A Curve has the equation y=kx^2 +1 And a line has the equation y=kx where

K is a
non-zero
Constant
1)Find the Set
the value of k
for which the
curve and line have no common point.
(1) state the value for which the line is a
tangent to the Curve and for this case, find the coordinates
of the point where the line
touches the curves

Answers

Answer 1

The set of the value for which the curve and line have no common point are is k ∈ (0 , 4).

The value for which the line is a tangent is k = 4.

The coordinates of the point where the line touches the curves is point of tangency = ( 1/2 , 2).

What is tangent?

Tangents in geometry are lines or planes that contact curves or surfaces at points where they are closer to the curve than any other lines or planes drawn through those points.

Given equations in the question:

y = kx² + 1  

y = kx

Equating y

kx² + 1   = kx

kx² -kx  + 1 =  0

This is Quadratic equation is of the form ax²+bx+c=0  where a  , b and c are real also  a≠0.

D =  b²-4ac is called discriminant.

and we know that,

D >0 roots are real and distinct

D =0 roots are real and equal

D < 0 roots are imaginary ( not real ) and different

For no common solution  D < 0

For tangent  D = 0

so,

kx² -kx  + 1 =  0

D = (-k)² - 4k  = k² - 4k = k(k - 4)

k(k - 4) < 0

if  0 < k < 4

Hence values of k for which the curve and the line have no common points is k ∈ (0 , 4).

for tangent

k(k - 4)  = 0

k is non zero

Hence k = 4

After putting the value of k, given equations are:

y = 4x² + 1  

y = 4x

solving these equations to get value of x and y:

4x² + 1   = 4x

4x² - 4x + 1 = 0

(2x - 1)² = 0

x = 1/2

y = 2

Point of tangency = ( 1/2 , 2)

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Related Questions

vantes si l'exponentiation a priorité sur la
d) 2³ x 2² =

Answers

d) the answer is 8*4=32
Solving using law of exponents ,

Given d)[tex] 2^{3} x 2^{2}[/tex]

if we observe carefully, it is in the form of [tex] a^{m} x a^{n} = a^{m+n}[/tex]

So now , the answer is [tex] 2^{3+2} = 2^{5}[/tex]

check attachment for rules...

Please help ASAP, will mark brainliest!

Type SSS, SAS, ASA, AAS, or HL to justify why triangle ABC is congruent to triangle FBD.

Answers

Answer:

SSS

Step-by-step explanation:

Please answer with show work. Trigonometry!

Answers

So cosine x is the ratio of adjacent side over hypotenuse
So I wrote cosx = 6.2/23
Thus x = cos^-1 (31/115)

explain 8 - 5 * 3 from a 7th grader

Answers

Answer:

-7

Step-by-step explanation:

5 * 3 = 15. 15 - 8 = 7; so, 8 - 15 = -7.

I dont quite understand what this question is asking for.

Answers

By using the table of values, we have the following:

The value of f(-7) is equal to 4.The value of f(15) is equal to 0.The value of f(3) is equal to 2.The value of f(-4) is equal to 15.If f(x) = 5, the value of x is equal to 4.If f(x) = 2, the value of x is equal to 5.If f(x) = 0, the value of x is equal to 15.If f(x) = -6, the value of x is equal to 2.

What is a function?

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable (x-value) to an output variable (y-value or f(x)).

In this exercise, you're required to determine the value of each function based on the value of x shown in the table above. Therefore, you would identify the input variable (x-value) that corresponds to the value of the output variable (y-value or f(x)) in the given table and vice-versa.

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solve for s 1.1=s+2.3/3

Answers

Answer:

s=1

Step-by-step explanation:

Find the value of s on one side of the equation to isolate it.

1.1=s+2.3/3

First, switch sides.

[tex]\sf{\dfrac{s+2.3}{3}=1.1}[/tex]

Multiply by 3 from both sides.

[tex]\sf{\dfrac{3\left(s+2.3\right)}{3}=1.1* \:3}[/tex]

Solve.

1.1*3=3.3

s+2.3=3.3

Then, subtract by 2.3 from both sides.

s+2.3-2.3=3.3-2.3

Solve.

Subtract.

3.3-2.3=1.0=1

s=1

Therefore, the final answer is s=1.

I hope this helps, let me know if you have any questions.

Write the perimeter of the triangle as a simplified polynomial. Then factor the polynomial.

Answers

Answer:

4x² + 29x + 7 = (4x + 1)(x + 7)

Step-by-step explanation:

Simplify the polynomial:

Like terms are terms with same variable and same power.

       Perimeter = sum of all the sides

                         = 3x² + 1 + 15x + 6 + x² + 14x

                         = 3x² + x² + 15x + 14x + 1 + 6

Combine like terms,

                        = 4x² + 29x + 7

Factorize:

        Sum = 29

  Product = 4*7 = 28

   Factors = 1 , 28    {28 + 1 = 29 & 28*1 = 28}

Rewrite the middle term using the factors,

                           = 4x² + x + 28x + 7

                           = x(4x + 1) + 7(4x + 1)

                           = (4x + 1)(x + 7)

If the temperature drops 5 degrees per hour , what is the change in temperature after 4 hours

Answers

Answer: -20 degrees

Step-by-step explanation:

The temperature drops 5 degrees/hour.

Find temperature after 4 hours.

Since we are not given a starting temperature, we can only say how much the temperature has dropped after the 4 hours.

5 degrees/hour x 4 hours = 20 degrees

Temperature has dropped so your answer will be negative.

q(x) = 1⁄2x−3; q(x) = −4

Answers

X= -1/2 is the answer
Solving with Functions

We can solve with functions exactly as we do algebraic equations. Our goal is to isolate the variable.

Solving the Question

We're given:

[tex]q(x) = \dfrac{1}{2}x-3\\\\q(x) = -4[/tex]

Solve using substitution:

[tex]\dfrac{1}{2}x-3=-4[/tex]

Isolate x:

[tex]\dfrac{1}{2}x=-4+3\\\\\dfrac{1}{2}x=-1\\\\x=-2[/tex]

Answer

x = -2

Sheila bought three books for $12.63, $9.05,
and $14.97. How much did she spend?

Answers

Adding the three numbers together, she spent a total of $36.65
1 1 1
12.63 21.68 Therefore, the answer is $36.65
+ 9.05 + 14.97
---------- ---------
21.68 36.65

Write at least three sentences to tell how you can convince others to stop littering. Use at least three different kinds of sentences in your writing.

Answers

As you should know, littering is a huge issue all across the world and with trash everywhere you look it can be quite compelling to call to action and tell people how it’s not only effecting the earth but the people who live on it as well, with numerous health conditions and lowering the quality of life for people all over the world.

How do you write 3 and 6/25 as a decimal

Answers

Answer: 1.44

Step-by-step explanation:

The fraction 3 and 6/25 is equal to 1.44 when written as a fraction.

Answer:

3.24

Step-by-step explanation:

6/25 can be read as 6 divided by 25, which is 0.24. Add that to 3 and you get 3.24.

Marine biologist studies the population of seals in research area. how many Seals are in the research area?​

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the perimeter of the square is 48 m. Find the area of a
circle whose circumference is the same as the square.

Answers

The area of the circle is 201 m².

What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

So, the area of the circle:

The perimeter of square: 4aCircumference of the circle: 2πr

We know that 4a = 2πr, now calculate r as follows:

4a = 2πr48 = 2πrr = 48/2πr = 48/2(3.14)r = 48/6.28r = 7.64

Rounding off: 8m

Area of circle:

πr²3.14(8)²3.14(64)200.96

Rounding off: 201 m²

Therefore, the area of the circle is 201 m².

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(7,10) and (8, 13) what’s the answer to it

Answers

Answer:54

Step-by-step explanation:

54mis the answer

I NEED HELP FAST

image is the question :)

Answers

0.3x4= 1.2 is like multiplying 3x4=12

need help again with a question

Answers

Answer: x = 58

Step-by-step explanation:

The angles are alternating interior angles. This means that the angles are equal.

So x = 58

For a project in his Geometry class, Yusuf uses a mirror on the ground to measure the
height of his school building. He walks a distance of 10.25 meters from the building,
then places a mirror flat on the ground, marked with an X at the center. He then
walks 1.65 more meters past the mirror, so that when he turns around and looks
down at the mirror, he can see the top of the school clearly marked in the X. His
partner measures the distance from his eyes to the ground to be 1.55 meters. How tall
is the school? Round your answer to the nearest hundredth of a meter.

Answers

Step-by-step explanation:

sadly we don't know anything about the size of the mirror on the ground, or if e.g. the 1.65 m from the mirror mean from the edge of the mirror or from the x at the center of the mirror.

so, we must assume the mirror as a dot without any significant lengths in the calculation.

we have 2 right-angled triangles.

1. the small one : from Yusuf's eyes to the ground at his feet to the x on the mirror on the ground.

2. the large one : from the top of the building to the bottom of the building on the ground to the x on the mirror on the ground.

the mirroring creates a dilation from the large triangle to the small triangle through the point x on the mirror.

in other words, all the angles stay the same, and there is one constant scale factor for all the lengths of one triangle to the other, making both triangles similar.

that means that the scale factor "f" of the ground distances from the small to the large triangle is

10.25 / 1.65 = 1025 / 165 = 6 35/165 = 6 7/33 =

= 6.212121212...

the scaling from Yusuf's height (well, his eye level) to the height of the school must follow the same ratio :

school height / Yusuf's eye level =

= h/1.55 = 10.25/1.65

h = 10.25 × 1.55 / 1.65 = 1025 × 155 / 16500 =

= 9.628787879... m ≈ 9.63 m

the school is approximately 9.63 m tall.

FYI : this is the same principle as with a camera. the lens (and the mirror inside if applicable) create a dilated "projection" onto a film or an array of digital light sensors, so that the captured image retains all the angles and all the length ratios of the original.

but to know from the picture e.g. how tall the original was, we need to know also the distance from which the picture was taken. otherwise this can't be answered.

Task 2 given the table and graph, evaluate the following functions:

Answers

Answer:

1) -12, 2) 22, 3) 9, 4) 31, 5) 4, 6) 3, 7) 5

Step-by-step explanation:

Use table for f(x) related questions and equation for g(x) related questions and both for the last one.

Q1 g(0) = 3*0 - 12 = 0 - 12 = - 12

Q2f(0) = 22, the value of f(x) against the x = 0

Q3g(7) = 3*7 - 12 = 21 - 12 = 9

Q4f(-3) = 31, the value of f(x) against the x = -3

Q5g(x) = 0 ⇒ 3x - 12 = 0 ⇒ 3x = 12 ⇒ x = 4

Q6f(x) = - 3, x = 3, the value of x against the f(x) = - 3

Q7f(g(6)) = f(3*6 - 12) = f(18 - 12) = f(6) = 5, the value of f(x) against x = 6

I need help!
Use the given information to select the factors of f(x). f(4)=0 f(-1)=0 f(3/2)=0. Make sure to select all correct answers for full credit.

Answers

Answer:4,3,8

Step-by-step explanation:

Please help ASAP, will mark brainliest!

Which of the following proves these triangles are congruent?

Answers

Answer:  ASA

Explanation:

ASA = angle side angle

It refers to knowing two pairs of congruent angles, and a pair of congruent sides between the angles.

The angle markers tell us which angles are congruent. The shared overlapped sides are congruent (since any segment is congruent to itself; aka reflexive property).

ASA is slightly different from AAS in that the congruent sides for AAS are not between the congruent angles.

Which is an equivalent expression for (3 to the power of 2 • 5 to the power of 4) to the power of 3?

Answers

The value that will be equivalent to the expression will be 5625³.

What is an expression?

It should be noted that an expression is simply used in Mathematics to illustrate or show the relationship between the variables.

The equivalent expression for (3 to the power of 2 • 5 to the power of 4) to the power of 3 will be illustrated as:

= (3² × 5⁴)³

= (9 × 625)³

= 5625³

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2-3x + 4 + x = -2x + 1

Answers

Answer:

No solution

Step-by-step explanation:

2- 3x + 4 + x = -2x + 1

2  -3x  + 4 + x = -2x + 1

6  -3x + x = -2x + 1

6  -3x + x = -2x + 1

6  -2x = -2x + 1

6  -2x = -2x + 1

move -2x to the right by adding 2x on both sides

6  -2x = -2x + 1

+2x         +2x

6  =  + 1

is 6 equal to 1?

No, so No solution

 

Can someone help me with this

Answers

Step-by-step explanation:

slope intercept form is: y = ax + b

so, 19x - 19y = 18

-19y = -19x +18

[tex]y = \frac{ - 19x}{ - 19} - \frac{18}{19} [/tex]

[tex]y = x - \frac{18}{19} [/tex]

i hope that this helps

a certain type of aluminum screen 2 feet in width has, on the average, three flaws in a 100-foot roll. we assume flaws occur randomly so the number of flaws follow some poisson distribution. what is the probability that the first 40 feet in a roll contain no flaws?

Answers

The probability of that the first 40 feet in a roll contain no flaws is ≈ .3012

What is probability ?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Calculation

Θ = μ = [tex]\frac{100 foot}{3 flaws}[/tex]

a ) We assume that the length until the first flaw follows an exponential distribution.

Probability density function of exponential distribution:

f(x) = [tex]\frac{1}{Θ} e^{\frac{-x}{Θ} } = \frac{1}{100/3}e^{-x/(100/3)} = \frac{3}{100}e^{-3x/100}[/tex]

The first 40 feet in a roll of 100 feet contain no flaws if the first flaw occurs after 40 feet.

The probability is the integral over the corresponding interval:

the further calculation has been shown in fig. attached

since equation was not possible to write here

b) We assume that the length until the first flaw follows an exponential distribution.

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Given the frequency table, what percentage of the students that like rap are also in grades 9–10? Round to the nearest whole percent. Show work
A. 16%
B. 38%
C. 40%

Answers

The percentage of the students that like rap are also in grades 9–10 is 32%.

Determining the percentage of rap in grades 9-10

Given data:

Grade 9-10 for Rap = 40

Row total for grade 9-10 = 125

Now let determine the percentage of rap in grades 9-10 using this formula

Percentage of rap in grades 9-10 = Grade 9-10 for Rap / Row total for grade 9-10

Let plug in the formula

Percentage of rap in grades 9-10 = 40 /125

Percentage of rap in grades 9-10 = 0.32 × 100

Percentage of rap in grades 9-10 = 32%

Therefore we can conclude that 32% is the percentage of rap grade 9-10.

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Your aunt bought a new television. The television screen is a
rectangle.
The length of the television screen is 54 inches and the width is
30.4 inches.
What is the area of the television screen? What is the perimeter
of the television screen?
Use the given information to complete the worksheet.
Problem apr20 Client Version 7.7.14 Server Version 73.14
O
Length of the Television Screen
Width of the Television Screen
Perimeter of the Television Screen
Area of the Television Screen
DELL
Diagram Label
SC
CR
Area Formulas:
• Parallelogram: A = bh
• Square: A = s²
.
Value
54
30.4
168.8
Triangle: A = bh
•Trapezoid: A=h(b₁+ b₂)
Units
inches
inches
inches
square inches
©2021 Carneg
Oct 13

Answers

Answer:

area: 1641.6 square inchesperimeter: 168.8 inches

Step-by-step explanation:

You want the area and perimeter of a rectangle that is 54 inches in length and 30.4 inches in width.

Area

The area formula is ...

  A = bh

We can use the length as the "base" and the width as the "height", so we have ...

  A = (54 in)(30.4 in) = 1641.6 in²

The area of the television screen is 1641.6 square inches.

Perimeter

The perimeter of a rectangle is given by the formula ...

  P = 2(L +W)

Using the given length and width, the perimeter is found to be ...

  P = 2(54 in + 30.4 in) = 2(84.4 in) = 168.8 in

The perimeter of the television screen is 168.8 inches.

The area of the rectangular television screen is 1641.6 square inches and the perimeter of the television screen is 84.4 inches.

What is the area of a rectangle?
The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the product of its length and breadth. Its area is the space that the rectangle's boundary encloses.
Mathematically, area of a rectangle = length * width = l * w
What is the perimeter of a rectangle?
The perimeter is defined as the sum of all sides of the rectangle. Mathematically, perimeter of a rectangle = 2(length + width) = 2*(l + w)

Given, the length of the television screen = l = 54 inches
The width of the television screen = w = 30.4 inches
Using the formula mentioned in the literature above,
Area of the television screen = l * w = 54*30.4 = 1641.6 square inches
Also, perimeter of the television screen = l + w = 54 + 30.4 = 84.4 inches
Thus, the area of the rectangular television screen is 1641.6 square inches and the perimeter of the television screen is 84.4 inches.

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Simplify the expression ∛81x^7y^9z^5 and please show your work!

Answers

By means of algebra properties for powers and roots, the radical expression [tex]\sqrt[3]{81\cdot x^7\cdot y^{9}\cdot z^{5}}[/tex] is equivalent to the expression [tex]4.327 \cdot x^{\frac{7}{3} }\cdot y^{3} \cdot z^{\frac{5}{3} }[/tex].

How to simplify an algebraic expression involving a cubic root operator and powers

In this question we need to simplify an expression by using algebra properties, that is, to transform an expression involving three variables (x, y, z), roots and power operators into an expression with only power operators, that is, where only we see power operators, no root operators of any kind. Now we proceed the entire procedure in detail:

[tex]\sqrt[3]{81\cdot x^7\cdot y^{9}\cdot z^{5}}[/tex]                                             Given[tex](81\cdot x^{7}\cdot y^{9}\cdot z^{5})^{\frac{1}{3} }[/tex]                                            Relationship between power and roots operators[tex]81^{\frac{1}{3}}\cdot (x^{7})^{\frac{1}{3} }\cdot (y^{9})^{\frac{1}{3} } \cdot (z^{5})^{\frac{1}{3} }[/tex]                               Power of a product[tex]4.327 \cdot x^{\frac{7}{3} }\cdot y^{3} \cdot z^{\frac{5}{3} }[/tex]                                           Definition of cubic root / Power of a power / Definitions of multiplication and division / Existence of multiplicative inverse / Commutative and associative properties /Result

In accordance to the algebra properties related to power and radical expressions, the radical expression [tex]\sqrt[3]{81\cdot x^7\cdot y^{9}\cdot z^{5}}[/tex] is equivalent to the power product [tex]4.327 \cdot x^{\frac{7}{3} }\cdot y^{3} \cdot z^{\frac{5}{3} }[/tex].

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-9^2 x 3
evaluate the experssion!!

Answers

Answer:

243

Step-by-step explanation:

-9^2 = -9 * -9 = 81

81 * 3 = 243

would you put a closed dot or an open dot on a number line for n > -8?

Answers

Answer:

a opened because a closed means that number ond more

Step-by-step explanation:

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