Two positive integers are 3 units apart on a number line. Their product is 108.

Which equation can be used to solve for m, the greater integer?

a). m(m – 3) = 108  
b.) m(m + 3) = 108
c.) (m + 3)(m – 3) = 108
d.) (m – 12)(m – 9) = 108

Given:

The sum of irrational number in the options.

To find:

The option that shows the sum of two irrational numbers can be irrational.

Solution:

In option A,

[tex](5+\pi)+(3-\pi)=5+\pi+3-\pi[/tex]

[tex](5+\pi)+(3-\pi)=5+3[/tex]

[tex](5+\pi)+(3-\pi)=8[/tex]

We know that 8 is a rational number. So, option A is incorrect.

In option B,

[tex]\sqrt{3}+\sqrt{5}[/tex]

Here both numbers are irrational and it cannot be simplified further.

So, [tex]\sqrt{3}+\sqrt{5}[/tex] is an irrational number and option B is correct.

In option C,

[tex](3+\sqrt{5})+(3-\sqrt{5})=3+\sqrt{5}+3-\sqrt{5}[/tex]

[tex](3+\sqrt{5})+(3-\sqrt{5})=3+3[/tex]

[tex](3+\sqrt{5})+(3-\sqrt{5})=6[/tex]

We know that 6 is a rational number. So, option C is incorrect.

In option D,

[tex](\dfrac{\pi}{3})+(-\dfrac{\pi}{3})=\dfrac{\pi}{3}-\dfrac{\pi}{3}[/tex]

[tex](\dfrac{\pi}{3})+(-\dfrac{\pi}{3})=0[/tex]

We know that 0 is a rational number. So, option D is incorrect.

Therefore, the correct option is B.

Answer:

Step-by-step explanation:

Answer:

C) 2+4^4x

Step-by-step explanation:

A) 2^(4x+2) = 2^4x • 2² = 16^x • 4

B) 4 • 16^x = 16^x • 4 (already done)

D) 2^2 • 4^x (over) 4^-x

= 4 • 4^x • 4^x = 16^x • 4

E) 4^(2x+1) = 4^2x • 4¹ = 16^x • 4

Answer:

-17/5 as an IMPROPER FRACTION

[tex]-3\frac{2}{5}[/tex] as a MIXED FRACTION

9514 1404 393

Answer:

  x = 4

Step-by-step explanation:

The parallel lines divide the sides proportionally, so ratios of corresponding sides are the same.

  (x +5)/15 = (5x +1)/35

Multiplying by 105, we have ...

  7(x +5) = 3(5x +1)

  7x +35 = 15x +3 . . . . . eliminate parentheses

  32 = 8x . . . . . . . . . subtract 7x+3 from both sides

  4 = x . . . . . . . . divide by 8

Answer:

x = 24

y = 59

Step-by-step explanation:

To solve for x, we can say that;

(5x) + (2x + 12) = 180

7x + 12 = 180

7x = 180 - 12

7x = 168

x = 168 / 7

x = 24

To solve fore y, we can say that;

(3y) + (y - 56) = 180

4y - 56 = 180

4y = 180 + 56

4y = 236

y = 236 / 4

y = 59

Hope this helps!

Answer:

82cm

Step-by-step explanation:

26+26+15+15=82

Answer:

N= -3

Step-by-step explanation:

4n+2 = 6(1/3n - 2/3)

4n+2 = 2n - 4

2n +2 = -4

2n = -6

n = -3

Answer:

- 3

Step-by-step explanation:

4n + 2 = 6 ( 1 / 3 n - 2 / 3 )

Divide 2 on both sides,

2n + 1 = 3 ( 1 / 3 n - 2 / 3 )

2n + 1 = 3n / 3 - 6 /3

2n + 1 = n - 2

2n - n = - 2 - 1

n = - 3

Answer:

Yes it is!

Step-by-step explanation:

If you want to know whether it is, use the pytheoream theory. a2+b2=c2

a is the shortest side, b is the second longest and c is the longest.

In this case, the equation will be:

8 sq + 15 sq = 17 sq

64 + 225 = 289

= It is a right-angled triangle!

Answer:

the answer is 66.205

Step-by-step explanation:

basically you look at the place value so

66.21 is basically the same as 66.210 then you look at the lowest number that can round UP to 66.210 which would be out of 1 to 9 would be 5 so the smallest number that can round up to 66.210 is 66.205 hope this helped :D

Answer:

4 = 2²

Step-by-step explanation:

Multiply 2 by itself till 4

Simple because you only do it once

2 * 2 = 4

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

1/8

1/2

3/8

3/8

1

3/8

Answer:

Figure 1 is 50 cm. Figure 2 is 225 mm.

Step-by-step explanation:

Answer:

A = 48 in²

Step-by-step explanation:

The area (A) of the triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

Here b = 24 and h = 4 , then

A = [tex]\frac{1}{2}[/tex] × 24 × 4 = 12 × 4 = 48 in²

Answer:

A = 48 in.^2

Step-by-step explanation:

Area of  triangle = (Base * height) / 2

Area of triangle = (24*4)/2

Area of triangle = 48 in.^2

Answer:

It's 6 - (-6)

Step-by-step explanation:

Two negatives make a positive so instead of subtracting you're now adding.

Answer:

not 100% sure, but i would put

Domain: all real numbers

Range: y >= 0

Step-by-step explanation:

Answer:

14 = x

Hope that this helps!

Answer:

means and extremes

Step-by-step explanation:

Answer:

Step-by-step explanation:

perimeter of rectangle=2(length + breadth)

=2(2p+q+p)

=2(3p+q)

=2*3p+2*q

=6p+2q cm

Step-by-step explanation:

Hey there!

From the figure;

Length (l) = 2p + q cm

Base (b) = pcm

Now;

Perimeter (p) = 2(l+b)

P = [2(2p+q) + p]

or, P = 2(3p+q)

or, P = 6p + 2qcm.

Therefore, perimeter (p) = 6p+2q cm.

Hope it helps!

Answer:

.5 = 50%

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

So probabilityof getting a head or tail, when an unbiased coin is tossed is = 1

Answer:

Length of missing side is 177.5

Step-by-step explanation:

sum of all angles of right triangle is 180 °

1.5° + 2° + c = 180°

combine like terms

2.5 ° + c = 180°

Subtract 2.5 from each side

2.5 ° - 2.5° + c = 180° - 2.5°

c = 177.5

Answer:

multiplyeach values on both sides

Answer:

x^2 +x -6

11 [tex]\frac{3}{10}[/tex]

[tex]\frac{77}{6}[/tex]

Step-by-step explanation:

Answer:

1 ≥ n

Step-by-step explanation:

30 ≥ 5(6n)

Distribute

30 ≥ 30n

Divide each side by 30

30/30 ≥ 30n/30

1 ≥ n  

30 >= 5(6n)

Divide both sides. Y 5:

6 >= 6n

Divide both sides by 6:

1 >= n

Rewrite as: n ≤ 1

Answer:

47, 76, 123

Step-by-step explanation:

Fibonacci Sequence

Answer:

47 , 76 , 123

Step-by-step explanation:

3rd term = 1st term + 2nd term = 1 + 3 = 4

4th term = 2nd term + 3rd term = 3 + 4 = 7

Next three terms:

8th term = 18 +29 = 47

9th term = 29 + 47 = 76

10th term = 47 + 76 =  123

Answer:

1,700 milliliters

Step-by-step explanation:

Convert the liters that Javier and his brother got into milliliters.

In 1 liter, there are 1000 milliliters.

So, Javier's brother bought 1000 milliliters of soda.

And, in 1/2 liter of soda, there are 500 milliliters. So, Javier bought 500 milliliters of soda.

Add these two amounts to how much Javier's mom bought:

500 + 1000 + 200

= 1700

So, for his party, Javier has 1,700 total milliliters of soda.

Answer:

$18.75

Step-by-step explanation:

15% = 15/100

125 × 15/100

=1875/100

=18.75