1. What are the next two terms of the following sequence?

1,5,9.........


A: 27, 211

B: 10, 11

C: 12, 15

D: 13, 17 *****

2. what is the common difference of the following Arithmetic sequence

102, 100, 98, 96....

A: 2

B: -2*****

C: -1

D: 102


3. What is the ninth term of the arithmetic sequence defined by the rule below?

A(n( = -14 + (n-1)(2)

A: 232

B: 230

C:2****

D: 4


4. Which function below represents the arithmetic sequence

3, 7 , 11, 15....?

A: F(n) = 4+3(n-1)

B: F(n) = 4+3n

C: F(n) = 3+4n

D: F(n) = 3+4(n-1)******

Answer: 1) C. (x+3)(x+7)

2) D. (x-3)(x-8)

3) C. (x-2)(x+4)

5) B. (x+9)(x-9)

Step-by-step explanation:

1)

x2 + 10x + 21

(we look for 2 numbers whose product gives 21 and whose sum gives 10, then replace 10x by those two numbers)

x2 + 7x + 3x +21

x(x+7) + 3(x+7)

(x+3)(x+7)

2)

x2 - 11x + 24

(we look for 2 numbers whose product gives 24 and whose sum gives -11, then replace -11x by those two numbers)

x2 -3x-8x +24

x(x-3) -8(x-3)

(x-3)(x-8)

3)

x2 + 2x - 8

(we look for 2 numbers whose product gives -8 and whose sum gives 2, then replace 2x by those two numbers)

x2 + 2x - 8

x2 + 4x - 2x - 8

x(x+4) -2(x+4)

(x+4)(x-2)

5)

x2 - 81

Its a difference of two squares

(x-9)(x+9)

Answer:

the answer is C.

Step-by-step explanation:

Final answer:

To find the measures of the angles with a ratio of 2:9:1, represent the angles as 2x, 9x, and x, set up the equation 2x + 9x + x = 180, solve for x, and then use x to calculate each angle. The measures of the angles are 30 degrees, 135 degrees, and 15 degrees.

Explanation:

To find the measures of the angles in a triangle with a given ratio, we apply the fact that the sum of the angles in a triangle is always 180 degrees. If we have the ratio of 2:9:1, we can represent the angles as 2x, 9x, and x, respectively. Since the angles must add up to 180 degrees, we can write the equation 2x + 9x + x = 180, which simplifies to 12x = 180.

Divide both sides of the equation by 12 to find the value of x: x = 180 / 12 = 15 degrees. Now, we can find each angle by multiplying x by the respective ratio number:

The first angle is 2x, which equals 2(15) = 30 degrees.

The second angle is 9x, which equals 9(15) = 135 degrees.

The third angle is 1x, which equals 1(15) = 15 degrees.

Therefore, the measures of the angles in the triangle are 30 degrees, 135 degrees, and 15 degrees.

Answer:

The vertex is (3,-16)  and axis of symmetry is 3

Step-by-step explanation:

The vertex of a quadratic equation [tex]f(x)=ax^{2}+bx+c[/tex] is calculated as [tex](\frac{-b}{2a},f(\frac{-b}{2a}))[/tex]

and the axis of symmetry is  [tex]\frac{-b}{2a}[/tex]

Compare equation [tex]y=x^{2}-6x-7[/tex] with [tex]f(x)=ax^{2}+bx+c[/tex]

Where a= 1 and b = -6

so, [tex]x=\frac{-b}{2a}=\frac{-(-6)}{2}[/tex]

      [tex]x=3[/tex]

Now, put the value of x=3 in [tex]y=x^{2}-6x-7[/tex]

[tex]y=(3)^{2}-6(3)-7[/tex]

[tex]y=9-18-7[/tex]

[tex]y=-16[/tex]

Therefore, the vertex is (3,-16)  and axis of symmetry is 3

-5.77 is the answer

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Final answer:

The expression 2.5 – 3.1 – 3.86 + 2.7 – 4.01 simplifies to -5.77 by adding the positive numbers together, adding negative numbers together, and then combining the two results.

Explanation:

To simplify the expression 2.5 – 3.1 – 3.86 + 2.7 – 4.01, we need to perform the subtraction and addition operations in sequence.

The simplified result of the expression is -5.77.

Answer:

Sample Response: Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.

Answer:

The answer to your question is about 5.5 hours.

Step-by-step explanation:

The equation is y = 35(3x)

Data

# of bacteria = 550 = y

time = ? h

    Then    550 = 35(3x)                         substitution

                 550 = 105x                           simplifying

                x = 5.23 h.

Answer:  The correct option is (B) 60.

Step-by-step explanation:  Given that the line BD is parallel ti the line XY.

We are to find the value of x.

We know that

if two parallel lines are cut by a transversal, then the measures of the alternate interior angles are equal.

In the given figure, BD is parallel to XY and they are cut by a transversal.

So, the angles with measures x° and 60° are alternate interior angles.

Therefore, we must have

[tex]x^\circ=60^\circ\\\\\Rightarrow x=60.[/tex]

Thus, the value of x is 60.

Option (B) is CORRECT.

For this case what we must do is observe the cut points of the function with the x axis.

The cut points with the horizontal axis are:

(-4, 0)

(-2, 0)

(6, 0)

Therefore, the intersections with the axis are:

x = -4

x = -2

x = 6

Answer:

The apparent x-intercept (s) of the function graphed are:

-4, -2, and 6

To find the interest rate that will cause Pablo's money to double in approximately 44 years, we can use the rule of 72. The interest rate is approximately 1.64%.

To find the interest rate that will cause Pablo's money to double in approximately 44 years, we can use the rule of 72. The rule of 72 states that dividing 72 by the interest rate will give you the approximate number of years it takes for money to double. In this case, we need to find the interest rate that makes the money double in 44 years. So, we divide 72 by 44 to get the interest rate.

Interest rate = 72 / 44 ≈ 1.6363636363636363

Therefore, the interest rate that will cause Pablo's money to double in approximately 44 years is approximately 1.64%.

Answer: A. All equilateral triangles can be mapped onto each other using dilations.

Step-by-step explanation:

We know that all equilateral triangles are similar to each but not congruent because they all have same measure of corresponding angles 60° but do not have same side-lengths.

So, equilateral triangles can be mapped onto each other using dilation because they maps similar shapes (sometimes congruent) where as rigid transformations always map congruent shapes so we cannot map all equilateral triangles by using  rigid transformations.

Answer:

SXF ~= GXT

Step-by-step explanation:

SX corresponds to GX,

XF corresponds to XT,

so SF corresponds to GT.

Answer:

[tex]\frac{4}{229}+\frac{30i}{229}[/tex]

Step-by-step explanation:

To prove the given equation involving tangent, we use trigonometric identities and simplification techniques to show that both sides of the equation are equal.

To prove the given equation: tan(π/4 x) - tan(π/4-x)/tan(π/4 x) tan(π/4-x) = 2sin(x)cos(x).

We can simplify this equation using the trigonometric identities for tan:

By substituting these identities, we get:

1 - 1/(tan(π/4-x)tan(π/4 x)) = 2sin(x)cos(x)

From here, we can simplify further and use the following trigonometric identities:

Using these identities, we can simplify the equation to:

-2sin(x)cos(x) = -2sin(x)cos(x)

Therefore, the given equation is proved to be true.

Zero Solutions

Since the two lines have equal slopes and different intercepts

The system of equations has no solution.

First, let's rewrite the second equation in slope-intercept form:

2y = 5x + 8

y = (5/2)x + 4

Now we can see that both equations have the same slope (5/2), but different y-intercepts (2 and 4). Since the slopes are the same, the lines are parallel and will never intersect. Therefore, this system of equations has no solution.

To simplify the expression (3.2b+0.8)+1.9b, combine like terms by adding the coefficients. The simplified expression is 5.1b + 0.8.

To simplify the expression (3.2b+0.8)+1.9b, we can combine like terms by adding the coefficients. The variable b remains unchanged. So, we have:

(3.2b + 1.9b) + 0.8

Combine the coefficients: 3.2 + 1.9 = 5.1

The simplified expression is therefore 5.1b + 0.8.

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