Carla is deep-sea diving with two friends. Frank is exploring a coral reef 6.7 meters in
front of Carla, and Lola is floating on the surface directly above Carla. If Lola and Frank are 9.7 meters apart, how far apart are Carla and Lola? If necessary, round to the nearest tenth.

The given quadratic equation is f(x) = x³ - 3x² + 2x-1. The two solutions to the equation are x = (3x + √(9x² + 4))/2x² and x = (3x - √(9x² + 4))/2x².

A quadratic equation is written in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

To solve this equation, we will use the quadratic formula.

The quadratic formula states that for a quadratic equation of the form ax² + bx + c = 0, the solutions are given by

x = [-b ± √(b² - 4ac)]/2a.

In this equation, a = x², b = -3x, and c = -1. Plugging these values into the formula, we get x = [3x ± √(9x² - 4(x²)(-1))]/2(x²). Simplifying this, we get

x = [3x ± √(9x² + 4)]/2x².

Now, we must solve for the two solutions. The first solution is x = (3x + √(9x² + 4))/2x². The second solution is

x = (3x - √(9x² + 4))/2x².

Therefore, the two solutions to the given equation are

x = (3x + √(9x² + 4))/2x² and

x = (3x - √(9x² + 4))/2x².

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Answer:

The given expression is:

p^2 + 4q^2 + 9 + 36 + pq + 3 + 4q + 6p

Rearranging the terms, we get:

p^2 + 6p + 4q^2 + pq + 4q + 48

Now, we can group the first three terms and the last three terms together as follows:

(p^2 + 6p + 9) + (4q^2 + pq + 4q + 39)

The first group can be factorized as a perfect square trinomial:

(p + 3)^2

The second group can be factorized by grouping the first two terms and the last two terms:

(pq + 4q) + (4q^2 + 39)

We can factor out q from the first two terms, and 4 from the last two terms:

q(p + 4) + 4( q^2 + 9)

Now, we can factor the second group as a sum of squares:

q(p + 4) + 4(q + 3)(q - 3)

Therefore, the fully factorized form of the expression is:

(p + 3)^2 + q(p + 4) + 4(q + 3)(q - 3) + 48

Note that this expression cannot be simplified further.

1-Is the sum of two prime numbers always a prime number?

Solution:

No. Here is an example.

3 + 7 = 10 , 3 and 7 are prime numbers but not their sum 10.

2-Is the product of two prime numbers also a prime number?

Solution:

Never because it will have 1 and itself as factors and also the two numbers involved in the product.

Example: 7 × 11 = 77 ,77 has 1, itself, 7 and 11 as factors.

3-Which is the largest 3 digit prime number?

Solution:

Start with the largest three digit number 999.

4- Which is the smallest 2 digit prime number?

Solution

Start with the smallest 2 digit number 10.

10 is not a prime number

Answer: 11 is a prime number

The cost of one dinner without any sides is $2, and the cost of 6 dinners without any sides is 6 times that amount, which is $12. Answer: $12.

An equation is a statement that asserts the equality of two expressions. Equations typically contain one or more variables, which are quantities that can take on different values. The goal of solving an equation is to find the values of the variables that make the equation true.Equations can take many different forms, but some common types include linear equations, quadratic equations, polynomial equations, and exponential equations.

An expression is a combination of numbers, variables, and mathematical operations that represents a value. Expressions can contain constants, variables, and operators, such as addition, subtraction, multiplication, and division.

In the given question,

There are different ways to approach this problem, but one possible method is to use ratios. Let's assume that the cost of a dinner without any sides is x dollars. Then, the cost of a dinner with salad is x plus some additional amount for the salad, which we don't know yet. Let's call this additional amount y dollars. Therefore, the cost of a dinner with salad is x + y dollars.

According to the problem, Russell can buy 6 dinners with salads for $114. This means that the total cost of 6 dinners with salads is $114. We can write this as an equation: 6(x + y) = 114

Simplifying this equation, we get: 6x + 6y = 114

Dividing both sides by 6, we obtain: x + y = 19

Now we need to find the cost of 6 dinners without any sides, which is 6 times the cost of a dinner without any sides. We already know that the cost of one dinner without any sides is x dollars, so the cost of 6 dinners without any sides is 6x dollars.

To find x, we can use the fact that x + y = 19, which we derived from the given information. We don't know y, but we can express it in terms of x by using the fraction of the salad price to the total price of a dinner with salad. From the long division, we have:

2x - 3

x + 1

This means that y is equal to the remainder of the division, which is -3/(x+1). Therefore, we have: y = -3/(x+1)

Now we can substitute this expression for y into the equation x + y = 19:

x - 3/(x+1) = 19

Multiplying both sides by x+1, we get: x(x+1) - 3 = 19(x+1)

Expanding the products and simplifying, we obtain a quadratic equation:

x^2 + 18x - 22 = 0

We can solve this equation by using the quadratic formula:

x = (-18 ± √(18^2 + 4122)) / (2*1)

x = (-18 ± √(400)) / 2

x = (-18 ± 20) / 2

x = -9 or x = 2

Since we are interested in the cost of a dinner without any sides, which should be a positive number, we discard the negative solution and take x = 2. Therefore, the cost of one dinner without any sides is $2, and the cost of 6 dinners without any sides is 6 times that amount, which is $12. Answer: $12.

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Answer:

10 small, 5 large

Step-by-step explanation:

if they were all small cars, 5x15 would be 75. there need to be 15 more spots, and each large can hold an extra 3. 15/3 is 5. so there are 10s and 5l

students would need to rent 5 small cars and 8 large cars

Based on the given information, you would be giving $5 per month or $60 per year to charity.

Starting with a monthly gross income of $5,000, we can calculate the amount set aside for family activities as 10% of the gross income, which is:

= $5,000 x 0.10

= $500

Now, we will calculate the monthly allowance as 10% of the family activity money, which is:

= $500 x 0.10

= $50

Since you give 10% of your monthly allowance to support a charity organization, you will be giving:

= $50 x 0.10

= $5 per month

Now, in order to calculate how much you would give to charity in one year, we simply multiply the monthly amount by 12 which gives us:

= $5 x 12

= $60 per year

Therefore, the amount we would be giving to the charity is $5 per month or $60 per year.

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Answer:

the answer is C.

Step-by-step explanation:

Put both equations in the slope intercept form of the line and then graph to estimate where the lines cross.

y = mx + b

7x - y = 7   The 7x is on the wrong side of the equal sign, so subtract 7x from both sides of the equation

7x - 7x -y = -7x + 7

-y = -7x + 7  We want the equation to start y = , not -y =. so divide all the way through by -1

[tex]\frac{-1y}{-1}[/tex] = [tex]\frac{-7x}{-1}[/tex]  + [tex]\frac{7}{-1}[/tex]

y = 7x - 7

x + 2y = 6   The x is on the wrong side of the equal sign.  Subtract x from both sides

x -x + 2y = -x + 6

2y = -x + 6  Divide all the way through by 2

[tex]\frac{2y}{2}[/tex] = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{6}{2}[/tex]

y = [tex]\frac{-1}{2}[/tex] x + 3

You can see from the graph attached where the lines cross.  

Helping in the name of Jesus.

There are initially 150 pharaoh ants in Southeast Asia, and every year the population increases by 950,000 ants.

The rate of change of a function refers to how much the output of the function changes with respect to changes in its input, typically expressed as the derivative of the function.

The initial value of a function refers to the value of the function at a specific point in its domain, often denoted as f(0) or f(x_0) for some value x_0 in the domain. It is called "initial" because it is usually the starting point for analyzing the behavior of the function over a range of inputs.

The given function is y=-150x+950,000, where x represents time in years and y represents the total population of pharaoh ants in Southeast Asia.

The initial value of the function is the y-intercept, which is 950,000. This means that at the beginning of the observation period (when x=0), there are 950,000 pharaoh ants in Southeast Asia.

The rate of change of the function is the coefficient of x, which is -150. This means that every year, the population decreases by 150,000 ants. Therefore, option A is correct because it states that the population decreases every year by 150,000 ants, which is the same as -150 multiplied by 1,000.

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Answer:

10 2/3 kg

8 X 1 1/3 kg = 10 2/3 kg

Answer:  1863[tex]\pi[/tex] cm^3  (option C)

Step-by-step explanation:

The volume is given by the equation

[tex]V=\pi r^2h[/tex]
Just placing the values:
[tex]V=\pi (9)^2(23)[/tex]
Notice the pi is left over, so just get the 9^2*23=1863
So the answer for the volume is 1863[tex]\pi[/tex] in cm^3

So your answer is just fine, 5849. Just notice the pi is not in it.

The net worth of the landscaping company is given by:

$187.205.

How to calculate the net worth?

The net worth of a company or of a person is given by the sum of all assets of the person subtracted by the sum of all debts of the person.

In the context of this problem, the assets, and it's values, of the company are given as follows:

Owned Inventory: $48,760.

Cash: $126,790.

Savings account: $32,436.

Owned equipment: $20,700.

Accounts receivable: $15,640.

Property value: $225,678.

Hence the sum of the assets is given by:

Assets = 48760 + 126790 + 32426 + 20700 + 15640 + 225678 = $469,994.

The debts of the company, with it's values, are given as follows:

Small Business Loan: $76,400.

Building Mortgage: $189,429.

Other debt: $16,970.

Hence the sum of the debts is given by:

Debts = 76400 + 189429 + 16970 = $282,799.

Then the net worth of the company is:

Net worth = Assets - Debt = 469,994 - 282,799 = $187,205.

Answer: Your welcome!

Step-by-step explanation:

The equivalent fractions for 3/10 and 1/7 using the least common denominator are 6/20 and 3/20. The least common denominator of 3/10 and 1/7 is 20, so the fractions must be multiplied by the same number to reach the denominator of 20. 3/10 multiplied by 2/2 is 6/20, and 1/7 multiplied by 3/3 is 3/20.

The wrapping paper used by Aaron is 9 and 2/3 feet of paper

To solve this problem, use the given information about how much wrapping paper is needed for each game and gaming console, and then multiplied by the number of games and consoles that Aaron wraps in one hour. For simple calculation convert mixed fractions into an improper fraction and solve the problem.

Here we have

Aaron wraps present in a store. In one hour, he wraps 8 games and one console.

From the given figure,

Each game takes 2/3 foot of wrapping paper

Each gaming console takes 4 1/3 feet of wrapping paper

From the data

Aaron wraps 8 games in 1 hour

The wrap is used for 8 games = 8 × [ 2/3 foot ] = 16/3 foot

He wraps one console.

The wrap used for 1 console = 4 1/3

Here 4 1/3 = 13/3  [ Converting mixed fraction to improper fraction ]

Hence,

Total amount of wrap used = 16/3 + 13/3

= [ 16 + 13]/3 = 29/3 = 9 2/3  

Therefore,

The wrapping paper used by Aaron is 9 and 2/3 feet of paper

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The different circumferences to go from the start to the finish are 21.98, 31.4, 37.68, and 65.94.

One of the ways of calculating the circumference is using the diameter of a circle (distance from one side to the next one) and applying the formula circumference = diameter x [tex]\pi[/tex]. Now, let's calculate the circumference.

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Answer:

3m=24

m=8

12m=96

24m=192

48m=384

96m=768

Answer:

Step-by-step explanation:

To find the constant of proportionality, we can use the formula for a proportional relationship: y = kx, where y is the total cost, x is the number of songs, and k is the constant of proportionality.

Using the table, we can find two pairs of values for y and x:

When x = 6, y = $1.80

When x = 12, y = $3.60

We can set up a proportion:

y1 / x1 = y2 / x2

$1.80 / 6 = $3.60 / 12

Simplifying, we get:

$0.30 = $0.30

This tells us that the constant of proportionality is $0.30.

We can check this by using another pair of values:

When x = 20, y = $6

Using the formula y = kx, we get:

$6 = ($0.30)(20)

Simplifying, we get:

$6 = $6

This checks out, so we can be confident that the constant of proportionality is $0.30.

Answer:

x < 5 because any value of x must have a bigger negative number than 5. In this case, formally you say that all x values must be less than 5.

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{4}}} \implies \cfrac{ 2 }{ -10 } \implies - \cfrac{ 1 }{ 5 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{ 1 }{ 5 }}(x-\stackrel{x_1}{4}) \\\\\\ y-2=- \cfrac{ 1 }{ 5 }x+\cfrac{4}{5}\implies y=- \cfrac{ 1 }{ 5 }x+\cfrac{4}{5}+2\implies {\Large \begin{array}{llll} y=- \cfrac{ 1 }{ 5 }x+\cfrac{14}{5} \end{array}}[/tex]

Answer: I believe the answer would be 130°

Step-by-step explanation:

Answer:

The angle A will remain the same irrespective of their rotation so it will be 130°.

Step-by-step explanation:

The possible lengths for AC are any values greater than the square root of 51.2 (approximately 7.15 feet).

If triangle ABC is isosceles, then AC must be equal to BC. Let's call the length of AC "x".

Using the Pythagorean theorem, we can find the length of the diagonal line segment BD (which is also the height of the peaked roof):

BD^2 = AB^2 - (AC/2)^2

BD^2 = 8^2 - (x/2)^2

BD^2 = 64 - x^2/4

To ensure that the roof is peaked, we need BD to be less than x (otherwise, the roof would be flat). So we can set up an inequality:

BD < x

√(64 - x^2/4) < x

64 - x^2/4 < x^2

256 - x^2 < 4x^2

5x^2 > 256

x^2 > 51.2

x > √(51.2)

Therefore, the possible lengths for AC are any values greater than the square root of 51.2 (approximately 7.15 feet).

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A curriculum is said to as "integrated" when it simultaneously targets learning objectives across different topic areas.

Children can pursue learning holistically with an integrated curriculum, free from the limitations frequently imposed by topic boundaries.

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1. The expression of each ratio as a fraction in the simplest form is as follows:

2. Writing the ratio of red to yellow pots of flowers three different ways are as follows:

3. Expressing each rate as a unit rate is as follows:

A ratio is the unit rate, which is the quotient of one value compared to another.

The quotient of the value is the division of one quantity by another.

a)  26:169 = 26/169 = 2/13

b. 36 to 78 = 36/78 = 12/26 = 6/13

The number of houses with a pot of red flowers = 32

The number of houses with a pot of yellow flowers = 24

The ratios of red to yellow pots of flowers in three different ways = 32: 24

The sum of ratios = 56 (32 + 24)

a) 32:24 = 4:3 = 1.75:1

b) 32:24 = 57% (32/56 x 100)

c) 32:24 = 0.57 (32/56)

a. 32 teams in 4 divisions = 8 team per division (32/4)

b. $2.70 for 15 ounces = $0.15 ($2.70/15)

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Answer: https://brainly.com/question/16257129

Answer:

3

Step-by-step explanation:

21 is 7 times the number three. You can get this answer by dividing 21 by 7 (answer is 3). You can check your work by multiplying 7 x 3 (you would get 21)

The y-intercept is (0, 9), and the parabola has no x-intercepts.

An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx+c, where m denotes slope and c denotes the y-intercept.

X-intercept and Y-intercept are the two main intercepts. The line's x-intercept and y-intercept are located where the line crosses the x and y axes, respectively.

To find the y-intercept of the parabola, we set x = 0 and solve for y:

y = 3x² - 9x + 9

y = 3(0)² - 9(0) + 9

y = 9

Therefore, the y-intercept is (0, 9).

To find the x-intercepts, we set y = 0 and solve for x:

0 = 3x² - 9x + 9

0 = x² - 3x + 3

Using the quadratic formula, we get:

x = [3 ± √((-3)² - 4(1)(3))]/(2(1))

x = [3 ± √(9 - 12)]/2

x = [3 ± √(-3)]/2

The square root of a negative number is not a real number.

The parabola does not intersect the x-axis, and therefore, there are no x-intercepts.

Therefore, the y-intercept is (0, 9), and the parabola has no x-intercepts.

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The linear regression line is:Y = 0.51X - 14.05

Number is a mathematical object used to count, measure, and label. It is a fundamental concept in mathematics, and is used in nearly every branch of the discipline. In everyday life, the notion of number is used to count objects, keep track of scores, measure amounts, and label objects.

City TV Commercials Car Sales
A 60 20
B 50 15
C 70 25
D 45 17
E 55 19

Calculating the linear regression line:

m = Slope = (NΣXY - (ΣX)(ΣY)) / (NΣX2 - (ΣX)2)
= (5(1475) - (325)(95)) / (5(5850) - (325)2)
= (7375 - 30875) / (29250 - 105625)
= -38500 / -75375
= 0.51

b = Intercept = (ΣY - m(ΣX)) / N
= (95 - 0.51(325)) / 5
= (95 - 165.25) / 5
= -70.25 / 5
= -14.05

Therefore, the linear regression line is:
Y = 0.51X - 14.05.

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Answer:

The total amount of capital invested is:

N2,000 + N4,000 + N1,500 = N7,500

The proportion of the profit that each man gets is equal to the proportion of the capital that he invested. Therefore, the first man gets:

N2,000 / N7,500 * N300 = N80

The second man gets:

N4,000 / N7,500 * N300 = N160

The third man gets:

N1,500 / N7,500 * N300 = N60

Therefore, each man gets N80, N160, and N60, respectively.

Step-by-step explanation:

Answer:

N80, N160, and N60

Step-by-step explanation:

The total amount of capital invested is:

N2,000 + N4,000 + N1,500 = N7,500

The proportion of the profit that each man gets is equal to the proportion of the capital that he invested. Therefore, the first man gets:

N2,000 / N7,500 * N300 = N80

The second man gets:

N4,000 / N7,500 * N300 = N160

The third man gets:

N1,500 / N7,500 * N300 = N60

Therefore, each man gets N80, N160, and N60, respectively.

Answer:

To find out which two students have the same median score, we need to find the median score for each student and compare them.

For James, the median score is 82 (the middle score when the scores are arranged in order).

For Rodney, the median score is 78 (the middle score when the scores are arranged in order).

For Traci, the median score is 82 (the middle score when the scores are arranged in order).

For Maddi, the median score is 67 (the middle score when the scores are arranged in order).

Therefore, the two students who have the same median score are James and Traci, as they both have a median score of 82.