What is the equation of this graphed line?

The prime factorization of 48 is  2⁴  ×  3.

Those greater than one are known as prime numbers. They simply have two variables: the number itself and factor 1. This indicates that these numbers cannot be divided without leaving a remainder by any number other than 1 and the number itself.

Given:

The number is 48,

Factorize 48 we get 2 × 2  × 2  × 2 × 3

= 2⁴  ×  3

Therefore, the prime factorization of 48 is  2⁴  ×  3.

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The probability of tossing a six-sided die with sides numbered 1 through 6 and getting a 5 is 0.166666 or 1/6.

Here in the question, we see that a six-sided die is tossed. So there will be a total of 6 outcomes.

So the sample space will be {1,2,3,4,5,6}

Of which the possible outcome of getting a 5 is 1

Let A be the event of getting a 5 on tossing a six-sided die

∴ the probability of getting a 5 on tossing a six-sided die is P(A)=1/6

∵ we know that the probability of an event is the possible outcome of the event divided by the total outcomes of that event.

So here the probability of getting a 5 is 0.166666 or 1/6.

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Answer: 16

Step-by-step explanation:

Imagine you had 4 apples and someone gave you 12 more. You would have 16 apples.

Answer:

3???

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

(7x - 4) and 73 are alternate exterior angles and are congruent , then

7x - 4 = 73 ( add 4 to both sides )

7x = 77 ( divide both sides by 7 )

x = 11

Answer:

[tex]x = 11[/tex]

Step-by-step explanation:

two angles are congruent for the parallelism of the two horizontal lines (external alternates). thus

[tex]7x - 4 = 73 \\ 7x = 77 \rightarrow x = 11[/tex]

The plumber will work for 4hrs and 30min. Which we can call in many ways as “four and half hours”.

The right side of the equation is represented by the expression to the right of the "=" sign, and the left side by the expression to the left of the "=" sign.

For instance, in, the left-hand side (LHS) is represented by x + 5 and the right-hand side (RHS) by y + 8.

      Plumber charges for coming home : $35

                Charge for work per hour: $60

      Total  charges of the plumber          : $305

Total  charges =   (charges for coming home) + ( Charge for work per hour) x (hours he worked)

The equation is 35 + 60X =305

305 = 35 + 270

270 = ( Charge for work per hour) × (X)      [Let hours he worked = x]

270 = 60 × (X)

270 ÷ 60 = (X)

X = 4.5

The plumber has worked for 4.5 hrs .

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The running total is  $95.27.

There are two types of records, Active and Inactive. There are also two major classifications, Vital and Important.

He opened the account with $299.88. He subsequently wrote many cheques, from which you deduct the sum of 299,88.

He deposited a check, thus 299.88-90.48= 209.40, 209.40 - 65.00= 144.40, and then he added $381.33 to 144.40 to get 525.73.

then you need to deduct more since he wrote more checks.

Consequently, 525.73-54.47=471.26, and 471.26-375.99=95.27, giving him a balance of $95.27.

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The current total is $95.27. Active and Inactive records are the two types of records. There are two major classifications as well: Vital and Important.

Good records are required to create reliable financial statements. Balance sheets and income (profit and loss) statements are included. These statements may help you manage your company and deal with your bank or creditors.

Good Records are documents that contain recorded data that demonstrate the effectiveness of the quality management system, regardless of format or feature.

Given,

He deposited into the account = $299.88

He then wrote a number of cheques, from which you deduct = $299,88.

He deposited a check, thus 299.88 - 90.48

= 209.40, 209.40 - 65.00

= 144.40

and then he added $381.33 to 144.40 to get 525.73.

then you need to deduct more since he wrote more checks.

Consequently,

525.73 - 54.47

=471.26  

and 471.26-375.99

= 95.27

As a result, The gives him a balance of $95.27.

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The volume is the amount of space thus the volume of the given prism will be 204.7 cm³ thus option (B) is correct.

Volume is the scalar quantity of any object that specified occupied space in 3D.

For example, the space in our room is referred to as volume.

Volume has units of cube example meter³,cm³, etc.

The volume of the given prism will be the area of the front triangle with a length of 12 cm.

The form triangle has been attached below,

The length x will be,

x = √(6² - 3.5²) = 4.87 cm.

The area of from triangle = (1/2) × 7 × 4.87

A = 17.06 cm²

The volume of the prism = A × length (12 cm)

Volume = 17.06 × 12 = 204.68 cm².

Hence "The volume is the amount of space thus the volume of the given prism will be 204.7 cm³".

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The complete question has been attached below ;

From the given set of equation the one which has same solution as

x² + 4x + 13 = -10 is given by (x+2)² = -19.

As given in the question,

Given equation is equal to:

x² + 4x + 13 = -10

Simplify it we get,

x² + 4x + 13 +10 =0

⇒ x² + 4x + 23 =0  ___(1)

General quadratic equation is

ax² + bx + c =0

a = 1 , b =4 , c =23

Simplify the given options we have:

a. (x+2)² = -19

⇒ x² + 4x + 4 = -19

⇒ x² + 4x + 4 + 19 =0

⇒ x² + 4x + 23 =0

Has same solution as given one.

b.  (x-2)² = -27

⇒ x² -4x + 4 +27 =0

⇒x² -4x +31 =0

'b' and 'c' value are different

Not have same solution.

c. (x-2)² =-19

⇒ x² -4x + 4 +19 =0

⇒x² -4x +23 =0

'b' value is different.

Not have same solution.

d. (x+2)² = -27

⇒ x² +4x + 4 +27 =0

⇒x² +4x +31 =0

'c' value is different

Not have same solution.

Therefore, from the given set of equation the one which has same solution as x² + 4x + 13 = -10 is given by (x+2)² = -19.

The complete question is:

Which equation has the same solution as x² + 4x + 13 = -10?

a. (x+2)² = -19

b. (x-2)² = -27

c. (x-2)² =-19

d. (x+2)² = -27

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The value of the function f(a+4) is  [tex]\frac{7}{a^{2} +8a+11}[/tex]

function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable called the dependent variable.

if f(x) = [tex]\frac{7}{x^{2} - 5}[/tex], which means this equation is a function of x,

To find another equation whose function is f(a + 4)

We substitute x for a + 4 in the above equation

f(a+4) = [tex]\frac{7}{(a+4) ^{2} - 5 }[/tex]

expanding [tex](a + 4)^{2}[/tex], and simplifying the denominator, we have

[tex]a^{2}[/tex] +8a + 16 - 5 = [tex]a^{2}[/tex] + 8a + 11

so the simplified form of the new function would be  [tex]\frac{7}{a^{2} +8a+11}[/tex]

In conclusion, the function f(a +4) =  [tex]\frac{7}{a^{2} +8a+11}[/tex]

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The axis of symmetry of the parabola, having the equation, f(x) = 3·(x - 5)² + 1 is the line x = h = 5

A parabola is the locus of a point that moves such that the distance of the point from a fixed point is the same as the distance of the moving point from a fixed line.

The graph of a parabola has the shape of an open umbrella

The given equation for the parabola is; f(x) = 3·(x - 5)² + 1

The equation is given in the vertex form, f(x) = a·(x - h)² + k, where;

(h, k) = The vertex of the parabola

The axis of symmetry of a parabola, which is the line that divides the parabola in two, passes through the vertex of the parabola

Comparing the equation, f(x) = 3·(x - 5)² + 1, to the vertex form of a parabola,  gives;

a = 3

(h, k) = (5, 1) (The vertex of the parabola)

Which gives; h = 5

The equation of the axis of symmetry is therefore the line, x = h = 5

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The intersection of A and I, A ∩ I = {-2, -1, 1}

The intersection of two sets A and B is the set of all common elements, it is denoted with A ∩ B.

Whereas the union of those two sets is the set of all elements that are either in A or in B, it is denoted by A ∪ B.

The given sets are,

A = {-2, -1, 0, 1, 7}

And I = {-2, -1, 1, 2, 8}

Intersection of A and I,

A ∩ I = {-2, -1, 1}

The intersection of A and I is {-2, -1, 1}.

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The coordinates of B are (-7,-2).

What do you mean by x and y coordinates?

The x and y coordinates are a component of the x-axis and y-axis in a 2D space in the Cartesian coordinate system. The x and y coordinates for a point in space are expressed as an ordered pair (x, y). The position of the point on the x-axis is shown by the first number, while its location on the y-axis is indicated by the second number.

According to the given data in the question,

if M is the location where line segment AB meets its midpoint.

Then, we will using the midpoint formula,

[tex](-5,2)=(\frac{-3+x}{2},\frac{6+y}{2})..............(1)[/tex]

Putting the x-coordinates in (1),

[tex]-5=\frac{-3+x}{2}\\ -10=-3+x\\-10+3=x\\x=-7[/tex]

Similarly, putting the y-coordinates in (1),

[tex]2=\frac{6+y}{2} \\4=6+y\\4-6=y\\y=-2[/tex]

Hence, the coordinates of B are (-7,-2).

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The measures of the remaining three angles of the decagon are 40, 50 and 130 degrees.

A decagon is a polygon with 10 sides. In a regular decagon, the interior angles add up to 1440 degrees, and the exterior angles add up to 360 degrees.

Therefore, seven of the angles of a decagon have measures whose sum is 1220. Of the remaining 3 angles, exactly two are complementary and exactly two are supplementary.

Complementary angles sum up to 90 degrees while supplementary angles sum up to 180 degrees.

Therefore,

1440 - 1220 = 220

Let the angles be a, b and c.

Therefore,

a + b + c  =220

a + b = 90

b + c = 180

Hence,

a = 220 - 180

a = 40°

b = 90 - 40

b = 50°

c = 180 - 50

c = 130°

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For Jeremy the new balance due was $8.9  .

In the question ,

it is given that ,

bill received by Jeremy with balance due =  $35.60  

also given that after an error occurred  ,

the new balance was 1/4 of the original balance due .

So , the new balance due is = (1/4) × (original balance due)

Substituting the value of original balance due ,

we get ,

new balance due = (1/4) × (35.60)

= 35.60/4

On Simplifying further ,

we get ,

= 8.9

Therefore , For Jeremy , the new balance due was $8.9  .

The given question is incomplete , the complete question is

Jeremy received a bill with a balance due of $35.60. After an error was corrected, the new balance was 1/4 of the original balance due. What was the new balance due ?

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Answer:

y = 12x + 35

95 pages

Step-by-step explanation:

Let y represent the total number of pages

Let x represent the total number of months

x = 5 (months)

so..

y = 12(5) + 35

y = 60 + 35

y = 95

P(A∪B)=24/35 when A and B are independent and P(A)=2/5,P(B)=2/7

Probability is the branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely it is that a claim is true. The probability of an event is a number between 0 and 1, with 0 signifying impossibility and 1 expressing certainty. The greater the likelihood of an occurrence, the more likely it will occur.

Probability theory, which is widely used in domains such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy, has given these concepts axiomatic mathematical formalization.

Given,

P(A)=2/5

P(A)=2/7

P(A∪B)=?

And also given that A and B are independent then,

P(A∩B)=0

P(A∪B)=P(A)+P(B)-P(A∩B)

P(A∪B)=(2/5)+(2/7)-0

P(A∪B)=(14+10)/35

P(A∪B)=24/35

Therefore, P(A∪B)=24/35 when A and B are independent.

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Answer:

Selling price = RS 3150

Loss percent = 10%

Step-by-step explanation:

1 quintal = 100kg

Cost price = 35*100

= RS 3500

Loss = RS 350

Selling price = RS 3500-350

Selling price = RS 3500-350 =RS 3150

Loss percent = Loss *100%

Cost Price

= 0.1 *100

= 10%

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The Mathematical Expression formed is 4(10-8)

What is a Mathematical Expression?

In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations.

Solution:

The mathematical expression formed frrom the statement;

Multiply the difference of 10 and 8 by 4

is as follows,

4(10-8)

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An eight pointed star have 8 rotational symmetry and 8 reflection symmetry

The rotational symmetry of a shape explains why an object's shape remains unchanged when rotated about its own axis.

The eight pointed star while standing on any of the edges will be symmetrical.

Symmetry with respect to reflections is known as reflection symmetry. Mirror or line symmetry are other names for reflection symmetry.

For a reflection symmetry to be in a figure, the figure must at least have one line dividing it into two parts, one of which is the mirror image of the other,

Each of the peak and crest in the star will make 8 reflection symmetry

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The pounds of trash that Janicka recycle is 3 3/5 pounds.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.

In this situation, Janicka picked up 5 2/5 lb of trash and 2/3 of what she collected was able to be recycled.

The amount to be recycled will be:

= 2/3 × 5 2/5

= 2/3 × 27/5

= 54 / 15

= 3 9/15

= 3 3/5

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Answer:

??

Step-by-step explanation:

where are the equations ?

Answer:

Step-by-step explanation:

Kinetic energy of a 64 kg object travelling at 12 m/s is 4.6kj.

Kinetic energy = KE = [tex]\frac{1}{2}mv^{2}[/tex]

Mass = m = 64 kg

Velocity = v = 12 m/s

KE = [tex]\frac{1}{2}*64*(12)^{2}[/tex]

    = 4608 J

1000 j = 1 kj

      1 j = 1/1000 kj

4608 j = 4608/1000 kj

          = 4.608 kj

Hence, kinetic energy is 4.6 kj.

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The Least number of baseball cards Isabella could have is 49

To solve the problem, the multiples of seven will be necessary to ascertain the one that will:

multiples of 7: 7 , 14 , 21 , 28 , 35 , 42 , 49 , 56 , 63....

14 is short of 1 when divided by 5 but it is divisible by 2 without remainder

49 is the least number that fall short of 1 card to make it a multiple of 5 and have a remainder one when divided by 2

Hence the answer is 49

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The time is 2 our 55 minutes when they will take to cultivate the piece of land when working together.

What is mean by Fraction?

A fraction is a part of whole number, and a way to split up a number into equal parts.

Or, A number which is expressed as a quotient is called fraction.

It can be written as the form of p : q, which is equivalent to p / q.

Given that;

Kepteo can cultivate a piece of land in 7 hr.

Wanjiku can do the same work in 5 hr.

Now,

Since, Kepteo can cultivate a piece of land in 7 hr.

Hence, Kepteo make work in 7 h

So, In 1 hour kepteo work = 1/7

And, Since, Wanjiku can cultivate a piece of land in 5 hr.

Hence, Wanjiku  make work in 5 h

So, In 1 hour Wanjiku work = 1/5

Thus, They make with together = 1/7 + 1/5

                                                = 12/35

Hence, When they working, they make = 12/35 work per hour

So, They need number of hour to working together = 35/12 hour

                                                                               = 2 hour 55 minutes.

Thus, The time is 2 our 55 minutes when they will take to cultivate the piece of land when working together.

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From the given condition of number written on the board, first student increased it by 12 and second multiply by 3 the result of first one is greater than the second by 2 then number written on the board is 5.

As given in the question,

Let x be the number written on the board.

First student increased the number on board by 12 = x +12

Second student multiply the number on board by 3 = 3x

Required equation as per given condition is:

x +12 = 3x + 2

⇒ 3x -x = 12 -2

⇒ 2x = 10

⇒ x = 10/2

⇒ x= 5

Therefore, for the number written on the board, first student increased it by 12 and second multiply by 3 the result of first one is greater than the second by 2 then number written on the board is 5.

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1) The height of one of these cylinders if its radius is 2 inches is

115.207 inches.

2) The height of one of these cylinders if its radius is 3 inches is

51.203 inches.

3) The height of one of these cylinders if its radius is 6 inches is

12.800 inches.

1) when radius is 2 inches then:

πr²h = 1447

h = 1447/ (3.14 x 2²) = 115.207 inches

2)when radius is 3 inches then:

πr²h = 1447

h = 1447/ (3.14 x 9²) = 51.202 inches

3) when radius is 6 inches then:

πr²h = 1447

h = 1447/ (3.14 x {36}²) = 12.800 inches

1) The height of one of these cylinders if its radius is 2 inches is

115.207 inches.

2) The height of one of these cylinders if its radius is 3 inches is

51.203 inches.

3) The height of one of these cylinders if its radius is 6 inches is

12.800 inches.

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Answer:

2/3 u need to walk to reach the clothing shop

Part A Write an inequality to represent the possible lengths of time

the tent can be rented

[tex]6.11\leq h\leq 11.66[/tex]

Part B. Using your inequality in Part A, what is one possible length of

time the tent could be rented

[tex]6hr 6min\leq h\leq 11hr39min[/tex]

The definition of a linear inequality

The inequality symbol is used to compare two mathematical expressions in what are referred to as linear inequalities. The expression could be both numerical and algebraic, or it could just be one.

What does a linear inequality in mathematics look like?

What Is an Example of Linear Inequality? An example is the linear inequality x - 5 > 3x - 10. The LHS is obviously greater than the RHS because the greater than symbol is being utilized in this inequality. After being resolved, the inequality appears as follows: 2x 5 x (5/2).

Given That

45h+225 is total cost in dollars for renting tent and parents are willing to spend between $500 and $750 for the tent.

Part A

[tex]500\leq 45h+225\leq 750\\500-225\leq 45h+225-225\leq 750-225\\275\leq 45h\leq 525\\\frac{275}{45} \leq h\leq \frac{525}{45} \\6.11\leq h\leq 11.66[/tex]

Part B

[tex]6.11hr\leq h\leq 11.66hr[/tex]

6.11 hr = 366 minute approx.

11.66 hr = 699 minute approx.

[tex]6hr 6min\leq h\leq 11hr39min[/tex]

Hence this is the answer

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