Lacey picks blueberries and raspberries from her garden. She has 1/5 as many pounds of blueberries as raspberries. If she picks 1 4/5 pounds more blueberries, she will have equal weights of berries. Let x represent the weight of raspberries. Which equations could be used to find the weight of blueberries Lacey has? Choose all the correct answers. Explain why you choose the one(s) you did.

a. (1/5)x - 1 4/5 = x

b. x - 1 4/5 = (1/5)x

c. (1/5)x = x - 1 4/5

d. x + 1 4/5 = (1/5)x - 1 4/5

e. (1/5)x + 1 4/5 = x

f. x = 1 4/5(1/5 + x)

Answer:

4

Step-by-step explanation:

I like to use the FOIL method! I've attached a quick picture of how it works below, but basically you multiply the first terms. Next, multiply the outside/outer terms. Then, multiply the inside/inner terms. Lastly, you multiply the last terms.

In this question, the binomial is (x + 2)².

You can expand this to be (x + 2)(x + 2).

When you expand it using the FOIL method, you get x times x, which is x².

Next, the outside/outer terms are x and 2, which is 2x.

Then, you multiply the inside/inner terms 2 and x, which is 2x.

Last, you multiply the last terms, which are 2 and 2, which is 4.

When you put them together, it looks like this:

x² + 2x + 2x + 4.

You can simplify this to x² + 4x + 4.

So your answer is 4.

Answer:

12:)

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

From what we know in April and May combined Joe has collected 61 stamps (27+34=61). To then work out how many Joe collected in June you would take the 61 we know he has already got away from the grand total of 94 (94-61=33) this means in June he collects 33 stamps. Hope this helps :)

Answer:

n= -35 .................................

Answer: $3,276

Step-by-step explanation:

To find the amount of interest needed to be paid, you needed to multiply the amount of money by your interesate rate.

= 3150 x 0.04

= 126

So, we add this extra amount to be paid to the exisiting total

= 3150 + 126

= $3,276

Answer:

\(f(x)=\dfrac{-50(x-1)(x-2)}{(x-5)(x+5)}\)

Step-by-step explanation:

Since f(x) has asymptotes at x = 5 and x = -5, then the denominator of the rational function contains the terms (x - 5) and (x + 5):

\(f(x)=\dfrac{?}{(x-5)(x+5)}\)

Since f(x) has x-intercepts at x = 2 and x = 1, then the numerator of the rational function contains the terms (x - 2) and (x - 1):

\(f(x)=\dfrac{A(x-1)(x-2)}{(x-5)(x+5)}\)

Now substitute the point (0, 4) and solve for A:

\(f(0)=4\\\\\implies \dfrac{A(0-1)(0-2)}{(0-5)(0+5)}=4\\\\\\\implies -\dfrac{2}{25}A=4\\\\\\\implies A=-50\)

So final rational function:

\(f(x)=\dfrac{-50(x-1)(x-2)}{(x-5)(x+5)}\)

Answer:

b and d

Step-by-step explanation:

The equations have at least one integer solution are equation B: √(3x) = 75 and equation D:√x = x - 12.

The value of x is known as the solution.

A.  √(4x) = 5

On squaring, we have

4x = 25

 x = 6.25

The value is not an integer.

B.  √(3x) = 75

On squaring, we have

3x = 5625

 x = 1875

The value is an integer.

C.  8√x = √16

On squaring, we have

64x = 16

    x = 0.25

The value is not an integer.

D.  √x = x - 12

On squaring, we have

          (x - 12)² = x

x² - 24x + 144 = x

x² - 25x + 144 = 0

  (x - 16)(x - 9) = 0

                    x = 9, 16

The value is an integer.

E.  √(10 - x) = x - 2

On squaring, we have

                (x - 2)² = 10 - x

          x² - 4x + 4 = 10 - x

           x² - 3x - 6 = 0

(x - 4.37)(x + 1.37) = 0

                          x = -1.37, 4.37

The value is not an integer.

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Both g(x) = 5 - x² and h(x) = \(5 - e^(6-^x^)\)have the same range as f(x) = -2√(x) - 3 + 8, which is (-∞, 5].

To determine which function has the same range as f(x) = -2√(x) - 3 + 8, we need to first find the range of f(x).

The square root function √(x) takes non-negative values as input and gives non-negative outputs, so the expression -2√(x) will always be non-positive. Therefore, the range of f(x) will be all real numbers less than or equal to -3 + 8, which is 5.

In other words, the range of f(x) is (-∞, 5].

So, we need to find a function whose range is also (-∞, 5]. One possible function is g(x) = 5 - x². We can see that when x is zero, g(x) is at its maximum value of 5, and as we increase or decrease x, g(x) will decrease, eventually approaching negative infinity.

Another possible function is h(x) = 5 - e^(-x). When x is negative infinity, e^(-x) is approaching positive infinity, so h(x) is approaching 0. As we increase x, e^(-x) is approaching zero, so h(x) is approaching 5.

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The graph shows f(x) to have a y intercept at -1, which is where the diagonal line crosses the y axis. We want the y intercept to move to 3. So we must add 4 to the old y intercept to get the new y intercept.

We do this with every single point on f(x) to get g(x) = f(x)+4. This shifts the graph up 4 units.

Answer: (x > -3).

Step-by-step explanation:

To solve the inequality 4(1 - x) < 16, we will simplify and solve for x:

4(1 - x) < 16

Distribute the 4:

4 - 4x < 16

Subtract 4 from both sides:

-4x < 12

Divide both sides by -4. Note that when dividing by a negative number, the inequality sign flips:

x > -3

The solution to the inequality is x > -3. This means that x must be greater than -3 for the inequality to hold true.

To graph the solution on a number line, we mark a shaded region to the right of -3, indicating that all values greater than -3 satisfy the inequality:

The open circle at -3 indicates that -3 is not included in the solution since the inequality is strict (x > -3).

here's the graph for 4(1-x)<16

Hello,

f'(x) = sin(x) - 65 → f(x) = -cos(x) - 65x

Answer:

3rd quadrant

Step-by-step explanation:

Given:

Point (-2, -9)

Computation:

In 1st quadrant (+ , +)

In 2nd quadrant (- , +)

In 3rd quadrant (- , -)

In 4th quadrant (+ , -)

So given point (-2, -9) is in 3rd quadrant.

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

100 will have to be added to both sides to complete the square

Step-by-step explanation:

Given:

x^2+20x+28=0

x² + 20x + 28 = 0

x² + 20x = -28

Using completing the square method of solving quadratic equation

Find the square of half of the coefficient of x

Coefficient of x = 20

Half of the coefficient of x = 20/2

= 10

Square of the half of the coefficient of x = 10²

= 100

Add the square of the half of the coefficient of x to both sides of the equation

x² + 20x = -28

x² + 20x + 100 = -28 + 100

(x + 10)² = 72

\(x^2 +20x -6 =0\\\\\implies x^2 + 2 \cdot 10 \cdot x +10^2 -10^2 -6 =0\\\\\implies (x +10)^2 -106=0\\\\\implies (x +10)^2 =106\\\\\implies x +10 = \pm\sqrt{106}\\\\\implies x = -10 \pm \sqrt{106}\)

It will take 150 minutes for the two containers to have the same amount of water.

To find the number of minutes it will take for the two containers to have the same amount of water, we need to use the following formula:

m = |A - B| / (a - b)

where m is the number of minutes, A is the initial amount of water in Container A, B is the initial amount of water in Container B, a is the rate at which water is being added to Container A, and b is the rate at which water is being drained from Container B.

In this case, the initial amount of water in Container A is 300 liters, the initial amount of water in Container B is 900 liters, the rate at which water is being added to Container A is 6 liters per minute, and the rate at which water is being drained from Container B is 2 liters per minute. Substituting these values into the formula, we get:

m = |300 - 900| / (6 - 2)

m = |-600| / 4

m = 600 / 4

m = 150 minutes

Therefore, it will take 150 minutes for the two containers to have the same amount of water.

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Answer: 6396

Step-by-step explanation:

Delta math

The first equation is incorrect.

The second equation is correct.

The third equation is correct.

Let's go through each equation and determine whether it is correct or incorrect:

(b²+7b-9)+(4b-6b²) = -8b² + 14b-9

To determine if this equation is correct, we need to simplify both sides and check if they are equal.

On the left side:

(b²+7b-9)+(4b-6b²) = b² - 6b² + 7b + 4b - 9 = -5b² + 11b - 9

On the right side:

-8b² + 14b - 9

Comparing both sides, we can see that -5b² + 11b - 9 is not equal to -8b² + 14b - 9. Therefore, the equation is incorrect.

(4a+6)-(3a²-9a+1)=-3a²+ 13a +5

Again, we need to simplify both sides of the equation and check if they are equal.

On the left side:

(4a+6)-(3a²-9a+1) = 4a + 6 - 3a² + 9a - 1 = -3a² + 13a + 5

On the right side:

-3a² + 13a + 5

Comparing both sides, we can see that -3a² + 13a + 5 is equal to -3a² + 13a + 5. Therefore, the equation is correct.

(12c-8c²)+(5c²- 10c) = -3c²+2c

Again, let's simplify both sides and compare them.

On the left side:

(12c-8c²)+(5c²- 10c) = 12c - 8c² + 5c² - 10c = -3c² + 2c

On the right side:

-3c² + 2c

Comparing both sides, we can see that -3c² + 2c is equal to -3c² + 2c. Therefore, the equation is correct.

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The statement about the linear equation 3a + 1/3(6a −9) = 1/2(10a − 6) that is true is: "The equation has an infinite number of solutions." (Option B)

A linear equation is defined as an equation with a maximum of one degree. A nonlinear equation is one with a degree greater than or equal to two.

On the graph, a linear equation looks like a straight line. On the graph, a nonlinear equation creates a curve.

To justify the above answer, we state the linear equation above:


3a + 1/3(6a −9) = 1/2(10a − 6) ; Simplified by opening the brackets, we have

3a + 2a − 3 = 5a − 3; collecting like terms on the left side, we have

5a -3 = 5a -3

Because 5a -3 = 5a -3, the expression holds true regardless of what integer or value a represents. Hence, it has an infinite number of solutions.

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The fraction of silver or brown canoes is 7/10.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Total canoes team = 10

5 teams have silver canoes team.

2 teams have brown canoes team.

Now,

The fraction of silver and brown canoes.

= (5 + 2) / 10

= 7/10

Thus,

7/10

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Answer:

c

Step-by-step explanation:

In thousands:

\(7858 - 4298 = 3560\)

\( \frac{3560}{4298} = .828\)

\(4298 \times 1.828 = 7857\)

Answer:

Step-by-step explanation:

4sin(x-π)cos(x-π) =√3

let (x-π) = (y)

2(2sin(y)cos(y)) = √3

sin(2y) = ½√3

  2y = arcsin(½√3)

  2y = ±π/3 + 2πn, ±2π/3 + 2πn

    y = ±π/6 + πn, ±π/3 + πn

x - π = ±π/6 + πn, ±π/3 + πn

    x = ±π/6 + π(n + 1), ±π/3 + π(n + 1)

As n = any whole number

    x = ±π/6 + π(n), ±π/3 + π(1)

so in the range 0 ≤ x ≤ 2π

x = + π/6 + 0π = π/6

x = + π/6 + 1π = 7π/6

x = - π/6 + 1π = 5π/6

x = - π/6 + 2π = 11π/6

x = + π/3 + 0π = π/3

x = + π/3 + 1π = 4π/3

x = - π/3 + 1π = 2π/3

x = - π/3 + 2π = 5π/3

in increasing magnitude

x = ​π/6, π/3, 2π/3, 5π/6 7π/6, 4π/3, 5π/3, 11π/6

We can write k(x) as the composition of g(x) and f(x).

k(x) = g(f(x))

A composition of two functions means that we need to evaluate one function in the other one.

Here we have the functions:

f(x)=  x²

g(x) = √(x - 1)

h(x) = 2x + 3

And we know that:

k(x) = √(x² - 1)

So we have a square root, then we need to evaluate g(x), and the argument is a square, then we need to evaluate in f(x), the composition is:

k(x) = g(f(x))

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Therefore, when h = 6 and j = 5, the value of hj - h² is -6.

Arithmetic operations are basic mathematical operations that involve manipulating numbers to perform calculations. There are four main arithmetic operations:

Addition: Adding two or more numbers together. The symbol used to represent addition is "+", and the result is called the sum.

Subtraction: Subtracting one number from another. The symbol used to represent subtraction is "-", and the result is called the difference.

Multiplication: Multiplying two or more numbers together. The symbol used to represent multiplication is "×" or "*", and the result is called the product.

Division: Dividing one number by another. The symbol used to represent division is "÷" or "/", and the result is called the quotient.

These operations can be combined to perform more complex calculations. Additionally, there are other arithmetic operations, such as exponentiation (raising a number to a power) and finding roots, which involve using arithmetic principles.

by the question.

To evaluate the expression hj - h² for h = 6 and j = 5, we simply substitute these values into the expression and perform the arithmetic operations:

hj - h² = (6)(5) - 6²

= 30 - 36

= -6

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Answer: 8000

Step-by-step explanation:

The 8 in the number 348,000 is in the thousands place.

So it represents the value of 8,000 .

Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

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Answer:

4x + 1

Step-by-step explanation:

g(f(x)) = (4x + 3) - 2

         = 4x + 1