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Answer:- The total number of roots in the given polynomial function is 2.

Explanation:-

We know that corollary of Fundamental Theorem of Algebra tells that polynomial will have exactly as many roots(m) as its degree(m>0).

The given polynomial function [tex]g(x)=5x-12x^2+3[/tex] is a quadratic polynomial with degree 2.

Thus by corollary of Fundamental theorem of algebra

The total number of roots in the given polynomial function must be 2.

Answer:

  D.  7x -4

Step-by-step explanation:

You want the simplified form of the expression 2x-4+5x.

An expression is simplified by eliminating parentheses and combining like terms. Here, there are no parentheses, but there are like terms: 2x and 5x. Combining them gives ...

  2x -4 +5x

  = (2 +5)x -4

  = 7x -4 . . . . . . . . . matches choice D

The value of x is AB/3, which is equal to KD/3.

In the given scenario, we have two similar triangles, HKD and KFD. Since they are similar, their corresponding sides are proportional. In triangle HKD, the width KD is equal to x, and in triangle KFD, the base KF is equal to 3x (proportional to AB). Therefore, the value of x is AB/3, which is equal to KD/3.

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Answer: x=16

Step-by-step explanation:

In the processes of the dilation each number displayed in the first triangle is multiplied by four in order for the second figure to be created. Therefore you would also multiple 4 x 4 in order to get 16.

Answer: equation of a linear function in point-slope form

Step-by-step explanation:

Given : The equation of a linear function in point-slope form passing through point [tex](x_1,y_1)[/tex] is

[tex]y -y_1 = m(x -x_1)[/tex]

The equation written by Harold correctly

[tex]y = 3(x - 7)[/tex]

It can be written as:[tex]y-0 = 3(x - 7)[/tex]

When we compare to the equation of a linear function in point-slope form, we get [tex]y_1=0,\ x_1=7[/tex]

Hence, the point used by Harold = [tex](x_1,y_1)=(7,0)[/tex]

Answer:

The correct option is all real numbers greater than or equal to -3.

Step-by-step explanation:

The concept of domain of a function refers to all the points in the x axis for which the function is defined. In the graph as you can see the function starts in x = -3 (includes that point) and growths towards positive values of x, to +∞. So its domain is [-3, ∞) or {R, x≥ -3} in other words "all real numbers greater than or equal to -3."

Answer:

The polygon that does NOT belong with the other three is a pentagon.

Step-by-step explanation:

A polygon is a 2 D shape formed with straight lines. Like - triangles, quadrilaterals, pentagons, hexagons etc.

Here in the given choices, parallelogram , rectangle and rhombus all are four sided polygons and has parallel sides.

Only pentagon has 5 sides with no parallel sides.

Hence, the polygon that does NOT belong with the other three is a pentagon.

The missing nucleus in the nuclear decay reaction of Thorium-232 into Radium-228 is an alpha particle, or Helium-4.

The question pertains to a nuclear decay reaction where Thorium-232 decays into Radium-228 and a missing nucleus. The missing nucleus can be determined by subtracting the atomic mass and atomic number of the daughter nucleus (Radium-228 with atomic number 88) from the parent nucleus (Thorium-232 with atomic number 90). This yields an alpha particle (He), which has an atomic mass of 4 and atomic number of 2. Here's how it works:

232 90Th (parent nucleus) → 228 88Ra (daughter nucleus) + 4 2He (missing nucleus).

Thus, the missing nucleus is an alpha particle (Helium-4).

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Answer:

The coefficients of the terms come from rows of the triangle.

If the exponent is n, look at the entries in row n.

Final answer:

The compound interest inequality for the investment account is 3500(1 + 0.08)^t < 6000. Solving this, we find that the account will have less than $6,000 for approximately 6 years.

Explanation:

To solve this problem, we will use the formula for compound interest which is [tex]A = P(1 + r)^t,[/tex] where:

We are trying to find the number of years, t, when the account will have less than $6,000, at an annual interest rate of 8%, i.e., r = 0.08.

The inequality will be:

[tex]3500(1 + 0.08)^t < 6000[/tex]

To solve for t, we first divide both sides by 3,500:

[tex](1 + 0.08)^t[/tex]< ≈ 1.7143

Now, take the natural logarithm of both sides:

[tex]ln((1 + 0.08)^t) < ln( 1.7143)[/tex]

t · ln(1.08) < ln(≈ 1.7143)

Divide both sides by ln(1.08) to isolate t and calculate:

t < ≈ ln(≈ 1.7143) / ln(1.08) < ≈ 6.6

Therefore, the investment account will have less than $6,000 for approximately 6 years.

Answer:

The domain is the all possible value of x which give the real value of y whereas Range is the all possible value of y after putting the values of x.

For example: We have function: f(x) = x²

Here Domain = All Real Numbers = (-∞, ∞) {∵ For every value of x f(x) give real value)

and, Range = All positive real number = (0, ∞) {∵ f(x) is giving only positive value no matter what the value of x is}

The required three decimals between 0.55 and 0.56 are 0.552, 0.553, and 0.554 which are shown in the number line.

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.

The numbers on the number line increase as one moves from left to right and decrease on moving from right to left.

We have to determine the three decimals between 0.55 and 0.56

As per the attached number line,

Three decimals between 0.55 and 0.56 are :

⇒ 0.552, 0.553, and 0.554

Hence, the required three decimals between 0.55 and 0.56 are 0.552, 0.553, and 0.554 which are shown in the number line.

Learn more about the number line here:

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(x^2 + 16 + 8^2 = 18 + 8^2

Yes 138,435 can be divided by 3 it equals to 46,145