Factorise the following quadratic:
m^2 - 5m + 6

The difference between the maximum value of g(x) and the minimum value of f(x) is 5.

Given function is:

[tex]f(x)=x^{2} -2x+8[/tex]......(1)

The general form of a quadratic equation is [tex]ax^{2} +bx+c=0[/tex] with [tex]a\neq 0[/tex].

As we know the minimum value of a quadratic function is [tex]\frac{4ac-b^{2} }{4a}[/tex] when a>0

For f(x) a>0 so minimum value of f(x) = [tex]\frac{4*1*8-(-2)^2}{4*1}[/tex]=7

From the graph, the maximum value of g(x) =12

So, the difference between the maximum value of g(x) and the minimum value of f(x) =12-7 =5

Hence, the difference between the maximum value of g(x) and the minimum value of f(x) is 5.

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Answer:

Answer is

a) 50%

b) 20%

c) 40%

Step-by-step explanation:

Answer:

391.3

Step-by-step explanation:

13x43=559

559-167.70=391.3

Answer:

5/72

Step-by-step explanation:

I am pretty sure its right

The variation from x to y is an illustration of a direct variation

The value of x when y = 2 is -19/7

The variation is a direct variation.

So, we have:

x = ky

Where k represents the constant of variation

Make k the subject

k = x/y

This gives

x1/y1 = x2/y2

So, we have:

-19/14 = x/2

Multiply both sides by 2

x = -19/14 * 2

Evaluate

x = -19/7

Hence, the value of x when y = 2 is -19/7

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Answer:

Step-by-step explanation:

Given :-

To Find :-

Solution :-

We know that,

Substituting the values, we get:

↠ Perimeter = 2(9 + 7)

↠ Perimeter = 2(16)

↠ Perimeter = 32 feet

Now,

Substituting the values, we get:

↠ Area = 9 × 7

↠ Area = 56 ft²

Hence,

Step-by-step explanation:

The number of seats in each row is 8 and the total number of seats is between 70 and 150.

Let x be the number of rows, then we have the inequality:

Divide all sides by 8 to get:

So the number of rows is between 9 and 19 both inclusive.

All possible number of rows

Answer:

1.  9 rows

2.  see below

3.  9, 10, 11, 12, 13, 14, 15, 16, 17, 18

Step-by-step explanation:

Please note that I believe there are typing errors in the question and that the given information should be:

Question 1

To determine the least possible number of rows in the auditorium, divide the least number of seats by the number of seats in a row:

⇒ 70 ÷ 8 = 8.75

As the answer is a decimal, round it up to the nearest whole number.

Therefore, the least possible number of rows in the auditorium is 9 rows.

Question 2

Find the greatest number of rows by dividing the greatest number of seats by the number of seats in a row:

⇒ 150 ÷ 8 = 18.75

As there should be fewer than 150 seats we cannot round the number up (as this would make there be more than 150 seats), so instead must round it down to 18.

Therefore, the greatest number of rows in the auditorium is 18 rows.

Question 3

As we have found the least number of rows in question 1 and the greatest number of rows in question 2, all we need to do is list all the numbers between (and including) these numbers.

Therefore, all the possible numbers of rows in the auditorium are:

9, 10, 11, 12, 13, 14, 15, 16, 17, 18

Answer:

8(a+4)=8a+32

Step-by-step explanation:

Answer:

264

Step-by-step explanation:

(11 x 6)/2 x 8 = 264

B x h = V

Answer: 28 cm.

Step-by-step explanation: To find the area of trapezoids, you need to add base 1 and base 2, multiply the height, and divide it all by 2.  The work is done below:

b1 + b2 x h / 2, where b1 and b2 are the bases and h is the height.

5 + 9 x 4 / 2 = ?

Step 1 (Add): 5 + 9 = 14.

Step 2 (Multiply):  14 x 4 = 56.

Step 3 (Divide): 56 / 2 = 28.

Therefore, 28 cm is your answer.

Hope this helps! :)

The amount of money that should be invested at 7% compounded daily is $199,421.68.

Mathematically, compound interest is given by this formula:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

Where:

Given the following data:

Future value = $200,000.

Interest rate = 7% = 0.07.

Time = 15 year.

Substituting the given parameters into the formula, we have;

[tex]200000=P(1+\frac{0.07}{365} )^{ 15}\\\\200000=P(1+0.00019)^{15}\\\\200000=P(1.00019)^{15}\\\\200000=1.0029P\\\\P=\frac{200000}{1.0029}[/tex]

P = $199,421.68.

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Answer:

The womans age is 25

mothers age is 50

Step-by-step explanation:

add those up and you get 75

Answer:

The woman is 25, and her mother is 50.

Step-by-step explanation:

The woman is half the mother's age.

That means the mother is twice the woman's age.

Let the woman's age be x

The mother's age is 2x.

The sum of the ages is 75.

x + 2x = 75

3x = 75

x = 25

2x = 2(25) = 50

Answer: The woman is 25, and her mother is 50.

Answer:

I disagree.

Step-by-step explanation:

An integer is a whole number ranging from -2,147,483,648 to 2,147,483,647.

A ratio of two integers with -4 could be -4/1, so -4 is a rational number.

I agree.

Hope it helps.

Do comment if you have any query.

Total deposite is the resultant amount we deposite. The total deposite that Art made is given by: Option B: $1,545.83

Resultant deposited amount = Deposited amount - The amount deducted.

We subtract the amount deducted from the amount deposited to get the resultant deposite amount that will go in bank.

Well, it might be that we deduced more than what we deposite, in that case net deposite will come as negative, indicating that there is deduction instead of deposite.

The missing image of the deposite ticket is attached below.

From that image, we can see that:

Thus, the net deposited amount is:

Net deposite = deposited amounts - deduced amounts

Net deposite = 13.50 + 942.06 + 75.53 + 670.14 -155.40

Net deposite = 1545.83 (in dollars).

Thus, the total deposite that Art made is given by: Option B: $1,545.83

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Answer:

B

Step-by-step explanation:

Answer:

1.3

Step-by-step explanation:

To find what x equals, you need to first divide by 48 and 37.

This is because that x is being multiplied by 37.

48 ÷ 37 = 1.297.......

The 97 in 1.297 is repeating and goes on forever.

Rounding the the nearest tenth would create the number 1.3 as the correct answer.

[tex] \tan(60) = \frac{x}{ \sqrt{7} } [/tex]

[tex] \sqrt{3} = \frac{x}{ \sqrt{7} } [/tex]

[tex]x = \sqrt{21} [/tex]

[tex]\frak{\fcolorbox{black}{pink}{Black Pink in your area$~$}}[/tex] ~←(>▽<)ﾉ

Answer:

√21

Step-by-step explanation:

30, 60, 90 triangle

Across from 30 is a, across from 60 is a√3

So, √7√3 is √21

Answer:  [tex]j \div 8[/tex]

We're dividing unknown number j over 8

We can write it as [tex]\frac{j}{8}[/tex] similar to how [tex]\frac{3}{4} = 3 \div 4[/tex]

The quotient is the result of a division problem (there may or may not be a remainder).

Answer: y=.256x

Step-by-step explanation:

This line has the smallest coefficient for x.

Answer:

I think it is B (16)

Step-by-step explanation:

Draw a rhombus with the diagonals.

4 right triangles are formed.

The intersection of the diagonals of a rhombus form 90 degree (right) angles (property of a rhombus).

The diagonals of a rhombus bisect each other. This means that they cut each other in half.

So, each of the right triangles have one side = 1, one side = 2.5 and the hypotenuse = unknown (sides of the

rhombus).

Triangle 1. ABC

side a = 2.5, side b = 1

tan A = a/b = 2.5/1 = 2.5

tan A = 2.5

tan 68.2 deg = 2.5

Since, angle C = 90 and angle A = 68.2

angle B = 21.8 deg. (180 - (90 + 68.2))

Since the diagonals bisect angles in each corner of a rhombus (property of a rhombus), therefore, one corner angle is 68.2 + 68.2 = 136.4 deg. and the same side other corner angle is 21.8 + 21.8 = 43.6 deg.

Adjacent sides (ones next to each other) of a rhombus are supplementary. This means that their measures add up to 180 degrees.

Therefore, the opposite corners are

180 - 136.4 = 43.6 and

180 - 43.6 = 136.4.

So, the four angles are,

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Answer:

Answers:

lower bound = 39001

upper bound = 40999

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

Explanation:

You'll have to think backwards to find what values round to 690,000 when rounding to the nearest thousand.

It turns out that if x is on the interval [tex]689,500 \le x \le 690,499[/tex], then x will round to 690,000 when rounding to the nearest thousand. The x refers to the population of Sheffield, so it's some integer in that range.

Through similar logic, if y is on the interval [tex]729,500\le y \le 730,499[/tex] then it will round to 730,000 when rounding to the nearest thousand. This represents the population of Nottingham.

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

Now let's say we go for the smallest possible value of x (689500) and the largest possible value of y (730499). This guarantees the two populations are the most spread out or distant from one another. Subtract those two values:

730,499 - 689,500 = 40,999

This is the largest difference possible of the two populations. It represents the upper bound, i.e. it's the ceiling.

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

On the other hand, let's now say x is as big as possible (690499) and y will be as small as possible (729500). Subtract those values:

729,500 - 690,499 = 39,001

This is the lower bound. It's the smallest the difference can be. It's considered the floor.

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

Let d be the difference in the populations. In other words, d = y-x

We found that the lower bound was 39,001 and the upper bound was 40,999

Meaning that

[tex]39,001 \le y-x \le 40,999[/tex]

or

[tex]39,001 \le d \le 40,999[/tex]

Answer:

A and B

Step-by-step explanation:

A. Since 2 angles are congruent you know that there has to be 2 equal sides

B. It has an obtuse angle which is 100 degrees.

C. Triangle has 2 congruent sides so this is incorrect

D. Not all sides are equal

E. Not all angles are acute

F. None of the angles are 90 degrees

Answer:

C. $250

Step-by-step explanation:

-To find the unit rate you need to divide the Amount Earned by Time worked

-When you do this you get 6.25

-Then you multiply 6.25 by 40

-That equals 250 and therefore the answer is C

Answer:

I just answered these with your most recent post.

Answer:

4a²-8a+4

Step-by-step explanation:

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

[tex](2a-2)(2a-2) = 4a^{2} -4a-4a+4[/tex]

[tex]4a^{2} -4a-4a+4=4a^{2} -8a+4[/tex]

Answer:

<M = 50

Step-by-step explanation:

The sum of the angles of a triangle is 180. 52+ 78+x = 180. Combine like terms. 130 +x = 180.

The value of m for the given combination of two right-angle triangles will be 7√5.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

In the bigger right-angle triangle suppose the missing length is x.

By Pythagora's theorem,

(28 + 7)² = x² + m²

x² = 35² - m²                   (1)

In the smaller right-angle triangle,

x² = 28² + n²                   (2)

By comparing equations (1) and (2).

35² - m² = 28² + n²

m² + n² = 35² - 28²

In the smallest right-angle triangle,

m² = n² + 7²

n² = m² - 7²

By substitution,

m² + m² - 7² = 35² - 28²

2m² = 35² - 28² + 7²

m² = 245

m² = 7² x 5

m = 7√5.

Hence "The value of m for the given combination of two right-angle triangles will be 7√5".

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Answer:

B

Step-by-step explanation:

(a^3/2) / a

= a^(1/2)

= √a

= B

Answer:

D. A ( a-1/2)

Step-by-step explanation:

Hello!!

You must cancel out the common factor or in this case, ( a3/2) on the top.

You will now have ( 3/2) which should then be simplified to ( 1 1/2) or in this case ( A- 1/2)

Hope this helped!. :)