Find f(2) if f(x) = (x + 1)^2.
9
6
5

Answer:

1.3

Step-by-step explanation:

The Rest Of Them Are Writen As Fractions

Answer:

[tex]\sqrt{10}[/tex]

NOTE: the other answer is WRONG...

irrational means can not be written as a fraction (with whole numbers)

4/3 = 1.33333333333

Step-by-step explanation:

Answer: (a), (b), (c), and (d)

Step-by-step explanation:

Check the options

[tex](a)\\\Rightarrow [\sin x+\cos x]^2=\sin ^2x+\cos ^2x+2\sin x\cos x\\\Rightarrow [\sin x+\cos x]^2=1+2\sin x\cos x\\\Rightarrow \Rightarrow [\sin x+\cos x]^2=1+\sin 2x[/tex]

[tex](b)\\\Rightarrow \sin (6x)=\sin 2(3x)\\\Rightarrow \sin 2(3x)=2\sin (3x)\cos (3x)[/tex]

[tex](c)\\\Rightarrow \dfrac{\sin 3x}{\sin x\cos x}=\dfrac{3\sin x-4\sin ^3x}{\sin x\cos x}\\\\\Rightarrow 3\sec x-4\sin ^2x\sec x\\\Rightarrow 3\sec x-4[1-\cos ^2x]\sec x\\\Rightarrow 3\sec x-4\sec x+4\cos x\\\Rightarrow 4\cos x-\sec x[/tex]

[tex](d)\\\Rightarrow \dfrac{\sin 3x-\sin x}{\cos 3x+\cos x}=\dfrac{2\cos [\frac{3x+x}{2}] \sin [\frac{3x-x}{2}]}{2\cos [\frac{3x+x}{2}]\cos [\frac{3x-x}{2}]}\\\\\Rightarrow \dfrac{2\cos 2x\sin x}{2\cos 2x\cos x}=\dfrac{\sin x}{\cos x}\\\\\Rightarrow \tan x[/tex]

Thus, all the identities are correct.

A. Not an identity

B. An identity

C. Not an identity

D. An identity

To check whether each expression is an identity, we need to verify if the equation holds true for all values of the variable x. If it is true for all values of x, then it is an identity. Let's check each option:

A. [tex]\((\sin x + \cos x)^2 = 1 + \sin 2x\)[/tex]

To check if this is an identity, let's expand the left-hand side (LHS):

[tex]\((\sin x + \cos x)^2 = \sin^2 x + 2\sin x \cos x + \cos^2 x\)[/tex]

Now, we can use the trigonometric identity [tex]\(\sin^2 x + \cos^2 x = 1\)[/tex] to simplify the LHS:

[tex]\(\sin^2 x + 2\sin x \cos x + \cos^2 x = 1 + 2\sin x \cos x\)[/tex]

The simplified LHS is not equal to the right-hand side (RHS) 1 + sin 2x since it is missing the sin 2x term. Therefore, option A is not an identity.

B. [tex]\(\sin 6x = 2 \sin 3x \cos 3x\)[/tex]

To check if this is an identity, we can use the double-angle identity for sine:[tex]\(\sin 2\theta = 2\sin \theta \cos \theta\)[/tex]

Let [tex]\(2\theta = 6x\)[/tex], which means [tex]\(\theta = 3x\):[/tex]

[tex]\(\sin 6x = 2 \sin 3x \cos 3x\)[/tex]

The equation holds true with the double-angle identity, so option B is an identity.

C. [tex]\(\frac{\sin 3x}{\sin x \cos x} = 4\cos x - \sec x\)[/tex]

To check if this is an identity, we can simplify the right-hand side (RHS) using trigonometric identities.

Recall that [tex]\(\sec x = \frac{1}{\cos x}\):[/tex]

[tex]\(4\cos x - \sec x = 4\cos x - \frac{1}{\cos x} = \frac{4\cos^2 x - 1}{\cos x}\)[/tex]

Now, using the double-angle identity for sine, [tex]\(\sin 2\theta = 2\sin \theta \cos \theta\),[/tex] let [tex]\(\theta = x\):[/tex]

[tex]\(\sin 2x = 2\sin x \cos x\)[/tex]

Multiply both sides by 2: [tex]\(2\sin x \cos x = \sin 2x\)[/tex]

Now, the left-hand side (LHS) becomes:

[tex]\(\frac{\sin 3x}{\sin x \cos x} = \frac{\sin 2x}{\sin x \cos x}\)[/tex]

Using the double-angle identity for sine again, let [tex]\(2\theta = 2x\):[/tex]

[tex]\(\frac{\sin 2x}{\sin x \cos x} = \frac{2\sin x \cos x}{\sin x \cos x} = 2\)[/tex]

So, the LHS is 2, which is not equal to the RHS [tex]\(\frac{4\cos^2 x - 1}{\cos x}\)[/tex]. Therefore, option C is not an identity.

D. [tex]\(\frac{\sin 3x - \sin x}{\cos 3x + \cos x} = \tan x\)[/tex]

To check if this is an identity, we can use the sum-to-product trigonometric identities:

[tex]\(\sin A - \sin B = 2\sin \frac{A-B}{2} \cos \frac{A+B}{2}\)\(\cos A + \cos B = 2\cos \frac{A+B}{2} \cos \frac{A-B}{2}\)[/tex]

Let A = 3x and B = x:

[tex]\(\sin 3x - \sin x = 2\sin x \cos 2x\)\(\cos 3x + \cos x = 2\cos 2x \cos x\)[/tex]

Now, we can rewrite the expression:

[tex]\(\frac{\sin 3x - \sin x}{\cos 3x + \cos x} = \frac{2\sin x \cos 2x}{2\cos 2x \cos x} = \frac{\sin x}{\cos x} = \tan x\)[/tex]

The equation holds true, so option D is an identity.

To know more about identity:

https://brainly.com/question/28974915

#SPJ3

Answer:

1

Step-by-step explanation:

64+32 =96 that'd how I got the answer

Answer:

[tex]{ \tt{8(2v + 8) = 96}} \\ { \tt{2v + 8 = 12}} \\ { \tt{2v = 4}} \\ { \bf{v = 2}}[/tex]

Answer:

$124.42.

Step-by-step explanation:

Given data

Principqp= $100

Rate= 5.5%

time=4 years

First, convert R as a percent to r as a decimal

r = R/100

r = 5.5/100

r = 0.055 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt            // Since we are compounding quarterly

A = 100.00(1 + 0.055/4)(^4)(4)

A = 100.00(1 + 0.01375)^(16)

A = $124.42

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $100.00 at a rate of 5.5% per year compounded 4 times per year over 4 years is $124.42.

B.

the solution is in the picture

Given:

A biased 3-colored spinner was spun 240 times. It landed on Red n times, on Orange 3n times and on Yellow 8n times.

To find:

The expected number of times it land on Red if you spin this spinner 1000 times.

Solution:

A biased 3-colored spinner was spun 240 times. It landed on Red n times, on Orange 3n times and on Yellow 8n times. So,

[tex]n+3n+8n=240[/tex]

[tex]12n=240[/tex]

[tex]n=\dfrac{240}{12}[/tex]

[tex]n=20[/tex]

The value of n is 20. It means the spinner land on red 20 times if the spinner was spun 240 times. So, the probability of getting red is:

[tex]P(Red)=\dfrac{20}{240}[/tex]

[tex]P(Red)=\dfrac{1}{12}[/tex]

If you spin this spinner 1000 times, then the expected number of times to getting red is:

[tex]E(Red)=1000\times P(Red)[/tex]

[tex]E(Red)=1000\times \dfrac{1}{12}[/tex]

[tex]E(Red)=83.333...[/tex]

[tex]E(Red)\approx 83[/tex]

Therefore, the expected number of times to land on red is 83.

Answer:

Correct answer 1

Step-by-step explanation:

Answer:

The circumference of Earth's equator is 40,080 km.

Step-by-step explanation:

Given that every 24 hours, Earth makes a full rotation around its axis, and Earth's speed of rotation at the equator is 1,670 km per hour, to determine what is the circumference of Earth's equator the following calculation must be performed:

24 x 1,670 = X

40,080 = X

Therefore, the circumference of Earth's equator is 40,080 km.

Answer:

1.47

Step-by-step explanation:

9.76/10=10% = 0.976 round to 0.98

5%=0.97/2 = 0.49

add them = 1.47 tip

Answer:

a shipping container ,the ones they use in large cargo ships

Answer:

1/9

You are being asked to "complete the square"

you need to find a value to make the quadratic a "perfect square:

the focus is -2/3 you need to "add" one half of -2/3 squared to the

equation (1/2 * -2/3)^2 .... (-2/6)^2 .... 4/36 .... 1/9

Step-by-step explanation:

Answer:

y = 7/5x + 7

Step-by-step explanation:

Answer:

x = 17

Step-by-step explanation:

If AB // DE, then angle 5 and angle 6 are alternate interior angle and they should be congruent.

5x + 16 = 3x + 50

Subtract 16 from both sides

5x = 3x + 50 - 16

5x = 3x + 34

Subtract 3x from both sides

5x - 3x = 34

2x = 34

Divide both sides by 2

x = 34/2

x = 17

Answer:

3x + 50 = 5x + 16

5x - 3x = 50-16

2x = 34

x = 17

Answer:

Step-by-step explanation:

[tex]\dfrac{7}{25} =0.28=28\%\\\\\dfrac{2}{3} \approx 0.67=67\%\\\\\dfrac{3}{8} =0.375=37.5%[/tex]

Answer:

Step-by-step explanation:

(cos 4a*cos 2a+sin 4a*sin 2a)/sin 4a

=[cos (4a-2a)]/sin 4a

=(cos 2a)/sin 4a

=(cos 2a) /(2 sin 2a cos 2a)

=1/(2 sin 2a)

=1/2 csc 2a

Answer:

The probability that this occurs is 25%, as 3/6 (chance to roll an odd number) multiplied by 1/2 (chance to flip a head) is .25.

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Follow 1 hour on the y axis to where it meets the line of best fit. In this case it is about 6 puzzles.

Answer:

19.005 ounces

Step-by-step explanation:

I believe that all you have to do is mutilply the 2 numbers which is 543 and 0.035 to find the amount of ounces it weighs. So 543 × 0.035 = 19.005. The answer is 19.005 ounces. (i hope)

Answer:

6 mps to the nearest mps.

Step-by-step explanation

The rocket that carried the Curiosity Rover to Mars traveled at a speed of 21,000 miles per hour. What is this speed to the nearest mile per second?

1 hr = 3600 sec

Since an hour is 3600 seconds (i.e., 60 x 60), you simply need to divide that number by 3600

→ 21000 mph = 21000 ÷ 3600 mps = 5 5/6 mps →

ANSWER : 6 mps to the nearest mps.

Answer:

Believe the other person

Step-by-step explanation:

I got a 100%, and also got this question.

Answer:

Zoe rode [tex]\frac{5}{6}[/tex] of a mile more than she walked.

Step-by-step explanation:

[tex]\frac{11}{12}-\frac{1}{12} =\frac{5}{6}[/tex]

Answer:

(a) [tex]x\³ - 6x - 6[/tex]

(b) Proved

Step-by-step explanation:

Given

[tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex] --- the root

Solving (a): The polynomial

A cubic function is represented as:

[tex]f = (a + b)^3[/tex]

Expand

[tex]f = a^3 + 3a^2b + 3ab^2 + b^3[/tex]

Rewrite as:

[tex]f = a^3 + 3ab(a + b) + b^3[/tex]

The root is represented as:

[tex]r=a+b[/tex]

By comparison:

[tex]a = $\sqrt[3]{2}[/tex]

[tex]b = \sqrt[3]{4}$[/tex]

So, we have:

[tex]f = ($\sqrt[3]{2})^3 + 3*$\sqrt[3]{2}*\sqrt[3]{4}$*($\sqrt[3]{2} + \sqrt[3]{4}$) + (\sqrt[3]{4}$)^3[/tex]

Expand

[tex]f = 2 + 3*$\sqrt[3]{2*4}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]

[tex]f = 2 + 3*$\sqrt[3]{8}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]

[tex]f = 2 + 3*2*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]

[tex]f = 2 + 6($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]

Evaluate like terms

[tex]f = 6 + 6($\sqrt[3]{2} + \sqrt[3]{4}$)[/tex]

Recall that: [tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex]

So, we have:

[tex]f = 6 + 6r[/tex]

Equate to 0

[tex]f - 6 - 6r = 0[/tex]

Rewrite as:

[tex]f - 6r - 6 = 0[/tex]

Express as a cubic function

[tex]x^3 - 6x - 6 = 0[/tex]

Hence, the cubic polynomial is:

[tex]f(x) = x^3 - 6x - 6[/tex]

Solving (b): Prove that r is irrational

The constant term of [tex]x^3 - 6x - 6 = 0[/tex] is -6

The divisors of -6 are: -6,-3,-2,-1,1,2,3,6

Calculate f(x) for each of the above values to calculate the remainder when f(x) is divided by any of the above values

[tex]f(-6) = (-6)^3 - 6*-6 - 6 = -186[/tex]

[tex]f(-3) = (-3)^3 - 6*-3 - 6 = -15[/tex]

[tex]f(-2) = (-2)^3 - 6*-2 - 6 = -2[/tex]

[tex]f(-1) = (-1)^3 - 6*-1 - 6 = -1[/tex]

[tex]f(1) = (1)^3 - 6*1 - 6 = -11[/tex]

[tex]f(2) = (2)^3 - 6*2 - 6 = -10[/tex]

[tex]f(3) = (3)^3 - 6*3 - 6 = 3[/tex]

[tex]f(6) = (6)^3 - 6*6 - 6 = 174[/tex]

For r to be rational;

The divisors of -6 must divide f(x) without remainder

i.e. Any of the above values  must equal 0

Since none equals 0, then r is irrational

Answer:

Yes, it shows direct variation

Step-by-step explanation:

Given

The above table

Required

Is it a direct variation?

The constant of variation (k) is:

[tex]k = y/x[/tex]

For each pair x and y, we have:

[tex]k = 5/15 = 1/3[/tex]

[tex]k = 6/18 = 1/3[/tex]

[tex]k =9/27 = 1/3[/tex]

Since the calculate constant have the same value for all pair or x and y, then the table shows direct variation

Answer:1

Step-by-step explanation:3/3=1

Answers:

y intercept = -4

slope = -1

==========================================

Explanation:

The given equation is the same as y = -1x + (-4)

Compare this to y = mx+b form, and we see that

m = -1 is the slope

b = -4 is the y intercept

To graph y = -x-4, you could plot the two points (0,-4) and (1,-5) and draw a straight line through them. Extend the line as far as you can in either direction.

Notice how going from (0,-4) to (1,-5) follows the process "down 1, right 1" which is directly pulled from the slope = -1 =  -1/1.

Hi!

y = ax + b

y = 14x + 2 → a = 14 ∧ b = 2

Parallel lines have the same slope factor (a) so line parallel to the line with the equation y = 14x + 2 will be y = 14x - 12

Answer:

B

Step-by-step explanation:

f(x) = g(x) at the intersection points of the two graphs.

The graphs intersect at x = -4 and x = 0.

At x = -4, f(-4) = g(-4).

At x = 0, f(0) = g(0)

Answer: B

Answer:

Can't See 7 clearly

8) (9,9)

Step-by-step explanation:

[tex]\frac{10+8}{2}[/tex] , [tex]\frac{10+8}{2}[/tex]

Add x's and divide by 2

Add y's and divide by 2

Like taking the average of the coordinates.

Answer:

option 4

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(x + 1)² + (y - 12)² = 25 ← is in standard form

with centre = (- 1, 12 ) and radius = [tex]\sqrt{25}[/tex] = 5

Answer:

every single angle is 90°

Step-by-step explanation:

remember that,

4 angles will form if two lines intersect and the sum of those 4 angles is 360°

we are given the sum of 3 angles i.e 270

so one of the angles should be

[tex] \displaystyle {360}^{\circ} - {270}^{\circ}[/tex]

simplify substraction:

[tex] \displaystyle {90}^{\circ}[/tex]

therefore since one of the angles is 90° the intercepting lines are Perpendicular as a result every single angle formed by the two intercepting lines is 90°

Answer:

90°

Step-by-step explanation:

We know that sum of angle around a point is 360° . Here its already given that sum of three Angles out of 4 is 270°

Therefore :-

Measure of remaining one angle ,

Therefore the measure of the fourth angle is 90°