What value makes 2 square root 51 equal to 10 square root 51x

Answer:

The answer is 33 bouncy balls in each machine

Step-by-step explanation:

In order to determine the answer, we need to divide every bouncy ball bags by two. The information about the amount of balls in every bag is:

bag 27 mm= 180 balls

bag 40 mm= 80 balls

The bag of 27 mm has an even amount of balls, so if we divide it by two, there will be 90 balls in each machine.

The bag of 40 mm has an even amount of balls, so if we divide it by two, there will be 40 balls in each machine.

Finally, considering the division in every bag, each machine has 130 balls.

The coordinates of the mid-point is 5 if the XY has endpoints at -13 and 23 after using the segment bisector formula.

A segment bisector is a line, ray, line segment, or point that divides a line segment into two equal halves at its center.

It is given that:

XY has endpoints at -13 and 23.

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

The coordinate of the mid-point = (-13 + 23)/2

The coordinate of the mid-point = (10)/2

The coordinate of the mid-point = 5

Thus, the coordinate of the mid-point is 5 if the XY has endpoints at -13 and 23 after using the segment bisector formula.

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The value of the exponent numerical expression (3.4)² will be 11.56.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ (3.4)²

Simplify the expression, then we have

⇒ (3.4)²

⇒ 3.4 x 3.4

⇒ 11.56

The value of the exponent numerical expression (3.4)² will be 11.56.

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The cost of the pen in terms of b is (2b - 6) dollars.

To write the cost of the pen in terms of b, we need to determine the cost of the pen relative to the cost of the markers.

Let's assign a variable to the cost of the shoulder bag. Since the shoulder bag costs twice as much as the box of markers, we can write the cost of the shoulder bag as 2b dollars.

Now, the pen costs $6 less than the shoulder bag, so the cost of the pen can be written as (2b - 6) dollars. Therefore, the cost of the pen in terms of b is (2b - 6) dollars.

The equations for the transformed function in vertex form and in standard form are as follows: Vertex form: [tex]\( y = -(x - 3)^2 + 2 \)[/tex], Standard form: [tex]\( y = -x^2 + 6x - 7 \)[/tex]

To arrive at these equations, let's go through the transformation steps:

1. The original function is [tex]\( y = x^2 \)[/tex].

2. Reflecting the graph in the x-axis changes the sign of the function, resulting in [tex]\( y = -x^2 \)[/tex].

3. Translating the graph 3 units right means replacing [tex]\( x \)[/tex] with [tex]\( x - 3 \)[/tex], giving us [tex]\( y = -(x - 3)^2 \)[/tex].

4. Finally, translating the graph 2 units up means adding 2 to the function, yielding the vertex form [tex]\( y = -(x - 3)^2 + 2 \)[/tex].

To convert this vertex form into standard form, we expand the vertex form and simplify:

[tex]\( y = -(x - 3)^2 + 2 \)\\ \( y = -(x^2 - 6x + 9) + 2 \)\\ \( y = -x^2 + 6x - 9 + 2 \)\\ \( y = -x^2 + 6x - 7 \)[/tex]

This is the standard form of the transformed quadratic function.

The solution to the quadratic equation is x = 2 ± √3

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

x² + 4x + 1 = 0   be equation (1)

And , roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

On simplifying , we get

x = [ -4 ± √ ( 4 )² - ( 4 ) ( 1 ) ( 1 ) ] / 2

x = [ -4 ± √ ( 16 - 4 ) ] / 2

x = [ -4 ± √12 ] /2

On further simplification , we get

x = [ -4 ± 2√3 ] /2

x = 2 ± √3

Therefore , the value of x is 2 + √3 or 2 - √3

Hence , the roots of the quadratic equations is x = 2 ± √3

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Answer:

40 minutes

Step-by-step explanation:

In the red line and the blue line trains just arrived at the station.

The red line arrives every eight minutes.

The Blue Line arrives every 10 minutes.

Next they will arrive at the station at the same time, LCM of 8 minutes and 10 minutes.

Because both train will come at same multiple of 8 and 10.

Factor of 8 : 2 × 2 × 2

Factor of 10 : 2 × 5

LCM : 2 × 2 × 2 × 5 = 40

Hence, After 40 minutes both train will arrive at station at same time.

The height of the box will be 5 inches considering the ribbon is wrapping over the perimeter along the height.

Perimeter is the addition of an external measure of sides it will always positive.

A perimeter is a length and has a degree of the unit as one.

For example

Perimeter of square = side + side + side + side

The perimeter of the circle = πd where d is the dia of the circle.

The total length of the ribbon = is 70 inches.

The bow takes 32 inches of ribbon.

So left = 70 - 32 = 38 inches.

Now,

38 inches = Perimeter along the height

2 ( L + 14 ) = 38

L + 14 = 19

L = 5 inches.

Hence "The height of the box will be 5 inches considering the ribbon is wrapping over the perimeter along the height".

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Answer:

The shorter piece is 5 ft long.

The longer piece is 15 ft long.

Step-by-step explanation:

Let's write this into an equation:

(5+2x)+x=20

5+3x=20

Subtract 5 from both sides

3x=15

x=5

The shorter piece is 5 ft long.

The longer piece is 5 feet longer than 2 times 5 ft (the shorter piece).

5+2*5

5+10

15

The longer piece is 15 feet long.

Hope this helped!

Final answer:

To form an equation with a sum of 34 using three numbers, one possible combination is 10, 12, and 12, resulting in the equation 10 + 12 + 12 = 34.

Explanation:

To find a combination of 3 numbers that equal 34, we can use simple addition. For example, let's choose three numbers such as 10, 12, and 12. Adding these together, we get the equation 10 + 12 + 12 = 34. This is just one of many possible combinations that satisfy the condition.

If we wanted a methodical approach to find different combinations, we could start with the first number and systematically increase it while decreasing one of the other numbers. It's important to test different combinations and remember that you can also use the same number more than once as we did with the number 12.

Remember, an equation must have an equal sign, while an expression is just a group of numbers and operations. In this case, we are looking for an equation since we want to show that the sum of the three numbers we pick is equal to 34.

The 7 pieces of pizza have been cut by drawing the straight line through diameter giving 4 parts and drawing the diagonal dividing into 6 parts. The 7th piece has been received by drawing a straight line through one of the pieces.

The pizza has been circular-shaped structure. The straight lines have been able to divide the pizza into 4 equal parts. The lines will be drawn as the horizontal and the vertical diameter to the circular pizza.

The required amount of the number of pizza pieces has been 7. The 2 straight lines divide it into 4 parts.

To attain the required 3 more parts, the pizza has been cut in a diagonal direction as well with 1 straight line giving a total of 6 pieces. The 1 piece has been attained by drawing a straight line through one of the pieces giving the total count of the 7 pizza slices of different shapes and sizes.

The image attached shows the division of the pizza slices into 7 pieces.

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Answer is b or the second option

Step-by-step explanation:

Answer:

1/5

Step-by-step explanation:

The total hours worked over the weekend are 44 hours, resulting in gross wages of $880.

To calculate the gross wages for the weekend, we need to multiply the hours worked each day by the hourly pay rate of $20. On Friday and Saturday, the working hours are from 7am to 11pm, which is 16 hours each day. On Sunday, the working hours are from 9am to 9pm, which is 12 hours.

To find the total hours worked over the weekend, we add the hours for each day:

Now we calculate the total hours: 16 + 16 + 12 = 44 hours.

Next, we calculate the total earnings by multiplying the total hours by the hourly rate:

= 44 hours x $20 per hour = $880.

Therefore, the gross wages for the weekend work are $880.

The given number is a rational number.

Given:

The given number is [tex]\dfrac{20}{6}[/tex].

To find:

Whether the given number is rational or irrational.

Explanation:

Rational number: It can be defined in the form of [tex]\dfrac{p}{q}[/tex], where [tex]p,q[/tex] are integers and [tex]q\neq 0[/tex].

Irrational number: It cannot be defined in the form of [tex]\dfrac{p}{q}[/tex], where [tex]p,q[/tex] are integers and [tex]q\neq 0[/tex].

The given number is in the form of [tex]\dfrac{p}{q}[/tex], where [tex]p=20,q=6[/tex] both non zero integers.

Therefore, the given number is a rational number.

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