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Part 1: Write a rule to describe each transformation​

Answer:

1. x = -1

2. y = -1, y = 2

3. y = -½ + i [tex]\frac{\sqrt{3} }{2}[/tex]; y = -½ - i [tex]\frac{\sqrt{3} }{2}[/tex]

4. x = -3; x = -6

Step-by-step explanation:

I will only produce work for questions 1 through 4, and you could follow the same steps for questions 5 and 6 so that you could learn and get used to solving quadratic equations. I am practically using the same techniques in solving questions 1 through 4 anyway.

1.) x² + 2x + 1 = 0

where a = 1, b = 2, c = 1

Determine the nature and number of solutions based on the discriminant, b² - 4ac:

b² - 4ac = 2² - 4(1)(1) = 4 - 4 = 0  

This means that the equation has one real root.  

Next, determine the factors of the quadratic equation.  

Use the perfect square trinomial factoring technique:

u² + 2uv + v² = (u + v)²

From the equation, x² + 2x + 1 = 0

where a = 1, b = 2, c = 1

Find factors with product a × c and sum b:

Possible factors:

product a × c :  1 × 1 = 1

sum b :  1 + 1 = 2

Therefore, the binomial factors of x² + 2x + 1 = 0 is (x + 1)²

To find the roots, set x = 0:

x + 1 = 0

Subtract 1 from both sides to isolate x:

x + 1 - 1 = 0 - 1

x = -1  (This is the root of the equation).

2)  y² - y - 2 = 0

where a = 1, b = -1, and c = -2

Determine the nature and number of solutions based on the discriminant, b² - 4ac:  

b²  - 4ac = (-1)² - 4(1)(-2) = 9  

Since b² - 4ac > 0, then it means that the equation will have two real roots.

From the equation, y² - y - 2 = 0

where a = 1, b = -1, and c = -2:

Find factors with product a × c and sum b:

 Product a × c :  

1 × -2 = -2

-1 × 2 = -2

Sum b:  

1+ (-2) = -1

-1 + 2 = 1

Therefore, the possible factors are: 1 and -2:

(y + 1) (y - 2)

To find the roots, set y = 0:

y + 1 = 0

Subtract 1 from both sides:

y + 1 - 1 = 0 - 1

y = -1

y - 2 = 0

Add 2 to both sides:

y -2 + 2 = 0 + 2

y = 2

Therefore, the roots of the quadratic equation, y² - y - 2 = 0 are: y = -1 and y = 2.

3.)  y² + y + 1 = 0

where a = 1, b = 1, and c = 1

Determine the nature and number of solutions based on the discriminant, b² - 4ac:  

b² - 4ac = (1)2 - 4(1)(1) = -3

Since b² - 4ac < 0, then it means that the equation will have two complex roots.

Use the Quadratic Formula:

[tex]y = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]

[tex]y = \frac{-1 +/- \sqrt{1^{2} - 4(1)(1)} }{2(1)}[/tex]

[tex]y = \frac{-1 +/- \sqrt{1 - 4} }{2}[/tex]

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

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

Therefore, the roots of the quadratic equation, y² + y + 1 = 0 are:

y = -½ + i [tex]\frac{\sqrt{3} }{2}[/tex]; y = -½ - i [tex]\frac{\sqrt{3} }{2}[/tex]

4) x² + 9x + 18 = 0

where a = 1, b = 9, and c = 18.

Determine the nature and number of solutions based on the discriminant, b² - 4ac:  

b² - 4ac = (9)2 - 4(1)(18) = 9

Since b² - 4ac > 0, then it means that the equation will have two real roots.

Use the Quadratic Formula:

[tex]x = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]

[tex]x = \frac{-9 +/- \sqrt{9^{2} - 4(1)(18)} }{2(1)}[/tex]

[tex]x = \frac{-9 +/- \sqrt{9} }{2}[/tex]

[tex]x = \frac{-9 + 3}{2}; x = \frac{-9 - 3}{2}[/tex]

[tex]x = \frac{-6}{2}; x = \frac{-12}{2}[/tex]

x = -3; x = -6

Therefore, the roots of the quadratic equation, x² + 9x + 18 = 0

are: x = -3 and x = -6.  

Answer:

2 miles

Step-by-step explanation:

In one hour, close and her dog can walk a total of 2 miles

Answer:

4

Step-by-step explanation:

2/3 x 6

2x2=4

Answer:

A 5-pound roast would take about 187.5 minutes to cook.

Divide 150 minutes by 4 pounds and you get 37.5 minutes. This would be how long it takes to cook each pound. So, you multiply 5 pounds by 37.5 and you get 187.5 minutes for a 5-pound roast to cook.

Answer:

(2/x)3 or 3(2/x

Step-by-step explanation:

The quotient of 2 and x is expressed as 2/x Multiplied by 3 can be expressed as (2/x)3 or 3(2/x)  

Answer:

Step-by-step explanation:

47 divided by 8

= 5.875

hope this helps

Answer:

Not necessarily. There are many ways to write a basic equation with a negative answer. For example, -3-4 = -7.

Step-by-step explanation:

Answer:

0,40789

Step-by-step explanation:

To pick 1 red marble (from 5 red) from all 20 marbles is 5/20 = 0.25

To pick 1 green marble (from 3 green) from 19 because we already took red marble is 3/19 = 0.15789

The probability of randomly choosing a green marble after you have chosen red is 3/68.

Given

A jar has 20 marbles: 3 green, 12 blue, 5 red.

In probability theory, an event is a set of outcomes of an experiment or a subset of the sample space.

The total number of marbles = 20

The number of green marbles= 3

The number of blue marbles = 12

The number of red marbles = 5

The probability of choosing a red marble = Number of red marbles / Total number of marbles

= 5/20

The probability of choosing a green marble is =  Number of green marbles / New total number of marbles

= 3/19

Therefore,

The probability of randomly choosing a green marble after you have chosen red is;

[tex]\rm=\dfrac{5}{20}\times \dfrac{3}{19}\\\\=\dfrac{1}{4}}\times \dfrac{3}{19}\\\\ = \dfrac{3}{68}[/tex]

Hence, the probability of randomly choosing a green marble after you have chosen red is 3/68.

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Answer:

seventeen plus twelve minus thirty

Step-by-step explanation:

17 + 12 - 30 = -1

Answer:

I hope this could be of good assistant

Step-by-step explanation:

L:B = 10:3

make L subject of formula

L = 10B/3

perimeter = 312

2( L + B ) = 312

L + B = 312/2

L + B = 156

10B/3 + B = 156

multiply all through by 3

10B + 3B = 156 X 3

10B + 3B = 468

13B = 468

B = 468/13 = 36

B = 36m

L = 10B/3

L = 10 X 36/3

L = 10 X 12 = 120m

L = 120m

Hence if your were asked to find the area

L X B

120 X 36 = 4320m²

C)50mph

speed= distance÷time

so ....

we find how much 25 miles took therefore we do

25÷0.5

which is

=50

Hope this helped you, have a good day bro cya)

Answer:

fast

Step-by-step explanation:

historical definition

Italian physicist Galileo Galilei is usually credited with being the first to measure speed by considering the distance covered and the time it takes. Galileo defined speed as the distance covered per unit of time.[3] In equation form, that is

{\displaystyle v={\frac {d}{t}},}v={\frac  {d}{t}},

where {\displaystyle v}v is speed, {\displaystyle d}d is distance, and {\displaystyle t}t is time. A cyclist who covers 30 metres in a time of 2 seconds, for example, has a speed of 15 metres per second. Objects in motion often have variations in speed (a car might travel along a street at 50 km/h, slow to 0 km/h, and then reach 30 km/h).

Instantaneous speed

Speed at some instant, or assumed constant during a very short period of time, is called instantaneous speed. By looking at a speedometer, one can read the instantaneous speed of a car at any instant.[3] A car travelling at 50 km/h generally goes for less than one hour at a constant speed, but if it did go at that speed for a full hour, it would travel 50 km. If the vehicle continued at that speed for half an hour, it would cover half that distance (25 km). If it continued for only one minute, it would cover about 833 m.

In mathematical terms, the instantaneous speed {\displaystyle v}v is defined as the magnitude of the instantaneous velocity {\displaystyle {\boldsymbol {v}}}{\boldsymbol {v}}, that is, the derivative of the position {\displaystyle {\boldsymbol {r}}}{\boldsymbol {r}} with respect to time:[2][4]

{\displaystyle v=\left|{\boldsymbol {v}}\right|=\left|{\dot {\boldsymbol {r}}}\right|=\left|{\frac {d{\boldsymbol {r}}}{dt}}\right|\,.}v=\left|{\boldsymbol  v}\right|=\left|{\dot  {{\boldsymbol  r}}}\right|=\left|{\frac  {d{\boldsymbol  r}}{dt}}\right|\,.

If {\displaystyle s}s is the length of the path (also known as the distance) travelled until time {\displaystyle t}t, the speed equals the time derivative of {\displaystyle s}s:[2]

{\displaystyle v={\frac {ds}{dt}}.}v={\frac  {ds}{dt}}.

In the special case where the velocity is constant (that is, constant speed in a straight line), this can be simplified to {\displaystyle v=s/t}v=s/t. The average speed over a finite time interval is the total distance travelled divided by the time duration.

Average speed

Different from instantaneous speed, average speed is defined as the total distance covered divided by the time interval. For example, if a distance of 80 kilometres is driven in 1 hour, the average speed is 80 kilometres per hour. Likewise, if 320 kilometres are travelled in 4 hours, the average speed is also 80 kilometres per hour. When a distance in kilometres (km) is divided by a time in hours (h), the result is in kilometres per hour (km/h).

Average speed does not describe the speed variations that may have taken place during shorter time intervals (as it is the entire distance covered divided by the total time of travel), and so average speed is often quite different from a value of instantaneous speed.[3] If the average speed and the time of travel are known, the distance travelled can be calculated by rearranging the definition to

{\displaystyle d={\boldsymbol {\bar {v}}}t\,.}d={\boldsymbol  {{\bar  {v}}}}t\,.

Using this equation for an average speed of 80 kilometres per hour on a 4-hour trip, the distance covered is found to be 320 kilometres.

Expressed in graphical language, the slope of a tangent line at any point of a distance-time graph is the instantaneous speed at this point, while the slope of a chord line of the same graph is the average speed during the time interval covered by the chord. Average speed of an object is Vav = s÷t

Difference between speed and velocity

Speed denotes only how fast an object is moving, whereas velocity describes both how fast and in which direction the object is moving.[5] If a car is said to travel at 60 km/h, its speed has been specified. However, if the car is said to move at 60 km/h to the north, its velocity has now been specified.

The big difference can be discerned when considering movement around a circle. When something moves in a circular path and returns to its starting point, its average velocity is zero, but its average speed is found by dividing the circumference of the circle by the time taken to move around the circle. This is because the average velocity is calculated by considering only the displacement between the starting and end points, whereas the average speed considers only the total distance travelled.

Answer:

She can plant 24 flowers in each row.

Step-by-step explanation:

Greatest common factor of 48 and 72 is 24

Answer:

x=4

Step-by-step explanation:

If Jim paid $48 to buy a package of 6 flea treatments for his dog. Then cost of one treatment is $6.

A division is a process of splitting a specific amount into equal parts.

Given,

Jim paid $48 to buy a package of 6 flea treatments for his dog

We need to find what is the cost a per treatment.

We have to divide split forty eight by six to find the cost of each treatment.

Forty eight divided by six

$48/6

When we divide by six we will get six.

$6

Hence if Jim paid $48 to buy a package of 6 flea treatments for his dog. Then cost of one treatment is $6.

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$SPJ2

Answer:

Deon

Step-by-step explanation:

Deon-12 ppd

Emily-9 ppd

Deon reads more pages per day

Answer:

Deon read  3 more  pages per day than Emily.

Answer:

1404

Step-by-step explanation:

Answer:

As coins, they are already in their simplest ratio, since 25 and 38 don't have any common factor to divide by. (1 doesn't really count...)

As money, you need to multiply the 25 nickels x 5 cents per nickel, which gives you 125 cents,

and 38 dimes x 10 cents per dime, which gives you 380 cents.

So your new ratio is 125:380, which you can simplify by dividing each by 5, which gives you

25:76

SO, as money the ratio in simplest terms is 25:76. As numbers of coins, it's 25:38

If you think about it, it makes sense because:

10 cents is twice as much as 5 cents, and

76 cents is twice as much as 38 cents.

Hope this helps!

Matt in New York

Ten cents cost twice as much as five cents, and 38 cents are equivalent to twice as much as 76 cents.

Explain about the Ratio?

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value

Since there is no

to divide 25 by and 38 by, they are already in their most basic ratio as coins. (1 is hardly significant...)

To convert the 25 nickels to money, multiply them by the nickel's value, which comes to 125 cents.

and 38 dimes multiplied by 10 cents each, giving you 380 cents.

By dividing each by 5, you can simplify your new ratio of 125:380 and get

25:76

Therefore, the ratio is 25:76 expressed simply as money. It is 25:38 in monetary terms.

It makes sense if you think about it since

Ten cents are twice as expensive as five cents, and

38 cents is double what 76 cents

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Answer:

1.6

Step-by-step explanation:

sorry if i'm wrong mate

is it a big number or short number

The required number of cars that can be washed by Damien in 40 hours is 25.

Given that,
Damien washes cars on his summer vacation to earn money. It took him 16 hours to wash 10 cars. Use scaling to complete the table to determine the number of cars Damien could wash in 40 hours, is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Let the number of cars that were washed in 40 hours be x,
Now, according to the question.
16 / 10 = 40 / x
x = 400 / 16
x = 25

Thus, the required number of cars that can be washed by Damien in 40 hours is 25.

Learn more about arithmetic here:

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Answer:

x=14/9

Step-by-step explanation:

Answer:

x = 0

Step-by-step explanation:

9x - 7 = -7

9x - 7 + 7 = -7 + 7

9x = 0

9/9x = 0/9

x = 0

Answer:

32

Step-by-step explanation:

Answer:

Step-by-step explanation:

w = width

3w = three times the width

3w-7=7 feet less than three times the width

l = length = 3w-7

A=length × width (lw)

66 = (3w-7) × (w)

66 = 3w^2 - 7w

3w^2 - 7w -66 =0

factor

3 = 3 × 1 and 66 = 6 × 11,

6 × 3 = 18,  11 × 1 = 11,  18 - 11 = 7

(3w   )(w   )=0 so far

(3w   )(w  6)=0 so far

(3w   11)(w   6)=0 so far

(3w+11)(w-6)=0

w-6=0

w=6

3w=3*6=18

3w-7=3*6-7=18-7=11

w=6 feet

l=11 feet

Answer:

The value of y is 1

Step-by-step explanation:

4 - (y - 3) = 3(y + 1) - 4(1 - y)

4 - y + 3 = 3y + 3 - 4 + 4y

7 - y = 7y - 1

7 + 1 = 7y + y

8y = 8

y = 1

Thus, The value of y is 1

-TheUnknownScientist 72

Answer:

Marcet has made her special chocolate cake many times.

Please mark as Brainliest, thank you!

Answer:

answer is A x = -4 and x = 3

Step-by-step explanation:

-4 , 3

switch the signs

Answer:

The answer is "A."

Step-by-step explanation:

x+4=0. x-3=0

x=0-4. x=0+3

x= -4. x= 3

x = -4 and x = 3

Answer:

y+2 = (-1/2)(x-3)

Step-by-step explanation:

6+8=14÷(-2)=-7-4=-11

Answer:

-11

Step-by-step explanation:

-4 + (6 + 8) / (-2)

-4 + (14) / (-2)

-4 + -7

-4 - 7

-11

Hopefully this helped!

Brainliest please?

Answer:

22 3/4 inches.

Step-by-step explanation:

First what I like to do is find least common denominator.

Since 2 of the ribbons are measured in /4's, and the other ribbon is measured by half ( /2). 4 will be your new denominator making the 18 1/2 in. long ribbon 18 2/4 inches.

Now, the Blue ribbon is 3/4 greater than the Red ribbon, making it the 18 2/4 inch ribbon.

The Yellow ribbon is 4 3/4 inches longer than the Blue ribbon which means add 4 3/4's to 18 2/4, and you get = 22 3/4 in. for the yellow ribbon.

Hopes this Help!