14 m
F. 2,352 m
G. 1,476 m
H. 392 m
I. 261.3 m
7 m
24 m
25 m

Answer:

  √5

Step-by-step explanation:

The distance from the given point to the curve can be found using the distance formula. The resulting expression can be minimized to find the minimum distance.

  d = √((x2 -x1)² +(y2 -y1)²)

__

A point on the parabola can be described by ...

  x -y² = 0

  x = y² . . . . . add y²

Then a point on this curve is ...

  (y², y)

The distance to it from (0, 3) is ...

  d = √((0 -y²)² +(3 -y)²) = √(y⁴ +y² -6y +9)

The distance will be minimized when the derivative of the radical expression is zero:

  d(y⁴ +y² -6y +9)/dy = 0 = 4y³ +2y -6

  0 = 2y³ +y -3 . . . . . . . . remove a factor of 2

This will have a rational root in the set {±1, ±3}.

Trial and error shows that y=1 is the only real solution to this equation.

__

Then the minimum distance is ...

  d = √(1⁴ +1² -6·1 +9) = √5

_____

Additional comment

The attached graph shows that a circle with radius √5 centered at (0, 3) will intersect the parabola at exactly one point. That confirms our solution.

1 mile per every 15 minutes

or 4 mph

Answer:

yes the boy can get 80 small action figures

Answer:

Yes

Step-by-step explanation:

Given

Solving

Answer: The answer is ellipse

Answer:

1a. 210 m^2  1b. 14 ft^2  1c. 199.5 in^2

2a. 270 cm^2  2b. 162 m^2  2c. 272 cm^2

3a. 348 ft^2  3b. 230 in^2  3c. 312.5

Step-by-step explanation:

The area of a triangle can be calculated with one equation...

A = 1/2bh

b stands for base, h stands for height

1a. A = 1/2(21)(20)

    One half divides 20 easily..

A = 21(10)

A = 210

1b. A = 1/2(7)(4)

    One half divides 4 easily..

A = 2(7)

A = 14

1c. A = 1/2(19)(21)

A = 1/2(399)

A = 199.5

2a. A = 1/2(36)(15)

    One half divides 36 easily..

A = 18(15)

A = 270

2b. A = 1/2(18)(18)

   One half divides 9 easily..

A = 9(18)

A = 162

2c. A = 1/2(32)(17)

  One half divides 32 easily..

A = 16(17)

A = 272

3a. A = 1/2(29)(24)

  One half divides 24 easily..

A = 12(29)

A = 348

3b. A = 1/2(23)(20)

  One half divides 20 easily..

A = 10(23)

A = 230

3c. A = 1/2(25)(25)

A = 1/2(625)

A = 312.5

Finding area of triangle --> [tex]\frac{1}{2}*b*h[/tex]

     Question 1:

         a.   [tex]Area = \frac{1}{2}*b*h = \frac{1}{2}*20*21 = 210 m^2[/tex]

         b. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2}*4*7 = 14 ft^2[/tex]

         c. [tex]Area = \frac{1}{2}*b*h= \frac{1}{2} *21*19=199.5in^2[/tex]

     Question 2:

         a. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *36*15 = 270cm^2[/tex]

         b. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *18*18 = 162m^2[/tex]

         b. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *17*32 = 272cm^2[/tex]

     Question 3:

         a. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *24*29 = 348ft^2[/tex]

         b. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *20*23 = 230in^2[/tex]

         c. [tex]Area = \frac{1}{2}*b*h = \frac{1}{2} *25*25 = 312.5cm^2[/tex]

Finding Area of Parallelogram --> b * h

     Question 1

         a. [tex]Area = b * h = 24 * 26 = 624cm^2[/tex]

         b. [tex]Area = b * h = 15 * 30 = 450in^2[/tex]

         c. [tex]Area = b * h = 21 * 31 = 651 mm^2[/tex]

      Question 2

         a. [tex]Area = b * h = 18 * 17 = 306 in^2[/tex]

         b. [tex]Area = b * h = 10.5 * 15 = 157.5m^2[/tex]

         c. [tex]Area = b * h = 12.5*11=137.5cm^2[/tex]

      Question 3:

          a. [tex]Area = b * h = 5.7*11.5=65.55in^2[/tex]

          b. [tex]Area = b * h = 8 * 12.5 = 100ft^2[/tex]

          c. [tex]Area = b * h = 1.7 * 3.6 = 6.12m^2[/tex]

Hope that helps!

Answer:

43

Step-by-step explanation:

The first increase from 9 to 16 is 7

The second increase from 16 to 24 is 8

The third from 24 to 33 is 9

Following the pattern the next increase must be by 10. 33+10=43

Answer:

[tex]\tt B)\;93^o[/tex]

Step-by-step explanation:

[tex]\tt 2(19x+1)+(19x+1)+15x=360[/tex]

[tex]\tt 38x+2+19x-2+15x=360[/tex]

[tex]\tt 38x+19x+15x+2-2=360[/tex] (Add similar elements)

[tex]\tt 72x+2-2=360[/tex] (2-2=0)

[tex]\tt 72x=360[/tex]

[tex]\tt \cfrac{72x}{72}=\cfrac{360}{72}[/tex] ( Divide both sides by 72)

[tex]\tt x=5[/tex]

Now,

m∠km:-

[tex]\tt 19x-2[/tex]

[tex]\tt 19(5)-2[/tex] (Multiply 19*5= 95)

[tex]\tt =95-2[/tex] (Subtract)

[tex]\tt = 93[/tex]

Therefore, m∠km=93° is the answer.

_____

In a randomized block design, it is expected treatments are randomly assigned within each block.

The purpose is to minimize the effect of certain factors such as age.

Based on the above, it is expected in this experiment the treatment is randomly assigned to a specific number of subjects within each block.

Learn more about experiment in: https://brainly.com/question/11256472

Answer:

BC

Seg AC

Ray KM

Answer:

8cm enlarged by a scale factor of 6.5 is 52cm I believe.

Step-by-step explanation:

8 times 6.5= 52cm

Answer:

hey pls help me I urgently need help

Recall that cos(x + y) = cos(x) cos(y) - sin(x) sin(y). So

cos(420°) = cos(360° + 60°)

cos(420°) = cos(360°) cos(60°) - sin(360°) sin(60°)

cos(420°) = cos(60°)

since cos(360°) = 1 and sin(360°) = 0. Then

cos(420°) = cos(60°) = 1/2

Answer:

i think c

Step-by-step explanation:

i hope this helped

Answer:

c

Step-by-step explanation:

Answer:

what??? I can't understand you sorry

we know that the multiplication comes first in the family then we start from left to right

4 x 5= 20

9-20 = -11

-11 + 6 = -5

there you go!

[tex]9 - 4 \times 5 + 6[/tex]

[tex]9 - 20 + 6[/tex]

[tex] - 11 + 6[/tex]

[tex] - 5[/tex]

Answer:

5.91

Step-by-step explanation:

35 is between the perfect squares 25 and 36.

√25 = 5

√36 = 6

     /            5         25       \

    |      d                       10   |

1  <              x          35         >    11

    |                                 1    |

     \            6          36       /

11/1 = 10/d

11d = 10

d = 0.909

√35 = 5 + d = 5.909

√35 = 5.91

Answer: i don't know

Step-by-step explanation: i don't know sorry

Answer:

A fairly weak positive correlation

Step-by-step explanation:

Answer:

B; A fairly weak positive correlation.

Step-by-step explanation:

Tip: You will know it's a negative if the line in the graph can be part of an N.

Answer:

look at pic

Step-by-step explanation:

In the given case, the value of "x" in the given isosceles triangle is 18 degrees.

The given triangle is an isosceles triangle, which means that it has two equal sides. Let's denote the length of each equal side as "x".

To find the value of "x", we need to use the properties of an isosceles triangle. In an isosceles triangle, the base angles (the angles opposite to the equal sides) are congruent (equal in measure).

Since the base angles are congruent, we can set up the following equation: 2x + 3x + 5x = 180 degrees

Combining like terms, we have: 10x = 180 degrees

To solve for "x", we divide both sides of the equation by 10: x = 18 degrees

Therefore, the value of "x" in the given isosceles triangle is 18 degrees.

To know more about   isosceles here

https://brainly.com/question/29793403

#SPJ2

Answer:

[tex]y-7=\frac{4}{3} (x+3)[/tex]

Step-by-step explanation:

Hi there!

We are given the point (-3, 7)

We want to write the equation of the line containing that point, in point slope-form, and that is also parallel to 4x-3y=7

Parallel lines contain the same slope

So first, let's find the slope of 4x-3y=7

To do that, we can convert the line from standard form (ax+by=c) to slope-intercept form (y=mx+b, where m is the slope, and b is the y intercept)

To do that, we need to isolate y on one side

So start by subtracting 4x from both sides

4x-3y=7

-4x      -4x

________________

-3y=-4x+7

Divide both sides by -3

y=[tex]\frac{4}{3}x[/tex]- [tex]\frac{7}{3}[/tex]

Since 4/3 is in the place of where m should be, the slope of the line is 4/3

It is also the slope of our new line, which we are trying to find

As stated earlier, we want to write this line in point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point

This is where the point we were given earlier comes in. We simply need to substitute our values (of the point and the slope) into the formula to find the equation.

First, with the slope; substitute 4/3 as m in the equation

[tex]y-y_1=\frac{4}{3} (x-x_1)[/tex]

Now substitute -3 as [tex]x_1[/tex] in the equation

[tex]y-y_1=\frac{4}{3} (x--3)[/tex]

We can simplify this to:

[tex]y-y_1=\frac{4}{3} (x+3)[/tex]
Now substitute 7 as [tex]y_1[/tex] into the equation

[tex]y-7=\frac{4}{3} (x+3)[/tex]

Hope this helps!

Answer:

B. 60 cm²

Step-by-step explanation:

The formula for the area of a trapezoid is: [tex]\frac{1}{2}(b_{1} + b_{2} )h[/tex]

Plugging in the given values, we can solve:

[tex]\frac{1}{2} (13+7)(6)\\\\\frac{1}{2}(20)(6)\\\\10(6)\\\\= 60[/tex]

hope this helps!

Answer:

41.53

Step-by-step explanation:

add all the numbers and divide by how much there is

623 /15

41.53

hope this helps!!

Answer:

That's cool

Step-by-step explanation:

Answer:

Thats cool and all but whats the wuestion

Step-by-step explanation:

[tex]\text{L.H.S}\\\\=\dfrac{\sin^4 A - \cos^4 A}{ \sin A + \cos A}\\\\\\=\dfrac{(\sin^2 A)^2-(\cos^2 A)^2}{\sin A + \cos A}\\\\\\=\dfrac{(\sin^2 A + \cos^2 A)(\sin^2 A-\cos^2 A)}{\sin A + \cos A}\\\\\\=\dfrac{1\cdot(\sin A+\cos A)(\sin A - \cos A)}{\sin A +\cos A}\\\\\\=\sin A - \cos A\\\\\\=\text{R.H.S}~~~ \\\\\text{Proved.}[/tex]

Answer:

heya! ^^

[tex] \\ \frac{ \sin {}^{4} (A) - \cos {}^{4} (A) }{ (\sin \: A + \cos \: A) } = ( \: sin \: A\: - \: cos \: A \: )\\[/tex]

[tex] \\LHS = \frac{ \sin {}^{4} (A) - \cos {}^{4} (A) }{ (\sin \: A + \cos \: A) } \\ \\ \frac{( \sin {}^{2} \: A + \cos {}^{2} \: A)( \sin {}^{2} A - \cos {}^{2} A) }{ (\sin \: A + \cos \: A) } \\ \\ we \: know \: that \: - \: sin {}^{2} A + cos {}^{2} A = 1 \\ \\ \therefore \: \frac{(1)(\sin {}^{2} \: A - \cos {}^{2} \: A)}{(\sin \: A + \cos \: A)} [/tex]

now , we're well aware of the algebraic identity -

[tex]a {}^{2} - b {}^{2} = (a + b)(a - b)[/tex]

using the identity in the equation above ,

[tex]\dashrightarrow \: \frac{(sin \:A - \: cos \: A)\cancel{(sin \:A + \: cos \: A )}}{\cancel{(sin \: A\: + \: cos \: A)}} \\ \\ \dashrightarrow \: (sin \: A \: - \: cos \: A) = RHS[/tex]

hence , proved ~

hope helpful :D

Answer:

Fraction 24 2/100 which equals 24 1/50 OR in decimal form 24.020

Step-by-step explanation:

Hope this helps! :)

Altitude (AB) = 6cm

Base (BC) = 8cm

Hypotenuse (AC) = ?

[tex] \fbox \text{According To Pythagoras Theorem = }[/tex]

[tex] \text{(Hypotenuse)² = (Altitude)² + (Base)²}[/tex]

Inserting The Values

[tex] \text{(Hypotenuse)²} =( {6})^{2} + (8) {}^{2} [/tex]

[tex] (\text{AC}) {}^{2} = (6) {}^{2} + (8) {}^{2} \\ \implies \text{(AC)} {}^{2} = 36 + 64 \\ \implies\text{AC} = \sqrt{100} \\ \implies\text{AC} = 10 \\ \\ \therefore \text{Hypotenuse (AC)} = 10 \text{cm}[/tex]

Correct Option D= 10cm

Answer:

-4 is your final answer in it

[tex]f(x) = \frac{3 + x}{x - 3} [/tex]

[tex]f(a + 2) = \frac{3 + a + 2}{a + 2 - 3} = \frac{a + 5}{a - 1} [/tex]