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3 years ago

The graph of y = 1/2 x2 + 2x + 3 is shown. What are the solutions to the equation 1/2 x2 + 2x + 3 = x + 7?

Mathematics

1 answer:

kirill [66]3 years ago

3 0

Answer:

Step-by-step explanation:

Let's organise our information :

the function is (1/2)x²+2x+3

we want to khow the value of x that gives us : (1/2)x²+2x+3=x+7

Now the trick is to write this expression as a quadratic equation with zero at one side :

(1/2)x²+2x+3=x+7

(1/2)x²+2x+3-x-7=0
(1/2)x²+x-4=0

Now let's solve this equation :

a= 1/2
b= 1
c= -4

Δ=1²-4*(1/2)*(-4)

= 9

So we have two solutions :

$\left \{ {{y=\frac{-1-3}{2*0.5} } \atop {x=\frac{-1+3}{2*0.5} }} \right.$

y= -4
x= 2

So the solutions are -4 and 2

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Suppose Y(t) = 25e^3t + 12 represents the number of bacteria present at time t minutes. At what time will the population reach 1

Levart [38]

Given:

The given function is:

$Y(t)=25e^{3t}+12$

Where Y represents the number of bacteria present at time t minutes.

To find:

The time taken by bacteria population to reach 100 bacteria.

Solution:

We have,

$Y(t)=25e^{3t}+12$

Putting $Y(t)=100$ , we get

$100=25e^{3t}+12$

$100-12=25e^{3t}$

$88=25e^{3t}$

Divide both sides by 25.

$\dfrac{88}{25}=e^{3t}$

Taking ln on both sides, we get

$\ln (\dfrac{88}{25})=\ln e^{3t}$

$\ln(\dfrac{88}{25})=3t$ $[\because \ln e^x=x]$

Divide both sides by 3.

$\dfrac{1}{3}\ln(\dfrac{88}{25})=t$

Therefore, the required time is $\dfrac{1}{3}\ln(\dfrac{88}{25})$ minutes.

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3 years ago

The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The d

krek1111 [17]

Answer:

34%

Step-by-step explanation:

According to the empirical rule, 68% of all of the data in a normal distribution falls within one standard deviation of the mean.

Applying to this particular case, 68% of the requests fall within (50 - 7) and (50+ 7). The percentage of requests from 43 to 50 is equal to the percentage of requests from 50 to 57.

Therefore, the percentage of light bulb replacement requests numbering between 50 and 57 is 68/2 = 34%.

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3 years ago

Find the equation of the linear function represented by the table below in slope-

Eva8 [605]

Answer:

f(x) = 5x - 5

Step-by-step explanation:

Let the equation of the linear function is,

f(x) = mx + b

Here, m = Slope of the graph

b = y-intercept

Slope of the line passing through $(x_1,y_1)$ and $(x_2,y_2)$ is given by,

m = $\frac{(y_2-y_1)}{(x_2-x_1)}$

From the table attached,

Slope of the line passing through (2, 5) and (6, 25) will be,

m = $\frac{25-5}{6-2}$

m = 5

Equation of the linear function will be,

f(x) = 5x + b

Since, a point (10, 45) lies on the function,

45 = 5(10) + b

b = 45 - 50

b = -5

Equation of the linear function will be,

f(x) = 5x - 5

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2 years ago

What’s (7(123456.789)4)0 but the 4 and 0 at the end are exponents

IrinaK [193]

Answer:

$7123456.789^{40}$ = 1.281244e+274

Step-by-step explanation:

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2 years ago

**WILL MARK BRAINLIEST AND THANK YOU**

omeli [17]

A is correct because f(1)=3^1+1 so f(1)=4 and g(x)=4 so f(x)=g(x)

B is also correct because the ordered pair we get is (1,4) and this is in quadrant 1

C is incorrect

D is incorrect

E is incorrect

Ans: A and B are correct

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3 years ago