f(x)=x²-3x + 20
Find f(5)

The sequence 78,75,72,69,66,63,60, . . . . is arithmetic and the common difference is 3

We can determine that the sequence is arithmetic, because two consecutive terms differ by "d".

To solve this exercise we are going to apply the formula of the arithmetic sequence:

d = aₙ₊₁ - aₙ

Where:

Information about the problem:

Calculating the common difference of the sequence (d), we have:

d = aₙ₊₁ - aₙ

d =78 - 75

d = 3

It is a series of numbers that increase or decrease by a constant amount called the ratio of the progression. It is increasing when the ratio is positive and decreasing when it is negative.

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There are 5 cups of 3/8 servings in 1 7/8 cups of apple cider

The number of cup servings is 3/8

The number of apple cider cups is 1 7/8

Therefore the number of cup servings can be calculated as follows

15/8 ÷ 3/8

convert to multiplication

= 15/8 × 8/3

= 15/3

= 5

Hence there are 5 cups of 3/8 servings in 1 7/8 cups of apple cider

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Answer:

Step-by-step explanation:

1-    8

3 -    8+2= 10      

The machine will take 6.25 minutes to grade 300 multiple choice tests.

Unitary method is a concept in which the value of a single unit is first found out and then multiplied by the necessary value to get the required answer.

Here, we are given that a grading machine can grade 96 multiple choice tests in 2 minutes.

This means that the machine will take 2/96 minutes to grade one multiple choice test

X = number of minutes taken by the machine to grade 300 multiple choice tests

Thus, we can use the proportion 2/96 to predict X in the following manner-

X = 2/96 (300)

X = 600/ 96

X = 100/ 16

X = 6.25

Thus, the machine will take 6.25 minutes to grade 300 multiple choice tests.

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Answer: 2200 yards

Step-by-step explanation:

First find the unit rate, 660/3 = 220

So, Owen can jog 220 yards in one minute.

220 times 10 to find how much Owen can jog in 10 minutes.

220*10 = 2200.

Answer:

2200

Step-by-step explanation:

According to the statement an inequality to describe the possible measures of  ∠Z = 23.

An inequality is a relationship that makes a non-equal comparison of two integers or any other mathematical expressions. It is most commonly used to compare two digits upon that number line based on their size. a statement of an order relationship—greater than, larger than the other or equal thereto, less than, or lesser than or equal to—between two integers or algebraic expressions

the sum of the angles' measurements

triangle is 180 and  ∠ X=157.

∠ X + ∠ Y +∠ Z = 180

∠ Y +∠ Z  = 23

If ∠Y  was 0, then ∠Z would equal 23. But since an angle must have

a measure greater than 0,  ∠Z must be less than

23, so z < 23.

an inequality to describe the possible measures of  ∠Z = 23.

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A capable listener have  find the most interesting or useful.

Here are 4 therapist secrets to help you hone this important skill -

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5.03 x 10²¹ atoms of calcium are equivalent to 8.6 × 10⁻³ moles of calcium atoms.

To convert atoms to moles we need a conversion factor: Avogadro's number. According to Avogadro's number: there are 6.02 × 10²³ calcium atoms in 1 mole of calcium atoms. The number of moles corresponding to 3.00 × 10²¹ atoms of calcium is:

Number of moles = 5.03 x 10²¹ /  6.02 × 10²³

Number of moles = 8.6 × 10⁻³ moles of calcium

5.03 x 10²¹ atoms of calcium are equivalent to 8.6 × 10⁻³ moles of calcium atoms.

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The solution of the given equation 5/2x - 2/3 = 1/x + 5/6 is at x = 9/11.

According to the given question.

We have an equation

5/2x -2/3 = 1/x + 5/6

Since, we have to solve the above equation for x.

Thereofore, the solution of the equation 5/2x -2/3 = 1/x + 5/6 is given by

5/2x -2/3 = 1/x + 5/6

⇒ 5/2x -1/x  = 5/6 + 2/3

⇒  (5 -2) /2x  =   5+ 2(3)/6

⇒ 3/2x = 11/6

⇒6(3)  = 11(2x)

⇒ 18 = 22x

⇒ 18/22  = x

⇒ 9/11 = x  or x = 9/11

Hence, the solution of the given equation 5/2x - 2/3 = 1/x + 5/6 is at x = 9/11.

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If two of the three numbers are 24 and 42, then the GCF of these two numbers is 6 and the third number is possibly 48.

Factor is a number which when a number is divided will result to another number(whole). For two or more numbers, the largest common factor that they have is called the Greatest Common Factor (GCF).

To find the GCF of 24 and 42, list all the factors of both numbers.

24 : 1, 2, 3, 4, 6, 8, 12, 24

42: 1, 2, 3, 6, 7, 14, 21, 42

Common Factors: 1, 2, 3, 6

Greatest Common Factor: 6

If the third number is grater than 42 and does not change the GCF, then the third number is possibly 48.

24 : 1, 2, 3, 4, 6, 8, 12, 24

42: 1, 2, 3, 6, 7, 14, 21, 42

48 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Common Factors: 1, 2, 3, 6

Greatest Common Factor: 6

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According to the question, to check whether the events are mutually exclusive or not for the even integers.

As per question, select random integer numbers from [tex]1[/tex] to [tex]20[/tex] to get either an even number or a number divisible by [tex]3[/tex].

Therefore , the probability can be written as:

[tex]P(e or d) = \frac{P(E)}{n(E)} = P(e)+P(d)-P(e and d)[/tex]  

              [tex]= \frac{10}{20} +\frac{6}{20} -\frac{3}{20} = \frac{13}{20} = 65%[/tex]

The event is not mutually exclusive.

Since, the calculated percentage is [tex]65%[/tex] and it is not nearest to tenth of a percent.

What are mutually exclusive events?

Mutually exclusive events are those events which cannot happen at the same time. For instance, in any event nobody can run forward or backward together at the same time.

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I bought 2 small notebooks and 4 large notebooks.  

Let us represent the number of small notebooks with x and number of large notebooks with y.

Forming equation according to bought number of books -

x + y = 6 - equation 1

Rewriting the equation according to x

x = 6 - y  - equation 2

Now, forming equation according to cost of notebooks -

8x + 10y = 56 - equation 3

Keep the value x from equation 2 in equation 3

8 (6 - y) + 10y = 56

Performing multiplication

48 - 8y + 10y = 56

Performing subtraction and shifting values to other side of equation

2y = 56 - 48

2y = 8

Shifting 2 to other side of equation and performing division

y = 8 ÷ 2

y = 4

Keep the value of y in equation 2

x = 6 - 4

x =  2

Hence, I bought 2 small notebooks and 4 large notebooks.

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Answer:

m = 18

n = 60

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180.

We can write the following equation to find, first value of m, then the value of n:

65 + 42 + 55 + m = 180 add like terms

162 + m = 180 subtract 162 from both sides

m = 18

Now the value of n:

65 + 55 + n = 180 add like terms

120 + n = 180 subtract 120 from both sides

n = 60

The sine for the right triangle  A is 3/5.

The ratio between the side opposite the angle and the triangle's hypotenuse is known as the sine (sin) of an acute angle in a right-angled triangle. A right angle in geometry and trigonometry is an angle that is exactly 90 degrees, or 2 radians, which is equivalent to a quarter turn. If a ray is positioned so that its terminal is on a line and they are equal, the neighbouring angles are right angles.

Sin(A) = opposite/hypotenuse

           =BC/AB

           =3/AB

Given,

BC = 3

AC = 4    

Now solve for AB using Pythagorean theorem:

BC2 + AC2  = AB2

32 + 42 = AB2

9 + 16 = AB2

25 = AB2

AB = 5

Hence,

The value of AB is 5.

BC/AB = 3/5

Therefore, The sin of triangle A is 3/5.

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Answer:

Step-by-step explanation:

x − 1. _. 3. = 3 by 3 gives x − 1 = 9 and then adding 1 to both sides of x − 1 = 9 gives x = 10. Choices A, B ... written as the equation 16 + 4x = 10 + 14, which is equivalent to 16 + 4x = 24. Subtracting

Answer:

d

Step-by-step explanation:

Answer:

It rose 6 degrees

Step-by-step explanation:

I hope that's what you're asking...

Answer:

3 upon 2. that's the answer ..

Answer: The nth term of the sequence whose integers are between 1 -9 such that there is the permission of repetition but no two consecutive digits must be even is 1.834 x [tex]10^{21}[/tex]

Step-by-step explanation:

Given data,

Two people pair up to create a sequence. Each of them pick five random digits from 1 to 9.

Define Consecutive numbers :

Consecutive numbers are numbers that follow each other in order. They have a difference of 1 between every two numbers. In a set of consecutive numbers, theme an and the median are Equal. If n is a number, then n, n+1, and n+2 would be consecutive numbers Examples. 1, 2, 3, 4, 5.

The numbers that are given:

Now, suppose a (n) denotes the number of n-digit positive integers as stated in the question, thereby using:

              = (9!) x (8!) x (7!) × (6!) × (5!) × (4!) × (3!) × (2!) × (1!)

             = 362880 x 40320 x 5040 x 720 x 120 x 24 x 6 x 2 x 1

            [tex]n^{th}[/tex] = 1.834 x [tex]10^{21}[/tex]

Therefore,

The nth term of the sequence whose integers are between 1 -9 such that there is the permission of repetition but no two consecutive digits must be even is 1.834 x [tex]10^{21}[/tex].

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hi

Slope is 2 .  

here is how you do the trick :  by reading on the graph

if you go forward of  1 on the X axis , how much did the line goes up or down ?  

Here at  0  on  X- axis, we are at 0 on the Y- axis.

If you go forward of  1 on X axis, you are at 2 on Y axis.  

So the slope is  + 2

Other technique by calculus  between two points.  

Take two diffents  point on the X axis.   Call them A and B  

Slope is  :   (  f(A) -f(B) )     /  A-B

exemple here :   we have two easy points . Take 0  as  A  and  1 as  B

We read on the graph :  

A = 0  and B = 1

f(A)= 0  and f(B) = 2

Now we apply  formula :    

(  f(A) -f(B) )     /  (A-B )

(0 -2 )  / (0-1)  =  -2/-1 =  2

Slope is 2

Easy, dont you think ?

Answer:

The value of x after simplification is 6, which when substituted in the given expression will make both the sides equal.

Step-by-step explanation:

It is given that the expression given below is to be simplified using the order of operations;

The given expression is;

=> (3×2)² + 8 = ___² + 8

Now, let us assume that the blank space is 'x' in the above-mentioned question;

Firstly,

We will solve the terms within brackets as per BODMAS rules that is multiplication of both the terms;

=> (3×2)² + 8 = x² + 8

=> 6²  + 8 = x² + 8

Now, we will solve the squares of the terms given above;

=> 36  + 8 = x² + 8

Now, we will add the terms as per BODMAS rules;

=> 44 = x² + 8

=> 44 - 8 = x²

Now, we will subtract the terms as per BODMAS rules;

=> 36 = x²

Now, we will square-root both the sides given above;

=> x = √36

=> x = 6

Therefore, the value of x after simplification is 6, which when substituted in the given expression will make both the sides equal.

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The two non negative real numbers with a sum of 40 have the largest possible product are 20 and 20.

Steps to find Maximum of a function f(x).

Step 1 : Differentiate the function F(x)

Step 2 : Equate f'(x) to zero to find the critical points .

Step 3 : Substitute the critical points in f''(x) , if

f''(x)< 0 them maximum value will be at the critical point.

in the given function

the sum of two non negative real numbers is 40.

Let the numbers be x and y .

So , x+y=40

y=40-x     ....(1)

We need to maximize the product i.e. x.y

Substituting the value of y from equation (1) we get

[tex]f(x)=x.y\\ \\ f(x)=x.(40-x)\\ \\ f(x)=40x-x^{2}[/tex]

Step (i) differentiating with respect to x we get

[tex]f'(x)=40-2x[/tex]

Step (ii) Equating f'(x) to 0

[tex]40-2x=0\\ \\ x=20[/tex]

x=20 will be the critical point .

Step (iii) Substituting the critical point in f''(x)

again differentiating with respect to x we get

[tex]f''(x)=-2\\ \\ f''(20)=-2[/tex]

Since -2<0. therefore , x=20 is the point where f(x) is maximum.

Substituting the value of x=20 in equation (1) we get

y=40-x

y=40-20

y=20.

Therefore , the two non negative real numbers with a sum of 40 have the largest possible product are 20 and 20.

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The Surface area of a cone is 308.647 sq. inches.

What is the Surface area of cone ?

The area occupied by the surface / boundary of a cone. It is always measured in square units. Stacking many triangles and rotating them around an axis gives the shape of a cone. As it has a flat base, thus it has a total surface area as well as curved surface area.

The surface area of the cone can be given by finding the area of the sector by using the formula,

Area of the sector (in terms of length of arc) = (arc length x radius) / 2 = ((2πr) x l) /2 = πrl.

We are given the height and radius

h = 19 inches

r = 5 inches

The formula for Surface Area is:

Surface Area = πrl

We have to find slant height first:

[tex]l=\sqrt{h^{2}+r^{2} }[/tex]

[tex]l=\sqrt{19^{2}+5^{2} }\\ l=\sqrt{361+25}\\l= \sqrt{386}[/tex]

[tex]l=19.467 inches[/tex]

Now, The Surface Area is:

SA = πrl (π = 3.14)

SA = 3.14 x 5 x 19.467

SA = 308.647 [tex]inches^{2}[/tex]

Hence, The Surface area of a cone is 308.647 sq. inches.

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The constant of variation in  y = (6)x is (6)

y = kx            (Where k is the constant)

Here,

⇒ y = (6)x

So, k = (6)

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Answer:

The series third has a sum of 5 option (C) is correct because the sequence represents the sum of the infinite terms.

What is a sequence?

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have a series shown in the picture.

The geometric sequence is shown in the options.

As we know, in the geometric sequence there is a first term and common difference

In the first sequence:

First term a = 2

Common difference = 2(0.1)/2

Common difference d = 0.1

The sum of the infinite series is:

S = a/(1 - r)

S = 2/(1 - 0.1)

S = 2.22

In the second sequence:

First term a = 15

Common difference = 15(0.3)/15

Common difference d = 0.3

The sum of the infinite series is:

S = a/(1 - r)

S = 15/(1 - 0.3)

S = 21.42

In the third sequence:

First term a = 4

Common difference = 4(0.2)/4

Common difference d = 0.2

The sum of the infinite series is:

S = a/(1 - r)

S = 4/(1 - 0.2)

S = 5

Thus, the series third has a sum of 5 option (C) is correct because the sequence represents the sum of the infinite terms.

Step-by-step explanation:

Give an example of a number that is not a rational number. [tex]\pi =3.14[/tex]

Why it is not rational?

What is an irrational number?

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Yes, the given set of numbers can be the measures of the sides of a triangle. The triangle is obtuse.

By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

4.2 + 6.4 > 7.6

6.4 + 7.6 > 4.2

7.6 + 4.2 > 2.6

Hence, these set of numbers can be the measures of the sides of a triangle.

According to the Pythagorean Inequality Theorem, a triangle whose sides measure a, b, and c where c is the largest, the triangle can be characterized as:

acute if [tex]a^{2} + b^{2} < c^{2}[/tex]

obtuse if  [tex]a^{2} + b^{2} > c^{2}[/tex]

right if  [tex]a^{2} + b^{2} = c^{2}[/tex]

∴The longest side is 7.6.

Hence, a = 4.2, b = 6.4 and c = 7.6;

Consider [tex]a^{2} + b^{2}[/tex] :

= [tex]4.2^{2} + 6.4^{2}[/tex]

= 58.6.

Now consider [tex]c^{2}[/tex] :

= [tex]7.6^{2}[/tex]

=57.76.

Thus,  [tex]a^{2} + b^{2} > c^{2}[/tex]

Hence, the triangle is obtuse.

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