(01.03) A box has dimensions of 14 inches long, 1.5 feet wide, and 7 inches high. What is the volume of the box

The solution for ( y ) is ( y = 3.5 ).

To solve for y in the equation [tex]\( 10y + 3.8 = 38.8 \)[/tex], follow these steps:

Start with the given equation:

[tex]\[ 10y + 3.8 = 38.8 \][/tex]

Subtract 3.8 from both sides to isolate the term with  y:

[tex]\[ 10y + 3.8 - 3.8 = 38.8 - 3.8 \][/tex]

[tex]\[ 10y = 35 \][/tex]

Divide both sides by 10 to solve for  y :

[tex]\[ \frac{10y}{10} = \frac{35}{10} \][/tex]

y = 3.5

So, the solution for ( y ) is ( y = 3.5 ).

Answer:

C. [tex]x=50[/tex], [tex]y=10[/tex]

Step-by-step explanation:

We have been given an image of two intersecting lines. We are asked to find the value of x and y for our given diagram.

We know that when two line intersect each other, then vertical angles are congruent.

Using vertical angles theorem, we will get a system of equations as sown below:

[tex]3y=x-20...(1)[/tex]

[tex]5x-100=y+140...(2)[/tex]

From equation (1), we will get:

[tex]x=3y+20[/tex]

Upon substituting this value in equation (2), we will get:

[tex]5(3y+20)-100=y+140[/tex]

[tex]5*3y+5*20-100=y+140[/tex]

[tex]15y+100-100=y+140[/tex]

[tex]15y=y+140[/tex]

[tex]15y-y=y-y+140[/tex]

[tex]14y=140[/tex]

[tex]\frac{14y}{14}=\frac{140}{14}[/tex]

[tex]y=10[/tex]

Therefore, the value of y is 10.

To find the value of x, we will substitute [tex]y=10[/tex] in equation (1) as:

[tex]3*10=x-20[/tex]

[tex]30=x-20[/tex]

[tex]30+20=x-20+20[/tex]

[tex]50=x[/tex]

Therefore, the value of x is 50 and option C is the correct choice.

Answer:

Option C) x = 50, y = 10

Step-by-step explanation:

We are given a two pairs of vertically opposite angle in the image.

Vertically opposite angle is formed when two lines intersect anf they are always equal.

Thus, we can write:

[tex]3y = x -20\\\Rightarrow x - 3y = 20\\5x-100 = y +140\\\Rightarrow 5x - y =240[/tex]

Solving the two equations in two variable, we get:

[tex]x - 3y = 20\\5x - y =240\\\text{Multiplying first equation by 5}\\5x - 15y = 100\\\text{Subtracting the equations}\\5x - 15y-(5x-y) = 100-240\\-14y = -140\\y = 10\\ x - 3(10) = 20\\x = 20 + 30\\x =50[/tex]

The value of x is 50 and y is 10.

Answer:

A. It has infinitely many solutions

Step-by-step explanation:

I took the Solving Linear Systems By Substitution Quiz on Edge

The given system of equations 3x-2y=12 and 6x-4y=24 has no solution.

As per the question, we have to determine the solution to the following system of equations, 3x-2y=12 and 6x-4y=24

The equation is the relationship between variables and is represented as y =ax +b is an example of a polynomial equation.

Here,
Given a system of the equation,
3x-2y = 12
x = 12 + 2y / 3 - - - - -(1)
6x - 4y =24 - - - - -(2)
Put the value of equation 1 in the equation
6 (12 + 2y / 3) - 4y = 24
2 (12 + 2y) - 4y = 24
24 +4y - 4y = 24
24 = 24

Thus, the given system of equations 3x-2y=12 and 6x-4y=24 has no solution.

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The equation 5.5 - x = -4.5 - x has no solution. After cancelling out the variable x, we are left with 5.5 = -4.5, which is a contradiction.

To solve the equation 5.5 - x = -4.5 - x, we first notice that the variable x is present on both sides of the equation. We can simply subtract or add x to both sides to cancel it out. This will give us an equation without variables:

5.5 - x + x = -4.5 - x + x

5.5 = -4.5

This equation suggests that 5.5 is equal to -4.5, which is not true. Therefore, we can conclude that there is no solution to the equation since the two sides of the equation do not balance.

Moreover, this type of equation is an example of a contradiction, meaning that it presents a statement that is inherently false regardless of the value of x. As there is no value of x that can make the equation true, we say that the equation has no solution.

Final answer:

The equation 5.5 - x = -4.5 - x simplifies to 5.5 = -4.5 when the x terms are cancelled out. Since 5.5 does not equal -4.5, the equation has no solutions.

Explanation:

To solve the equation 5.5 - x = -4.5 - x, we can first try to simplify it by adding or subtracting the same value from both sides. This method is based on the principle that whatever you do to one side of the equation, you must do to the other to maintain balance.

In this case, if we add x to both sides of the equation, the x terms will cancel out on both sides, which leaves us with 5.5 = -4.5. Here, we notice that both sides of the equation represent constant values and no longer contain the variable x.

Therefore, since 5.5 and -4.5 are not equal, we can conclude that there is no value of x that can satisfy this equation. This equation is a contradiction, which means there are no solutions.

The distance from a to b if the units of the coordinated system are meters is 10m.

A line that has two endpoints and a fixed measurement is called a line segment.

It is given that point a is located at coordinates (5, 3) and point b is located at coordinates (-3, 9)

D = √[(x-p)² + (y-q)²]  

Substituting the points we get;

D = √[(-3 - 5)² + (9 - 3)²]  

D = √[(-8)² + (6)²]  

D = √[(64) + (36)]  

D = √100

D = 10

Hence, the distance from a to b if the units of the coordinated system are meters is 10 m.

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Final answer:

The distance between point A (5, 3) and point B (-3, 9) is calculated using the distance formula, resulting in a distance of 10 meters.

Explanation:

The question is asking for the distance between two points in a coordinate system. To find the distance between point A (5, 3) and point B (-3, 9), we can use the distance formula which is derived from Pythagorean theorem. The distance d between two points (x1, y1) and (x2, y2) is given by:

d = √((x2 - x1)² + (y2 - y1)²)

For point A and point B, we substitute the coordinates into the formula:

d = √((-3 - 5)² + (9 - 3)²)
= √(64 + 36)
= √100
= 10 meters

Therefore, the distance from A to B is 10 meters.

The graph shows the costs of purchasing two types of flowers.

Select some value [tex]x_0[/tex] for x and draw vertical line

[tex]x=x_0.[/tex]

This line intersects the graphs of Flower A and the graph of Flower B in points A and B, respectively. The point A lies on this vertical line higher than the point B. This means that y-coordinate of  point A is greater than y-coordinate of point B.

If y-coordinate of  point A is greater than y-coordinate of point B, then Flower A is more expensive than Flower B (or Flower B is less expensive than Flower A).

Answer: correct choice is B

The mathematical expression is,

⇒ 2x + 6 = - 24

And, The value of number = - 15

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

''The product of 2, and a number increased by 6, is -24''

Now,

Since, The algebraic expression is,

''The product of 2, and a number increased by 6, is -24''

Let a number = x

Hence, We can formulate;

⇒ 2x + 6 = - 24

Solve for x as;

⇒ 2x = - 24 - 6

⇒ 2x = - 30

⇒ x = - 15

Thus, The value of number = - 15

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y =-2x-4

x = 0, y = -2(0)-4 = -4

x=1, y = -2(1) -4 =-2-4 = -6

x=2, y = -2(2)-4 = -4-4 =-8

x=3, y = -2(3) - 4 = -6-4 =-10

Answer is B

Answer:

B

Step-by-step explanation:

The required trinomial expression that is equivalent to  (2x+5)(3x-2) is 6x² + 11x - 10.

According to the question, we have to determine the trinomial expression that is equivalent to the  (2x+5)(3x-2).

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the quadratic equation, cubic equation, etc. ax+b is a polynomial.

Here,
Given expression in the question,
=  (2x+5)(3x-2)
Following the distributive property
= 2x (3x - 2) + 5 (3x - 2)
= 6x² - 4x + 15x - 10
= 6x² - 11x - 10

Thus, the required trinomial expression that is equivalent to  (2x+5)(3x-2) is 6x² + 11x - 10.

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Final answer:

The trinomial expression equivalent to (2x+5)(3x-2) is calculated using the FOIL method, resulting in 6x² + 11x - 10.

Explanation:

To write a trinomial expression equivalent to the product of two binomials, (2x+5)(3x-2), we perform the multiplication by using the distributive property (also known as the FOIL method).

Multiply the first terms: 2x × 3x = 6x²

Multiply the outside terms: 2x × (-2) = -4x

Multiply the inside terms: 5 × 3x = 15x

Multiply the last terms: 5 × (-2) = -10

Combine like terms:

6x² + (15x - 4x) - 10 = 6x² + 11x - 10

The trinomial expression equivalent to (2x+5)(3x-2) is 6x² + 11x - 10.

Answer:

[tex] 5.15\times 3.16=16.2740[/tex]

Step-by-step explanation:

Maria wants to find the product of [tex]5\frac{3}{20}[/tex] multiplied by[tex]3\frac{4}{25}[/tex]

First we change mixed fraction to fraction and then change into decimal.

#First fraction:  

[tex]5\frac{3}{20}\Rightarrow \dfrac{103}{20}[/tex]

[tex]\dfrac{103}{20}\Rightarrow \dfrac{103\times 5}{20\times 5}=5.15[/tex]

#Secondfraction:  

[tex]3\frac{4}{25}\Rightarrow \dfrac{79}{25}[/tex]

[tex]\dfrac{79}{25}\Rightarrow \dfrac{79\times 4}{25\times 4}=3.16[/tex]

Now we find the product of both decimal

[tex]\Rightarrow 5.15\times 3.16[/tex]

Using calculator product of 515 and 316 = 162740

Both number has decimal digits two

So, total number of decimal digits is 4

In multiply result write decimal before 4 digits from right.

Therefore,

[tex] 5.15\times 3.16=16.2740[/tex]

Answer: dy/dx = y^3 - 12x^2 - 2yx / x(x-3y^2)

Step-by-step explanation: Differentiate each term with respect to x, then solve for y.

I hope this helps you out!