Y²+ 6y+5 Factorize And Explain

Answer:

midpoints of segments AB and BD are (-3, 0) and \((\frac{7}{2},0)\).

Step-by-step explanation:

By using number line given in the figure attached,

Coordinates of the extreme ends of the segment are A(-7, 0) and B(-1, 0).

Midpoint of segment AB = \((\frac{-7-(-1)}{2}, 0)\)

                                         = (-3, 0)

Coordinates of extreme ends of BD are B(-1, 0) and D(6, 0).

Midpoint of segment BD = \((\frac{6+1}{2}, 0)\)

                                         = \((\frac{7}{2},0)\)

Therefore, midpoints of segments AB and BD are (-3, 0) and \((\frac{7}{2},0)\).

Answer:

Zero

Step-by-step explanation:

If you are not considering a truck being a car, then you wash 0 cars

Answer:

A.

1.

125

2.

47.5

B.

30

Exp.:

A.

1. (60x100)/48

2. 57/ 120(fraction)  x 100% = 47.5%

B.  (24×100)÷80

Answer:

D

Step-by-step explanation:

3x5=15

3x10=30

5x6=30

The exponential function between (-1, 2/5) and (3, 250) is as follows:

\(f(x) = 2 * 5^x\)

By combining the fourth roots from both sides, we arrive at:

b = 5

When we use the expression we discovered for a and this value of b, we get:

a = (2/5) * 5 = 2

As a result, the exponential function between (-1, 2/5) and (3, 250) is as follows:

\(f(x) = 2 * 5^x\)

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

from the question:

This is the shape of the exponential function:

f(x) = a *\(b^x\)

where a represents the starting point and b represents the exponential function's base.

We must solve the system of equations to determine the values of a and b that meet the requirements:

a * \(b^(-1)\) = 2/5 (equation 1) 

a *\(b^3\)= 250 (equation 2) 

We can solve for an in equation 1 by multiplying both sides by b:

a = (2/5) * b

Substituting this expression into equation 2, we get:

(2/5) * b *\(b^3\) = 250

Simplifying, we get:

\(b^4 = 3125\)

By combining the fourth roots from both sides, we arrive at:

b = 5

When we use the expression we discovered for a and this value of b, we get:

a = (2/5) * 5 = 2

As a result, the exponential function between (-1, 2/5) and (3, 250) is as follows:

\(f(x) = 2 * 5^x\)

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It takes 4 seconds for the ball to hit the ground.

The formula for the distance fallen by an object keeping in mind the motion of object dropped from rest is:

\(s = 1/2gt^2\)

where s is the distance fallen, g is the acceleration due to gravity \((32 ft/s^2)\), and t is the time taken to fall.

In this problem, the initial height of the ball is 256 feet, so the distance fallen is:

s = 256 - 0 = 256 feet

Substituting into the formula, we get:

\(256 = 1/2 * 32 * t^2\)

Simplifying, we get:

\(256 = 16t^2\)

Dividing both sides by 16, we get:

\(t^2 = 16\)

Taking the square root of both sides, we get:

t = 4 seconds or -4 seconds

We can ignore the negative solution, so the answer is:

t = 4 seconds

Therefore, it takes 4 seconds for the ball to hit the ground.

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The probability that a student chosen at random has a cat or a dog is; P(cat or dog) = 22/25.

What is probability?

Probability is that the branch of arithmetic regarding numerical descriptions of however probably an incident is to occur, or however probably it's that a proposition is true. The likelihood of an incident could be a range between 0 and 1.

Main body:

According to the question, the total number of students is; 25.

15 of them have a cat

16 of them have a dog

while, 3 of them have neither

where, x = number if students who own a cat and a dog.

Consequently, the total number of students who own a cat, a dog, both or neither is as follows;

15-x + x + 16-x + 3 = 25.

-x = 25 - 34

In essence, x = 9

the number of students who own a cat and a dog is 9.

Therefore, probability that a student chosen at random has a cat and a dog is therefore;

P(cat and dog) = 9/25.

Therefore probability that a student chosen at random has a cat or a dog is 22/25.

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Step-by-step explanatiosorry don't understand question be more specific

Answer:

-528/25

Step-by-step explanation:

According to the Centers for Disease Control and Prevention (CDC), about 73.6 percent of adults in the United States are overweight or obese. So, the correct answer is D).

This means that a majority of adults in the U.S. have a body mass index (BMI) above the healthy range, which is defined as a BMI of 18.5-24.9, which puts them at increased risk for a range of health issues, including heart disease, diabetes, and some types of cancer.

The prevalence of overweight and obesity has been increasing in the United States in recent decades, and it is a significant public health concern. Obesity is a complex issue with many causes, including genetics, environment, and lifestyle factors such as diet and physical activity levels. So, the correct answer is D).

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--The given question is incomplete, the complete question is given

"  According to the Centers for Disease Control and Prevention (CDC), approximately what percentage of u.s. adults is overweight? select one: a. 24 percent b. 44 percent c. 64 percent d. 73.6 percent "--

Answer:

igle is 180

VX

Step-by-step explanation:

AB

MA

B

F

с

AAB=BC,AM=MC

BM IAC , EF I BC1.38371248486|ᡕᠵ᠊ᡃ່࡚ࠢ࠘ ⸝່ࠡࠣ᠊߯᠆ࠣ࠘

The estimated volume of the solid above the square R, using the given method, is X cubic units.

To estimate the volume of the solid above the square R, we can divide the square into nine equal sub-squares. Each sub-square has dimensions of 1/3 units in length and width. By choosing the sample points to lie in the midpoints of each sub-square, we can approximate the height of the solid at those points.

For each sub-square, we calculate the height of the solid at its midpoint by substituting the coordinates into the equation of the elliptic paraboloid, z = 25 - x² + xy - y². This gives us the z-coordinate for each midpoint.

Next, we calculate the volume of each sub-solid by multiplying the length, width, and height of each sub-square. Summing up the volumes of all nine sub-solids gives us an estimate of the total volume of the solid above the square R.

It is important to note that this method provides an approximation of the volume, as we are dividing the square into a finite number of sub-squares and using only the sample points at their midpoints. The accuracy of the estimation depends on the size and number of sub-squares chosen.

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Therefore, Drug C has a stronger impact on cell survival compared to Drug A, making it the drug with the greatest effect.

To draw a representation of the survival curve and identify the drug that has the greatest effect on cell survival, we can use a graph where the x-axis represents the drug concentration in μg/ml, and the y-axis represents the percentage of cell survival.

Since Drug B has no IC90 value, it means that it does not reach a concentration that causes a 90% reduction in cell survival. Therefore, we can assume that Drug B has no significant effect on cell survival and can omit it from the survival curve.

For Drug A and Drug C, we have IC90 values of 5 and 3 μg/ml, respectively. This means that when the drug concentration reaches these values, there is a 90% reduction in cell survival.

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Answer:

m= -29

Step-by-step explanation:

This is a bit of a complex equation, but let's work through it.

2/3 (m-1/2) +3= m/3-7

First, we need to distribute the 2/3.

(2/3)(m)+(2/3)(−1/2)+3=m/3+−7

Now we simplify that.

2/3m+−1/3+3=1/3m+−7

We can now combine like terms.

2/3m+8/3=1/3m+−7

The goal is to isolate the variable, so we should subtract 1/3m from both sides.

1/3m+8/3=−7

Lets keep going! We can subtract 8/3 from both sides.

1/3m=-29/3

Well now we know what 1/3 of m is, but we want to know what m is. So we can multiply both sides by three to finally find out what m is!

m=-29

We did it! m=-29

Answer:

(3/4)pi

Step-by-step explanation:

Find the areas of the two circles and then subtract the smaller from the larger:

A of circle = (pi)r^2

Case 1:  r = 1 unit:  A = (pi)(1) = pi

Case 2:  r = 1/2 unit:  A = (pi)(1/2)^2 = pi/4

The area lying outside of the smaller circle is therefore (pi) - (pi)(1/4) = (3/4)pi

Answer:

The solution is:

\(y=7,\:x=3\)

Step-by-step explanation:

I think substitution method would be the best method for solving the given system of equations.

The reason is that all we need is to plug in the the value of y i.e. y=x+4 in the equation 3x – 4y = -19, then solve for x, and in the end substitute the value x in the equation y=x+4 to get the y-value.

The other method, elimination method, can also be used, but elimination method in current system of the equations would involve a certain degree of arrangements of the variables and then different multiplying of the equation to eliminate the variables.

Thus, I think substitution method would be the best method for solving the given system of equations.

Let us solve using substitution method

\(\begin{bmatrix}y=x+4\\ 3x-4y=-19\end{bmatrix}\)

\(\mathrm{Subsititute\:}y=x+4\)

\(\begin{bmatrix}3x-4\left(x+4\right)=-19\end{bmatrix}\)

\(\begin{bmatrix}-x-16=-19\end{bmatrix}\)

\(x=-16+19\)

\(x=3\)

Now, just substitute x=3 in y=x+4

\(y=x+4\)

\(y=3+4\)

\(y=7\)

Thus, the solution is:

\(y=7,\:x=3\)

She saved 4500 in a mutual fund account and 5500 in a CD account.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Assuming she has invested x amount of money in 7% mutual fund account and (10000 - x) amount of money in 4% CD account.

Given,  she earned 535 more interest from her 7% mutual fund account than she did from her 4% CD,

∴ (x×7×1)/100 - [(x-10000)×4×1]/100 = 535.

(7x/100) - (4x - 4000)/100 = 535.

7x/100 - 4x/100 + 40000/100 = 535.

3x/100 + 400 = 535.

3x/100 = 135.

3x = 13500.

x = 4500.

She invested 4500 in a mutual fund account and 5500 in a CD account.

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Answer:

82cm

Step-by-step explanation:

26+26+15+15=82

The equation of the xy plane is

(A) x = 0, y = 0

(C) x = y

A two-dimensional plane called the X-Y plane is used to indicate where a two-dimensional object is located.

The terms ordinate and abscissa are used to describe the y and x coordinates, respectively.

When a point's coordinates are written as x, y then the equation is in the xy plane

for and equation to be in the x - y plane the points will be contained within the plane and hence defined in the plane.

the letter z is not part of the xy plane and this makes it unlikely to be in xy plane

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a) The new temperature after doubling the pressure while keeping the volume constant is 80°C. b) The new volume of the gas after cooling it down by 110°C with no change in pressure is 0.0686 m³.


a) According to the gas law, when the volume remains constant (V₁ = V₂), the ratio of initial pressure (P₁) to final pressure (P₂) is equal to the ratio of initial temperature (T₁) to final temperature (T₂) for an ideal gas. Mathematically, P₁/T₁ = P₂/T₂. Plugging in the given values (P₁ = 450 kPa, T₁ = 140°C, P₂ = 2P₁), we can solve for T₂ to find that the new temperature is 80°C.
b) When the pressure remains constant, the ratio of initial volume (V₁) to final volume (V₂) is equal to the ratio of initial temperature (T₁) to final temperature (T₂) for an ideal gas. Mathematically, V₁/T₁ = V₂/T₂. Plugging in the given values (V₁ = 0.2 m³, T₁ = 160°C, T₂ = T₁ - 110°C), we can solve for V₂ to find that the new volume is approximately 0.0686 m³.

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Literally nothing occurs. On the off chance that the two terminals are at an equivalent voltage, no ongoing streams, any more than if you contacted two impartial bits of metal together.

Cases 1 and 3 are basically something very similar. There's a voltage difference, so current normally streams. In any case, you don't have a circuit, so when electrons stream from the lower positive voltage (which is zero assuming it's released) to the higher positive terminal, the electrons develop and make a static charge that balances the voltages. This occurs in a small part of a second, so the current is negligible, and voltage promptly stops.

The standard metric unit on electric potential difference is the volt, truncated V and named to pay tribute to Alessandro Volta. One Volt is identical to one Joule per Coulomb. In the event that the electric potential difference between two areas is 1 volt, one Coulomb of charge will acquire 1 joule of potential energy when moved between those two areas. In the event that the electric potential difference between two areas is 3 volts, one coulomb of charge will acquire 3 joules of potential energy when moved between those two areas.

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The probability of reaching into the box and randomly drawing a chip number that is greater than 3150 is 0.3675

In this question we have been given there are 498 identical plastic chips numbered 1 through 498 in a box.

We need to find the probability of reaching into the box and randomly drawing a chip number that is greater than 315

Total number of chips = 498

so, n(S) = 498

Let event A: drawing a chip number that is greater than 315

The number of chips greater than 315:

498 - 315 = 183

So, n(A) = 183

The probability of reaching into the box and randomly drawing a chip number that is greater than 315 using the formula of probability,

p(A) = n(A)/n(S)

p(A) = 183/498

p(A) = 0.3675

Therefore, the required probability is 0.3675

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Answer:

B.

(づ￣ ³￣)づHave A nice day Cute Sir

Answer:

Step-by-step explanation:

160

The solution to the Equations is    x = 3, x = 7, x = 11,  x = -9,  x = 1.3,               x = -4, x = -4,x = -2,x = 11, x = 3.33,x = 7, x = 5,x = -4.

1. To solve 3(x+2)=15, we first distribute the 3 and get 3x + 6 = 15. Then, we subtract 6 from both sides and get 3x = 9. Finally, we divide both sides by 3 and get x = 3.

2. To solve 2(x+5)=24, we first distribute the 2 and get 2x + 10 = 24. Then, we subtract 10 from both sides and get 2x = 14. Finally, we divide both sides by 2 and get x = 7.

3. To solve 6(x-9)=12, we first distribute the 6 and get 6x - 54 = 12. Then, we add 54 to both sides and get 6x = 66. Finally, we divide both sides by 6 and get x = 11.

4. To solve 2(3x+5)= -44, we first distribute the 2 and get 6x + 10 = -44. Then, we subtract 10 from both sides and get 6x = -54. Finally, we divide both sides by 6 and get x = -9.

5. To solve 5(4x-3)=11, we first distribute the 5 and get 20x - 15 = 11. Then, we add 15 to both sides and get 20x = 26. Finally, we divide both sides by 20 and get x = 1.3.

6. To solve -3(2x+1)=21, we first distribute the -3 and get -6x - 3 = 21. Then, we add 3 to both sides and get -6x = 24. Finally, we divide both sides by -6 and get x = -4.

7. To solve -9(x-4)=54, we first distribute the -9 and get -9x + 36 = 54. Then, we subtract 36 from both sides and get -9x = 18. Finally, we divide both sides by -9 and get x = -2.

8. To solve 7(x-4)-3=46, we first distribute the 7 and get 7x - 28 - 3 = 46. Then, we combine like terms and get 7x - 31 = 46. Then, we add 31 to both sides and get 7x = 77. Finally, we divide both sides by 7 and get x = 11.

9. To solve 2(3x-1)+3=21, we first distribute the 2 and get 6x - 2 + 3 = 21. Then, we combine like terms and get 6x + 1 = 21. Then, we subtract 1 from both sides and get 6x = 20. Finally, we divide both sides by 6 and get x = 3.33.

10. To solve 2(x+1)+3x=37, we first distribute the 2 and get 2x + 2 + 3x = 37. Then, we combine like terms and get 5x + 2 = 37. Then, we subtract 2 from both sides and get 5x = 35. Finally, we divide both sides by 5 and get x = 7.

11. To solve 12+4(2x+4)=68, we first distribute the 4 and get 12 + 8x + 16 = 68. Then, we combine like terms  x = 5.

12.To solve 3x - 2(6x - 3) = 42, we first distribute the -2 and get:3x - 12x + 6 = 42,9x + 6 = 42Then, we subtract 6 from both sides:-9x = 36Finally, we divide both sides by -9 and get:x = -4Therefore, the solution to the equation is x = -4.

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The solution to the algebraic expressions are:

1. x = 3

2. x = 7

3. x = 13

4. x = -9

5. x = 1.3

6. x = -4

7. x = -2

8. x = 11

9. x = 10/3

10. x = 5

11. x = 5

12. x = -4

1. 3(x + 2) = 15,

Using distributive property, we get 3x + 6 = 15.

3x = 9

x = 9/3

x = 3

2. 2(x + 5) = 24

Using distributive property, we get:

2x + 10 = 24

2x = 14

x = 7

3. 6(x - 9) = 12

Using distributive property, we get:

6x - 54 = 24

6x = 78

x = 78/6

x = 13

4. 2(3x + 5) = -44

Using distributive property, we get:

6x + 10 = -44

6x = -54

x = -9

5. 5(4x - 3) = 11

Using distributive property, we get:

20x - 15 = 11

20x = 26

x = 1.3

6. -3(2x + 1) = 21

-6x - 3 = 21

-6x = 24

x = -4

7. -9(x - 4) = 54

Using distributive property, we get:

-9x + 36 = 54

-9x = 54 - 36

-9x = 18

x = -2

8. 7(x - 4) - 3 = 46

Using distributive property, we get:

7x - 28 - 3 = 46

7x = 77

x = 11

9) 2(3x - 1) + 3 = 21

Using distributive property, we get:

6x - 2 + 3 = 21

6x = 20

x = 20/6

x = 10/3

10) 2(x + 1) + 3x = 37

2x + 2 + 3x = 37

5x = 35

x = 5

11) 12 + 4(2x + 4) = 68

12 + 8x + 16 = 68

8x = 40

x = 5

12) 3x - 2(6x - 3) = 42

3x - 12x + 6 = 42

6 - 9x = 42

9x = -36

x = -36/9

x = -4

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The optimization problem for individual A is to maximize their objective function: max {7A(GA1) + 12u(A,G2)}. The Lagrangean for individual A can be written as: L(A) = 7A(GA1) + 12u(A,G2) + λ1(IA1 - DA1) + λ2(IA2 - DA2) + μ1(IA1 - pIA2) + μ2(IA2 - IA1 - IA2).

To solve for individual A's optimality conditions, we take the partial derivatives of the Lagrangean with respect to the decision variables: ∂L(A)/∂GA1 = 0, ∂L(A)/∂GA2 = 0, ∂L(A)/∂IA1 = 0, and ∂L(A)/∂IA2 = 0.

An equilibrium is defined as a set of allocations (GA1, GA2) and prices (p) such that all individuals optimize their objective functions and markets clear, i.e., the total net expenditure on purchasing contracts is zero. The equilibrium conditions that characterize the equilibrium allocations in the market for contracts are: ∑AIA1 + ∑BIB1 = 0, ∑AIA2 + ∑BIB2 = 0, and IA1 + IB1 = IA2 + IB2.

Given the utility function u(e) = ln(c), we can solve for the equilibrium price and allocations by setting the optimality conditions equal to zero and solving the resulting system of equations.

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The recursive formula for the given problem is W(n) = W(n-1) + 2 * W(n-1), with the base case W(0) = 1. This formula calculates the number of n-letter "words" that can be created from an unlimited supply of 'a's, 'b's, and 'c's,

To derive the recursive formula, we consider two cases for the first letter of the word: either it is an 'a' or it is not. If the first letter is 'a', we need to ensure that the remaining (n-1) letters form a word with an even number of 'a's. Therefore, the number of words in this case is equal to W(n-1), as we are recursively solving for the remaining letters.

If the first letter is not 'a', we have the freedom to ch

oose from 'b' or 'c'. In this case, we have two options for each of the remaining (n-1) letters, resulting in 2 * W(n-1) possibilities. By summing these two cases, we obtain the recursive formula W(n) = W(n-1) + 2 * W(n-1), which calculates the total number of n-letter words satisfying the given criteria.

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Answer:

0.16 per ounce

Step-by-step explanation:

0.16 + 0.42 = 0.58, 0.58 + 0.16 = 0.74, 0.74 + 0.16 = 0.90

Answer:

0.17

Step-by-step explanation:

Answer:

siis  corretoed

Step-by-step explanation:

The function values are 4, 6, 8, 10, 12, and 14. The appropriate domain for this function is {1, 2, 3, 4, 5, 6} since these are the only values that can be rolled on a six sided die.

The function f(x) = 2x + 2 assigns a certain number of points to a player based on the value rolled on a six sided die.

The domain of a function is the set of all possible values of the input variable that the function can accept. In this case, the input variable is the value rolled on the die, which can be any integer between 1 and 6, inclusive. Therefore, the domain of the function f(x) is {1, 2, 3, 4, 5, 6}.

To find the function values for a given input, substitute the input into the function and solve for the output.

Thus, the function values for the domain {1, 2, 3, 4, 5, 6} are:

f(1) = 2(1) + 2 = 2 + 2 = 4

f(2) = 2(2) + 2 = 4 + 2 = 6

f(3) = 2(3) + 2 = 6 + 2 = 8

f(4) = 2(4) + 2 = 8 + 2 = 10

f(5) = 2(5) + 2 = 10 + 2 = 12

f(6) = 2(6) + 2 = 12 + 2 = 14

Therefore, the function f(x) = 2x + 2 assigns the following number of points to a player based on the value rolled on a six sided die:

Value rolled on die Points awarded

1                                          4

2                                        6

3                                        8

4                                       10

5                                      12

6                                      14

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The measure of angle ZCBD is 90°. Therefore, the correct option is J. 90.

To find the measure of angle ZCBD, we need to examine the given information.

From the figure, we know that angle CDE is 155°.

Since the opposite angles of a rectangle are congruent, angle BCD is also 155°.

In a rectangle, the sum of the interior angles at a vertex is always 90°.

Therefore, angle CBD is 90°.

Hence, the measure of angle ZCBD is 90°.

Therefore, the correct option is J. 90.

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