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Correct question is;

Among all pairs of numbers with a sum of 149, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms

Answer:

The pair whose product is maximum is 149/2 and 149/2

Step-by-step explanation:

We are told that pair of number with sum as 149 and to find the product that is maximum.

Now,let x and y be the numbers. Thus;

x + y = 149 and xy is maximum.

So, y = 149 - x

Thus, plugging 149 - x for y into the product equation gives; x(149 - x). This can be expanded to be -x² + 149x.

Using method of completing the square, we will arrive at;

-(x² - 149x) = -(x² -149x + (149/2)²) + (149/2)² = (149/2)² - (x - (149/2))²

Now, the expression gotten will have a maximum of (149/2)² when (x - (149/2))² has its minimum value of zero. This means that when x = 149/2, as x moves away from 149/2, (149/2)² would be reduced by the square of the difference between the value of x and 149/2, and the square would always be positive.

Thus, the maximum product in it's simplest form is x = y = 149/2

Answer:

3+(-5) = -2

Step-by-step explanation:

If you were at 3 in the number line then went back 5 spaces (which represents -5) it would be -2

Answer:

There will be 108 interactions for 9 children.

Answer:The answer is Sympathy

Step-by-step explanation:

The correct answer is Consolation

If we look at the flow of the first sentence, ointment is the instrument that is used to soothe a burn.

The implication of this is that we also need to find the word that best describes that which can be used to soothe grief.

When a person is grieving, such a person is in need of consolation hence the correct answer is consolation.

For more about the meaning of the word consolation, see

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Answer:

[tex] \boxed{ \bold{ \huge{\boxed{ \sf{(12.5 \: , \: 11.5)}}}}}[/tex]

Step-by-step explanation:

Let the points be A and B

Let A ( 13 , 15 ) be x₁ , y₁ and B ( 12 ,8 ) be x₂ , y₂

Finding the midpoint

[tex] \bold{ \boxed{ \sf{midpoint \: = (\: \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2}) }}}[/tex]

[tex]\dashrightarrow{ \sf{ (\frac{13 + 12}{2} , \: \frac{15 + 8}{2} )}}[/tex]

[tex] \dashrightarrow {\sf {(\frac{25}{2} \: , \: \frac{23}{2} )}}[/tex]

[tex] \dashrightarrow{ \sf{(12.5 \: , \: 11.5)}}[/tex]

Hope I helped!

Best regards! :D

Answer:

-6.7x + 3.3y

Step-by-step explanation:

Step 1: Write out expression

3.5x + y - 10.2x + 2.3y

Step 2: Combine like terms (x)

-6.7x + y + 2.3y

Step 3: Combine like terms(y)

-6.7x + 3.3y

Answer:

3.3 y - 6.7 x

Step-by-step explanation:

Rewriting for clarity.

(2.3y + y) + (3.5x - 10.2x)

(3.3y) + (-6.7x)

3.3y - 6.7x

Answer:

.95

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

The formula is [tex]\sqrt{(x_{1}-x_{2})^{2} +(y_{1}-y_{2}})^{2} }[/tex]

[tex]x_{1}[/tex]=-3 [tex]x_{2}[/tex]=0

[tex]y_{1}[/tex]=5 [tex]y_{2}[/tex]=1

[tex]x_{1}- x_{2}[/tex]=-3

[tex]y_{1}- y_{2}=4[/tex]

Therefore: [tex]\sqrt{(-3)^{2}+4^{2} } =\sqrt{9+16} =\sqrt{25}=5[/tex]

Answer:

B, D, and E

Step-by-step explanation:

B) m<1 + m<2=m<4 TRUE. If you and 1, 2, and 3,  you get 180.  If you add 3 and 4, you get 180.  So 1 and 2 must be the same as 4.

D) m<4 is greater than m<2

E) m<4 is greater than m<1

Answer:

Step-by-step explanation:

Let the original price be x

The discounted price for a clearance sale = 30% of x

If the price tag after discounting = $199.

Using the relationship to find the original price x

Original price - discounted price = Current price tag after discounting

x - 0.3x = 199

0.7x = 199

Divide both sides by 0.7

0.7x/0.7 = 199/0.7

x = $284.29

Hence the suit's original price is approximately $284.29

Answer:

Just do 60 divided by 10

Step-by-step explanation:

60=10 x  10 times 6 = 60 so x=6

Answer: [tex]x=6[/tex]

Divide both sides by 10

[tex]10x=10=60/10\\x=6[/tex]

Answer:

In the first sequence, the next term here is 1. In the second sequence; the next term is 162.

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

In the first sequence,  256, 64, 16, 4, ...

Consider ratio of the next term with its preceding term, so we will get the common ratio;

4/ 16 = 1/4

So, we can see that the next term of the sequence is 1/4 times the previous term.

Hence, the unknown term will be; 1/4 times of previous term.

That is , 1/4 × 4 = 1

Therefore, the next term here is 1

In the second sequence; 2, 6, 18, 54, ...

Do the same procedure as above, we will get the common ratio as :

54 / 18 = 3

Thus, the next term is 3 times the preceding term, that is :

3 × 54 = 162

Hence, the next term is 162

Learn more about arithmetic sequence here:

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Answer:

a. 5/20, 8/20

Step-by-step explanation:

1/4 and 2/5

a. 5/20, 8/20

5/20

Divide both numerator and denominator by 5

= 1/4

8/20

Divide both numerator and denominator by 4

= 2/5

b. 1/20, 2/20

1/20 =1/20

2/20

Divide both numerator and denominator by 2

= 1/10

c. 1/9, 2/9

Both fractions can't be further simplified

= 1/9, 2/9

d. 5/20, 4/20

5/20

Divide both numerator and denominator by 5

= 1/4

4/20

Divide both numerator and denominator by 4

= 1/5

The correct answer is a. 5/20, 8/20

= 1/4, 2/5

5 / 20 and 8 / 20 are pairs of fractions with a common denominator that are equivalent to 1/4 and 2/5

We are ask to find the equivalent of the pairs of fractions with a common denominator 1 /4 and 2 / 5.

The logic is to reduce by dividing the options with same numerator and denominator to get the equivalent of the fraction required.

Therefore,

5 / 20 and 8 / 20

5 / 20 ÷ 5  / 5 = 1 / 4

8 / 20 ÷ 4 / 4  = 2/5

Base on the answer you can see that when we reduced option A fractions, they are the same with the required fractions.

Therefore, 5 / 20 and 8 / 20 are pairs of fractions with a common denominator that are equivalent to 1/4 and 2/5

learn more on fraction here: https://brainly.com/question/17447977?referrer=searchResults

Answer:

See attached image

Step-by-step explanation:

If you have two marbles in a bag and you are choosing the marbles randomly twice, then we can look at fractions.

Each time, you have a 0.5 chance of picking the silver marble. After you pick that, you have another 0.5 chance of picking the silver marble again.

This applies with any combination.

This means that the probability of you getting two silvers in a row is 0.25.

Since the marbles are the same size and nothing is stopping you from choosing one, this probability applies to all combinations possible.

Hope this helped!

Answer:

Step-by-step explanation:

Answer:

Hey there!

0.28 times 0.86 is equal to 0.2408

Let me know if this helps :)

Answer: ACE

Step-by-step explanation:

The expression first, third, and fourth becomes zero when plugging x  = -1 in the equation.

It is defined as the combination of constants and variables with mathematical operators.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

First,

[tex]=\rm \dfrac{4\left(x+1\right)}{4x+5}[/tex]

Plug x = -1

The expression value becomes zero.

Second,

[tex]= \rm \dfrac{4\left(x-1\right)}{5-4x}[/tex]

Plug x = -1

= -8/9

Third,

[tex]\rm \dfrac{4\left(x-\left(-1\right)\right)}{4x+5}[/tex]

Plug x = -1

The expression value becomes zero.

Fourth,

[tex]\rm \dfrac{4\left(x+\left(-1\right)\right)}{4x+5}[/tex]

Plug x = -1

The expression value does not become zero.

Fifth,

[tex]\rm \dfrac{4\left(x+1\right)}{5-4x}[/tex]

Plug x = -1

The expression value becomes zero.

Thus, the expression first, third, and fourth becomes zero when plugging x  = -1 in the equation.

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Answer:

x = 24

Step-by-step explanation:

x = 2 ÷ 12⁻¹

x = 2 * 12

x = 24

Answer:

  x = 24

Step-by-step explanation:

The applicable rule of exponents is ...

  1/a^-b = a^b

__

The problem simplifies to ...

  x = 2 ÷ 12^-1 = 2 · 1/12^-1

  x = 2 · 12^1 = 2·12

  x = 24

Answer:

they are in the link. i answered each on in the same order they are in the picture soooo here u are.

Answer:

27

Step-by-step explanation:

Let x be the number

2/3 x+4 = 22

Subtract 4 from each side

2/3x +4-4 = 22-4

2/3 x = 18

Multiply each side by 3/2

3/2 ( 2/3x) = 18 * 3/2

x = 27

Answer:

[tex]\Huge \boxed{27}[/tex]

Step-by-step explanation:

Let the number be x.

[tex]\frac{2}{3} x+4=22[/tex]

Solve for x.

Subtract 4 from both sides.

[tex]\frac{2}{3} x+4-4=22-4[/tex]

[tex]\frac{2}{3} x=18[/tex]

Multiply both sides by [tex]\frac{3}{2}[/tex].

[tex]\frac{2}{3} x \cdot \frac{3}{2} =18 \cdot \frac{3}{2}[/tex]

[tex]x=27[/tex]

The number is 27.

Answer:

29

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

Absolute values are always positive.

The absolute value is |1/4|

To understand this let's first understand the definition of absolute value.

Absolute value - The non-negative value of a number without regard to its sign. For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5. The absolute value of a number may be thought of as its distance from zero along real number line.

Therefore the absolute value of -1/4 is just 1/4.

Also, remember that to indicate that it's the absolute value you have to add a " | " before and after the number. Like this |1/4|

Hope this helped ~

Answer:

15 years

Step-by-step explanation:

Given:

Building inequality:

Adding current year to 14 we get 15 years as answer

The answer is Day 3. The blue bar for day 3 is the tallest, which means that was the highest amount.

On day 3 the sharpest boost in accumulated tips. Therefore, option C is the correct answer.

Given that, the graph shows Marc's individual and cumulative tips for 7 days.

We need to find which day gave Marc the sharpest boost in accumulated tips.

Bar graphs are the pictorial representation of data (generally grouped), in the form of vertical or horizontal rectangular bars, where the length of bars is proportional to the measure of data. They are also known as bar charts. Bar graphs are one of the means of data handling in statistics.

Now, in the given graph we can see that on day 3 tip is more.

On day 3 the sharpest boost in accumulated tips. Therefore, option C is the correct answer.

To learn more about the bar graphs visit:

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Answer:

A

Step-by-step explanation:

x = 18

Multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, ...

The two digit numbers in that list above all have their digits adding to some other multiple of 3

and so on.

Therefore, the rule is: If the digits add to a multiple of 3, then the original number is a multiple of 3.

Answer:

y= -6x +1

Step-by-step explanation:

The equation of a line is usually written in the form of y=mx +c, where m is the gradient (or slope) and c is the y-intercept.

In order to find the equation of a line, you would need 2 things:

① Gradient (← can be found)

② Coordinate (✓ we have 2 coordinates here)

To find the gradient, use the gradient formula below:

[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]

[tex]m = \frac{ - 5 - ( - 17)}{1 - 3} \\ m = \frac{ - 5 + 17}{ - 2} \\ m = \frac{12}{ - 2} \\ m = - 6[/tex]

Substitute the value of m into the equation:

y= -6x +c

To find the value of c, substitute a pair of coordinates.

When x=1, y= -5,

-5= -6(1) +c

c -6= -5

c= 6 -5

c= 1

Thus, the equation of the line is y= -6x +1.