How can a mixed number be written as a sum?

Final answer:

Lisa needs to score at least 12 points to win, so the inequality to represent this scenario is 'p >= 12', where 'p' is the number of points she scores on her next turn.

Explanation:

To represent the number of points Lisa needs to win the game with an inequality, we can let p stand for the points she will score on her next turn.

Since she needs to score at least 12 points, the inequality would be p \">= 12".

This reads as 'p is greater than or equal to 12,' meaning Lisa needs to score 12 or more points to win.

PQ = 2 units

height = 4 units

 area = 2*4 = 8/2 = 4 square units

Answer:

(d-5)

Step-by-step explanation:

we know that

The phrase"five fewer than d days" is equal to subtract 5 from the number d

so

d minus 5-----> (d-5)

Answer:

d-5

Step-by-step explanation:Just trust

Answer:

10 soccer club members are going to the tournament.

Step-by-step explanation:

Let x be the number of soccer club members who are going to the  tournament,

Given,

The cost of transportation of x students = $ 192

⇒ The cost of transportation of 1 student = [tex]\frac{192}{x}[/tex]

⇒ The cost of transportation of (x+2) student = [tex]\frac{192}{x-2}[/tex]

According to the question,

[tex]\frac{192}{x}-\frac{192}{x+2}=3.20[/tex]

[tex]192(\frac{1}{x}-\frac{1}{x+2})=3.20[/tex]

[tex]192(\frac{x+2-x}{x(x+2)})=3.20[/tex]

[tex]\frac{384}{x^2+2x}=3.20[/tex]

[tex]3.2x^2+6.4x=384[/tex]

[tex]3.2x^2+6.4x-384=0[/tex]

By the quadratic formula,

[tex]x=\frac{-6.4\pm \sqrt{40.96+4915.2}}{6.4}[/tex]

[tex]\implies x = \frac{-6.4\pm 70.4}{6.4}[/tex]

[tex]\implies x = 10\text{ or } x = -12[/tex]

Since, the number can not be negative,

Hence, 10 soccer club members are going to the tournament.

To find the number of soccer club members going to the tournament, we set up an equation based on the total cost of the van and the drop in cost per person when two additional students join. Solving the quadratic equation reveals that the number of soccer club members is 10.

The question asks us to determine the number of soccer club members going to the tournament given that the cost of the van is $192 and that the cost per person drops by $3.20 when 2 additional students join the trip. Let's denote the number of club members as 'x'. Before the 2 students join, the cost per person is $192 / x. After they join, the cost per person becomes $192 / (x + 2), which is $3.20 less than the original cost per person, so:

192 / x - 192 / (x + 2) = $3.20

Multiplying through by x(x + 2) to clear the denominators gives us:

192(x + 2) - 192x = 3.20x(x + 2)

This simplifies to:

192x + 384 - 192x = 3.20x^2 + 6.4x

The term 192x cancels out on both sides, so we have:

384 = 3.20x^2 + 6.4x

To solve for 'x', we divide both sides by 3.20:

120 = x^2 + 2x

Now we solve the quadratic equation x^2 + 2x - 120 = 0. Factoring this equation, we get (x + 12)(x - 10) = 0. Thus, x can be -12 or 10. However, since we can't have a negative number of club members, the number of soccer club members is 10.

The equation of line is slope intercept form is y = 2x + 3

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

2x - y = -3   be equation (1)

Adding 3 on both sides of the equation , we get

2x - y + 3 = 0

Adding y on both sides of the equation , we get

y = 2x - 3

Now , equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

Therefore , the value of A is 2x - 3  , where the slope is m = 2

Hence , the equation of line is y = 2x - 3

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Final answer:

To convert the equation 2x-y=-3 into slope-intercept form, y must be isolated. The steps involve rearranging the equation to solve for y, resulting in the slope-intercept form y = 2x + 3, where the slope (m) is 2 and the y-intercept (b) is 3.

Explanation:

To convert the equation 2x-y=-3 into slope-intercept form, we need to solve for y. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope, and b represents the y-intercept.

Let's solve for y:

Therefore, the equation 2x - y = -3 in slope-intercept form is y = 2x + 3.

The larger number is (-7+14)/2 = 3.5.

The smaller number is (-7-14)/2 = -10.5.

_____

The two equations a+b=-7, a-b=14 can be solved to get these results. It is genrally convenient to solve them by adding one to the other, or subtracting one from the other.

Answer:

Area of the border is 142.80 ft²

Step-by-step explanation:

The given figure consist of three figures = 2× semicircles + 1 square.

We will calculate area of the figure including border

Area of one semicircle = (1/2)π×r²= (1/2)×π×(12/2)² = (1/2)π×(6)² = 18π ft²

Area of square = side² = 12² = 144 ft²

Total area = 144 + 18π + 18π = (144 + 36π) ft²

Now we will calculate area without border.

Area of the semicircle = (1/2)π×r² =(1/2)π×[(12-4)/2]²=(1/2)π×(4)² = 8π ft²

area of square = side²= (12-4)²= 8² = 64 ft²

Total area = 64 + 8π + 8π = (64 + 16π) ft²

Now the area of the border = Area with border - Area without border

= (144 + 36π) - (64 + 16π) = 20π + (144 - 64) = 20π + 80

= 20×3.14 + 80 = 142.80 ft²

Area of the border = 142.80 ft²

The area of the flower border surrounding the heart-shaped pond is approximately 142.80 square feet.

The given figure consists of three parts: two semicircles and one square. Let's calculate the area of the border step by step:

1. Area of the Semicircles:

  - The semicircles form the rounded top of the heart shape.

  - Each semicircle has a radius of half the width of the pond, which is [tex]\(12 \, \text{ft}\)[/tex].

  - Area of one semicircle = [tex]\(\frac{1}{2} \pi r^2\)[/tex]

[tex]\[ = \frac{1}{2} \pi (6)^2 = 18\pi \, \text{ft}^2\][/tex]

  - Total area contributed by both semicircles = [tex]\(2 \times 18\pi = 36\pi \, \text{ft}^2\)[/tex]

2. Area of the Square:

  - The square section of the pond has sides of [tex]\(10 \, \text{ft}\)[/tex] each.

  - Area of the square = side squared

[tex]\[ = 10^2 = 100 \, \text{ft}^2\][/tex]

3. Total Area Including Border:

  - Total area = Area of semicircles + Area of square

[tex]\[ = 144 + 36\pi \, \text{ft}^2\][/tex]

4. Area Without Border:

  - To find the area without the border, we subtract the area of the pond from the total area:

  [tex]\[ = 100 + 16\pi \, \text{ft}^2\][/tex]

5. Area of the Border:

  - The area of the border is the difference between the total area and the area without the border:

[tex]\[ = (144 + 36\pi) - (100 + 16\pi) = 20\pi + 80 = 20 \times 3.14 + 80 = 142.80 \, \text{ft}^2\][/tex]

Therefore, the area of the flower border surrounding the heart-shaped pond is approximately 142.80 square feet.

Final answer:

The equation 'x over five equals three over four' is solved by cross-multiplying to get 4x = 15, and then dividing both sides by four to find x = 3.75.

Explanation:

The equation presented by the student 'x over five equals three over four' translates to the algebraic equation x/5 = 3/4. Solving this involves finding the value of x that makes the equation true. To solve for x, we can cross-multiply to get 4x = 15, and then divide both sides of the equation by four to isolate x, giving us x = 15/4 or x = 3.75. Thus, the solution to the equation x/5 = 3/4 is x = 3.75.