Find the roots of the function f(x) = (2^x − 1) - (x2 + 2x − 3) with x ∈ R.

Answers

Answer 1

Answer: There are no real roots.

Step-by-step explanation:

To find the roots of the function

f(x) = (2^x − 1) - (x2 + 2x − 3) with x ∈ R.

First open the bracket

2^x - 1 - x^2 - 2x + 3 = 0

Rearrange and collect the like terms

2x^2 - x^2 - 2x + 3 - 1= 0

X^2 - 2x + 2 = 0

Factorizing the above equation will be impossible, we can therefore find the root by using completing the square method or the quadratic formula.

X^2 - 2x = - 2

Half of coefficient of x is 1

X^2 - 2x + 1^2 = -2 + 1^2

( x - 1 )^2 = - 1

( x - 1 ) = +/- sqrt(-1)

X = -1 + sqrt (-1) or -1 - sqrt (-1)

The root of the function is therefore

X = -1 + sqrt (-1) or -1 - sqrt (-1)

Since b^2 - 4ac of the function is less than zero, we can therefore conclude that there is no real roots


Related Questions

can someone in here help me with this question I'm stuck and I don't know to do it​

Answers

Answer:

Substitute -3,-2,-1,0,1,2,3 in d equation given to u at first to complete the table

Pleasseeee help me It's for a test Mars is extremely far from the Earth. Scientists estimate that it could take astronoauts 245​​​​​​​ days to travel from Earth to Mars. This is more than half of a year! Suppose astronauts travel to Mars when the distance between Earth and Mars is 108 million miles. If the trip takes 245 days, on average, how many miles would be traveled each day? In your calculator, write the large number as a multiple of a power of 10 to compute the answer. Round to the nearest mile.

Answers

Answer:

440,816 miles per day

Step-by-step explanation:

The scale on a map indicates that 1 inch represents 10 miles. If two cities are 2 3 4 inches apart on a map, how many miles apart are the two cities?

Answers

Answer:

Step-by-step explanation:

2340 miles

Given

1 inch represents 10 miles

thus,

1 inch on map = 10 miles in real

given the two cities are 234 inches apart on map

1 inch on map = 10 miles in real

multiplying both side by 234

1 inch*234 on map = 10 miles*234 in real

234 inch on map = 2340 miles in real.

Thus, two cities are 2340 miles apart.

Answer:

27.5 miles

Step-by-step explanation:

You need to multiply 2 3/4 by 10, because it says every inch represents 10 miles.

2 3/4 * 10

11/4 * 10/1 = 55/2

27 1/2 or, 27.5

Which statement is the Law of Syllogism? I will make you a brainllest

Answers

Answer:

The answer is P - Q and Q - R are true statements, the P - R is a true statment

What is the length of PR?
15
25°
P 5
E
1140
Q
25°
1140
X
21
R
F

Answers

Answer:

7

Step-by-step explanation:

Since the triangles are similar, we can use ratios

15        21

----- = ---------

5         PR

Using cross products

15 PR = 21*5

Divide each side by 15

PR = 21*5/15

PR = 7

Answer: yes it would be 7

Step-by-step explanation:

Mention
rational numbers which are
less than 5​

Answers

Answer:

Here are some rational numbers less than 5:

4, 4.2, -3, 0, 1/10, -5/16

A rational number is a number than can be written as a fraction of integers.

Answer:

rational numbers below 5 are 4,3,2,1,-1,-2,-3,-4 e.t.c

PLEASE HELP!!!! BRAINLIEST FOR RIGHT ANWSER

Answers

Answer:

d.tigers have a great IQR because they were some very heavy tigers.(high outliers)

Please please urgently helpp❤️

Answers

1. The car is 10km/h faster than the bus

Explanation:

50/2.5=20
50/5=10
20-10=10

2. m=-1.5

Explanation

5+7=12
-5-3=-8
12/-8=-1.5

3. f(-4)=-22

Explanation:

f(-4)=4(-4)-6


4. x=37

Explanation
44=2x-30
74=2x
x=37

Which of the following is a perfect square trinomial ? PLEASE HELP!!!!!!!!!!!!!!!!!

Answers

Answer:

The answer is C. 16x² - 56xy + 49y²

Step-by-step explanation:

A perfect square trinomial is the result of a squared binomial, the perfect square trinomial would be a² + 2ab + b², as that is what you get when you expand the brackets.

Q3. Samir spins a fair coin and records the results. In the first four spins ‘Heads' comes up each time. Samir says, ‘A head is more likely than a tail'. Is he correct? YES/ NO Give a reason for your answer.

Answers

Answer:

The conclusion drawn by Samir is Not correct.

Step-by-step explanation:

The spinning of a fair coin is a Bernoulli experiment.

There are only two outcomes: Heads (H) or Tails (T).

Theoretically, each of the two outcomes has an equal probability of occurrence i.e. P (H) = P (T) = 0.50.

Now, suppose an experiment is conducted to test this theory.

The law of large numbers, in probability concept, states that as the number of times an experiment is conducted, say n, in increased, the average value of the experiment approaches the expected value.

To determine whether ‘A head is more likely than a tail', the experiment of spinning the coin must be repeated more than n = 4 times.

In statistics, n = 30 is considered as a large enough sample.

So, the conclusion drawn by Samir is Not correct.

What is the Square root of -100

Answers

Answer:

[tex]10i[/tex]

Step-by-step explanation:

√(-100)

Use the imaginary number rule  [tex]i=\sqrt{-1}[/tex]

√(-1) × √(100)

i × √(10²)

i × 10

= 10i

Answer:

It does not have a square root because it is a minus digit.

Step-by-step explanation:

The square root of one number is the number which is multiplied by itself to form the square number.

But, no negative number has a square root, because

- x - = +

+ x + = +

As you can see, no two same signs multiply together to form a negative.

Hope this helps.

Good Luck

Given right triangle XYZ, what is the value of sin(Y)? (Hint: Special Right)


A.) 1/2
B.) SqRt3/3
C.) SqRt3/2
D.) (2SqRt3)/3

Answers

Answer:

sinY = 2

or

x = 2

Step-by-step explanation:

None of the above answer choices are correct. If you solve for sinY:

sin30° = x/4

4sin30° = x

x = 2

Now that we have x, we use our special right triangle rules for 30-60-90 triangles. The angle across the 30° is x, the angle across the 60° is x√3 and our hypotenuse is 2x. Our answer would still be x = 2, so none of the answer choices are correct.

Answer: 1/2

Step-by-step explanation:

Which property can be used to solve the equation? StartFraction d Over 10 EndFraction = 12 addition property of equality subtraction property of equality multiplication property of equality division property of equality

Answers

Answer:

multiplication property of equality

Step-by-step explanation:

Given the equation d/10 = 12. To get the value of d, the follwoing steps can be used to solve for the value of d;

Multiply both sides by 10

d/10 * 10 = 12*10

d = 120

It can be seen from the calculation above that multiplication operation was used to get the solution to the equation. It can therefore be concluded that the multiplication property of equality  was used to solve the equation.

factorize xsquare-25

Answers

Answer:

The answer is (x + 5)(x - 5).

Step-by-step explanation:

Assuming that 25 is a perfect square so you can apply :

[tex](a + b)(a - b) = {a}^{2} - {b}^{2} [/tex]

Test :

[tex](x+5)(x-5) = {x}^{2} - 5x + 5x - 25 [/tex]

[tex](x+5)(x-5) = {x}^{2} - 25 [/tex]

Answer:

[tex]\boxed{(x-5)(x+5)}[/tex]

Step-by-step explanation:

x² - 25

Factor out square.

(x)² - (5)²

Apply difference of two squares formula.

a² - b² = (a-b)(a+b)

a = x

b = 5

x² - 25 = (x-5)(x+5)

please help, tysm if you do
the length of a rectangle is 2 cm less than three times the width. the perimeter of the rectangle is 92 cm. find the dimensions of the rectangle. A. 11, 31 cm
B. 12, 34 cm
C. 12, 38 cm
D. 13, 37 cm

Answers

Answer:

I hope it will help you.......

Determine whether the samples are independent or dependent. upper a data set includes the morning and evening temperature for the lasta data set includes the morning and evening temperature for the last 90 days.90 days.

Answers

Answer:

Dependent sample

Step-by-step explanation:

The sample: a data set includes the morning and evening temperature for the last 90 days.

The samples are dependent in that they are paired measurements on just one set of item which is the temperature.

These measurements are related in such a way that the each observation in one sample can be paired with an observation in the other sample.

Pls help ima mark BRAINLIST


Answers

Answer:

G.

Step-by-step explanation:

Since the y-int is (0, 4), you know you have to have an equation that has a +4 in it. When you calculate for the slope, you should get 4/3, and so the only equation that has those 2 is G.

4x 10x h = 4x
h = 10x

Answers

Step-by-step explanation:

the answer would be 40 4x 10x h = 4x

Find the area of the shape shown below Please help :(

Answers

Answer:

18 units^2

Step-by-step explanation:

Formula for Area of trapezoid:    ( base 1 + base 2 / 2) * height

(3 + 9 / 2) * 3 = (12 / 2) * 3 = 6 * 3 = 18 units^2

I hope this helps

Answer:

18²

Step-by-step explanation:

Formula for a trapezium:

Area = base1 + base2/2 × height

3 + 9/2 × 3

= 12/2 × 3

18²

The revenue from selling x shirts is f(x) = 15x.
The cost of buying x shirts is c(x) = 7x + 20.
The profit from selling x shirts is p(x) = f(x) - cx).
What is p(x)?

Answers

Answer:

p(x) = 8x - 20

Step-by-step explanation:

revenue from selling x shirts is f(x) = 15x

The cost of buying x shirts is c(x) = 7x + 20

p(x) = f(x) - c(x)

To solve this, we need to substitute value of f(x) and c(x) in formula for p(x)

p(x) = f(x) - c(x)

p(x) = 15x -( 7x + 20)

=>  p(x) = 15x - 7x -20

=>  p(x) = 8x -20

Thus, profit is p(x) = 8x - 20.

Find the square of this equation

Answers

Hope you understand :)

Answer:

9f^2 - 12f + 4.

Step-by-step explanation:

(3f - 2)^2

= (3f - 2)(3f - 2)

= 9f^2 - 6f - 6f + 4

= 9f^2 - 12f + 4

9[tex]f^{2}[/tex] - 12f + 4.

Hope this helps!

whats the cube root of 3375 by prime factorization

Answers

Answer:

15

Step-by-step explanation:

Prime factors of 3375 are 3, 3, 3, 5, 5, 5.

Since you need the ∛ of 3375, ∛3375=15

Answer:

15

Step-by-step explanation:

15x15x15=3375

what can you say about the y-values of the two functions f(x) =3x^2-3 and g(x)=2^x-3

Answers

Answer:

The answers are A and C. for A P E X.

Step-by-step explanation:

The option(A) minimum y-value of g(x) approches -3 and option(C) f(x) has the smallest possible y-value are correct.

What is a function?

It is defined as a special type of relationship and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

[tex]\rm f(x) = 3x^2-3[/tex]

As we can see in the graph the first term is 3x² and is always positive for all x.

The range for f(x) ∈ [-3, ∞)

When x = 0

f(x) = -3

The above value is the smallest possible value on the y-axis.

For function:

[tex]\rm g(x) = 2^x-3[/tex]

[tex]\rm 2^x[/tex] is also a positive quantity and it is an exponential function.

The range for the g(x) ∈ (-3, ∞)

It means g(x) never toches the y-axis at -3.

We can say the minimum value of g(x) approaches -3

Thus, the option(A) minimum y-value of g(x) approches -3 and option(C) f(x) has the smallest possible y-value are correct.

Learn more about the function here:

brainly.com/question/5245372

What is the value of x in the equation 3x – 1/9 = 18, when y = 27?

Answers

Answer:

Here you go mate!

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

3x - 1/9y = 18

Put y as 27 and evaluate.

3x - 27/9 = 18

3x - 3 = 18

Add 3 on both sides.

3x = 21

Divide 3 on both sides.

x = 7

PLEASE HELP, AND PLAESE EXPLAIN!!!

Answers

Answer:

D.   22.5 sq. un.

Step-by-step explanation:

W divides BU so that there is a ratio of 1;2 meaning that there are 3 parts.

That means that 3 parts is BUV; we know that one of those parts is 4.5 sq. un. so 4.5*3=13.5 sq. un.  - Also 4.5*2=9 to get WUV

V is the midpoint of the line BS so that means that BUV and UVS are equal

we know that BUV is 13.5 so we multiply that by 2 to get the whole triangle

=27

The last step is to get rid of BVW which we know is 4.5

27-4.5=22.5

If h(x) = 5 + x and f(x) = 5, which expression is equivalent to (kn)(x)?

Answers

Answer:

Step-by-step explanation:

The question is not correctly written, here is the correct question.

If h(x) = 5 + x and k(x) = 5, which expression is equivalent to (koh)(x)?

(koh)(x) can be rewritten as k{h(x)}

Since h(x) = 5+x then,  k{h(x)} = k(5+x)

Note that k(x) can be written as 5x°

k(5+x) = 5(5+x)°

Since any value raise to the power of zero is 1, then;

k(5+x) = 5(1)

k(5+x) = 5

(koh)(x) =  k{h(x)}  = 5

For (hok)x;

(hok)x = h{k(x)}

= h(5)

= h(5x°)

Since h(x) = 5+x

h(5x°) = 5+5x°

h(5x°)= 5+5 = 10

(hok)x = h(k(x)) = 10

If x + 12 55- yand 5 - ys 2(x-3), then which statement is true?
OA.
X+ 12 205 -
OB.
x + 12 32x-3
OC.
X + 12 = 2(x-3)
OD. x + 12 sy-5

Answers

Answer:

C

Step-by-step explanation:

so

a≤b

b≤c

definitely a can't be more of c

at last, equal

so a≤c

Help plz and plz write it down on paper and send me a picture ❤️

Answers

Answer:

Step-by-step explanation:

(27)^2/3=∛27²=∛3³*3³=3*3=9

√36³=√36*36*36=√6²*6²*6²=6*6*6=216

(-243)^3/5=5√2-42³=-27

Pls help me on this equation

Answers

I think the answer is A

which graph represents the hyperbola x2/32-y2/82=1?

Answers

Answer:

Step-by-step explanation:

You have the following hyperbola:

[tex]\frac{x^2}{32}-\frac{y^2}{82}=1[/tex]              (1)

The general for of a hyperbola:

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]

To construct the graph you take into account the rectangle formed by the lines x=±a and y=±b, and the asymptotes of the diagonals of the rectangles.

Furthermore, you take into account the foci of the hyperbola, which are

(0,±a).

Then, you have the lines

x = ± √32

y = ± √82

And the foci:

(0, ± √32)

The graph is shown in the attached image.

Answer:

D

Step-by-step explanation:

On edg

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