The curve y=(k-6)x^2-8x+k cuts the x-axis at two points and has a minimum point. Find the range of values of k.

Answers

Answer 1

Answer:

Hello,

answer:  -2 < k < 8

Step-by-step explanation:

As there are 2 roots: Δ>0

As there is a mininum, k-6 <0 ==> k<6,

minimum :y'=0 ==> (k-6)*2x-8=0 ==> x=4/(k-6)

[tex]\Delta=8^2-4*k*(k-6)\\=64-4k^2+24k\\=-4(k^2-6k+9)+36+64\\=100-4(k-3)^2\\=4(8-k)(k+2)\\\\\Delta\ is\ positive\ for\ -2 < k < 8[/tex]


Related Questions

A boy on top of a building observe that the angle of depression of a goat in horizontal ground is 47.if the goat is 23m away from the foot of the building,how high is the building,correct to the nearest meter? (ignore the height of the boy)​

Answers

Answer:

Step-by-step explanation:

tan 47° = opposite side /adjacent side

=>1.072 = AB/BC

=>1.072 × BC = AB(height of the building)

=>1.072 × 23 = h ( As assumed height of building is h )

h = 24.656

= 25 metres ( nearest metre )

adhiambos entertainment hall has a rectangular floor measuring 30m by 24m ,she wants to cover it with square tiles. each tile has a surface area of 900cm. the tiles are packed in cartons each containing ten tiles. How many cartons of tiles does she require?

Answers

1 meter = 100 cm

Convert the dimensions of the room to cm:

30m x 100 = 3000 cm

24 m x 100 = 2400 cm

Area of floor = 3000 x 2400 = 7,200,000 square cm

Find number of tiles by dividing area of room by area of a tile:

7,200,00 / 9000 = 800

They will need 800 tiles

800 tiles / 10 tiles per carton = 80

They will need 80 cartons

i Needdd helppp with this??

Answers

Answer:

B I'm thinking, I have to answer any question so I might be wrong here, also eat some salad it's nasty I know

Answer:

option c. ±[tex] \sqrt{65} [/tex]

Step-by-step explanation:

In the given right angled triangle we can see that :-

hypotenuse is 9 adjacent is 4 opposite is x

by Pythagoras theorem

hypotenuse² = adjacent ² + opposite ²

9² = 4² + x²

81 = 16 + x²

combining like terms

81 - 16 = x²

65 = x²

x = ±[tex] \sqrt{65} [/tex]

Determine a simplified expression for the shaded area

Answers

Answer:

4x^2-3x

Step-by-step explanation:

3x(2x+5) = 6x^2+15x

2x(x+9) = 2x^2+18x

(6x^2+15x)-(2x^2+18x) = 4x^2-3x

Answer:

11x

Step-by-step explanation:

-2b^2-18b^2
Help me. Plz

Answers

Answer:

[tex]{ \tt{ - {2b}^{2} - 18 {b}^{2} }} \\ = - {20 {b}^{2}} [/tex]

Two factory plants are making TV panels. Yesterday, Plant A produced 8000 panels. Four percent of the panels from Plant A and 1% of the panels from Plant B were defective. How many panels did Plant B produce, if the overall percentage of defective panels from the two plants was 2%?

Answers

Answer:

The answer is "16,000"

Step-by-step explanation:

In this question the amounts of panels created by B the x.

[tex]\therefore[/tex]

Calculating the amounts of defective panels from B:

[tex]\to \frac{1}{100} \times x = 0.01x[/tex]

Calculating the amounts of defective panels from A:

[tex]\to \frac{4}{100} \times 8000 = 320[/tex]

Calculating the total defective panels are :

[tex]\to 320+ 0.01x[/tex]

Calculating the total panels manufactured:

[tex]\to 8000 + x[/tex]

when the overall percentage of the defective panels is [tex]2\%[/tex]

[tex]\to \frac{(320 + 0.01x)}{(8000 + x)} = 0.02\\\\\to (320 + 0.01x) = 0.02 (8000 + x)\\\\\to 320 + 0.01x = 160 + 0.02x\\\\\to 320 -160 = -0.01x + 0.02x\\\to 160 = 0.01x\\\\\to x=\frac{160}{0.01}\\\\\to x=16,000\\\\[/tex]

matematicas
[tex]6. \binom{ \sqrt{3} }{2} - ( - 2.5 )= [/tex]

Answers

Answer:

3.36602540378

Step-by-step explanation:

The way I read the question, the unknown in the first set of parenthesis is a fraction. If I am wrong, please correct me so my answers are better in the future.

This is the answer.

There is a bag with 50 popsicles inside. 5 are red, 15 are orange, 12 are blue, 8 are
yellow and 10 are purple. If you were to
grab one popsicle from the bag, what is
the probability that it is red or not orange?
P(red or not orange)

Answers

I think the probability is 5 out of 45.

Solve the system of equations using the substitution method.
y = 5x
7x + 2y = -17
(x, y) = ( , )

PLSSS HELP

Answers

Answer:

1. = 5 10 15 20 25

2. 2 4 6 8 10 12 14

X, y =10

using the graph, determine the coordinates of the roots of the parabola​

Answers

Answer:

x = 1, x = 7

Step-by-step explanation:

The roots are the values of x where the graph crosses the x- axis

The graph crosses the x- axis at 1 and 7 , then

the roots are x = 1, x = 7

Answer:

(1,0) and (7,0)

Step-by-step explanation:

Roots are also known as the zeroes, or x-intercepts. This is where the line crosses the x axis, here it crosses where x is 1 and where x is 7.

Find the surface area of the solid given the net

Answers

Surface area = 17*(sqrt(1155) + 19)

h^2 = 19^2 - 17^2/4
=> h = sqrt(4*19^2 - 17^2)/2 = sqrt(1155)/2
Surface area = 4(1/2*h*17) + 17*19 = 17(sqrt(1155) + 19)

NEED HELP ASAP I HAVE 3 MINS

Answers

Answer:

Step-by-step explanation:

System of a equation has no solution when both the lines are parallel.

In other words, if the equations of a system have equal slopes there will be no solution.

1). x + 4y = 23

   4y = -x + 23

   [tex]y=-\frac{1}{4}x+23[/tex] ------(1)

   -3x = 12y + 1

   12y = 3x - 1

    [tex]y=\frac{1}{4}x-\frac{1}{12}[/tex] -------(2)

Since, both the equations have different slopes, system will have at least one solution.

2). 2x + 4y = 22 -----(1)

    -x = 2y - 11

    -x - 2y = -11

    x + 2y = 11

    2x + 4y = 22 ------(2)

   Since, both the equations are same, there will be infinite number of solutions.

3). 2x + y = 15 ------(1)

    x = 15 - 2y

    x + 2y = 15 -----(2)

   Both the equations are different, therefore system of equations will have at least one solution.

4). 2x + y = 17 ------(1)

    -4x = 2y - 34

    -4x - 2y = -34

    2x + y = 17 -----(2)

   Both the equations are different, therefore, system of equations will have infinite solutions.

5). 3y = 10 - x

    x + 3y = 10

    2x + 6y = 20 -------(1)

    2x + 6y = 7 ---------(2)

    Since, both the lines are parallel (Same slopes), system will have no solution.

6). y = 13 - 2x ------(1)

   4x - y = -1

   -y = -4x - 1

   y = 1 + 4x --------(2)

   Since, both the equations are different, system of equations will have at least one solution.

multiply 3/7 by the reciprocal of -3/14​

Answers

Multiplying 3/7 by the reciprocal of -3/14,

[tex] \frac{3}{7} \times \frac{14}{ - 3} \\ = \frac{1}{1} \times \frac{2}{ - 1} \\ = \frac{2}{ - 1} \\ = - 2[/tex]

Hope it helps!!

what is the square root of 25 ​

Answers

the answer would be 5 because 5*5 or 5 squared (5^2) is equal to 25, hope this helps!

Answer:

5

Step-by-step explanation:

What does square root even mean?

A Square root of a number is a value that when multiplied by itself gives the number

Example: 4^2 = 16 so square root of 16 = 4

Which expression is equivalent to the given expression?

Answers

Answer:C

Step-by-step explanation:

a^0=1 so youre left with 6ab/b8

then,

6a•b^(1-8)

6a•b^-7

therefore, 6a/b^7 is the answer

160 pupils in a sports centre are surveyed. The pupils can only use the swimming pool, the gym and the tennis courts. 21 pupils use the swimming pool, the gym and the tennis courts. 55 pupils use the swimming pool and the gym. 48 pupils use the gym and the tennis courts. 40 pupils use the tennis courts and the swimming pool. 11 pupils use the swimming pool only. 7 pupils use the gym only. 35 pupils use the tennis courts only. Find the probability to select a pupil that uses the tennis courts.

Answers

Answer:

0.6375 = 63.75% probability to select a pupil that uses the tennis courts.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Total:

In total, there are 160 pupils.

Uses the tennis courts:

21 pupils use the swimming pool, the gym and the tennis courts.

48 pupils use the gym and the tennis courts, which adds 48 - 21 = 27 to the number of those who use the tennis courts.

40 pupils use the tennis courts and the swimming pool, which adds 40 - 21 = 19 to the number of those who use the tennis courts.

35 use the tennis courts only.

So

21 + 27 + 19 + 35 = 102 use the tennis courts.

Find the probability to select a pupil that uses the tennis courts.

102 out of 160, so:

[tex]p = \frac{102}{160} = 0.6375[/tex]

0.6375 = 63.75% probability to select a pupil that uses the tennis courts.

The function g(x) = x2 is transformed to obtain function h:
h(x) = g(x − 3).
Which statement describes how the graph of h is different from the graph of g?

A. The graph of h is the graph of g horizontally shifted right 3 units.
B. The graph of h is the graph of g horizontally shifted left 3 units.
C. The graph of h is the graph of g vertically shifted up 3 units.
D. The graph of h is the graph of g vertically shifted down 3 units.

Answers

Answer:

A

Step-by-step explanation:

The graph of h(x) = (x-3)^2. The (x-3) indicates that the graph is shifted horizontally right 3 units because the change takes place inside the parantheses. Because the units are being subtracted, the graph will shift to the right. I highly recommend using Desmos to find your answer next time.

F(x)=-3x^2+4x+4
G(x)=x(-7x-7)

Which expression is equal to f(x)+g(x)

Answers

Answer:

A

Step-by-step explanation:

f(x)+g(x)=-3x^2+4x+4+x(-7x-7)= -3x^2+4x+4 -7^2-7x

= -10x^2-3x+4

If anyone knows the answer plz tell me, thank you

Answers

Answer:

A

Step-by-step explanation:

plug it in

(-3)^2+(4)^2=9+16=25

Answer:

[tex]\text{A) }x^2+y^2=25[/tex]

Step-by-step explanation:

The equation of a circle with center [tex](h, k)[/tex] and radius [tex]r[/tex] is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex].

We're given:

The circle's center is at the origin (0, 0)The point (-3, 4) is on the circle

Since we're given the circle's center, we just need to find the radius. Because the center of the circle is at (0, 0), the radius will be equal to the distance from (-3, 4) and (0, 0).

For points [tex](x_1, x_2)[/tex] and [tex](x_2, y_2)[/tex], the distance between them is given by the formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Let:

[tex](x_1, y_1)\implies (0, 0)\\(x_2, y_2)\implies (-3, 4)[/tex]

The distance between these two points must be:

[tex]d=\sqrt{(-3-0)^2+(4-0)^2},\\d=\sqrt{9+16},\\d=\sqrt{25},\\d=5[/tex]

Therefore, the radius of the circle is 5 and the equation of the circle is:

[tex](x-0)^2+(y-0)^2=5^2,\\\boxed{x^2+y^2=25}[/tex]

can someone answer this

Answers

Answer:sadwer

Step-by-step explanation:

differentiate with product rule

Answers

Answer:

[tex]{ \boxed{ \bf{ \frac{dy}{dx} = v \frac{du}{dx} + u \frac{dv}{dx} }}}[/tex]

u = ( x + 1 )

v = ( 2x + 5 )²

[tex]{ \tt{ \frac{dy}{dx} = {(2x + 5) {}^{4} .(1) + (x + 1).(2)(2x + 5) {}^{3} } }} \\ = { \tt{ {(2x + 5)}^{3} ((2x + 5) +(2x + 2) }} \\ = { \tt{ \frac{dy}{dx} = {(2x + 5)}^{3}(4x + 7) }}[/tex]

Which is the graph of f(x) = 3 (2/3)x ?

Answers

Step-by-step explanation:

.....................

Factorise:
What is the answer for 3x²+ 11xy + 6y²​

Answers

Answer:

(3x+2y)(x+3y)

Step-by-step explanation:

First:

(3x²+ 2xy) + (9xy + 6y²​)

then:

x(3x+2y) + 3y (3x+2y)

s0:

(3x+2y)(x+3y)

if we put a marble in 10 ml of water how can we find its volume
please answer
i will mark brainliest

Answers

Answer: See below

Step-by-step explanation:

This relates to the usage of water displacement.

Have the 10 ml of water ready in a measuring flask (or any container that has a scale)Put the marble into the waterObserve how much did the water riseSubtract the current water level by the original 10 mlThe final answer would be the volume.

------------------------------------------------------------------------

EXTRA (Only for advanced purposes, if you do not understand, it is totally fine)

Refer to the attachment below to finish the question.

Assuming the water levels are integer,

The original water level is 13.33 mlAfter the rock is put in, the water level is raised to 30 ml

Then, we do the fourth step which is subtraction

30 - 13.33 = 16.66 ml

Hope this helps!! :)

Please let me know if you have any quesitons

Can someone please help me solve this problem

Answers

Step-by-step explanation:

Step 1:  After adding 875 to both sides of the original equation, you get

[tex]x^2+10x+\text{ ----- }=875[/tex]

Step 2: b is the coefficient of the x term, so b = 10.  Divide in half (always half for completing the square!).

[tex]\frac{10}{2}=5[/tex]

Square that result to get 25.  That's c, the amount to add to both sides of the equation.

Step 3:  Adding c to both sides produces

[tex]x^2+10x+25=875+25[/tex]

Step 4: The result of Step 3 is [tex]x^2+10x+25=900[/tex], and the left side factors as a perfect square.

[tex](x+5)^2=900[/tex]

Step 5: After taking square roots of both sides, you get

[tex]x+5=\pm 30[/tex]  which represents "two equations in one."

Separate them.

[tex]x+5=30 \text{ or } x+5 =-30\\x=25 \text{ or } x=-35[/tex]

Which of the following points is a solution of the inequality y < |x - 2|?
(-2, 0)
(2, 1)
(2, 0)

Answers

Answer:

(-2,0)

Step-by-step explanation:

y < |x - 2|

Substitute the points in and check

(-2,0)

0 < |-2 - 2|

0 < |-4|

0 < 4  True

(2,1)

1 < |2 - 2|

1 < |0|

1 < 0  False

(2,0)

0 < |2 - 2|

0 < |0|

0 < 0 False

Frogs are released into a pond where there are no other frogs of this species. The
function f(t) can be used to model the population of this new species after t years.
Below are 4 forms of the function that model this situation. Which form most clearly
shows the monthly population growth?

Answers

Answer:

[tex]f(t)=12(1.0139)^{12t}[/tex]

Step-by-step explanation:

Let the initial number of frogs = 12

And their population is growing with the annual growth rate = 16.68% per year

Function modeling the population after 't' years will be,

[tex]P(t)=12(1+r)^{t}[/tex]

Here, r = Annual growth rate

t = Number of years

If we convert the annual growth rate to monthly growth rate,

Expression modeling the population will be,

[tex]f(t)=12(1+\frac{r}{12})^{12t}[/tex]

       [tex]=12(1+\frac{16.68}{12})^{12t}[/tex]

       [tex]=12(1.0139)^{12t}[/tex]

Therefore, [tex]f(t)=12(1.0139)^{12t}[/tex] will be the answer.

Roma swims at a rate of 54 metre per minute. At this rate how long does she take to swim 270 metre ?​

Answers

Answer:

Step-by-step explanation:

54 times 270 = 14580

Write a formula that connects the number of sides of the end face,
S
, with the number of vertices,
V
.
Hence, find the number of vertices of a prism whose cross-section is a 30-sided polygon.

Answers

Answer:

56

Step-by-step explanation:

Euler theorem is a theorem used to show the relationship between the face, vertices and edge of a three dimensional shape (polyhedron)

Euler theorem is given as:

Face + vertex = Edge + 2

We can prove this theorem using the table attached.

For triangular prism: 5 + 6 = 9 + 2

For rectangular prism: 6 + 8 = 12 + 2

For pentagon prism: 7+ 10 = 15 + 2

For hexagonal prism: 8 + 12 = 18 + 2

The relationship between the vertex and face is:

vertex = face + (face - 4)

Therefore, for a prism with 30 sides, that is 30 faces, we have:

vertices = 30 + (30 - 4) = 30 + 26 = 56

what is the solution to this equation?
3x+x-13+4-6x=12


A. x= -21/2
B. x= 21/2
C. x= 3/2
D. x= -3/2

Answers

Answer:

A.

Step-by-step explanation:

3x + x - 13 + 4 - 6x = 12

we try to combine the elements with the same power of x (including the ones without any x) :

3x + x - 6x

-13 + 4

so, we get

-2x - 9 = 12

-2x = 21

x = -21/2

Answer:

A

Step-by-step explanation:

group the like terms

3x+x-6x-13+4=12

-2x=12+9

divide both sides by -2

-2x/-2=21/-2

x= -21/2

hope it helps

Other Questions
why is nepal still lagging behind in developnment What is significant about Orwell's depiction of the hard-working woman in the courtyard? Help please!!!I need this assignment done today One charge is fixed q1 = 5 C at the origin in a coordinate system, a second charge q2 = -3.2 C the other is at a distance of x = 90 m from the origin.What is the potential energy of this pair of charges? This is my school exercises. Can you help me? Which of the following is a characteristic of the Enlightenment? 15 a2 - 6ab- 8 a2+ 20 - 5ab - 31 + a2- ab 1Which element of plot comes after the conflict has already been established, but before the outcome can be predicted? * Solve the simultaneous equations! ! 5x+3y=41! ! 2x+3y=20 The volume of a Rubiks cube is 512/216 cubic inches. Find the length of a side of the cube. The Director of Taco Bells in-house creative agency described the workplace as an "ego-free zone," suggesting openness to his team members ideas, also called Multiple Choice staff validity. task validity. boundary spanning. decision informity. hierarchical sensitivity. 6. The perimeter of a square room is 48 m, how much square metre carpet required it cover it ? Answer ASAP please! define average velocity B. Complete the sentences with the present simple forms of the be verb A: Where are we now? B: You just in front of our house. A: Are you hungry? B: Yes, I ....... a little bit hungry. A: Is your sister at school? B: No, she at school. A: Where are your parents? B: My mum and dad at work, A: I think these stories are very interesting. B: Really? The stories interesting at all. Which would be the best approach to concluding a personal narrative? (3 points) End the narration with the last action you remember. Review the key point and reflect on how the event changed you. Suggest you may never understand what happened to you. Tell readers it is their job to make sense of the event. 18. explain what perlemoen are? what are the two law/legislation that protects citizens against the human trafficking Question 16 of 30Use the formula to help you answer the question below. Do not include unitsin your answer.Rate Time = DistanceHow many hours will it take to complete a 76-km bike ride if you go 16 km perhour the whole time?Answer here 8. Point Mis 6 units away from the origin. Circle the letter by each pair of possible coordinates. A. (3.0) B. (4.2) C. (5,3) D. (0.6) E. (4.4) F. (1,5)