15 POINT QUESTION! Multiply and simplify. (4x−2)(3x^2−2x+1)

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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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.

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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In the conditional logic given, 'If it is June, then it is summer' and 'It is summer', we can infer the conclusion 'It can be June'. However, it is important to note this is a potential conclusion and not a definite one since other months exist in the summer. This kind of conclusion is an example of the converse fallacy, or affirming the consequent.

The question provided presents a logical statement in the form of a conditional statement. In logical reasoning and mathematics, a conditional statement is a statement of the form 'if P then Q', where P and Q are both statements. Here, the statement 'If it is June, then it is summer' is the given condition. The statement 'It is summer' is the second statement. A conclusion can be drawn using both of these statements. According to the rules of the logic, we can conclude that 'It can be June.' Remember, we cannot definitively say it 'is' June because there could be other months during the summer. This type of conclusion comes under the inference rule known as the 'converse fallacy' or 'affirming the consequent', where if the consequent (Q - the 'then' clause) is true, the antecedent (P - the 'if' clause) might also be true, but it could also possibly be false due to other factors.

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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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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.

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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