The length of a rectangle is 1 more meter than twice its width. The rectangle has an area of 1275 m².


Let w represent the width of the rectangle. What quadratic equation, in standard form, represents this situation?



Answer: _____________________________

The length of a rectangle is 1 more meter than twice its width. The rectangle has an area of 1275 m².
What is the length of the rectangle? Show your work.
A. 1 m
B. 21 m
C. 25 m
D. 51 m

Answer:Therefore the two numbers are -20 and -40

Step-by-step explanation:

Let the two numbers be a and b,

It is given that their sum is 60, so a + b = -60,

It is also given that their difference is 20, so a - b = 20,

Since we don’t know yet which one out of a and b is greater, assume any one of them to be larger than the other (a in my case),

Add the above two equations, you get,

2a = -40 or a = -20,

Substitute this value of a in any of the formed equations,

a + b = -60,

-20 + b = -60 or b = -40,

Let the two numbers be a and b,

It is given that their sum is 60, so a + b = -60,

It is also given that their difference is 20, so a - b = 20,

Since we don’t know yet which one out of a and b is greater, assume any one of them to be larger than the other (a in my case),

Add the above two equations, you get,

2a = -40 or a = -20,

Substitute this value of a in any of the formed equations,

a + b = -60,

-20 + b = -60 or b = -40,

Therefore the two numbers are -20 and -40

The smaller number is 17, and the larger number is 43. The two equations formed from the given information are solved simultaneously to find these numbers.

To solve this problem, we need to set up two equations based on the given information. Let's denote the smaller number by s and the larger number by l.

The sum of the two numbers is 60: s + l = 60.

If twice the smaller number is subtracted from the large number, the result is 9: l - 2s = 9.

We can solve these equations simultaneously. First, rearrange the second equation to express l in terms of s: l = 2s + 9. Next, substitute this expression into the first equation:

s + (2s + 9) = 60

3s + 9 = 60

3s = 51

s = 17

Now we have found the smaller number is 17. To find the larger number, we substitute s back into the equation for l:

l = 2(17) + 9

l = 34 + 9

l = 43

So the two numbers are 17 and 43

Answer:

The amount of stock for which both brokers would charge the same commission is $2500.

Step-by-step explanation:

i) Let the amount of stock to be traded be worth $x

ii) therefore for both the brokers to charge the same commission we can write

   1% of x  = $25 [tex]\RIghtarrow[/tex][tex]\Rightarrow[/tex]  0.01 [tex]\times[/tex] x  = 25  [tex]\therefore[/tex]   x = [tex]\frac{25}{0.01} = 2500[/tex]

The amount of stock for which both brokers would charge the same commission is $2500.

Answer:

 P = 2x + 2y + 8, Answer is A

Step-by-step explanation:

I got it right on the test so yea.

To evaluate the expression[tex]\(3x^3 - \frac{2}{y^6}x^2y^2 + xy\) for \(x = \frac{2}{3}\) and \(y = \frac{1}{2}\),[/tex]let's substitute these values into the expression:

[tex]\[3\left(\frac{2}{3}\right)^3 - \frac{2}{{\left(\frac{1}{2}\right)}^6}\left(\frac{2}{3}\right)^2\left(\frac{1}{2}\right)^2 + \frac{2}{3} \times \frac{1}{2}\][/tex]

Let's simplify this step by step.

1. [tex]\(3\left(\frac{2}{3}\right)^3 = 3 \times \frac{8}{27} = \frac{24}{27} = \frac{8}{9}\)[/tex]

2.  [tex]\(- \frac{2}{{\left(\frac{1}{2}\right)}^6}\left(\frac{2}{3}\right)^2\left(\frac{1}{2}\right)^2 = - 2 \times 2^6 \times \frac{1}{3^2} \times \frac{1}{2^2} = - 2 \times 64 \times \frac{1}{9} \times \frac{1}{4} = - \frac{128}{9}\)[/tex]

3   .[tex]\(\frac{2}{3} \times \frac{1}{2} = \frac{1}{3}\)[/tex]

Now, let's add these results together:

[tex]\[\frac{8}{9} - \frac{128}{9} + \frac{1}{3} = \frac{8 - 128 + 3}{9} = \frac{-117}{9} = -\frac{13}{3}\][/tex]

So, [tex]\(3x^3 - \frac{2}{y^6}x^2y^2 + xy\) evaluated at \(x = \frac{2}{3}\) and \(y = \frac{1}{2}\) is \(-\frac{13}{3}\).[/tex]

Answer: 11625.8

Step-by-step explanation:

The total amount in the account after 17 years, with an annual interest rate of 7.5%, is approximately $7420.50.

To calculate the amount in the account after 17 years, we use the formula for simple interest: Total future amount (with simple interest) = Principal + (Principal × Interest Rate × Time). In this case, the principal is $3400, the interest rate is 7.5%, and the time is 17 years. Plugging in these values, we get:

Total future amount = 3400 + (3400 × 0.075 × 17)

Calculating this, the total future amount in the account will be approximately $7420.50.

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Work Shown:

AB + BC = AC .... see diagram below

(3x)+(2x-2) = 18 ... plug in given expressions

5x-2 = 18

5x-2+2 = 18+2 ... add 2 to both sides

5x = 20

5x/5 = 20/5 ... divide both sides by 5

x = 4

Given points A, B and C are collinear, with B between A and C, and the distances between them expressed in terms of 'x'. We use the fact that AB + BC = AC to form an equation, solve it to find 'x' = 4.

To solve for 'x' in this problem, we need to utilize the fact that points A, B, and C are collinear and that point B is between A and C.

Given AB = 3x, BC = 2x - 2, and AC = 18.

When points are collinear and one is between the other two, the sum of the distances between the points equals the total distance. So, we know that AB + BC = AC.

Substitute the known values into this equation to get 3x + 2x - 2 = 18.

Combine like terms to give 5x -2 = 18. Rearrange this to make 'x' the subject, you get 5x = 20, then x = 4.

So the value of 'x' that satisfies the given conditions is 4.

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Answer:

1. x = 12

2. 3∛4 feet.

Step-by-step explanation:

1. We are given the equation of x as [tex]\sqrt{x - 3} + x = 9[/tex] and we have to find the extraneous solution of the equation.

Now, [tex]\sqrt{x - 3} + x = 9[/tex] ............. (1)

⇒ [tex]\sqrt{x - 3} = 9 - x[/tex]

Squaring both sides we get,

⇒ x - 3 = 81 - 18x + x²

⇒ x² - 19x + 84 = 0

⇒ x² - 12x - 7x + 84 = 0

⇒ (x - 12)(x - 7) = 0

⇒ x = 12 or 7.

Now, putting x = 12 in the equation (1) we get,

[tex]\sqrt{12 - 3} + 12 \neq 9[/tex]

Again, putting x = 7 in the equation (1) we get,

[tex]\sqrt{7 - 3} + 7 = 9[/tex]

Therefore, x = 12 is an extraneous solution of this equation. (Answer)

2. The volume of a cube with side lengths a ft. is given to be 108 ft³.

So, a³ = 108

⇒ a = 3∛4 feet.

Therefore, the length of the sides of the cube are each 3∛4 feet. (Answer)

Square of m reduced by 49 = m²- 49

Step-by-step explanation:

Let us consider the variable as m.

Square of m is given as m².

Reduction factor is 49.

So the expression for the square of m reduced by 49 is given as m²- 49.

Answer:

Patty spent $71.75

Step-by-step explanation:

20.50 x 3.5 = 71.75

Answer: 71.75

3.5* 20.50

Answer:

  x = -37 7/15

Step-by-step explanation:

1. Find the terms with the variable. They are 4.3x on the left and 4.0x on the right.

2. Identify the term with the least coefficient*. It is 4.0x on the right.

3. Subtract that term from both sides of the equation.

  4.3x -4.0x +19.35 = 8.11 +4.0x -4.0x

  0.3x +19.35 = 8.11 . . . . . . simplify

4. Identify any constant term on the side of the equation with the variable. It is 19.35 on the left.

5. Subtract that constant from both sides of the equation.

  0.3x +19.35 -19.35 = 8.11 -19.35

  0.3x = -11.24 . . . . . . . simplify

6. Divide both sides of the equation by the coefficient of the variable. That coefficient is 0.3 in this equation.

  (0.3x)/0.3 = (-11.24)/0.3

  x = -37.466666... (repeating decimal)

__

If you like, you can express the solution as a mixed number:

  x = -11.24/0.30 = -1124/30 = -562/15

  x = -37 7/15

_____

You are expected to be able to do the math using the numbers in any form they might appear: integers, mixed numbers, fractions, decimals, scientific notation. You can convert the problem here to an integer problem by multiplying both sides by 100:

  430x +1935 = 811 +400x

The answer still has a fraction in it: x= -1124/30 = -37 7/15.

_____

* You subtract the term with the least coefficient so the variable term in the result has a positive coefficient. That may be desirable, but is not necessary. You can subtract either variable term to get the variable on one side of the equal sign. You have to pay attention to the resulting sign when you divide by the variable's coefficient.

Answer:

The answer is (-2,0)

Step-by-step explanation:

When you put both points on the graph. Draw a line through them.

See where the line hits a point from in between the points.

The function g(x) is the function f(x) scaled down by a factor of 2/5, resulting in a vertical compression of the graph. Thus, the correct answer is A. The graph of g(x) is f(x)'s graph vertically compressed.

The function g(x) = 2/5 x2 is f(x) = x2 multiplied by a scalar factor of 2/5. This means that every y-coordinate in the graph of f(x) is scaled down by a factor of 2/5 to produce the corresponding y-coordinate in the graph of g(x). It does not flip the graph over the x-axis. Therefore, the graph of g(x) is simply the graph of f(x) compressed vertically. So, the correct answer is A. The graph of g(x) is the graph of f(x) compressed vertically.

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The function rule that relates y (circumference) to x (diameter) is y = π x [pi × x]

Since x represents the diameter of the circle and y represents the circumference.

For a circle with radius r, circumference of the circle (y)equals,

y = 2πr ................................(1)

Diameter of a circle is twice the radius of the circle.

Assuming x as the diameter

[tex]x = 2\times r = 2r[/tex] ...........................(2)

Substituting (2) in (1), we get

y = π(2r) = πx ..............................................(3)

A function rule is an equation that determines the relation between a dependent variable and an independent variable. The relation between diameter of a circle and its circumference can be given as

Circumference = Pi × Diameter of circle

y = π × x

where π = 3.142

Answer:

Step-by-step explanation:

Answer:

19.55

Step-by-step explanation:

21.25

- 1.7

_____

19.55

Answer:

(2004+2005) divided by 2

Step-by-step explanation:

3.)

Variables:

New tablet cost (575),

Money already saved, (56),

Money saved per week(14w)

Write an Equation:

The amount of weekly money you need to earn must cover the leftover cost needed to buy the tablet, therefore:

money_needed - money_you_have = money_earned_per_week

575 - 56 = 14w

Solving:

575 - 56 = 14w

519 = 14w

37.071428 = w

37 weeks needed

You solve the other two on your own.

Answer:

2.4 miles

Step-by-step explanation:

If Hans ran 3 miles in 25 minutes, that would mean he ran 0.6 miles every five minutes. So, 0.6*4=2.4, as 4/5*25=20.

The number 846 does have a component in the tens place, which is the digit 4, representing 40 when viewed in terms of place value. Understanding the concept of place value, including the tens place, is fundamental in mathematics for efficient calculation and comprehension of numbers.

The question seems to be asking whether the number 846 can be classified in terms of its placement in the tens place value or not. To understand this, let's break down the number 846 in terms of place value. The number 846 is comprised of three digits, each representing a different place value in the base-10 numbering system. Starting from the right, the first digit (6) represents the ones place, the second digit (4) represents the tens place, and the third digit (8) represents the hundreds place.

Therefore, yes, 846 does have a component in the tens place, which is the digit 4. This means that the number 846 has 4 tens or 40 when breaking it down by place value. Understanding place value is crucial in mathematics as it helps in doing calculations, understanding the value of numbers, and in various operations such as addition, subtraction, multiplication, and division. The tens place specifically is important when dealing with numbers ranging from 10 to 99 and beyond, as it helps in grouping numbers in units of ten, simplifying calculations, and enhancing comprehension of numbers' sizes.

Answer:

[tex]Each\ of\ other\ two\ experiments\ required\ 3\ test\ tubes.[/tex]

Step-by-step explanation:

[tex]Let\ each\ of\ other\ experiment\ requires\ x\ test\ tube\\\\Total\ number\ of\ test\ tubes\ needed=8\\\\Test\ tubes\ used\ in\ the\ experiments=sum\ of\ number\ of\ test\ tubes\ in\ each\ experiment\\\\Test\ tubes\ used\ in\ the\ experiments=2+x+x\\\\2+x+x=8\\\\2+2x=8\\\\Subtract\ 2\ from\ both\ sides\\\\2+2x-2=8-2\\\\2x=6\\\\divide\ both\ sides\ by\ 2.\\\\x=3[/tex]

[tex]Each\ of\ other\ two\ experiments\ required\ 3\ test\ tubes.[/tex]

Answer:

a=1

-2a + 3 < 9 − 3a

5a − 4a + 6 < 8

2a + 3 > 10 − 3a

a=2

-4 + 3a + 8 < 16

14 + 5a < 12a + 1

3a − 2a + 1 > 2

Step-by-step explanation:

i did the test

Answer:

a=1

-2a + 3 < 9 − 3a

5a − 4a + 6 < 8

2a + 3 > 10 − 3a

a=2

-4 + 3a + 8 < 16

14 + 5a < 12a + 1

3a − 2a + 1 > 2

Step-by-step explanation:

i just did the test

Answer:

(12,10)

Step-by-step explanation:

Let the midpoint of the side opposite this vertex have coordinates B(a,b)

We have the centroid at C(8,7) and the vertex of the triangle at A(0,1).

The centroid divides AB internally in the ratio 2:1

We use the formula:

[tex](\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})[/tex]

where m:n=2:1 is the ratio of internal division.

We substitute the coordinates of A and B and the ratio to get:

[tex](\frac{2a+1*0}{2+1},\frac{2b+1*1}{2+1})[/tex]

This should simplify and give us the centroid.

[tex](\frac{2a}{3},\frac{2b+1}{3})=(8,7)[/tex]

This implies that:

[tex]\frac{2a}{3}=8,\frac{2b+1}{3}=7[/tex]

We solve for a and b

[tex]2a=24,2b+1=21[/tex]

[tex]a=12,b=10[/tex]

Therefore the midpoint of the side opposite this vertex is (12,10)

Answer:

76/11 ; 7.32 ; 7.546 ; 151/20

Step-by-step explanation:

Given data:

The numbers are listed as below

151/20 ; 76/11 ; 7.32 ;7.546

The numbers are written in the same format that is in decimal form

7.55 ; 6.90901 ; 7.32 ; 7.546

Arranging the numbers starting with the least number

6.90901 ; 7.32 ; 7.546 ; 7.55

76/11 ; 7.32 ; 7.546 ; 151/20

Please note the value of 151/20 is exactly 7.550 which makes it larger than 7.546.

Answer: 26

Step-by-step explanation: I think so...

Answer:

26

Step-by-step explanation:

Payton will play 180 games in 3 hours.

Step-by-step explanation:

Given,

Games played in 15 minutes = 15 games

We will find unit rate;

15 minutes = 15 games

Dividing both sides by 15

[tex]\frac{15}{15}\ minutes=\frac{15}{15}\ games\\\\1\ minute = 1\ game[/tex]

Time = 3 hours = 3*60 = 180 minutes

180 minutes = 180*games per minute

180 minutes = 180*1 games

180 minutes = 180 games

Payton will play 180 games in 3 hours.

Keywords: unit rate, multiplication

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Answer:

SinB = Sin30 = 0.5

Step-by-step explanation:

Ok lets use sine rule

a/SinA = b/SinB = c/SinC

a/Sin60 = b/SinB = 12/Sin90

b/Sin30 = 12/Sin90

b = (12 × Sin30) ÷ Sin90

b = (12 × 0.5) ÷ 1

b = 6cm

SinB = Sin30 = 0.5

Answer:

lool at the picture shown

-1/2x < -12

Divide both sides by -1/2

Also because you are dividing by a negative number you need to reverse the inequality sign.

X > 24