9.5 , 9 3/4 , 9.125 , 9 3/4 from greatest to least

Koby did not solve the equation correctly. The correct solution for 4(x - 3) = x + 2 is x = 14/3 or approximately 4.667. The steps include distribution, combining like terms, and isolating the variable.

The student's solution contains errors in the algebraic process. The correct steps to solve the original equation 4(x - 3) = x + 2 are as follows:

Distribute the 4 into the parentheses: 4x - 12 = x + 2.

Subtract x from both sides to get all the x terms on one side: 4x - x - 12 = 2.

Simplify the equation: 3x - 12 = 2.

Add 12 to both sides to isolate the variable term: 3x = 14.

Divide both sides by 3 to solve for x: x = 14/3.

The correct solution is x = 14/3 or approximately 4.667, not x = 2 as Koby had. To check the solution, you substitute the value back into the original equation:

4(14/3 - 3) = 14/3 + 2

which simplifies to:

56/3 - 12 = 14/3 + 2

and further to:

56/3 - 36/3 = 14/3 + 6/3

resulting in an identity:

20/3 = 20/3.

Answer:

c

Step-by-step explanation:

Final answer:

To complete the inequality, we convert the fractions to decimal form or find a common denominator to compare them. The number that completes the inequality is three-fourths (0.75), as it is larger than two-thirds but smaller than seven-ninths.

Explanation:

The student is asking which number fulfills the inequality between two-thirds and various other fractions. To determine the correct number that completes the inequality, we should consider the values of the fractions in decimal form or by comparing them to each other after finding a common denominator.

For example, two-thirds is approximately 0.666..., three-fifths is 0.6, seven-ninths is approximately 0.777..., three-fourths is 0.75, and six over nine is equivalent to two-thirds (as six-ninth simplifies to two-thirds).

Considering these values, the number that fills the gap should be bigger than two-thirds and smaller than the smallest fraction among the given options that is bigger than two-thirds. Therefore, three-fourths (0.75) fits the inequality because it is larger than two-thirds (approximately 0.666...) but less than seven-ninths (approximately 0.777...).

Answer:

Option D

Step-by-step explanation:

Just took the quiz :)

Answer:

it is the last answer

Step-by-step explanation:

Answer:

factorize form of the equation is  [tex]24(x-1)=0[/tex]  , where  [tex]x=1[/tex]

Step-by-step explanation:

Given Equation:

                        [tex]3x + 21x-24=0[/tex]    

  Adding the terms of 'x' and taking constants on the other side.                        

                    [tex]24x-24=0[/tex]

The sign of the constant will change on changing the side of it.                

                         [tex]24x=24[/tex]

                           [tex]x=\frac{24}{24}[/tex]

                            [tex]x=1[/tex]

So, the value of  'x' is 1

The factorized form of the equation can be made by taking the common value from the equation i.e  

                      [tex]24x-24=0\\[/tex]

                   [tex]24(x-1)=0[/tex]

Answer:

Probablity of getting six in at most three roll= 0.199.

Step-by-step explanation:

Given: Dice rolled at most 3 times untill a 6 occurs.

First, finding the probablity of getting 6 in a dice if rolled once.

Probablity= [tex]\frac{chances\ of\ occurance}{Total\ number\ of\ event}[/tex]

We know, dice have six side, therefore, total number of event will be 6.

∴ Probablity of getting six in one roll= [tex]\frac{1}{6}[/tex]

As given, Dice is rolled at most 3 times.

Now, finding the probablity of getting 6 in a dice if rolled 3 times.

∴ Probablity of getting six in three roll= [tex]\frac{1}{6}+(\frac{1}{6})^{2} +(\frac{1}{6})^{3}[/tex]

⇒ Probablity of getting six in three roll=  [tex]\frac{1}{6}+\frac{1}{36} +\frac{1}{216}[/tex]

Taking LCD 216

⇒Probablity of getting six in three roll= [tex]\frac{1\times 36+ 6\times 1+1}{216}[/tex]

⇒Probablity of getting six in three roll= [tex]\frac{43}{216}[/tex]

∴Probablity of getting six in three roll=0.199

Answer:

2km

Step-by-step explanation:

- Abby walked 3 km west: Abby is 3km west from her starting point.

- Then she walked  twice as far going east: she walks 6km east so she's 3 km east from her starting point

- She continued east  for another kilometre: She's is 4 km east from her starting point

- Stopping 2 km east  of Lauren's home: She's currently 2 km east from Lauren's home and 4km east from her starting point. Therefore, Abby's starting point is 4km - 2km = 2km west from Lauren's home

Answer:

Step-by-step explanation: solution.. 8/10 of candy bar left over to be split into 1/3 pieces...

(8/10)÷1/3=12/5=2.4pieces

Answer:

it's supplementary angles

Step-by-step explanation:

1 + 2 =180

Answer:

60

Step-by-step explanation:

5 x (9 + y)

= 5 x ( 9 + 3)

= 5 x (12)

=60

Final answer:

The algebraic expression is 5(9 + y), which becomes 5(12) when y equals 3, resulting in a value of 60.

Explanation:

The algebraic expression for the product of 5 and the sum of 9 and y is 5(9 + y). To find the value of this expression when y equals 3, you substitute 3 for y in the expression, getting 5(9 + 3). Following the order of operations, calculate the sum inside the parentheses first, which gives you 5(12), and then multiply by 5 to find the product, resulting in a final value of 60.

Answer:

c=144

Step-by-step explanation:

The given equation is [tex]x^2-c=0[/tex]

If this equation has 12 and -12 as roots, then the roots must satisfy the equation.

We substitute x=12 to obtain

[tex]12^2-c=0[/tex]

[tex]144-c=0[/tex]

Solve for c to get:

[tex]144=c[/tex]

This implies that:

[tex]c=144[/tex]

We could have also substitute x=-12 to get the same result.

Answer:

Step-by-step explanation:

diameter of plate=30+5=35 cm

circumference of cake board=2π r=π d=35 d cm

Answer:

35π cm

Step-by-step explanation:

The circumference (C) of a circle is calculated as

C = πd ← d is the diameter

Here the diameter = 30 + 5 = 35 cm, thus

C = 35π cm

Answer:

4096

Step-by-step explanation:

4*4=16

16*4=64

64*4=256

256*4=1024

1024*4=4096

if this doesn't work, try the other products

Answer:

1,024

Step-by-step explanation:

Five generations after Amanda.

So, Amanda would be considered generation 0.

1st Generation- 4^1=4

2nd Generation-4×4=16

3rd Generation-16×4=64

4th Generation-64x4=256

5th Generation-256×4=1,024

Answer:

c

Step-by-step explanation:

brainlist

Answer:

Therefore,

Slopes are Equal, Hence the Lines are not Perpendicular.

Step-by-step explanation:

Given:

[tex]y-4=2(x-2)=2x=-4\\\\y=2x[/tex] .......Equation ( 1 )

[tex]4x-2y=5\\2y=4x-5\\\\y=2x-\dfrac{5}{2}[/tex]  .......Equation ( 2 )

Comparing with,  

[tex]y=mx+c[/tex] ......General Slope point form  

Where m =slope  

We get  

[tex]Slope = m1 = 2[/tex]   For Equation ( 1 )

[tex]Slope = m2 = 2[/tex]   For Equation ( 2 )

Hence,

[tex]m1=m2[=2[/tex]

Therefore, Slopes are Equal Hence the Lines are Parallel not Perpendicular.

For Perpendicular we require

[tex]m1\times m2=-1[/tex]

Therefore,

Slopes are Equal, Hence the Lines are not Perpendicular.

The area of the yard is 50,600 square feet.

Option: C.

Step-by-step explanation:

The given information forms a trapezoid.

The AB is the upper base (a) and its length is 200 feet.

The CD is the lower base (b) and its length is 260 feet.

A straight line distance from AB and CD is the height (h) and its measures as 220 feet.

The area of trapezoid A= [tex]\frac{a+b}{2} (h)[/tex].

A= [tex]\frac{200+260}{2} (220)[/tex].

=[tex]\frac{460}{2}(220)[/tex].

=230(220).

=50600 [tex]ft^2.[/tex]

Thus the area of John's yard is 50,600 square feet.

Answer:

x = - 100

Step-by-step explanation:

Given

[tex]\frac{x}{5}[/tex] + 6 = - 14 ( subtract 6 from both sides )

[tex]\frac{x}{5}[/tex] = - 20

Multiply both sides by 5 to clear the fraction

x = 5 × - 20 = - 100

Answer:

11

3Step-by-step explanation:

Given

3(x - 1)² + 2x - 7 ← substitute x = 3 into the expression

= 3(3 - 1)² + 2(3) - 7

= 3(2)² + 6 - 7

= 3(4) - 1

= 12 - 1

= 11

The first step in evaluating the expression is to substitute 3 for x.

The first step in evaluating the expression 3(x-1)^2 + 2x - 7 for x=3 is to substitute 3 for x. This is because before you can simplify or combine like terms, you need to know the value of the variables involved. Once substitution is done, you can proceed with further simplification such as distributing and combining like terms.

Answer:

Step-by-step explanation:87

87

Answer:

[tex]1\frac{4}{5}[/tex]

Step-by-step explanation:

Each is dived into 5 section. so section is 1/5

Option C:

[tex]\sum_{n=1}^{5} 3(0.2)^{n-1}=3.75[/tex]

Solution:

Given expression:

[tex]\sum_{n=1}^{5} 3(0.2)^{n-1}[/tex]

Summation means sum of the numbers.

Put n = 1  to 5 and sum all the numbers.

[tex]\sum_{n=1}^{5} 3(0.2)^{n-1}[/tex]

           [tex]=3(0.2)^{1-1}+3(0.2)^{2-1}+3(0.2)^{3-1}+3(0.2)^{4-1}+3(0.2)^{5-1}[/tex]

           [tex]=3(0.2)^{0}+3(0.2)^{1}+3(0.2)^{2}+3(0.2)^{3}+3(0.2)^{4}[/tex]

Using exponential rule: [tex]a^0=1[/tex], so that [tex]0.2^0=1[/tex]

           [tex]=3(1)+0.6+0.12+0.024+0.0048[/tex]

           [tex]=3.7488[/tex]

           = 3.75

[tex]\sum_{n=1}^{5} 3(0.2)^{n-1}=3.75[/tex]

Option C is the correct answer.

Hence approximate value of [tex]\sum_{n=1}^{5} 3(0.2)^{n-1}[/tex] is 3.75.

Answer:

C

Step-by-step explanation:

edge

Answer:

- 6r³.

Step-by-step explanation:

Here, we have to find the product of r², - 3 and 2r.

Now, the product is, P = (r²)(- 3)(2r)

⇒ [tex]P = (- 3) \times (2) \times r^{2}\times r[/tex]

{Seperating each terms as the terms are in product form}

⇒  [tex]P = - 6 \times r^{2 + 1}[/tex]

{Using the property of exponent that [tex]x^{a}\times x^{b} = x^{a + b}[/tex]}

⇒ P = - 6r³ (Answer)

Total distance walked by Layla is 300 yards

Solution:

Given that,

Layla is walking in a rectangular park

She walks one side that is 50 yards and then the other  side that is 120 yards

Length = 120 yards

Width = 50 yards

Layla develops a cramp in her leg and walks diagonally through the park  to head back home

Let us find the length of diagonal of rectangle

[tex]d=\sqrt{w^2+l^2}[/tex]

[tex]d = \sqrt{50^2+120^2}\\\\d = \sqrt{2500+14400}\\\\d = \sqrt{16900}\\\\d = 130[/tex]

Thus length of diagonal is 130 yards

What is the total distance that layla walked?

Given that Final answer is  perimeter of the triangle park

The diagonal and length and width forms a right angle triangle

Perimeter of triangle = diagonal length + width + length

Perimeter of triangle = 130 + 50 + 120 = 300

Thus total distance walked by Layla is 300 yards

The total distance Layla walked, including the two sides of the park and the diagonal path, is calculated using the Pythagorean theorem to be 300 yards.

The question asks us to find the total distance Layla walked while going through the rectangular park diagonally. Layla first walks one side of the park which is 50 yards long and then the adjoining side which is 120 yards long. To do this, we will first find the length of the diagonal using the Pythagorean theorem and then add it to the sum of the two sides she walked to get the total distance. The Pythagorean theorem states that in a right-angled triangle the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as c2 = a2 + b2.

Applying the Pythagorean theorem to find the diagonal (hypotenuse):

Now, we can find the total distance Layla walked:

Therefore, the total distance Layla walked is 300 yards.

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Answer:The kid is 11 and the mother is 33

Step-by-step explanation:

do the math

Step-by-step explanation:

Let the present age of son be x years

Therefore, mother's age = 3x years

11 years after:

Son's age = (x + 11) years

Mother's age = (3x + 11) years

According to the given condition:

3x + 11 = 2 (x + 11)

[tex] \therefore \: 3x + 11 = 2x + 22 \\ \therefore \: 3x - 2x = 22 - 11 \\ \therefore \: x = 11 \\ \implies \: 3x = 3 \times 11 = 33 \\ thus \\ Present \: age \: of \: mother = 33 \: years \\ Present \: age \: of \: son= 11 \: years \\ [/tex]

Answer:

104

Step-by-step explanation:

Any expression multiplied by 0 equals 0

when adding or subtracting 0, the quantity doesn't change

Answer:

I think it is 4 or 104. There are 2 ways to look at it.

Way #1:

50 + 50 = 100

100 - 25 = 75

75 x 0 = 0

2 + 2 = 4

0 + 4 = 4

Way #2:

50 + 50 = 100

25 x 0 = 0

100 - 0= 100

2 + 2 = 4

100 + 4 = 104

The maximum height of the football is approximately 15.21 yards.

The given equation for the path of the football is y = –0.04x^2 + 1.56x, where x is the horizontal distance in yards and y is the corresponding height in yards. To find the maximum height of the football, we need to determine the vertex of the parabolic function represented by the equation. The vertex represents the point where the function reaches its maximum or minimum value.

The vertex of a quadratic function in the form y = ax^2 + bx + c can be found using the formula x = -b/(2a). In this case, a = -0.04 and b = 1.56. Plugging these values into the formula, x = -1.56/(2*-0.04) = 19.5. Substituting this value back into the equation, we can find the corresponding y value which represents the maximum height of the football.

y = –0.04(19.5)^2 + 1.56(19.5) = -0.04(380.25) + 30.24 = 15.21 yards

Answer:

12.57

Step-by-step explanation:

Answer:

12.57 i did on the calculator

Step-by-step explanation:

Answer:

3493.70

Step-by-step explanation:

if you multipy all these in a calculator you get a long number, look at the third digit behind the decimal, if its 5+ then make the second digit behind the decimal one number higher. If its 4 or under than keep the number the same. To round, cut off all the digits behind the second digit thats past the secimal

Answer:

[tex]6\ cm[/tex]

Step-by-step explanation:

First Rectangle:

[tex]length(l_1)=24\ cm\\\\Width(b_1)=9\ cm[/tex]

Second Rectangle:

[tex]length(l_2)=16\ cm\\\\Let\ Width=b_2\ cm[/tex]

[tex]Since\ these\ two\ rectangles\ are\ similar\\\\\frac{l_2}{l_1}=\frac{b_2}{b_1}\\\\\frac{16}{24}=\frac{b_2}{9}\\\\16\times 9=24\times b_2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ cross\ multiplication\\\\b_2=\frac{16\times 9}{24}\\\\b_2=6\ cm[/tex]

Answer:

Check the attachment, then plug in values as needed

Step-by-step explanation: