Convert the standard equation to vertex form.
f(x) = 3x^2+ 18x – 7

0.0043 is the number which contains a digit or digits which are not significant

In scientific notation, the significant figures are those digits that carry meaning in terms of the accuracy or precision of the measurement.

The non-significant digits are those that are present in the number but do not add any value to the measurement in terms of accuracy or precision.

In  0.0043, there are only two significant figures: 4 and 3.

The leading zeros are not significant as they only serve as placeholders to indicate the position of the decimal point.

Therefore, this number contains a digit that is not significant.

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The correct value of this algebraic expression is -1/16

Given the expression, \(\large \sf \dfrac{-b}{2a}\), let's just: change the letters to the numbers and then perform the given operations.

*Equal signs will be positive ⇒ (-) (-)= + & (+) (+) = +

*Different signs will be negative ⇒ (-) (+) = - & (+) (-) = -

\(\\\large \sf \dfrac{-b}{2a} , \ a=-8 \ , \ b=-1\)

\(\large \sf \dfrac{-(-1)}{2 \cdot (-8)}\)

\(\large \sf \dfrac{1}{2 \cdot (-8)}\)

\(\large \sf \dfrac{1}{-16}\)

\(\blue{\boxed{\large \sf -\dfrac{1}{16} }}\\\)

Therefore, the final answer to this simplification will be -1/16

Answer:

1.55

Step-by-step explanation:

you just change the fractions to decimals

Using the area of a triangle, the length of the unknown side in the cross section is: 18 yards.

The area of a triangle = 1/2 * base * height.

The cross section is a triangle with an area of 243 square yards and a base length that is equal to x, and an height of 27 yd.

Therefore:

Height = 27 yards

Area = 243 square yards

Base = x yards

Plug in the values:

243 = 1/2 * x * 27

2*243 = 27x

486 = 27x

486/27 = x

x = 18 yards

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Given :

On average, a refrigerator door is opened 99 times each day.

Len has two refrigerators in his house.

To Find :

How many times in a 8−week period are the refrigerator doors opened.

Solution :

Number of times door opened for 2 refrigerator , n = 99×2 = 198.

Number of days in 8 week , d = 8×7 = 56 days.

So, total number of times doors open in a period of 8-week is :

\(T=n\times d\\\\T=198\times 56\\\\T=11088\ times\)

Therefore, refrigerator doors are opened about 11088 times.

Hence, this is the required solution.

To establish whether findings from a sample may be extrapolated to the entire population, we use inferential statistics.

A population is the total group about which you want to reach conclusions. A sample is the specific group from which you will collect data. Always, the sample size is less than the whole population. The term "population" in research rarely refers to people. Using an office as an example, all of the employees would represent the Population, and all of the managers would represent the Sample. To create a comparison, picture your population as an ocean, and your sample as an aquarium.

Inferential statistics is a branch of statistics that uses data to draw inferences and generalizations about a certain situation or fact.

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Answer:

whole numbers: 0

integers: -9

natural: 4 & 100

rational: 1.44 & 1/2

irrational: √17, √29, √60, & π (pie)

Step-by-step explanation:

When f(x) = g(x), x^4 - 8x^2 = 8x^2.

x^4 - 16x^2 = 0

x^2(x^2 - 16) = 0.

Either x^2 = 0 or x^2 = 16.

The possible values of x are {-4, 0, 4}.

The values of x for which f(x) = g(x) will be {-4, 0, 4}.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable. Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division

Given expression is f(x) = x⁴ – 8x², g(x) = 8x²

The value of x will be calculated as:-

When f(x) = g(x), x⁴ - 8x² = 8x².

x⁴ - 16x² = 0

x²(x² - 16) = 0.

Either x² = 0 or x² = 16.

The possible values of x are {-4, 0, 4}.

Therefore, the values of x for which f(x) = g(x) will be {-4, 0, 4}.

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Here's a more detailed explanation: To determine if a graph is a function, you can use the vertical line test. The vertical line test states that if you can draw a vertical line that intersects the graph in more than one place, then the graph is not a function.

Determining whether a graph represents a function is an important concept in mathematics, especially in algebra and calculus. A function is a set of ordered pairs where each input is associated with exactly one output.

So, if you take a ruler or a straight edge and place it vertically on the graph, and it intersects the graph in two or more points, then the graph is not a function. This is because if two points in the graph have the same x-value, they must have different y-values, since functions can only have one output for each input.

On the other hand, if you place a vertical line anywhere on the graph and it intersects the graph in only one point, then the graph is a function.

It's also important to remember that a function must also pass the horizontal line test, which means that no horizontal line can intersect the graph in more than one place.

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Mean of country A is $29600 and median $29000. Mean of country B is $49800 and median is $29000. Country B has greater income inequality. So option B is the correct answer.

Mean of incomes in country A = (9000+ 21000+ 29000 + 39000+ 50000)/5   =  $29600

Median income of country A = (5+1)/2 th term = 3rd term = $29000

Mean to median ratio = 29600/ 26000= 1.02

Mean income of country B = ( 9000+ 21000+ 29000+ 39000+ 151000)/5 = $ 49800

Median income = (n+1)/2 th term = (5+1)/2 = 3rd term = 29000

Mean to median ratio of country B = 49800/29000 = 1.71

Since mean and median are closer to each other, standard deviation is less. The mean to median ratio is greater for country B. So country B has greater income inequality.

If the income inequality has been increasing, then the mean-median ratio will increase, due to the extreme values, mean will increase. So option B is the correct answer.

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Answer:

Direct proportion

4 boys = 5 girls

20 boys = 25 girls

Answer: 36

cause i know it is

Answer:

Step-by-step explanation:

x + 44x = 180

45x = 180

x = 4

180-x = 176

answer is 4

Answer:

Way too many

Step-by-step explanation:

(92)

\( \huge \boxed{\mathfrak{Question} \downarrow}\)

\( \sf1 - 3 n \gt - 1 - 4 ( 2 n - 8 )\)

\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)

\( \sf1 - 3 n \gt - 1 - 4 ( 2 n - 8 )\)

\( \sf1-3n>-1-8n+32 \)

\( \sf1-3n>31-8n \)

\( \sf1-3n+8n>31 \)

\( \sf1+5n>31 \)

\( \sf5n>31-1 \)

\( \sf5n>30 \)

\( \sf \: n>\frac{30}{5} \\ \)

\( \boxed{ \boxed{ \bf \: n>6 }}\)

Answer:

3 roots.

Step-by-step explanation:

To determine how many roots a polynomial has, you have to look at the term with the highest exponent. That exponent is how many roots the polynomial will have.

Then, for:

Since this polynomial is factored already equalizing 0, we can see that there are three roots:

Using MATLAB command, we get the equation is: s^4 + 24s^3 + 249s^2 + 996s + 29800.

In MATLAB, type the following command:

coefficients = [1, 24, 249, 996, 29800];
roots_eq = roots(coefficients);

After obtaining the roots, identify the dominant roots (closest to the origin) and use them to estimate the system's time constant (τ), damping ratio (ζ), and oscillation frequency (ωn).

To find the dominant roots, you can examine the real parts of the roots, as the dominant roots will have the smallest real parts.

Once you identify the dominant roots, you can use them to calculate τ, ζ, and ωn using the following relationships:

τ = 1/abs(real(dominant_root))
ζ = abs(real(dominant_root))/ωn
ωn = sqrt(real(dominant_root)^2 + imag(dominant_root)^2)

The MATLAB command roots to obtain the roots of the fourth-order characteristic equation is shown below:s +24s^3 +249s^2 +996s+29800The MATLAB command roots produces the roots of a polynomial equation. Here, the given equation is a fourth-order characteristic equation, so we can use the roots function in MATLAB as follows:

roots([1 24 249 996 29800])The roots of the fourth-order characteristic equation are -49.69, -12.48, -0.83, and -0.40.Therefore, the dominant roots (i.e. closest to the origin) are -0.83 and -0.40.The formulas for the system's time constant, damping ratio, and oscillation frequency are as follows:

Time constant = 1/abs(real(dominant pole))Damping ratio = -real(dominant pole)/abs(dominant pole)Oscillation frequency = abs(imag(dominant pole))Therefore, the system's time constant is 1.20, damping ratio is 0.94, and oscillation frequency is 0.55.
To find the roots of the given fourth-order characteristic equation using MATLAB, use the 'roots' function.

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The missing base for the expression x² = 100 is given by:

± x = 10.

The expression in this problem is given as follows:

x² = 100.

The missing base is represented by the variable x, hence we have to solve the above expression x² = 100 for the variable x.

To solve for x, we need to isolate the variable x, applying the inverse operation to the second power, which is the square root, hence the variable x is isolated as follows:

x = plus/minus square root of 100.

The plus/minus sign is necessary because the x-squared function is even, then the missing base is obtained as follows:

x = ± 10.

Plus/minus 10 because both of these statements are true:

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Answer: Answer in the photo

Step-by-step explanation:

Answer:

12.91

Step-by-step explanation:

find the square roots ;

10.39 + 11.18 - 8.66 = 12.91

Answer:

The height of flag pole is 841.8 ft.

Step-by-step explanation:

Let the height of the flag post is h.

x = 1660 ft

According to the triangle, ABC

\(tan 41 = \frac{y}{1660}\\\\y = 1443 ft\)

Now According to the triangle ABD

\(tan 54 = \frac{h + y }{1660}\\\\h + 1443 = 2284.8\\\\h = 841.8 ft\)

Answer:

2.4cm²

Step-by-step explanation:

base = 2cm

height = 12mm = 1.2cm

To go from mm to cm you have to divide by 10

area = base x height

area = 2 x 1.2

area = 2.4cm²

Based on the information provided, it seems that you are encountering some issues with a module called "binary_finder."

The phrase "content loaded" suggests that you have loaded some content, possibly related to this module. "Binary not linear" indicates that the nature of the content or code you're dealing with is binary, which means it consists of zeros and ones.

You mentioned having two pictures, one showing the question code and another displaying an answer from Chegg, which you find insufficient. However, the actual content of those pictures was not provided. If you can share the code or describe the specific problem you're facing with the binary_finder module, I'll be happy to assist you further.

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The answer choice A is x(x + 6)(x + 4), which is the polynomial \(x^3 + 10x^2 + 24x\)  fully factored form.

The quadratic expression enclosed in parenthesis can be factored:

x(x + 6)(x + 4)

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.\(x^2+x-12\) is an illustration of a polynomial with a single variable.

from the question:

The given polynomial is\(x^3 + 10x^2 + 24x.\)

From each term, we may factor out the common factor of x:

\(x(x^2 + 10x + 24)\)

The quadratic expression enclosed in parenthesis can be factored:

x(x + 6)(x + 4)

As a result, solution option A is the fully factored version of the polynomial \(x^3 + 10x^2 + 24x\) , which is x(x + 6)(x + 4).

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A solution to this system of linear equations is (1, -2).

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

4x - 2y = 8     ......equation 1.

y = -2     ......equation 2.

Next, we would use an online graphing calculator to plot the given function as shown in the graph attached below.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant IV and it is given by the ordered pair (1, -2).

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Answer:

$15.98

Step-by-step explanation:

25% off means it is 75% of its normal cost

0.75 x 20 = 15

The scarf is $15 after 25% discount. Then we calculate its final cost after tax:

6.5% = 0.065

1.065 x 15 = 15.975 which rounds to $15.98

Answer: 15.98

Step-by-step explanation: 25% off 20 is 15. 6.5% times 15 is .98 so the answer is 15.98

d.0.003 choice correctly shows 0.3% as a decimal.

Here, we have,

given that,

the percent is: 0.3%

now, we know that,

percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity. percentage.

now, we get,

0.3%

=0.3 ÷ 100

=0.003

now, we know, 0.003 is a decimal.

so, we get,

d.0.003 choice correctly shows 0.3% as a decimal.

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Height of the triangle is the altitude of the triangle and which is drawn perpendicular from the vertex of the triangle to the opposite side. The height of the tringle is 24 units. Hence option 2 is the correct option.

The triangle for the given problem is shown in the image below.

Form the figure the length of the each side is \(16 \sqrt{3}\) units.

As all the sides are equal thus the \(\Delta MNO\) is a equilateral triangle in which the height of the divides the triangle into two equal part of the length \(8\sqrt{3}\) at point R.

Height of the triangle is the altitude of the triangle and which is drawn perpendicular from the vertex of the triangle to the opposite side.

Now in the  \(\Delta MRN\), the length of the hypotenuse is \(16 \sqrt{3}\) units and the length of the base is \(8\sqrt{3}\) units. Let h is the height of the triangle thus by the Pythagoras theorem,

\((16\sqrt{3})^2 =(8\sqrt{3})^2+h^2\)

Solve for h,

\(\begin{aligned}h^2 &=(16\sqrt{3})^2 -(8\sqrt{3})^2\\h^2 &=16\times16\times3 -8\times8\times3\\h^2 &=576\\h &=\sqrt{576}\\h &=24\\\end\)

Thus the height of the tringle is 24 units. Hence option 2 is the correct option.

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Answer:

b. 24

Step-by-step explanation:

edge

Using the central angle theorem, the degree measure of x is 53°.

The length of AB is 18.8 units.

Given a circle.

We have the central angle theorem,

We have that the angle subtended by an arc of a circle at the center is twice the angle subtended by the same arc at any point on the circle.

Here, the arc is semicircle.

Angle subtended by semicircle at the center= 180°

So, ∠ADB = 180° / 2 = 90°

Interior angles of a triangle sum up to 180°.

x = 180 - (37 + 90) = 53°

sin (x) = BD / AB

sin (53) = 15 / AB

AB = 15 / sin (53)

AB = 18.78 ≈ 18.8 units

Hence the measure of x is 53° and the length of AB is 18.8 units.

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