the length of a rectangle is 5 less than twice its width. if the perimeter is 26 meters, find the dimensions of the rectangle

To order the numbers from least to greatest: -2.8, -1.25 (-5/4), -1.17 (-7/6), 1.3, 1.33 (4/3). Decimal conversion helps compare their values, with negative numbers being smaller than positive ones.

To order the numbers from least to greatest, we need to compare their values. Negative numbers are less than positive numbers, and among negative numbers, the one with the smaller absolute value is greater. We can convert the fractions to decimals to make it easier to compare all the numbers:

Now we order them from least to greatest:

The lowest terms would be 3/16 because you could divide top and bottom by 4

The lowest it vould be is 4:16

This is because the BCF is 4.

The inverse function is [tex]\( f^{-1}(x) = \frac{x + 7}{4} \)[/tex].

To find the inverse function of [tex]\( f(x) = 4x - 7 \)[/tex], we follow these steps:

1. Replace [tex]\( f(x) \) with \( y \): \( y = 4x - 7 \)[/tex].

2. Swap[tex]\( x \) and \( y \): \( x = 4y - 7 \)[/tex].

3. Solve this equation for [tex]\( y \)[/tex].

So, let's solve for [tex]\( y \)[/tex]:

[tex]\[ x = 4y - 7 \][/tex]

Add 7 to both sides:

[tex]\[ x + 7 = 4y \][/tex]

Divide both sides by 4:

[tex]\[ \frac{x + 7}{4} = y \][/tex]

Thus, the inverse function of [tex]\( f(x) = 4x - 7 \)[/tex] is:

[tex]\[ f^{-1}(x) = \frac{x + 7}{4} \][/tex]

Gotcha!

The 1st answer is x=-13 or x=13

The 2nd answer is -5<y<-3

The 3rd answer is t=-6 or t=6

The 4th answer is a=-1/8 or a=1/8

Remark

Question B is a bit of a guess, but A is pretty straight forward.

A

Let P = Platinum Gym's income (total)

Let M = Platinum Gym's Registration Fee.

Number of people who received free membership registrations = 50

The total income from anyone who had to register was

P = (124 - 50)*M

P = 74 * M

B

Monthly Fee = MF

n = number of months = 6

c = customer base  = 124

Equation

P = Registration Fee (found in A) + n * c * MF

Solution

P = 74*M + 6*124*MC

P = 74M + 744*MC

The question is, do you count the registration fee at the beginning or not? I would.

[tex]\dfrac{1}{2}x+2=1\qquad\text{subtract 2 from both sides}\\\\\dfrac{1}{2}x=-1\qquad\text{multiply both sides by 2}\\\\\boxed{x=-2}[/tex]

B. This is because falling represents negatives, or subtracting. 3-5 is -2.

Answer-

The abs. minimum value of the given function was found to be 3.

Solution-

Here, the given function is,

[tex]f(x)=x^4-x^2-2x+5[/tex]

Then, calculating its first derivative,

[tex]{f}'(x)=4x^3-2x-2[/tex]

Then, calculating its second derivative,

[tex]{f}''(x)=12x^2-2[/tex]

Then, calculating all the critical values of the given function by equating the first derivative to 0,

[tex]\Rightarrow {f}'(x)=0[/tex]

[tex]\Rightarrow 4x^3-2x-2=0[/tex]

[tex]\Rightarrow 2x^3-x-1=0[/tex]

[tex]\Rightarrow 2x^3-x-1=0[/tex]

[tex]\Rightarrow 2x^3-2x+x-1=0[/tex]

[tex]\Rightarrow 2x(x^2-1)+(x-1)=0[/tex]

[tex]\Rightarrow 2x(x+1)(x-1)+(x-1)=0[/tex]

[tex]\Rightarrow (x-1)(2x(x+1)+1)=0[/tex]

[tex]\Rightarrow (x-1)(2x^2+2x+1)=0[/tex]

[tex]\Rightarrow (x-1)=0[/tex]    ( ∵ ignoring the imaginary roots)

[tex]\Rightarrow x=1[/tex]

Putting the value of x, in the second derivative,

[tex]{f}''(1)=12(1)^2-2=10[/tex]

As, the value of f"(x) is positive, the function attains its minimum value at x=1.

So, f(1) will give the absolute minimum value of the function,

[tex]f(1)=(1)^4-(1)^2-2(1)+5=3[/tex]

∴ The abs. minimum value of the given function is 3.

well I think it is 7.214  give me brainiest if i got it right plz

To divide a number by a 1-digit divisor, simply divide the number by the divisor. For example, 15 divided by 3 is 5, and 21 divided by 7 is 3. Practice makes perfect in this fundamental aspect of mathematics.

I understand you are trying to learn how to divide by 1-digit divisors. It is a fundamental topic in mathematics that you will use many times in the future.

Let's take the numbers 3 and 7 as examples. To divide by 3 or 7, simply take the number you are wanting to divide and divide it by either 3 or 7. For example, if we want to divide 15 by 3, you would simply perform 15 ÷ 3, which results in 5.

Now, if we want to divide 21 by 7, you would do 21 ÷ 7, which gives you a result of 3. It's that simple! Remember, the biggest key to success here is practice. The more you practice these divisions, the better you'll get at them.

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1/11 is half of 2/11.  (1/11 + 1/11 = 2/11)

As 2/11 = 0.18, 1/11 must equal half of 0.18.

Half of 0.18 is 0.09.  Thus the decimal for 1/11 is 0.09.

Answer:

The decimal for 1/11 is 0.09

Step-by-step explanation:

We have two options to get the answer, the first one is when we know that 1/11 is half of 2/11, so 1/11 will be half of 0.18. We have to divide 0.18 by 2:

0.18÷2 = 0.09

The other way to do it is to divide 1÷11 = 1/11

The answer is 0.09

Wx + yz = h

yz = h - wx

z = (h - wx) / y

Answer

z = (h - wx) / y

Solution: The function that represents the Grace earning each week is defined as [tex]e(h)=9h[/tex], where [tex]e(h)[/tex] is in dollar and [tex]h[/tex] is the time in hours. domain of the function [tex]e(h)=9h[/tex] is [10,20].

Explanation:

Let, Grace works for h hours per week.

For one hour she get $9.

For h hours she get [tex]\$(9\times h)=\$9h[/tex].

So, the function that represents the Grace earning each week is defined as [tex]e(h)=9h[/tex].

It is given that she works from 10 to 20 hours per week, therefore the value of h lies between 10 to 20. Hence the Grace's earnings for each week is defined as [tex]e(h)=9h[/tex] and the domain of the function [tex]e(h)=9h[/tex] is [10,20].

.5x>=25

x>=50

50 is the least number for x; it makes the equation equal 45

50 is the least number for x it makes the equation equal 45

120*0.8 is the expression, because you can put 80% as 80/100 and that is equal to .8 so you just put that in a calculator and thats your answer. Hope that helped :)

Answer:

[tex](0.80)120[/tex]

Step-by-step explanation:

We are asked to find an expression that represents 80% of 120.

We know that % means per hundred. 80% would be 80 divided by 100.

[tex]80\%\text{ of }120=\frac{80}{100}\times 120=(0.80)120[/tex]

Therefore, the expression [tex](0.80)120[/tex] represent 80% of 120.

[tex]3\frac{3}{8} = \frac{8(3) + 3}{8} = \frac{27}{8}[/tex]

[tex]5\frac{1}{4} = \frac{4(5) + 1}{4} = \frac{21}{4}[/tex]

[tex]\frac{21 (miles)}{4}[/tex] ÷ [tex]\frac{27 (miles)}{8 (hour)}[/tex]

= [tex]\frac{21 (miles)}{4} * \frac{8 (hours)}{27 (miles)} = \frac{21(8)hours}{4(27)} = \frac{42}{27}hours[/tex]

[tex]\frac{42}{27} hours[/tex] = [tex]\frac{14}{9}= 1\frac{14-9}{9} hours = 1\frac{5}{9}hours[/tex]

Answer:  [tex]1\frac{5}{9}hours[/tex]

Hey mate!!

Answer

4/7 and 8/14 are equivalent fractions, because they are both equal to 4/7 when they are simplified.

Correct answer is D. 8/14

Hope it helps you!

The expression is

[tex]AUD/1.38 = USD[/tex]

Step by step conversion is as following;

1 USD = 1.38 AUD, or its reciprocal

Where,

1.38 recent currency rate

AUD = Australian dollar

USD = US dollar

So, by rearranging

[tex]1 AUD = 1/1.38 USD[/tex]

Then

[tex]22AUD/1.38 = 15.94 USD[/tex]

The answer is

[tex]22A UD = 15.94 USD[/tex]

The product for these two fractions is equal to 12/55

The three consecutive odd integers are 23, 25,27

What is Algebraic expression ?

Algebraic expressions are numbers expressed using letters or alphabets without specifying their values. Algebra taught us how to express unknown values using letters such as x, y, and z. There can also be a single value that is placed before and multiplied by a variable in an algebraic expression in addition to these letters, which are called variables.

Let the three consecutive odd integers be x , x + 2 , x+ 4 then,

the sum of these three odd integers is 17 less than four times the smallest integer that is :

x + (x+2) + (x+4) = 4x -17

3x + 6 = 4x -17

4x - 3x  = 6 + 17

x = 23

x + 2 = 25

x +  4 = 27

Therefore, the three consecutive odd integers are 23, 25,27

more on algebraic expression at :

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1st slot: 10 possibilities  

2nd slot: 9 possibilities  

3rd slot: 9 possibilities  

4th slot: 9 possibilities  

5th slot: 9 possibilities  

10 * 9 * 9 * 9 * 9 = 65610 Possibilities

The total number of possible 5-digit codes for the garage door opener, where no two adjacent digits are the same, is 59,049.

This is a combinatorics problem in mathematics. A simple way to solve this problem is to calculate the total number of 5-digit code combinations possible without any constraint, which is 10^5 = 100,000.

However, the condition given in the problem is that no two adjacent digits can be the same. The possible codes for the first digit are 10 (0-9). For the second digit, because it cannot be the same as the first, there are 9 possibilities, the third digit also has 9 possibilities because it cannot be the same as the second, and so on.

Therefore, the total number of possible codes is 10 * 9 * 9 * 9 * 9 = 59,049. Hence, the garage door opener can have 59,049 different codes.

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25% is the same is 1/4 of something. So you have to find what 1/4th of 48 is. To do that, just divide 48 by 4. and you get 12.

A 25% payment on a CD player that costs $48 would be $12. Hope that helps!

Let the width of rectangle= x centimeter

According to condition length =  (x+2) centimeter

As accoding to formula

perimeter of rectangle = 2( lenght +width)

so Perimeter = 2{(x+2) +(x)}     equation 1

Give perimeter = 60cm          equation 2

comparing  equation 1 and equation 2

2{(x+2) +(x)} = 60

Solving   2{2x+2} =60

4x+4 =60  

subtracting 4 both sides

4x= 56

dividing 4 both sides.

x=14  width of rectangle

AS we have assume length = x+2 ⇒ 14 +2

Length =16

The series is A.P. with first term = 44 and common difference = 39-44=-5 = 34- 39

Sum of A.P. is S = n/2(2a+ (n-1)d)

Where a is first term ,d is common difference and n no. Of terms

Here a = 44 ,d= -5 and n = 23

S = 23 /2(2×44+ (23-1)(-5))

S=23/2(88-110)

S = 23/ 2(-22)

S = 23×-11

S = -253

What even is this ???

 -9.75 + 3.25x

= -3.25(3) + 3.25(x)

= -3.25(3)  -  -3.25(x)     notice they have the same factor of -3.25

= -3.25(3 - x)

Answer: A

Answer:

Negative 2.

Step-by-step explanation:

2x -1 would have an outcome of a negative number since 2 is positive and one is negative. if they were both positive numbers or negative numbers then the answer would be positive

Answer

83

Step-by-step explanation:

she had 90.

turned in to 78.

now she has  83

5, -1, -7, -13, -19

 -6   -6  -6   -6     the difference between the numbers is -6

[tex]a_{n} = a_{1} + d(n - 1)[/tex]  ; where a₁ is the first term, d is the difference, and n is the term

[tex]a_{n} = 5 - 6(n - 1)[/tex]

[tex]a_{n} = 5 - 6n + 6)[/tex]

[tex]a_{n} = 11 - 6n[/tex]

f(1) = 5

[tex]a_{1} = 11 - 6(1)[/tex]

      = 11 - 6

       = 5

 TRUE