Suppose $\frac{1}{2} + \frac{1}{3} + \ldots +\frac{1}{x} > 1\frac{1}{2}$. What is the smallest possible value for $x$?

Answer:

4√2 cm

Step-by-step explanation:

ABCD is a square.

Each side measures 8 cm.

So,

AB = BC = CD = AD = 8 cm

P, Q, R, and S are mid - points of ABCD.

P is the mid - point of AB.

So,

AP = PB

AP + PB = AB

AP + AP = AB

2AP = 8

AP = 8 / 2

AP = 4 cm

S id the mid - point of AD.

So,

DS = SA

DS + SA = AD

SA + SA = AD

2SA = 8

SA = 8 / 2

SA = 4 cm

Property of a square : The angle between two sides is 90°.

So,

The angle between side SA and AP is 90°.

So,

SA, AP and SP forms a right angled triangles.

By Pythagoras theorem,

( SP)² = ( SA )² + ( AP )²

( SP )² = 4² + 4²

= 16 + 16

( SP )² = 32

SP = √32

SP = 4√2 cm

Since PQRS is also a square.

In square, all sides are equal.

So,

PQ = QR = RS = SP

Since SP = 4√2 cm

Hence,

PQ = 4√2 cm

Therefore,

the length of PQ is 4√2 cm.

Answer: 5.7

Step-by-step explanation:

Midpoint means the middle of line. So to find the middle of the line I just need to divide the line by 2.

So the midpoint of AB is:

8/2=4 = BP

Since Q is also a midpoint so BQ is equal to 4.

We know BP=BQ=4. Looking at the diagram we can tell PBQ is a triangle.

The hypotenuse of the triangle is PQ.

Pythagoras's theorem helps us to find the hypotenuse. So we just plug in the values to find PQ.

P's Theorem : a²+b²=c²

basically in the case of this question it means:

(BP)²+(BQ)²=(PQ)²

now we just subsiture the values and solve for PQ:

4²+4²=(PQ)²

16+16=(PQ)²

32=(PQ)²

PQ=5.65...

= 5.7(rounded to one decimal place)

Step-by-step explanation:

make sure to number your equations

[tex]2x - y - 3 = 0 \: \: \: \: \: \: \: \: \: \: \: (1)[/tex]

[tex]4x + y - 3 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: (2)[/tex]

In equation 2 make y the subject

[tex]y = - 4x + 3 \: \: \: \: \: \: \: \: \: (3)[/tex]

subs 3 into 1

[tex]2x - ( - 4x + 3) - 3 = 0[/tex]

[tex]2x + 4x - 3 - 3 = 0[/tex]

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

[tex]6x = 6[/tex]

[tex]x = 1 \: \: \: \: \: \: \: \: \: \: \: (4)[/tex]

sub's 4 into 2

[tex]4(1) + y - 3 = 0[/tex]

[tex]4 + y - 3 = 0[/tex]

[tex]y = - 4 + 3[/tex]

[tex]y = - 1[/tex]

29,060,000

When writing this out, it is important to make sure you include the commas and the exact amount of zero's by the way.

Answer:29,060,000

Step-by-step explanation:

with every three zeros your number grows bigger 100,00= One hundred thousand. 29,000,000 = thwenty-nine million

Answer:

B. 30/65 and experimental

Step-by-step explanation:

Answer:

Hello!!!

[tex]y = - 2x + 4 \\ 0 = - 2x + 4 \\ 2x = 4 \\ x = 2[/tex]

Step-by-step explanation:

That is the answer :D

Answer:

it would be solved by it mom

The quadratic equation has two solutions if b^2 - 4ac > 0

Given the equation ax^4 + bx^2 + c=0

Substitute into the formula to have:

The equation becomes aP^2 + bP + c = 0

For us to have a unique solution, the discriminant b^2 - 4ac must be greater than zero. Hence the quadratic equation has two solutions if b^2 - 4ac > 0

learn more on discriminant here; https://brainly.com/question/1537997

the x-intercept is the point where the line touches the x-axis. The x-intercept is (4,0)

the y-intercept is the point where the line touches the y-axis. The y-intercept is (0,-2)

Answer:

4.92

Step-by-step explanation:

Answer: 4.92

Step-by-step explanation:

To round a three decimal integer like 4.922, you look at the trailing digit or last decimal (2) in this case.

Then determine if greater or less than 5. If greater or equal to 5, remove last digit 2 and then add 1 to the number before (2) or 2nd decimals place.

So we have 4.922 with last decimals being 2.

Therefore, we do not add and keep last decimals before the same.

Answer is 4.92

Answer:

y=14x

Step-by-step explanation:

f(x) is linear.

g(x) is exponential.

F(x) is linear! Remember, linear functions have a set amount of rate of change, in this case it’s 2! G(x) is a exponential function because instead of going down by a certain amount, it’s simply going down by half.

Hope this helps!

Answer:

y = -6x + 70

Step-by-step explanation:

Since the amount of oil in the tank decreases constantly, we need to create a linear function. Using the base form, y = mx + b, we can replace -6 for m because volume decreases by 6 (or increases by -6) each hour, and +70 for b because we start off with 70 liters of oil. So we get y = -6x + 70, with x representing the number of hours, and y representing the volume of oil remaining.

Answer: store B store C store A

Step-by-step explanation: by multiplying the amount the price is with the sale which is .9 for 90% .8 for the 80% and .85 for the 85% by the previous amount you can find how much it is after the sale

Answer:

1. B

2. Seven Hundred thousand nine hundred and four

Step-by-step explanation:

Answer:

the answer is d

Step-by-step explanation:

Answer:

Solved for n: n < 1.3

Step-by-step explanation:

Are there answer choices included?

Answer:i cant see it that well its blurry

Step-by-step explanation:

Answer:

The domain of the graph is {-3, -1, 1, 4}. The range of the graph is {-4, -1, 1, 4}

The domain of the set of ordered pairs is {-4, -3, 1}. The range of the set of ordered pairs is {1, 3, 4}

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

3(2x + 7) ≤ 6(x - 4) ← divide both sides by 3

2x + 7 ≤ 2(x - 4)

2x + 7 ≤ 2x - 8 ( subtract 2x from both sides )

7 ≤ - 8 ← False statement

This means the inequality has no solution

Answer:

8000

Step-by-step explanation:

Since 8 is bigger than 5, you can increase it

7829 to the nearest ten: 7830

7829 to the nearest hundred: 7800

Hope this helps!

The value 829 > 500 thus rounding of 7829 to the nearest 1000 is 8000.

To round up or down tens place then we need to look at the unit place if it is less than 5 then we need to keep it as it and if it is greater than 5 then we need to round up the tens digit.

For example round of 346 will, be350 and round of 344 will be 340

Given the digit,7829

9 → unit place

2 → tens place

8 → hundred place

7 → thousand place

In order to round to the nearest thousand we need to look at a hundred places if it is > 500 then we will round up.

Since 829 > 500 so 7829 → 8000

Hence "The value 829 > 500 thus rounding of 7829 to the nearest 1000 is 8000".

To learn more about rounding a digit,

https://brainly.com/question/116595

#SPJ2

Step-by-step explanation:

where slope is equal to y2-y1/x2-x1

Answer:

  3, 5, 2, 1, 4

Step-by-step explanation:

In step 2, parentheses are eliminated: distributive property.

In step 3, x is subtracted: subtraction property.

In step 4, 12 is added: addition property.

In step 5, the equation is divided by 17: division property.

__

The properties are listed in the order of statements ...

  3, 5, 2, 1, 4

Answer:

x = -3

Step-by-step explanation:

hope this helps!!

Answer:

7

Step-by-step explanation:

25% of 28 =

= 0.25 × 28

= 7

Answer: 7

Answer:

Quintic Trinomial (2nd option)

Step-by-step explanation:

We know that this is a quintic polynomial because the degrees add up to 5. If we expand the polynomial, we have [tex]-3x(x^2-4)(2x^2+5)=(-3x^3-12x)(2x^2+5)=-6x^5-45x^3-24x^3-60x=-6x^5-69x^3-60x[/tex]

So, there are 3 terms, which is a trinomial.

first you have to choose one of the equations and isolate one of the variables

3x - 6y = 2

-6y = 2 - 3x

y = 2/-6 + 1/2

then you have to substitute it in the other equation

4x-6(2/-6 + 1/2) = 2

4x + 2  - 3 = 2

4x - 1 = 2

4x = 3

x = 3/4

after that you solve for y

3 (3/4) - 6y = 2

9/4 - 6y = 2

-6y= - 1/4

y= 24

THIS MAY NOT BE RIGHT BTW

Rewrite both fractions with a common denominator:

8/11 x 5 = 40/55

3/5 x 11 = 33/55

40/55 is greater than 33/55 so 8/11 is greater than 3/5

The answers are underneath each problem. The reason this makes sense is  due to the distributive property.

27. GCF of 27 and 12 is 3

3(4+9)

28. GCF of 12 and 36 is 12

12(1+3)

29. GCF of 16 and 20 is 4

4(4+5)

30. GCF of 2x and 8 is 2

2(x+4)

31. GCF of 30 and 12x is 6

6(5+2x)

32. GCF of 42x and 49 is 7

7(6x+7)

To do this, find the GCF and then divide each number by so. Then, add them in parenthisis and multiply it by the GCF