Exponential decay, please help

The roots of the quadratic equation 2[tex]x^{2}[/tex] -9x +9 =0 are 1.5 and 0.75

given equation

2[tex]x^{2}[/tex] -9x +9 =0

now , we need to find the roots of the above equation

roots = - b ± [tex]\sqrt{b^{2} - 4ac}[/tex] /4a

a = 2

b =-9

c = 9

roots = -(-9) ± [tex]\sqrt{(-9)^{2} - 4(2)(9)}[/tex] / 4(2)

        = 9 ± [tex]\sqrt{81-72}[/tex] / 8

        = 9 ± [tex]\sqrt{9}[/tex] /8

       = 9 ± 3 /8

      = 9+3/8 and 9-3/8

     = 12/8 and 6/8

    = 1.5 and 0.75

The roots of the quadratic equation 2[tex]x^{2}[/tex] -9x +9 =0 are 1.5 and 0.75

In algebra, a quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as

a[tex]x^{2}[/tex] +bx +c =0

where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.) The numbers a, b, and c are the coefficients of the equation and may be distinguished by respectively calling them, the quadratic coefficient, the linear coefficient and the constant or free term.

The values of x that satisfy the equation are called solutions of the equation, and roots or zeros of the expression on its left-hand side. A quadratic equation has at most two solutions. If there is only one solution, one says that it is a double root. If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two complex solutions that are complex conjugates of each other. A quadratic equation always has two roots, if complex roots are included; and a double root is counted for two. A quadratic equation can be factored into an equivalent equation

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As described in Analytical Geometry the relationship between quantities of  a qualitative graph are explained below.

What is Analytical Geometry?

The area of algebra known as analytical geometry uses an ordered pair of numbers known as coordinates to determine the position of a point on a plane. It is utilised to model many plane objects, including points, lines, and others. The terms Coordinate geometry and Cartesian geometry are both used to refer to analytical geometry.

Cluster Use functions to model relationships between quantities. Standard Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear).

A linear relationship between two quantities will produce a graph of a straight line. The line represents every possible solution for the range of the function. In order to create the line, we use the function equation and evaluate the range, or output, values based upon several of the domain, or input, values.

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Answer:

Below

Step-by-step explanation:

Filter out the - 2

y =   -2 ( x^2 - 5/2 x)     - 1      Now 'complete the square'

y = -2 ( x^2 - 5/2x + 25/16)  +  50/16     -1      Now simplify:

 =   -2(x-5/4)^2 + 34/16         This will have vertex at  5/4, 34/16

Answer:

5%

Step-by-step explanation:

To solve this problem, we need to use the formula for simple interest, which is I = PRT, where I is the interest earned, P is the principal amount, R is the interest rate, and T is the length of time the money is invested. We know that I = 1350, P = 3000, and T = 9, so we can rearrange the formula to solve for R: R = I / (P * T) = 1350 / (3000 * 9) = 0.05. Therefore, the interest rate is 5%.

Answer: 5% per year

Step-by-step explanation:

First, take 1350 divided by 3000, then times 100% = 45% for 9 years

Then take 45 divided by 9 = 5% per year

Answer:

about 43% or 43.3%

Step-by-step explanation:

First, add up the total amount of computers in the computer lab:

14 + 16 = 30

We are told that 16 of the 30 computers are laptops so we can think of this percentage problem as its own equation

13    is    what percent   of  30

13    =            %              x     30

now to solve by dividing 13 by 30 using a calculator:

13/30 = 0.433...

This approximates to 43% or 43.3%

The point (3,-1) is situated in the fourth quadrant.

The coordinate system's two axes, the x-axis and the y-axis, constitute a region called a quadrant. The quadrants are generated when the two axes, the x-axis and the y-axis, cross at a 90-degree angle. These areas include coordinates, or positive and negative values of the x- and y-axes. The intersection of the x-axis (the horizontal number line) and the y-axis in the cartesian system divides the coordinate plane into four equal pieces (the vertical number line). Because each of these four areas occupies a quarter of the entire coordinate plane, they are collectively referred to as quadrants.

Given

Quadrant of (3, -1)

Due to the fact that x is positive and y is negative, the point is situated in the fourth quadrant.

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Dilation

By maintaining the object's orientation or shape, this type of translation either expands or contracts the object. This is referred to as resizing.

What is Graph Transformation?

A graph can be transformed to produce a different version of the one that came before it. The x-y plane can be used to translate or shift the graphs. In addition to these modifications, they may also be stretched.

Types of Stretching of Graphs

Consider the case where we need to lengthen a graph by a factor of 2. Next, change the y value. Now, each point of the function F's form (x, y) shifts to the point (x, 2y)*

Adjust the x value if a graph needs to be stretched horizontally by a factor of two. The point (2x, y) in function F is now the new location for all points with the form (x, y) in function F.

Types of Translation in Graphs

A graph is horizontally translated by moving the base graph to the left or right in relation to the x-axis. Consider that if we want to move a graph horizontally by 1 unit, we would also need to change the x value.

A graph's base graph is moved up or down in the y-axis direction when it is vertically translated. Each point on a graph is moved b units vertically to translate the graph in that many directions.

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The length of the sides a and b with one decimal place value are 9.4 cm and 12 cm.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

Applying the Pythagorean theorem.

a² = 8² + 5²

a² = 64 + 25

a = √89

a = 9.4 cm

17² = b² + 12²

289 = b² + 144

b² = 289 - 144

b² = 145

b = √145

b = 12 cm

Thus,

The length of side a is 9.4 cm.

The length of side b is 12 cm.

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Answer:

1 foot and 4 inches.

Step-by-step explanation:

1 feet = 12 inches

3 feet = 12*3 = 36 inches

Then:

3 feet and 2 inches = 36 + 2 = 38 inches

if the chair measured 20 inches:

36 - 20 = 16 inches

16 inches = 12inches + 4 inches

= 1 foot and 4 inches

Answer:

theans its a= exist 4.0million

By using the volume of the cylinder, it can be calculated that

Volume of the cylinder is 75.360 cubic inches

What is volume of a cylinder?

Volume of a cylinder is the total space taken by the cylinder.

If r is the radius of the cylinder and h is the height of the cylinder, then volume of the cylinder is calculated by-

V = [tex]\pi r^2h[/tex]

Here,

Height of the cylinder = 6 inches

Radius of the cylinder = 2 inches

Volume of the cylinder = [tex]3.14 \times 2^2 \times 6[/tex] = 75.360 cubic inches

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Complete Question

A cylinder has a height of 6 inches and a radius of 2 inches. What is its volume? Use a 3.14 and round your answer to the nearest hundredth.​

To see the graph of y = 2x−5 with the points (5/2,0) and (0,−5)

Now, According to the question:

y = 2x - 5 is a line. Determine the two points that this line intersects with the axes then connect these points to graph it.

y = 2x - 5

Take y = 0

then, solve for the abscissa

y = 2x - 5

0 = 2x - 5

2x = 5

x = 5/2

We now have the point (5/2 , 0)

Take x = 0

then, solve for the ordinate

y = 2x - 5

y = 0 -5

y = -5

We now have the point (0 , -5)

We now simply draw a line passing thru the two points (5/2 , 0) and

(0 ,-5)

Kindly see the graph of y = 2x−5 with the points (5/2,0) and (0,−5)

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The definition of SSS, SAS, and AAS congruency conditions is shown.

SSS condition:

In accordance with the SSS rule, two triangles are considered to be congruent if their corresponding three sides are equal on both triangles.

SAS condition:

The two triangles are congruent if two sides and the included angle of one triangle match those of a second triangle by two sides and the included angle.

AAS condition:

The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

Therefore, the definition of SSS, SAS, and AAS congruency conditions is shown.

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To find an expression for V(t), we can integrate V'(t) with respect to t. Doing so, we have:

V(t) = ∫V'(t) dt = ∫5700(t − 10) dt = 5700 ∫(t − 10) dt = 5700 [t^2/2 - 10t] + C

Since V(t) is the resale value of the computers, the constant of integration C should be the initial value of V(t), which is the cost of the computers. Therefore, we have:

V(t) = 5700 [t^2/2 - 10t] + 300000

Now, to find the value of the computers after 5 years, we can substitute t = 5 into the expression for V(t):

V(5) = 5700 [5^2/2 - 10*5] + 300000 = 5700 [25/2 - 50] + 300000 = 5700 [-12.5] + 300000 = -67500 + 300000 = 232500

Thus, the computers would sell for approximately $232,500 after 5 years.

Explanation: The function V'(t) gives the rate at which the resale value of the computers changes with time. In other words, it gives the slope of the function V(t) at any point in time. To find the function V(t) itself, we need to integrate V'(t) with respect to t. The constant of integration C is added to the result of the integration to ensure that the initial value of V(t) is equal to the cost of the computers. Once we have the expression for V(t), we can find the value of the computers at any point in time by substituting the appropriate value for t into the expression. In this case, we found that the value of the computers after 5 years is approximately $232,500.

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The mean and standard deviation of the sampling distribution of the sample proportion are: (d) 0.55, 0.0497.

In Mathematics and Statistics, a sample proportion can be defined as the proportion of individuals in a sample that have a specified characteristic or trait.

The mean of the sampling distribution of the sample proportion is equal to 0.55. Mathematically, the standard deviation of the sampling distribution of the sample proportion can be calculated by using this formula:

σp = √(p(1 - p)/n)

Substituting the given parameters into the standard deviation formula, we have;

Standard deviation, σp = √(0.55(1 - 0.55)/100)

Standard deviation, σp = √(0.55(0.45)/100)

Standard deviation, σp = 0.002475

Standard deviation, σp = 0.0497

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Complete Question:

In a large population, 55% of the people get a physical examination at least once every two years. An SRS of 100 people are interviewed and the sample proportion is computed.

The mean and standard deviation of the sampling distribution of the sample proportion are:

(a) 55, 4.97.

(b) 0.55, 0.002.

(c) 55, 2.

(d) 0.55, 0.0497.

(e) The standard deviation cannot be determined from the given information.

The roots of the quadratic equation 2x² + 5x + 3 = 0 are x = -3 and x = -1/2.

To find the roots of a quadratic equation, we must first convert the equation into the standard form ax² + bx + c = 0. In this case, the given equation is already in this form, so we can proceed with solving. To solve, we use the quadratic formula, which is x = (-b ± √(b² - 4ac))/2a.So, we have x = (-5 ± √(25 - 4(2)(3))/2(2). Simplifying, we get x = (-5 ± √(13))/4. The quadratic formula yields the values x = -3 and x = -1/2. Therefore, the roots of the quadratic equation 2x² + 5x + 3 = 0 are x = -3 and x = -1/2.

x = (-5 ± √(25 - 4(2)(3))/2(2)

= (-5 ± √(13))/4

= -3, -1/2

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Answer:

Step-by-step explanation:

Simplifying the expression (m^4n)^3 can be done by using the laws of exponents. The first law states that when two terms with identical bases are being multiplied, you add their exponents together. In this case, m is the base and 4n is its exponent; therefore, when we multiply them together three times (or raise to the third power), then our result should be m raised to a power of 12n.

Answer: y intercept (0,-15), x intercept (5,0), yes, (2,-9) is a solution

Step-by-step explanation:

the y intercept is when x=0, so plug in 0 for x -> y=3(0)-15

y=-15, y intercept is (0,-15)

the x intercept is when y=0

so plug in 0 for y -> 0=3x-15

then solve for x,

add 15 to both sides -> 15=3x

divide both sides by 3, 5=x

x intercept is (5, 0)

to test if (2, -9) solution, lets plug in 2 for x and see if we get an answer of -9

so y=3(2)-15

y=6-15

y=-9

so yes, (2,-9) is a real solution

The relationship between the volumes of a cylinder and a cone both of which have equal radii and vertical heights:

the volume of cone = 1/3 ×  volume of cylinder

In this question we need to find the relationship between the volumes of a cylinder and a cone both of which have equal radii and vertical heights.

Consider a cylinder with radius r and vertical height h.

We know that the formula for the volume of cylinder.

V1 = π × r² × h                  ..........(1)

Now consider a cone with radius r and vertical height h.

Using the formula for the volume of cone,

V2 = 1/3 × π × r² × h

From equation (1),

V2 = 1/3 × V1

the volume of cone = 1/3 ×  the volume of cylinder

Therefore, volume of cone = 1/3 ×  volume of cylinder

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According to question,

Given data,

2x-3y=-12……… (1)

Y=-5x/3-3……… (2)

3y= -5x-9………… (3)

Solving the equation,

(1) and (3)

5x-3y=-9

2x-3y=-12

To solve both equation

3x=3

x=1

the value of x, putting equation 1

5x-3y= -9

5×1-3y=-9

5-3y=-9

-3y=-9-5

-y=-14

y=14/3

y=4.6

the value of x=1 and y=4.6

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Q-find the greatest common factor.ab4c7,a7b4c.

We know that,

Greatest common factor= the greatest common factor is the greatest factor that divides both numbers.

According to question.

Given data,

Factor of a= a

Factor of b=b× b× b× b

Factor of c=c× c× c× c× c× c× c

Therefore,

Factor of a=a× a× a× a× a ×a ×a

Factor of b4=b ×b ×b× b

Factor of c=c

Greatest common factor=ab4c

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The area of the rectangle formed by 4 squares is 36 sq inches.

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

We know the perimeter of any plane figure is the sum of the lengths of all the sides.

Let each side of this square be 'a'.

∴ (a + a + a + a) + a + (a + a + a + a) + a = 30.

4a + a + 4a + a  = 30.

2(4a + a) = 30.

2(5a) = 30.

10a = 30

a = 3.

So, the length of the rectangle is 4a and the width is a.

∴ The area of the rectangle is (4a×a) = 4a².

= 4(3)².

= 4(9).

= 36 sq inches.

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When numbers are arranged in ascending order, they are done so from least to largest.

When numbers are arranged in ascending order, they are done so from least to largest.

We must first compare the numbers before we may arrange them in any order.

Compare first, then order.

Numbers arranged in ascending order: Determine how many digits each number has.

Numbers can be arranged in ascending order, from the least value to the highest value.

The arrangement is left to right.

Increasing order is another name for ascending order.

An ascending sort will organize numbers from smallest to largest and text from A to Z because ascending signifies moving upward.

For numbers, descending is going from largest to smallest, and for text, it's from Z to A.

Therefore, when numbers are arranged in ascending order, they are done so from least to largest.

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Rotation would be the first answer...Your second answer would be dilation. If this is wrong, I'm so sorry

Answer:

15 weeks

Step-by-step explanation:

read the graph at the number of words correct

those past 15.words count the weeks in the y.axis

Answer:

Yes

Step-by-step explanation:

Yes because if you insert -39 for x and 42 for y then your equation is:

42 = -39 + 81

If you were to solve this equation it would be true.

Answer:

Step-by-step explanation:

You want the values of y and z in the figure showing a triangle with exterior angle 135° opposite remote interior angles (5y+5)° and (4z+9)°, where angle (4z+9)° is adjacent to exterior angle (9y-2)°.

The exterior angle of a triangle is equal to the sum of the remote interior angles. This can be used to find both y and z.

The lower left interior angle is 180° -135° = 45°, so the right-side exterior angle is ...

  (9y -2)° = (5y +5)° +45°

  4y = 52 . . . . . . . . . . . . . divide by °, add 2-5y

  y = 13 . . . . . . . . . . divide by 4

The lower left exterior angle is ...

  135° = (5y +5)° +(4z +9)°

  135 = 5(13) +5 +4z +9 . . . . . . . . . divide by °, substitute value of y

  56 = 4z . . . . . . . . . . . . . . . . subtract 79

  14 = z . . . . . . . . . . . . divide by 4

The values of y and z are 13 and 14, respectively.

The x-coordinate of the ordered pair for the solution of the system of given equations is 10.4.

To find the solution to a system of equations, we need to find the values of the variables that make both equations true at the same time.

In this case, we are looking for the x-coordinate of the solution. To find this, we can solve the system of equations by eliminating one of the variables.

We can start by eliminating y from the equations by substituting the expression for y in the first equation into the second equation:

x + 6(-x + 10) = 8

x - 6x + 60 = 8

-5x + 60 = 8

-5x = -52

x = 10.4

The x-coordinate of the solution is 10.4.

This solution tells us that the x-coordinate of the point where the two lines intersect is 10.4, and the y-coordinate can be found by substituting this value into either of the original equations and solving for y.

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x + 6(-x + 10) = 8

x - 6x + 60 = 8

-5x + 60 = 8

-5x = -52

x = 10.4

The x-coordinate of the solution is 10.4.

This solution tells us that the x-coordinate of the point where the two lines intersect is 10.4, and the y-coordinate can be found by substituting this value into either of the original equations and solving for y.

The formula z = (x-μ)/σ allows us to determine the z-score for a sample mean on the distribution of means.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values.

Standard deviations from the mean are used to measure Z-score.

A Z-score of zero means the data point's score is the same as the mean score.

Z-scores are calculated using the formula z = (x-μ)/σ, where x represents the raw score, the population mean, and the population standard deviation.

The z-score is simply the raw scoreless the population means, divided by the population standard deviation, as the calculation demonstrates.

Therefore, the formula z = (x-μ)/σ allows us to determine the z-score for a sample mean on the distribution of means.

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The vertical asymptotes can be simply found by equating the denominator of a function to zero and solving for x, but the vertical asymptotes requires consideration of the highest degrees of x in numerator and denominator.

A vertical asymptote is a vertical line that guides the graph of the function but is not part of it. Because it appears at an x-value outside of the function's scope, the graph can never cross it. There may be several vertical asymptotes for a given function.

A graph's horizontal asymptote is a horizontal line with the equation y = b, where the graph moves closer to the line as the inputs go closer to 0 or -1.

Find the x values where the function is undef for the purpose of determining a function's vertical asymptotes. Consider the degree of the numerator and the degree of the denominator while looking for a function's horizontal asymptotes. The horizontal asymptote is y = 0 if the degree of the numerator is smaller than the degree of the denominator. There is no horizontal asymptote if the degree of the numerator is higher than the degree of the denominator. The horizontal asymptote is y = the coefficient of the highest-degree term in the numerator divided by the coefficient of the highest-degree term in the denominator if the degree of the numerator and denominator are equal.

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