How many solutions does this linear system have?



y = y equals StartFraction 2 over 3 EndFraction x plus 2.x+ 2



6x – 4y = –10



one solution: (–0.6, –1.6)


one solution: (–0.6, 1.6)


no solution


infinite number of solutions

Armando use the wrong demensions for the triangular prism?Answer:

Step-by-step explanation:

The mistake is Armando used the wrong dimensions for the triangular prism, the correct option is C.

Suppose the base of the pyramid has length = l units, and width = w units.

Suppose that the height of the pyramid is of h units, then:

[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex]

is the volume of that pyramid.

The base is a rectangle with length = L units, and width = W units, so its area is:

[tex]b = l \times w\: \rm unit^2[/tex]

We are given that;

Height of pyramid= 6in

Dimensions of prism= 8*18*5

Now,

To find the area of the triangular base, he should have used:

A=21​bh

A=21​(18)(6)

A=54

Therefore, by the rectangular prism the answer will be Armando used the wrong dimensions for the triangular prism.

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Answer:

D

Step-by-step explanation:

The x-coordinate of the solution is -2 .

7+2+5=????? will mark brainest 14

The expression that can be used to find the volume of the rectangular prism is 20825 cm³.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

The formula for the volume of a rectangular prism is given by:

V = A x h

where A is the area of the base and h is the height of the prism.

In this case,

The area of the base is given as 245 cm^2 and the height is given as 85 cm.

Therefore, we can substitute these values into the formula to get:

V = 245 x 85

Multiplying these values together, we get:

V = 20825 cm³

Therefore,

The expression that can be used to find the volume of the rectangular prism is 20825 cm³.

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Answer:

4.5

Step-by-step explanation:

2.18 x 7.31 = 15.9358

15.9 + 4.92 = 20.85

20.85 = 4.5

4.5 , hope this helps! and have a great day

-Dhruva;)

1. outcome

2. probability

3. equally likely

4. likely

5. certain

6. unlikely

7. impossible

Hope this helps! If you have any more questions or need further clarification then please comment down below or message me! Good luck!

Option C, [tex]y = 3x^2[/tex], is the equation that could represent the parabola with a vertex at (0, 0).

To determine which of the given equations could represent the parabola with a vertex at (0, 0), we need to consider the standard form of a parabolic equation: [tex]y = ax^2[/tex]

In this standard form, 'a' is a constant that determines the shape and orientation of the parabola. For a parabola with a vertex at (0, 0), the equation will be of the form [tex]y = ax^2[/tex].

Let's examine each option:

A. [tex]x = 3y^2[/tex]: This equation is not in the standard form [tex]y = ax^2.[/tex] It is a different type of equation and does not represent a parabola with a vertex at (0, 0).

B. x = -3y: Similarly, this equation is not in the standard form [tex]y = ax^2[/tex]. It represents a linear relationship between x and y, not a parabola.

C. [tex]y = 3x^2[/tex]: This equation is in the standard form [tex]y = ax^2[/tex], where a = 3. It represents a parabola with a vertex at (0, 0), so it could be the equation of the parabola in question.

D. y = -3: This equation is not in the standard form [tex]y = ax^2[/tex]. It represents a horizontal line with a constant value of -3, not a parabola.

Based on the analysis, Option C, [tex]y = 3x^2[/tex], is the equation that could represent the parabola with a vertex at (0, 0) in the standard form.

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Let x represent number of redwood trees and y represent number of spruce trees.

We have been given that a park ranger bought 12 trees. We can represent this information in an equation as:

[tex]x+y=12...(1)[/tex]

[tex]y=12-x...(1)[/tex]

We are also told that redwood trees cost $24 each, so cost of x redwood trees would be [tex]24x[/tex].

Each spruce tree costs $16, so cost of y spruce trees would be [tex]16y[/tex].

Since the park ranger spent $208 on trees, so we can represent this information in an equation as:

[tex]24x+16y=208...(2)[/tex]

Upon substituting equation (1) in equation (2), we will get:

[tex]24x+16(12-x)=208[/tex]

[tex]24x+192-16x=208[/tex]

[tex]8x+192=208[/tex]

[tex]8x+192-192=208-192[/tex]

[tex]8x=16[/tex]

[tex]\frac{8x}{8}=\frac{16}{8}[/tex]

[tex]x=2[/tex]

Therefore, the park ranger bought 2 redwood trees.

Upon substituting [tex]x=2[/tex] in equation (1), we will get:

[tex]y=12-x\Rightarrow 12-2=10[/tex]

Therefore, the park ranger bought 10 spruce trees.

The park ranger bought 2 redwood trees and 10 spruce trees.

To solve this problem, we can set up a system of equations based on the given information:

We have two pieces of key information:

This gives us two equations:

We can solve this system using substitution or elimination. Let's use substitution:

Therefore, the park ranger bought 2 redwood trees and 10 spruce trees.

Answer:

24.39262183530094+33.33166662499792 is the answer

Step-by-step explanation:

57.72428846029885

therefore the first digit is 5

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Answer:

57.7242884603 its 5

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

First you would need to look at the line at the right. It has 2 parts, 3 and 2. When added you get 5.

As when you look at the other side it only has 2 and x.

To make it simple 5 - 1 = 4.

That is your final answer.

Hope this helps!

Answer:

x = 4

Step-by-step explanation:

In triangle BAC, DE || AC.

Therefore, by basic proportionality theorem:

[tex] \frac{x + 2}{x} = \frac{3}{2} \\ 2(x + 2) = 3x \\ 2x + 4 = 3x \\ 4 = 3x - 2x \\ 4 = x \\ x = 4[/tex]

Answer:

Point R

Step-by-step explanation:

Go back 12 points

Answer:

Point R

Step-by-step explanation:

Count back in points and you will figure it out

Answer:

The maximum profit of $  10277.32____ can be made when the selling price of the dog food is set to $ _34___ per bag.

Step-by-step explanation:

Profit = Revenue - Cost

P(x) = R(x) -C(x)

       = -31.72x^2 + 2,030x -( -126.96x + 26,391)

Distribute the minus sign

       = -31.72x^2 + 2,030x+126.96x - 26,391

 Combine like terms

      =   -31.72 x^2 + 2156.96 x - 26391

This is a parabola.  It is facing downwards.  The maximum profits is at the vertex ( where the max is)

vertex = h = -b/2a = -(2156.96)/(2*-31.72) = -2156.96/-63.44=34

Evaluate P(x) at x=34 to determine the profit

P(34) =  -31.72 (34)^2 + 2156.96 (34) - 26391

          -36668.32+73336.64-26391

          10277.32

The maximum profit of $10,243.32 can be made when the selling price of the dog food is set to $947.17. per bag.

1. Define the profit function: Profit [tex](\( P(x) \))[/tex] is calculated by subtracting the cost function [tex](\( C(x) \))[/tex] from the revenue function [tex](\( R(x) \)):[/tex]

[tex]\[ P(x) = R(x) - C(x) \][/tex]

2. Substitute the given revenue and cost functions:

[tex]\[ R(x) = -31.72x^2 + 2,030x \][/tex]

[tex]\[ C(x) = -126.96x + 26,391 \][/tex]

3. Plug in the revenue and cost functions into the profit function:

[tex]\[ P(x) = (-31.72x^2 + 2,030x) - (-126.96x + 26,391) \][/tex]

[tex]\[ P(x) = -31.72x^2 + 2,156.96x - 26,391 \][/tex]

4. Find the x-coordinate of the vertex of the profit function:

  The x-coordinate of the vertex is given by:

[tex]\[ x = \frac{-b}{2a} \][/tex]

  where [tex]\( a = -31.72 \) and \( b = 2,156.96 \).[/tex]

[tex]\[ x = \frac{-2,156.96}{2*(-31.72)} \][/tex]

  x ≈ 34

5. Calculate the maximum profit:

  Substitute x ≈ 34  into the profit function:

P(34) ≈ [tex]-31.72(34)^2 + 2,156.96(34) - 26,391[/tex]

P(34) ≈ 10,243.32

6. Determine the selling price per bag that maximizes profit:

  Plug x ≈ 34 into the revenue function to find the corresponding revenue:

[tex]\[ R(34)[/tex] ≈ [tex]-31.72(34)^2 + 2,030(34)[/tex]

[tex]\[ R(34)[/tex] ≈ [tex]32,183.68[/tex]

  Divide the revenue by the quantity x ≈ 34  to find the selling price per bag:

[tex]\[ \text{Selling price per bag}[/tex] ≈ [tex]\frac{32,183.68}{34}[/tex] ≈ [tex]947.17[/tex]

So, the maximum profit is approximately $10,243.32, and the selling price per bag that maximizes profit is approximately $947.17.

Answer:

V≈302ft^3

Step-by-step explanation:

The equation for finding volume of a cone with slant height and radius is 1/3πr^2√l^2-r^2 input the values and solve, then round to the nearest cubic foot and you get 302

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The fraction 3/2 and square root of 2 are not equivalent because their decimal approximations (1.5 and about 1.41 respectively) are not the same.

To determine if a fraction like 3/2 is equal to the square root of 2, we would need to compare their decimal values.

First, divide 3 by 2 to get the decimal value for the fraction, which is 1.5.

For the square root of 2, we can use a calculator and find that its approximate decimal value is 1.41.

Therefore, since 1.5 is not equal to 1.41, the fraction 3/2 is not equivalent to the square root of 2.

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The fraction 3/2 is not equal to the square root of 2. By comparing the values directly or using fractional exponents, we can see that squaring 3/2 gives us 9/4, which is not equal to 2, and numerically the square root of 2 is approximately 1.414.

To determine if the fraction 3/2 is equal to the square root of 2, we can compare them directly or convert them into the same format. Recall that fractional exponents serve as another way to represent roots. Specifically, an exponent of 1/2 equates to taking the square root of a number. Thus, [tex](3/2)^{2}[/tex] would equal 3/2 multiplied by itself, which is 9/4, and that is not equal to 2. Therefore, 3/2 is not the square root of 2. We can also numerically evaluate the square root of 2, which is approximately 1.414, and see that it does not equal 3/2, which is 1.5.

Another consideration is that the square root of any number x can be expressed as [tex]x^{1/2}[/tex]. For instance, [tex](\sqrt{2})^2[/tex] = 2 because [tex](2^{1/2})^2[/tex] equals [tex]2^{1/2 * 2}[/tex] = 2. When we do this with 3/2, we would have [tex](3/2)^{1/2} * (3/2)^{1/2}[/tex] = 3/2, which does not satisfy the equation for the square root of 2. Therefore, 3/2 is not equal to the square root of 2.

Answer:

A

Step-by-step explanation:

Focus on what the question is telling you, as it's given to you in the question. It's saying five times, which means "×5" the number of person B, so it'll always be 5 times quicker, since they're breathing more times in a certain period of time than person B.

Hopefully this helped!

Person A is breathing five times as fast as person B. Therefore, the period of the graph for person A is 5 times shorter than the period of the graph for person B.

In this scenario, person A is breathing five times as fast as person B. The period of a graph represents the time it takes for one complete cycle. Since person A is breathing faster, the period of their graph will be shorter than the period of person B's graph. So, the correct statement is:

The period of the graph for person A is 5 times shorter than the period of the graph for person B.

Answer:

3/8 = 9/24

because

3/8 = 0.375

and

9/24 = 0.375

Answer:

9/24.

Step-by-step explanation:

We can see this by finding how 9/24 is simply 3/8 but not simplified down all the way. Notice how when you try simplifying the others, they are either unable to be simplified further or simplify into something else.

2/7--> unable to simplify further.

8/3--> unable to simplify further.

9/24--> simplifies to 3/8.

5/10--> simplifies to 1/2.

Answer:

120 minutes

Step-by-step explanation:

15 x 8 = 120

40 x 3 = 120

The Number of hours passed for both buses to arrive at the same time is the value of the least common multiple of the stop made by each bus. Hence, 120 minutes will pass before the buses arrive at the same time.

Bus route A = 15 minutes

Bus route B = 40 minutes

Multiples of :

The least multiple common to both 15 and 40 is 120.

Therefore, 120 minutes will pass before both buses arrive at the same time.

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Answer:

[tex]\frac{9}{5}[/tex] miles.

Step-by-step explanation:

This problem requires you to multiply the length of Laura's walk by 3 to solve for Isaiah's walk to school.

[tex]\frac{3}{5}[/tex]×[tex]\frac{3}{1}[/tex]=  [tex]\frac{9}{5}[/tex] miles.

Answer:

Its 25.

Step-by-step explanation:

Answer: +25

Step-by-step-Explanation: Absolute value means distance from zero on a number line.

So for the absolute value of -25, it's important to understand

that -25 is 25 units from zero on a number line.

So the absolute value of -25 is +25.

Whenever you are asked to find the absolute value of a negative number, just think about finding the positive version of that number.

Answer:

I think it is b but let me check my answer

Step-by-step explanation:

Answer:

A. (-6,0) I got it right

Step-by-step explanation:

Answer:

y= 2x + 1

Step-by-step explanation:

We are asked to write an equation of that line that passes through points (3, 7) and (5, 11).

First of all, we will find slope of our given line using the coordinates of given points as:

Now, we will write our given equation in slope-intercept form , where m represents slope and b represents y-intercept.

Let us find the y-intercept using coordinates of point (3,7) and slope as:

Therefore, our required equation in slope-intercept form would be.

Answer:

The correct answer is B.

Answer:

B) 7/3

Step-by-step explanation:

To find the slope of a line using a graph, locate two points. In this example, the points are (0, -2) and (3, 5).

Then, find the distance between the two points. To do so in this example, find the difference between 0 and 3, and -2 and 5.

3 - 0 = 3

5 - (-2) = 7

Since we're dealing with slope, the answer will be in y/x form. 7 is the distance between the y-coordinates and 3 is the difference between the x-coordinates, the answer is 7/3.

Answer: 7/3

Step-by-step explanation:

Count how many spaces you are going up from the first point to the second point and how many spaces over to the point

Answer:

-2.4

Step-by-step explanation:

The solution to the given expression is -2.4.

In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

Based on the information provided, we have the following mathematical expression:

[tex]\frac{16.8 - 1.2^2}{-4.3+3(-0.7)} =\frac{16.8 - 1.44}{-4.3 +(-2.1)}\\\\\frac{15.36}{-4.3-2.1} =\frac{15.36}{-4.3-2.1}\\\\\frac{15.36}{-6.4} =\frac{15.36}{-6.4}[/tex]

-2.4 = -2.4

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Complete Question:

Evaluate the expression.

[tex]\frac{16.8 - 1.2^2}{-4.3+3(-0.7)} =\frac{16.8 - 1.44}{-4.3 +(-2.1)}[/tex]

Answer:

x=4

Step-by-step explanation:

f(x) = 3x- 1 and g(x)=2x-3

f(2) means x=2

f(2) = 3(2)-1

f(2) = 6-1 =5

We want g(x) =5

5 = 2x-3

Add 3 to each side

5+3 = 2x-3+3

8 = 2x

Divide by 2

8/2 =2x/2

4=x

g(x) = f(2)  when x=4