The swiss mathematician leonhard euler and the french mathematician rene descartes both discovered a pattern in the numbers of​ edges, vertices, and faces of polyhedrons. solve problems 810.

Answer:

Step-by-step explanation:

Remark

What you want to do is get r on one side of the equal sign and everything else on the other.

Givens

V = pi r^2 h

Solution

Divide by pi

V/pi = pi r^2 h/pi

V/p = r^2 * h

Divide by h

V / h pi = r^2 h / h              Cancel h on the right side. Turn equation around

r^2 =  V / h pi

Take the square root of both sides

√r^2 = √(V / h pi )

r = √ (V / h pi)

Answer r =√ (V / h pi)

[tex]\sin \angle F~~= \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\~~~~~~~~~~~~=\dfrac{GE}{EF}\\\\~~~~~~~~~~~~=\dfrac 2 3\\\\\implies \angle F=\sin^{-1} \left(\dfrac 23} \right)=41.8^{\circ}\\\\\text{Hence the measure of angle F is}~ 41.8^{\circ}[/tex]

Answer: 1 1/2 cup of water

Step-by-step explanation: 3 3/4 - 2 1/4 = 1/2   |  3 - 2 = 1   |  3/4 - 1/4 = 2/4 = 1/2

Answer:

sqrt (120)

Step-by-step explanation:

Use pythag theorem

Leg1 ^2 + Leg2^2 = Hypot ^2

 13^2    + Leg2^2  =  17^2

    Leg2^2  =  17^2  -  13^2

    Leg2  =  sqrt (120)

Answer:

Equation: 1=1

Length of the road after 16 days: 16 miles (if not adding to 53. if adding to 53, the answer is 69)

Explanation:
If they add one mile of road every day, its 1(mile) = 1(day.
Since its one mile every day, 16 days is 16 miles. Adding 53 + 16 = 69

If we start at zero and move a units to the right, and then move the same number of units to the left, we will be back at 0. We can also represent this symbolically. Since a and b are the same distance from zero but are on opposite sides of zero, we know that they are opposites, so b = -a

Answer:

If we start at zero and move a units to the right, and then move the same number of units to the left, we will be back at 0. We can also represent this symbolically. Since a and b are the same distance from zero but are on opposite sides of zero, we know that they are opposites, so b = -a.

set : {31, 76, 34, 35, 39, 49, 55}

arrange ascending to descending:

{ 31, 34, 35, 39, 49, 55, 76 }

given,

I.Q.R:

Answer:

21

Step-by-step explanation:

Place the numbers in order from smallest to largest:

31, 34, 35, 39, 49, 55, 76

The median (Q2) is the middle value = 39

Q1 is the middle value of the numbers smaller than the median = 34

Q3 is the middle value of the numbers larger than the median = 55

IQR = Q3 - Q1

      = 55 - 34

      = 21

Answer:

  (a)  ∠1 and ∠5

Step-by-step explanation:

Complementary angles are angles whose measures total 90°. The angles do not have to be adjacent.

__

In this geometry, we can see that angles 1 and 2 are complementary, as are angles 4 and 5, since their respective sums are right angles. Angles 2 and 5 are vertical angles, so have the same measure.

  ∠1 + ∠2 = 90° . . . . . . adjacent angles that total a right angle

  ∠1 +∠5 = 90° . . . . . substitute ∠5 for ∠2, since measures are equal

This means angles 1 and 5 are complementary.

Answer:

$180 + $72 = $252

Step-by-step explanation:

$180 * 40%

$180 * 0.40 = $72

$180 + $72 = $252

Answer: 48

Step-by-step explanation:

Answer:

3-is 85

2- is 95

4-95

Step-by-step explanation:

for 1 is 85

85-180=95

As no graph is shown some basic information of parabola can be helpful

And a coordinate is given check it whether it is equal to second part of options

We get

Last two are radar now

As a must be negative option D has such similarities.

Answer:

[tex]\sf y = -0.006x^2 + 0.35x + 6\quad and\quad y = 0.2x[/tex]

Step-by-step explanation:

As the archer shoots the arrow up, the trajectory of the arrow can be modeled as a parabola that opens downwards.  Therefore, this is a quadratic equation with a negative leading coefficient.

From inspection of the answer options, the path of the arrow is :

[tex]y=-0.006x^2+0.35x+6[/tex]

This means the options for the line equation are [tex]y=-x[/tex] and [tex]y=0.2x[/tex]

We are told that the point of intersection of the line and the parabola is at (46.5, 9.3).  As both the x-value and y-value are positive, the equation of the line must be [tex]y=0.2x[/tex]

To confirm, substitute [tex]x=46.5[/tex] into the equation:

[tex]\implies y=0.2(46.5)=9.3[/tex]

Answer:

The first one is geometric. The second one is gemetric. The last one is arithmetic.

Step-by-step explanation:

Answer:

2) 4,2

Step-by-step explanation:

Factor by grouping:

[tex]x^2-6x+8\\\\x^2-4x-2x+8\\\\x(x-4)-2(x-4)\\\\(x-2)(x-4)[/tex]

Setting the expression equal to 0 and using the Zero Product Property, [tex]x=2[/tex] and [tex]x=4[/tex], which are the factors of the original polynomial.

Answer:

The factors are x-2 and x-4.

Step-by-step explanation:

x^2 - 6x + 8

= (x - 2)(x - 4)

Answer:

2 = 22

3 = 19

5 = 13

6 = 10

Step-by-step explanation:

To help with future questions, take whatever is for the x and plug it into the equation

Answer:

22,19,13,10

Step-by-step explanation:

First, Replace the x in the equation with parenthesis (), then inside of the () put the x value in the table so it would look like: y=28-3(2). Then solve by multiplying 2 by 3 so you have y=28-6. Then just subtract 6 from 28 to get 22. Rinse and repeat for the rest of the values. Your first value will be 22, second 19, third 13, and lastly 10. Hope this helps!

Answer:

38.08 m²

Step-by-step explanation:

Given:

Formula:

[tex]\text{Area of trapezium} = \dfrac{\text{Sum of parallel sides}}{2} \times \text{Height}[/tex]

[tex]\implies \text{Area of trapezium} = \dfrac{\text{Sum of parallel sides}}{2} \times \text{Height} \\\\\\ \implies \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \dfrac{\text{10.8 + 2.8}}{2} \times 5.6[/tex]

[tex]\\\\\\\implies \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \dfrac{\text{13.6}}{2} \times 5.6 \\\\\\ \implies \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = {\text{13.6}} \times 2.8 \\\\\\ \implies \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \boxed{38.08 \ \text{m}^{2}}[/tex]

Answer:

2010

Step-by-step explanation:

I do not think so

Answer:

The son is 24 and the father is 48

Step-by-step explanation:

If you let x = the age of the child, then the father is 2x old since the father is twice as old as the son. The sum of their ages would be 1x + 2x which simplifies to 3x.

Since the problem gives the total of their ages as 72, we know that 3x = 72.

Dividing both sides by 3, we get x = 24, which we said was the age of the child.

Since the age of the father is 2x, we can say that 2x = 2(24), or 2x = 48 for the age of the father.

Answer:

14.7÷41.4=0.355

the answer is 0.355

Answer:

A. Volume

Step-by-step explanation:

Volume is how much space is in a substance so that means it is A

Answer:

Volume

Step-by-step explanation:

The amount of space that a substance or object occupies is called Volume.

Answer:

a=84.25cm

Step-by-step explanation:

To find this answer, we need to understand how to get the Volume.

We get the volume by the formula: L x W x H

L = Length

W = Width

H = Height

So, we can see that there are 3 units required to know for getting the volume, if that's true, then, to do the inverse operation of finding the volume. That can be done by using thie formula:

[tex]V=a^3[/tex]

a= edge

Solving for a

a=V⅓=216⅓=6

now, let's look at how to find whether our answer is right or wrong

6x6=36

36x6=216

So hence, our answer is right!

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The length of a betta fish tank that has a shape of a cube and volume of 216 cubic inches is 6 inches.

A cube has all its sides equal to each other. Therefore,

volume of cube = L³

where

Therefore,

L = >

volume = 216 cubic inches

volume of cube = L³

216 = L³

cube root both sides

∛216 = ∛L³

L = ∛216

L = 6 inches

learn more on volume here: https://brainly.com/question/10961243

Answer:

7 inches

Step-by-step explanation:

The area of a parallelogram is Base x Height.

Area = 28 in^2 = (4 in)*(Height)

Height = 7 inches

Answer:

238

Step-by-step explanation:

Given equation:  [tex]a^2+1=6a[/tex]

Rearrange so that it is equal to zero:

[tex]\implies a^2-6a+1=0[/tex]

Quadratic formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]

Using the quadratic formula to solve the given equation:

[tex]\implies a=\dfrac{-(-6) \pm \sqrt{(-6)^2-4(1)(1)} }{2(1)}[/tex]

[tex]\implies a=\dfrac{6 \pm \sqrt{32}}{2}[/tex]

[tex]\implies a=3 \pm 2\sqrt{2}[/tex]

[tex]\implies a^2=17 \pm 12\sqrt{2}[/tex]

Substituting this into [tex]7\left(a^2+\dfrac{1}{a^2}\right)[/tex]

[tex]\implies 7\left(17 \pm 12\sqrt{2}+\dfrac{1}{17 \pm 12\sqrt{2}}\right)[/tex]

For [tex]17+12\sqrt{2}[/tex]:

[tex]\implies 7\left(17+12\sqrt{2}+\dfrac{1}{17+12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{(17+12\sqrt{2})^2}{17+12\sqrt{2}}+\dfrac{1}{17+12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{(17+12\sqrt{2})^2+1}{17+12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{289+408\sqrt{2}+288+1}{17+12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{578+408\sqrt{2}}{17+12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{34(17+12\sqrt{2})}{17+12\sqrt{2}}\right)[/tex]

[tex]\implies 7(34)[/tex]

[tex]\implies 238[/tex]

For [tex]17-12\sqrt{2}[/tex]:

[tex]\implies 7\left(17-12\sqrt{2}+\dfrac{1}{17-12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{(17-12\sqrt{2})^2}{17-12\sqrt{2}}+\dfrac{1}{17-12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{(17-12\sqrt{2})^2+1}{17-12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{289-408\sqrt{2}+288+1}{17-12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{578-408\sqrt{2}}{17-12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{34(17-12\sqrt{2})}{17-12\sqrt{2}}\right)[/tex]

[tex]\implies 7(34)[/tex]

[tex]\implies 238[/tex]

Answer:

(x² + 14x)/(9x²)

Step-by-step explanation:

To do this calculation process:

The first term: 2x/x² = 2/x.

Then: (2/x) + (x - 4)/(9x).

We should common the denominator by multiplying the denominators of the two terms (9x)(x) = 9x² and dividing each denominator by the common denominator.

So, it will be equal:

[(2)(9x) + (x - 4)(x)]/9x² = (18x + x² - 4x)/9x² = (x² + 14 x)/9x².

If Boyce had started investing when he was 20 the amount he would have more than he does in his retirement savings would be b. $321,946.93.

First convert the interest to a monthly rate:

= 4% / 12 months

= 1 / 3 %

Period:

= (63 - 34) x 12 months a year

= 348 months

Amount saved:

= Amount x ( (1 + rate) ^ number of periods - 1) / rate

= 450 x ( (1 + 1/3%)³⁴⁸ - 1 ) / 1/3%

= $294,811.07

If he started saving at 20, the number of periods would be:

= (63 - 20) x 12

= 516 months

Amount saved:
= 450 x ( (1 + 1/3%)⁵¹⁶ - 1 ) / 1/3%

= $616,758

The difference is:

= 616,758 - 294,811.07

= $321,946.93

Find out more on future value savings at https://brainly.com/question/26662056.

Answer:

68 is the perimeter.

Step-by-step explanation:

You can find the perimeter by adding up all of the sides. 13 + 11 + 3 + 7 = 34. To find the other sides of the shape you do 11 + 7 and 13 + 3. 11 + 7 = 18. 13 + 3 = 16. 18 + 16 = 34. 34 + 34 = 68.