What is 8 cm enlarged by a scale factor of 6.5

This question has to do with the Mathematical sub-topic in Geometry called Ellipse.

An ellipse is a circle that has been stretched in one direction so that it is no longer symmetrical but oval in shape.

Let us assume that the points on the ellipse is (cosθ, √3 sinθ)

Next let's minimize their distance squared from (-1, 0)  taking a point on the ellipse as (cos θ- -1)² + (√3 sin θ)² =

cos²θ + 2cos θ + 1 + 3 sin² θ

(Substituting sin² θ + cos² θ = 1)

2 + 2 cos θ + 2 sin² θ

The derivative is given as

-2 sin θ + 4 sin θ cos θ =

-2 sin θ (2 cos θ - 1)

The above translates to 0 at sin θ = 0 or cos θ = 1/2, which results in 0°, 180°, 60°, 300°

Assuming we re-write the first derivative as - 2sin θ+ 2sin 2θ, the second derivative becomes:

-2 cos θ + 4 cos 2 θ

At 0°, 180°, 60°, 300°, we get 2, 6, -3, -3.

Therefore, our relative minima is given at 0°, 180°, while the relative maxima at 60°, 300°.

It is safe to declare, therefore that due to the nature of the function, the global minima and maxima will be among the four locations indicated above.

In addition to that,, 180° is the global minimum. This is because it is at the actual point, while  60° and 300° give the same value of the distance squared, thus both will each be maxima.

(cos θ, √3 sin θ) at  60°, 300° is (1/2, 3/2) and (1/2, -3/2)

Learn more about Point on Ellipse at:
https://brainly.com/question/4399570

See the definition of a circle here:
https://brainly.com/question/8952990

Answer:

About 25%

Step-by-step explanation:

The median is 25, and you know there are quartiles. From the median to a consecutive quartile, there is a range of 25%. For less than 20, It's from 5-20. Since there is a consecutive quartile, you get 25%!

Answer:

25%

Step-by-step explanation:

I took the test                                                                                                                                         Hope this helps :)

Answer:

158 in²

Step-by-step explanation:

Surface area of a rectangular prism:

2(lw + lh + wh), where w is the width, l is the length and h is the height.

= 2((8 x 5) + (8 x 3) + (5 x 3))

= 2(40 + 24 + 15)

= 2(79)

= 158 in²

Answer: D

Step-by-step explanation:

Diagonals of a square are perpendicular, so the measure of angle 1 is 90 degrees.

Answer:

The whole number : 3

Fraction : 2/8

I'm pretty sure this is correct

Answer:

Step-by-step explanation:

To find the slope of the line, you have to use a slope formula.

Slope formula:

[tex]\Longrightarrow:\sf{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]

⇒ y2=(-15)

⇒ y1=1

⇒ x2=1

⇒ x1=(-1)

Rewrite the whole problem down.

[tex]\Longrightarrow: \sf{\dfrac{-15-1}{1-\left(-1\right)}=\dfrac{-16}{2}=\boxed{\sf{-8}}[/tex]

I hope this helps you! Let me know if my answer is wrong or not.

Answer: (4)

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

If ΔDGH ~ ΔDEF , then [tex]\frac{DG}{DE}[/tex] = [tex]\frac{GH}{EF}[/tex]

[tex]\frac{x+3}{2x-1}[/tex] = [tex]\frac{52}{91}[/tex]

After cross-multiplication: 52(2x - 1) = 91(x + 3)

104x - 52 = 91x + 273

13x = 325

x = 25

Answer:

Step-by-step explanation:

DGH~DEF ⇒ their corresponding sides are proportional

then

[tex]\frac{DG}{DE} =\frac{GH}{EF}[/tex]

then

[tex]\frac{52}{91} =\frac{x+3}{2x-1}[/tex]

then

[tex]\frac{4}{7} =\frac{x+3}{2x-1}[/tex]

then

4(2x-1) = 7(x+3)   [cross multiply]

then

8x - 4 = 7x + 21

then

8x - 7x = 21 + 4

then

x = 25

Answer: D

Step-by-step explanation: You're Welcome

Answer:

3x-3y=63 = -1

Step-by-step explanation:

so the anwer is -1

Answer: False

Step-by-step explanation:

68%

Key Takeaways. The Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean. Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean.

Answer:

random sampling

Step-by-step explanation:

There are no rules or criteria that are set to choose which Starbucks are chosen to be surveyed.

Answer:

!!! please use the correct units.. m² and m !!!

the answer is in the picture

Answer:

$537.87

Step-by-step explanation:

First, we need to determine our total pay which will be 40 hours times our $15 per hour to be $600. For the extra hours above 40, we are payed 1.5 times as much.

$15 * 1.5 = $22.5 * (44-40) = $90 additional pay

$600 + $90 = $690 total pay

Now, we calculate all of our deductions.

Subtract social security to be

690 * (1-0.0625) = $646.875

Medicare Deduction

646.875 * 0.9855 = $637.50

Health Insurance

$637.50-83 = $554.50

401k Deduction

$554.50 * 0.97 = $537.87

Answer

0

Step-by-step explanation:

Because 110+50+10= 170 and every triangle has 180º

Answer:

I'm sure it's the second one

Answer:

second answer is correct

Slit the shape into a rectangle and two triangles:

Rectangle = 9 x 8 = 72 sq. Ft.

Triangle = 1/2 x 8 x 2.5 = 10 sq. Ft x 2 = 20 sq. Ft.

Total area = 72 + 20 = 92 sq. Ft.

3 coats x 92 = 276 sq ft worth of paint.

1 quart covers 200 so he would need to buy 2 quarts:

2 x $8.97 = $17.94 total

Answer:

∠KPL = 80°

Step-by-step explanation:

As KM is perpendicular to KP, this means that KM is the diameter of the circle, as the tangent of a circle is always perpendicular to the radius.

The angle at the circumference in a semicircle is always a right angle.  So if KM is the diameter then ΔKLM is a right triangle with ∠KLM = 90°

The sum of the interior angles of a triangle is 180°.

Therefore, ∠KLM + ∠KML + ∠LKM = 180°

As ∠KLM = 90° and ∠KML = 50°

⇒ 90° + 50° + ∠LKM = 180°

⇒ ∠LKM = 40°

As ∠PKM = 90° then

⇒ ∠PKL = 90 - ∠LKM

              = 90 - 40

              = 50°

Tangents from a common point to a circle are always equal in length, so as PK and PL are tangents from point P, then PK = PL

Therefore, ΔLPK is an isoceles triangle and so its base angles ∠PKL and ∠PLK will be equal.

Since ∠PKL = 50° then ∠PLK = 50°

Again, as the sum of interior angles of a triangle is 180°:

⇒ ∠KPL + ∠PKL + ∠PLK = 180°

⇒ ∠KPL + 50° + 50° = 180°

⇒ ∠KPL = 80°

Answer:

56 Chickens

36 Cows

Step-by-step explanation:

You can set this up as a system of equations:

(x=chickens, y=cows)

[tex]\left \{ {{92 = x+y} \atop {256=2x+4y}} \right. \\[/tex]

To solve this system, first we can solve for x in the top equation:

[tex]x=92-y[/tex]

Next, we can plug in x to the second equation and solve for y:

[tex]256=2(92-y)+4y\\256=184+2y\\2y=72\\y=36[/tex]

And now that we have y, we can plug it into the first equation and solve for x:

[tex]92=x+36\\x=56[/tex]

Answer:

A

Step-by-step explanation:

(m / 3) = (12 / 3) = 4

1/2 x 4 = 2

2 + n = 2 + 3/5 = 2 and 3/5 = 13/5

Answer:

13/5

Step-by-step explanation:

Answer:

[tex]h(x)=\frac{1}{5}x[/tex]

Step-by-step explanation:

To write a formula for a function, such as h(x), you need to solve for y.

[tex]6x+y=4x+11y[/tex]
[tex]-4x[/tex]      [tex]-4x[/tex]
[tex]2x+y=11y[/tex]
    [tex]-y[/tex]       [tex]-y[/tex]
[tex]2x=10y[/tex]
[tex]/10[/tex]   [tex]/10[/tex]
[tex]\frac{2}{10}x=y[/tex]
[tex]y=\frac{1}{5}x[/tex]

y and h(x) mean the same thing, so you can subsitute h(x) for y in order to fit the question.

Therefore, [tex]h(x)=\frac{1}{5}x[/tex]

Answer: pages 1-1,450

pages 1-9 = 9 digits

pages 10-99 = 90*2 = 180 digits

pages 100-999 = 900*3 = 2,700 digits

pages 1000-1450 = 451*4 = 1,804 digits

sum = 4,693 digits

Answer:

6

Step-by-step explanation:

The formula for the area of a triangle is 1/2(bh).

4 1/2=9/2, 2 2/3= 8/3

9/2x8/3=72/6,

12. However, you still have to divide by two, which gets you 6

Answer:

6

Step-by-step explanation:

The formula for the area of a triangle is 1/2(bh).

4 1/2=9/2, 2 2/3= 8/3

9/2x8/3=72/6,

Answer:

Top Left

I sincerely hope this is right and that you get g really good mark ;)

Answer:

84

Step-by-step explanation:

supplementary means two angles that add to 180

180-96=84

Answer: 5 + 5 = 10

Reason: Imagine that you have 5 pencils in one hand, then you add another 5 pencils into that hand, and you would have 10 pencils. Thus 5 + 5 in this case is 10

Hope that helps!

Answer:

109/150

Step-by-step explanation:

Answer: 109/150

6% = 6/100

6/100 = 18/300 (Multiply Numerator and Denominator by 3)

2/3 = 200/300 (Multiply Numerator and Denominator by 100)

200/300 + 18/300 = 218/300

218/300 = 109/150 (Simplify by Dividing Numerator and Denominator by 2)