Same set up as the problem to the left

Answer: x∈(-∞,3]      x∈(-∞,1.5)

Step-by-step explanation:

2(3x+1)≤20

Divide both parts of the equation by 2:

3x+1≤10

3x+1-1≤10-1

3x≤9

Divide both parts of the equation by 3:

x≤3

Thus, x∈(-∞,3]

[tex]\displaystyle\\4(x-1) < 2\\\\Divide\ both\ parts\ of\ the\ equation \ by \ 4:\\\\x-1 < \frac{2}{4} \\\\x-1 < 0.5\\\\x-1+1 < 0.5+1\\\\x < 1.5\\\\Thus,\ x\in(-\infty,1.5)[/tex]

The solution in interval notation, x∈(-∞,3] and x∈(-∞,1.5)

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

An inequality is a mathes that compares two values or expressions using a relational operator, such as less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), or not equal to (≠). Inequalities is used to describe relationships between quantities or to express constraints or conditions.

WE are given that the inequality  as;2(3x+1)≤20

Divide both parts of the equation by 2:

3x+1≤10

3x+1-1≤10-1

3x≤9

Now Divide both parts of the equation by 3:

x≤3

Thus, x∈(-∞,3]

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Answer:

y^2 - 4y + 16 - 65/y + 4

Answer:

2a.The difference is that question 1b has been ordered by PEDMAS

2b. The fact that Add(A) comes before Subtract(S).

2c. The order of the subjects in Bidmas.

Step-by-step explanation:

The base-ten number for the number 29 is 29

The number is given as

29

The base of the above number is not stated

When the base of a number is not stated, then the base of the number is base 10

This means that the number 29 is in base ten

Hence, the base-ten number for the number 29 is 29

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The speed of her plane in feet per second is 50 feet per second and the plane high was 1750 feet.

i. The speed of Hailey’s plane is 50 feet per second.

As Hailey’s plane took 90 seconds to climb 4,500 feet,

X= 4,500 ÷ 90

X= 50 feet per second.

ii. The plane was at 1750 feet at 35 seconds.

As the plane climb 50 feet per second,

X= 50 * 35

X= 1750 feet.

Jetliners typically fly between 240 and 285 km/h during take-off (130–154 km; 149–177 mph). Light aircraft, such a Cessna 150, accelerate to about 100 km/h after take-off (54 km; 62 mph). Even slower take-off speeds apply to ultra-lights.

Hence, the speed of her plane in feet per second is 50 feet per second and the plane high was 1750 feet.

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The speed of her plane in feet per second is 50 feet per second and the plane high was 1750 feet.

i. The speed of Hailey’s plane is 50 feet per second.

As Hailey’s plane took 90 seconds to climb 4,500 feet,

X= 4,500 ÷ 90

X= 50 feet per second.

ii. The plane was at 1750 feet at 35 seconds.

As the plane climb 50 feet per second,

X= 50 * 35

X= 1750 feet.

Jetliners typically fly between 240 and 285 km/h during take-off (130–154 km; 149–177 mph). Light aircraft, such a Cessna 150, accelerate to about 100 km/h after take-off (54 km; 62 mph). Even slower take-off speeds apply to ultra-lights.

Hence, the speed of her plane in feet per second is 50 feet per second and the plane high was 1750 feet.

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The equation which represents the real world problem involving a rectangle as described in the task content is; 9/14 = 3/7 × 3/2.

It follows from the task content that the equation which represents the real world problem involving a rectangle be determined.

It follows from plane shape measures that the area of a rectangle is;

Area = length × width.

Hence, from the parameters given; we have;

Area = 3/7 × 1 1/2

Area = 3/7 × 3/2

Ultimately, the model according to the given parameters which hold true is;

9/14 = 3/7 × 3/2.

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Answer:

[tex]2.50c \: + \: 3.25b \: \leqslant \: 35[/tex]

Step-by-step explanation:

The total amount spent needs to be less than 35 dollars but it can also equal that amount. It can't be greater than 35 dollars because you can't spend money you don't have

Answer:13

Step-by-step explanation:51 goes into 66 one time so 66-51=15

then 153/51=3 so 13

Step-by-step explanation:

51 goes into 66 one time so 66-51= 15 then 153/51 = 3 so 13

Greetings from Brasil...

The expression that allows using the equation of a circle is:

(X - Xc)² + (Y - Yc)² = R²

as

Xc = - 4, Yc = 4 and R = 4, then

or

X² + 8X + Y² - 8Y + 16 = 0

The value of x is 3.6 and the value of y is 13.35.

We are given the equations that:

15 x - 26 = 28°

12 x + 1 = (4 y - 9)°

Now,

15 x - 26 = 28°

Add 26 to both the sides:

15 x = 28 + 26

15 x = 54

Divide both sides by 15, we get that:

x = 54 / 15

x = 3.6

Now, we have:

12 x + 1 = (4 y - 9)°

Substitute x = 3.6

12 (3.6) + 1 = 4 y - 9

43.2 + 1 = 4 y - 9

44.2 = 4 y - 9

4 y = 44.2 + 9

4 y = 53.2

y = 53.2 / 4

13.35

Therefore, we get the value of x as 3.6 and the value of y as 13.35.

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Answer:

The value of x is 3.6 and the value of y is 13.35.

Step-by-step explanation:

The required height of the streetlight is 11.5 feet.

Given that,
A person 54 inches tall is standing 13 feet from a streetlight. If the person casts a shadow 96 inches ​long, how tall is the​ streetlight is to be determined.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Here,
Let the
13 feet = 13 * 12 inch = 156 inches
Ratios of height and distance would be equal
54 / 96 = x / 96 + 156
54 * 252/96 = x
x = 138 inches
x = 11.5 feets

Thus, the required height of the streetlight is 11.5 feet.

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Answer:

I would say 144

Step-by-step explanation:

I say 144 Because 3 to the square root of 16 is 12

And twelve to the second power is 2

The required cost of each cookie become when buying in dozen is $0.54.

Given that,
Bought 12 cookies (each cookie for 0.99).
A dozen pack is for 6.55.
how much more would each cookie cost if bought by the dozen is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
In a dozen cookies, there are 12 cookies
Now cost of a dozen cookies = 6.55
Now 12 cookies = $6.55
1 cookie = 6.55 / 12
cost of 1 cookie = $0.54

Thus, the required cost of each cookie become when buying in dozen is $0.54.

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Answer:

does that help?

The finance charge is $13.60, whereas the new balance at the end of the month is  $933.60

What is the finance charge on the credit card balance?

The finance charge which is the monthly interest payable on the credit card balance is based on the average daily balance for the month, it is determined as the  average daily balance for the month multiplied by the annual percentage rate(APR) divided by 12 , since the requirement is to compute one month finance charge and not for a whole year

finance charge=$742*21.99%/12

finance charge=$13.60

The new balance is the balance at the end of the month plus the finance charge

new balance=$$920+$13.60

new balance=$933.60

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Answer:

13.60

933.60

Step-by-step explanation:

To determine the finance charge, use the formula:

FinanceCharge=APR12×AverageDailyBalance

Substitute 21.99% for the APR, and $742 for the average daily balance, and calculate:

FinanceCharge=0.219912×$742=$13.60

So, the finance charge will be $13.60

Next, determine the new balance by adding the finance charge to the balance at the end of the month:

$920+$13.60=$933.60

The new balance will be $933.60

The interest that y dollars earn in one day at a rate of 1.75% compounded daily is 0.0175

An equation is an expression that shows the relationship between two or more numbers and variables.

Let I represent the total interest gotten from investing y dollars. Since y dollars is invested at a rate of 1.75% compounded daily, hence:

Interest = y * 0.0175 = 0.0175

The interest that y dollars earn in one day at a rate of 1.75% compounded daily is 0.0175

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The completion of Jean's Dress Shop's cash budgets for the following months is as follows:

Cash Budget                                     July            August        September

Section 1: Cash receipts  

Beginning cash balance               $25,000      $10,000        $10,000

Add cash receipts                           90,000      100,000        120,300

Total cash available                     $115,000     $110,000      $130,300

Section 2: Cash payments  

For inventory purchases              $82,750        $70,115       $87,076

For S&A expenses                         27,250         30,280          30,716

For interest expense                               0                 50                54.45

Total budgeted disbursements $110,000     $100,445      $117,846.45

Section 3: Financing activities  

Surplus (shortage)                        $5,000     $9,555       $12,453.55

Borrowing (repayments)                5,000   455        ($2,453.55)

Ending cash balance                  $10,000       $10,000       $10,000

The Cash Budget is an estimate of an entity's cash flows (cash outflows and cash inflows) over a specific period.

The Cash Budget can be prepared monthly, quarterly, semi-annually, or yearly.

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Complete the cash budget by filling in the missing amounts.

Cash Budget                                     July            August        September

Section 1: Cash receipts  

Beginning cash balance               $25,000  

Add cash receipts                           90,000      100,000        120,300

Total cash available                     $115,000    $

Section 2: Cash payments  

For inventory purchases              $82,750        $70,115        $87,076

For S&A expenses                         27,250         30,280           30,716

For interest expense                               0        

Total budgeted disbursements $110,000  

Section 3: Financing activities  

Surplus (shortage)                        $5,000  

Borrowing (repayments)                5,000  

Ending cash balance                  $10,000        $10,000     $10,000

The expression equivalent to [tex](x+2)+[4x-(\frac{x^{2}+6x+8 }{x+4})][/tex] is  option (A) 4x.

As per the question statement, we are given with an expression  [tex](x+2)+[4x-(\frac{x^{2}+6x+8 }{x+4})][/tex].

We are required to simplify the above mentioned expression.

To solve this question, let us simplify the expression, part by part.

First, We are considering the part (x² + 6x + 8), which can be rewritten as

[tex][( (x^{2} + 6x + 9) - 1][/tex]...(1)

Now, [tex](x^{2} +6x +9)=[(x)^{2} +(2*x*3)+(3)^{2}][/tex]...(2)

Comparing [tex][(x)^{2} +(2*x*3)+(3)^{2}][/tex] with the standard form of

[(a + b)² = (a² + 2ab + b²)], we get, (a = x) and (b = 3).

Therefore, [tex][(x^{2} +6x +9)=(x+3)^{2}][/tex], then,

[tex][( (x^{2} + 6x + 9) - 1] = [(x+3)^{2} -1]\\or, (x^{2} + 6x + 8)=[(x+3)^{2}-(1)^{2}][/tex]...(3)

Again, comparing [tex][(x+3)^{2}-(1)^{2}][/tex] with the standard expansion of

[(c²- d²) = (c + d)(c -d)], we get, [(x + 30 = c] and (d = 1).

Therefore, [tex][(x+3)^{2}-(1)^{2}]=[(x+3+1)(x+3-1)][/tex]

[tex]or, (x^{2} + 6x + 8) = (x+4)(x+2)[/tex].

Using the simplified value of (x² + 6x + 8) in the expression  [tex](x+2)+[4x-(\frac{x^{2}+6x+8 }{x+4})][/tex], we get,

[tex](x+2)+[4x-(\frac{x^{2}+6x+8 }{x+4})]=(x+2)+[4x-\frac{(x+4)(x+2)}{(x+4)} ]\\or, (x+2)+[4x-(\frac{x^{2}+6x+8 }{x+4})]=(x+2)+[4x-(x+2)]\\or, (x+2)+[4x-(\frac{x^{2}+6x+8 }{x+4})]=(x+2)+[(4x-x)-2]\\or, (x+2)+[4x-(\frac{x^{2}+6x+8 }{x+4})]=(x+2)+(3x-2)\\or, (x+2)+[4x-(\frac{x^{2}+6x+8 }{x+4})]=[(x+3x)+(2-2)]\\or, (x+2)+[4x-(\frac{x^{2}+6x+8 }{x+4})]=4x[/tex]

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The equation, in point-slope form, matches the graphed line is y + 7= 2/5(x - 4)

The point on the line is given as

Point = (4, -7)

The slope (m) of the line is given as

m = 2/5

The linear equation is then represented as

y - y1 = m(x - x1)

So, we have

y + 7= 2/5(x - 4)

Hence, the equation, in point-slope form, matches the graphed line  is y + 7= 2/5(x - 4)

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Answer:

16.8

Step-by-step explanation:

Set up a proportion.  

w = width and l = length

I would put the length and the width of the model in the first fraction and the length of the actual building on the right.

[tex]\frac{w}{l}[/tex] =[tex]\frac{w}{l}[/tex]

[tex]\frac{7}{58.7}[/tex] = [tex]\frac{w}{140.9}[/tex]  Multiply both sides of the equation by 58.7 and 140.9 and you get:

140.9(7) = 58.7x

986.3 = 58.7x  Divide both sides by 58.7

16.8023850085 = x  I will round to the nearest tenths' place

16.8

La rueda recorre una distancia de 75.420 metros tras 60 vueltas. (Correct choice: A)

La rueda se desplaza sobre el suelo mediante un tipo de movimiento conocido como rodadura, en la que la rueda experimenta rotación y traslación, cuyo centro instantáneo de rotación es el punto de contacto entre la rueda y el suelo.

Si no existe deslizamiento de la rueda con respecto al suelo, entonces la distancia recorrida tras una revolución de la rueda (s), en metros, es descrita por la siguiente ecuación:

s = 2π · r         (1)

Donde r es el radio de la rueda, en metros.

Si tenemos que r = 0.20 m, entonces la distancia recorrida es:

s = 2π · (0.20 m)

s ≈ 1.257 m

Asimismo, la distancia recorrida es directamente proporcional al número de revoluciones de la rueda es y la distancia recorrida tras 60 vueltas es determinada por regla de tres simple:

S = 60 vueltas × (1.257 m / 1 vuelta)

S = 75.420 metros

La rueda recorre una distancia de 75.420 metros tras 60 vueltas.

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Answer:

You will need 10 gallons of pure acid to mix with 5 gallons of a 70% acid solution to get a 90% solution.

Step-by-step explanation:

.70(5) + x = .90(x + 5)  I want to multiply both sides by 100 to clear the decimal

70(5) + 100x = 90(x + 5) Distribute the 70 and the 90

350 + 100x = 90x + 450  Subtract 90x from both sides

350 + 10x = 450  Subtract 350 from both sides

10x = 100  Divide both sides by 10

x = 10

A plane is a flat surface that has length and width but no depth and can extend indefinitely.

In two dimensions, a plane has no limits. It has no thickness at all. A coordinate plane is an illustration of a plane. In the coordinate plane, a type of geometric plane, we plot points. A number line that runs up and down forever and one that runs from left to right indefinitely both exist on the coordinate plane. There are many different kinds of planes, including intersecting and parallel ones. In cursive writing, the upper case letter P stands for a plane.

Flat forms are also known as plane geometric figures, which include 2-dimensional shapes including squares, rectangles, triangles, and circles. Contrarily, 3-dimensional geometric forms such a cone, cube, cuboid, cylinder, etc. are used in solid geometry.

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Answer: freee points?

Step-by-step explanation: You gave the answer to your own question.

Hence , the store owner's profit will be $ 102 .

It is providing a store owner orders twenty five calculators that price ​$30 every.

Original cost = number of calculators × cost per calculator

                       = 25 ×  30

                       = $ 750

Sales revenue  = 22 ×  39

                         = $ 858

Return loss = 3 ×  2

                   = $ 6

Profit = Sales revenue - ( Original cost + Return loss )

          =  858 - ( 750 + 6 )

          = 858 - 756

          = $ 102

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Answer:

0.00001338081

Step-by-step explanation:

24v^4=33176v

54v^6=24794911296

33176v/24794911296v

The two v's cancel out so you have:

331776/24794911296

331776/24794911296=0.00001338081

So, your answer is 0.00001338081.

The number of child ticket sold on that day is 69.

At the movie theatre, child admission is $5.80 and adult admission is $9.30 . On Wednesday, 122 tickets were sold for a total sales of $893.10 .

Therefore,

let use variables to represents the number of child and adult tickets sold.

let

variable x = number of child ticket sold

variable y = number of adult tickets sold

Therefore,

5.80x + 9.30y = 893.10

x + y  = 122

multiply equation(ii) by 5.80

5.80x + 9.30y = 893.10

5.80x + 5.80y = 707.6

3.5y = 185.5

y = 185.5 / 3.5

y = 53

Therefore,

x = 122 - 53

x = 69

Hence, the number of child ticket sold on that day is 69.

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