12a2 + 4b for a = 8 & b = -6.
PLease help

In the given parabola equations, the third equation \(y = 2x - 3x^{2}\) has a maximum value.

What is the Maximum parabola?

If a parabola opens up, it has the lowest point, and if it opens down, it has the highest point. For a parabola to have a maximum value, it must be the case that the parabola opens down. Algebraically, this means that the leading coefficient in the equation of a parabola is negative (a < 0).

We have,

                              \(y = 0.1x^{2} - 3x\\\\y = 4x^{2} + 24x +23\\\\y = 2x - 3x^{2}\\\\y = x^{2} + 2x + 20\)

For a parabola to have a maximum value, the parabola must open downward. Algebraically, this means that the leading coefficient in a parabola equation is negative (a < 0).

By Simplifying the third equation we get its leading coefficient is negative (a < 0).

                              \(y = -3x^{2} + 2x\)

Hence in the given parabola equations, the third equation has a maximum value.

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In summary: Sequence 1 has no term out of increasing order. Sequence 2 has the first term out of increasing order at position 2. Sequence 3 has the first term out of increasing order at position 7. Sequence 4 has the first term out of increasing order at position 4. Sequence 5 has the first term out of increasing order at position 3.

1 5 78 99 101 202 400: This sequence is in increasing order throughout, so there is no term that breaks the increasing pattern.

5 2 7 90 85 80 72: The sequence starts with 5, then decreases to 2 (out of increasing order) at position 2.

5 6 9 10 14 21 20: The sequence is increasing until position 6, where it reaches 21. However, the next term, 20, is lower than the previous term, 21 (out of increasing order) at position 7.

3 7 10 9 8 14 17: The sequence starts with 3 and increases until position 3 (10). However, at position 4, the next term, 9, is lower than the previous term, 10 (out of increasing order).

5 77 25 45 22 94 58 99: The sequence is increasing until position 2, where it reaches 77. However, at position 3, the next term, 25, is lower than the previous term, 77 (out of increasing order).

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Graham's Law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. So, for two gases A and B, the ratio of their rates of diffusion (rA/rB) can be expressed as: rA/rB = √(MB/MA).

In the Graham's Law experiment, the ratio of rates should have been calculated by dividing the rate of effusion/diffusion of gas A by the rate of effusion/diffusion of gas B.

The ratio of rates should ideally be equal to the square root of the reciprocal of the molar masses of the gases being compared. However, there may be differences due to experimental error, variations in temperature, pressure, and other factors that may affect the results. To account for these differences, it is important to repeat the experiment multiple times and take the average of the results.

Additionally, it may be necessary to adjust the experimental conditions to minimize any sources of error and ensure accurate measurements.

To determine the ratio of rates for the Graham's Law experiment, you can follow these steps:

1. Identify the two gases involved in the experiment and their molar masses.
2. Calculate the square root of the inverse molar masses for each gas.
3. Divide the result for the lighter gas by the result for the heavier gas.

Graham's Law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. So, for two gases A and B, the ratio of their rates of diffusion (rA/rB) can be expressed as:
rA/rB = √(MB/MA)

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Answer: True

Step-by-step explanation: am i wrong

Answer:

false

Step-by-step explanation:

in a rhombus all interior angles are not equal even though they have equal sides.while in a square all sides are equal including interior angles. so no a rhombus does not have the same properties

Answer:

Step-by-step explanation:

Answer:

. X^2+6x-3=0

x²+6x+9-9-3=0

(x+3)²=12

x+3=√12

x=√12-3=0.46410161513

To find the value of x in the given problem, we can apply the Law of Sines. The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

In the given problem, we have the angles A, B, and C, and the side lengths a, b, and c. The Law of Sines can be expressed as:

sin A / a = sin B / b = sin C / c

We are given the values of angle A (27 degrees), angle B (15 degrees), and side b (11). We need to find the value of side a (x).

Using the Law of Sines, we can set up the following equation:

sin A / a = sin B / b

Plugging in the known values:

sin 27° / x = sin 15° / 11

To solve for x, we can cross-multiply and then isolate x:

x = (11 * sin 27°) / sin 15°

Using a calculator to compute the sine values and performing the division, we find:

x ≈ 17.3

Rounding to the nearest tenth, the value of x is approximately 17.3.

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\(625=5^{7x-3}\implies 5^4=5^{7x-3}\implies 4=7x-3 \\\\\\ 7=7x\implies \cfrac{7}{7}=x\implies 1=x\)

Answer:

Step-by-step explanation:   The graph of a quadratic function is a parabola whose axis of symmetry is parallel to the y -axis. The coefficients a,b, and c in the equation y=ax2+bx+c y = a x 2 + b x + c control various facets of what the parabola looks like when graphed.

Hope you like it.

Using the z-distribution, the 90% confidence interval for the difference of proportions is given by: (-0.0534, 0.0434).

For each sample, the mean and the standard error are given as follows:

For the distribution of differences, they are given by:

The interval is given by:

\(\overline{p} \pm zs\)

In this problem, we have a 90% confidence level, hence\(\alpha = 0.9\), z is the value of Z that has a p-value of \(\frac{1+0.9}{2} = 0.95\), so the critical value is z = 1.645.

Hence the bounds of the interval are:

\(\overline{p} - zs = -0.005 - 1.645(0.0294) = -0.0534\)

\(\overline{p} + zs = -0.005 + 1.645(0.0294) = 0.0434\)

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Nominal scale- A nominal scale is a discrete classification of data, in which data are neither measured nor ordered but subjects are merely allocated to distinct categories.

Measurements on an interval scale have substantial differences between the values. In other words, the disparities between the scale's points are exact and measurable.

Ratio scales are interval scales where lengths are expressed in relation to a rational zero.

Ordinal scale: a scale where data is presented merely in terms of order of magnitude because there is no accepted method for determining differences.

Since there are 5 categories: Blue, Red, Green, Yellow, Orange, so by the above definition we can say that for this question we would use Nominal scale for measurement.

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The perimeter of the sector is 96.34 m if the radius of the circle is 48 m and the measure of the central angle is 115 degrees.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have given a part of the circle.

As we know:

s = rθ

s is the arc length

r is the radius of the circle

θ is the central angle in radians

The central angle is 115 degrees which is in radians:

θ = 2.00713

s = 48×(2.00713)

s = 96.34 m

The perimeter of the sector = s = 96.34 m

Thus, the perimeter of the sector is 96.34 m if the radius of the circle is 48 m and the measure of the central angle is 115 degrees.

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The solution to the system is (x, y) = (7, 13), which means Lena bought 7 small postcards and 13 large postcards.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

Let x be the number of small postcards that Lena bought, and let y be the number of large postcards she bought.

From the problem statement, we know that:

Lena bought a total of 20 postcards, so x + y = 20.

Lena bought 6 more large postcards than small, so y = x + 6.

Now we can substitute the second equation into the first one to eliminate y:

x + (x + 6) = 20

Simplifying the equation, we get:

2x + 6 = 20

2x = 14

x = 7

So Lena bought 7 small postcards and y = x + 6 = 13 large postcards.

The solution to the system is (x, y) = (7, 13), which means Lena bought 7 small postcards and 13 large postcards.

Interpretation: Lena bought more large postcards than small postcards, and the difference between the two is 6. Out of the 20 total postcards, 13 were large and 7 were small.

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Answer: The result would be 11/6 or 1 5/6 though both are of the same value.

Step-by-step explanation:

We need to turn the fractions to like fractions.

First, we'll have to find the Least Common Multiple (LCM) of the denominators, namely 2, 3, and 6.

Since

2 = 2^1

3 = 3^1

6 = 2^1 x 3^1

LCM = 2^1 x 3^1

        = 6

All denominators should be 6.

1/2 = 3/6

The numerator is 3 because 6 divided by 2 is 3, so the numerator will be 1 x 3, which is 3.

Same goes for 2/3.

2/3 = 4/6

The numerator is 4 because 6 divided by 3 is 2, so the numerator will be 2 x 2, which is 4.

4/6 already has 6 as its denominator.

So,

1/2 + 2/3 + 4/6

= 3/6 + 4/6 + 4/6

Then, add all numerators together, but just let the denominator be.

= (3+4+4)/6

= 11/6 (This is an improper fraction, but still correct)

To make 11/6 into a mixed fraction,

11 divided by 6 = 1 R5

1 will be the whole number and 5 will still be the numerator for the fraction, while 6 will still be the denominator.

So,

11/6

= 1 5/6  (This is a mixed number, also correct)

The complete square of the given numbers are-

Part a: 6(x + 1/4)^2 + 69/8

Part b: (x + 5/2)^2 + 27/2

Part c: -(x + 3)^2 + 18

For the given question

Part a: 6x^2+3x+9

Tale 6 commom;

6(x^2 + x/2 + 3/2)

Add and subtract 1/16 to the equation;

6(x^2 + x/2 + 1/16 - 1/16 + 3/2)

6((x^2 + x/2 + 1/16) - 1/16 + 3/2)

6((x + 1/4)^2 + 23/16)

6(x + 1/4)^2 + 69/8

Part b: x^2+5x+26

Add and subtract 25/4 to the equation;

x^2 + 5x + 25/4 - 25/4 + 26

(x^2 + 5x + 25/4) - 25/4 + 26

(x + 5/2)^2 + 27/2

Part c: -x^2+6x+9

Taking - 1 common.

-(x^2 - 6x - 9)

Add and subtract 9 in the equation;

-(x^2 - 6x + 9 ) - 9  - 9)

-((x^2 - 6x + 9 ) - 9  - 9)

-((x + 3)^2 -18)

-(x + 3)^2 + 18

Thus, the complete square of the umber are found.

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Answer: 123

Step-by-step explanation:

what you mean bae

Answer:

A theater group has 7 boys and 19 girls. What is the ratio of girls to the entire group?

Step-by-step explanation:

One ratio problem would be:

A theater group has 7 boys and 19 girls. What is the ratio of girls to the entire group?

In order to solve this problem we would first need to calculate the total number of individuals in the theater group. We do this by adding the number of boys with the number of girls.

7 + 19 = 26

Now since we know there are 19 girls, the ratio would be 19 girls for every 26 individuals, or in ratio format it would be ...  19 : 26

Answer:

\(\frac{1}{-2}\)

Step-by-step explanation:

To do this you would do a formula that is \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)  so you would plug in the coordinates so you get \(\frac{-2-(-3)}{-5-(-3)}\) which simplifies to \(\frac{1}{-2}\) so the slope would be \(\frac{1}{-2}\)

The time when the concentration is at a maximum is approximately t ≈ 1.914 hours.

To find the time when the concentration is at a maximum, we need to determine the critical points of the concentration function \(c(t) = 0.1t(t^2 - 11).\).

First, we take the derivative of c(t) with respect to t:

\(c'(t) = 0.1(t^2 - 11) + 0.1t(2t)\\= 0.1t^2 - 1.1 + 0.2t^2\\= 0.3t^2 - 1.1\)

To find the critical points, we set c'(t) = 0 and solve for t:

\(0.3t^2 - 1.1 = 00.3t^2 = 1.1\\t^2 = 1.1 / 0.3\\t^2 = 3.6667\)

t ≈ ±√3.6667

t ≈ ±1.914

Since time cannot be negative in this context, we discard the negative value. Therefore, the time when the concentration is at a maximum is approximately t ≈ 1.914 hours.

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Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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Answer:

y=mx+b

y=-4x +12 is your equation

m= yo

your slope

Step-by-step explanation:

Answer:

The equation of the line that passes through the points (-1,8) and (2,-4) is:

Step-by-step explanation:

Given the points

\(\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(\left(x_1,\:y_1\right)=\left(-1,\:8\right),\:\left(x_2,\:y_2\right)=\left(2,\:-4\right)\)

\(m=\frac{-4-8}{2-\left(-1\right)}\)

\(m=-4\)

As the point-slope form of the line equation is

\(y-y_1=m\left(x-x_1\right)\)

where m is the slope.

substituting the values m = -4 and the point (-1,8)

\(y-\(8\right=-4\left(x-\left(-1\right)\right)\)

\(y-8 = -4(x+1)\)

Add 8 to both sides

\(y-8+8=-4\left(x+1\right)+8\)

\(y=-4x+4\)

Therefore, the equation of the line that passes through the points (-1,8) and (2,-4) is:

Answer: -10x+38

Step-by-step explanation:

Take your given equation

-2(3x-5)+4(7-x)

Distribute the -2 and 4 into the parenthesis'

-6x+10+28-4x

Combine like terms

-10x+38

Answer: No

Step-by-step explanation: The two variable, lets say that y = x5

This is an ex. of. a related function

If its and inequality, ex. y < x5 This can not be a function for it doesnt have an equal sign

Given:

Consider the given function is:

\(f(x)=x^2-8x+13\)

To find:

The average rate of change of the function over the interval \(-1\leq x\leq 6\).

Solution:

The average rate of change of the function f(x) over the interval [a,b] is:

\(m=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}\)

We have,

\(f(x)=x^2-8x+13\)

At \(x=-1\),

\(f(-1)=(-1)^2-8(-1)+13\)

\(f(-1)=1+8+13\)

\(f(-1)=22\)

At \(x=6\),

\(f(6)=(6)^2-8(6)+13\)

\(f(6)=36-48+13\)

\(f(6)=1\)

Now, the average rate of change of the function f(x) over the interval \(-1\leq x\leq 6\) is:

\(m=\dfrac{f(6)-f(-1)}{6-(-1)}\)

\(m=\dfrac{1-22}{7}\)

\(m=\dfrac{-21}{7}\)

\(m=-3\)

Therefore, the average rate of change of the function f(x) over the interval \(-1\leq x\leq 6\) is -3.

Answer:

1. 9 inches, 12 inches and 15 inches

2. 54 square inches

Step-by-step explanation:

1. The first part of this question would lead to a quadratic equation. Let the shorter leg be represented by x.

shorter leg = x

other leg = x + 3

hypotenuse = 15 inches

Applying the Pythagoras theorem, we have;

\(/15/^{2}\) = \(/x/^{2}\) + \(/x+3/^{2}\)

225 = \(x^{2}\) + \((x+3)^{2}\)

225 = \(x^{2}\) + \(x^{2}\) + 6x + 9

       = 2\(x^{2}\) + 6x + 9

2\(x^{2}\) + 6x + 9 - 225 = 0

2\(x^{2}\) + 6x - 216 = 0

divide through by 2 to have

\(x^{2}\) + 3x - 108 = 0

From the quadratic formula;

x = (-b ± \(\sqrt{b^{2}-4ac }\) ) ÷ 2a

but, a = 1, b = 3, c = -108

x = (-3 ± \(\sqrt{(3)^{2}-4(1)(-108)}\)) ÷ 2

  = (-3 ± \(\sqrt{441}\)) ÷ 2

= (-3 ± 21) ÷ 2

Thus,

x = (-3 + 21) ÷ 2 OR x = (-3 - 21) ÷ 2

x = 9 OR x = -12

So that, x = 9 inches

The shorter leg is 9 inches, and the other leg is 12 inches.

2. The area of the triangle can be determined by applying Heron's formula:

A = \(\sqrt{s(s-a)(s-b)(s-c)}\)

where s is the average value of the sum of the three sides a, b, and c.

Let, a = 9, b = 12 and c = 15

s = \(\frac{a +b+c}{2}\)

  = \(\frac{(9+12+15}{2}\)

  = 18

A = \(\sqrt{18(18-9)(18-12)(18-15)}\)

   = \(\sqrt{18*9*6*3}\)

   = \(\sqrt{2916}\)

A = 54

Area of the triangle is 54 square inches.

Answer:

K = 4

Step-by-step explanation:

Scale factor of 4: (x,y) => (4x,4y)

J (-2,-4) => J'(-8,-16) which is (4x-2,4x-4)

K(-5,0) => K'(-20,0) which is (4x-5, 4x0)

L(3,1) => L'(12,4) which is (4x3,4x)

A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 35 books.

The system of equation will be x+y = 7 and 20x+35y = 225.

Let x be the no of small boxes and y be the no. of large boxes.

Given here each small box can hold 20 books and each large box can hold 35 books.

A total of 7 boxes were sent.

So, x+y = 7.......equation 1

Also given that 7 boxes can hold 225 books altogether.

So, 20x+35y = 225.....equation 2

Hence the system of equation will be x+y = 7 and 20x+35y = 225.

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Trevor and Kim will be situated 21 kilometers apart from each other at 1:30 PM. They will be separated by a distance of 21 km when the clock strikes 1:30 in the afternoon.

To determine at what time Trevor and Kim will be 21 km apart, we can set up a distance-time equation based on their relative speeds and distances.

Let's assume that t represents the time elapsed in hours since noon. At time t, Trevor would have traveled a distance of 8t km, while Kim would have traveled a distance of 6t km in the opposite direction.

Since they are running in opposite directions, the total distance between them is the sum of the distances they have traveled:

Total distance = 8t + 6t

We want to find the time when this total distance equals 21 km:

8t + 6t = 21

Combining like terms, we have:

14t = 21

To solve for t, we divide both sides of the equation by 14:

t = 21 / 14

Simplifying, we find:

t = 3 / 2

So, they will be 21 km apart after 3/2 hours, which is equivalent to 1 hour and 30 minutes.

Therefore, Trevor and Kim will be 21 km apart at 1:30 PM.

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Answer:

Where are the drop down menus ?

Step-by-step explanation:

Answer:

32 cups

Step-by-step explanation:

need 2 gallons

4 cups - 1 quart

4 quarts - 1 gallon

there are 16 cups in 4 quarts so if you times 16 × 2 you will get 32.