Your goal in this section is to take a closer look at some aspects of the topic finding solutions of
quadratic equations. You are going to think deeper and test further your understanding about solving
quadratic equations using any of the four methods discussed.
1. Sheryl says that the solutions of the quadratic equations w² = 49 and
w² +49 = 0 are the same. Do you agree with Sheryl? Justify your answer.
2. Patricia says that it's more appropriate to use the method of factoring
than extracting square roots in solving the quadratic equation
4x² - 9 = 0. Do you agree with Patricia? Explain your answer.
3. If you are to choose between completing the square and factoring in
finding the solutions of each of the following equations, which would you
choose? Explain and solve the equation using your preferred method.
b. x² + 7x + 12 = 0
a. 4x² - 20x = 11
4. The values of a, b, and e of a quadratic equation written in standard form
are -2, 8, and 3, respectively. Another quadratic equation has 2, -8, and
-3 as the values of a, b, and c, respectively. Do you agree that the two
equations have the same solutions? Justify your answer.
"pa answer po please"..​

Answer:

Exact Form --  -7/8   Decimal Form --  -0.875

Step-by-step explanation:

I Didn't Now If U Wanted It Explained So...

Answer: -7/8

Step-by-step explanation:

convert from mixed number to fraction:

-5/2 ÷ 20/7

use the fraction rule

[tex]\frac{a}{b}[/tex]÷[tex]\frac{c}{d} = \frac{a}{b}[/tex]×[tex]\frac{d}{c}[/tex]

-5/2 x 7/20

cross cancel

- 1/2 x 7/4

from there multiply numerators together and denominators together

(-1*7) / (2*4)

-7/8

The abbreviated formula is -4xy (5x(x-y) - y(4x + y)).

The answer to the question is that common words outside of the brackets can be used to simplify the supplied equation.

Therefore,

Required expression is -4xy(5x2 - 9xy -y2), which is equivalent to -4xy(5x2 - 5xy - 4xy -y2).

The final formula will be: -4xy(5x(x-y) - y(4x + y)).

Therefore, the abbreviated formula is: -4xy(5x(x-y) - y(4x + y)).

In mathematics, simplification is a technique that makes a complex equation simpler in a less complex way. This approach makes expression calculation possible.

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Answer:

Uhh the answer should be x^3 + y^3 + z^3 for k

Step-by-step explanation:

That's what it says in question, which is the answer.

Pls brainlieset :0?

ieiejeieieiweisns xx xnsiwiwksniz

The equation x + 7 = 2 will have the value of x as 5.

We are given the equation:

x + 2 = 7

We need to solve the equation to find the value of x.

We will first subtract 2 from both the sides:

x + 2 - 2 = 7 - 2

So, subtracting 2 from both the sides, we get that:

x = 5

the value of x for the equation will be 5.

Therefore, the equation x + 7 = 2 will have the value of x as 5.

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Answer: 3x=13

Step-by-step explanation:

The person is blind. They did what they were supposed to except the fact that they didn't multiply the 8 by the -1.

Answer: The error is in step 3

Explanation:

In step 2, they multiplied both sides by 8 to clear out the fractions. In step 3, they forgot to distribute the 8 to each term inside the parenthesis.

This is what the steps should look like

[tex]\frac{3\text{x}}{8}-1=\frac{5}{8}\\\\\\8\left(\frac{3\text{x}}{8}-1\right)=8\left(\frac{5}{8}\right)\\\\\\3\text{x}-8 = 5\\\\\\3\text{x} = 13\\\\\\\text{x} = \frac{13}{3}\\\\\\[/tex]

In step 4, we added 8 to both sides. Afterward, divide both sides by 3 to fully isolate x.

The improper fraction 13/3 is the same as the mixed number 4 & 1/3.

The measure of side HI is 10.74 for the triangle EFG which is similar to HIJ.

Similar triangles are those triangles which have corresponding sides in proportion to each other and the corresponding angles of two triangles are equal to each other. Similar triangles look the same but they differ in terms of the sizes of the two triangles.

In short, If two triangles are similar that means,

All corresponding angle pairs of triangles will be equal.

All corresponding sides of triangles will be proportional.

Now, it is given in the question that ΔEFG is similar to ΔHIJ then, their corresponding sides will be in proportion.

⇒ GE/EF = HJ/HI

⇒ 19/34 = 6/HI

⇒ HI = 6 x 34/19

⇒ HI = 10.74

Therefore, the measure of side HI is 10.74.

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The firefighter needs to climb a height of 22.91 foot to reach the cat.

What is the Pythagorean Theorem ?

Pythagorean Theorem states that the square of the hypotenuse of a right triangle equals the sum of squares of the lengths of the other two sides.

It is given that the hypotenuse of the ladder is 25 foot and it's base is 10 feet away from base of tree.

Using the Pythagorean theorem which states that :

H² = P² + B²

where ;

H = Hypotenuse , P = Perpendicular and B = base

We can find out the height up to which the firefighter needs to climb to reach the cat. And it is given by :

25² - 10² = P²

625 - 100 = P²

or

P = √525

P = 22.91 foot

Therefore , the firefighter needs to climb a height of 22.91 foot to reach the cat.

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Statistical considerations for the use of composite health-related quality-of-life scores in randomised trials

This is a research paper whose author is Andrew J. Vickers.

Abstract:

Conclusions:

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Answer:

x = 1/3

Step-by-step explanation:

•3x - 1 = 1 - 3x *group like terms*

•3x + 3x = 1 + 1 *remember whenever you transpors the sign changes*

•6x/6 = 2/6

• x = 1/3

The solutions are (4.5, 4.5) and (6, 3).

Here,

The equations are;

x + y = 9

x²- 3xy + 2y² = 0​

We have to solve the equations.

What is Expression?

Expression in math is defined as the collection of the numbers, variables and functions by using signs like addition, subtraction, multiplication, and division

Now,

The equations are;

x + y = 9

x²- 3xy + 2y² = 0​

Since, x + y = 9 ⇒ y = 9 - x

And, solve the equation as;

x²- 3xy + 2y² = 0​

x²- 2xy - xy + 2y² = 0​

x (x - 2y) - y (x - 2y) = 0

(x - y) (x - 2y) = 0

(x - y) = 0 or (x - 2y) = 0

For, (x - y) = 0

Given, x + y = 0

Hence, Solve equation (x - y) = 0 and (x + y) = 9 we get;

2x = 9

x = 4.5

And, y = 4.5

For  (x - 2y) = 0

x = 2y put in equation (x + y) = 9 we get;

(x + y) = 9

2y + y = 9

3y = 9

y = 3

And, x = 6

Therefore, The solutions are (4.5, 4.5) and (6, 3).

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Solutions are (4.5,4.5) and (6,3)

What are Quadratic equations ?

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).

Given,

x + y = 9 => y = 9-x  equation 1

x^2 - 3xy + 2y^2 = 0  equation 2

(x - y)(x - 2y)=0

x - y = 0 or x - 2y = 0

1. Equating x-y=0 and x + y = 9,

x + y = 9

x - y = 0

2x = 9

x = 4.5

y = 4.5

because y = x

2. Equating x - 2y = 0 and x + y = 9,

2x + 2y = 18

x - 2y = 0

3x = 18

x = 6

y = 9 - x = 3

therefore, possible solutions are (4.5,4.5) and (6,3)

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Answer: 45 yrs old

Step-by-step explanation:

Car A  = 9 yrs old

Car B = X yrs old

The ratio for the cars are

Car A : Car B

or

2 : 5

You want to make it easier to read so you make both the ratio number and the given age number (9) the same number.

Multiply Car A age by 2 to make it 18 and the Ratio 2 by 9 to make it 18. This makes them the same number. Since you did this to one side, you have to do it on the other side by multiplying the 5 by 9 which is 45.

Your new ratio is now

18 : 45

This means Car B is 45 yrs old

The number of 8-inch long pieces of ribbon that the other class cut is 9.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

Given that Students in 3 art classes cut 728 inches of ribbon into 8-inch long pieces. Therefore, the number of ribbon that 3 classes together cut is,

Number of ribbon cut by 3 classes together = 728 inches / 8 inches = 91

Further, it is given that two of the classes together cut 656 inches of ribbon. Therefore, the number of ribbon that 2 classes together cut is 656.

Number of ribbon cut by 2 classes together = 656 inches / 8 inches = 82

Now, the number of  8-inch long pieces of ribbon that the other class cut can be written as,

Number of pieces cut by other class

= Number of ribbon cut by 3 classes together - Number of ribbon cut by 2 classes

= 91 - 82

= 9

Hence, the number of 8-inch long pieces of ribbon that the other class cut is 9.

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The water gauge pressure at the house will be 9.63×10⁵ N/m².

Firstly we will be calculating the total height which will comprise of height from tank to house and elevated height. The formula for total height will be -

Total height = 5 + 110 sin 58°

Keep the value of sin 58° in formula and performing multiplication followed by addition

Total height = 5 + 110×0.848

Total height = 5 + 93.28

Total height = 98.28 meters

Now, calculating the water gauge pressure at house. The formula to be used is -

P = ρ×g×h, where P is pressure, ρ is density of water, g refers to acceleration due to gravity and h represents total height. We are aware that density of water is 1000 kg/m³ and accelerate due to gravity is 9.8 m/s².

Keep the values in formula to find the gauge pressure.

P = 1000 × 9.8 × 98.28

Performing multiplication

P = 963,144 N/m² or 9.63×10⁵ N/m²

Hence, the water gauge pressure at the house will be 9.63×10⁵ N/m².

The complete question is -

A house at the bottom of a hill is fed by a full tank of water 5m deep and connected to the house by a pipe that is 110m long at an angle of 58 degrees from the horizontal. Determine the water gauge pressure at the house.

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in fig. 3.1 the value of  x  is 20° , in fig. 3.2 the value of  x  is 40° ,  in fig.  the value of  3.3 x  is 10° ,  in fig. 3.4 the value of  x  is 120°.

In planar geometry, an angle is a shape made up of two rays or lines that share an endpoint. The English word "angle" derives from the Latin word "angulus," which means "corner." The vertex and the two rays are referred to as the sides of an angle, respectively, and are the shared termini of two rays.

3.1

straight lines makes an angle of 180° thus ,

              x + 2x + 120 = 180

                3x = 60

                  x = 20°

3.2

    sum of the angles of triangle is = 180°

     105 + 35 + x = 180

      140 + x = 180

       x = 40°

3.3

       since it is an isoceles triangle so the opposite angles to equal sides are equal

140 + 4x = 180

4x = 40

x = 10°

3.4

parallel  line theorem  state that alternate angles are equal

so ,

    180= x + 60

x = 120 °

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The value of the functions are:

(a) ( f - g )( 1 ) = - 1

(b) ( f · g )( 4 ) = 0

Before performing operations on functions, we must first comprehend the various function rules and how to get the function value at a given x-value. By applying this concept, we can determine the function value.

From the graphs, we have the functions,

f(x) = 2( | x - 2 | )

g(x) = - x + 4

Now,

(a) ( f - g )( 1 )

( f - g )( 1 ) = f( 1 ) - g( 1 )

( f - g )( 1 ) = 2 ( | 1 - 2 | ) - ( - 1 + 4 )

( f - g )( 1 ) = 2 ( | - 1 | ) - ( 3)

( f - g )( 1 ) = 2 - 3

( f - g )( 1 ) = - 1

(b) ( f · g )( 4 )

( f · g )( 4 ) = f( 4 ) · g( 4 )

( f · g )( 4 ) = 2( | 4 - 2| ) · ( - 4 + 4 )

( f · g )( 4 ) = 0

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Answer:

[tex] \sf \: 19c + 30 [/tex]

Step-by-step explanation:

Given expression,

→ 1(19c + 30)

Let's simplify the expression,

→ 1(19c + 30)

→ 1(19c) + 1(30)

→ (1 × 19)c + (1 × 30)

→ (19)c + (30)

→ 19c + 30

Hence, answer is 19c + 30.

Answer:

A

Step-by-step explanation:

Answer:

x=44

Step-by-step explanation:

x32=10+x/2

Multiply the 2 from x over 2 to reverse the division equation.

2*x32=10+x/2*2

That results in 2 multiplying 32x and 2 multiplying the 2 in x over 2.

Because multiplication is the reverse of division, the 2's will cancel out and reduce x over to 2 to simply x.

2*32 is 64, include the x before the 64 just like the given equation exemplifies with the x before the 32.

The equation looks like the following once put together: x64=10+x

Subtract the x from the 10+x side of the equation underneath the x64.

x64=10+x

-x          -x

Which equals x63=10.

To receive the answer to this question, you have to divide the 63 on both sides.

63 divided by 63x leaves you with just the x.

63 divided by 10 leaves you with 6.3 in decimal form.

Thus, x equals 6.3.

To check if it's right, insert 6.3 for both x's.

(6.3)*32=10+(6.3)/2

Solve.

201.6=10+3.15

201.6=13.15

Clearly, this doesn't work.

So, I'm assuming you actually meant: 32=10+x/2.

Hence, you would multiply 2 on both sides.

2*32=10+x/2*2

We've established that 32*2 is 64 and the 2's would cancel out.

64=10+x

Subtract the 10 on both sides.

54=x

To see if this one is correct, plug in 54 to the x.

32=10+(54)/2

Divide 54 by 2 which equals 27.

32=10+27

32=37

Nope, that doesn't work either.

Thus, instead of multiplying by 2, we would first need to subtract the 10.

32=10+x/2

-10 -10

32-10 is 22 and it would leave the other side with just x over 2.

22=x/2

Now, we would have to multiply the 2 on both sides.

22*2=44 and x/2*2 gives us x.

So, 44=x.

Let's check.

32=10+(44)/2

32=10+22

32=32

Finally, we have our match.

In conclusion, x=44.

Hope this helps.

Answer:

The true statements are the 1st, 2nd, and 4th statement.

We can use inequality, 24. |m| greater than or equal to 10 then the possible to value is =  |14|.

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Based on the given conditions, formulate,

24. |m| greater than or equal to 10

So, we can write,

24 + m ≥ 10

m ≥ 10 - 24

We can sum or difference,

m ≥ -14

Then,

|m| ≥ |-14|

Hence,

|m| ≥  |14|

Therefore,

24. |m| greater than or equal to 10 then the possible to value is =  |14|.

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Answer:

focus

Step-by-step explanation:

Answer:

Step-by-step explanation:

Focus = (8,-6¹/2), directrix is y= -5¹/2

The coordinates of the point on the directed line segment will be (1, -6).

Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have

x = (mx₂ + nx₁) / (m + n)

y = (my₂ + ny₁) / (m + n)

The coordinates of the point on the directed line segment from (-1, -8) to (5, -2). The ratio is 1: 2.

Then the coordinates of the point will be

x = (1(5) + 2(-1)) / (1 + 2)

x = (3 / 3)

x = 1

y = (1(-2) + 2(-8)) / (3)

y = - 18 / 3

y = - 6

The coordinates of the point on the directed line segment will be (1, -6).

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The Perimeter of polygon ABCD = 21.6 units.

The perimeter of figure ABCD = sum of all its sides = AB + BC + CD + AD.

To find each of the sides, apply the distance formula, d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

A(-5, 5)

B(0, 3)

C(-2, -2)

D(-7, 0)

AB = √[(0−(−5))² + (3−5)²]

AB = √29

AB ≈ 5.4 units

BC = √[(0−(−2))² + (3−(−2))²]

BC = √29

BC ≈ 5.4 units

CD = √[(−7−(−2))² + (0−(−2))²]

CD = √29

CD ≈ 5.4 units

AD = √[(−7−(−5))² + (0−5)²]

AD = √29

AD ≈ 5.4 units

The Perimeter of polygon ABCD = 5.4 + 5.4 + 5.4 + 5.4 = 21.6 units.

Therefore, the Perimeter of polygon ABCD = 21.6 units.

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Answer:

this is the answer of about the image is even

Answer: (1/75)

Step-by-step explanation:

[{6*(10^4)*(3^3)}/{(6^5)*(5^6)}]

= (1/75)

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{6\times10^4\times3^3}{6^5\times5^6}}[/tex]

[tex]\mathsf{= \dfrac{6\times10\times10\times10\times10\times3\times3\times3}{6\times6\times6\times6\times6\times5\times5\times5\times5\times5\times5}}[/tex]

[tex]\mathsf{= \dfrac{6\times100\times100\times9\times3}{36\times36\times6 \times25\times25\times25}}[/tex]

[tex]\mathsf{= \dfrac{6\times 10,000\times9\times3}{1,296\times6 \times 625\times5}}[/tex]

[tex]\mathsf{= \dfrac{60,000\times 27}{7,776\times 15,625}}[/tex]

[tex]\mathsf{= \dfrac{1,620,000}{12,150,000}}[/tex]

[tex]\mathsf{= \dfrac{1,620,000\div 1,620,000}{12,150,000\div1,620,0000}}[/tex]

[tex]\mathsf{= \dfrac{1}{75}}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{\dfrac{1}{75}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

g=−28

Step-by-step explanation:

-74 = g/7 + -70

Let's solve your equation step-by-step.

−74=g/7−70

Step 1: Simplify both sides of the equation.

−74=g/7−70

−74=1/7g+−70

−74=1/7g−70

Step 2: Flip the equation.

1/7g−70=−74

Step 3: Add 70 to both sides.

1/7g−70+70=−74+70

1/7g=−4

Step 4: Multiply both sides by 7.

7*(1/7g)=(7)*(−4)

g=−28

Answer: four friends went out for dinner. the bill , including tax , totaled $64.00 if they want to leave a 15% tip and want to share the bill and tip equally

Step-by-step explanation: