What mathematical relationship exists between human population and time

Answer: 1) Value is placed on top of the X =90

2) Value is placed on the bottom of the X =21

3)  Factored form will be (3x+5)(3x+2)

Step-by-step explanation:

Since we have given that

[tex]9x^2 + 21x + 10[/tex]

As we know the quadratic form :

[tex]ax^2+bx+c=0[/tex]

1) Value is placed on top of the X is given by

[tex]a\times c=9\times 10=90[/tex]

2) Value is placed on the bottom of the X is given by

[tex]b=21[/tex]

3) Factorised form:

We will use "Split the middle term":

[tex]9x^2 + 21x + 10\\\\=9x^2+15x+6x+10\\\\=3x(3x+5)+2(3x+5)\\\\=(3x+2)(3x+5)[/tex]

Hence, Factored form will be

(3x+5)(3x+2)

Answer:

SXF ~= GXT

Step-by-step explanation:

SX corresponds to GX,

XF corresponds to XT,

so SF corresponds to GT.

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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Answer:

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

Step-by-step explanation:

Answer:

the answer is C.

Step-by-step explanation:

-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.

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.

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 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:

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

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.

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

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)

Final answer:

To find the uniform width of the deck around a 4 yd by 5 yd rectangular pool, with the combined area of the deck and pool being 90 square yards, we form a quadratic equation based on the dimensions. After solving the equation, we obtain the width of the deck as the positive solution.

Explanation:

The student has a rectangular pool and wants to build a concrete deck of a uniform width around it such that the combined area of the pool and deck is 90 square yards. To solve this problem, we first need to recognize that the area of just the pool is length times width, which is 4 yd by 5 yd. This gives us an area of 20 square yards for the pool alone.

Next, we consider that the deck surrounds the pool uniformly. If we let 'w' be the width of the deck, then the new length and width of the pool plus the deck becomes (4 + 2w) yd and (5 + 2w) yd respectively, since the deck is added to all four sides of the pool.

The combined area is therefore (4 + 2w) * (5 + 2w) = 90 square yards. Expanding the left side of the equation and simplifying, we get 20 + 18w + 4w2 = 90. This simplifies further to 4w2 + 18w - 70 = 0 when we subtract 90 from both sides.

To solve for 'w', we factor the quadratic equation or use the quadratic formula. Upon factoring, we find that w could have two potential values (one positive and one negative), but since width cannot be negative, we discard the negative value. The positive value gives us the width of the deck.