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2 years ago

If f(x) = -4x2 - 6x-1 and g(x) = – x2 - 5x + 3, find (f+ g)(x).

Mathematics

2 answers:

Anastaziya [24]2 years ago

7 0

Answer:

-5x^2 -11x +2

Step-by-step explanation:

f(x) = -4x^2 - 6x-1

g(x) = – x^2 - 5x + 3,

Add them together

f(x) = -4x^2 - 6x-1

+ g(x) = – x^2 - 5x + 3,

-----------------------------------

-5x^2 -11x +2

ziro4ka [17]2 years ago

4 0

Answer:

- 5x² - 11x + 2

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

f(x) + g(x)

= - 4x² - 6x - 1 + (- x² - 5x + 3)

= - 4x² - 6x - 1 - x² - 5x + 3 ← collect like terms

= - 5x² - 11x + 2

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Find the radius of a sphere whose surface area is 154cm².with stepss

worty [1.4K]

Answer:

THIS IS YOUR ANSWER:

$area \: of \: spere \: = 4\pi \: r {}^{2} \\ 154cm {}^{2} = 4 \times \frac{22}{7} \times r {}^{2}$

$\frac{154 \times 7}{4 \times 22} = r {}^{2} \\ r {}^{2} = 12.25 \\$

$r = \sqrt{12.25} \\ r = 3.5cm$

✍️HOPE IT HELPS YOU ✍️

7 0

2 years ago

Read 2 more answers

The probability density function of the time to failure of an electronic component in a copier (in hours) is f(x) for Determine

salantis [7]

The question is incomplete. Here is the complete question.

The probability density function of the time to failure of an electronic component in a copier (in hours) is

$f(x)=\frac{e^{\frac{-x}{1000} }}{1000}$

for x > 0. Determine the probability that

a. A component lasts more than 3000 hours before failure.

b. A componenet fails in the interval from 1000 to 2000 hours.

c. A component fails before 1000 hours.

d. Determine the number of hours at which 10% of all components have failed.

Answer: a. P(x>3000) = 0.5

b. P(1000<x<2000) = 0.2325

c. P(x<1000) = 0.6321

d. 105.4 hours

Step-by-step explanation: Probability Density Function is a function defining the probability of an outcome for a discrete random variable and is mathematically defined as the derivative of the distribution function.

So, probability function is given by:

P(a<x<b) = $\int\limits^b_a {P(x)} \, dx$

Then, for the electronic component, probability will be:

P(a<x<b) = $\int\limits^b_a {\frac{e^{\frac{-x}{1000} }}{1000} } \, dx$

P(a<x<b) = $\frac{1000}{1000}.e^{\frac{-x}{1000} }$

P(a<x<b) = $e^{\frac{-b}{1000} }-e^\frac{-a}{1000}$

a. For a component to last more than 3000 hours:

P(3000<x<∞) = $e^{\frac{-3000}{1000} }-e^\frac{-a}{1000}$

Exponential equation to the infinity tends to zero, so:

P(3000<x<∞) = $e^{-3}$

P(3000<x<∞) = 0.05

There is a probability of 5% of a component to last more than 3000 hours.

b. Probability between 1000 and 2000 hours:

P(1000<x<2000) = $e^{\frac{-2000}{1000} }-e^\frac{-1000}{1000}$

P(1000<x<2000) = $e^{-2}-e^{-1}$

P(1000<x<2000) = 0.2325

There is a probability of 23.25% of failure in that interval.

c. Probability of failing between 0 and 1000 hours:

P(0<x<1000) = $e^{\frac{-1000}{1000} }-e^\frac{-0}{1000}$

P(0<x<1000) = $e^{-1}-1$

P(0<x<1000) = 0.6321

There is a probability of 63.21% of failing before 1000 hours.

d. P(x) = $e^{\frac{-b}{1000} }-e^\frac{-a}{1000}$

0.1 = $1-e^\frac{-x}{1000}$

$-e^{\frac{-x}{1000} }=-0.9$

${\frac{-x}{1000} }=ln0.9$

-x = -1000.ln(0.9)

x = 105.4

10% of the components will have failed at 105.4 hours.

5 0

3 years ago

Please help FAST I need the answer along with you explaining the steps so I can get it thanks! I’ll give Brainlist also!

kupik [55]

Answer:

The equation of required line is: $\mathbf{5x-8y+34=0}$

Step-by-step explanation:

We need to write equation in the form Ax+By+C=0 of the line parallel to $5x-8y+12=0$ and through the point (-2,3)

First we need to find slope and y-intercept of the required line.

Using equation of line $5x-8y+12=0$ to find slope.

Since the given line and required lines are parallel there slope is same.

Writing equation in slope intercept form: $y=mx+b$ where m is slope.

$5x-8y+12=0 \\-8y=-5x-12\\\frac{-8y}{-8y}=\frac{-5x}{-8}-\frac{12}{-8}\\y=\frac{5}{8}x+\frac{3}{4}$

So, the slope m = 5/8

The slope of required line is $m=\frac{5}{8}$

Now finding y-intercept using slope $m=\frac{5}{8}$ and point(-2,3)

$y=mx+b\\3=\frac{5}{8}(-2)+b\\3=\frac{-5}{4}+b\\b=3+\frac{5}{4}\\b=\frac{3*4+5}{4}\\b=\frac{12+5}{4}\\b=\frac{17}{4}$

So, the equation of required line having slope $m=\frac{5}{8}$ and y-intercept $b=\frac{17}{4}$

$y=mx+b\\y=\frac{5}{8}x+\frac{17}{4}\\y=\frac{5x+17*2}{8}\\y= \frac{5x+34}{8} \\8y=5x+34\\5x-8y+34=0$

So, The equation of required line is: $\mathbf{5x-8y+34=0}$

3 0

2 years ago

What is -2 1/2+1 1/2

eduard

The correct answer is -1

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2 years ago

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What is the diamater of a circle with 14 in.

Iteru [2.4K]

Answer:

The diameter is two times the radius, or 2r. The radius of this circle is 7 inches, so the diameter is 2(7) = 14 inches. The diameter is 14 inches.

Step-by-step explanation:

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3 years ago