Work out the value of (√2)4

Answer:

n=10

Step-by-step explanation:

The given equation is  

[tex]10+12+14+...+2n=90[/tex]        ...(1)

Let nth term is 2n.

We need to find the values of n.

It is clear that [tex]S_n=10+12+14+...+2n[/tex] is sum of A.P., whose first term is 10 and common difference is 2.

Sum of A.P. is  

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]

where, a is first term and d is common difference.

Substitute a=10 and d=2 in the above formula.

[tex]S_n=\dfrac{n}{2}[2(10)+(n-1)2][/tex]

[tex]10+12+14+...+2n=n[10+n-1][/tex]

[tex]10+12+14+...+2n=n[9+n][/tex]     ...(2)

From (1) and (2), we get

[tex]n(9+n)=90[/tex]

[tex]n^2+9n-90=0[/tex]

Splitting middle term, we get

[tex]n^2+15n-6n-90=0[/tex]

[tex]n(n+15)-6(n+15)=0[/tex]

[tex](n+15)(n-6)=0[/tex]

[tex]n=-15,6[/tex]

Since, n represents the number of terms so n cannot be a negative number, therefore number of term is 6.

Note: nth term and variable n both are different.

[tex]a_n=a+(n-1)d[/tex]

[tex]a_6=10+(6-1)2=10+10=20[/tex]

Sixth term is 20. So,

[tex]2n=20[/tex]

[tex]n=10[/tex]

Therefore, the value of n is 10.

Answer:

see below

Step-by-step explanation:

This is an arithmetic sequence. The explicit formula for an arithmetic sequence is aₙ = a₁ + (n - 1)d where a₁ is the first term and d is the common difference. In this case a₁ = 9 and d = 6 so we have:

aₙ = 9 + (n - 1) * 6

aₙ = 9 + 6n - 6

aₙ 6n + 3

Answer:

x=6

Step-by-step explanation:

FG + GH = FH

4+x-3 = 2x-5

Combine terms

x+1 = 2x-5

Subtract x from each side

x+1-x = 2x-5-x

1 = x-5

Add 5 to each side

1+5 = x-5+5

6 =x

Answer:

x=6

Step-by-step explanation:

F G + G H = F H

4+x-3 = 2x-5

Answer: 22

Step-by-step explanation:

22+5= 27

27-4=23

23+7=30

30-8=22

Answer:

22+m+ 7n - 8

Step-by-step explanation:

22+5m-4m+7n-8

22+m+ 7n - 8

you subract 4m from 5m because there are like terms

none of the others are like terms so you cant add or subract them

Answer:

C and D

Step-by-step explanation:

The given expressions written in standard form are;

A) 21 × 10⁷

B) 5 × 10²

This is about expression of given algebra in standard form making use of laws of indices.

A) We are given;

(7 × 10⁵) × (3 × 10²)

Now according to the law of indices, when we want to multiply 2 numbers with same bases and different exponents, we retain the bases and add the exponents.

Also, when we want to multiply 2 numbers with different bases and same exponent, we multiply the bases and retain the exponent.

Applying that to our question gives;

(7 × 3)¹ × (10)⁽⁵ ⁺ ²⁾

⇒ 21 × 10⁷

B) We are given;

(2 × 10⁵)/(4 × 10²)

According to the law of indices, when we want to divide 2 numbers with same bases and different exponents, we retain the bases and subtract the exponents.

Also, when we want to divide 2 numbers with different bases and same exponent, we divide the bases and retain the exponent.

Thus;

(2/4)¹ × (10)⁽⁵ ⁻ ²⁾ = 0.5 × 10³

0.5 can also be expressed as; 5 × 10⁻¹

Thus, 5 × 10⁻¹ × 10³ = 5 × 10²

Read more at; brainly.in/question/18681990

Answer:

hope this helps you

Answer:

Step-by-step explanation:

answer b

Answer:

Option B

Step-by-step explanation:

Let us consider that these right triangles form a sort of proportion among one another. If that is so, we can list out which sides of one triangle correspond to which side of the other triangle;

[tex]BA and DE,\\AC and EC,\\BC and DC[/tex]

With this being said, it is given that BA = 84, and DE = 7. To prove that the could be proportional, let us form a like fraction;

[tex]DE / BA =\\84 / 7 = \\12\\\\Conclusion, BA = 12 * DE\\Conclusion, Sides Of Triangle DEC = 12 * Sides Of Triangle BAC[/tex]

With that, the length of AC in respect to EC can be represented as such;

[tex]AC = 12 * EC,\\156 - x = 12 * x,\\156 - x = 12x,\\156 = 13x,\\\\x = 12[/tex]

[tex]AC = 156 - x = 156 - 12 = 144[/tex]

Solution - Option B

Answer:

2.61

Step-by-step explanation:

To find the amount of space between the two points, subtract -2.61 from 0.

0 - (-2.61)       Distribute the negative

0 + 2.61          Add

2.61

Answer:

complementary

Step-by-step explanation:

to complete 90 gradus

_________________________________

Hey!!

<a and <b are complementary angles.

Hope it helps

Good luck on your assignment

__________________________________

Answer:

108.3%

Step-by-step explanation:

The manufacturer spends $12,000 in buying the car parts and sells the car for $25,000

Selling price= $25,000

Cost price=$12,000

Gain= selling price-cost price

= 25000-12000

= $13000

The percentage profit can be calculated by applying the formular below

Profit= Gain/cost price×100/1

=13000/12000×100/1

=1.083×100

= 108.3%

Hence the percentage profit is 108.3%

Answer:

52%

Step-by-step explanation:

Step one

In this problem we we have to calculate the profit made after spending a certain amount on the car

Step two

Given that he spent $12000 for parts

And he sold the car for $25000

The profit made is

=Cost of car - cost of repair

= 25,000-12,000

=$13,000

The profit made is $13,000

Step three

Using the cost of the car and the profit realized we can calculate the percentage of the profit made

= (13,000/25,000)*100

= 0.52*100

=52%

Answer:

no mistakes

Step-by-step explanation:

There are no mistakes in the derivation of the quadratic formula by completing the square

Step 1

Move c to the right hand side

Step 2 Get x^2 to have a coefficient of 1

Step 3 complete the square by adding ( b/2a) ^2 to each side

Step 4 Write in the completed square form  ( x+ b/2x) ^2 = -c/a + ( b/2a) ^2

Step 5 take the square root of each side, remembering the plus and minus

Step 6 subtract  (b/2a) from each side

Step-by-step explanation:

-4 (A)

because the minimum value of f(x) is f(-2)= -3

the range is between {-3,7}

Answer:

A. -4

Step-by-step explanation:

Answer: 4 feet < Length < 21 feet

Step-by-step explanation:

From the question, the length of the rectangular fence is 4 feet more than its width and the perimeter of the fence is less than 42 feet. The range of the lengths of the fence will be:

Length is greater than 4 feet (4 feet more than the width. This means that the length must be at least 4 feet) and less than 21 feet i.e the length must be less than 1/2 of the perimeter which is 42/2 = 21. Therefore, the answer will be:

4 feet < Length < 21 feet

Answer:

12.5

its right

Step-by-step explanation:

Answer:

Step-by-step explanation:

No it does not cause the 8 To the 17 overpasses the coordinates 0,-9 so the perimeter of the imaginary circle it expands loosely over the designated area

Answer:

Answer C

Step-by-step explanation:

EDGE2021

Answer:

the approximate area of the compass is 615.75mm2

Answer:

180 cm³

Step-by-step explanation:

Volume = base area x height

4x9x5

Answer:

180 cm^3

Step-by-step explanation:

Vol = base time height times length

4 times 9 times 5 = 180

Answer:

5 units

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh

30 = 1/2 (12)h

Multiply

30 = 6h

Divide each side by 6

30/6 = 6h/6

5 = h

Answer:

5 units

Step-by-step explanation:

Next time please supply the formula, which was apparently given in this question:

A = (1/2)(base)(height)

Here, A = 30 units^2 = (1/2)(12 units)(height), or

                30 units^2 = (6 units)(height)

Solving for (height), we get

                 30 units^2

(height) = ------------------ = 5 units

                   6 units

The height is 5 units

Answer:

log7(in the baes)49=2

Step-by-step explanation:

Answer:

256

Step-by-step explanation:

Assuming that the length of his garage is the longer dimension (16), the area of the square yard must be 16*16=256 square units. Hope this helps!

Answer:

y = 3x - 6

Step-by-step explanation:

Slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

15x - 5y = 30

Subtract 15x from each side

15x-15x - 5y =-15x+ 30

-5y = -15x+30

Divide each side by -5

-5y/-5 = -15x/-5 +30/-5

y = 3x - 6

Answer:

[tex]y = 3x - 6[/tex]

Step-by-step explanation:

[tex]15x - 5y = 30 \\ - 5y = 30 - 15x \\ \frac{ - 5y}{ - 5} = \frac{30 - 15x}{ - 5} \\ y = - 6 + 3x \\ y = 3x - 6[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

He can ride his bike 5/34 of a mile per hour.

Step-by-step explanation:

If Ryan can ride the bike 5 miles per 34 hours, then all you have to do is divide the hours and the miles by 34. This way, you would be left with only one hour and 5/34 of a mile.

Answer:

Step-by-step explanation:

Answer:

Option C.

Step-by-step explanation:

Let as consider f(x) is a function.

If [tex]f(-x)=f(x)[/tex], then f(x) is even function.

If [tex]f(-x)=-f(x)[/tex], then f(x) is odd function.

It means, if (x,y) is a point of the function, then (-x,-y)is also a point of the function.

In option A, (-5,3) is a point of the function, but (5,-3) is not a point of the function.

So, function in option A is not an odd function.

In option B, (-4,2) is a point of the function, but (4,-2) is not a point of the function.

So, function in option B is not an odd function.

In option C,

If (-4,0) is a point of function, then (4,0) is also the point of the function.

Similarly, (-3,1) and (3,-1), (-2,-3) and (2,3), (-1,-2) and (1,2) are points of the function.

So, function in option C is an odd function.

In option D, (-4,3) is a point of the function, but (4,-3) is not a point of the function.

So, function in option D is not an odd function.

Answer:

C

Step-by-step explanation:

on EDGE 2023

Answer:

100 x 25 x 4 = 10000[tex]m^{3}[/tex]

Step-by-step explanation:

Answer:

a) k = 3 b) k = 4

Step-by-step explanation:

a) 3 x 7 = 21

b) 4 x 3 = 12

Answer:

1) k=3 (2) k=4

Step-by-step explanation:

[tex]21=k\cdot \:7\quad \\\mathrm{Switch\:sides}\\k\cdot \:7=21\\\frac{k\cdot \:7}{7}=\frac{21}{7}\\k=3\\2)\\12=k\cdot \:3\\Switch\:sides\\k\cdot \:3=12\\\frac{k\cdot \:3}{3}=\frac{12}{3}\\k=4[/tex]

Answer:

130 times

Step-by-step explanation:

If you convert the time to minutes, 120 seconds is 2 minutes. Since Ran's heart beats 65 times a minute, you multiply 65 by 2 and get 130

The length c is the hypotenuse of the triangle WYZ, and the value of c is 5 units

Considering the triangle WYZ, we make use of the following Pythagoras theorem

c² = 4² + 3²

Evaluate the exponents

c² = 16 + 9

Evaluate the sum

c² = 25

Take the positive square root of both sides

c = 5

This means that the value of c is 5 units

Read more about right triangles at:

https://brainly.com/question/2217700

#SPJ5