Describe the graph of the function at its roots.

f(x) = (x − 2)3(x + 6)2(x + 12)

At x = 2, the graph the x–axis.
A) Crosses
B) Touches

△ XYZ∼ △ DEF, YZ is 10 meters, ​ XZ ​ is 15 meters, and EF is 8 meters. What is ​ DF?

Solution:

As, △ XYZ∼ △ DEF , so the ratio of sides of triangle is equal.

So, we have, [tex] \frac{XY}{DE} =\frac{YZ}{EF} =\frac{XZ}{DF} [/tex]

Using, [tex] \frac{YZ}{EF} =\frac{XZ}{DF} [/tex]

So, we get,[tex] \frac{10}{8} =\frac{15}{DF} [/tex]

Now, to solve for DF, we must simplify

Simplifying,[tex] \frac{10}{8} =\frac{5*2}{4*2}=\frac{15}{DF) [/tex]

[tex] \frac{5}{4} =\frac{15}{DF} [/tex]

To simplify, Let us multiply by 4*DF on both sides

[tex] \frac{5*4DF}{4} =\frac{15*4DF}{DF} [/tex]

[tex] \frac{5DF}{1} =\frac{15*4}{1} [/tex]

So, 5 DF=15*4=60

To solve for DF, let us divide by 5 on both sides

[tex] \frac{5}{5} DF=\frac{60}{5} [/tex]

[tex] \frac{1}{1} DF=\frac{12}{1} [/tex]

So, DF=12meters

Answer: The distance from point R to point T is 1.5 miles.

Step-by-step explanation:

In the map, the scale is,

1 inches = 0.5 miles,

3 inches = 3 × 0.5 = 1.5 miles,

Thus, in the map 3 inches shows 1.5 miles,

Since, in the map, the distance from point R to point P = 3 inches,

Thus, the actual distance from point R to point P = 1.5 miles.

⇒ Option C is correct.

Answer:

  0.364 horsepower

Step-by-step explanation:

You want to know a pump's power output if it raises 2 tons of water 15 ft in 5 minutes.

The power is conveniently measured in horsepower. One horsepower is 33,000 ft·lb/minute.

Here, we have (2t · 2000 lb/t · 15 ft)/(5 min) = 12000 ft·lb/min

In terms of horsepower, that is ...

  (12000 ft·lb/min) / (33000 ft·lb/min/hp) = 4/11 hp ≈ 0.364 hp

The power output of the pump is about 0.364 horsepower.

__

Additional comment

That's about 271 watts.

The distance dimensions are in feet, so we assume the tons are US short tons of 2000 lb each.

The new coordinates of Q are (-8, -3).

When reflecting a point across the X-axis, the X-coordinate remains unchanged, while the Y-coordinate changes its sign. From the figure attached, we find coordinates of Q are (-8,3). Therefore:

As a result, the coordinates of point Q after reflection along the X-axis will be (-8, -3).

Therefore, the new coordinates of point Q are (-8, -3).

Final answer:

The ratio of the cost of 6 pairs of canvas shoes to the cost of 3 pairs of leather shoes is D. 2/5.

Explanation:

To find the ratio of the cost of 6 pairs of canvas shoes to the cost of 3 pairs of leather shoes, we need to calculate the total cost of each option.

For 6 pairs of canvas shoes, the cost is $7 per pair, so the total cost is 6 x $7 = $42.

For 3 pairs of leather shoes, the cost is $35 per pair, so the total cost is 3 x $35 = $105.

Therefore, the ratio is $42 : $105, which simplifies to 2/5.

Answer:

218.4

Step-by-step explanation:

The temperature in degrees​ Fahrenheit, T is 68°F.

Dolbear's law states that the number of chirps per minute that a snowy tree cricket makes is related to the air temperature in degrees Fahrenheit by the following formula:

T = 50 + (N - 40)/4

where:

T is the temperature in degrees Fahrenheit

N is the number of chirps per minute

If N = 98, then the temperature is:

T = 50 + (98 - 40)/4 = 68 degrees Fahrenheit

So the answer is 68 degrees Fahrenheit.

Here is an explanation of the calculation:

We are given that N = 98 chirps per minute.

We substitute this value into the formula for Dolbear's law to get:

T = 50 + (98 - 40)/4 = 68 degrees Fahrenheit

Therefore, the temperature is 68 degrees Fahrenheit.

Here are some additional things to consider:

The number of chirps per minute that a snowy tree cricket makes is not always an accurate measure of the air temperature. The number of chirps can also be affected by other factors, such as the humidity and the time of day.

Dolbear's law is a simplified model of the relationship between the chirping rate of snowy tree crickets and the air temperature. The actual relationship is more complex and can be affected by a number of factors.

To learn more about temperature here:

https://brainly.com/question/7510619

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0.673 rounded to the nearest hundredth as 0.67

The digit in the smallest location is unaffected if it is less than 5 in number. Rounding down is the process of reducing a number to zero after a certain number of digits. The digit in the smallest location is added with +1 if it is bigger than or equal to 5.

To round off 0.673 to the nearest hundredth means hundredth digit after decimal, To do so take a look on the thousandth digit after decimal, If it is greater than 5 or equal to 5 increase the hundredth digit after decimal by 1 otherwise no change,

Here, the thousandth digit is 3, 3<5. So, no increment is required.

It will remain as 0.67.

Thus, 0.673 is 0.67 after rounding off to the nearest hundredth.

Learn more about round off, here:

brainly.com/question/31754034

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Step-by-step explanation:

For USATestprep people.

Answer: x = 3.06

Step-by-step explanation:

You do 30 divided by 9.8 and you get 3.06

The dilation's scale factor will be 1/4.

The division method is used to divide a bunch of items into equal portions.

Division is the inverse of multiplication. For instance, dividing 20 by 2 means dividing 20 into two equal groups of ten.

Given this,

The blue figure is a magnified version of the black one.

Furthermore, the origin is the center of dilatation.

Now,

Because the blue figure is a dilatation of the black one.

Furthermore, the origin is the center of dilatation.

In this case, the length of the black figure equals 16 units.

Furthermore, the length of the blue figure equals 4 units.

As a result, the dilation scale factor is 4/16.

= 1/4