MATHEMATICS HIGH SCHOOL

If an object is dropped from a height of 144 feet, the function h(t) = -16t2 + 144 gives the height of the object after t seconds. When will the object hit the ground? A) 9 seconds

B) 6 seconds

C) 1.5 seconds

D) 3 seconds

Answers

Answer 1
Answer:

So this question is asking for the zeros, or the x-intercepts, of this equation. For this, we have to set h(t) to zero to solve for it.

For this, we will be using the quadratic formula, which is x=(-b+√(b^2-4ac))/(2a),(-b-√(b^2-4ac))/(2a) (a = t^2 coefficient, b = t coefficient, and c = constant). In this case, our equation is t=(-0+√(0^2-4*(-16)*144))/(2*(-16)),(-0-√(0^2-4*(-16)*144))/(2*(-16)) . From here we can solve for t.

  1. Firstly, solve the exponents and multiplications: t=(-0+√(0+9216))/(-32),(-0-√(0+9216))/(-32)
  2. Next, solve the additions and subtractions: t=(√(9216))/(-32),(-√(9216))/(-32)
  3. Next, square root 9216: t=(96)/(-32),(-96)/(-32)
  4. Lastly, divide and your answers are going to be t=-3,3

Since we cannot have negative time,the object hits the ground at 3 seconds, or D.

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Which of the following statements is always true of similar polygons?A. Corresponding angles of similar figures have the same measure.

B. The lengths of corresponding sides form equivalent ratios.
C. The lengths of corresponding sides have the same measure.
D. both (a) and (b)

Answers

In this question, there are two correct choices. The corresponding angles of a similar figures have the same measure and the lengths of corresponding sides form equivalent ratios will be the correct choices. 

Work out (25/9) to the power of -3/2

Answers

To work out (25/9) to the power of -3/2, we can use the property of exponentiation. The negative exponent signifies taking the reciprocal of the base raised to the positive exponent. Additionally, the fractional exponent indicates taking the square root of the base raised to the numerator and then taking the reciprocal of the result raised to the denominator. Let's calculate it step by step.

What is the image of (-6, -2) after a dilation by a scale factor of 4 centered at the origin?​

Answers

The image of the point (-6, -2) after dilation by a scalefactor of 4 centered at the origin is (-24, -8).

What is a scale factor?

A scalefactor is defined as the ratio between the scale of a given original object and a new object,

We have,

To find the image of the point (-6, -2) after dilation by a scale factor of 4 centered at the origin, we can use the following formula:

(x', y') = (kx, ky)

where (x, y) are the coordinates of the original point, (x', y') are the coordinates of the image after dilation, k is the scale factor, and (0, 0) is the center of dilation.

Substituting the values given in the problem, we get:

(x', y') = (4*(-6), 4*(-2))

Simplifying,

(x', y') = (-24, -8)

Therefore,

The image of the point (-6, -2) after dilation by a scalefactor of 4 centered at the origin is (-24, -8).

Learn more about scalefactors here:

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Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = -1.

Answers

(x;\ y)-the\ coordinates\ any\ point\ on\ the \ parabola.\n\nDistance\ between\ the\ point\ (x;\ y)\ and\ the\ focus\ (-5;\ 5)\nand\ distance\ between\ the\ point\ (x;\ y)\ and\ a\ direct\ are\ equal.\n\nDistance\ between\ (x;\ y)\ and\ (-5;\ 5):\n√((x-(-5))^2+(y-5)^2)=√((x+5)^2+(y-5)^2)\n\nDistance\ between\ (x;\ y)\ and\ y=-1:\n|y-(-1)|=|y+1|\n\nWe\ equate\ the\ two\ expressions:\n√((x+5)^2+(y-5)^2)=|y+1|

Square\ both\ sides:\n(x+5)^2+(y-5)^2=(y+1)^2\n\nUse:(a\pm b)^2=a^2\pm2ab+b^2\n\nx^2+2\cdot x\cdot5+5^2+y^2-2\cdot y\cdot5+5^2=y^2+2\cdot y\cdot1+1^2\nx^2+10x+25+\not y^2-10y+25=\not y^2+2y+1\nx^2+10x-10y+50=2y+1\n2y+1=x^2+10x-10y+50\ \ \ \ |subtract\ 1\ from\ both\ sides\n2y=x^2+10x-10y+49\ \ \ \ |add\ 10y\ to\ both\ sides\n12y=x^2+10x+49\ \ \ \ |divide\ both\ sides\ by\ 12\n\n\boxed{y=(1)/(12)x^2+(5)/(6)x+(49)/(12)}

When trying to gather information in order to identify a problem, it is important to _______.a. Evaluate the best course of action
b. Find reliable sources
c. Embrace your assumptions
d. Generate multiple solutions

Answers

When trying to gather information in order to identify a problem, it is important to find reliable sources.

What is a reliable source?

A reliable source is known to be that source of information that gives a thorough, well-think through theory, argument, etc. and it is one that is found to be true.

So therefore, When trying to gather information in order to identify a problem, it is important to find reliable sources.

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Answer:

B. Find reliable resources

Step-by-step explanation:

Subtract 2ab from -2ab

Answers

Answer:

-4ab.

Step-by-step explanation:

If the temperature is -2 degrees and it goes down another 2 degrees the new temperature is -2-2 = -4.

-2ab - 2ab = -4ab.

Answer:

-4ab because if you have a balance of negative two dollars and you spend two more dollars you have a balance of negative 4 dollars

Step-by-step explanation:
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