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3 years ago

If f(x) = x² + 1 for what x value is f(x) = 2?

Mathematics

1 answer:

MaRussiya [10]3 years ago

6 0

Answer:

x = ±1

Step-by-step explanation:

Step 1: Define variables

f(x) = x² + 1

f(x) = 2

Step 2: Substitute

2 = x² + 1

Step 3: Solve for <em>x</em>

0 = x² - 1

0 = (x - 1)(x + 1)

x - 1 = 0

x = 1

x + 1 = 0

x = -1

∴ x = ±1

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Paulina swims 5 miles down a creek with a current for 2 hours. It takes her 4

Westkost [7]

Answer: her swimming speed = 1.875 mph

Speed of current = 0.625 mph

Step-by-step explanation:

Let x represent her swimming speed.

Let y represent the speed of the current.

Paulina swims 5 miles down a creek with a current for 2 hours. Since this is faster, it means that she swam with the current. Her total speed would be (x + y) mph

Distance = speed × time

Therefore,

5 = 2(x + y)

dividing both sides by 2, it becomes

2.5 = x + y- - - - - - -1

It takes her 4 hours to swim the same 5 miles back to her original destination against the

same current. It means that her total speed was (x - y) mph

Distance covered would be

5 = 4(x - y)

Dividing both sides by 4, it becomes

1.25 = x - y- - - - - - - 2

Adding equation 1 to equation 2, it becomes

3.75 = 2x

x = 3.75/2

x = 1.875

Substituting x = 1.875 into equation 1, it becomes

2.5 = 1.875 + y

y = 2.5 - 1.875

y = 0.625

4 0

3 years ago

Solve and check the following equation. −75 = −5d − 150d =

AleksandrR [38]

Answer:

15/31 is the answer.

Step-by-step explanation:

-75 = -5d- 150d

-5d- 150d= - 155d

divide -75 from -155d

-155d / -155= -75 / -155

=15 / 31

4 0

3 years ago

Read 2 more answers

1 The San Diego Safari Park charges $18 for parking, plus an admission fee of $56. This can be represented by the equation c = 5

enyata [817]

Answer: No

Step-by-step explanation:

Given: The San Diego Safari Park charges $18 for parking, and an admission fee of $56.

This can be represented by the equation c = 56p + 18, where c is the total cost and p is the number of people.

Equation of direct proportion: $k=\dfrac{y}x$

But here we have a y-intercept as 18.

So, we cannot say there is a proportional relation ship between c and p.

4 0

3 years ago

3(2x + 2) - 1x - 2 = 39

sammy [17]

Answer:

x=7

Step-by-step explanation:

6x+6-x-2=39

5x+4=39

-4 -4

5x=35/5

4 0

3 years ago

Read 2 more answers

If $600 is deposited into a savings account which pays 4.8% interest, compound continuously (A = Pe^rt), how long will it take t

mariarad [96]

Answer:

$22.9\ years$

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$t=?\ years\\ P=\$600\\ r=0.048\\ A=\$600*3=\$1,800$

substitute in the formula above and solve for t

$\$1,800=\$600(e)^{0.048t}$

Simplify

$3=(e)^{0.048t}$

apply ln both sides

Remember that

$ln(e)=1$

$ln(3)=0.048t*ln(e)$

$ln(3)=0.048t$

$t=ln(3)/0.048=22.9\ years$

8 0

3 years ago