10 people each wants 3 slices but a box has 8 slices

Answer:

k = ±2√5 + 3

Step-by-step explanation:

[tex]k=3+2\sqrt5\ or\ k=3-2\sqrt5[/tex]

[tex]k^2-6k=11[/tex]

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[tex]k^2-6k+(6\times\frac{1}{2})^2=11+(6\times\frac{1}{2})^2[/tex]

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[tex]k^2-6k+3^2=11+3^2[/tex]

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[tex](k-3)^2=11+3^2[/tex]

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[tex](k-3)^2=11+9[/tex]

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[tex](k-3)^2=20[/tex]

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[tex]k-3=\sqrt{20}\ or\ k-3=-\sqrt{20}[/tex]

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                                 [tex](k-3=\sqrt{20})[/tex]

[tex]k=\sqrt{20}+3\\ k=2\sqrt{5}+3[/tex]

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                               [tex](k-3=-\sqrt{20})[/tex]

[tex]k=\sqrt{20}+3\\ k=-2\sqrt{5}+3[/tex]

_____________________________________________________

[tex]k=2\sqrt{5}+3\ or\ k=-2\sqrt{5}+3[/tex]

_____________________________________________________

[tex]k=2\sqrt{5}+3\ or\ k=-2\sqrt{5}+3[/tex]

_____________________________________________________

I hope this helps you

:)

Answer:

Step-by-step explanation:

To solve for x and y, take advantage of the relationships between angles and diagonals in a rhombus. Each diagonal bisects the vertex angle, and the acute angles in each right triangle are complementary.

__

The angles created by the diagonal at the lower left vertex are congruent:

  y° = 21°

__

The angles x° and y° are complementary:

  x° = 90° -21°

  x° = 69°

Answer:

6x - 8x + 4 + 36 - 9x

= 40 - 11x

Answer:320 cubic cm

Step-by-step explanation:  if you  multiply 16x20m  you get 320  cm

Answer:

  234 square millimeters

Step-by-step explanation:

You want the area of the irregular polygon shown.

There are always several ways you can find the area of a figure like this. In the attachment we have shown extensions of the vertical and horizontal lines that will divide the figure into a triangle and two rectangles.

The triangle has a base of 12 mm and a height of 13 mm. Its area is ...

  A = 1/2bh

  A = 1/2(12 mm)(13 mm) = 78 mm²

The upper rectangle has a width of 8 mm and a length of 14 mm. Its area is ...

  A = LW

  A = (14 mm)(8 mm) = 112 mm²

The lower rectangle has a width of 4 mm and a length of 11 mm. Its area is ...

  A = (4 mm)(11 mm) = 44 mm²

The area of the figure is the sum of the areas of its parts:

  total area = triangle area + upper rectangle + lower rectangle

  total area = 78 mm² + 112 mm² + 44 mm² = 234 mm²

The area of the figure is 234 square millimeters.

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Answer:

C. $104

Step-by-step explanation:

First, we need to figure out what percent $120 is of $1500.

120 ÷ 1500 = 0.08 = 8%. So, $120 is 8% of $1500, and this is the percentage that'll be used to calculate Sunday's commission.

0.08 (8%) × 1300 = 104

Thus, you earned $104 on Sunday.

Answer:

The exact value of sin 22.5° using the half-angle formula is √(2 - √2) / 2 or 0.38

Step-by-step explanation:

Let us consider θ = 22.5 º

Therefore, sin2θ =  [(1− cos 2θ) / 2] -------(1)

If θ = 22.5° then 2θ is 45°.

On substituting the value of θ in equation (1), we get

sin2 22.5° =  [(1− cos (2 × 22.5°)) / 2]

sin2 22.5° =  [(1− cos 45°) / 2]

sin2 22.5°=  [ [1 - (1 / √2)] / 2 ]

sin2 22.5°=  (2 - √2) / 4 [ on simplifying the above RHS value ]

sin 22.5° = [√(2 - √2) / 2]

After substituting the value of √2 as 1.414 in the above equation, we get

sin 22.5°= 0.38

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Here's the solution ~

As we know, we can calculate the circumference of a circle in terms of its diameter as :

[tex]\qquad \sf  \dashrightarrow \:c = \pi d[/tex]

where, c = circumference and d = diameter

And also, circumference of circle is terms of radius (r) is :

[tex]\qquad \sf  \dashrightarrow \:c = 2\pi r[/tex]

Now, let's move on to questions ~

[tex]\qquad \sf  \dashrightarrow \:3.14 \times 5.9 [/tex]

[tex]\qquad \sf  \dashrightarrow \: \approx18.53 \: ft[/tex]

・ ．━━━━━━━†━━━━━━━━━．・

[tex] \qquad \sf  \dashrightarrow \: \approx10.048 \: ft[/tex]

・ ．━━━━━━━†━━━━━━━━━．・

[tex]\qquad \sf  \dashrightarrow \:3.14 \times 6.1[/tex]

[tex]\qquad \sf  \dashrightarrow \: \approx19.15 \: ft[/tex]

・ ．━━━━━━━†━━━━━━━━━．・

[tex]\qquad \sf  \dashrightarrow \:2×3.14 \times 3.7[/tex]

[tex]\qquad \sf  \dashrightarrow \: \approx2×11.62 \: m[/tex]

[tex]\qquad \sf  \dashrightarrow \: \approx23.24 \: m[/tex]

・ ．━━━━━━━†━━━━━━━━━．・

[tex]\qquad \sf  \dashrightarrow \:2×3.14 \times 6.2[/tex]

[tex]\qquad \sf  \dashrightarrow \: \approx2× 19.47 \: units[/tex]

[tex]\qquad \sf  \dashrightarrow \: \approx38.94 \: m[/tex]

・ ．━━━━━━━†━━━━━━━━━．・

[tex]\qquad \sf  \dashrightarrow \:2×3.14 \times 5.1[/tex]

[tex]\qquad \sf  \dashrightarrow \: \approx2×16.01 \: ft[/tex]

[tex]\qquad \sf  \dashrightarrow \: \approx \: 32.02m[/tex]

➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖

Answer:

B. Square root of 48

Step-by-step explanation:

Using Pythagorean theorem. A^2 = B^2 + C^2

4^2 + x^2 = 8^2

16 + x^2 = 64

x^2 = 48

x = square root of 48

Answer:

the 1/2w +22 one is a binomial

Step-by-step explanation:

a binomial is a equation with one two separate numbers AFTER simplifcation. so "1+1" is not a binomial because its equal to just 2, but "1 + x" is a binomial because its simplifed

The length of the dilated line segment is 80 units.

Dilation is the increase or decrease in the size of a figure or object.

The segment with endpoints (10,40) and (70,120) is dilated by a factor of 4/5 to get (8, 32) and (56, 96).

The distance between points (8, 32) and (56, 96) is:

[tex]Distance = \sqrt{(96-32)^2+(56-8)^2} =80\ units[/tex]

The length of the dilated line segment is 80 units.

Find out more on dilation at: https://brainly.com/question/10253650

Answer:

Volume: 37.7cm3

It will melt in 21 minutes.

Step-by-step explanation:

Volume of a sphere: 4/3 x pi x r^2

4/3 X pi x 3^2 = 37.7cm3

37.7/1.8=20.943 minutes

The fraction of the game that Daniel's team scores 2 or more runs is 1/4 of the game.

A box plot is used to study the distribution and level of a set of scores. Scores are distributed into 4 groups. Each group has a value of 25%

The first quartile, is the first line on the box. The first quartile represents 1/4 of the score.

To learn more about box plots, please check: https://brainly.com/question/27215146

Answer:

A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign. The solutions to quadratic inequality always give the two roots. The nature of the roots may differ and can be determined by discriminant (b2 – 4ac).

Answer:

34? Idek

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

To maximize the length of the third side, which I'll call x, it needs to be the longest side.

So by the triangle inequality theorem, 19+15>x, meaning the maximum whole number value of x is 33.

Step-by-step explanation:

For this problem, we need to use the fact that the circle with center (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2.

This gives us that the equation of the circle is (x-1)^2 + (y-1)^2 = 25.

Answer:

Five feet

Step-by-step explanation:

H = A ÷ L

H = 65 ÷ 13

H = 5 ft

Answer:

The roots you found should be [tex](3x-4)(x+1)=0[/tex], which shows that [tex]x = \frac{4}{3} \\ x=-1[/tex]

Step-by-step explanation:

You likely messed up when trying to one or both of the roots back into the equation.

Answer:

1

Step-by-step explanation:

[tex] \tan( \frac{5\pi}{4} ) \times \frac{\pi}{180} = 1.19[/tex]

The question wants in radian, not in degrees since using the unit circle. Hope this helps

Answer:

a) 1

Step-by-step explanation:

Tan 5pi/4: 1

Tan (-5pi/4): -1

Tan 5pi/4 in degrees: tan (225°)

The amount of orange that Manny and Josh have leftover after eating lunch is 1.

A fraction is a non-integer. A fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below

Oranges Manny has left = 1 - 4/9 = 5/9

Oranges Josh has left = 1 - 5/9 = 4/9

Oranges they both have left = 5/9 + 4/9 = 1

To learn more about subtraction of fractions, please check: https://brainly.com/question/915789

Answer:

[tex]\filldraw (10,0) rectangle ++(3pt,3pt);[/tex]

Answer:

22 feet

Step-by-step explanation:

The area of a circle is π · r².

So, step one is to figure out the radius, so taking that equation, we can say π · r² = 121π.

Divide both sides by π to get r² = 121

Then, you take the square root of both sides to leave r = 11.

The diameter is twice as long as the radius, so multiply 11 · 2 to get 22.

The diameter is 22 feet long.

Answer:

20 square units

Step-by-step explanation:

as its a square, we just add all the sides together. like a+b+c+d..

5+5+5+5=20 units

Answer:

17.5

Step-by-step explanation:

The area for a triangle is (base*height)/2 this means

(5*7)/2 = 17.5 units^2

Answer:

Step-by-step explanation:

base = b = 5 units

height = h = 7 units

[tex]\bf \boxed{\text{Area of triangle = $\dfrac{1}{2}bh$}}[/tex]

                           [tex]=\dfrac{1}{2}*5*7\\\\\\=\dfrac{35}{2}\\\\\\= 17.5 \ square \ units[/tex]

The function [tex]y = -5t^2 + 125[/tex] of the nickel is quadratic function

It will take 5 seconds for the coin to hit the ground

The function is given as:

[tex]y = -5t^2 + 125[/tex]

When the nickel hits the ground, the value of the function is:

y = 0

So, we have:

[tex]-5t^2 + 125 = 0[/tex]

Subtract 125 from both sides

[tex]-5t^2 =- 125[/tex]

Divide both sides by -5

[tex]t^2 =25[/tex]

Take the square root of both sides

[tex]t = 5[/tex]

Hence, it will take 5 seconds for the coin to hit the ground

Read more about quadratic functions at:

https://brainly.com/question/1214333

Definition of a trapezoid: a quadrilateral with one pair of parallel sides

Thus PQRS is a trapezium because Line PQ is parallel to line SR

Hope that helps!

Answer:

yes your answer is 45 degree

Answer:

105°

Step-by-step explanation:

There 360° in a circle, so...

360°-150°-105°=105°

check: 150°+105°+105°= 360°

[Answer] 105°