Write the following in factored form by factoring out the greatest common factor. 40p^6q+15p^5q^4 + 35p^3q^2

The system of equations 4x + 3y = - 2 and 8x + 6y = - 4 coincide and have an infinite number of solutions.

We know two simultaneous equations have a unique solution when they intersect at a point,

when they are parallel they have no solution and when they are coinciding they have an infinite no. of solutions.

Given, A system of equations,

4x + 3y = - 2 and 6y = - 4 - 8x.

Rearranging the equations,

4x + 3y = - 2 and 8x + 6y = - 4.

Now, The second equation is a multiple of the first as,

2(4x + 3y) = 2(-2).

Therefore, The system of equations 4x + 3y = - 2 and 8x + 6y = - 4 these two lines coincide and they have an infinite number of solutions as each point of one line lies to another.

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Answer:

Step-by-step explanation:

Hi:

So first, subtract 61$ by 6$ since John needs to have lunch with that money.

61-6=55$

Then just divide by 5$ because it is asking how much tickets he can buy with 55$.

55/5= 11 Tickets as answer

Answer:

11/500

Step-by-step explanation:

calculator bro

Answer:

R=T

Step-by-step explanation:

We could say that the same symbol = makes it look like a true statement.

We could say that the same symbol makes us see a true statement.

In this case we are showing that R corresponds to T therefore it is true or confirmed, regardless of the value that R has.

Step-by-step explanation:

\(2x + 8 = 26 \\ \)

\(2x + 8 - 8 = 26 - 8\)

\(2x = 18\)

\(x = \frac{18}{2} \\ \)

\(x = 9\)

Answer:

Step-by-step explanation:

\(\tt 2x + 8 = 26\)

Subtract 8 from both sides:-

\(\tt 2x+8 \bf{-8}= \tt 26 \bf{-8}\)

\(\tt 2x=18\)

Divide both sides by 2:-

\(\tt \cfrac{2x}{\bf2}=\cfrac{18}{\bf2}\)

\(\tt x=9\)

___________________

Hope this helps!

Have a great day!

part 1 of the question is asking us to evaluate expressions to the power of 2. To do that let's remember the following:

Ther is, when a number is elevated to second power it means we have to multiply that number by itself. For example:

In the second part of this question, we are asked to evaluate the square root of a number. Let's remember that the square root is the inverse operation of elevating a number to the second power. That is if we have:

it means:

For example:

The third part of the questions asks us to solve for "x" the following equation:

To do that we take square root on both sides:

Since the square root of a number to the second power is the same number and the square root of 9 is 3, we get:

When we compare the two numbers the value of -9 < 8.

When numbers are arranged in a straight line with rising or decreasing values from left to right or right to left, respectively, it is called a number line. A number line may be stretched endlessly in any direction and can be used to represent both positive and negative integers.

Finding out whether number is larger or smaller than another or more numbers is the process of comparing numbers. Numbers to the right of a number line are higher than those to the left. The absolute value of the difference between the numbers at any two places on a number line is the distance between them.

The given numbers are -9 and 8.

We know that -9 lies on the left of the number line, whereas 8 lies to the right.

Hence, when we compare the two numbers the value of -9 < 8.

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Answer: it's not clear so i can't tell you the equation as it requires the slope but i can tell you the y-intercept is 4

Step-by-step explanation:

Answer:Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

Step-by-step explanation:

The equation for distance of the flowerbed from the hive.

(d/10)+(d/6) = 240

The distance of  the flowerbed from the​ hive = 900ft

To calculate speed, divide the journey's distance by the time it took to travel, so speed = distance divided by time. Divide the distance by the speed to get the time. Multiply speed by time to find the distance. These equations can be simplified to s=d/t, where s represents speed, d is distance, and t is time.

Let the distance of flower bed from hive to be = d

Time the bee stays at the flower bed = 11

Time the bee is away from the hive = 15

Time the bed was flying to the flower bed and back to the hive will be;

15 -11=4 minutes--------------changes to seconds by multiplying by 60

=4*60

=240 seconds

Formular for time is Distance/speed

Time of fright=240 seconds

Form expression for time of flying;

Time for flying from hive to flowerbed= d/10ft/s

Time for flying from flower bed to Hive= d/6ft/s

Solving these two equation we get:

A. (d/10)+(d/6) = 240

B. distance of  the flowerbed from the​ hive:

(8d/30) = 240

8d = 7200

d = 7200/8

d = 900

The distance of  the flowerbed from the​ hive = 900ft

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I understand that the question you are looking for is:

A bee flies at 10 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 11 ​minutes, and then flies directly back to the hive at 6 feet per second. It is away from the hive for a total of 15 minutes. a. What equation can you use to find the distance of the flowerbed from the​ hive?

a. Write the equation. Let d be the distance of the flowerbed from the hive.

b. How far is the flowerbed from the​ hive?

Answer:

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a right triangle to represent the situation:

        |\

        | \

   h    |  \   9 ft

        |   \

        |    \

        |     \

        -------

        6 ft

Here, h represents the height on the wall where the ladder touches. We want to find the angle of elevation θ.

Using the right triangle, we can write:

sin(θ) = h / 9

cos(θ) = 6 / 9 = 2 / 3

We can solve for h using the Pythagorean theorem:

h^2 + 6^2 = 9^2

h^2 = 9^2 - 6^2

h = √(9^2 - 6^2)

h = √45

h = 3√5

So, sin(θ) = 3√5 / 9 = √5 / 3. We can solve for θ by taking the inverse sine:

θ = sin^-1(√5 / 3)

θ ≈ 37.5 degrees

Therefore, to the nearest tenth of a degree, the angle of elevation the ladder makes with the ground is 37.5 degrees.

Answer:

The answer would be team D as their range is 24.

Step-by-step explanation:

Team A: range of 27

Team B: Range of 32

Team C: Range of 27

Team D: Range of 24

Team D has the lowest range found by subtracting the larger number 46 by the smaller number 22.

Answer:

C

Step-by-step explanation:

Answer:

355 plus the amount of d will be greater than or equal to 575

Step-by-step explanation:

Area = pi x r^2

R = 7/2 = 3.5

Area = 3.14 x 3.5^2

Area = 38.5 m^2

So, Bob is 12 years old and his father is 36 years old solved by using the substitution method.

To determine the ages of Bob and his father, let's use the given information and set up two equations.

Let Bob's age be represented as B and his father's age as F. The terms provided are:

1. Bob's father is three times as old as he is: F = 3B
2. Four years ago, Bob's father was four times as old as he is: F - 4 = 4(B - 4)

Now, we can solve these equations simultaneously. Substituting the first equation into the second equation, we get:

3B - 4 = 4(B - 4)

Simplify the equation:

3B - 4 = 4B - 16

Add 4 to both sides:

3B = 4B - 12

Subtract 4B from both sides:

-B = -12

Finally, divide by -1:

B = 12

Now that we know Bob's age, we can find his father's age using the first equation:

F = 3B
F = 3(12)
F = 36

So, Bob is 12 years old and his father is 36 years old.

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Answer:

.

Step-by-step explanation:

.

Answer: √29 or 5.38

Step-by-step explanation:

move every point 5 units right and 2 units up. Use the result as object. You can use formulas to solve the rest.

Answer:

They are congruent by AAS.

Step-by-step explanation:

Side BD is common to both  triangles and 2 pairs of corresponding angles are congruent.

A price floor is a law that limits the minimum price at which a good, service, or factor of production can be sold while a price ceiling is a regulation that limits the maximum price at which a good, service, or factor of production can be sold

Price floors are commonly implemented to support producers, while price ceilings are typically put in place to protect consumers from higher prices that might result from shortages or monopolies.

Example of Price Floor:Agricultural subsidies are a common example of price floors. Government price floors ensure that farmers receive a minimum price for their crops.

If the market price of wheat falls below the government-established price floor, the government may buy the excess supply at the guaranteed price, ensuring that farmers are able to make a profit. If there is a price floor, the minimum price is set above the equilibrium price.

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(x+1) & (x-5) are the factors of given equation.

The given Equation is,

x3- \(3x^{3}\) - 9

Here, If we substitute x =5, in the given equation, then we find

     (5)3 - 3(5)3 - 9*5 -5 = 0

x-5 is factor of given equation to find another factor dividing given equation by x-5

    we will get =(x2+2x+1) after dividing the equation by x - 5

Hence x3- \(3x^{3}\) - 9 =(x2+2x+1) (x-5)

                            =(x+2)2 (x-5)

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Answer:

empezando multiplicar todos los números seria un total de 1785  que lo pondremos con m3  que un metro cubico seria 1000L entonces con los 1785 los ponemos por 1 000  

Step-by-step explanation:

respuesta 1 785 000

Solutions with y(0) > 2 diverge to infinity

To draw a direction field for the differential equation y' = y(y - 2)^2, we will choose a set of points in the (t, y)-plane and plot small line segments with slopes equal to y'(t, y) = y(y - 2)^2 at each of these points.

Here is the direction field:

               |     /

               |   /

               | /

               |/

               /|

             /  |

           /    |

         /      |

       /        |

     /          |

   /            |

 /              |

/________________|

The direction field shows that there are two equilibrium solutions: y = 0 and y = 2. Between these two equilibrium solutions, the direction field shows that the solutions y(t) are increasing for y < 0 and y > 2 and decreasing for 0 < y < 2.

To see how the solutions behave as t → ∞, we can examine the behavior of y'(t, y) as y → 0 and y → 2. Near y = 0, we have y'(t, y) ≈ y^3, which means that solutions with y(0) < 0 will approach 0 as t → ∞, while solutions with y(0) > 0 will diverge to infinity as t → ∞. Near y = 2, we have y'(t, y) ≈ -(y - 2)^2, which means that solutions with y(0) < 2 will converge to 2 as t → ∞, while solutions with y(0) > 2 will diverge to infinity as t → ∞.

Therefore, the behavior of y as t → ∞ depends on the initial value of y at t = 0. Specifically, solutions with y(0) < 0 approach 0, solutions with 0 < y(0) < 2 decrease to 0, solutions with y(0) = 2 converge to 2, and solutions with y(0) > 2 diverge to infinity.

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The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.

The sample variance is a measure of how much the individual data points in a sample vary from the mean.

It is calculated by finding the average of the squared differences between each data point and the mean.

To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:

Calculate the mean (average) of the data set:

Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90

Subtract the mean from each data point and square the result:

(93 - 90)^2 = 9

(89 - 90)^2 = 1

(91 - 90)^2 = 1

(87 - 90)^2 = 9

(91 - 90)^2 = 1

(89 - 90)^2 = 1

Calculate the sum of the squared differences:

9 + 1 + 1 + 9 + 1 + 1 = 22

Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):

Variance = 22 / 5 = 4.4

It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.

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The height of the tree and its shadow, and the height of the person and its shadow, at the same time of the day, form two similar right triangles:

Since both triangles are similar, then the corresponding sides are at the same ratio so that:

From this expression, you can determine the height of the tree, just multiply both sides of the equal sign by 5:

The height of the tree is 15 feet.

Answer: 168,750 chocolates

Step-by-step explanation:

If there are 90 chocolates in a box and there are 1,875 boxes, you multiply 1,875 by 90 to get the total number of chocolates needed to complete the order.

1,875 * 90 = 168,750

There are 168,750 chocolates needed to complete the order.

Answer:

Step-by-step explanation:

its 9

\(f(x) = (-x^{3} /3) + (3x^{2} /2) + C_{1}x + C_{2} ,\) where C₁ and C₂ are arbitrary constants.

The generic equation of a single direction is two dimensions, for instance, is y=mx+c, in which m but also c are arbitrarily defined constants that stand for the line's gradient and y intercept, respectively. And c is a freely chosen constant whose value may be predicted by a boundary condition, thus 2x dx=x 2+c.

As long as a constant's value is independent of the other factors in an argument or expression, it can be considered to have any value. A constant that isn't arbitrary often only has one possible value.

f'(x) = ∫(f"(x) dx) = ∫\((-2x + 3 dx) = -x^{2} + 3x + C_{1}\)

where C₁ is an arbitrary constant of integration.

Now, we need to anti differentiate f'(x) to get f(x).

f(x) = ∫(f'(x) dx) = ∫\((-x^{2} + 3x + C₁ dx) = (-x^{3} /3) + (3x^{2} /2) + C_{1}x +C_{1}\)

where C₂ is another arbitrary constant of integration.

Therefore, the solution for f(x) is:

\(f(x) = (-x^{3} /3) + (3x^{2} /2) + C_{1}x + C₂\)

where \(C_{1}\) and \(C_{2}\) are arbitrary constants.

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