5.

Explain how rays AB and AC form both a line and an angle.

zzz [12365]

Answer:

Step-by-step explanation:

If CAB represents a line and has arrows indicating its endpoints, then CAB is identified as a straight line, which also corresponds to a straight angle measuring 180°.

6 0

3 months ago

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Triangle KLM was dilated according to the rule DO,0.75 (x,y). What is true about the image △K'L'M'? Check all that apply. DO, 0.

Zina [12379]

The accurate statements are 0.75 (x,y) = (0.75x, 0.75y), LM is parallel to L'M', and "the vertices of the image are nearer to the origin relative to the pre-image".

Explanation:

It is stated that the triangle ABC underwent dilation as per the rule DO,0.75 (x,y)

DO, 0.75(x,y) signifies the dilation rule, where both x and y values are scaled by 0.75, indicating that the dilation, centered around the origin, has a scale factor of 0.75. The representation for this dilation would be,

$(x,y)\rightarrow (0.75x,0.75y)$

Consequently, the first statement holds true.

Since both x and y coordinates are scaled down by 0.75, the sides of the image are parallel, but shorter, with a scale of 0.75 compared to the pre-image’s sides.

Thus, the second statement "LM is parallel to L'M'" is also accurate, while the third and fifth statements are incorrect.

The scale factor of 0.75, being less than 1, suggests that the vertices of the image are closer to the origin compared to those of the pre-image.

Hence, the fourth statement "The vertices of the image are nearer to the origin compared to the pre-image" is indeed correct.

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2 months ago

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If 30,000 cm2 of material is available to make a box with a square base and an open top, what is the largest possible volume (in

Inessa [12570]

Answer:

The highest achievable volume for the box is 2000000 cubic meters.

Step-by-step explanation:

Below is an outline of the volume ( $V$ ), measured in cubic centimeters, and surface area ( $A_{s}$ ), measured in square centimeters, for a box featuring a square base:

$A_{s} = l^{2}+h\cdot l$ (1)

$V = l^{2}\cdot h$ (2)

Where:

$l$ - The length of the base's side, in centimeters.

$h$ - The height of the box, in centimeters.

Using (2), we isolate $h$ in the formula:

$h = \frac{V}{l^{2}}$

Then, we substitute into (1) and simplify the outcome:

$A_{s} = l^{2}+ \frac{V}{l}$

$A_{s}\cdot l = l^{3}+V$

$V = A_{s}\cdot l -l^{3}$ (3)

Next, we calculate the first and second derivatives of this expression:

$V' = A_{s}-3\cdot l^{2}$ (4)

$V'' = -6\cdot l$ (5)

If $V' = 0$ and $A_{s} = 30000\,cm^{2}$ , then we find that the critical value for the base's side length is:

$30000-3\cdot l^{2} = 0$

$3\cdot l^{2} = 30000$

$l = 100\,cm$

Subsequently, we assess this outcome using the second derivative's expression:

$V'' = -600$

According to Second Derivative Test, this critical value signifies an absolute maximum. Consequently, the largest volume obtainable for the box is:

$V = 30000\cdot l - l^{3}$