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3 years ago

What two numbers add up to 45 and multiply and get 121

1 answer:

4 0

Let the two numbers be x and y.

We have x+y=45
⇒ y= 45-x.

The two numbers multiply and get 121, so we have another equation:
x*y = 121 (1)

Plug y= 45-x in (1), we have:
x* (45-x)=121
⇒ 45x - x^2 = 121 (distributive property)
⇒ x^2 - 45x = -121 (multiply -1 on both sides)
⇒ x^2- 45x + 121= 0
⇒ x= 42.128 or x= 2.872

y= 45- 42.128= 2.872
or y= 45- 2.872= 42.128.

Because it does not matter what number, x or y, is larger, the two numbers are 2.872 and 42.128.

Hope this helps~

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What orderd pair represents the y intercept of the graph of y=2x-5

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3 years ago

What is the equation, in standard form, of a parabola that models the values in the table? x~ -1 0 2

Inessa05 [86]

<h2>Steps</h2>

Standard Form Equation: f(x) = ax² + bx + c

So firstly, since (0,5) is one of our values we can plug it into the standard form equation to solve for the c variable (since 0 will cancel out the a and b variable):

$5=a*0^2+b*0+c\\5=c$

Now we know that the value of c is 5. Next, plug in (-1,12) into the standard form equation and simplify (remember to also plug in 5 for the c variable):

$12=a*(-1)^2+b*(-1)+5\\12=a-b+5\\7=a-b$

Next, plug (2,15) into the standard form equation and simplify:

$15=a*2^2+b*2+5\\15=4a+2b+5\\10=4a+2b\\5=2a+b$

Now, with our last two simplified equations we will create a system of equations:

$7=a-b\\5=2a+b$

Now, I will be using the elimination method with this system. With the system, add up the equations together and you will get:

$12=3a$

From here, we can solve for the a variable. With it, just divide both sides by 3:

$4=a$

Now that we know the value of a, plug it into either equation to solve for the b variable:

$7=4-b\\3=-b\\-3=b\\\\5=2(4)+b\\5=8+b\\-3=b$

<h2>Answer</h2>

Putting all of our obtained values together, your final answer is:

$f(x)=4x^2-3x+5$

8 0

3 years ago

Concrete blocks are produced in lots of 2000. Each block has probability 0.85 of meeting a strength specification. The blocks ar

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Answer:

Step-by-step explanation:

Let us assume a normal distribution

The formula for normal distribution is

z = (x - u)/s

Where

u = mean = np

s = standard deviation = √npq

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n = number of blocks sampled

From the information given,

p = 0.85 = probability that the block will meet the strength specification.

q = 1 - p = 1 - 0.85 = 0.15 = probability that the block will not meet the strength specification.

n = 2000

u = np = 2000 × 0.85 = 1700

s = √npq = √1700×0.15 = 15.97

We want to find the P(x lesser than 1690). It becomes

z = (1690 - 1700)/15.97

z = -10/15.9 = -0.63

Looking at the normal distribution table for the corresponding z score, it is 0.2644

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P(x lesser than 1690) = 0.2644

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4 years ago

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Digiron [165]

Answer:

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3 years ago

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Ostrovityanka [42]

Answer:

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Step-by-step explanation:

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