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Difference quotient for f(x) = √x at (16,4) is  √16+h - 4 / h

Difference quotient is mathematical operation used to solve derivation of function by using following formula :

difference quotient = [tex]\frac{f(x+ h) - f(x) }{h}[/tex]

For the function f(x) =  √x at point (16,4)

f(x +h) = [tex]\sqrt{x+h}[/tex]  

putting value in formula

difference quotient =  [tex]\frac{\sqrt{x+h} -\sqrt{x} }{h}[/tex]

now , putting x = 16 ,

difference quotient = √16+h - √16 / h

taking square root of 16 ,

= √16+h - 4 / h

So, the required Difference quotient for the function at (16,4) is √16+h - 4 / h

option (d) is correct

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For given functions  f(x)= x^2 +2x-8 and g(x)= x+2,

(fog)(x) = x^2 + 6x

For given functions f(x)= x^2 +2x-8 and g(x)= x+2,

we need to find (fog)(x).

We know that the composition of function f(x) and g(x) would be,

(fog)(x)

= f(g(x))

= f(x + 2)

= (x + 2)^2 + 2(x + 2) - 8

= x^2 + 4x + 4 + 2x + 4 - 8

= x^2 + 6x + 8 - 8

= x^2 + 6x

Therefore, for given functions  f(x)= x^2 +2x-8 and g(x)= x+2,

(fog)(x) = x^2 + 6x

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The expression 3 tens 8 ones × 1000 can be evaluated and the value is; 38,000.

It follows from the task content that the value of the expression represented by the word phrase as given is to be determined.

On this note, it follows that we have;

First, 3 tens and 8 ones can be written as;

(3 × 10) + (8 × 1)

= 30 + 8

= 38.

Therefore, the result of the evaluation is; 38 × 1000 = 38, 000.

Ultimately, the result of the expression is; 38,000.

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Answer:

a + (a+1)²

Step-by-step explanation:

The following of the number "a" is:

a+1

Then:

The sum of a number with the square of its following algebraic language is:

a + (a+1)²

The algebraic expression for the sum of a number with the square of its following number can be written as:

Where x is the given number and (x + 1 )² represents the square of the following number.

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The best compatible number to use for 24 x 18 = 432.

24 can be written as 25

18 can be written as 20.

So,

20 x 25 = 500

Option B is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The number of roses in one centerpiece = 18 roses.

The number of roses in 24 centerpieces.

= 24 x 18

= 432

The best compatible number to use for 24 x 18 = 432.

24 can be written as 25

18 can be written as 20.

So,

20 x 25 = 500

Thus,

The best compatible number to use for 24 x 18 = 432.

24 can be written as 25

18 can be written as 20.

So,

20 x 25 = 500

Option B is the correct answer.

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1) The linear system has only one solution.

2) The linear system has infinite number of solutions.

3) The linear system has only one solution

4) The linear system has only one solution.

5) The linear system has only no solution.

In the algebraic form y= mx+ b, where m denotes the slope and b the y-intercept, a linear equation is defined as a first-order (linear) term and a constant. The aforementioned is occasionally described as a linear equation with two variables, where x and y are the variables.

An equation is linear if the graph of the equation is a straight line. This will happen once x has the highest power of 1, which is. The equation is linear if it can be represented as a straight line.

1) x+y+7=0

x-y+1=0

By solving these two equations we get,

x=-4

y=-3

(x, y)=(-4,-3)

Consequently, there is only one solution to the linear system.

2) 3x+y-2=0

6x+2y-4=0

a₁/a₂=3/6

a₁/a₂=1/2

b₁/b₂=1/2

c₁/c₂=1/2

Therefore,

a₁/a₂=b₁/b₂=c₁/c₂

So, the linear system has infinite number of solutions.

3) x-y-5=0

x+5y+7=0

By solving these two equations we get,

y=-2 and x=3

(x, y)=(3, -2)

Consequently, there is only one solution to the linear system.

4) x+y-4=0

2x-3y-3=0

By solving these two equations we get,

x=3 and y=1

(x, y)=(3,1)

Consequently, there is only one solution to the linear system.

5) 5x-y-5=0

5x-y-15=0

a₁/a₂=1

b₁/b₂=1

c₁/c₂=1/3

∴ a₁/a₂=b₁/b₂≠c₁/c₂

Therefore, the linear system has no solution.

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The values that make the inequality -2h ≤ -40 true are

Equivalent form of the inequality is written as

Inequality is a means of representing the relationship existing between the positive and negative parts of equations, using other terms aside exactly using only "equal to"

solving the inequality

-2h ≤ -40

dividing through by a negative number changes the inequality

diving through by -2 gives

h ≥ 20

Therefore, h are values greater than 20 and 23, 25, and 30 are all greater than or equal to 20

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Answer:

11 seconds

Step-by-step explanation:

[tex] - 16 {t}^{2} + 1936 = 0[/tex]

[tex] - 16 {t}^{2} = - 1936[/tex]

[tex] {t}^{2} = 121[/tex]

[tex]t = 11[/tex]

If he borrowed $1400 at 9% simple interest to be paid back in 2 years. The  interest he will pay is $1,663.34.

Using this formula

Interest = Principal ( 1+ Interest rate)^ time

Where:

Interest =?

Principal = $1400

Interest rate = 9% or 0.09

Time = 2 years

Let plug in the formula

Interest = $1,400 ( 1+ 0.09) ^ 2

Interest = $1,400 ( 1.09) ^2

Interest = $1,400 ( 1.1881)

Interest = $1,663.34

Therefore he will pay the amount of $1,663.34 as interest.

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Answer:

1. Given.

2. Definition of a linear pair.

3. Given.

4. Congruent Supplements Theorem.

Step-by-step explanation:

Statement 1

∠JKM and ∠MKL form a linear pair.

Reason:  Given

Statement 2

∠JKM and ∠MKL are supplementary

Reason:  Definition of supplementary angles.

A linear pair is a pair of adjacent, supplementary angles.

If ∠JKM and ∠MKL form a linear pair then they are supplementary by definition.

Statement 3

∠JKM and ∠LKN are supplementary.

Reason:  Given.

Statement 4

∠MKL ≅ ∠LKN

Reason:  Congruent Supplements Theorem.

If two angles are supplements of the same angle, then the two angles are congruent.
As ∠MKL and ∠LKN are both supplementary to ∠JKM then ∠MKL and ∠LKN are congruent.

Answer:

Greater than

Step-by-step explanation:

3/8 = 6/16

6<11

therefore, 11/16 is greater than 3/8

The given set written on set builder notation is:

{x| x ∈ R, 3 ≤ x ≤ 9}

We want to write the given set using set builder notation, the set is the set of all real numbers that are greater than or equal to 3 and less or equal to 9.

So the set can be written as an inequality as:

3 ≤ x ≤ 9

To define the set using the set builder notation, we also need to clarify that x belongs to the real number set, this is x ∈ R.

Then the set that we need to write is:

{x| x ∈ R, 3 ≤ x ≤ 9}

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Answer:

13685

Step-by-step explanation:

8050 x 0.70 = 5635

8050 + 5635 = 13685

Answer:

41

Step-by-step explanation:

9² + 40² = 1681

the s.r of 1681 is 41

We s.r the answer because we need the singular of C, not C²

Hope this helps

Answer:

Step-by-step explanation:

Formula for geometric sequence is:

[tex]a_{n} =a_{1} (r)^{n-1}[/tex]

Now we substitute the values in:

[tex]165=a_{1} (3)^{3-1}[/tex]

165=a1(-2x3)^2

165=a1x9

Answer is 23

The value of x in the algebraic equation x = 15.3568 - 1(1+x)^25 is 0.115

Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

These basic mathematical operations (+, -, ×, and ÷) we use in our everyday life. Whether we need to calculate the annual budget or distribute something equally to a number of people, for every such aspect of our life, we use arithmetic operations.

In this case, we have to solve for x in the algebraic equation using mathematical operation.

x = 15.3568 - (1 + x)^25

Collect like terms

x + (1+x)^25 = 15.3568

Solving for x

x = 0.115

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The perimeter of the triangle ABC with respect to the given information is 78.

Whether it be a two-dimensional shape or a one-dimensional length, a perimeter is a closed path that contains, surrounds, or delineates it. A circle's or an ellipse's circumference is its furthest boundary. Numerous real-world uses exist for calculating perimeter. Adding the lengths of all the sides and edges that surround a shape yields its perimeter. It is calculated using linear length units like centimeters, meters, inches, and feet.

Given,

In triangle QRS,

A is the midpoint of QR, B is the midpoint of RS, and C is the midpoint of SQ.

And also given that QA=10, BR=15, SQ=28

Let p represent the triangle ABC's perimeter.

QR + RS +SQ = p

2(QA) + 2(BR) + SQ = p

2(10) +  2(15)+ 28 = p

20 + 30+ 28 = p

78=p

Therefore, the perimeter of triangle ABC is 78

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The value of k from the given equation as in the task content is; 93.24.

It follows from the task content that the value of k for which the given equation is true is to be determined.

On this note, since the given equation is;

k / 12.6 = 7.4

Therefore, to isolate k, both sides of the equation must be multiplied by; 12.6 as follows;

k = 7.4 × 12.6

Ultimately, the value of k for which the given equation is true is; 93.24.

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Answer:

She needs 8 cups of soil
one cup per pot

Step-by-step explanation:

Answer:

Domain: (negative infinity, positive infinity)

Range: (negative infinity, 1]

Step-by-step explanation:

The equivalent two-term expression of 2x - 3 is 2(x - 1) - 1

Two expressions are equivalent if they can be simplified to the same third expression or if one of the expressions can be written like the other. In addition, you can also determine if two expressions are equivalent when values are substituted in for the variable and both arrive at the same answer.

2x - 3 can be written by expressing -3 as a sum of two numbers in which one of the numbers is -2, those two numbers are -1 and -2

so that,

2x -2 -1

now we can factorize 2x -2, which is 2(x - 1)

Finally the expression becomes 2( x - 1) -1

To check that it is equivalent we substitute any number in to 2( x -1 ) -1 and 2x - 3, if it gives same answer, then they are equivalent.

using x = 1

2( 1 - 1) -1 = -1

2(1) -3 = -1

In conclusion, 2(x-1) -1 is the equivalent expression

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Answer:

It's wrong because you don't add fractions the way you would add normal numbers.

Step-by-step explanation:

To add 1/5 to 1/2 you would need to write all numerators above the least common denominator which is 10. Then add the numerators, 5 + 2, which gives you 7/10.

Answer:

1800

Step-by-step explanation:

c = 2a;

b = 2d;

c + 2d = a + 2b

2a + b = a + 2b

a = b

a = b

c = 2a

d = b/2

Assume a = 100.

b = 100

c = 200

d = 50

This cannot be, but we can continue.

Add them: 100 + 100 + 200 + 50 = 450

The total must be an even multiple of 450.

The total can be 900, 1800, 2700, etc.

Answer: 1800

Answer:

Question 1:

The angle m∠DOX is greater than 90 degrees, but less than 135 degrees.

Looking at the diagram we see that:

m∠DOX = 120 degrees.

Question 2:

The angle m∠COX is the sum of two angles that in total are 80 degrees.

Therefore, the equation is:

m∠COX = m∠AOX + m∠COA

Question 3:

The BOA angle measurement is given by:

BOA = 60 - 40

BOA = 20 degrees

Therefore, an angle that measures 20 degrees is:

BOA.

Question 4:

From the previous question we have:

m∠BOA = 60 - 40

m∠BOA = 20

The measure of m∠BOA is 20 degrees

Question 5:

The measure of the angle EOD is given by:

m∠EOD = 140 - 120

m∠EOD = 20 degrees

THANKS

50

4.8

(41 votes)

Step-by-step explanation:

The solution to the equation as written is y = -96/161.

The term linear equation has to do with an equation in which the highest power of the variable is 1. In this case, we have been given a word problem and we would have to convert it to equation.

The equation is now to be written as;

5y + 7/3y = 5/8y - 4

Collect like terms and apply BODMAS;

5y + 7/3y  - 5/8y = -4

22y/3 - 5/8y = -4

161y/24  = -4

24(-4) = 161y

y = 24(-4)/161

y = -96/161

Having solved the equation, the solution that is obtained for the linear system is y = -96/161

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The graph of the given absolute function is attached below and the end points (-5,0) (0, 5) of the rays are marked in it.

Absolute value function:

The  function that contains an algebraic expression within absolute value symbols is called as absolute value function.

Given,

Here we have the absolute value function f(x) = |-x - 5|

Now, we have to plot the graph for this function and we have to mark the end point of the rays.

Here the given function is written as,

=> f(x) = | -x - 5|

In order to plot the graph for the function we need the table of values to point it on the graph,

For that we have to take following sample values,

When x = -5, then f(-5) = |-5 -5| = 0

When x = 0,  then f(0) = |0 - 5| = 5

Therefore, the end points of the rays are (-5,0) and (0,5)

Now, we have to plot these values on the graph.

Then we get the graph like the following.

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The cost of each CD is $21 and the cost of each cassette tape is $11.

According to the question,

We have the following information:

Todd purchased two CDs and three cassette tapes for $75. Paulena went to the same music store and purchased one CD and five cassette tapes for $76.

Now, let's take the cost of each CD to be $x and the cost of each cassette tape to be $y.

So, we have the following expressions:

2x+3y = 75 ..(1)

x+5y = 76

x = 76-5y ..(2)

Putting the value of x in equation 1:

2(76-5y)+3y = 75

152-10y+3y = 75

152-7y = 75

Subtracting 152 from both sides:

-7y = 75-152

-7y = -77

y = 77/7

y = $11

Putting this value in equation 2:

x = 76-5y

x = 76-5*11

x = 76-55

x = $21

Hence, the cost of each CD is $21 and the cost of each cassette tape is $11.

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Answer:

0.4294

Step-by-step explanation: