plz i need help badly.
lesya [120]

Answer:

c=10

Step-by-step explanation:

6^2+8^2=c^2

36+64=c^2

100=c^2

10=c

8 0
3 years ago
Peaches are being sold for $2 per pound. if x represents the number of pounds of peaches bought and y represents the total cost
hichkok12 [17]
The correct answer to this question is the fourth statement. <span> The value of x can be any real number greater than or equal to 0, but the value of y must be an integer greater than or equal to 0.</span>
4 0
3 years ago
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