A trapezoid has an area of 24 square meters. The length of the bases of the trapezoid are 5 meters and 7 meters. What is the height of the trapezoid?

To find the dimensions of the volleyball court, set up a system of equations using the perimeter and area formulas. Solve the equations to find the possible dimensions of the court.

To find the dimensions of the volleyball court, we can set up a system of equations using the given information. Let's represent the length of the court as 'l' and the width as 'w'. We know that the perimeter of a rectangle is given by the formula 2l + 2w, so we can set up the equation 2l + 2w = 52. Additionally, we know that the area of a rectangle is given by the formula lw, so we can set up the equation lw = 153.

Using these equations, we can solve for the dimensions of the volleyball court. Let's solve the first equation for l: 2l = 52 - 2w. Dividing both sides by 2 gives us l = 26 - w. Now we can substitute this value of l into the second equation: (26 - w)w = 153. Expanding this equation gives us w^2 - 26w + 153 = 0. We can solve this quadratic equation using factoring, the quadratic formula, or by graphing. After solving for w, we can substitute this value back into the equation l = 26 - w to find the length of the court.

After solving the quadratic equation, we find two possible values for the width: w = 9 and w = 17. Plugging each value into the equation l = 26 - w, we find the corresponding lengths: l = 17 and l = 9. Therefore, the possible dimensions of the volleyball court are 17m by 9m or 9m by 17m.

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Answer: [tex]76\ m^2[/tex]

Step-by-step explanation:

The surface area of a rectangular prism is given by :-

[tex]\text{Surface area}=2(lw+wh+hl)\\\\\Rightarrow\ \text{Surface area}=2(4\cdot5+2\cdot5+2\cdot4)\\\\\Rightarrow\ \text{Surface area}=2(20+10+8)\\\\\Rightarrow\ \text{Surface area}=2(38)\\\\\Rightarrow\ \text{Surface area}=76\ m^2[/tex]

Hence, he surface area of this right rectangular prism= [tex]76\ m^2[/tex]

Starting from your school's location (2,-1), by subtracting 5 from the x-coordinate for walking west, and adding 2 to the y-coordinate for walking north, the location of your house corresponds the ordered pair (-3,1).

Given your school is at (2,-1) and you walk 5 blocks west and 2 blocks north to reach your school, we can determine the location of your house. If we think of the coordinate system with east being positive along the x-axis and north as positive along the y-axis, then walking west (the opposite direction of positive x) means subtracting from the x-coordinate and walking north (the positive y direction) means adding to the y-coordinate.

So, starting from the school's location (2,-1), to account for your walk, subtract 5 (for walking west) from the x-coordinate, resulting in -3, and add 2 (for going north) to the y-coordinate, resulting in 1. Thus, the location of your house corresponds to the ordered pair (-3,1).

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Final answer:

Miguel ran different distances on Monday and Friday. We calculate how much farther he ran on Friday than on Monday to find the difference in distance.

Explanation:

Miguel ran 1 3/10 miles on Monday. On Friday, Miguel ran 3 times as far as he did on Monday. To find out how much farther Miguel ran on Friday than on Monday, we first calculate how far he ran on Friday, which is 1 3/10 miles x 3 = 3 9/10 miles. The difference in distance is 3 9/10 - 1 3/10 = 2 6/10 miles.

Answer:

720

Step-by-step explanation:

the guy above got it right thanks man/gal

The slope of the line passing through the points (−3, 8) and (4, −6) is calculated using the slope formula and results in a slope of −2.

To find the slope of the line that passes through the points (−3, 8) and (4, −6), we apply the slope formula m = (y2 − y1) / (x2 − x1). Let's designate the first point (−3, 8) as (x1, y1) and the second point (4, −6) as (x2, y2). Plugging these values into the formula, we get:

m = (−6 − 8) / (4 − (−3))

m = −14 / 7

m = −2

Therefore, the slope of the line between the two points is −2. The negative sign indicates that the line is descending from left to right.

Final answer:

To calculate the slope of a line that goes through the points (-3, 8) and (4, -6), apply the slope formula m = (y2 - y1) / (x2 - x1). After substituting the values, the slope is found to be -2.

Explanation:

To find the slope of the line that passes through the points –(3, 8) and (4, –6), we can use the slope formula, which is m = (y2 - y1) / (x2 - x1).

Using the given points, Point 1 (x1, y1) is (-3, 8) and Point 2 (x2, y2) is (4, -6). Substituting these values into the slope formula gives us:

m = (-6 - 8) / (4 - (-3))

m = (-14) / (7)

m = -2

Therefore, the slope of the line that passes through the given points is -2.

Final answer:

Justice and revenge differ in intentions and outcomes. Justice focuses on fairness and societal laws, while revenge is driven by personal vendettas. It's crucial to differentiate between the two concepts to avoid perpetuating harm.

Explanation:

Justice and revenge both involve the desire for consequences towards a wrongdoing, but they differ in their intentions and outcomes. While justice aims for fairness and upholding societal laws, revenge seeks to harm those who have caused harm, often driven by personal emotions.

One key difference between justice and revenge is that justice is typically carried out within a legal framework and aims to restore balance in society, whereas revenge is driven by personal vendetta and can perpetuate cycles of violence.

It's essential to differentiate between the two concepts, as justice aligns with societal norms and legal systems, while revenge risks leading to further harm and conflict.

Answer:

Step-by-step explanation:

H(t) = 50 - t/5

h(35)=50-35/5

=50-7

=43

h(35) = 43

The quantity represented by h(t) is -125 at time t=35.

The function h(t) represents a certain quantity (for example, height, distance, etc.) as a function of time ‘t’. Here, you want to find the value of h(t) at t=35.

We can substitute t=35 into the function h(t):

h(35) = 50 - 5*35

Now, calculate the expression on the right side to find the value of h(35). This will give you the desired quantity at time t=35. Remember to follow the order of operations (multiplication before subtraction). Let’s calculate it:

h(35) = 50 - 5*35 = 50 - 175 = -125

So, h(35) = -125. This means that the quantity represented by h(t) is -125 at time t=35.

Answer:

The answer is actually 1 because any number to the zero power is just the product of no numbers at all, which is the multiplicative identity, 1.

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

because i got it right on my test