simplify the equation

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:

Givens

Notice that the window is a square, that means all four sides are congruent, so it has 8 meters in total, which would cost 24 euros plus the crystal. Therefore, the total cost of a window with 2 meters side is 24+12 = 36 euros.

Specifically, the function of the cost is: [tex]C(x)=3x+12[/tex], where [tex]x[/tex] represents meters of sides. (C)

[tex]60=3x+12\\60-12=3x\\x=\frac{48}{3}=16[/tex]

The window has 16 meters between the four sides, which gives 5 meters per side.

The graph of the function is attached.

Answer:

the approximate area of the compass is 615.75mm2

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:

hope this helps you

Answer:

3/4

Step-by-step explanation:

There is 2 Os and 8 in total.

So the probability of selecting O is 1/4

As the question asks everything but O, you subtract that answer from 1. 1-1/4=3/4

Answer:

x = 98

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

x = 53+45

x = 98

Answer:

x°=98°

Step-by-step explanation:

Since a triangle's interior angles add up to 180°, then ∠G is 180°-45°-53° or 82°. Since ∠G and ∠x add up to 180° (they form a straight line), then x° is 180°-82° or 98°.

x°=98°

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:

500 liters

Step-by-step explanation:

We want to find the total amount of water that was drained.

He drained 62.5 liters of water per minute and this went on for 8 minutes. The total amount of water drained is:

62.5 * 8 = 500 liters of water

Answer: 17.75 deliveries made per hour

Step-by-step explanation:

71/4 = how many deliveries made per hour.

Answer: 12 child tickets

Step-by-step explanation:

We can use system of equations to find how many child tickets were sold. Let's say x is adult and y is child.

Equation 1

5.25x+3.05y=498.6

This equation comes from the cost of tickets.

Equation 2

x+y=100

This equation comes from the number of tickets.

We can use elimination method to solve for y.

5.25x+3.05y=498.6

5.25x+5.25y=525

Now, we can subtract the equations for x to cancel out and to solve for y.

-2.2y=-26.4

y=12

Answer:

12

Step-by-step explanation:

60% of $12

(60 × 20) ÷ 100 = 12

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:

Step-by-step explanation:

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:

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:

300 inches tall or a flat surface is the best way you could use it to be

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:

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: 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:

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:

The expression 7x represents the height of the container.

Step-by-step explanation:

From the question:

We are being informed that; if the length of the container is half of a foot longer than its width.

Let the width be x;

Then the length of the container can now be ; x+1/2

We all known that the volume of a rectangular prism is : V= l×w×h

here;

l = length

w = width

h = height  

If we rewrite the given expression :

[tex]\mathbf{7x^3+3.5x^2}[/tex];

Then we factor we make a similar coefficient  of  the above equation, the  remaining entities left in the parenthesis should be a linear term  with a leading coefficient of 1 to match the expression for the length of the container.

i.e

[tex]\mathbf{7x^3+3.5x^2}} \\ \\\mathbf{7x^2(x+1/2)} \\ \\\mathbf{7*x*x*(x+1/2)}[/tex]

Hence, if the length of the container is half a foot longer than its width, x, then the expression 7x represents the height of the container.

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

here is your ansewewrew

Answer:

the slope is 12

Step-by-step explanation:

y=12x+1 is from the formula y=mx+b where m is the slope and b is the y-intercept.

Since 12 has replaced m, it is the slope.

Since 1 has replaced b, it is the y-intercept.

"the slope is 12" is the correct answer choice.

Answer:

78 square ft.

The answer is 75 ft

explanation

12ft x 2.5ft = 30ft

12ft x 2ft = 24ft

12ft x 1.5ft = 18ft

1.5ft x 2ft = 3ft

30 + 24 + 18 + 3 = 75

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