The roots of the equation $2x^2-mx+n=0$ sum to $6$ and multiply to $10$. What is the value of $m+n$?

Answer:

A

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 6, - 6) and (x₂, y₂ ) = (6, 0) ← 2 points on the line

m = [tex]\frac{0-(-6)}{6-(-6)}[/tex]= [tex]\frac{0+6}{6+6}[/tex] = [tex]\frac{6}{12}[/tex] = [tex]\frac{1}{2}[/tex]

[tex]x^2-5x+22=7x+2\implies x^2-12x+20=0 \\\\[-0.35em] ~\dotfill\\\\ \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-12}x\stackrel{\stackrel{c}{\downarrow }}{+20}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ (-12)^2-4(1)(20)\implies 144-80\implies 64[/tex]

The licenses have space for 6 characters.

We need to note that there are 26 alphabets and 10 numbers to pick from.

So, for the first character, any of the 26 alphabets can take this spot.

For the second character, 25 alphabets are now available for that space. (Since repetition is not allowed)

For the third character, 24 alphabets are available for that.

For the fourth character, any of the 10 numbers can take up that spot.

For the fifth character, only 9 numbers can take this spot now. (No repetition rule too)

For the sixth character, 8 numbers can take that spot.

So, mathematically, the number of license tags possible will be

[tex]\bold{26 \times 25 \times 24 \times 10 \times 9 \times 8 = \underline{11,232,000} \ possible \ license \ tags}[/tex]

Answer:

11,232,000

Step-by-step explanation:

26 choices for the first letter.

25 choices left for the second letter (can't repeat letters)

24 choices left for the third letter

26 x 25 x 24 = 15,600 = possible first 3 characters.

10 choices for the first number

9 choices left for the second number (can't repeat numbers)

8 choices left for the third number

10 x 9 x 8 = 720 = possible last 3 characters.

chatgpt

R2, since the model only has one independent variable.

Find R2:

R^{2} = [tex]\frac{SSR}{SST}[/tex]

R^{2} = [tex]\frac{18.26347892}{26.24578040}[/tex]

R^{2} = 0.6958634

[tex]R^{2} = 0.6959}}[/tex]

Part 2 of 3:

Find Ra2:

[tex]R^{2}_{a}= 1-\frac{(1-R^{2}) \\times (n-1)}{n-k-1}[/tex]

where

n = 9

since dftotal = n -1 = 8

thus n = 8+1=9

and k = number of independent variables = 1

Thus

[tex]R^{2}_{a}= 1-\frac{(1-0.6958634 ) \\times (9-1)}{9-1-1}[/tex]

[tex]R^{2}_{a}= 1-\frac{0.3041366 \\times 8}{7}[/tex]

[tex]R^{2}_{a}= 1-0.3475846[/tex]

[tex]R^{2}_{a}= 0.6524154[/tex]

[tex]R^{2}_{a}= 0.6524}}[/tex]

Part 3 of 3:

R2, since the model only has one independent variable.

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The diameter of the lake is 6.2 m.

The diameter is the distance from one edge of the circle to the next across the center.

The diameter can be determined given the circumference and pi, since circumference is pi x diameter.

The number of times Gracie walks around the circular lake = 15 times

The total distance covered by the walk = 2,178 meters

The circumference (the distance around the edge of the circular lake) is 145.2 m (2,178 ÷ 15).

Circumference = C = 2πr = πd

Diameter = C/π

145.2  ÷ 3.143

= 46.2 m

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The length of the arc of the circle that has a radius of 16 inches and a central angle of 75 degrees is calculated as 6.66π inches (to two decimal places).

The length of an arc is calculated using the formula below:

arc length = θ/360 * 2 * π * r

Given the variables:

Central angle (θ) = 75 degrees

radius (r) = 16 inches

Plug in the values:

arc length = 75/360 * 2 * π * 16

length of arc ≈ 6.66π inches (to two decimal places).

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The prominent similar feature between f(x) and g(x) is the present y-intercept.

Since the discriminant is negative, there are no possible solutions to the given equation, which implies that f(x) has no x-intercepts.

It should be noted that to identify the y-intercept, we set x = 0 and evaluate f(x):

f(0) = 2(0)² - 3(0) + 4

f(0) = 4,

The y-intercept of f(x) can be determined as (0, 4).

Moreover, the function g(x) = 2x-4 is a power function having a negative exponent, which makes it a reciprocal function. It's domain comprises all real numbers but 0, while its range includes all real numbers excluding 0.

In order to obtain the x-intercept of g(x), we set g(x) equal to zero and solve for x:

0 = 2x-4

2x = 4

x = 2

Consequently, the x-intercept of g(x) is (2, 0), together with the y-intercept (0, -4).

The prominent similar feature between f(x) and g(x) is the present y-intercept. On the other hand, f(x) does not contain any x-intercepts, whereas g(x) has a single x-intercept. Also, f(x) is categorized as a second-degree polynomial function, whereas g(x) is classified as a reciprocal function.

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Answer: In that picture the slope is increasing

Step-by-step explanation: positive rise and positive run (uphill from left to right)

Answer: 4/5

Step-by-step explanation: In decimal form: 0.8

Answer:

!

Step-by-step explanation:

BGC or AGF

Adjacent means next to or adjoining something else and both of the mentioned angles are next to angle AGB.

Answer: Angle aeb

Step-by-step explanation: To be supplementary, the angle(s) must add up to 180. Angle AEB and angle DEA add to 180. Another way to find this is to find the angle that the angle is adjacent to in a straight line.

Answer:To evaluate the function for f(2), we simply substitute x = 2 into the function

:f(2) = 8(2) + 7

Simplifying the expression:

f(2) = 16 + 7f(2) = 23

Therefore, f(2) = 23.

Step-by-step explanation:

The curve is defined as follows

A. absolute minima

B. absolute maxima

C. neither

D. relative minima

E. relative maxima

F. neither

G.  neither

When examining a function, its absolute minimum refers to the lowest possible value it can reach throughout its entire domain.

In a similar manner, absolute maximum pertains to the highest value that said function is capable of attaining within the same specified range, without consideration of separate intervals or regions.

To reiterate, these values denote the smallest and largest outcomes the function can yield over its complete set of input values, regardless of where those values may be located.

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After using synthetic division, the answer are given as follows;

first row          = -4, 4, 12

Second Row = -2 2 -6 -5

Answer = 6 + [-5/x-2]

-2x^3+6x^2-10x+7 / x-2

Coefficient of the numerator polynomial are:

- 2, 6, -10 , 7

the zeros of the denominator are:

x -2 = 0
x = 2

              X³       X³    X¹     X⁰
               -2        6     -10    7

2                                                  

      X³       X³    X¹     X⁰
               -2        6     -10    7

2               ↓        -4        4   -12                

                 -2        2     -6     -5

So the quotient is -2x² +2x - 6 remainder -5

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Answer:

We can use the formula:

average speed = total distance / total time

To find the total distance, we add the distances for each event:

total distance = 1.5 km (swimming) + 40 km (cycling) + 1 km (running) = 42.5 km

To find the total time, we add the times for each event:

time for swimming = distance / speed = 1.5 km / 2.5 km/h = 0.6 hours

time for cycling = 40 km / 12 km/h = 3.33 hours

time for running = 1 km / 9 km/h = 0.11 hours

total time = 0.6 hours + 3.33 hours + 0.11 hours = 4.04 hours

Now we can calculate the average speed:

average speed = total distance / total time = 42.5 km / 4.04 hours ≈ 10.52 km/h

Therefore, Farhan's average speed for the entire competition is approximately 10.52 km/h.

The linear equations from the options given are expressed as: y = 5 and y = -2/5x + 4.

An equation is linear can be expressed in the following forms:

y = mx + b

x = b

y = b

In the above, y is the dependent variable and x is the independent variable, m = slope, and b = y-intercept.

Note that in a linear equation the exponent of the variable is always 1. On the other hand, a nonlinear equation has an exponent that is not equal to 1 and can be expressed as:

y = x²

Therefore, the equations that are linear are:

y = 5 and y = -2/5x + 4.

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The measure of the angle ADC is: 20°

The parameters are given as:

∠ABC = 40°

∠ADC = ?

We know from circle geometry that:

Angle subtended at the center is twice the angle subtended at the circumference.

Therefore:

∠ABC = 2 x ∠ADC

On substituting the value we get:

40° = 2 * ∠ADC

∠ADC = 20°

Therefore, the measure of the angle ADC is 20°

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Complete question is:

A circle is centered on point B. Points A, C and D lie on it's circumference.

If ABC measures 40 degrees, what does ADC measure?

Answer:

83 degrees

Step-by-step explanation:

See attachment below:

Answer:

c c c c c c c c c c c c c c c c c c c c c c c c c c c c c

The numbers are characterized as rational and irrational numbers as below

1. 3.2 x 10³ - R (Rational)

2. 4/3 - R (Rational)

3. 1.423... - I (Irrational)

4. TT/6 - I (Irrational)

Rational numbers harmonized with a fraction of two integers where the denominator must not be zero. In simpler terms, it can be conveyed as p/q whereby both "p" and "q" are integers while "q" is unequal to zero.

As opposed to rational numbers, irrational ones cannot be expressed in a fraction or quotient of two integers. It's not possible to write them down in terms of the figure p/q whereby "p" and "q" are integers, differing from one another, and "q" is also inequivalent to zero.

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Answer:

  x+3 . . . . if x > 5

Step-by-step explanation:

You want the meaning of |x+3| if x > 5.

The absolute value function is a piecewise defined function:

  [tex]y=|x|=\begin{cases}-x&\text{for }x < 0\\x&\text{for }x\ge0\end{cases}[/tex]

The expression (x+3) is zero when x=-3. So, your absolute value function will have the piecewise definition ...

  [tex]|x+3|=\begin{cases}-(x+3)&\text{for }x < -3\\x+3&\text{for }x\ge-3\end{cases}[/tex]

You are interested in the value for x > 5, which is definitely greater than -3. That means only the second part of this definition is applicable.

  x+3 . . . . if x > 5

__

Additional comment

The attache graph shows the given absolute value expression (dashed red line). The blue line is (x+3) for x > 5. You can see that it matches the given expression in that region.

The number of triangles formed by triangle ABC is 1

In order to calculate the possible number of triangles ABC that can be made with the specified parts, it is essential to employ conditions for triangle congruence, which includes the Triangle Inequality Theorem.

If sides a, b, and angle A can create a valid triangle, then they must follow these requirements:

a + b > c

a + c > b

b + c > a

By replacing given values with assigned variables, we get:

38 + 77 > c,

38 + c > 77,

77 + c > 38.

After solving these inequalities, we determine that c should be

However, if the Triangle Inequality Theorem is not observed, an unfeasible configuration results. Therefore, it would be impossible to generate a triangle using the following: AB = 38, AC = 77, and angle BAC = 74 degrees.

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Answer: 1204 cm²

Step-by-step explanation:

The upper bound of the area of a page would be the area of a rectangle with the upper bound of the length and width measurements.

Given that each page of the newspaper is a rectangle measuring 43 cm by 28 cm, both correct to the nearest centimetre, the upper bound of the length would be 43.5 cm (since we round up to the nearest centimetre) and the upper bound of the width would be 28.5 cm.

Therefore, the upper bound of the area of a page would be:

43.5 cm x 28.5 cm = 1240.25 cm²

Rounding this value to the nearest whole number, we get:

1204 cm²

So, the upper bound of the area of a page is 1204 cm².

Answer:

1204 cm 2

Step-by-step explanation:

The probability that an adult chosen at random will be willing to change their diet is 0.29 or 29%.

what is probability?

In general terms, probability is the measure of the likelihood or chance of an event occurring. It is a mathematical concept that is used to quantify uncertainty or randomness in various situations.

In formal terms, probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes in an event. It is usually represented as a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The probability of an adult being willing to change their diet can be calculated using the given information as follows:

Probability of an adult being willing to change diet = Number of adults willing to change / Total number of adults

Total number of adults = 400 (as given in the question)

Number of adults willing to change = 116 (as given in the question)

Therefore, the probability of an adult being willing to change their diet can be calculated as:

Probability = 116/400

Probability = 0.29 or 29%

So, the probability that an adult chosen at random will be willing to change their diet is 0.29 or 29%.

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The coordinates of all four vertices of quadrilateral BPQF, we can use the shoelace formula to find its area. The shoelace formula states that the area of a polygon with vertices (x1, y1), (x2,

A triangle is a closed, two-dimensional geometric shape that has three sides and three angles. It is one of the basic shapes in geometry and can be formed by connecting three non-collinear points. Triangles can be classified based on their side lengths and angles.

To solve this problem, we can use the fact that the area of a triangle is equal to half the product of its base and height. Let's first find the length of the sides of the square.

Since the area of the square is 1320 square centimeters, we can find its side length by taking the square root of 1320:

√(1320) ≈ 36.32

So the side length of the square is approximately 36.32 cm.

Next, let's find the coordinates of points E and F. Since E is the midpoint of AB, its coordinates are:

E = ((0+36)/2, (36+0)/2) = (18, 18)

Similarly, since F is a quarter point of BC close to point B, its coordinates are:

F = (36, (3/4)36) = (36, 27)

Now let's find the equation of line CE. Since we know two points on the line (C and E), we can use the point-slope form of a linear equation to find its equation:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is one of the points on the line. We can find the slope of the line by taking the difference in y-coordinates and dividing by the difference in x-coordinates:

m = (0 - 36)/(36 - 18) = -2

Using the point-slope form with point C, we get:

y - 0 = -2(x - 36)

y = -2x + 72

Similarly, the equation of line DB can be found using points D and B:

m = (0 - 36)/(0 - 18) = 2

y - 0 = 2(x - 0)

y = 2x

Finally, we can find the coordinates of point P by solving the system of equations:

y = -2x + 72

y = 2x

Setting the two expressions for y equal to each other, we get:

-2x + 72 = 2x

4x = 72

x = 18

Substituting x = 18 into either equation, we get:

y = 2x = 36

So the coordinates of point P are (18, 36). To find the coordinates of point Q, we can use the fact that it lies on line DF. Since we know two points on the line (D and F), we can again use the point-slope form of a linear equation:

m = (27 - 0)/(36 - 0) = 3/4

y - 0 = (3/4)(x - 0)

y = (3/4)x

To find the intersection point of lines DF and CE, we need to solve the system of equations:

y = (3/4)x

y = -2x + 72

Setting the two expressions for y equal to each other, we get:

(3/4)x = -2x + 72

(11/4)x = 72

x = 64/11

Substituting x = 64/11 into either equation, we get:

y = (3/4)(64/11) ≈ 14.73

So the coordinates of point Q are (64/11, 14.73).

Hence, Now that we have the coordinates of all four vertices of quadrilateral BPQF, we can use the shoelace formula to find its area. The shoelace formula states that the area of a polygon with vertices (x1, y1), (x2,

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Answer:

The lower quartile corresponds to the 25th percentile of the data set. To find the maximum value for the lower quartile, we need to find the largest number that is at or below the 25th percentile.

The range of the numbers that the random number generator can pick is 69 - 7 + 1 = 63. The 25th percentile corresponds to the value that is 25% of the way through this range, which is:

0.25 * 63 = 15.75

Since we can't pick a fractional number, we need to round down to 15. Therefore, the maximum value for the lower quartile is 15.