Ethan has $1.25 in dimes, nickels, and pennies. He has twice as many dimes as pennies, and the number of nickels is one less thank the number of pennies. How many dimes, nickels, and pennies does he have?

Answer:

24:2=36:3=66:5.5=108:9=180:15

Step-by-step explanation:

24:2=36:3=66:5.5=108:9=180:15

The complete statement is -

24 : 2 = 36 : 3 = 66 : 5.5 = 108 : 9  = 180 : 15

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Ratio is a quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

We have the following statement -

24 : 2 = _ : 3 = _ : 5.5 = 108: _ = _ : 15

We have -

24 : 2 = x : 3 = y : 5.5 = 108 : z  = k : 15

We can solve it partly -

24/2 = x/3

x = (24 x 3)/2

x = 36

Now, we have -

36/3 = y/5.5

(36 x 5.5)/3 = y

y = 12 x 5.5

y = 66

Moving further -

66/5.5 = 108/z

z = (108 x 5.5)/66

z = 9

Finally -

(108/9) = (k/15)

k = (108 x 15)/9

k = 12 x 15

k = 180

Therefore, the complete statement is -

24 : 2 = 36 : 3 = 66 : 5.5 = 108 : 9  = 180 : 15

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Given

∠MQL=180°

∠XQR=180°

Hence ∠MQL=∠XQR

(We know that ∠MQL is the sum of ∠MQR and ∠RQL

and ∠XQR is the sum of ∠XQM and ∠MQR)

lets plug in these in our equation

∠MQL=∠XQR

∠MQR + ∠RQL = ∠XQM + ∠MQR

We can cancel out ∠MQR

hence ∠RQL = ∠XQM

hence we can infer that the opposite angles of intersecting lines are equal

similarly

∠MQR = ∠XQL

which is

125-10b = -5b+115

Hence the right option is A)

Answer: These three planes are consistent and independent.

Explanation:

Since,  if the system of planes has a solution then it is  called Consistent, While, if it does not have any solution then it is called inconsistent.

Further, If the consistent system has infinite solution then it is dependent but if it has only a unique solution then it is called independent.

Here, given equations of planes are

12x+5y-3z=36           -------(1 )

x-2y+4z=3                 -------(2)

9x-10y+5z=27          -------(3)

From equation (1), 3z=12x+5y-36⇒z=4x+5y/3-12   ------(4)

after putting this value in equation (2) and (3), we will get two equation in variables x and y

So, x-2y+4(4x+5y/3-12)=3 ⇒x-2y+16x+20y/3-48=3⇒3x-6y+48x+20y-144=9⇒51x+14y=153   --------(5)

And, 9x-10y+5(4x+5y/3-12)=27⇒ 9x-10y+20x+25y/3-60=27⇒ 27x-30y+60x+25y-180=81⇒87x-5y=261   --------(6)

after solving equation equation (5) and (6) we will get x=3 and y=0

substituting these values in equation (4) we will get z=0

Thus the solution of these three plane (1), (2) and (3) is x=3, y=0 and z=o

Which is the unique solution, Thus the given planes are consistent and independent.

The given system of equations is consistent and independent so, [tex]\fbox{\begin\\\ \bf option (3)\\\end{minispace}}[/tex] is correct.

Further explanation:

A system of equations is said to be a consistent system if the solution exists and if the solution does not exist then it is an inconsistent system.  

If a consistent system has a unique solution then it is an independent system of equations but if the number of solutions is infinite then it is a dependent system of equations.

Label the given equations as shown below:

[tex]\boxed{x-2y+4z=3}[/tex]               …… (1)

[tex]\boxed{12x+5y-3z=36}[/tex]         …… (2)

[tex]\boxed{9x-10y+5z=27}[/tex]         …… (3)

The augmented matrix for the above equations is, as follows:

[tex]\left[\begin{array}{ccc}1&-2&4\\12&5&-3\\9&-10&5\end{array}\Biggm\vert\begin{array}{c}3\\26\\27\end{array}\right][/tex]

Apply row transformation [tex]R_{2}\rightarrow R_{2}-12R_{1}[/tex] and [tex]R_{3}\rightarrow R_{3}-9R_{1}[/tex] as,

[tex]\left[\begin{array}{ccc}1&-2&4\\0&29&-51\\0&8&-31\end{array}\Biggm\vert\begin{array}{c}3\\0\\0\end{array}\right][/tex]  

Now, apply row transformation [tex]R_{2}\rightarrow R_{2}-4R_{3}[/tex] and [tex]R_{3}\rightarrow R_{3}-3R_{2}[/tex] as,

[tex]\left[\begin{array}{ccc}1&-2&4\\0&-3&73\\0&-1&188\end{array}\Biggm\vert\begin{array}{c}3\\0\\0\end{array}\right][/tex]  

Now, apply row transformations [tex]R_{2}\rightarrow -R_{2}+2R_{3}[/tex] and [tex]R_{3}\rightarrow R_{3}+R_{2}[/tex] as,

[tex]\left[\begin{array}{ccc}1&-2&4\\0&1&303\\0&0&491\end{array}\Biggm\vert\begin{array}{c}3\\0\\0\end{array}\right][/tex]  

The equations obtained from the above augmented matrix are,

[tex]\begin{aligned}x-2y+4z&=3\\y+303z&=0\\491z&=0\end{aligned}[/tex]  

The first equation is simplified to obtain the value of z as,

[tex]\begin{aligned}491z&=0\\z&=0\end{aligned}[/tex]  

Substitute [tex]0[/tex] for [tex]z[/tex] in the equation [tex]y+303z=0[/tex]  to obtain the value of [tex]y[/tex] as,

[tex]\begin{aligned}y+(303\cdot0)&=0\\y&=0\end{aligned}[/tex]

Now, substitute [tex]0[/tex] for [tex]z[/tex] and [tex]0[/tex] for [tex]y[/tex] in the equation [tex]x-2y+4z=3[/tex] to obtain the value of [tex]x[/tex] as,

[tex]\begin{aligned}x-(2\cdot0)+(4\cdot0)&=3\\x&=3\end{aligned}[/tex]  

Therefore, the value of [tex]x[/tex] is [tex]3[/tex], the value of [tex]y[/tex] is [tex]0[/tex] and the value of [tex]z[/tex] is [tex]0[/tex] and the system has a unique solution.

Thus, the given system of equations is consistent and independent.

Option (1)

Here, the first option is inconsistent and dependent.

There exists a solution of the given system of equations so it is consistent.

Therefore, option (1) is incorrect.

Option (2)

Here, the second option is consistent and dependent.

There exists a solution of the given system of equations so it is consistent.

Also, the solution is unique therefore the system of equations is independent.

Therefore, option (2) is incorrect.

Option (3)

Here, the third option is consistent and independent.

There exists a solution of the given system of equations so it is consistent.

Also, the solution is unique therefore the system of equations is independent.

Therefore, option (3) is correct.

Option (4)

Here, the fourth option is inconsistent and independent.

There exists a solution of the given system of equations so it is consistent.

Therefore, option (4) is incorrect.

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Answer details

Grade: High school

Subject: Mathematics

Chapter: System of linear equations

Keywords: Equations, unique solution, independent, dependent, consistent, inconsistent, infinite solutions, homogeneous equation, non- homogeneous equation, determinant.

Answer:

The given statement is true.

Step-by-step explanation:

Measurement is the use of numbers according to a standard.

This statement is true.

Measurements should always be taken with respect to a fixed standard.

For example- If we are weighing something, the measurements should be in pounds or kilograms or ounces etc. Otherwise, we can never know the weight of anything.

Answer: If drew drew a pair of lines and draw the segment between them, in a way that the segment is delimited by both lines, then:

If two lines are parallel, then they will never overlap each other, and if you draw a segment between them, then the segment will have two endpoints (one at each intersection with the lines)

So the correct answer is that the parallel lines extend infinitely in both directions, and the line segment has two endpoints.

Alexa exchanges 27 stamps for 8 sugar cubes. To find the length of a sugar cube, we calculate the volume of each cube and then find the cube root of the total volume.

In this scenario, Alexa buys 27 stamps, each with an area of 1 square unit. She exchanges them for 8 sugar cubes, whose total volume is equal to the total area of the stamps. To find the length of a single sugar cube, we need to calculate the volume of each sugar cube and then find the length of one side.

Therefore, the length of a cube of sugar is approximately 3 units.

The correct answer is C. 39.375 square feet.

The student's question pertains to finding the area of the actual banner when a scale transformation is applied to a triangular design. To calculate the area of the actual banner, we need to scale the base and the height of the triangle from the drawing size to the actual size and then use the formula for the area of a triangle.

First, we convert the measurements of the base and the height from inches to feet using the given scale of 1 inch = 1.5 feet:

We then apply the area formula for a triangle which is Area = (base × height) / 2:

Area = (7.5 feet × 10.5 feet) / 2 = 39.375 square feet

Therefore, the correct answer is C. 39.375 square feet.

Answer:

Step-by-step explanation:

Since it is given that when two lines intersect, the angle on the top left is 53° and 127°, thus they both form supplementary angles  as the sum of both angles that is 53+127=180°.

Also, from the given information, the angle on the top is 34° and on the bottom is 56°, they both form a complementary angle pair, a sthe sum of both the two angles is 90° as 56+34=90°.

Also, the angle on the top left is =67° and the angle on the bottom right =67°, they both form vertical pair angles as both the angles are vertically opposite to each other.

t = (C - 3*A)/B + 3

i dont know if its correct but hope it helps!

The radius is approximately 1.9 in and the circumference is approximately 11.94 in, both rounded to the nearest hundredth.

We have,

If we let d be the diameter of a circle, then the radius of the circle, r, is half of the diameter.

Therefore, we can find the radius of the circle by dividing the diameter by 2:

r = d/2

In this problem,

d ≈ 3.8 in, so we have:

r = 3.8/2 = 1.9 in

To find the circumference of the circle, we can use the formula:

C = 2πr

where π is approximately equal to 3.14 and r is the radius we just found. Substituting in the values, we get:

C = 2 x 3.14 x 1.9 ≈ 11.94 in

Therefore,

The radius is approximately 1.9 in and the circumference is approximately 11.94 in, both rounded to the nearest hundredth.

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Answer:

  (3, 4) and (5, 12)

Step-by-step explanation:

The points where the two curves intersect are the solutions to the system of equations:

  (3, 4) and (5, 12)

Answer:

Step-by-step explanation:

Final answer:

The expression 4xy + xy - 7x + x simplifies to 5xy - 6x by combining like terms, specifically combining 4xy and xy to get 5xy, and -7x and x to get -6x.

Explanation:

The expression 4xy + xy - 7x + x can be simplified by combining like terms. The terms 4xy and xy are like terms, as they both have the same variables x and y to the same power. Similarly, the terms -7x and x are like terms because they both contain the variable x to the same power. To simplify, we combine 4xy and xy to get 5xy and combine -7x and x to get -6x. Therefore, the simplified expression is 5xy - 6x.

Steps involved:

The expression is 4xy + xy - 7x + x.

Combine like terms: 4xy + xy = 5xy

Combine like terms: -7x + x = -6x

Therefore, the simplified expression is 5xy - 6x.