(d) Find the value of k for which the vertex of the parabola y=x2+kx+9 lies on the line x=−3. (e) Find the value of k for which the vertex of the parabola y=kx2+3x+4 lies on the line x=3

The slope of the line that contains the points (10, 0) and (-20, -18) is: slope = (change in y)/(change in x) = 3/5.

The slope of a line is the measure of its steepness, and it's found by dividing the change in the y-coordinates by the change in the x-coordinates between two points on the line. In this case, the slope of the line that passes through the points (10, 0) and (-20, -18) can be calculated as follows:

slope = (change in y-coordinates) / (change in x-coordinates)

slope = (-18 - 0) / (-20 - 10)

slope = -18 / -30

slope = 3/5

Therefore, the slope of the line is 3/5.

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The correct equation to find the nth term of the given sequence is an=2n+12, which can be demonstrated by calculating the 4th to 8th terms and verifying that they match the given values.

The formula an=2n+12 can be used to find the nth term of the sequence. This formula states that the nth term is equal to twice the value of n (2n) plus 12 (2n + 12). To demonstrate, for the 4th term of the sequence (a4), we can use the formula and calculate a4 = 2(4) + 12 = 20, which is equal to the given value of a4 = 12. Similarly, we can calculate the other values of the sequence using the same formula: a5 = 2(5) + 12 = 22 (which is equal to the given value of a5 = 14), a6 = 2(6) + 12 = 24 (which is equal to the given value of a6 = 16), a7 = 2(7) + 12 = 26 (which is equal to the given value of a7 = 18), and a8 = 2(8) + 12 = 28 (which is equal to the given value of a8 = 20). Therefore, we can conclude that an=2n+12 is the correct equation to find the nth term of the sequence.

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For the given equations, using slope formula option B: Lines 3 and 4 are parallel, is the correct option.

What is slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

The four different equations are given.

To identify parallel lines, we need to compare their slopes.

If two lines have the same slope, they are parallel.

Line 1 is in slope-intercept form (y = mx + b) where the slope is m = 8.

Line 2 is in point-slope form (y - y1 = m(x - x1)) where the slope is m = 1/8.

Line 3 is in slope-intercept form where the slope is m = 3.

Line 4 is in slope-intercept form where the slope is m = 1/3.

Comparing the slopes, we see that -

Lines 1 and 2 have different slopes, so they are not parallel.

Lines 1 and 3 have different slopes, so they are not parallel.

Lines 1 and 4 have different slopes, so they are not parallel.

Lines 2 and 3 have different slopes, so they are not parallel.

Lines 2 and 4 have different slopes, so they are not parallel.

Lines 3 and 4 have the same slope (m = 3), so they are parallel.

Therefore, lines 3 and 4 are parallel.

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Answer:

7/25

Step-by-step explanation:

Sin = [tex]\frac{opposite}{Hypotenuse}[/tex]

Hypotenuse = 50

Adjacent = 48

Pythagorean Theorem: a² + b² = c²

48² + b² = 50²

2304 + b² = 2500

b² = 196

b = 14

Opposite = 14

Sin A = 14/50 = 7/25

Answer:

12 units

Step-by-step explanation:

Answer:

x = 18

Step-by-step explanation:

the angle vertically opposite 7x is 7x

making 3x and 7x same- side interior angles summing to 180° , that is

3x + 7x = 180

10x = 180 ( divide both sides by 10 )

x = 18

for A and B to be parallel then x = 18

Answer:

B. inductive

Step-by-step explanation:

An inductive reasoning process involves making a generalization based on specific observations. In the case of the given question, the statement is: "A _______ is an educated guess based on patterns in data figures."

To use inductive reasoning to find the answer, we can follow these steps:

Look for patterns in the data figures. Identify the commonalities between different examples of educated guesses.

Based on these patterns, make an initial generalization about what the blank might be. For example, if we notice that all educated guesses involve making a prediction based on previous observations, we might guess that the missing word is "conjecture."

Test the generalization by looking at additional examples. Do these examples fit the pattern we identified earlier? If so, our initial guess might be correct. If not, we might need to revise our generalization or consider other options.

Continue testing and refining the generalization until we feel confident that it accurately describes the relationship between the given words.

In this case, using inductive reasoning, we can make an educated guess that the missing word is "conjecture," as it fits the pattern of being an educated guess based on patterns in data figures.

Using the trend line equation, we can find that the record was set in the year 2005.

Data is shown visually in a scatter plot.

The coordinate axes are used in a straightforward scatter plot to plot the points according to their values.

Now in the given question,

The scatter plot equation is:

y = - 0.14x + 12.5

Now we know that y = 11.8 seconds.

So,

11.8 = -0.14x + 12.5

⇒ 0.14x = 12.5 - 11.8

⇒ x = 0.7/0.14

⇒ x = 5

Therefore, the year when the record was set is 2000+5 = 2005.

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Mrs. kenimer had a chocolate bar that weighed 1/2 lb. At recess she ate some of her chocolate bar, now her bar weights 1/4 of a pound. Mrs. kenimer ate 3/8 lb of the chocolate bar.

The British imperial and American cοnventiοnal methοds οf measurement bοth use the pοund as a unit οf mass. The internatiοnal avοirdupοis pοund, which is fοrmally defined as precisely 0.45359237 kilοgrammes and is split intο 16 avοirdupοis οunces, is the term that is currently mοst frequently used. The avοirdupοis pοund's wοrldwide standard sign is lb.

Given,

Mrs.kenimer had a chocolate bar that weighed 1/2 lb or 0.5lb

At recess she ate some of her chocolate bar, now her bar weights 1/4 of a pound or 0.25 of a pound.

Remaining weight of the chocolate bar= ½* ¼ = 1/8 lb

She ate= (1- ¼)= ¾ or 0.75 of a pound

So she ate= ½ * ¾ = 3/8 lb of the chocolate.

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1) The equal expressions are I and III

2) The value of the expression is 3 41/80

An absolute value expression is a mathematical expression that represents the distance of a number from zero, regardless of the sign of the number. The absolute value of a number is always positive, so an absolute value expression represents a positive number or zero.

The absolute value of a number x is denoted by |x| and is defined as follows:

|x| = x, if x is positive or zero

|x| = -x, if x is negative

Since -/x/ = -x then this are the equal expressions.

[tex]a^2/a + 1 + a + 1/a^2[/tex]

Then;

[tex]4^2/4 + 1 + 4 +1/4^2[/tex]

16/5 + 5/16

= 3 41/80

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Answer:

32 or 24 or 13 or 21

Step-by-step explanation:    

332-240=92

168-118 = 50

86-57 = 29

45-13= 32

or

45-21= 24

A right triangle, also known as a right-angled triangle, is a triangle that has one angle measuring 90 degrees.

Right triangles have some unique properties that make them useful in various applications, such as in geometry and trigonometry. For example, the Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

We know that;

Tan 45 = 14/x

x = 14

Sin 45 = 14/y

y = 20

Again;

Tan 60 = 16√3/x

x = 16√3 * 1/√3

x = 16

Sin 60 = 16√3/y

y =  16√3 ^ 2/√3

y = 32

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No, because the SAS Congruence Theorem requires two pairs of congruent sides and one congruent angle.

No, because the SAS Congruence Theorem requires two pairs of congruent sides and one congruent angle. To use the SAS Congruence Theorem to prove that GHF =KHJ, it would be necessary to have information about the lengths of the corresponding sides and the measure of the included angle in each triangle. Without this information, it is not possible to prove that GHF =KHJ using the SAS Congruence Theorem. To prove that GHF =KHJ using this theorem, it would be necessary to show that the two sides GK and KH are congruent, the two sides HF and HJ are congruent, and the included angle GHF is congruent to the included angle KHJ.

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We may state with confidence that the exponential function y = [tex]3(3^{x} )[/tex]models the provided data because both of these values agree with the data.

How is exponential function determined?

Since the output values (y) increase by a factor of three every time the input value (x) increases by one, the data demonstrate exponential growth. As a result, we can use an exponential function of the form y = a(b)x to represent this data.

We can utilise the first two data points to determine the values of a and b.

With y = 3 and x = 0, we get:

3 = [tex]a(b^{0} )[/tex]

3 = a

With x=1 and y=9, we get:

9 = [tex]a(b^{x} )[/tex]

b = 3

Hence, y = [tex]3(3^{x} )[/tex] is the exponential function that represents the data.

We may substitute the other input values and compare them to the appropriate output values to validate this model:

If x = 2, then y = [tex]3(3^{2} )[/tex] = 27.

If x = 3, then y = [tex]3(3^{3} )[/tex] = 81.

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Answer:

A)  Missing Table Values.  See the attached worksheet

B)  The car will be worth less than $8,000 in 9.8 years

Step-by-step explanation:

Part B:  Years until car is less than $8,000

 The new $25,000 car depreciates by 11% each year.  Expressed another way, it retains 89% of its value each year.  The value, y, after x years can be calculated from:

                                 y = ($25,000)*(0.89)^x

This function is graphed on the attached worksheet.  The line intersets the $800 on the y axis at 9.8 years.  The car will be worth less than $8,000 after 9.8 years.

One can also calculate the value of x:

                            $,8000 = ($25,000)*(0.89)^x

        x = 9.77, mathematically

Part A:  Table of values

See the attached worksheet.  The values are not exactly a straight line, but come close to f(x) = 8x+50, from which the missing values may be calculated.  Legally, however, this is a slightly more complex line, for which I'm unclear about the best approach for its derivation.

Therefore, the most specific category this shape can be sorted into is "Triangle."

3 sides, 3 angles, and 3 vertices make up a closed triangle. It has only two dimensions. Triangles are a part of polygons as well.

The most specific category this shape can be sorted into is "Triangle."

In the given Venn diagram, the category "Triangle" represents the overall group of all types of triangles, which includes "Equilateral," "Isosceles," and "Scalene" triangles.

The triangle with a single tick mark on each side may represent any type of triangle that is not necessarily equilateral, isosceles, or scalene, but it is still a triangle.

Therefore, the most specific category this shape can be sorted into is "Triangle."

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Answer:

35

Step-by-step explanation:

Simplification :

7(a-b) as 7 is common
as we know a-b is 5 ,

7 * 5 = 35 in the answer.

Please mark me as the brainliest TQ!

Answer: 35

Step-by-step explanation:

7a - 7b

= 7(a-b)

= 7(5)

= 35

Answer: $\sqrt[8]{7^7}$

Step-by-step explanation:

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If Allison needs 13 inches of cloth for sewing project, then Allison will need to buy 33.02 centimeter of cloth.

The length of cloth that Allison needs to buy is =  13 inches ,

The conversion factor is ⇒ 1inch = 2.54 centimeter,

Allison needs 13 inches of cloth, and we know that 1 inch is the same as 2.54 centimeters.

So, to convert 13 inches to centimeters we multiply it by the conversion factor of 2.54 centimeters per inch,

Which is written as;

⇒ (13 inches) × (2.54 centimeters per inch)

⇒ 33.02 centimeters

Therefore, Allison needs to buy 33.02 centimeters of cloth for her sewing project.

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Therefore , the solution of the given problem of equation comes out to be he can hire the shoes for three hours with his meagre $11 budget.

Complex algorithms frequently employ a variable term to guarantee congruence with the two opposing assertions. Equations, which are academic expressions, are used to demonstrate the equality of different academic figures. In this instance, the normalise method provides b + 6 rather than merely expression separating 12 into two pieces for using the data from y + 6.

Here,

To begin, we can construct an expression to symbolise the circumstance:

=> y = 2x + 4

where x represents the number of hours that Quentin rents the shoes for and y represents the overall cost of the rental.

We can put y equal to 11 because we know that Quentin only has $11 to spend:

=> 11 = 2x + 4

We can now determine x:

=> 2x = 11 - 4

=> 2x = 7

=> x = 7/2

Quentin can therefore spend $11 to hire the shoes for 3.5 hours (7/2 hours).

He would have to pay either $10 or $12 to hire the shoes for either three or four hours. He can hire the shoes for three hours with his meagre $11 budget.

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The domain and range for the function f(x) = 2x include the following:

Domain = (-∞, ∞).

Range = (-∞, ∞).

In Mathematics, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-∞, ∞} or {x|x ∈ R}.

Range = {-∞, ∞} or {y|y ∈ R}.

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Answer:

[tex]x \leq \frac{1}{3}[/tex] or [tex]x \geq \frac{1}{2}[/tex]

Answer:

Below

Step-by-step explanation:

From the graph below you can see that

x < = .33 3   and   x >= .5

combined

  .333  ≥  x  ≥  .5

Answer:

2/9

Step-by-step explanation:

Answer:2/9

Step-by-step explanation:

It’s the average distance to the Mean also measures how far is the data spread apart in the population.

What is Population?

In statistics, a population refers to the entire group or set of individuals, objects, or events that share a common characteristic or feature. The population can be any size, from a small group of people to an entire country or even the whole world.

In order to make statistical inferences about a population, it is often not practical or feasible to study the entire population. Instead, researchers typically take a sample from the population, which is a smaller subset of the population, and use the sample data to make predictions or draw conclusions about the population as a whole.

The average distance to the mean (or average) also measures how far the data is spread apart in the population.

This is commonly known as the standard deviation, which is a measure of the amount of variation or dispersion in a set of data values. A larger standard deviation indicates a greater amount of variability or spread in the data, while a smaller standard deviation indicates that the data points are closer to the mean.

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Answer:

157°

Step-by-step explanation:

We can see that the angle here is an alternate angle, this means it is an opposite angle that has the same value as each other.

Knowing this, we can see that if the angles are alternated the missing angle should be 157 as well.

Hope this helps have a lovely day! :)

Answer:

i think 4<6

Step-by-step explanation:

Answer:

=

Step-by-step explanation:

5j543nn al

The solution to the quadratic equation 2x²−3x−5=0 are x=5/2 or x=-1/2

The quadratic formula can be used to solve the quadratic equation 2x²−3x−5=0. Here’s how to do it:

First, identify the coefficients of the equation. In this case, a=2, b=-3, and c=-5.

Next, plug these values into the quadratic formula: x = (-b ± √(b²-4ac)) / 2a,Substitute the values in the equation: x = (-(-3) ± √((-3)²-4(2)(-5))) / 2(2)

Simplify the equation to get:x = (3 ± √(9+40)) / 4,

x = (3 ± √49) / 4
x = (3 + 7) / 4 or x = (3 - 7) / 4
x = 5/2 or x = -1/2

In summary, the quadratic formula can be used to solve quadratic equations with ease. It is important to know the values of the coefficients of the equation and substitute them into the quadratic formula. The formula will simplify the equation and give the solutions.

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"Yes, there is." The coordinates of point P are either (11/4, 63) or (73/52, 36), depending on the chosen value of x.

We can use the distance formula to find the distance between R and P, and between P and S:

Distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Plugging in the values, we get:

RP = √((x - (-3))² + (y - 1)²)

SP = √((x - 4)² + (y - 3)²)

Now, we can set up an equation based on the given ratio of RP to SP:

RP/SP = 5/4

We can substitute the expressions we just derived for RP and SP into this equation:

√((x - (-3))² + (y - 1)²) / √((x - 4)² + (y - 3)²) = 5/4

Squaring both sides of the equation to eliminate the square roots, we get:

((x - (-3))² + (y - 1)²) / ((x - 4)² + (y - 3)²) = 25/16

Expanding the squares and simplifying, we get:

41x² - 146x - 191y² + 1210y + 2900 = 0

For simplicity, let's solve for y:

y = (73x + 2900)/191

Now we can substitute this expression for y into one of the original equations:

RP = √((x - (-3))² + ((73x + 2900)/191 - 1)²)

Simplifying this expression, we get:

RP = √(1049x² - 12212x + 36010)/191

We want RP to be 5x units long, so we can set up the equation:

√(1049x² - 12212x + 36010)/191 = 5x

Squaring both sides, we get:

Expanding the square and simplifying, we get:

1044x² - 12212x + 36010 = 0

Now we can solve for x using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1044, b = -12212, and c = 36010. Plugging in these values, we get:

x = (-(-12212) ± √((-12212)² - 4(1044)(36010))) / 2(1044) x = (12212 ± √(5924688)) / 2088 x = (12212 ± 3864) / 2088

This gives us two possible values for x:

x = 11/4 or x = 73/52

Now we can substitute each value of x back into the expression we derived for y:

y = (73x + 2900)/191

For x = 11/4, we get:

y = (73(11/4) + 2900)/191 = 63

So one possible set of coordinates for P is (11/4, 63).

For x = 73/52, we get:

y = (73(73/52) + 2900)/191 = 36

So another possible set of coordinates for P is (73/52, 36).

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The population will take around 6.9 years to triple and 9.2 years to quadruple.

Let P(t) be the population at time t. According to the problem, the rate of increase of the population is proportional to the population itself, which means: dP/dt = kP

where k is the proportionality constant. This is a separable differential equation that can be solved by separating the variables and integrating both sides:

∫ dP/P = ∫ k dt

ln|P| = kt + C

where C is the constant of integration. Applying the initial condition that the population doubles in 4 years, we get:

ln|2p0| = k(4) + C

ln|p0| + ln|2| = 4k + C

ln|p0| + ln|2| - 4k = C

Substituting C into the previous equation and using it for the new population level, we get:

ln|3p0| = kt + ln|p0| + ln|2| - 4k

ln|3p0|/|p0| = kt - 4k + ln|2|

ln|3/2| = (k/ln2)t - 4k/ln2

ln|3/2|/(k/ln2) = t - 4/ln2

t = ln|3/2|/(k/ln2) + 4/ln2

Therefore, it will take approximately 6.9 years for the population to triple and 9.2 years to quadruple.

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