Two consecutive positive numbers have a sum of 27. What are the two numbers?

The smaller number is The larger number is k _________________ _________________

Answer:

The sum of the arithmetic series

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

Step-by-step explanation:

Explanation

Let  a , a+d , a+2 d , ..........a+(n-1)d +....... is an arithmetic sequence

The sum of the sequence is called arithmetic series

The [tex]n^{th}[/tex] term of the sequence

[tex]t_{n} = a + (n-1) d[/tex]

The sum of the arithmetic series

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

Here 'a' is the first term of the sequence

and 'd' be the difference between two values

sum of first term

put n=1  ⇒  [tex]S_{1} = a[/tex]

Put n =2 ⇒ [tex]S_{2} = \frac{2}{2} (2 a + (2-1)d)[/tex]

                  [tex]S_{2} = 2 a + d[/tex]

......and so on

The sum of the  arithmetic series

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

Answer:

42 degrees.

Step-by-step explanation:

[tex]\angle BOC+\angle AOB=90^\circ $(Complementary Angles)\\6x - 6^\circ+5x + 8^\circ=90^\circ\\6x+5x-6^\circ+ 8^\circ=90^\circ\\11x+ 2^\circ=90^\circ\\11x=90^\circ-2^\circ\\11x=88^\circ\\$Divide both sides by 11\\x=8^\circ\\$Therefore:\\m\angle BOC=6x - 6^\circ\\=6(8) - 6^\circ\\=48-6\\=42^\circ[/tex]

The measure of angle BOC is 42 degrees.

Answer:

BOC = 42º

Step-by-step explanation:

Angle BOC is equal to 42 degrees, due to these steps -

1. Create the equation which will result to be -

6x - 6 + 5x + 8 = 90

2. Simplify by adding variables and numbers together -

11x + 2 = 90

3. Subtract 2 from both sides to get -

11x = 88

4. Divide by 11 on both sides to get-

x = 8

5. Substitute x in angle BOC as 8 to get this equation -

6(8) - 6

6. Solve

48 - 6 =

42º

Your final answer for angle BOC is 42º!

The probability that Laura will go first and Andy second is 1/210

Answer:

Domain: ∞

Range: y ≥ -4

Step-by-step explanation:

The domain of any quadratic function is always infinite or ∞. The range ends where the minimum value is or the maximum value depending on which way the parabola is facing- upward or downward.

Answer:

9a + 3b

Step-by-step explanation:

Given

5(3a + b) - 2(3a + b) ← distribute both parenthesis

= 15a + 5b - 6a - 2b ← collect like terms

= 9a + 3b

Answer:

The final answer would be [tex]9a + 3b[/tex] .

Step-by-step explanation:

Solve the following equation:

[tex]5(3a+b)-2(3a+b)[/tex]

Use Distributive Property:

[tex]5(3a+b)-2(3a+b)[/tex]

[tex]15a + 5b - 6a - 2b[/tex]

-Combine [tex]15a[/tex] and [tex]6a[/tex]:

[tex]15a + 5b - 6a - 2b[/tex]

[tex]9a + 5b - 2b[/tex]

-Combine [tex]5b[/tex] and [tex]-2b[/tex]:

[tex]9a + 5b - 2b[/tex]

[tex]9a + 3b[/tex]

So, the answer is [tex]9a + 3b[/tex] .

Answer:

y = 5/6x +1

Step-by-step explanation:

5x - 6y = -6

We want the equation in the form

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

Subtract 5x from each side

5x -5x - 6y =-5x -6

-6y = -5x -6

Divide each side -6

-6y/-6 = -5x/-6  -6/-6

y = 5/6x +1

Answer:

c find the value

Step-by-step explanation:

plz workout

Answer:

Step-by-step explanation:

Let's write a system.

Let's say that the variables are x and y.

xy=48

x+y=14

Solve for one of the variables, let's say, x.

x=14-y.

Now substitute x into the 1st equation.

(14-y)y=48

Simplify.

-y²+14y=48

Make it into a quadratic equation.

-y²+14y-48=0

Make sure y²'s coefficient is one. Divide everything by -1

y²-14y+48=0

Now factor!

What factors add up to 14 and multiply to 48.

6 and 8!

Since the 2nd term is negative, and the 3rd term is positive, the factors have to be negative.

y²-6y-8y+48=0

Group.

(y²-6y)+(-8y+48)=0

y(y-6)-8(y-6)=0

(y-8)(y-6)=0

y-8=0

y-6=0

y=8 y=6

now let's substitute each y value into y²-14y+48=0

8²-14(8)+48=0

64-112+48=0

0=0. so y=8 checks out!

6²-14(6)+48=0

36-84+48=0

0=0 so y=6 also checks out!

Choose one y value and solve for x, in each equation :

xy=48

x+y=14

8x=48

x+8=14

x=6

x=6

It checks out!

so the factors are

x=6 y=8.

Answer: They need to use 1,638 square meters of flooring.

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given, and  apply the next formula:

Area of a rectangle: length x width

Replacing with the values given and solving for the area (A):

A = 42 x 39 = 1,638 m2

They need to use 1,638 square meters of flooring.

Feel free to ask for more if needed or if you did not understand something.

Answer:

5:4

Step-by-step explanation:

In Mrs. Nathan's class,  the ratio of girls to boys is 5:4.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, In Mrs. Nathan's class, there are 16 boys and 20 girls.

the ratio of girls to boys = 20/16

the ratio of girls to boys = 5/4

Therefore, the ratio of girls to boys in Mrs. Nathan's class is 5: 4.

Learn more about ratios here:

https://brainly.com/question/13419413

#SPJ1

answer: $1,012.50

Step-by-step explanation:

12.5 ÷ 100 = 0.125

0.125 × 800 = 100

800 + 100= 900 ( half-yearly interest)

0.125 × 900 = 112.5

900 + 112.5 = $1,012.50 ( end of first year interest)

Answer:

30⁰ , 60⁰ , 90⁰

Step-by-step explanation:

Let the angles x , 2x , 3x

By angle sum property:

x + 2x + 3x = 180⁰

6x = 180⁰

x = 30⁰

Angles are : 30⁰ , 60⁰ , 90⁰

Answer:

30°, 60°, 90°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the parts of the ratio, 1 + 2 + 3 = 6 parts

Divide to find the value of one part of the ratio

180° ÷ 6 = 30° ← value of 1 part of the ratio, thus

2 parts = 2 × 30° = 60°

3 parts = 3 × 30° = 90°

Thus angles are 30°, 60° and 90°

Answer:

A

Step-by-step explanation:

Answer:

[tex]E(n)=75000 \times 2^n[/tex]

Complete question:

write a function that gives mapiyas cumulative earnings E(n), in dollars when she has written n sequel's

Step-by-step explanation:

According to the question, she earned $75000 for the first book.

Also,We are  given that her cumulative earnings double with each sequel that she writes.

Assuming she has written n sequel's

Now since we are given that her cumulative earnings double with each sequel

So, her initial earning will be [tex]2^n[/tex] times

So, her earning will be : [tex]75000 \times 2^n[/tex]

Now we are given that cumulative earnings is denoted by E(n)

So, the function becomes :[tex]E(n)=75000 \times 2^n[/tex]

Hence a function that gives Mapiya's cumulative earnings E(n), in dollars when she has written n sequel's  is  [tex]E(n)=75000 \times 2^n[/tex]

Answer:

311 pounds

Step-by-step explanation:

Here, we are to calculate the average weight of the upper-class men offensive players

To calculate this, we need to sum up all the weights and divide by their count

Mathematically, that would be;

Average weight = (322+290+321+326+330+315+311+292+290)/9 = 2,797/9 = 310.77778

Now this written in 3 significant figures would be 311 pounds

Answer:

311

Step-by-step explanation:

You add all of the numbers first (2797)

Then you divide by how many numbers there were (9)

You get 310.7778

Then you round with 3 sig figs.

That is 311

Hope this helps:D

37.68 is the area of the Pac-Man

Answer:

Step-by-step explanation:

<2=180-(1+B)

<3=180-(4+D)

trg ACB=trgACD(<2=<3, AC =AC, <1=<4

ASA

Answer:

4

Step-by-step explanation:

I love your name. my friend is also named like that. and she has a twin that is named jessicamarie.......oof!

Answer:

3.6 units (nearest tenth)

Step-by-step explanation:

distance formula

= [tex] \sqrt{(x1 - x2)^{2} + (y1 - y2)^{2} } [/tex]

Thus, distance between the 2 points

= √[(5 - 3)² + (1 - 4)²]

= √[ 2²+ ( - 3)²]

= √13

= 3.6 units (nearest tenth)

Answer:

35 seconds

Step-by-step explanation:

At negative values he is inside the volcano,  when he reaches 0 he will be at the top of the volcano

At 35 seconds, the elevation is 0, so he is at the top of the volcano

Answer:

a) Area of wall to be painted = 114 sq ft

b) Number of cans required = 2×5 = 10

c) Total cost of paint = $338.43

Step-by-step explanation:

We are asked to find the area of wall that needs to be painted.

we need to subtract the area of window from the area of wall.

We know that area of a rectangular shape is given by

Area = Width×Length

Area of whole wall = 8×15 = 120 sq ft

Area of window = 2×3 = 6 sq ft

Area of wall to be painted = 120 - 6 = 114 sq ft

1 can of paint will cover 25 sq ft of area.

So to cover the area of wall to be painted,

114/25 = 4.56

since number of cans cannot be in fraction so we would need 5 cans

Since two coats of paints are needed so

Number of cans required = 2×5 = 10

1 can of paint costs $29.95

We have total 10 cans

$29.95×10 = $299.5

There is also a 13% tax so the total cost is

$299.5×0.13 = $38.93

Total cost of paint = $299.5 + $38.93

Total cost of paint = $338.43

Answer:

1. 47 correct, 0 wrong and 3 unanswered

2. 48 correct, 1 wrong and 1 unanswered

Step-by-step explanation:

Given;

Total number of questions = 50

For correct answers = 2

For wrong answers = -2

Unanswered questions = 0

Yash scored 94 marks

Let c, w and u represent the number of correct, wrong and unanswered questions

2×c - 2 × w + 0×u = 94

2c -2w = 94 .....1

And;

c + w + u = 50 .....2

We have 2 equations and 3 unknowns

By observing the problem, we can see two possible solutions;

Case 1: Assuming he did not miss (get wrong) any answer;

He needs to score 47 answers right;

47 × 2 = 94

Then;

c = 47 w = 0 and u = 50 - (47+0) = 3

47 correct, 0 wrong and 3 unanswered

Case 2: Assuming he got one answer wrong;

He would need to score one more answer right compared to the first case;

(47+1) × 2 - 1 × 2 = 96 - 2 = 94

c = 47+1 = 48

w = 1

u = 50 - (48+1) = 1

So he need to score 48 correct answers, 1 wrong answer and 1 unanswered.

Answer:

[tex]343[/tex]

Step-by-step explanation:

[tex]1^{3} =1\\2^{3} =8\\3^{3} =27\\4^{3} =64\\5^{3} =125\\6^{3} =216\\7^{3} =343\\8^{3} =512[/tex]

[tex]\sqrt[3]{x } >500[/tex]

[tex]\sqrt[3]{343} >500[/tex]

Answer:

x>−2

Step-by-step explanation:

Let's solve your inequality step-by-step.

x−2x+5<7

Step 1: Simplify both sides of the inequality.

−x+5<7

Step 2: Subtract 5 from both sides.

−x+5−5<7−5

−x<2

Step 3: Divide both sides by -1.

−x

−1

<

2

−1

x>−2

Answer:

x>−2

Answer:

Volume = 1,017.4m^3 .

Step-by-step explanation:

[tex]V = \frac{1}{3} pir^{2}h \\h (height) = 12m\\r (radius ) = 9m\\PI = 3.14\\V =\frac{1}{3} * 3.14 *9^{2} *12\\\\V = 1,017.36\\V = 1,017.4m^{3} .[/tex]

Answer:

iuhi on edge its c

Step-by-step explanation:

Answer:

C. 3√3

Step-by-step explanation:

Remember your 30-60-90 triangle rules.

They give you 3 as a side in the 30-60-90. That side length 3 will be your x. The side opposite of it is x√3. Simply plug in 3 as it is x and you should get 3√3 as your answer.

Answer:

C

Step-by-step explanation:

In all 30 60 90 triangles, the side opposite the 60 degree angle will be the short leg times [tex]\sqrt{3}[/tex]

So, the length of that side in this triangle will be 3[tex]\sqrt{3}[/tex]