Classify the triangle with sides 1, 4, and 7. select one.

The expressions are simplified to give;

7. 4n³(3n² + 4)

8. -3x(3x² - 4)

9. 5(k² - 8k + 2)

10. -10(6 + 6n² + 5n³)

11. 3(6n³ - 4n - 7)

12. 9(7n³ + 9n + 2)

Algebraic expressions are defined as mathematical expressions that are composed of variables, coefficients, terms, factors and constants.

These algebraic expressions are also made up of arithmetic operations, such as;

To factorize the expressions, we have;

12n⁵ + 16n³

Find the common term

4n³(3n² + 4)

-9x³ - 12x

find the common term

-3x(3x² - 4)

5k² - 40k + 10

find the common terms

5(k² - 8k + 2)

-60 + 60n² + 50n³

find the common term

-10(6 + 6n² + 5n³)

18n³ -12n - 21

find the common term

3(6n³ - 4n - 7)

63n³ + 81n + 18

Find the common term

9(7n³ + 9n + 2)

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Answer:

Step-by-step explanation:

1) 35 = 5 * 7

  14 = 2 * 7

LCM = 2 * 5 * 7 = 70

2)  15 = 3 * 5

    12 = 2 * 2 * 3

LCM = 2* 2 * 3 * 5 = 60

3) 5 = 5

    9 = 3 * 3

  15 = 3 * 5

LCM = 3*3 * 5 = 45

4)8 = 2 * 2 * 2 = 2³

  10 = 2 *5

   12 = 2 * 2 *3 = 2² * 3

LCM = 2³ * 3 * 5 = 120

The measure of angle c is 70 degrees.

If angle a and angle b are complementary, it means that the sum of their measures is equal to 90 degrees.

Given:

Measure of angle a = 10x + 10

Measure of angle b = 20

We can set up the equation:

(10x + 10) + 20 = 90

Simplifying the equation:

10x + 30 = 90

Subtracting 30 from both sides:

10x = 60

Dividing both sides by 10:

x = 6

Now, we have found the value of x to be 6.

To find the measure of angle c, we can substitute the value of x into the equation for angle a:

Measure of angle a = 10x + 10

Measure of angle a = 10(6) + 10

Measure of angle a = 60 + 10

Measure of angle a = 70

As a result, angle c has a measure of 70 degrees.

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Answer:

4 I think

Step-by-step explanation:

A vertex is a point where two or more edges meet (i.e the sharp points of the figure).

A vertex (plural: vertices) is a point where two or more line segments meet. It is a Corner.

Answer:

Step-by-step explanation:

True

TRUE   AHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

To find the factors of the expression 12x^2 - 4x - 1, we can use the factor theorem. The factor theorem states that if a polynomial expression evaluates to zero when a certain value is substituted for the variable, then that value is a factor of the polynomial.

To determine if a certain value is a factor of the expression, we can use synthetic division. Synthetic division involves dividing the polynomial expression by the possible factor to check if the remainder is zero. If the remainder is zero, then the value is a factor.

Let's start by checking if x = 1 is a factor of the expression:

    1 | 12 - 4 - 1
      |     12   8
      |____________
       12   8   7

Since the remainder is not zero, x = 1 is not a factor of the expression.

Next, let's check if x = -1 is a factor of the expression:

   -1 | 12 - 4 - 1
      |    -12  16
      |____________
       12 -16  15

Again, the remainder is not zero, so x = -1 is not a factor of the expression.

Now, let's check if x = 2 is a factor of the expression:

    2 | 12 - 4 - 1
      |     24 40
      |____________
       12  20 39

Once again, the remainder is not zero, so x = 2 is not a factor of the expression.

Finally, let's check if x = -2 is a factor of the expression:

   -2 | 12 - 4 - 1
      |    -24 56
      |____________
       12 -28 55

As we can see, the remainder is not zero, so x = -2 is not a factor of the expression.

After checking all the possible factors, we can conclude that none of the values tested (1, -1, 2, -2) are factors of the expression 12x^2 - 4x - 1.

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The solution to the formula using f as the subject is given by f = 9/(a + 7)

a = 9/f - 7

Add 7 to both sides

a + 7 = 9/f

cross product

f(a + 7) = 9

divide both sides by a + 7

f = 9/(a + 7)

Hence, the formula a = 9/f - 7 can be written as f = 9/(a + 7) using f as the subject.

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Answer:

Step-by-step explanation:

Given inequality:

Solution is:

Since the number line is restricted to -9, + 9 interval, the solution will appear as shaded part to the right from 4 through 9, where 4 is included point.

Correct answer choice is C

answer:

8417yd

Step-by-step explanation:

The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:

"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."

The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.

Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.

In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.

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La base y la altura del rectángulo mide 7 y 13 centímetros, respectivamente.

Por geometría sabemos que el área de un rectángulo (\(A\)), en centímetros cuadrados, es igual al producto de la base (\(b\)) y la altura (\(h\)), ambas en centímetros.

Mediante álgebra tenemos la siguiente expresión:

\(x\cdot (x+ 6) = 91\)

\(x^{2}+6\cdot x - 91 = 0\) (1)

Las raíces de este polinomio se determinan mediante la fórmula cuadrática:

\(x_{1} = 7\), \(x_{2} = 13\)

En consecuencia, la base y la altura del rectángulo mide 7 y 13 centímetros, respectivamente. \(\blacksquare\)

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Rectangle

3 * 8 = 24

Triangle

4 * 3 = 12

12 / 2 = 6

Now add those two areas together, and you get 30

Answer: 19 minutes

Step-by-step explanation:

Here is the complete question:

takes Andrew 720 seconds to take a shower. He spends an additional 420 seconds eating breakfast.

How many minutes does it take Andrew to take a shower and eat breakfast?

From the question, we are told that Andrew spends 720 seconds to take a shower and also spends an additional 420 seconds eating breakfast. The total time spent by Andrew will be:

= 720 seconds + 420 seconds

= 1140 seconds

We will then convert 1140 seconds to minutes. We should note that 60 seconds = 1 minute. Therefore,

1140 seconds = 1140/60

= 19 minutes

Andrew uses 19 minutes to take a shower and eat breakfast.

The positive graph of y = 2x + 5 changes to the negative graph which moves downward from left to right when the slope is changed to -2.

Slope of a line is defined as the difference in the y coordinates divided by the difference in the x coordinates of two points.

Slope of a line is usually denoted by the letter m.

First let us take the graph of y = 2x + 5.

Take x intercept and y intercept of this graph.

x intercept is the point where line touches X axis and y intercept is the point where line touches Y axis.

From the equation of the line, y intercept = 5

So we get a point (0, 5)

Now to find x intercept, let y = 0 in the equation, then x = -2.5

So we get another point (-2.5, 0)

So the line y = 2x + 5 passes through the points (0, 5) and (-2.5, 0).

Now if the slope changed to -2, equation becomes y = -2x + 5.

y intercept is same.

So one point of the line will be (0, 5)

To find x intercept, let y = 0 in the second equation, then x = 2.5

So the second line passes through the points (0, 5) and (2.5, 0)

That is, the graph which goes upward from left to right changed to the graph downward from left to right.

Hence, when the slope changed to -2, the graph goes downward from left to right.

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Answer:

(f + g)(x) = 7x - 1

Step-by-step explanation:

Given :  f(x) = 5x – 2 and g(x) = 2x + 1

We have to find  (f + g)(x)

Consider  (f + g)(x) = f(x) + g(x)

Also, given  f(x) = 5x – 2 and g(x) = 2x + 1

Substitute, we have,

f(x) + g(x) = 5x - 2 + 2x + 1

LIKE TERMS are terms having same variable with same degree.

Simplify by adding like terms,  we have,

f(x) + g(x) = 5x + 2x - 2  + 1

f(x) + g(x) = 7x  - 1

Thus, (f + g)(x) = 7x - 1

Answer:

-2

Step-by-step explanation:

If you substitute x for 4, you have -4+2 to get -2.

Answer:

Table 3

Step-by-step explanation:

In a proportional relationship there must be a constant rate of change.

The first table:

6-5 / 9-7 = 1/2

5-3 / 7-4 = 2/3

These are not equal so it is not proportional.

The second table:

10-8 / 150-120 =2/30

8-5 / 120-75 = 3/45

These are not equal so it is not proportional

The third table:

10-8 / 12-10 =2/2 = 1

8-6 / 10-8 =2/2 = 1

These are equal so this table is proportional.

The quadratic function that models his path through the air, where x is his horizontal distance from the start line in meters and y is his height, in cm is given as follows:

y = -x² + 12x - 27.

Considering it's roots x' and x'', a quadratic function is modeled according to the rule presented as follows:

y = a(x - x')(x - x'')

In which a is the leading coefficient.

A long-jumper lifts off 3 m after starting his run, and lands 6 m later (9m from the start), hence the roots of the parabola are given as follows:

x' = 3, x'' = 9.

Hence:

y = a(x - 3)(x - 9)

y = a(x² - 12x + 27).

When he is 8 m from the start line, he is 5 cm above the ground, meaning that when x = 8, y = 5, hence the leading coefficient a is calculated as follows:

5 = a(8² - 12(8) + 27)

-5a = 5

5a = -5

a = -1.

Hence the equation of the parabola is given as follows:

y = -x² + 12x - 27.

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The number is 28 bleacher seats, and 1 lower reserved seat were bought.

To solve this problem, we need to use a system of equations. Let x be the number of bleacher seats and y be the number of lower reserved seats. Then we have two equations:
x + y = 29  (since there were a total of 29 seats bought)
10x + 25y = 913  (since the total cost was $913)

To solve for x and y, we can use substitution or elimination. Let's use substitution. Solve the first equation for x:
x = 29 - y

Now substitute this expression for x in the second equation:
10(29 - y) + 25y = 913

Expand and simplify:
290 - 10y + 25y = 913
15y = 623
y = 41.5

Since we can't have half a seat, we know that y must be a whole number. But we made an assumption that x and y were both integers, so we need to go back and check if that assumption was correct.

If y = 41, then x = 29 - y = 29 - 41 = -12. That doesn't make sense, so we know that y must be 42.

Now we can solve for x:
x = 29 - y = 29 - 42 = -13

Again, that doesn't make sense, so we made another assumption that x and y were both positive.
If y = 1, then x = 29 - y = 29 - 1 = 28.

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The result of an average of more than 100% in a survey of tenants on cleaning chores in shared apartments is likely due to social desirability bias.

The average tenant response of more than 100% in a study about cleaning duties in shared apartments is probably the product of social desirability bias. Social desirability bias occurs when respondents give answers that they think are socially acceptable or desirable, rather than their true opinions or behavior.

In this case, tenants may have overstated their contribution to cleaning the apartment, in order to appear more helpful or responsible, leading to an average percentage higher than 100%.

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Answer:

77c + 21

Step-by-step explanation:

distributive property

7(11c) + 7(3)

77c + 21

Answer:

x=15

Step-by-step explanation:

\(a^2+b^2=c^2\\a^2+20^2=25^2\\a^2+400=625\\a^2=225\\a=\sqrt{225} \\a=15\)

Answer:

(2,5)

Step-by-step explanation:

Answer:

\(\frac{2}{5}\)

Step-by-step explanation:

40% = \(\frac{40}{100}\) ( divide numerator and denominator by 20 )

40% = \(\frac{2}{5}\)

Answer:

Step-by-step explanation:

40%= 40/100

Percent is out of 100 and written as % so there for it is 40 out of 100 or 40 over 100

40/

Remember that the general formula of an arithmetic sequence is:

Where:

• An is the n-term

• d is the common difference

• n is the number of the step

Using the given data,

Therefore, the 13th term of the arithmetic sequence is 73

The method of reduction of order is a technique used to find a second solution to a homogeneous linear differential equation when one solution is already known.

However, it cannot be directly used for nonhomogeneous linear differential equations. In nonhomogeneous equations, the method of undetermined coefficients or variation of parameters is typically used to find a particular solution.

Therefore, the statement "the method of reduction of order can also be used for the nonhomogeneous equation" is false. It is important to understand the different techniques for solving differential equations, and to choose the appropriate method based on the type of equation and boundary conditions given.

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Answer:

10

Step-by-step explanation:

(21-1)/2

(b) There are two Nash equilibria in this game:(S, S): Both A and B choose to Stop. Neither player has an incentive to deviate as they both receive a payoff of 0, and any deviation would result in a lower payoff.

(C, C): Both A and B choose to Continue. Similarly, neither player has an incentive to deviate since they both receive a payoff of -1, and any deviation would result in a lower payoff. (c) There is no dominant strategy in this game. A dominant strategy is a strategy that yields a higher payoff regardless of the actions taken by the other player. In this case, both players' payoffs depend on the actions of both players, so there is no dominant strategy. (d) The Subgame Perfect Nash equilibria (SPNE) can be found by considering the game as a sequential game and analyzing each subgame individually.

In this game, there is only one subgame, which is the entire game itself. Both players move simultaneously, so there are no further subgames to consider. Therefore, the Nash equilibria identified in part (b) [(S, S) and (C, C)] are also the Subgame Perfect Nash equilibria of this game.

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