A rectangle is 1/2 feet long and 3/4 feet wide. What is the area of the rectangle?

Use the given times and velocities to make two points:  (1,4) and (2,2)   

Part A: 

Slope is the change in Y over the change in X from the two pints you made:

 Slope =  (2-4) / (2-1 )= -2

Now you have the slope, calculate the Y-intercept

y = -2x + b

Using (1,4)

4 = -2(1) + b = 4 =-2 +b. b = 6

 Equation is: y = -2x+6

Part B:

using the above equation replace x with 1, 2, 3, and 4 and solve for the Y

 then plot those onto a graph

The graph of the equation [tex]3x - y - 1 = 0[/tex] is attached below.

Further explanation:

The linear equation with slope m and intercept c is given as follows.

[tex]\boxed{y = mx + c}[/tex]

The formula for slope of line with points [tex]\left( {{x_1},{y_1}} \right)[/tex] and [tex]\left( {{x_2},{y_2}} \right)[/tex] can be expressed as,

[tex]\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}[/tex]

Given:

The equation is [tex]3x - y - 1 = 0.[/tex]

Explanation:

The given equation is [tex]3x - y - 1 = 0.[/tex]

Solve the equation to obtain the standard form.

[tex]\begin{aligned}3x - y - 1&= 0\\y&= 3x - 1\\\end{aligned}[/tex]

Compare [tex]y = 3x - 1[/tex] to the standard equation [tex]y= mx + c.[/tex]

The slope of the line is 3 and the y-intercept is -1.

Substitute 0 for [tex]x[/tex] to obtain the value of [tex]y[/tex].

[tex]\begin{aligned}y &= 3 \times 0 - 1\\y&= 0 - 1\\y&= - 1\\\end{aligned}[/tex]

Substitute 1 for [tex]x[/tex] to obtain the value of [tex]y[/tex].

[tex]\begin{aligned}y&= 3 \times 1 - 1\\y&= 3 - 1\\y&= 2\\\end{aligned}[/tex]

Substitute 2 for [tex]x[/tex] to obtain the value of [tex]y[/tex].

[tex]\begin{aligned}y&= 3 \times 2 - 1\\y&= 6 - 1\\y&= 5\\\end{aligned}[/tex]

The graph of the equation [tex]3x - y - 1 = 0[/tex] is attached below.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: numbers, slope, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation, origin.

Final answer:

The width of the garden is 15 meters and the length is 36 meters.

Explanation:

To solve this problem, we can use the formulas for perimeter and length. Let's assume that the width of the rectangular garden is x.

According to the given information, the length is 6 meters longer than twice the width, so the length can be represented as 2x + 6.

The perimeter is the sum of all four sides of the rectangle, which is given as 102 meters. We can set up the equation:

2(2x + 6) + 2x = 102

Simplifying the equation, we get:

6x + 12 = 102

6x = 90

x = 15

Therefore, the width of the garden is 15 meters and the length is 2(15) + 6 = 36 meters.

Donna can make a maximum of 94 biscuits on the rectangular cookie sheet at once.

To find the maximum number of biscuits Donna can make on the rectangular cookie sheet, we need to calculate the area of the sheet and divide it by the area of each biscuit.

The area of the sheet is given by length x width, so it is 30 cm x 50 cm = 1500 cm².

The area of each biscuit is given by πr², where r is the radius (half the diameter) of the biscuit. In this case, the radius is 8 cm / 2 = 4 cm. So the area of each biscuit is π x 4 cm x 4 cm = 16π cm².

To find the maximum number of biscuits, we divide the area of the sheet by the area of each biscuit:

Maximum number of biscuits = Area of the sheet / Area of each biscuit = 1500 cm² / 16π cm² ≈ 94.25 biscuits.

Since we can't have a fraction of a biscuit, the maximum number of biscuits that Donna can make on the sheet at once is 94 biscuits.

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A ship's navigator can keep the ship in safe waters by staying outside the 300-degree arc between two lighthouses and using the beams as navigational guides. Additionally, in areas with water breaks, navigators should account for wave diffraction to determine the safest angles for mooring.

To navigate safely and avoid the unsafe waters near the coastline marked by the 300-degree arc between two lighthouses at points A and B, a ship's navigator should use both lighthouses as reference points for establishing a safe navigational path. Typically, lighthouses are equipped with rotating beams, which can serve as a guide to determine a ship's position relative to hazardous areas. If the ship maintains a course outside of the direct line of sight between the two lighthouses, it can stay within the safe waters.

The navigator should also consider wave action when near a coastline or harbor entrance. If any breakwater structure or water break exists, such as a rock barrier with an opening, the navigator would need to be mindful of the wave patterns. As waves enter the opening, they diffract, and boats are generally safest at angles where the wave intensity is minimized.

Final answer:

To provide 275 balloons when they are sold in packs of 2, the clown will need to purchase 138 packs, which will include one extra balloon as you cannot buy half a pack.

Explanation:

The clown needs 275 balloons for a party and they come in packs of 2. To find out how many packs of balloons the clown needs to buy, one must divide the total number of balloons by the number in each pack.

The calculation is as follows:

Since packs cannot be purchased in halves, the clown will need to buy 138 packs to have enough balloons, understanding that this means having one extra balloon.

Answer:- The second graph shows a system of equations with a solution at (–1, 1) .

Explanation:-

In the given pictures we have different lines intersecting parabola .

Given point is (-1,1) ,here x coordinate is negative and y coordinate is positive , which happen only in second quadrant of a Cartesian plane.

Answer:

4. [tex]7\sqrt{x}=14[/tex]

Step-by-step explanation:

Radical equation is a equation that has a variable under the radical .

From the given options we have radical square root

We need to choose an option that has a variable under the square root.

1.[tex]x+\sqrt{5}=12[/tex]

This equation has 5 under the radical square root. Variable is outside, So this is not a radical equation.

2. x^2=16

Here there is not radical . So this is not a radical equation.

3. [tex]3+x\sqrt{7}=13[/tex]

This equation has 7 under the radical square root. Variable is outside, So this is not a radical equation.

4. [tex]7\sqrt{x}=14[/tex]

This equation has x under the radical square root. So this is a radical equation.

The mean of the combined group is 71.78.

Arithmetic mean is defined as the ratio of the sum of observations to the total number of observations.

Let the total sum of the scores of the first class of 36 students be ∑x.

Here, the mean is 75.2 .

⇒  ∑x/36 = 75.2

⇒ ∑x = (75.2)(36)

⇒ ∑x = 2707.2

Also, let the total sum of the scores of the second class of 28 students be ∑y.

Here, the mean is 67.4.

⇒ ∑y/28 = 67.4

⇒ ∑y = (67.4)(28)

⇒ ∑y = 1887.2

The total students in combined group = 36+28 =64

The sum of their scores =  ∑x + ∑y = 2707.2  + 1887.2 = 4594.4

The mean of the combined group = (∑x + ∑y)/64

The mean of the combined group = 4594.4/64 = 71.78

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To find the mean of the combined group of two classes, calculate the total sum of scores of each class, combine them, and then divide by the total number of students. The mean of the combined group is approximately 71.8.

To calculate the mean of the combined groups of students, you can use the total sum of scores from both classes divided by the total number of students. The first class has 36 students with a mean score of 75.2, and the second class has 28 students with a mean score of 67.4.

First, find the total sum of scores for each class:

Next, combine the total sums and the number of students:

Finally, divide the combined total sum by the combined number of students to find the mean:

Mean of combined group = 4594.4 / 64 = 71.7875

Therefore, the mean of the combined group is approximately 71.8.

The answer to this question is D.

Answer with explanation:

If we have to visualize important events in the history of the U.S. space program, we have to keep following things in mind

Year                              Program

19...                                         Satellite A

19..                                        On Moon ....

....                                        ............

......                                     .........

So, while scaling , we will keep year , that is time on any of the axis and program on another axis.

→→The Appropriate option will be

(a)  Time line

Answer:              

The answer is capitalism.      

Step-by-step explanation:              

Capitalism is friendliest to entrepreneurs and market economies also rely on capitalism. This is because capitalism and free enterprise helps to create a marketplace where producers and consumers are free to sell and buy what they choose.                

Answer:

-80

Step-by-step explanation:

Answer:

brain

consciousness

memory

In the proportion a/b = c/d, if this is true then the product of the extremes (a*d) is equal to the product of the means (b*c). Any statement that contradicts this property is considered false.

Looking at the given condition, a/b = c/d, it represents a proportion or a statement of equality between two fractions. Within this proportion, `a` and `d` are referred to as the extremes, while `b` and `c` are known as the means.

If the proportion is true, meaning it accurately reflects a relationship of equality between two ratios, several properties become applicable. Importantly, the product of the means equals the product of the extremes. In other words, in a valid proportion, `a*d` is equal to `b*c`.

Consequently, if any statement contradicts these properties, it is false. So, without knowing the specific statements to analyze here, we cannot accurately decide on the false one. Always remember, you need to comply with the stated properties of a proportion in mathematical contexts.

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The required area of the playground is given as, 192 square meters.

Given that,
A rectangular playground is 888 meters wide. It is 333 times as long as it is wide. The area of the playground is to be determined.

Surface area is defined as the measure of a region or surface is called as surface area.

Here,
The area of the playground = l × w
As mentioned in the question,
l = 3w = 3 × 8 = 24
Area = 24 × 8
Area = 192 square meters.

Thus, the required area of the playground is given as, 192 square meters.

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The farmer originally planted 15 apple trees.

Let's denote the original number of rows as [tex]\( r \)[/tex] and the original number of columns as [tex]\( c \).[/tex]

In the original arrangement, the total number of trees is [tex]\( r \times c \).[/tex]

If 5 more rows and 3 fewer columns are added, the new number of rows becomes [tex]\( r + 5 \)[/tex] and the new number of columns becomes [tex]\( c - 3 \).[/tex]

According to the given information, the new arrangement has 25 more trees than the original arrangement. So, we can set up the equation:

[tex]\[ (r + 5) \times (c - 3) = r \times c + 25 \][/tex]

Expanding the left side:

[tex]\[ r \times c + 5r - 3c - 15 = r \times c + 25 \][/tex]

Now, let's simplify:

[tex]\[ 5r - 3c - 15 = 25 \][/tex]

[tex]\[ 5r - 3c = 40 \][/tex]

Now, let's solve this equation to find the relationship between [tex]\( r \)[/tex] and [tex]\( c \).[/tex]

Given the information, let's make some assumptions about the number of rows and columns to fit the situation realistically.

Let's start with 1 row and 3 columns ( [tex]\( r = 1, c = 3 \)[/tex] ):

[tex]\[ 5(1) - 3(3) = 5 - 9 = -4 \][/tex]

It doesn't satisfy the condition.

Next, let's try 2 rows and 4 columns ( [tex]\( r = 2, c = 4 \)[/tex] ):

[tex]\[ 5(2) - 3(4) = 10 - 12 = -2 \][/tex]

Still doesn't satisfy the condition.

Next, let's try 3 rows and 5 columns ( [tex]\( r = 3, c = 5 \)[/tex] ):

[tex]\[ 5(3) - 3(5) = 15 - 15 = 0 \][/tex]

This satisfies the condition.

So, the original arrangement had 3 rows and 5 columns, and the total number of trees is [tex]\( 3 \times 5 = 15 \)[/tex].