can somebody please help me with this (geometry)

Given:

The function are:

[tex]f(x)=Kx^2+4x-3[/tex]

[tex]g(x)=2x-7[/tex]

The graph of f(x) intersect the line g(x) at one point.

To find:

The value of K.

Solution:

The graph of f(x) intersect the line g(x) at one point. It means the line g(x) is the tangent line.

We have,

[tex]f(x)=Kx^2+4x-3[/tex]

Differentiate this function with respect to x.

[tex]f'(x)=K(2x)+4(1)-(0)[/tex]

[tex]f'(x)=2Kx+4[/tex]

Let the point of tangency is [tex](x_0,y_0)[/tex]. So, the slope of the tangent line is:

[tex][f'(x)]_{(x_0,y_0)}=2Kx_0+4[/tex]

On comparing [tex]g(x)=2x-7[/tex] with slope-intercept form, we get

[tex]m=2[/tex]

So, the slope of the tangent line is 2.

[tex]2Kx_0+4=2[/tex]

[tex]2Kx_0=2-4[/tex]

[tex]x_0=\dfrac{-2}{2K}[/tex]

[tex]x_0=-\dfrac{1}{K}[/tex]

Putting [tex]x=x_0,g(x)=y_0[/tex] in g(x), we get

[tex]y_0=2x_0-7[/tex]

Putting [tex]x=-\dfrac{1}{K}[/tex] in the above equation, we get

[tex]y_0=2(-\dfrac{1}{K})-7[/tex]

[tex]y_0=-\dfrac{2}{K}-7[/tex]

Putting [tex]x=-\dfrac{1}{K}[/tex] and [tex]f(x)=-\dfrac{2}{K}-7[/tex] in f(x).

[tex]-\dfrac{2}{K}-7=K\left(-\dfrac{1}{K}\right)^2+4(-\dfrac{1}{K})-3[/tex]

[tex]-\dfrac{2}{K}-7=\dfrac{1}{K}-\dfrac{4}{K}-3[/tex]

[tex]-\dfrac{2}{K}-7=\dfrac{-3}{K}-3[/tex]

Multiply both sides by K.

[tex]-2-7K=-3-3K[/tex]

[tex]-2+3=7K-3k[/tex]

[tex]1=4k[/tex]

[tex]\dfrac{1}{4}=K[/tex]

Therefore, the value of K is [tex]\dfrac{1}{4}[/tex].

Answer:

It must be a positive number since it represents a number of hours.

Step-by-step explanation:

Given Pieter's equation :

7h – 5(3h – 8) = –72

Opening up the bracket

7h - 15h + 40 = - 72

7h - 15h = - 72 - 40

-8h = - 112

Divide both sides by -8

-8h / -8 = - 112 / - 8

h = 14

Since, h represents the number of hours, and the value of h equals 14 (h cannot be negative), hence, option 2 is correct.

Answer:

B.It must be a positive number since it represents a numbers of hours.

Step-by-step explanation:

Given:

Cost of 200 g of mixed nuts = $2.50.

To find:

The price of 450 g of nuts.

Solution:

We have,

Cost of 200 g of mixed nuts = 2.50 dollars

Cost of 1 g of mixed nuts = [tex]\dfrac{2.50}{200}[/tex] dollars

Cost of 450 g of mixed nuts = [tex]\dfrac{2.50}{200}\times 450[/tex] dollars

                                               = [tex]\dfrac{2.50}{4}\times 9[/tex] dollars

                                               = [tex]5.625[/tex] dollars

Therefore, the price of 450 g of nuts is $5.625.

Answer:

i think (4,2)

Step-by-step explanation:

[tex]\sf \: {x}^{2} + 4xy - 21 {y}^{2} [/tex]

[tex]\sf \: Rewrite \: the \: equation⟹( {x}^{2} - 3xy) + (7xy - 21y {}^{2} )[/tex]

[tex]\sf \: 1)( {x}^{2} - 3xy) = x(x - 3y)[/tex]

[tex]\sf2) \: (7xy - 21 {y}^{2} ) = 7y(x - 3y)[/tex]

[tex]\sf \: Now \: the \: equation \: becomes \: ⟹ \\ \sf \: x(x - 3y) + 7y(x - 3y)[/tex]

[tex]\sf \: Factor \: out \: the \: common \: term \: (x - 3y) \\ \sf =( x - 3y) + (x + 7y) \\ [/tex]

Answer ⟶ [tex]\boxed{\sf {B) (x-3y)(x+7y)}}[/tex]

Answer:

a.) r = 60ft

b.) ball_distance = 68ft

Step-by-step explanation:

Use Pythagorean theorem:

(r^2) + (32ft)^2 = (r + 8ft)^2

r^2 + 1024sqft = r^2 + (16ft)×r + 64sqft

960sqft = r×(16ft)

(960sqft) / (16ft) = r

r = 60ft

Radius is green. Ball is 8ft further than green. 68ft.

Answer:

If there are two line which is parallel in a triangle the triangle has a ratio

Step-by-step explanation:

So we can see one side has 6cm and 4cm length. and other side has 20cm in totally. But we know that the small line divided the side with 6/4 ratio and we can say ?=12 and other is 8

Answer:

Step-by-step explanation:

60° because it's an equilateral triangle

Answer:

Step-by-step explanation:

Given:

A line passes through the point (1,4) and is parallel to the x-axis.

To find:

The equation of the line.

Solution:

If a line is parallel to x-axis, then the line is a horizontal line. We know that the slope of a horizontal line is always 0. So, the slope of the required line is 0.

The point-slope form of a line is:

[tex]y-y_1=m(x-x_1)[/tex]

Where, m is the slope and [tex](x_1,y_1)[/tex] is the point.

The slope of the required line is 0 and it passes through the point (1,4). So, the equation of the line is:

[tex]y-4=0(x-1)[/tex]

[tex]y-4=0[/tex]

[tex]y-4+4=0+4[/tex]

[tex]y=4[/tex]

The required equation is [tex]y=4[/tex].

Therefore, the correct option is B.

Answer:

Total chairs = 18×22= 396

so no. of extra chairs need = 468-396 = 72

Now( 72/18) rows = 4 rows

Therefore 4 more rows are needed here

Hope it helps you

Answer: 4

Step-by-step explanation:

The amount of chairs in the hall can be found by multiplying 22 by 18 and getting 396. The amount of chairs needed is 468, so 468-396 gets you the amount of chairs still needed and the number 72. There are 18 chairs in each row, and 72/18 is 4. So 4 more rows are needed.

Answer: where's the pic?

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

a+b^2

Let a=2 and b=3

2+3^2

2 + 9

11

Answer: 11

2 + (3 x 3 )

2 + 9

The required answer would be 11 :)

Step-by-step explanation:

Answer:

3053.63

Step-by-step explanation:

Not sure how to explain-

but i hope it helps c:

Answer:

5m-n-4p

4a^2+6x-3

Step-by-step explanation:

3m-4n +7p

-5m +9n -6p

+7m -6n -5p

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

Combine like terms

3m-4n +7p

-5m +9n -6p

+7m -6n -5p

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

(3-5+7)m  +(-4+9-6)n  +(7-6-5)p

5m-n-4p

a^2  -3x +1

a^2   +9x -6

2a^2 +0x +2

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

Combine like terms

a^2  -3x +1

a^2   +9x -6

2a^2 +0x +2

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

(1+1+2)a^2 +(-3+9+0)x +(1-6+2)

4a^2+6x-3

#1

[tex]\\ \sf\longmapsto 3m-4n+7p+(-5m+9n-6p)+7m-6n-5p[/tex]

[tex]\\ \sf\longmapsto 3m-4n+7p-5m+9n-6p+7m-6n-5p[/tex]

[tex]\\ \sf\longmapsto 3m-5m+7m-4n+9n-6n+7p-6p-5p[/tex]

[tex]\\ \sf\longmapsto 5m-n-4p[/tex]

#2

[tex]\\ \sf\longmapsto a^2-3x+1+a^2+9x-6+2a^2+2[/tex]

[tex]\\ \sf\longmapsto a^2+a^2+2a^2-3x+9x+1-6+2[/tex]

[tex]\\ \sf\longmapsto 4a^2+6x-3[/tex]

Answer:

dodndbdie9ejrnfudowp2ejdnsmwo2oeidndndoep

Answer:

Please check explanations

Step-by-step explanation:

The diameter is twice the height;

if diameter is d and height is h

Then;

d = 2h

But, we know that the radius is half the diameter size. Which means that the diameter is twice the radius

Thus;

2r = 2h

Then r = h

Mathematically the total surface area of a cylinder is;

2pi r (r + h)

substitute h for r

2pi h(h + h)

= 2pi * h * 2h

= 4 pi h^2 (QED)

Answer:

sin A = 12 /13

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin A = opp / hyp

sin A = 12 /13

Answer: 3000 stamps

Step-by-step explanation:

Given

Chris and Josh have 1800 stamps

Josh and Jessica have 2200 stamps

Jessica and Chris have 2000 stamps

Suppose Chris, Josh, and Jessica have [tex]x,y, \text{and}\ z[/tex] stamps

[tex]\therefore x+y=1800\quad \ldots(i)\\\Rightarrow y+z=2200\quad \ldots(ii)\\\Rightarrow z+x=2000\quad \ldots(iii)\\\text{Add (i), (ii), and (iii)}\\\Rightarrow 2(x+y+z)=1800+2200+2000\\\Rightarrow x+y+z=3000[/tex]

Thus, all three have 3000 stamps

Answer:

-4/5

Step-by-step explanation:

sin theta = opp/ hyp

sin theta = -3 /5

Using the Pythagorean theorem

opp ^2 + adj ^2 = hyp ^2

(-3) ^2 + adj ^2 = 5^2

9+ adj ^2 = 25

adj ^2 = 25 - 9

adj ^2 = 16

Taking the square root of each side

adj = ±4

Since we are in the 3rd quadrant  sin and cos are both negative so adj must be negative

adj = -4

cos theta = adj / hyp

cos theta = -4/5

Answer:

B

Step-by-step explanation:

Domain is the set of x values

Looking at the table we can say that the set of x values ( domain ) is {1,2,3,4}

Answer:

0.125

Step-by-step explanation:

1=40000

x-5000

x=5000÷40000=1/8=0.125

Answer:

add 2 equations given

3y+x+2y- x = 10

5y =10

y = 2

find x using the value of y

x = - 2

these values of x and y are can satisfy both equations .so (-2,2) lies on both lines

Answer:

C. 2%

Step-by-step explanation:

when you have a decimal and are looking for the percentage, simply move the decimal two places to the right. so .0201= 2%

Answer: C. 2%

Step-by-step explanation:

STEP ONE: Convert the decimal into a percentage

Percentage = Number × 100%

Percentage = 0.0201 × 100%

Percentage = 2.01%

STEP TWO: Round to the nearest ones

2.01% ≈ 2%

Hope this helps!! :)

Please let me know if you have any questions

Answer:

140 degrees

Step-by-step explanation:

(n-2) times 180

9-2 times 180

7 times 180

1260

1260/9 = 140

Interior angle sum of the given regular polygon of 9 sides is 1260°.

A regular polygon is a closed figure where all sides are equal. Interior angles of a regular polygon are the angles formed between the edges of the polygon. The formula for calculating the sum of interior angles of a regular polygon = (n-2) * 180

where, n is the number of sides of a regular polygon.

Number of sides in the regular polygon  = 9

n = 9

Sum of interior angle of the regular polygon =

(n-2) * 180 = (9-2) * 180 = 7 * 180 = 1260°

Learn more about polygon here

https://brainly.com/question/17756657

#SPJ2

Answer:

3x

Step-by-step explanation:

factoring it we get

3x(4x-3)

Answer:

Hello,

[tex]16\pi[/tex]

Step-by-step explanation:

[tex]I=\dfrac{Area}{4} =\int\limits^4_0 {\sqrt{16-x^2} } \, dx \\\\Let\ say\ x=4*sin(t),\ dx=4*cos(t) dt\\\\\displaystyle I=\int\limits^\frac{\pi }{2} _0 {4*\sqrt{1-sin^2(t)} }*4*cos(t) \, dt \\\\=16*\int\limits^\frac{\pi }{2} _0 {cos^2(t)} \, dt \\\\=16*\int\limits^\frac{\pi }{2} _0 {\frac{1-cos(2t)}{2}} \, dt \\\\=8*[t]^\frac{\pi }{2} _0-[\frac{sin(2t)}{2} ]^\frac{\pi }{2} _0\\\\=4\pi -0\\\\=4\pi\\\\\boxed{Area=4*I=16\pi}\\[/tex]

Answer: yes

A prime factor is number that can only divided by itself and one

Since, 17 can only be divided by 17 and 1, the student is correct

Step-by-step explanation: