Prove that the expression x^2 +2x+2 can only have positive values

The interval of x-values over which the function is decreasing is ( - 1,1).

In mathematics, a polynomial is an expression that solely uses the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables. It is made up of coefficients and indeterminates.

By differentiating the given function, it is possible to find the range of x-values across which the provided function is decreasing: (-1,1).

Given function is , f(x) = x³ – 3x – 2.

The following steps can be used in order to determine the interval in which the given function is decreasing:-

Step 1 - Write the given function.

f(x) = x³ – 3x – 2.

Step 2 - Now, differentiate the above function with respect to 'x'.

F'(x) = 3x² - 3

Step 3 - Now, equate the above expression to zero.

x² = 1

x = 1 or -1

Therefore, the interval of x-values over which the function is decreasing is ( - 1,1).

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Answer:

C

Step-by-step explanation:

took the test

Answer:

she receives 76 Dollars

The radius that can he use for the garden is H. 8

A circle's outside boundary is called the circumference and can be measured, or calculated, by using

Circumference = 2πr

where r is the radius of circle.

Now it is given that,

Length of fence = 50 feet

⇒ Circumference of  vegetable garden = 50 feet

Since, Circumference = 2πr

⇒ 2πr = 50

⇒ r = 50/2π

⇒ r = 50/6.28

⇒ r = 7.96

⇒ r ≈ 8 feet

Thus, the radius that can he use for the garden is H. 8

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The missing 2nd term of the given arithmetic sequence 25, _, 53,...(a₂ = 39).

The difference between the two different numerical orders is a fixed number in Arithmetic Progression (AP). Another name for it is Arithmetic Sequence.

We'd come along through a few specific words in AP that were labeled as:

The AP can also be understood in terms of common differences, as shown below.

Now, for the given AP;   25, _, 53....

Let the initial term be 'a₁' = 25

Let the second term be 'a₂' = ?

Let the third term be 'a₃' = 53.

The AP must have the same common difference. So,

d =  a₂ - a₁ or d = a₃ - a₂

Equating the common difference to find the 2nd missing term.

a₃ - a₂ = a₂ - a₁

Substitute the given values;

53 - a₂ = a₂ - 25

Bring the variable part on one side.

2a₂ = 53 + 25

a₂ = 78/2

a₂ = 39

Therefore, the 2nd missing value of an AP is found to be 39.

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Answer:

Step-by-step explanation:

2w = 2w + 1

2w - 2w = 1

w(2 - 2) = 1

0w = 1

w = 1/0

w is undefined

The greatest integer solution = 0

|x| = greater integer function

i.e,. if |x| ≤ 2, then its range is -2≤ x ≤2

We have,

|-2x-5| - 3≤ 2

Now we have to find the value of x

|-2x-5|≤5

-5≤ -2x - 5≤ 5

0 ≤-2x ≤10

-10≤ 2x ≤0

-5≤ x ≤0

Therefore the value of x = -5, -4, -3, -2, -1, 0

so the greatest integer solution = 0

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The slope of the line that contains the given points G(8,1), H(8,-6) is -1.

It is given in the question that the line contains the points G(8,1) and H(8,-6).

We know that:-

The formula to find the slope of a line that contains points (a,b) and (c,d) is given by:-

m = (d-b)/(c-a)

Here, we have

m = slope of the line

(a,b) = (8,1)

(c,d) = (8,-6)

Hence, putting the values of (a,b) and (c,d) , we get

Slope of the line that contains the given points A(8,1), F(8,-6) is given by:-

(-6-1)/(8-1) = -7/7 = -1

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Answer:

Use the given functions to set up and simplify

[

3

,

4

]

Step-by-step explanation:

The statement which represents the expression one over seven raised to the third power is Option (C) one over three hundred forty-three is the correct option.

We are given the expression:

one over seven raised to the third power

This can be written as:

(1 / 7) ³

Simplifying and solving the expression by finding the cube of 1 and 7.

1³ = 1

7³ = 343

So, the expression will now become:

(1 / 7) ³ = 1 / 343

which can also be written as:

one over three hundred forty - three

Therefore, option (C) one over three hundred forty-three is the correct option which represents the expression one over seven raised to the third power.

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Answer:

Step-by-step explanation:

Answer:

x² + [tex]\frac{1}{x^2}[/tex] = 5

Step-by-step explanation:

using the identity

(a - b)² = a² + b² - 2ab , then given

(x - [tex]\frac{1}{x}[/tex] ) = [tex]\sqrt{3}[/tex] ( square both sides )

(x - [tex]\frac{1}{x}[/tex] )² = ([tex]\sqrt{3}[/tex] )² , that is using the above identity

x² + [tex]\frac{1}{x^2}[/tex] - 2(x × [tex]\frac{1}{x}[/tex] ) = 3

x² + [tex]\frac{1}{x^2}[/tex] - 2(1) = 3

x² + [tex]\frac{1}{x^2}[/tex] - 2 = 3 ( add 2 to both sides )

x² + [tex]\frac{1}{x^2}[/tex] = 5

[tex]\displaystyle\\Answer:\ x^2+\frac{1}{x^2}=5[/tex]

Step-by-step explanation:

[tex]\displaystyle\\(x-\frac{1}{x} )=\sqrt{3} \\[/tex]

Let's square both parts of the equation:

[tex]\displaystyle\\(x-\frac{1}{x} )^2=(\sqrt{3})^2 \\(x)^2-2*x*\frac{1}{x} +(\frac{1}{x})^2 =3\\x^2-2*1+\frac{1}{x^2}=3\\ x^2-2+\frac{1}{x^2}+2 =3+2\\x^2+\frac{1}{x^2}=5[/tex]

Answer:

67 is the answer

Answer:

67 would be the nearest whole number.

The expression for the given condition is: 8n + 3 = 9

Number is a mathematical word that is used to measure various attributes or count items. In essence, it is arithmetic values. Natural numbers, whole numbers, rational or irrational numbers are among the several types of counting numbers.

The supplied condition is three greater than the product of a number, and eight equals nine, according to the query.

So let's suppose that n is the number.

Three is more than the result of a number and eight, according to the question:

The necessary formula will be: 8n + 3 = 9.

Now, n has been computed to be worth: n = 6/8 = 3/4.

As a result, 3/4 is the value of the supposed integer "n."

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Answer:

1.15 is 115%

Step-by-step explanation:

7/8 is 0.875 so it makes it 87.5%

The percentage form of the given number is:

1.15 as a percent is 115%

7/8 as a percent is 187.5%

To convert a decimal to a percent,

we need to multiply it by 100.

So for 1.15,

Multiply it by 100 to get 115%.

To convert a mixed number to a percent,

We have to convert it to an improper fraction first.

To do that, we multiply the denominator by the whole number and add the numerator.

Then we put that answer over the original denominator.

For 7/8, the improper fraction would be,

(8 x 1) + 7 = 15/8.

To convert this to a percentage,

We need to divide the numerator by the denominator and multiply by 100.

So 15/8 as a decimal is 1.875, and when we multiply that by 100 we get 187.5%.

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Answer:

Step-by-step explanation:

p= AB+BC+AC

AB=[tex]\sqrt{(-5-(-5))^2+(4-(-2))^2} =6[/tex]

BC=[tex]\sqrt{(-5-6)^2+(4-(-2))^2} =\sqrt{157}[/tex]

AC=[tex]\sqrt{(6-(-5))^2+(-2-(-2))^2} =11[/tex]

p= 17+[tex]\sqrt{157\\[/tex]

Answer:

I believe the correct answer would be C.

Step-by-step explanation:

Have a great day! :)

Step-by-step explanation:

Pythagoras :

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90° angle).a and b are the legs of the right-angled triangle.

so,

x² + 12² = (x + 8)² = x² + 16x + 64

144 = 16x + 64

16x = 80

x = 5

Answer:

x=-16

Step-by-step explanation:

3/4x-4=-16

Add 4 to both sides.

3/4x=-12

Divide 3/4 from both sides.

x=-16

Hope this helps!

Please mark as brainliest if correct!

Have a great day!

Answer:

x = -16

Step-by-step explanation:

The height of Andy 68 inches is greater than the minimum requirement which is 54 inches. Yes, And can ride.

Conversion means to convert the same thing into different units.

The sign in front of the Electric storm roller coaster states that all riders must be at least 54 inches tall to ride. If Andy is 5 feet 8 inches tall.

Convert height of Andy into inches only. Then we have

⇒ 5 feet + 8 inches

⇒ 5 x 12 inches + 8 inches

⇒ (60 + 8) inches

⇒ 68 inches

The height of Andy 68 inches is greater than the minimum requirement which is 54 inches. Yes, And can ride.

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The perimeter of right isosceles ΔABC with midsegment DE is 16 + 8√2.

If right isosceles ΔABC has hypotenuse length h, then the two other sides are congruent.

side a = side b

Using Pythagorean theorem, c^2 = a^2 + b^2

h^2 = a^2 + b^2      a = b

h^2 = 2a^2

a = h/√2

If DE is a midsegment not parallel to the hypotenuse, then it is a segment that connects the midpoints of one side of a triangle and the hypotenuse. See photo for reference.

ΔABC and ΔADE are similar triangles.

a : b : h = a/2 : 4 : h/2

If a/2 = a/2, then b/2 = 4.

b/2 = 4

b = 8

If a = b, then a = 8.

If a = h/√2, then

8 = h/√2

h = 8√2

Solving for the perimeter,

P = a + b + h

P = 8 + 8 + 8√2

P = 16 + 8√2

P = 27.3137085

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Answer:

Decimal Form:

389.58823529

Mixed Number Form:

389  [tex]\frac{10}{17}[/tex]

Step-by-step explanation:

[tex]\frac{6623}{17}[/tex]

Decimal Form:

389.58823529

Mixed Number Form:

389  [tex]\frac{10}{17}[/tex]

Answer:

Well, (2,3) is transformed into (-3,2)

(-3,-1) changes into (1,-3)

and (2,-1) changes into (1,2)

Step-by-step explanation:

Smort

The perfect square equation is f(x) = (x + 7/2)^2 - 9/4

The equation of the function is given as

f(x) = x^2 + 7x + 10

Rewrite the equation as

x^2 + 7x + 10 = 0

Subtract 10 from both sides of the equation

So, we have

x^2 + 7x = -10

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

Take the coefficient of x

k = 7

Divide by 2

k/2 = 7/2

Square both sides

(k/2) = 49/4

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

Add 49/4 to both sides of the equation

So, we have

x^2 + 7x + 49/4 = -10 + 49/4

Express as a perfect square

So, we have

(x + 7/2)^2 = -10 + 49/4

Evaluate the sum

So, we have

(x + 7/2)^2 = 9/4

This gives

(x + 7/2)^2 - 9/4 = 0

So, we have

f(x) = (x + 7/2)^2 - 9/4

Hence, the perfect square equation is f(x) = (x + 7/2)^2 - 9/4

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The probability that a nut selected from the jar at random will be a cashew = 0.29

The correct answer is option (B) 0.29

In this question,

A jar contains 150 peanuts and 60 cashews.

So, the total number of nuts = 150 + 60

                                               = 210

We need to find the probability that a nut selected from the jar at random will be a cashew.

To find the probability we use the formula,

P = number of possible outcomes / total number of outcomes

Let event A: a nut selected from the jar at random is a cashew

n(A) = 60

total number of nuts n(S) = 210

So, the probability that a nut selected from the jar at random will be a cashew,

P(A) = 60/210

P(A) = 0.29

Therefore, the probability that a nut selected from the jar at random will be a cashew = 0.29

The correct answer is option (B) 0.29

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Answer:

1056 feet

Step-by-step explanation:

5280/5=1056

Answer:

14.   [tex]-3(x+2)+4[/tex]

12.   [tex]4[/tex]

15.   [tex]0[/tex]

Step-by-step explanation:

Question 14

To find the function in terms of "x+2", simply replace "x" in the original equation with "x+2":

[tex]f(x+2)=-3(x+2)+4[/tex]

Now simplify by distributing the 3:

[tex]f(x+2)=-3x-6+4[/tex]

Finish by adding the constants:

[tex]f(x+2)=-3x-2[/tex]

Question 12

This one follows the same concept! Replace "x" in the original equation with 1/2:

[tex]F(\frac{1}{2})=-2(\frac{1}{2} )+5[/tex]

Simplify:

[tex]f(\frac{1}{2})=-1+5\\f(\frac{1}{2})=4[/tex]

Question 15

For this question, it looks like you are given a set of coordinate pairs in the function. You are asked to find "f(4)". Essentially, you are being asked to find the value of y given 4 as the value of x.

The given coordinate pair (4,0) has 4 as the x value, so the y value when x=4 is 0!

The simplified expression for (10-22 / 8-17) is 4/3 .

The given expression is,

( 10-22 / 8-17 )

First we need to solve the numerator which is (10-22) and on simplifying the numerator we can write,

Numerator = ( 10 - 22 ) = -12                         equation 1

Similarly, now we can proceed to solve the denominator which is (8 - 17) and on simplifying the denominator we write,

Denominator  = (8 - 17) = -9                       equation 2

Now we can substitute the value of numerator and the denominator from equation 1 and equation 2 in the given expression ( 10-22 / 8-17 ) as,

(Numerator / Denominator) = (10-22 / 8-17) = ((-12)/(-9)) = 4/3

The simplified expression for (16-12 / 15-11) is 4/3 .

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The required value of x is 9 / 40.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of y

let k be the constant of proportion

When a quantity varies directly with others, then we have a relation, y = kx      —-- 1

Now, find k for given x = 3 / 4 and y = 5 / 3, we need to put these values in equation 1, i.e.

5 / 3 = k(3 / 4)

k = (5 × 4) / 9

k = 20 / 9

Further calculate x for given y = ½ and constant of proportion = 20/9i.e.

½ = (20 / 9)x

x = 9 / 40

Hence, the required value of x is 9 / 40.

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The solution of the given equation 5-4t = 12 is at t = -7/4.

According to the given question.

We have a linear equation in one variable.

5 - 4t = 12

As we know that, linear equation in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofre, th esolution for the given equation 5 - 4t = 12 is given by

5 - 4t = 12

⇒ -4t = 12 - 5      (subtracting 5 from both the sides)

⇒ -4t = 7

⇒ -t = 7/4          (dividing both the sides by 4)

⇒ t = -7/4

Hence, the solution of the given equation 5-4t = 12 is at t = -7/4.

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