What are the coordinates of the centroid of a triangle with vertices X(−4, 0) , Y(−1, 4) , and Z(2, 2) ? Enter your answer in the boxes.

The ratio of male fish with egg cells to male fish without egg cells is 130:290, which simplifies to 13:29.

To determine the ratio of male fish with egg cells to those without, you must subtract the number of male fish with egg cells from the total number of surveyed male fish. According to Anna's survey, she found that 130 male fish out of 420 had egg cells. This implies that 420 - 130 = 290 male fish do not have egg cells.

Now, to find the ratio:

Male fish with egg cells: 130

Male fish without egg cells: 290

The ratio of male fish with egg cells to male fish without egg cells is 130:290. This ratio can also be simplified by dividing both parts by the greatest common divisor, which is 10 in this case. After simplification, the ratio becomes 13:29.

Option: A is the correct answer.

     A.   always

Right Triangle Altitude Theorem--

It states that when an altitude is drawn from the the vertex containing the right angle to the opposite side i.e. hypotenuse then the length of the altitude is the geometric means between the segments on the hypotenuse.

i.e. if we consider a right angled triangle ΔCAB with right angle at A.

Then if  a altitude AD is drawn from vertex A then we have:

[tex]AD=\sqrt{CD\cdot DB}[/tex]

The inverse function of y = 3x + 2 is y = ( -x + 2 )/3 obtained by switchig the places of x and y.

A function can be thought of as an output for the given set of inputs.

To find the inverse of a function algebraically first we have determine whether the given function is one-to-one or not. A one-to-one function is a function in which each different value of the domain corresponds to a different value in the range of the function.

Suppose we have a function f(x) = 3x + 2 which can be written as y = 3x + 2.

Now to obtain the inverse of this function we have to switch x and y in their respective places and solve for y.

∴ y = 3x + 2

x = 3y + 2.

3y = - x + 2.

y = ( -x + 2 )/3.

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A city council has to use its resources to improve either the water supply or the drainage system. At which level is this decision made?

The asnswer is: Government

Answer: I think its 3

Step-by-step explanation:

4.5+4.5=9 and 3*3=9 so 18-9=9 so K=3

The value of k is 3.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 99 is an equation.

We have,

4.5 + 1.5k = 18 - 3k

Combine like terms on one side.

1.5k + 3k = 18 - 4.5

4.5k = 13.5

Divide both sides with 4.5

k = 3

Thus,

The value of k is 3.

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Using the formula of average distance = total distance traveled / total time taken, we find that Phaelon had the fastest average speed of 10.86 mi/hr.

To find out who had the fastest average speed, we'll need to calculate the average speed for each person. We can do this by dividing the total distance traveled by the total time taken.

Serra's average speed: 15 mi / 1.5 hr = 10 mi/hr

Phaelon's average speed: 38 mi / 3.5 hr = 10.86 mi/hr

Justice's average speed: 22 mi / 2.25 hr = 9.78 mi/hr

So, by comparing these speeds, we can conclude that Phaelon had the fastest average speed of 10.86 mi/hr.

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Answer:

  (√6)/2 square units

Step-by-step explanation:

The area of a triangle is half the magnitude of the cross product of the vectors representing adjacent sides.

  QR = (4-3, -1-(-4), -4-(-5)) = (1, 3, 1)

  QS = (3 -3, -5-(-4), -6-(-5)) = (0, -1, -1)

The cross product is the determinant ...

[tex]\text{det}\left|\begin{array}{ccc}i&j&k\\1&3&1\\0&-1&-1\end{array}\right|=-2i+j-k[/tex]

The magnitude of this is ...

  |QR × QS| = √((-2)² +1² +(-1)²) = √6

The area of the triangle is half this value:

  Area = (1/2)√6 . . . . square units

The ordered pair (-2, 9) is not a solution of the equation y = x – 7.

To determine if the ordered pair (-2, 9) is a solution of the equation y = x – 7, we can substitute the values of x and y into the equation and see if it is true.

Plugging in the values, we have 9 = -2 - 7. Simplifying, we get 9 = -9. Since this statement is false, the ordered pair (-2, 9) is not a solution of the equation y = x – 7.

Final answer:

The ordered pair (-2, 9) is not a solution to the equation y = x − 7 because when you substitute x with -2, the equation yields y = -9, not y = 9 as suggested by the ordered pair.

Explanation:

To determine if the ordered pair (-2, 9) is a solution to the equation y = x − 7, we need to substitute the x-value from the ordered pair into the equation and see if the resulting y-value matches the one in the ordered pair.

Let's substitute x = -2 into the equation:

y = (-2) − 7

y = -2 − 7

y = -9

This means that when x is -2, y should be -9 according to the equation. However, the y-value given in the pair is 9, not -9. Therefore, the ordered pair (-2, 9) is not a solution to the equation y = x − 7.

For the given expression, the simplified form is [tex]\frac{2x\sqrt{3y} }{3y}[/tex]

From the question, we are to simplify the expression sqrt(4x^2/3y).

The expression is [tex]\sqrt{\frac{4x^{2} }{3y} }[/tex]

We can write that,

[tex]\sqrt{\frac{4x^{2} }{3y} } = \frac{\sqrt{4x^{2}}}{\sqrt{3y}}[/tex]

Then,

[tex]\frac{\sqrt{4x^{2}}}{\sqrt{3y}} = \frac{2x}{\sqrt{3y} }[/tex]

To simplify further, we can rationalize the denominator

We get

[tex]\frac{2x}{\sqrt{3y} } = \frac{2x}{\sqrt{3y} } \times \frac{\sqrt{3y} }{\sqrt{3y} }[/tex]

Then,

[tex]\frac{2x}{\sqrt{3y} } \times \frac{\sqrt{3y} }{\sqrt{3y} } = \frac{2x\sqrt{3y} }{3y}[/tex]

Hence, for the given expression, the simplified form is [tex]\frac{2x\sqrt{3y} }{3y}[/tex]

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Answer: A) IH ≅ AG

Step-by-step explanation:

A property of congruent triangles is known as CPCTC which says that the congruent parts of the corresponding triangle are congruent.

We are given that Δ ITH ≅ Δ APG , then the every part of Δ ITH must be congruent to the corresponding part of  Δ APG.

i.e. Corresponding sides of Δ ITH and Δ APG  are congruent.

Since Side IH in Δ ITH  is corresponding to side AG in Δ APG  [First and last letter]

Then, IH ≅ AG

Answer:

4500 fans per hour

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

His friend's garden is 18.22 meters long.

R (Read):

Leeland's garden is 15 meters and 24 centimeters long.

His friend's garden is 2 meters and 98 centimeters longer than Leeland's.

We need to find the length of his friend's garden.

D (Define):

Let L be the length of Leeland's garden in meters.

Let F be the length of his friend's garden in meters.

W (Write):

We can write the given information as equations:

L = 15.24 meters (converting 24 cm to meters)

F = L + 2.98 meters

Solve:

Substitute equation 1 into equation 2:

F = (15.24 meters) + 2.98 meters

F = 18.22 meters

Final answer:

To determine how long Loretta's father drives, we deduct the distance Loretta drives (220 miles) from the total trip distance, then divide the remainder (390 miles) by her father's average speed (65 mph), resulting in 6 hours of driving time for her father. The total trip time is 10 hours.

Explanation:

The question is about calculating travel times and distances using average speed. Loretta and her family are traveling 610 miles with Loretta driving the first 4 hours of the trip at 55 mph and her dad driving the remainder at 65 mph. To calculate the distance Loretta drives, we multiply her driving time by her average speed (4 hours * 55 mph = 220 miles). Then, we subtract that distance from the total trip distance to find out how far her dad drives (610 miles - 220 miles = 390 miles). To calculate how long her dad drives, we divide his driving distance by his average speed (390 miles / 65 mph).

Now let's solve the dad's driving time:
390 miles / 65 mph = 6 hours. So, Loretta's dad would drive for 6 hours. The total driving time for the trip is the sum of both Loretta's time and her dad's time: 4 hours + 6 hours = 10 hours.

The pressure exerted on the ice by the skater, who weighs 500-N and has blade contact area of 0.001 m², is 500,000 Pa (Pascals).

The question is asking about the pressure exerted on the ice by a skater. To find the pressure, we use the formula P = F/A, where P is the pressure, F is the force, and A is the area in contact with the ice.

If the skater weighs 500-N and is gliding on one skate blade, which has an area of contact of 0.001 m2, the pressure is calculated by dividing the weight by the area. Using the provided data from the similar situation of a skater with a weight of 736 N and a blade area of 5.0 × 10-4 m2, we would calculate the pressure using these figures. However, we need to calculate the pressure using the data specific to this skater, with a weight of 500-N and a blade area of 0.001 m2.

The pressure exerted on the ice can be calculated as:

P = 500 N / 0.001 m2 = 500,000 Pa (Pascals)