Find The Set Of Values Of K For Which The Line Y= 2x-k Meets The Curve Y= X2+kx-2 At Two Distinct Points (2024)

The price of the rechargeable drill in the home improvement stores is P(m) = 1.2m + 4, where m is the manufacturing total cost.

P(m) = 1.2m + 4

P(m) = 1.2(manufacturing cost) + 4

P(m) = 1.2m + 4

The manufacturer of tools charges $4 more than its manufacturing cost for a rechargeable drill to a chain of home improvement stores. Following that, the chain sells each drill for 120 percent of what it paid the manufacturer.. Therefore, the price of the rechargeable drill in the home improvement stores can be represented by the function P(m), where m is the manufacturing cost of the drill. The equation P(m) = 1.2m + 4 shows that the price of the rechargeable drill in the home improvement stores is equal to 1.2 times the manufacturing cost plus $4. This equation indicates that the manufacturer of tools charges $4 more than its manufacturing cost and the home improvement stores then increase the price of the drill by 20% of the price they paid to the manufacturer. Therefore, the total cost of the rechargeable drill in the home improvement stores is 1.2m + 4, where m is the manufacturing cost of the drill.

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Answer:

28 Pizza

Step-by-step explanation:

how many toppings8x4pizzas 4 with 8 toppings=28

The maximum height of the projectile is 3.72 units.

What is maximum height of projectile?

When a particle is hurled obliquely near the surface of the earth, it travels along a curved path while accelerating continuously in the direction of the planet's center (we assume the particle stays close to the surface of the globe). Such a particle's motion is known as projectile motion, and its route is referred to as a projectile.

The highest vertical position along the object's trajectory is considered to be its maximum height. The range of the bullet is defined as its horizontal displacement. The initial velocity of the object affects the projectile's range.

The projectile on a planet is given as:

[tex]h(t) = -42t^2 + 25t[/tex]

The maximum height is determined by using the differentiation and equating the differentiation to zero.

[tex]\frac{d}{dt} [ -42t^2 + 25t] = -84t + 25[/tex]

Substituting the value to 0 we have:

-84t + 25 = 0

t = -25/-84

t = 0.29

Thus, we get the maximum height at t=0.29.

Substituting the value of t = 0.29 we have:

h(0.29) = -42(0.29)² + 25(0.29)

h(0.29) = 3.72

Hence, the maximum height of the projectile is 3.72 units.

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E letter is the direction of the line of symmetry different from that of the others.

A line of symmetry is what?

A form or item is divided into two equally and symmetrical portions by a line of symmetry. So it separates the figure symmetrically and the separated portions resemble mirror images of one another, we also refer to this line as the axis of symmetry or the mirror line.

What are the three symmetry lines?

A triangular equilateral shape has three symmetry lines. An equilateral triangle has the most lines of symmetry, as opposed to other types of triangles like scalene, isosceles, or right-angled triangles.

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Answer:

x=27

Step-by-step explanation:

14=x-13

14+13=x

27=x

Answer:

x=27

Step-by-step explanation:

In order to solve this problem you must isolate your variables onto one side which in this case is x. And in order to isolate it you must get rid of the -13 this can be done by adding 13 to both sides which would leave x on one side and 27 on the other resulting in x being 27.

Hope this helps! :)

Answer:

x = 23

y = 137

Step-by-step explanation:

Alternate interior angles have the same measurement (congruent)

3x - 20 = 2x + 3 Subtract 2x from both sides

3x - 2x - 20 = 2x - 2x + 3

x - 20 = 3 Add 20 to both sides

x = 23

Adjacent angles add to 180

3x - 20 + y - 6 = 180 Substitute 23 for x

3(23) -20 + y -6 = 180

69 - 20 + y -6 = 180 Combine like terms

43 + y = 180 Subtract 43 from both sides

y = 137

the integration can be simplified to

∫ t⁻³ with the limits cosx and 0 (sorry it's difficult to type it >.<)

you then integrate the value to get:

∫ -1/2t⁻² with the limits cosx and 0

then sub in your limits to get;

( -1/2(cosx)⁻² ) - ( -1/2(0)⁻² )

= - cosx⁻² / 2

i hope this helps, if you're struggling to understand i can try get a written working out instead :D (not sure if i got this right too...)

Answer: Sally baked 11 cakes

Step-by-step explanation:

Alright, so you should go about solving this by setting up two equations. We will use b to represent Brad and s to represent Sally:

b+s=27

b=s+5 (because Brad made 5 more cakes than sally)

Solve using systems of equations. I will show the substitution method because it is faster in this scenario:

(s+5)+s=27

Solve for s:

s+5+s=27

2s=22

s=11

So Sally baked 11 cakes, which makes sense because that means that Brad baked 16

Answer:

a. 50:65

b. 200:150

c. 675:550

d. 40:60

e. 180:240

Answer: 15.6 miles !

Step-by-step explanation:

MMMCMXXXIII should be added to 54 roman numerals to get MMMCMLXXXVII.

LIV Roman Numerals:

LIV Roman Numerals can be written as numbers by combining the transformed roman numerals i.e. LIV = L + V - I = 50 + 5 - 1 = 54. The higher roman numerals precede the lower numerals resulting in the correct translation of LIV Roman Numerals. In this article, we will explain how to convert LIV Roman numerals in the correct number translation.

LIV = L + IV

LIV = 50 + 4

LIV = 54

We will write MMMCMLXXXVII and LIV in numbers, i.e. LIV = 54 and MMMCMLXXXVII = 3987. Now, 3987 - 54 = 3933. And, 3933 = MMMCMXXXIII. Therefore, MMMCMXXXIII should be added to 54 roman numerals to get MMMCMLXXXVII.

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The only ordered pair that is a solution to the equation 2x+5y=20 is (5,2), which is option C.

What is linear equation ?

Linear can be defined as equation in which highest degree is one.

To check which of the following ordered pairs is a solution to the equation 2x+5y=20, we can substitute the values of x and y from each ordered pair into the equation and see if the equation is true.

The ordered pairs are:

A. (2,3)

B. (3,2)

C. (5,2)

D. (4,3)

Let's check each one:

A. (2,3)

2(2) + 5(3) = 4 + 15 = 19

This is not equal to 20, so (2,3) is not a solution.

B. (3,2)

2(3) + 5(2) = 6 + 10 = 16

This is not equal to 20, so (3,2) is not a solution.

C. (5,2)

2(5) + 5(2) = 10 + 10 = 20

This is equal to 20, so (5,2) is a solution.

D. (4,3)

2(4) + 5(3) = 8 + 15 = 23

This is not equal to 20, so (4,3) is not a solution.

Therefore, the only ordered pair that is a solution to the equation 2x+5y=20 is (5,2), which is option C.

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The coordinates of the point of intersection are (1, -1). The solution is obtained by graphing the equations.

What is graphing of an equation?

The method of graphing an equation involves creating the graph of a relevant equation. Straightforward equations like direct, quadratic, etc., are very simple to graph, but complex equations require a deeper understanding of a few key concepts. If the curve accurately depicts the equation, then every point on the curve will satisfy the equation.

We are given two equations as y = 2x - 3 and y = -3x + 2

The graph for the equations has been plotted and attached below.

In the graph, red line represents y = 2x - 3 and blue line represents

y = -3x + 2.

We can see from the graph that the two lines intersect at (1, -1).

Hence, the coordinates of the point of intersection are (1, -1).

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Since, there are multiple questions so, the question answered above is as follows

Question: Determine the coordinates of the point of intersection for the following linear system by graphing

y = 2x - 3 and y = -3x + 2

A quadratic function f(x) = ax² + bx + c is minimum when the leading coefficient 'a' > 0 and the minimum point is (-b/2a, 0)

We know that the general form of quadratic function is f(x) = ax² + bx + c

Also, the graph of the quadratic function is a parabola.

A quadratic function f(x) is minimum when the leading coefficient 'a' > 0 (the parabola opens upward) and f(x) is maximum when a < 0 (the parabola opens downward)

When parabola opens upward then the vertex of the parabola is nothing but the minimum of quadratic function.

And when parabola opens downward then the minimum of parabola cannot be determined.

Thus, if parabola opens up then the vertex of parabola tis the the minimum value of the quadratic function.

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A regular pentagon has five rotational symmetries when it is turned around its centre. A regular pentagon has five bands of reflectional symmetry in addition to rotational symmetry.

What are the Pentagon's 5 sides?

Any five-sided shape or 5-gon is referred to as a pentagon in mathematics. In a straightforward hexagon, the interior angles add up to 540°. A hexagon could be straightforward or self-intersect.

What role does the Pentagon play?

The Potus and the Defense Secretary have exerted global command and control over the nation's military forces from the Pentagon. Since its construction, the Pentagon has served as a national and international emblem. It is, above all, a metaphor for American strength and influence, with all the positive and negative connotations that entails.

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The simplified form of the square root of 12 is indeed 2 times the square root of 3.

The square root of 12 can be simplified to 2 times the square root of 3. To see why, we can factor 12 into its prime factors, which are 2 and 3, as follows:

12 = 2 × 2 × 3

Next, we can group the two 2's together and take their square root, which gives us 2. Then, we can take the square root of the remaining 3, which gives us the square root of 3. So, the simplified form of the square root of 12 is:

√12 = √(2 × 2 × 3) = 2√3

To verify this mathematically, we can use a calculator or long division to approximate the square root of 12, which is approximately 3.464. Then, we can simplify 2 times the square root of 3, which is approximately 3.464 as well. This confirms that the simplified form of the square root of 12 is indeed 2 times the square root of 3.

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There are approximately 28.28 quarts in 905 ounces.

A quart is a unit of volume measurement commonly used in the United States. One quart is equal to 32 fluid ounces.

To find out how many 905 ounces are in a quart, we need to divide 905 by 32.

905 oz ÷ 32 oz/qt = 28.28 qt

Therefore, there are approximately 28.28 quarts in 905 ounces.

Overall, it's important to understand the different units of measurement and how they relate to each other in order to perform accurate conversions between them. In this case, we used the conversion factor of 32 fluid ounces per quart to convert from ounces to quarts.

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The minimum score needed to be in the top 2% of the exam is 90.5, which is two standard deviations above the mean.

To calculate the minimum score needed to be in the top 2%, we need to find the value of two standard deviations above the mean. This can be done using the formula x = μ + (2σ), where μ represents the mean and σ represents the standard deviation. In this case, μ = 76.4 and σ = 6.1. We substitute these values into the formula to get x = 76.4 + (2*6.1), which equals 90.5. Therefore, the minimum score needed to be in the top 2% is 90.5. To further understand this calculation, it is important to note that the normal distribution curve is symmetrical. This means that the area under the curve that is two standard deviations above the mean is 2%, which is the same as the area under the curve that is two standard deviations below the mean. Therefore, the score that is two standard deviations above the mean is the minimum score needed to be in the top 2%.

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Considering the function f(x) = 2 / (7 - x). The following can be deduced

a. f(7) = ∞

b. (-∞ 7)] ∪ [7 ∞)

c. g(3) = 11

d. f(g(3)) = -1/2

How to find the f(7)

Using the function f(x) = 2 / (7 - x), f(7) is solved as follows

f(7) = = 2 / (7 - 7)

= 2/0

= ∞

The domain of the function is

(-∞ 7)] ∪ [7 ∞)

Using g(x) = 2x + 5 , then g(3)

g(3) = 2(3) + 5

g(3) = 11

f(g(3))

f(g(3)) = 2 / (7 - 11)

f(g(3)) = 2 / -4

f(g(3)) = -1/2

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There is no solution to the given system of inequalities.

What are systems of inequalities?

At least two linear inequalities in the same variables make up a system of a linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.

We have a system of inequalities,

y < -3x - 2

And y > -3x + 8.

The graph of the inequalities is given below.

And the lines are parallel.

That means there is no solution to the system.

Therefore, there is no solution to the system.

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We can see that the vertex of Fountain B is higher than that of Fountain A.The Fountain B's water flows to a greater height.

What is vertex?

The vertex of a function is the point on the graph where the function reaches either its maximum or minimum value.

For example, in a quadratic function of the form y = ax^2 + bx + c, the vertex is the point at which the parabola changes direction and reaches either its highest or lowest point.

The vertex is an important point on the graph because it provides information about the shape of the function and its behavior. It is also useful for finding the axis of symmetry, which is a line that divides the graph into two symmetric halves.

The vertex can be calculated using a variety of methods, such as completing the square or using the formula d = -b/2a.

The vertex of Fountain A can be found by using the formula:

d = -b/2a, where a = -1 and b = 2

Substituting the values, we get:

d = -2/2(-1) = 1

So, the vertex of Fountain A is (1, 6)

For Fountain B, we can see that the maximum height reached is 11 feet, which occurs at x = -3.

So, the vertex of Fountain B is (-3, 11).

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1) The reaction is single replacement

2) KI and Cl2

3) KCl and I2

4) Cl2 + 2KI → 2KCl + I2

What is a single replacement reaction?

A single replacement reaction, also known as a single displacement reaction, is a type of chemical reaction in which one element or ion in a compound is replaced by another element. The general form of a single replacement reaction is:

A + BC → B + AC

Single replacement reactions can also occur with non-metals, in which case the non-metal replaces another non-metal in a compound. For example, when chlorine gas (Cl2) is added to a solution of potassium iodide (KI), a single replacement reaction occurs:

Cl2 + 2KI → 2KCl + I2

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The amount of 4 GiB is equal to 4,096 Megabytes (MB), or 4,194,304 Kilobytes (KB), or 4,294,967,296 Bytes (B). Therefore, 4 GB is equal to 3.8 GiB.

4 GB stands for 4 Gigabytes, while GiB stands for Gibibytes. A Gigabyte is a unit of digital information storage, while a Gibibyte is a unit of computer memory or data storage equal to 1024 mebibytes. One Gigabyte is equal to 1,073,741,824 bytes, while one Gibibyte is equal to 1,073,741,824 bytes. Therefore, 4 Gigabytes is equal to 3.8 Gibibytes.

In more detail, 4 Gigabytes is equal to 4,096 Megabytes (MB), or 4,194,304 Kilobytes (KB), or 4,294,967,296 Bytes (B). It is important to note that these values can vary slightly depending on the system of measurement and the type of computer memory being used. For example, a computer system may use a different method to calculate the storage of data and may report larger or smaller values than the standard.

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Answer: We can simplify the expression 64 ×1 /16^2x as follows:

64 ×1 /16^2x = 4^3 × 4^(-2x) [since 64 = 4^3 and 16 = 4^2]

Using the law of exponents which states that when we multiply two powers with the same base, we add the exponents, we get:

4^3 × 4^(-2x) = 4^(3 - 2x)

Therefore, 64 ×1 /16^2x can be expressed as a power of 4 in terms of x as:

4^(3 - 2x)

Step-by-step explanation:

If Kayla decides to choose the best deal, then, 1200 beads will cost $48.

How to get the best deal

In order to get the best deal, Kayla should find the unit cost of the beads in all categories listed. The unit costs are as follows:

For 100 beads sold for $6, the unit cost is $0.06.

For 200 beads sold for $10, the unit cost will be $0.05.

For 400 beads sold for $16, the unit cost will be $0.04.

For 600 beads sold for $30, the unit cost will be $0.05.

For 1000 beads sold for $55, the unit cost will be $0.055.

When we multiply 1200 beads for the given unit costs, we will have; $72, $60, $48, $60, and $66. The cheapest of all these is $48 and this is Kayla's best deal.

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The Surface area of Cuboidal box is 320 inch².

What is Surface Area?

A 3D object's surface area is the entire area that all of its faces cover. For instance, the surface area of a cube is its surface area if we need to determine how much paint is needed to paint it. It is consistently expressed in square units.

Given:

length = 10 inch

width = 4 inch

height = 8 inch

So, Surface Area of Cuboid = l x w x h

= 10 x 4 x 8

= 40 x 8

= 320 inch²

Thus, the Surface area is 320 inch².

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Answer:

6

Step-by-step explanation:

If you push two triangle tables together you just multiply 3*2

The rate of change of the proportional relationship is given as follows:

k = 8/3.

Hence Nadia is correct.

What is a proportional relationship?

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The constant represents the rate of change, and is obtained as follows:

k = y/x.

From the graph, when x = 3, y = 8, hence the rate of change of the proportional relationship is given as follows:

k = 8/3.

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Answer:

Step-by-step explanation:

Slope-intercept form and point-slope form are two different ways to express the equation of a straight line.

Slope-intercept form is 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. This form is useful for graphing and making calculations based on the slope and y-intercept. For example, given the equation y = 2x + 1, we know that the slope of the line is 2 and the y-intercept is 1.

Point-slope form is written in the form y - y1 = m(x - x1), where "m" is the slope of the line and (x1, y1) is a point on the line. This form is useful for finding the equation of a line when given a point on the line and the slope of the line. For example, given a line with slope 3 passing through the point (2, 5), the equation in point-slope form would be y - 5 = 3(x - 2).

Answer:

y = mx + b

y - y1 = m(x - x1)

Step-by-step explanation:

If Jamil and Vicki have one child , age 3 , then the tax credit will reduce their tax liability by $2000 , the correct answer is (e) .

Based on the current tax laws in the United States, Jamil and Vicki may be eligible for a tax credit of up to $2,000 for their child who is age 3. This tax credit is known as the Child Tax Credit (CTC).

The CTC is a non-refundable tax credit, which means it can only be used to reduce the amount of taxes owed.

If Jamil and Vicki's tax liability is less than $2,000, the CTC will only reduce their tax liability to zero.

If their tax liability is more than $2,000, the CTC will reduce their tax liability by $2,000.

Therefore, the correct answer is Option(e) $2000.

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