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3 years ago

Solve the linear equation: 3(4 + 2b) - b = 27 A b = 15 B b = 5 C b = 3 D b = -3

Mathematics

1 answer:

nikklg [1K]3 years ago

6 0

Answer:

Multiply the numbers in parentheses by 3.

Which gives you 12 + 6b - b =27

Combine like terms

12 + 5b = 27

Then subtract 12 from both sides

Which leaves you with

5b = 15

Divide both side by 5

which gives you

answer C

You might be interested in

F(x) = 2x, find the ordered pair when x = 1. O (1,2) 0 (4,1) (2,1) O (1,4)

kenny6666 [7]

Answer:

The ordered pair is (1, 2) ⇒ A

Step-by-step explanation:

In the function f(x) = y

x is the domain of the function

y is the range of the function

The domain is all the x-coordinates of the points lie on the graph of the function

The range is all the y-coordinates of the points lie on the graph of the function

That means any ordered pair (x, y) satisfy the function f(x) = y, lies on the graph of the function

∵ f(x) = 2x

→ That means y = 2x

∵ x = 1

→ Substitute the value of x in the function above

∴ f(1) = 2(1)

∴ f(1) = 2

→ That means at x = 1, y = 2

∴ The ordered pair is (1, 2)

6 0

3 years ago

Ivy is running errands for her mother. She bikes along straight paths to the supermarket, the bank, and then back home.Find the

chubhunter [2.5K]

The distance between Ivy's house and the supermarket and the distance between the supermarket and the bank:
H&S = 1,014 M; and S&B = 854m. This is resolved using the Sine Theorem.

<h3>What is the calculation backing the above solution?</h3>

Notice that the Angles of a Triangle add up to 180° That is

∠A + ∠B + ∠C = 180°

Thus,

∠C = 180° - 32° - 109°

= 39°

Recall the Sine Theorem which indicates;

a/SinA = b/SinB = c/SinC

thus given that

AC = 1,523m

We have

AC/SinB = BC/SinA

BC = AC/SinB * SinA

= 1523/Sin109° * Sin32°

BC =854m

Therefore

AC/SinB = AB/SinC
Thus,

AB = AC/SinB * SinC

= 1523/Sin109° * Sin39°
AB ≈ 1,014m

Learn more about the Sine Theorem at;
brainly.com/question/27174058
#SPJ1

5 0

1 year ago

A train leaves a station and travels north at a speed of 105105 km/h. twotwo hours later, a second train leaves on a parallel

hram777 [196]

Let x = hours to meet

train one has a 2 hour head start or 210 km head start

210 + 105x = 135x
30x = 210
x = 7 hours to meet

6 0

3 years ago

Fiona’s Number:

Amanda [17]

Answer:

He should dial 289-743-1560

Step-by-step explanation:

The first three digits: "My first three digits are the square of an integer less than twenty"

Step 1: We can get the first three by looking at the squares of the integers from 1 to 19. We need a three digit number, so starting with 10, since 10² = 100, we list the squares of the integers from 10 to 19

10² = 100

11² = 121

12² = 144

13² = 169

14² = 196

15² = 225

16² = 256

17² = 289

18² = 324

19² = 361

Step 2: "The first three digits are in ascending order" and no digits can repeat, so we eliminate the answers above that don't satisfy both of these condintions. This leaves just 3 choices:

13² = 169

16² = 256

17² = 289

*We will come back to this once we have more information.

The last 2 numbers: "the last two digits are multiples of sixty".

The only 2 digit number that is a multiple of 60 is 60, so 6 and 0 are the last 2 digits. This rules out two answers from Step 1 since no digits can repeat. Only 289 works since 169 and 256 each have a 6 in them. So now we know the first 3, and last 2 numbers!

2 8 9 _ _ _ _ _ 6 0

The last 4 numbers: "the last 4 digits are multiples of sixty"

We want to find a 4 four digit number that has 60 as the last 2 digits. Notice a pattern when you multiply 60 by certain digits...

60 x 1 = 60

60 x 2 = 120

...

60 x 6 = 360

60 x 11 = 660

60 x 16 = 960 (these all don't work since they are not 4 digits)

60 x 21 = 1260 (this is the first 4 digit result, but it doesn't work because

there is a '2' in it, and 2 has already been used as the

first digit of the number)

60 x 26 = 1560 (this number could work, so lets try it and see if we can

satisfy the rest of the statements)

Now our number is

2 8 9 _ _ _ 1 5 6 0

The second three digits: "The second three digits are in descending order" and "The sum of the second three digits is 14"

If we assume that 1, 5, 6 and 0 are the last four digits, we know that 2, 8 and 9 are the first three digits, this leaves 3, 4 and 7 as the three remaining digits.

3 + 4 + 7 = 14 so that condition is satisfied. We just need to write then in descending order, so our final number is

289-743-1560

3 0

3 years ago

Read 2 more answers

Use induction to prove that 2? ?? for any integer n>0 . Indicate type of induction used.

Hoochie [10]

Answer with explanation:

The given statement is which we have to prove by the principal of Mathematical Induction

$2^{n}>n$

1.→For, n=1

L H S =2

R H S=1

2>1

L H S> R H S

So,the Statement is true for , n=1.

2.⇒Let the statement is true for, n=k.

$2^{k}>k$

---------------------------------------(1)

3⇒Now, we will prove that the mathematical statement is true for, n=k+1.

$\rightarrow 2^{k+1}>k+1\\\\L H S=\rightarrow 2^{k+1}=2^{k}\times 2\\\\\text{Using 1}\\\\2^{k}>k\\\\\text{Multiplying both sides by 2}\\\\2^{k+1}>2k\\\\As, 2 k=k+k,\text{Which will be always greater than }k+1.\\\\\rightarrow 2 k>k+1\\\\\rightarrow2^{k+1}>k+1$

Hence it is true for, n=k+1.

So,we have proved the statement with the help of mathematical Induction, which is

$2^{k}>k$

3 0

3 years ago