Lola takes the train from Paris to Nice. The distance between the two cities is about 900,000 meters. If the train travels at a speed of 180 kilometers per hour, how long will it take Lola to travel from Paris to Nice?

Final answer:

Use the law of sines when you have two angles and one side, or two sides and a non-inclusive angle. Use the law of cosines when you have two sides and the included angle or all three sides. Apply trigonometric identities for vector addition and resolving forces.

Explanation:

Deciding when to use the law of sines or the law of cosines depends on the information given in a triangle problem. The law of sines is most useful when you know either two angles and one side (AAS or ASA) or two sides and a non-enclosed angle (SSA). The law states that the ratio of the length of a side to the sine of its opposing angle is consistent for all sides and angles in a triangle, often written as a/sin A = b/sin B = c/sin C.

The law of cosines is handy when you have either two sides and the included angle (SAS) or when you have all three sides (SSS). This law relates the lengths of the sides of a triangle to the cosine of one of its angles, following the formula c² = a² + b² - 2ab cos C.

For vector addition problems or when decomposing forces into components, trigonometric identities involving sine and cosine are employed. If you're resolving a weight into components, you may use sine to find the component opposite the angle and cosine for the component adjacent to the angle.

The total amount of rain for the two days is 2/3 inch.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

Yesterday it rained 5/8 inch.

and,  Today it rained 1/8 inch.

So, in two days the amount of rain fall

= 5/8+ 1/8

= 6/8

= 2/3

Hence, total amount of rain is 2/3 inch.

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The two triangles are not similar because y=60 so it is impossible to have three congruent angles.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In △ABC has interior angles with measures x°, 100°, and 70°,

And, △DEF has interior angles with measures y°, 70°, and 50°.

Hence, Measure of x is,

x + 100 + 70 = 180

x + 170 = 180

x = 180 - 170

x = 10

And, Measure of y is,

y + 70 + 50 = 180

y + 120 = 180

y = 180 - 120

y = 60

Thus, The two triangles are not similar because y=60 so it is impossible to have three congruent angles.

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Option B.The height of a cone is 15 inches.

To find the height of the cone, we will use the formula for the volume of a cone:

V = (1/3) * π * r² * h

We know the volume (V) is 180 cubic inches and the radius (r) is 6 inches.
We need to solve for the height (h).
First, let's plug in the known values:

180 = (1/3) * π * (6)² * h

180 = (1/3) * π * 36 * h

540 = π * 36 * h

540 / 36π = h

We can simplify this further, h = 15/π. Since we do not use π for the answer:

By rational observation of given options, B. 15 in. seems accurate.

The second root will be a + √b the missing sign is positive because the roots are always in the pair.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

The quadratic formula:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

Here the roots are in pairs:

One root is a - √b

The second root will be a + √b

Thus, the second root will be a + √b the missing sign is positive because the roots are always in the pair.

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Elephants have ivory tusks, which are elongated incisor teeth, primarily for digging, stripping bark, and defense, and they may have evolved for sexual selection and competitive interactions among males.

Elephants have ivory tusks because they are actually elongated incisor teeth. These tusks are composed of dentine and are covered by a layer of enamel, just like our teeth. Elephants use their tusks for various purposes, such as digging for water, stripping bark from trees, and as a weapon for defense. However, the primary reason they have tusks is not entirely understood. It's believed that tusks might have evolved for sexual selection and display, as well as for competitive interactions among male elephants.

Answer:

Step-by-step explanation:

Quadratic equation is given by x²-24x+c

This is in the form expansion of (a-b)², that is a²-2ab+b²

Comparing

            a² = x²,    a = x

            -2ab = -24x

             -2xb = -24x

                  b = 12

           c = b² = 12² =144

   x²-24x+144 = (x-12)²

Option D is the correct answer

The median is the better measure of center when dealing with data sets that have outliers or extreme values.

The median is the better measure of center when a data set contains several outliers or extreme values. It is less sensitive to measurements with extreme values, providing a more robust estimation of central tendency. The median can be thought of as the middle number in a series, where 50% of the measurements are above it and 50% are below.

Using proportions, it is found that the correct sentence is:

Decreased 10% from last quarter's goal of 250 consumers retained, hence, the number of customers is:

[tex]0.9(250) = 225[/tex]

The current rate has to be increased by 16%, hence, the goal is:

[tex]1.16(225) = 261[/tex]

Hence, the sentence is:

"That means our target is 261 consumers retained."

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