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.

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.

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.

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

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

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.

Answer:

1. = 5 10 15 20 25

2. 2 4 6 8 10 12 14

X, y =10

Answer:sadwer

Step-by-step explanation:

Step-by-step explanation:

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

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

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)

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!!

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]

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

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 )

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.

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:

Answer: See below

Step-by-step explanation:

This relates to the usage of water displacement.

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

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,

Then, we do the fourth step which is subtraction

Hope this helps!! :)

Please let me know if you have any quesitons

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

Answer:

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

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

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.

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:

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]

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]

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.

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 :-

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]

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]

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

Answer:

Step-by-step explanation:

54 times 270 = 14580