Stretch Your Thinking Ann arranges her marbles in groups, with 8 marbles in each group. She writes the fraction 5/8 to show the fraction of marbles in each group that is red. What equivalent fraction names the fraction of marbles in 6 groups that are Red? Explain.

Answer:

Both equations has different slope , so the system of equation have one unique solution.

Step-by-step explanation:

[tex]2x+y=4[/tex] , [tex]2y=6-2x[/tex]

To determine that the system of equation has unique solution, we need to find out the slope.

To find slope, we write the equation in the form of y=mx+b

Where m  is the slope and b is the y intercept

[tex]2x+y=4[/tex]

Subtract 2x on both sides

[tex]y=-2x+4[/tex]

here, m= -2 is the slope

[tex]2y=6-2x[/tex]

Divide both sides by 2

[tex]y=3-x[/tex]

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

Slope m = -1

Both equations has different slope , so the system of equation have one unique solution.

The system of equations x + 3y = 0 and 9y = -3x is actually the same line, therefore there are an infinite number of solutions since the equations represent the same line with a slope of -3 and y-intercept of 0.

The student has given the linear equations x + 3y = 0 and 9y = -3x. To determine how many solutions this system has, we need to normalize the second equation. If we divide the second equation by 9, we get y = -\frac{1}{3}x, which, when reorganized, becomes x + 3y = 0. These two equations are actually the same line. In other words, every solution of the first equation is also a solution of the second equation, and vice versa.

Therefore, the system of equations has an infinite number of solutions because the lines represented by these equations overlap; they are the same line. This is an example of a dependent system where both equations represent the same relationship between x and y. In graph terms, the slope (m) of both lines is -3, and their y-intercept (b) is 0. This is evident from both the algebraic expression of the equations and from their graphical representation.

The system of equations has one solution.

The given system of equations is:

x + 3y = 0

9y = -3x

To solve this system, we can use the second equation to express y in terms of x.

Dividing both sides of the second equation by 9, we get:

y = (-3/9)x

Simplifying, we have:

y = (-1/3)x

We can observe that the equations of the lines represented by both equations in the system have the same slope, which is -1/3.

Since the lines have the same slope but different y-intercepts (0 for the first equation and 0 for the second equation), they will intersect at exactly one point, resulting in one solution for the system of equations.

Answer:

[tex][2, 7][/tex]

Step-by-step explanation:

5 + p = 2p + 3

- 2p - 2p

______________

5 - p = 3

-3 - 3

________

2 - p = 0

-2 - 2

________

-p = -2

2 = p [Plug this back into both equations above to get the n-term of 7]; 7 = p

I am joyous to assist you anytime.

Answer:

cos 41°

Step-by-step explanation:

this is the correct answer, not the one above.

if entered on the calculator (texas instruments TI-30X2S)

sin (49)= 0.75470958

2nd → cos → 2nd → (-)

which would look like this→ cos-1(0.75470958)

answer= cos 41

Answer:

Step-by-step explanation:

A tube has a radius of a 9 inches and a height of 7 inches. What's its approximate volume

Answer:

Your Answer will be

-4/5   ,   -1/14    , 7/9

GradPoint Answer

Answer:

The measure of AC is 41°

Step-by-step explanation:

Given : ∠ABC = (4x-3.5)°

            Arc AC = (4x+17)°

An inscribed angle: An angle with its vertex on the circle and whose sides are chords.

The intercepted arc : The arc that is inside the inscribed angle and whose endpoints are on the angle.

The Inscribed Angle Theorem : The measure of an inscribed angle is half the measure of its intercepted arc.

Uisng the theorem

[tex]\angle{ABC}=\frac{1}{2} \text{arc(AC)}[/tex]

[tex](4x-3.5)^{\circ}=\frac{1}{2} (4x+17)^{\circ}[/tex]

[tex]2*(4x-3.5)^{\circ}= (4x+17)^{\circ}[/tex]

[tex]8x-7= 4x+17[/tex]

[tex]4x=24[/tex]

[tex]x=\frac{24}{4}[/tex]

[tex]x=6[/tex]

So, Arc AC = (4x+17)° = (4*6+17)° = (24+17)° = 41°

Hence the measure of AC is 41°

Let x and y represent the number of grandstand and bleacher tickets sold respectively.

We know that the total number of tickets sold is 5716. Therefore, we will get the equation:

x+y = 5716

Therefore, x=5716-y.............................(Equation 1)

Now, we also know that the total value of tickets sold is $3416.90 or 341690 Cents.

We also know that the price of one grandstand ticket is 65 Cents. Thus, the price of x grandstand tickets will be 65x cents.

Likewise, since the price of one bleacher ticket is 40 cents, the price of y bleacher tickets will be 40y cents.

The information presented above gives us:

65x+40y=341690..........................(Equation 2)

Substituting x from (Equation 1) to (Equation 2) we get:

[tex] 65(5716-y)+40y=341690 [/tex]

Let us solve the above equation for y.

[tex] 65\times 5716-65y+40y=341690 [/tex]

[tex] 371540-25y=341690 [/tex]

[tex] \therefore 25y=371540-341690=29850 [/tex]

[tex] y=1194 [/tex]

Therefore, the total number of bleacher tickets sold was 1194.

The quantity of fabrics the machine can produce in 1 hour given the ratio is 60 yards

let

x = quantity of fabrics produced in 1hr

conversion of time

Ratio of fabrics to time taken

6 : 2 = x : 60 minutes

6/2 = x / 60

6 × 60 = 2 × x

120 = 2x

x = 120/2

x = 60 yards

Therefore, the quantity of fabrics the machine can produce in 1 hour given the ratio is 60 yards

Learn more about ratio:

https://brainly.com/question/2328454

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Hear hear! For I have brought you the correct answer... (I took a "snip" of it so you can't see the entire graph but you can see the whole answer.)

By plotting the lines 2x - y = 4 and x - y = -2 using a graphing tool or on graph paper.

To graph these lines, you can start by rearranging them into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

For 2x - y = 4:

-y = -2x + 4

y = 2x - 4

This equation has a slope of 2 and a y-intercept of -4.

For x - y = -2:

-y = -x - 2

y = x + 2

This equation has a slope of 1 and a y-intercept of 2.

Now, you can graph these lines on a coordinate plane by plotting the y-intercepts and using the slopes to find additional points.

Once you have the two lines graphed, their point of intersection represents the solution to the system of equations.

For similar question on slope-intercept form.

https://brainly.com/question/31071238

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To find the number of 1/3 cups of flour Chris needs, we need to divide the total amount of flour needed by the amount that can be measured with the 1/3 cup measuring cup. In this case, Chris needs 28 1/2 cups of flour.

To find the number of 1/3 cups of flour Chris needs, we need to divide the total amount of flour needed (3 1/2 cups) by the amount that can be measured with the 1/3 cup measuring cup.

To do this, we convert the whole number 3 to thirds by multiplying by 3, which gives us 9 thirds. Then we add the 1/2 cup, which is equivalent to 3/6 or 6/12. So, the total amount in thirds is 9 + 6/12 = 9 1/2 thirds.

Now, we divide the total number of thirds by the number of thirds in one 1/3 cup.

9 1/2 thirds ÷ 1/3 third/cup = (9 1/2) ÷ (1/3) = (19/2) ÷ (1/3) = 19/2 × 3/1 = 19/2 × 3/1 = 57/2 = 28 1/2 cups.