X^2 + 5x + c find the value of c that makes each trinomial a perfect square

The given sequence is geometric with a common ratio of 3, which is identified by dividing any term by its preceding term and finding a consistent value.

To determine whether the given sequence is geometric, we should check if there is a common ratio between successive terms. A sequence is geometric if each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Looking at the sequence 2, 6, 18, 54, ..., we can divide each term by the previous term to find the common ratio.

Since each term is obtained by multiplying the previous term by 3, we have a common ratio of 3.

Therefore, the given sequence is geometric and the common ratio is 3.

After walking for 2 days she raised a total of $12.5.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, Ana participated in a charity walk. She raised $0.25 for each 1/2 mile that she walked.

Since, for 1/2 miles she earns money = 0.25

Thus,

For 1 mile she will earn a total of money = 0.25* 2

For 1 mile she will earn a total of money = 0.5

Since Ana ran for 2 days, The first day Ana walked 11 miles. On the second day, she walked 14 miles.

So,

Total of miles she walked = 11 + 14

The total of miles she walked = 25

Thus,

She raised a total amount of money = 25 *0.5

She raised a total amount of money = 12.5$

Therefore, after walking for 2 days she raised a total of $12.5.

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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.

Abu bought the GPS system approximately 6.55 years ago.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

We can use the exponential decay formula to solve this problem.

The formula is:

[tex]A = A_0 \times e^{-kt}[/tex]

Where A is the current value, A0 is the initial value, k is the annual rate of decay, and t is the time in years.

We know that Abu bought the GPS system for $12500,

So,

[tex]A_0[/tex] = 12500.

We also know that the current value of the GPS system is $8600,

So,

A = 8600.

The annual rate of decay is given as k = 0.062.

Plugging these values into the formula, we get:

8600 = 12500 x [tex]e^{-0.062t}[/tex]

Dividing both sides by 12500, we get:

0.688 = [tex]e^{-0.062t}[/tex]

Taking the natural logarithm of both sides, we get:

log (0.688) = -0.062t

Solving for t.

t = ln(0.688) / (-0.062)

t ≈ 6.55 years

Therefore,

Abu bought the GPS system approximately 6.55 years ago.

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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.

The perimeter of given square is 4(s + 3)

Given that:

One side of square has length  = (s+3)

A square is a geometric figure having 4 equal straight sides and all internal angles are of 90 degrees.

Perimeter of a closed figure is a measure  of length of all the lines needed to construct that figure.

Perimeter of square of side a is thus a + a + a + a = 4a.

Here given is a = (s+3)

Thus perimeter of given square with side (s+3) is 4(s+3).

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Sheena originally had 248 stamps as per given condition.

To solve a problem involving basic arithmetic and algebraic reasoning to find the original number of stamps that Sheena had.

Let's start with the second part of the problem to find out how many stamps Eric had after receiving stamps from Sheena and before giving stamps to Raju:

Firstly, if Eric ended up with 96 stamps after giving away 1/5 of his stamps to Raju, we can calculate how many stamps he had before giving them away.

To do so, we can think of 96 as being 4/5 of his total stamps at that time, since he kept 4 parts out of 5.

We can represent this with the equation: (4/5) × total stamps = 96. Solving this gives us a total of stamps = 120.

Next, we know Eric originally had 58 stamps and ended up with 120. The difference must be the stamps Sheena gave him, which was 1/4 of her original total. If we represent Sheena's original number of stamps as S, we can say 58 + (1/4)S = 120.

Lastly, we solve for S: ((1/4)S = 120 - 58), which simplifies to (1/4)S = 62.

Multiplying both sides of the equation by 4 yields S = 248.

Therefore, Sheena originally had 248 stamps.

To find the percent error, subtract the estimate from the actual value, divide the difference by the actual value, and multiply by 100. To find the original price, set up an equation using the formula for finding the sale price and solve for the unknown variable. The percent error is approximately 7.41% and the original price was $299.

To find the percent error, you need to compare the estimate to the actual value.

1. Subtract the estimate from the actual value: 54 - 50 = 4.

2. Divide the difference by the actual value: 4 / 54 ≈ 0.0741.

3. Multiply the result by 100 to get the percent error: 0.0741 * 100 ≈ 7.41%

So the percent error is approximately 7.41%.

To find the original price, you can set up an equation using the formula for finding the sale price: Original price - (Discount * Original price) = Sale price.

Let x be the original price. Using the given values, the equation becomes: x - (0.75 * x) = 74.75.

Simplifying the equation, you get: x - 0.75x = 74.75.

Combining like terms, you get: 0.25x = 74.75.

Dividing both sides by 0.25, you get: x = 74.75 / 0.25 = 299.

So the original price was $299.

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Answer:

d and/ or the other dude

Step-by-step explanation:

There is a relationship between price and gift baskets sold, and the relationship is that as the price increases, the gift baskets sold decreases.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given that an An online store sold a gift basket at five different prices and recorded the number of gift baskets that were sold at each price.

We need to find the correct statement which is represented by the scatterplot.

A scatterplot is a type of data display that shows the relationship between two numerical variables.

As we observe the scatterplot, as the  price decreases, the gift baskets sold increases or the price increases, the gift baskets sold decreases..

Hence, there is a relationship between price and gift baskets sold, and the relationship is that as the price increases, the gift baskets sold decreases.

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To solve for r, add 3 to both sides of the equation.

To solve for r, you need to isolate it on one side of the equation. Begin by adding 3 to both sides of the equation to cancel out the -3 on the right side. This gives you -15 = r. Therefore, the value of r is -15.

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The dimensions of the square that has twice the area of the given square is 19.80 in.

What is scaling ?

It is the technique to resize drawing with comparing to actual size of object which uses proportion or ratio. For example, Mapping of earth, drawing prototype of automobiles.

It is given that :

the side of square measure = 14 inches

so the area of square will be :

A = a²

  = 14 x 14

  = 196 square inches

The square that has twice the area of this square means double the area :

196 x 2 = 392 square inches

To find one side of the square:

A = a²

a = √A

  = √392

  = 19.80 inches

Therefore, the dimensions of the square that has twice the area of the given square is 19.80 in.

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Answer:

Concentration.

Step-by-step explanation:

Concentration: It is define as the amount of substance  per unit volume.

Or

Concentration is defined as the ratio of solute in a solution to either solvent or total solution.

Concentration usually is expressed in terms of mass per unit volume.

When the amount of a substance in a given volume is increased then it alter the concentration of reactant.When the concentration of reactant is increase then the rate of reaction  increases.Because when the concentration is increases then more ions or molecules interact to form new compounds therefore, the rate of reaction  increases.When the concentration of reactant decrease then less number of ions or molecules interact to form new compounds therefore, the rate of reaction decreases.