Generating Equations and Inequalities

Answer:

33.33%

Step-by-step explanation:

The value of a variable change from 12 units to 16 units in a month.

We have to calculate the percentage increase for that month.

Therefore, the increase of value from 12 to 16 means by (16 - 12) = 4 units

So, the percentage increase for the month is [tex]\frac{4}{12} \times 100 = 33.33[/tex]%. (Rounded to the two decimal). (Answer)

Answer: 6, 570

Step by step explanation:  If Minnie and Mickey have 5 girls and 5 boys every 3 weeks for 52 weeks this means they will have 17 pregnancies. At the end of one year Minnie and Mickey alone will have produced 170 children. It takes these children 6 weeks to grow up and be ready to reproduce. Every 6 weeks 10 new rats will be able to have children at a rate of 10 per 3 weeks. This means that a single set of 10 offspring will have 100 children every 3 weeks. There will be 8 sets of offspring that can reproduce before the year is over. This means if the sets have 100 children every 3 weeks starting with one set and adding one more set every 6 weeks, at the end of the year the offspring's offspring will total 6,400. 6,400 + 170 will equal 6,570. The total population is 6,570.

Answer:    -1.75

Step-by-step explanation:

Answer:

-1.75 is the answer ....

Answer:

-198

Step-by-step explanation:

you will deal with the ones in the bracket first

that is [3×104]=312

[5×102]=510

312-510=-198

according to me there is no answer in your option my answer is negative198

Answer:

√125 + 5 or 16.180

Step-by-step explanation:

√5 · 5 · 5 + √5 · 5

√25 · 5 + √25

√125 + 5 or 16.18

Answer:

3

Step-by-step explanation:

Answer:

115

Step-by-step explanation:

1/10 of 850= 85

he spent and additional RS 85 on its repairs

cost price + repairs price =935

he sold it for 1050

to find his gain =1050-935

=115

Answer:

[tex]\large\boxed{\log_6\dfrac{1}{36}=-2}[/tex]

Step-by-step explanation:

[tex]\text{We know:}\\\\\log_ab=c\iff a^c=b\\\\\log_6\dfrac{1}{36}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\=\log_636^{-1}=\log_6(6^2)^{-1}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\log_66^{(2)(-1)}=\log_66^{-2}\qquad\text{use}\log_ab^n=n\log_ab\\\\=-2\log_66\qquad\text{use}\ \log_aa=1\\\\=-2(1)=-2[/tex]

[tex]\log_6\dfrac{1}{36}=-2\ \text{because}\ 6^{-2}=\dfrac{1}{6^2}=\dfrac{1}{36}[/tex]

The solution of logarithmic function is, - 2

We have to given that,

Logarithmic function is,

⇒ log ₆ (1/36)

Now, We can apply the logarithmic rule to solve as,

⇒ log ₆ (1/36)

⇒ log ₆ (36)⁻¹

⇒ log ₆ (6)⁻²

⇒ - 2 log ₆ (6)

⇒ - 2 × 1

⇒ - 2

Therefore, The solution of logarithmic function is, - 2

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Answer:16

Step-by-step explanation:

If 4x=18 then 4x-2=16

Answer:

The weekly savings of first person = $900

The weekly savings of second person = $700.

Step-by-step explanation:

Let us assume the income of first person = $ m

Now, as the difference in the income is $200.

⇒ And the income of first person  -  income of first person =  $200

⇒ Income of second person    =    m -  $200

So, according to the question:

Ratio of   Income of First person : Second Person's Income  =  9: 7

or, m : ( m - 200)   =  9: 7  

[tex]\implies  \frac{m}{m - 200 }  = \frac{9}{7}[/tex]

[tex]7 \times m = (m - 200) \times 9\\\implies 7 m = 9m - 1800\\\implies 7m - 9m = -1800\\\implies -2m = -1800\\m = \frac{1800}{2}   = 900[/tex]

or,m = $900

Hence, the weekly savings of first person = $900

and the weekly savings of second person = m - 200 = $900 - 200 = $700.

Final answer:

To find the weekly incomes of two persons with a ratio of 9:7 and a difference of $200, represent their incomes as 9x and 7x. Solving for x, we get $100, so their incomes are $900 and $700 respectively.

Explanation:

The question asks us to solve for the weekly incomes of two persons given that the ratio of their incomes is 9:7 and the difference between their incomes is $200.

Let's represent the incomes of the two persons as 9x and 7x respectively, where x is a common multiplier. According to the information provided,

9x - 7x = $200

Solving for x:

(9x - 7x) = 2x

2x = $200

x = $200 / 2

x = $100

Now calculating each person's income:

Person A: 9x = 9 * $100 = $900

Person B: 7x = 7 * $100 = $700

Therefore, the weekly incomes of the two persons are $900 and $700 respectively.

Answer:

Median = 46.5

Minimum = 32

Maximum = 62

Lower quartile = 38

Upper quartile = 59

Step-by-step explanation:

Before we can proceed to solving any of these, it is best you arrange your data first from least to greatest

32  34  37  39  41  45  48  53  58  60  61  62

First we have the median. The Median is the middle value. In this case we an even number of data, which is 12 data points. The middle value of the data would be found in between the 6th and 7th data point:

45 and 48

To get the middle value, you need to solve for the value that is in the middle of 45 and 48 by getting the sum of both numbers and dividing it by two.

45 + 48 = 93

93 ÷ 2 = 46.5

The minimum and maximum value is merely the least and greatest number.

Here we have:

Minimum = 32

Maximum = 62

To get the lower and upper quartiles, just remember that quartiles divide the data into 4 equal parts. All you need to do is find the value that is in between each quarters of the data:

            Q1 (Lower)  Q2(Median) Q3(Upper)

32  34  37 |  39  41  45 | 48  53  58 | 60  61  62

Like the median, we will find the value that comes in between each quarter.

Q1

37 + 39 = 76

76 ÷ 2 = 38

Lower quartile = 38

Q3:

58 + 60 = 118

118 ÷ 2 = 59

Upper quartile = 59

Answer:

the person on top has it right ^^^^^^^^^^ did the work and it right thx :))

Answer:

OPTION B: y = [tex]$ \frac{1}{2} $[/tex]x - 2

Step-by-step explanation:

To find the equation of the line substitute the value of x and compare the corresponding value of y.

OPTION A:  

y = 2x + 4

Substitute x = 0. We get, 2(0) + 4 = 4

When x = 0, y = -2 [tex]$ \ne $[/tex] 4.

OPTION B:

y = [tex]$ \frac{1}{2} $[/tex]x - 2

Substitute x = 0, we get [tex]$ \frac{1}{2} (0) - 2$[/tex]

= -2

When x = 2, [tex]$ \frac{1}{2}(2) - 2 $[/tex] = 1 - 2

=-1

Similarly, When x = 4, [tex]$ \frac{1}{2}(4) - 2 = 2 - 2 $[/tex]

= 0.

Since, all the values are satisfied, OPTION B is the answer.

Substitute OPTION C and OPTION D. They do not satisfy the values either.

Answer:

the answer is c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Twenty times a square of a positive integer, plus 50 equals negative 40 times the square of the positive integer, plus one-hundred and ten times the positive integer. Which equation could be used to solve for the unknown positive integer.

A) 60x2 + 110x + 50 = 0  

B) 60x2 + 110x − 50 = 0  

C) 60x2 − 110x + 50 = 0  

D) 60x2 − 110x − 50 = 0

The correct equation to solve for the unknown positive integer is 60x^2 - 110x + 50 = 0.

To solve for the unknown positive integer, you'll need to form an equation. Start by writing down the mathematical expressions as given in the equation.

20x^2 + 50 = -40x^2+ 110x based on the statement given. Then, to simplify the equation, combine like terms. To do this, you'll need to move -40x^2 to the left side of the equation and move 50 to the right side of the equation. This gives us: 20x^2 + 40x^2 =  110x - 50. The result is 60x^2 - 110x + 50 = 0. The correct answer is choice C: 60x^2 - 110x + 50 = 0.

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answer: 74

explanation:

7-3=4

74

+47

---

121

Answer:

Step-by-step explanation:

In a two-digit number we have the unit's digit and the ten's digit. The unit's digit is represented by [tex]u[/tex]. Then ten's digit must be represents with a number 10 as a coefficient, and the variable would be [tex]d[/tex]. So, the numerical vale of the number would be:

[tex]10d+u[/tex]

Also, we know that [tex]d=u+3[/tex], because the unit digit is three less than tens digit, or tens digit is three more units than the unit digit.

Then, the sum of the reversed number and the original number is 121, this would be expressed:

[tex]10d+u+10u+d=121\\11d+11u=121[/tex]

But, we know that [tex]d=u+3[/tex], so, we replace it:

[tex]11(u+3)+11u=121\\11u+33+11u=121\\22u+33=121\\22u=121-33\\u=4[/tex]

Then, if tens digits is 3 more, [tex]d=7[/tex]

Therefore, the digits are 7 and 4. The number would be 74.

Answer:

1099.3

Step-by-step explanation:

9 hundreds = 900

9 ones = 9

19 tens = 190

3 tenths = 0.3

Answer:

1099.3

Step-by-step explanation:

9 hundreds          => 900

19 tens                  =>  190

9 ones                  =>      9

3 tenths                 =>       0.3

This number is:           1099.3

Answer:

{6, 8, 10} is a set which represents the side length of a right triangle.

Step-by-step explanation:

In a right triangle:

[tex](Base)^{2}  + (Perpendicular)^{2}   = (Hypotenuse)^{2}[/tex]

Now, in the given triplets:

(a) {4, 8, 12}

Here, [tex](4)^{2}  + (8)^{2}   = 16 + 64  = 80\\\implies H = \sqrt{80}  =  8.94[/tex]

So, third side of the triangle   8.94 ≠ 12

Hence,  {4, 8, 12} is NOT a triplet.

(b) {6, 8, 10}

Here, [tex](6)^{2}  + (8)^{2}   = 36 + 64  = 100\\\implies H = \sqrt{100}  =  10[/tex]

So, third side of the triangle  10

Hence,  {6, 8, 10} is  a triplet.

(c) {6, 8, 15}

Here, [tex](6)^{2}  + (8)^{2}   = 36 + 64  = 100\\\implies H = \sqrt{100}  =  10[/tex]

So, third side of the triangle  10  ≠ 15

Hence,  {6, 8, 15} is  NOT a triplet.

(d) {5, 7, 13}

Here, [tex](5)^{2}  + (7)^{2}   = 25 + 49  = 74\\\implies H = \sqrt{74}  =  8.60[/tex]

So, third side of the triangle  8.60  ≠ 13

Hence, {5, 7, 13} is  NOT a triplet.

Answer:

Part A: Section A- 8, Section B- 32.

Part B: 4 times.

Step-by-step explanation:

The function is given by [tex]f(x) = 4(2)^{x}[/tex].

Section A is from x = 1 to x = 2.

Now, f(1) = 4 × 2 = 8 and f(2) = 4 × 2 × 2 = 16

Again, section B is from x = 3 to x = 4.

Now, f(3) = 4 × 2 × 2 × 2 = 32 and f(4) = 4 × 2 × 2 × 2 × 2 = 64

Part A:

In section A, the average rate of change is = [tex]\frac{f(2) - f(1)}{2 - 1} = 16 - 8 = 8[/tex] (Answer)

And in section B, the average rate of change is  = [tex]\frac{f(4) - f(3)}{4 - 3} = 64 - 32 = 32[/tex] (Answer)

Part B:

Therefore, the number of times the average rate of change of section B is greater than section A is [tex]\frac{32}{8} = 4[/tex] (Answer)

Answer:

Part A: Section A- 8, Section B- 32.

Part B: 4 times.

Step-by-step explanation:

The function is given by .

Section A is from x = 1 to x = 2.

Now, f(1) = 4 × 2 = 8 and f(2) = 4 × 2 × 2 = 16

Again, section B is from x = 3 to x = 4.

Now, f(3) = 4 × 2 × 2 × 2 = 32 and f(4) = 4 × 2 × 2 × 2 × 2 = 64

Part A:

In section A, the average rate of change is =  8

And in section B, the average rate of change is  =  32

Part B:

Therefore, the average rate of change of section B is greater than section A is (32 / 8 = 4)

Answer:

34

Step-by-step explanation:

i just know t hat this is th answer

Answer:

46

Step-by-step explanation:

7x+4

7(6)+4

42+4

46

Step-by-step explanation:

7x+4=6

substitute 6 in x

7(6)+4

42+4=46

Answer:

(a) P  =  - 200 T + 9,400

(b) After 22  months the student  will owe $5000.

Step-by-step explanation:

Here, the amount loaned out to the student = $9,400

The installment amount of each month  = $200

(a) P : Amount remaining to be paid

    T: time in months

Now, the remaining amount = Actual amount - Amount paid in T months

or,      P = 9,400 - $200 (T)

⇒ P  =  - 200 T + 9,400 ( y = mx + C form)

(b) The remaining amount left = $5000

As we know, P = 9,400 - $200 (T)

⇒ 5,000 = 9,400 - 200 T

⇒200 T = 9,400 - 5,000 = 4,400

⇒ T = 4400/200 =  22

or T = 22 Months

Hence,  After 22  months the student  will owe $5000.

Answer:

f=2

Step-by-step explanation:

1.25f+2.75f= 10-2

You must take positive two to the other side to get negative 2. Also, you should take the negative 2.75f to the other side to get positive 2.75f.

4f= 8

f= 2

Answer:

f=2

Step-by-step explanation:

Answer:

False.  [tex]8x^2-36[/tex] is not a Linear expression.

Step-by-step explanation:

Given: [tex]8x^2-36[/tex]

we need to find whether it is a linear expression or not.

By Definition of Linear expression we say,

Linear expression is an algebraic expression where the power of variable(s) is equals to 1

Or we can say that:

Polynomial having power of variable(s) as 1, is known as Linear Expression

In the above expression the power of variable is 2 hence it is not a linear expression.

Hence the statement is False, the [tex]8x^2-36[/tex] is not a Linear expression.

Answer:

$18.20/0.65=28 minutes

Step-by-step explanation:

$18.20 was the cost of the rental divide it by the cost per minute and that will give you the total number of minutes used which is 28.

Answer:

since one mins = 0.65

for 18.20= 18.20/0.65= 28mins

Answer:

I'm pretty sure the answer is 5.2h-2.9d-16

Answer:

A, C, F

Step-by-step explanation:

Answer:

1,3&6

Step-by-step explanation:

line

distance along a line

point

Dimensions of rectangular garden is: length = 39 feet and width = 18 feet

Given that length of the rectangle garden is three more than twice its width.

The perimeter of the garden is 114 feet

Need to determine width of the garden

Let assume width of the garden be represented by variable "x"

=>Twice of the width = [tex]2 \times x = 2x[/tex]

=> 3 more than Twice of the width= 3 + 2x = 2x + 3

As length of the rectangle garden is three more than twice its width ,

=> Length of the rectangle garden = 2x + 3  

Perimeter of the rectangle = 2( length + width)

=> Perimeter of the rectangular garden = 2 (Length of the rectangle garden + width of the garden)

= 2 (2x + 3 + x) = 2 (3x + 3 ) = 6x + 6

=> Perimeter of the rectangular garden = 6x + 6

As it is also given that Perimeter of the rectangular garden = 114 feet

=> 6x + 6 = 114 feet

=> 6x = 114 – 6

x = 18

Width of the garden = x = 18 feet

Length of the garden = = 2x + 3 = 2(18) + 3 = 39 feet

Hence dimensions of rectangular garden is length = 39 feet and width = 18 feet

Answer:

90°, 60°, and 30°

60°.

Step-by-step explanation:

The triangle ABC has side lengths √6, √2, and 2√2 units.

It is clear that the triangle ABC is right triangle because (2√2)² = (√6)² + (√2)² that means the side lengths satisfy the Pythagoras Theorem.

Now, if the angle between hypotenuse (2√2 units) and base (√2 units) is [tex]\theta[/tex], then

[tex]\cos \theta = \frac{\sqrt{2} }{2\sqrt{2} }  = \frac{1}{2}[/tex]

Hence, [tex]\theta[/tex] = 60°

Therefore, the three angles of the triangle are 90°, 60°, and 30°.

Now, if the base of the triangle is 16 units, then other two side lengths will also change proportionally to remain the triangle a right triangle.

And in that case the base angle will remain 60°. (Answer)

Ben's gross income was $28,500.

Step-by-step explanation:

Sales for the month = $950000

Commission rate = 3%

Amount of commission = 3% of sales for the month

Amount of commission = [tex]\frac{3}{100}*950000[/tex]

Amount of commission = [tex]\frac{2850000}{100}[/tex]

Amount of commission = $28500

Ben's gross income was $28,500.

Keywords: percentage, division

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Answer:

Do you have a photo

Step-by-step explanation:

I'll be happy to help