Part A Which solution do you get when you use the quadratic formula to solve the equation –4x2 – 12x – 9 = 0?

Answer:

3x - (4x - 11) = 3x - 4x + 11 = -x + 11

Step-by-step explanation:

Jerry will have $1825 in his account after 3 years and Jerry will have $6125 in his account after 10 year when compounded.

Simple interest is computed just using the principle, which is the initial sum borrowed or put into an investment. The interest rate is constant throughout time and solely applies to the principal sum. Short-term loans or investments frequently employ simple interest.

The given situation can be modeled as a linear equation given by:

y = mx + c

For Jerry we have:

y = 50x + 125

For 3 years = 36 months we can substitute x = 36:

y = 50(36) + 125

y = 1825

For x = 10:

y = 50(120) + 125

y = 6125

Hence, Jerry will have $1825 in his account after 3 years and Jerry will have $6125 in his account after 10 year.

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With a [tex]12[/tex]% price rise, the smart mug now costs AED [tex]1003.52[/tex].

The sale price is the price an user pays to purchase a thing or a commodity. It is a cost that is higher than the market cost and also includes a portion of the profit. The cost price refers to the price paid by the seller for the item or service.

Price is the process of figuring out how much a something or service is worth. Price establishes a customer's cost, although it can or cannot be linked to the price a firm pays to manufacture a good or service.

We need to multiply the initial price by [tex]1.12[/tex] which represents a [tex]12[/tex]% increase in decimal form,

New price [tex]=[/tex] Initial price [tex]*[/tex] (1 [tex]+[/tex] Percent increase in decimal form)

New price[tex]= 896 * (1 + 0.12)[/tex]

New price [tex]= 896 * 1.12[/tex]

New price [tex]= 1003.52[/tex]

Therefore, the new price of the smart mug is AED [tex]1003.52[/tex] after a [tex]12[/tex]% increase.

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Answer:

A.) The axis of symmetry:

To find the axis of symmetry, use the formula x = -b/2a, where a and b are the coefficients of the x^2 and x terms, respectively.

In this case, a = 2 and b = -12, so:

x = -(-12) / 2(2) = 3

The axis of symmetry is x = 3.

B.) The vertex:

To find the vertex, plug in the x-coordinate of the axis of symmetry (3) into the function and evaluate:

f(3) = 2(3)^2 - 12(3) + 3 = -33

So the vertex is (3, -33).

C.) The X-intercepts:

To find the x-intercepts, set y (or f(x)) equal to 0 and solve for x:

0 = 2x^2 -12x +3

Using the quadratic formula, we get:

x = (6 ± sqrt(6^2 - 4(2)(3))) / (2(2))

x = (6 ± 3sqrt(2)) / 4

x = (3/2) ± (3/2)sqrt(2)

So the x-intercepts are approximately (-0.68, 0) and (4.18, 0).

D.) The Y-intercept:

To find the y-intercept, set x = 0 and evaluate the function:

f(0) = 2(0)^2 - 12(0) + 3 = 3

So the y-intercept is (0, 3).

E.) The domain and range:

The domain of the function is all real numbers, since there are no restrictions on the values of x that can be plugged into the function.

To find the range, note that the coefficient of the x^2 term (2) is positive, which means that the parabola opens upwards. Therefore, the minimum value of the function occurs at the vertex, and the range is all real numbers greater than or equal to the y-coordinate of the vertex. In this case, the range is (-33, ∞).

Answer:

x = 4[tex]\sqrt{2}[/tex]

Step-by-step explanation:

using the cosine ratio in the lower right triangle and the exact value

cos45° = [tex]\frac{1}{\sqrt{2} } }[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex]  ( cross- multiply )

x = 4[tex]\sqrt{2}[/tex]

The reason we can't use the mean when a data set has one or two values that are much higher than all of the others is that it skews the average, making it not representative of the rest of the data.

The mean is a numerical measure of the central tendency of a data set. It is calculated by dividing the sum of all the values in a data set by the number of data points.

A data set is a collection of observations or measurements that are analyzed to obtain information. It can be represented graphically, in tabular form, or in any other format. The data set may be a sample or the entire population.

If a data set has one or two extremely high or low values, it can significantly impact the mean. These values are known as outliers. The outliers can cause the mean to be higher or lower than the actual middle value of the data.

Hence, in such cases, the median is a better choice for finding the central tendency of the data. The median is the middle value of the data set, and it is less affected by outliers than the mean. The mode, which is the value that occurs most frequently in the data set, is also a measure of central tendency that is less sensitive to outliers than the mean.

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Answer:

29.12 square cm

Step-by-step explanation:

     Side = a = 8.2 cm

    [tex]\boxed{\bf Area \ of \ equilateral \ triangle = \dfrac{\sqrt{3}}{4}a^2}[/tex]

                                                       [tex]\sf = \dfrac{\sqrt{3}}{4}*8.2*8.2\\\\= \sqrt{3}*4.1 * 4.1\\\\= 1.732 * 4.1 *4.1\\\\= 29.12 \ cm^2[/tex]

Considering flow over a flat plate, and by using the Thwaites-Walz method and the Pohlhausen method are very similar, but they differ significantly from the exact solution.

The Thwaites-Walz Method for flow over a flat plate:

          The Blasius method can be used to obtain the non-dimensional velocity distribution over a flat plate. But the computation of the shear stress and friction coefficient from this velocity distribution requires the knowledge of the second derivative of u with respect to y which is difficult to obtain.

          The Thwaites method is an alternative method for computing the friction coefficient, which avoids the computation of the second derivative of u with respect to y. This method involves the solution of an ordinary differential equation.

            This method is particularly useful for computing the friction coefficient in the early stages of the boundary layer. The equations for the Thwaites method are as follows:

                 [tex]\frac{d^2\delta}{dx^2} =\frac{\delta}{u^2}\left(1+ \frac{\delta}{2}\frac{dU/dx}{U}\right)C_f[/tex]

                                                         = [tex]\frac{0.288\delta}{Re_x}(\frac{d\delta}{dx})^{1/2}Re_x[/tex]

                                                         = [tex]\frac{\rho u(x)x}{\mu}\tau_w[/tex]

                                                         = [tex]\rho u_\infty C_f/2x[/tex]

                                                         = [tex]\frac{1}{C_f}\int_{0}^{\delta}u_\infty \left(1- \frac{u}{u_\infty}\right)dy$$[/tex]

The following are the predictions using the Thwaites-Walz method to predict d, d*, 8, and

                   [tex]Cvs x.*d = 0.375 x^(1/5)*d*[/tex]

                                    = [tex]4.91 x^(1/5)*8[/tex]

                                    = [tex]0.664 x^(3/5)*Cv[/tex]

                                    = [tex]1.328 x^(1/5)[/tex]

        The Pohlhausen method is a simple method for computing the shear stress and the friction coefficient, which is based on an approximate solution of the boundary layer equations. The Pohlhausen method is based on the assumption that the velocity distribution is a parabolic function of the distance from the wall.

             The equations for the Pohlhausen method are as follows:

                      [tex]u(x,y)= U(x)\left(1-\left(\frac{y}{\delta}\right)^2\right)\tau_w[/tex]

                                 = [tex]\rho u_\infty \frac{dU}{dx}\frac{\delta^2}{3}C_f[/tex]

                                 =  [tex]\frac{2}{3}\frac{\tau_w}{\rho u_\infty^2}x[/tex]

                                 =  [tex]\frac{1}{C_f}\int_{0}^{\delta}u_\infty \left(1- \frac{u}{u_\infty}\right)dy$$[/tex]

The following are the predictions using the Pohlhausen method to predict d, d*, 8, and

                       Cvs x.• d = 0.37 x^(1/5)• d*

                                       = 4.9 x^(1/5)• 8

                                       = 0.664 x^(3/5)• Cv

                                       = 1.328 x^(1/5)

The following are the exact solutions for flow over a flat plate. Equations (2.21) and (2.22) are for the shear stress and friction coefficient respectively.

                           [tex]$$ \tau_w = \rho u_\infty C_f/2[/tex]

                                =  [tex]\frac{0.664 \rho u_\infty^2 x^{3/5}}{Re_x^{1/5}}C_f[/tex]

                                 =   [tex]\frac{0.664}{Re_x^{1/2}}[/tex]

          The following are the predictions using the exact solutions for flow over a flat plate.

                                  [tex]*d = 0.664 x^(3/10)*d*[/tex]

                                        = [tex]4.91 x^(1/5)*8[/tex]

                                       = [tex]0.664 x^(3/5)*Cv[/tex]

                                       = [tex]1.328 x^(1/5)[/tex]

         Hence, the predictions using the Thwaites-Walz method and the Pohlhausen method are very similar, but they differ significantly from the exact solution.

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In equation A the missing number is 955, In equation B the missing number is 90 and In equation C the missing number is 805.

A) To find the missing number in the equation 872 + ? + 173 = 2000, we need to subtract 872 and 173 from 2000, which gives us:

2000 - 872 - 173 = 955

Therefore, the missing number is 955.

B) To find the missing number in the equation 9180 ÷ ? = 102, we need to divide 9180 by 102, which gives us:

9180 ÷ 102 = 90

Therefore, the missing number is 90.

C) To find the missing number in the equation ? - 99 = 706, we need to add 99 to 706, which gives us:

706 + 99 = 805

Therefore, the missing number is 805.

To obtain the indicated results with the same numbers and operations, we need to use parentheses to change the order of operations.

A) 3 + (5x7) - 2 = 40

B) (3 + 5) × 7 - 2 = 54

C) 3 + (5 × (7-2)) = 28

Equations are used extensively in various fields of science, engineering, economics, and finance, to name a few. It is formed by placing an equal sign between the two expressions. Equations are used to solve problems and find unknown values.

An equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The variables in an equation represent unknown values that need to be found, while the constants are known values that are already given. Solving an equation involves manipulating the expressions on both sides of the equal sign using mathematical operations to isolate the variable on one side and constants on the other. The final solution obtained is the value of the variable that satisfies the equation..

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Complete Question: -

Find unknown numbers of these operations

A ) 872 +. + 173 = 2000

B ) 9180:. = 102

C ). -99 = 706

With the same numbers and the same operations we can obtain different results, place the parentheses so that the indicated results are obtained.

A ) 3 + 5 x 7-2 = 40

B ) 3 + 5 × 7-2 = 54

C ) 3 + 5 × 7-2 = 28

IT'S FOR TODAY PLEASE ☹, CAN DO IN A LEAF OR WRITE ASI BUT EXPLAIN WELL!!!!!!HELP IF THEY DON'T KNOW NO RESPOND

A sampling distribution is normal only if the population is normal. This  statement is false because A sampling distribution is normal only if n≥30.

If the underlying population is normally distributed, the sampling distribution (such as the sample mean distribution, also known as the xbar distribution) is also normally distributed. Even though the population is not normally distributed, the x(bar) distribution is approximately normal if n > 30, due to the central limit theorem. Some textbooks may use values ​​above 30, but after a certain threshold the x(bar) distribution is effectively "normal".

Option B is close, but misses the normal population part. n > 30 is not necessary if we know the population is normal.

A sampling distribution is the probability distribution of a statistic obtained from a large number of samples drawn from a particular population. The sampling distribution for a given population is the frequency distribution of a range of different outcomes that can occur in the population.

In statistics, a population is the entire basin from which a statistical sample is drawn. A population can refer to an entire population of people, objects, events, hospital visits, or measurements. Thus, a population can be said to be a global observation of subjects grouped by common characteristics.

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Answer:

Step-by-step explanation:

To solve this problem, we need to use the formula for compound interest:

A = P*e^(rt)

where A is the final amount, P is the principal (initial investment), e is the base of the natural logarithm (approximately 2.71828), r is the interest rate (expressed as a decimal), and t is the time (in years).

For Sophie's account, we have:

P = $92,000

r = 6 1/8% = 0.06125 (as a decimal)

t = 14 years

A = 92000*e^(0.06125*14)

A = $219,499.70 (rounded to the nearest cent)

For Damian's account, we have:

P = $92,000

r = 6 5/8% = 0.06625/12 = 0.005521 (as a monthly decimal rate)

t = 14*12 = 168 months

A = 92000*(1+0.005521)^168

A = $288,947.46 (rounded to the nearest cent)

Now we can subtract Sophie's final amount from Damian's final amount to find the difference:

Difference = $288,947.46 - $219,499.70

Difference = $69,447.76

Therefore, Damian would have about $69,448 more in his account than Sophie, to the nearest dollar.

The error is the substitution of coordinates. Coordinates are ordered pairs of points that help us locate any point in a 2D plane or 3D space.

Cartesian coordinates, also known as the coordinates of a point in a 2D plane, are two integers, or occasionally a letter and a number, that identifies a specific point's precise location on a grid. This grid is referred to as a coordinate plane.

The distance between two points A(x₁, y₁) and B(x₂, y₂) is given by

[tex]AB = \sqrt{(x_{1} , x_{2})^{2} + (y_{1} - y_{2})^{2} }[/tex]

Observe that the x-coordinate of B is subtracted from the x-coordinate of A. This goes with the y-coordinates.

Therefore, the error is the substitution of coordinates.

The correct computation is

[tex]AB = \sqrt{(6-1)^{2} + [2 - (-4)]^{2} }[/tex]

[tex]= \sqrt{5^{2} + 6^{2} }[/tex]

[tex]= \sqrt{25 + 36} \\[/tex]

[tex]= \sqrt{61}[/tex]

≈ 7.81

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The complete question is as follows:

Describe and correct the error in finding the distance between A(6, 2) and B(1, -4). AB = √[(6 - 2)² + {2 - (-4)}²] = √(4² + 5²) = √(16 + 25) = √41 ≈ 6.4.

Step-by-step explanation:

The area of a rectangle is 1,872 ft2. The ratio of the length to the width is 9:13. Find the perimeter of the rectangle.

176 ft

You want to make a scale drawing of your bedroom to help arrange your furniture. You decide on a scale of 3 in. = 2 ft. Your bedroom is a 12 ft by 14 ft rectangle. What should the dimensions of your drawing be?

18 in. by 21 in.

If 5/y + 7/x=24 and 12/y + 2/x=24, find the ratio of x to y.

5/7

Simplify the ratio 8ft/12in. Use the conversion 12 in. = 1 ft.

8/1

Analyze the proportion below and complete the instructions that follow.

2x+5/3 = x-5/4

-7

If a+b/2a-b = 5/4 and b/a+9 = 5/9, find the value of b.

30

Analyze the ratio below and complete the instructions that follow.

$30:$6

Simplify the ratio.

5:1

If 14/3 = x/y then 14/x =

3/y

Analyze the diagram below and complete the instructions that follow.

In the diagram, AB:BC is 3:4 and AC = 42. Find BC.

24

Analyze the diagram below and complete the instructions that follow.

If AB:BC is 3:11, solve for x.

9

If a, b, c, and d are four different numbers and the proportion a/b = c/d is true, which of the following is false?

b/a = c/d

Analyze the diagram below and complete the instructions that follow.

Find the ratio of the width to the length of the rectangle, then simplify the ratio. Use the conversion 100 cm = 1 m.

3/4

Simplify the ratio 3 gal./24 qt. Use the conversion 4 qt = 1 gal.

1/2

The area of a rectangle is 4,320 ft2. The ratio of the length to the width is 6:5. Find the length of the rectangle.

72 ft

Analyze the diagram below and complete the instructions that follow.

Given that CB/CA = DE/DF, find BA.

10.5

Analyze the proportion below and complete the instructions that follow.

2/3 = 8/x

3, 8

Analyze the diagram below and complete the instructions that follow.

Are the polygons shown here similar? Justify your answer. The images are not drawn to scale.

Yes, PQR ~TSV with a scale factor of 1:√3

All __________ are similar.

squares

Analyze the diagram below and complete the instructions that follow.

Determine which 2 triangles are similar to each other. The images are not drawn to scale.

GHI ~ JKL

Analyze the diagram below and complete the instructions that follow.

Pentagon PQRST ~ pentagon XYZVW. Find the value of b. The images are not drawn to scale.

3

Analyze the diagram below and complete the instructions that follow.

If ABC ~ XYZ, find XY. The images are not drawn to scale.

24

ABC is a right triangle. The legs of ABC are 9 ft and 12 ft. The shortest side of XYZ is 13.5 ft, and ABC ~ XYZ How long is the hypotenuse of XYZ?

22.5 ft

Answer:The concession stand sold

46

hot dogs and

32

hamburgers.

Explanation:

The first thing to do in algebraic problems is assign variables to things we don't know, so let's start there:

We don't know how many hot dogs the concession stand sold, so we will call that number

d

.

We don't know how many hamburgers the concession stand sold, so we will call that number

h

.

Now we translate the statements into algebraic equations:

The number of hot dogs and hamburgers that were sold is

78

, so

d

+

h

=

78

.

If each hot dog is sold for

1.25

, then the total revenue from hot dogs is given by

1.25

d

. In the same way, the total revenue from hamburgers is

1.50

h

. The total revenue from both hot dogs and hamburgers should be the sum of these, and since we are told the total revenue is

105.50

, we can say

1.25

d

+

1.5

h

=

105.5

.

We now have a system of two linear equations:

d

+

h

=

78

1.25

d

+

1.5

h

=

105.5

We can solve it using several methods, though I'm going to go with substitution. Use the first equation to solve for

d

:

d

+

h

=

78

→

d

=

78

−

h

Now plug this in for

d

in the second equation:

1.25

d

+

1.5

h

=

105.5

→

1.25

(

78

−

h

)

+

1.5

h

=

105.5

Solving for

h

, we have:

97.5

−

1.25

h

+

1.5

h

=

105.5

0.25

h

=

8

h

=

8

.25

→

h

=

32

Since

h

+

d

=

78

,

32

+

d

=

78

→

d

=

46

Step-by-step explanation:

Answer:

The point z = 3+4i is plotted as a blue dot, and the two square roots are plotted as a red dot and a green dot. The magnitudes of z and its square roots are shown by the radii of the circles centered at the origin.

Step-by-step explanation:

qrt(z) = +/- sqrt(r) * [cos(theta/2) + i sin(theta/2)]

where r = |z| = magnitude of z and theta = arg(z) = argument of z.

Calculate the magnitude of z:

|r| = sqrt((3)^2 + (4)^2) = 5

And the argument of z:

theta = arctan(4/3) = 0.93 radians

Now, find the two square roots of z:

sqrt(z) = +/- sqrt(5) * [cos(0.93/2) + i sin(0.93/2)]

= +/- 1.58 * [cos(0.47) + i sin(0.47)]

= +/- 1.58 * [0.89 + i*0.46]

Using a calculator, simplify this expression to:

sqrt(z) = +/- 1.41 + i1.41 or +/- 0.2 + i2.8

Answer:

Step-by-step explanation:

To factor 25x^6 + 10x^3 + 12, we can first factor out the greatest common factor of the three terms which is 1, then use a substitution:

Let's substitute y = x^3. Then, the expression becomes:

25y^2 + 10y + 12

We can now try to factor this quadratic expression. However, since the discriminant (b^2 - 4ac) of this quadratic equation is negative (10^2 - 4*25*12 = -440), this expression cannot be factored using real numbers.

Therefore, the final answer for the factoring is:

25x^6 + 10x^3 + 12 = (unfactorable)

From the given information provided, the value of angle LMP and angle NMP is 77 and 103 degrees respectively.

Since LMN is a straight angle, it measures 180 degrees.

We are given the measures of LMP and NMP, and we are told that LMP + NMP = LMN. Therefore, we can set up an equation:

LMP + NMP = LMN

(-16x + 13) + (-20x + 23) = 180

Simplifying and solving for x, we get:

-36x + 36 = 180

-36x = 144

x = -4

Now that we have found the value of x, we can substitute it back into the expressions for LMP and NMP to find their measures:

LMP = -16x + 13 = -16(-4) + 13 = 77 degrees

NMP = -20x + 23 = -20(-4) + 23 = 103 degrees

Therefore, the measures of LMP and NMP are 77 degrees and 103 degrees, respectively, and the measure of LMN is 180 degrees.

Question - LMN is a straight angle. LMP = -16x + 13 NMP =  -20x + 23 LMP + NMP = LMN What are the measures?

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Step-by-step explanation:

it would mean that she made 53 batches of soap and 4 batches of lotion.

now, is it a solution ?

then both inequalities must be true with these values.

5×53 + 15×4 <= 325

265 + 60 <= 325

325 <= 325 correct

20×53 + 35×4 <= 1200

remember, 1 hour = 60 minutes.

1060 + 140 <= 1200

1200 <= 1200 correct

so, (53, 4) is the intersection point of both limit lines. and it is as such an extreme point and optimum.

The growth rate of a bacterial colony after a 2 hours  is given by the derivative of its population function with respect to time is 36 .

The growth rate of a bacterial colony is given by the derivative of its population function.

Thus, we need to find the derivative of the population function p(t) with respect to time t, and then evaluate it at t = 2 to get the growth rate after 2 hours.

p(t) = 3t² + 24t + 200

Taking the derivative of p(t) with respect to t, we get:

p'(t) = 6t + 24

Now, evaluating p'(t) at t = 2, we get:

p'(2) = 6(2) + 24 = 36

Therefore, the growth rate of the bacterial colony after 2 hours is 36.

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Answer:

x = 45.

Step-by-step explanation:

We know the full angle of this is 180 degrees.

Given: (2x+45) + x = 180

First, collect like terms ( in this case 2x and x, 180 and 45 )

2x + x = 180 - 45

Then calculate:

3x = 135. ( Divide both sides by 3 )

x = 45

The value οf a = 1/2  and b = 19/4 in the equatiοn x² - x + 5 = (x-a)² + b.

The part οf mathematics in which letters and οther general symbοls are used tο represent numbers and quantities in fοrmulae and equatiοn is called algebra.

x² - x + 5 = (x-a)² + b

x² - x + 5 = x² + a² - 2xa + b

-x + 5 = -2xa + a² + b

By matching cοrrespοnding terms,

2a = 1          and        a²+ b = 5

a= 1/2          and        a²+ b = 5

Substituting value οf "a"

(1/2)² + b = 5

1/4 + b = 5

b = 5- 1/4

b = 19/4

Thus, a = 1/2  and b = 19/4.

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A) x = 5 is not a linear function since it is a vertical line and does not have a slope. B) The table description does not provide enough information to determine if it is a linear function. C) x + 7 = 4y is a linear function in slope-intercept form (y = (1/4)x + 7/4).

A linear function is a mathematical function that can be represented by a straight line with a constant slope. The equation of a linear function can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). Option A (x = 5) is not a linear function, as it is a vertical line with an undefined slope. Option B is a linear function, as the table describes points that can be plotted to form a straight line. Option C is also a linear function, but it is in a different form (x + 7 = 4y). This equation can be rearranged to y = (1/4)x + 7/4, which is in the standard form of a linear function.

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Answer: C.) x + 7 = 4y and  D

Step-by-step explanation: i hope this helps

Answer:

To find the average distance away from the mean, we need to first find the mean distance from the mean. To do this, we need to find the mean of the distances from the mean:

|32 - 33| = 1

|45 - 33| = 12

|23 - 33| = 10

|35 - 33| = 2

|30 - 33| = 3

Mean distance from the mean = (1 + 12 + 10 + 2 + 3) / 5 = 6. However, the question asks for the average distance away from the mean, so we need to take the absolute value of this result:

Average distance away from the mean = |6| = 6

To find the mean absolute deviation, we first need to find the deviations from the mean:

12.7 - 15.2 = -2.5

22 - 15.2 = 6.8

23.5 - 15.2 = 8.3

24 - 15.2 = 8.8

11 - 15.2 = -4.2

22 - 15.2 = 6.8

Next, we need to take the absolute value of each deviation:

|-2.5| = 2.5

|6.8| = 6.8

|8.3| = 8.3

|8.8| = 8.8

|-4.2| = 4.2

|6.8| = 6.8

The sum of these absolute deviations is:

2.5 + 6.8 + 8.3 + 8.8 + 4.2 + 6.8 = 37.4

To find the mean absolute deviation, we divide this sum by the number of data points:

Mean absolute deviation = 37.4 / 6 = 6.23

Therefore, the answer is not listed among the choices given.

Answer:

B. 33

Step-by-step explanation:

1) Find the mean

32+45+23+35+30/5

165/5

=33

Answer: 2

Step-by-step explanation:

To graph the solution to the inequality -5 + x ≥ -3 on the number line, we first need to isolate x.

Adding 5 to both sides of the inequality, we get:

x ≥ 2

This means that any value of x greater than or equal to 2 will satisfy the inequality. To graph this solution on a number line, we draw a closed circle at the point 2 and shade all the points to the right of 2, including the point 2 itself.

The resulting graph looks like this:

     ------•-------------------------------->

           2

The shaded region on the right of 2 represents all the values of x that make the inequality true.

The equation of the quadratic function represented by the given table is  y = -x² + 4x - 7.

A quadratic function is a function of the form:\sf(x) = ax^2 + bx + c\swhere a, b, and c are constants and x is the parameter. The graph of a quadratic function is a parabola, which is an Inverted curve. Whether the parabola opens up (if a > 0) or down (if a 0) depends on the sign of the coefficient a.

The width of the parabola is also determined by the coefficient a. The parabola is narrow if |a| is greater than 1. (i.e. it has a small width relative to its height). The parabola is wide if |a| is greater than 1.

The standard form of the quadratic equation is given as:

y = ax² + bx + c

Substitute the value of x and y from the table:

3 = a(2)² + b(2) + c

4a + 2b + c = 3........(1)

For point (4, -1):

-1 = a(4)² + b(4) + c

16a + 4b + c = -1..........(2)

For (6, -13):

-13 = a(6)² + b(6) + c

36a + 6b + c = -13..........(3)

From 1 we have:

c = 3 - 4a - 2b

Substitute the value of c in equation 2 and 3:

16a + 4b + 3 - 4a - 2b = - 1

12a + 2b = - 4........(4)

36a + 6b + 3 - 4a - 2b = -13

32a + 4b = -16.......(5)

Multiply equation 4 with 2 and subtract with equation 5:

32a + 4b = -16

-(24a + 4b = - 8)

a = -1

Substitute the value of a in equation 5:

32(-1) + 4b = -16

-32 + 4b = -16

b = 4

Substitute the value of a and b in equation 1:

16a + 4b + c = -1

16(-1) + 4(4) + c = -1

-16 + 8 + c = -1

-8 + c = -1

c = 7

Using the algebraic techniques we have:

a = -1

b = 4

c = 7

Hence, the equation of the quadratic function represented by the given table is y = -x² + 4x - 7.

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if the members are in tension or compression. Identify all zero force members: Likewise, we can find the reaction force at A by taking minutes about point A: RA x 8m - 5kN x 8m - 5kN x 8m = 0 RA = 5kN

To begin with, we really want to find the reaction forces at An and G.

We can do this by taking minutes about point G.

We realize that the amount of minutes at any point is zero when the framework is in equilibrium.

Consequently, we can compose: 5kN x 8m - RA x 10m = 0 RA = 4kN

Likewise, we can find the reaction force at A by taking minutes about point A: RA x 8m - 5kN x 8m - 5kN x 8m = 0 RA = 5kN

Since we have two distinct qualities for RA, we can presume that the framework isn't in equilibrium.

This really intends that there should be some outside force following up on the framework.

The two obscure forces are at first thought to be ductile (for example pulling away from the joint). In the event that this underlying supposition is mistaken, the registered upsides of the pivotal forces will be negative, meaning pressure.

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the complete question is:

Question l Find the forces in members HE; FH, FE; and FC of the truss as shown in Figure Q1. State if the members are in tension or compression. Identify all zero force members: (10 marks) 8 m 5 KN 8 m 8 m 5 KN 8 m 10 m Figure Q1.

An expression for the length of the rectangle in terms of A is [tex]$\boxed{L=x+5}$[/tex]

We are given that the area of a rectangle is [tex]$A=x^2+x-15$[/tex], and we want to find an expression for the length of the rectangle in terms of A.

Recall that the area of a rectangle is given by the formula: [tex]$A=L\cdot W$[/tex], where L is the length and W is the width. We can use this formula to write L in terms of A and W as [tex]$L=\frac{A}{W}$[/tex].

We know that the rectangle has a length and a width, so we need to find an expression for the width W in terms of A. We can rearrange the given formula for A to solve for W:

[tex]&& \text{(substitute }L=x+5\text{)}[/tex]

[tex]W&=\frac{x^2+x-15}{x+5} && \text{(divide both sides by }x+5\text{)}[/tex]

Now that we have an expression for W in terms of A, we can substitute it into our expression for L to get:

[tex]L&=\frac{A}{W}[/tex]

[tex]&=\frac{x^2+x-15}{\frac{x^2+x-15}{x+5}} && \text{(substitute the expression we found for }W\text{)}\&=x+5[/tex]

Therefore, an expression for the length of the rectangle in terms of A is [tex]$\boxed{L=x+5}$[/tex]

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Dimension of photograph is 35cm and 22cm.

And external dimension of photo frame is 45cm and 30cm

So, the area of the border surrounding the photograph=Area of photo frame−Area of photo.

So, The area of the border surrounding the photograph [tex]=45\times30-35\times22[/tex]

[tex]=1350-770=580cm^2[/tex]