A 5-mile race takes place along a straight course. The number line shows the distance, in miles, from start to finish. The race director would like to place a water station along the course such that the distance from the start to the water station and the water station to the finish line is in a 7:5 ratio. Where would the water station be located? Round to the nearest tenth of a mile, if necessary. The water station will be placed about miles from the start.

Answer:

The area of the biggest possible square that fit into the circle is 18 cm²

Step-by-step explanation:

* Lets talk about the square inscribed in a circle

- The square is fit into the circle if its four vertices lie on the

  circumference of the circle

- The diagonal of the square is the diameter of the circle

- The vertices of the square divide the circle into 4 equal arcs

* Look to the attached figure

- The square ABCD fit into the circle M

- A , B , C , D lie on the circumference of the circle M

- The four arcs AB , BC , CD , AD are equal in measure and length

- The diagonal of the square is DB

- The diameter of the circle M is DB

∵ The radius of the circle is 3 cm

∵ The diameter = twice the radius

∴ The diameter of the circle = 2 × 3 = 6 cm

∴ DB = 6 cm

- The rule of the area of the square = (diagonal)²/2

∵ The length of the diagonal is 6 cm

∴ The Area of the square = (6)²/2 = 36/2 = 18 cm²

* The area of the biggest possible square that fit into the circle is 18 cm²

Answer:

The area of the biggest possible square = 36 cm²

Step-by-step explanation:

From the figure attached with this answer shows that, the biggest possible square that would fit into a circle having a radius of 3 cm.

To find the area of square

Side of square  = 2 * radius of circle = 2 * 3 = 6 cm

Area of square = side * side = 6 * 6 = 36 cm²

[tex]\bf \cfrac{4^2-20\div 5}{1-5+7}\implies \cfrac{\stackrel{\downarrow }{16}-20\div 5}{1-5+7}\implies \cfrac{16-\stackrel{\downarrow }{4}}{1-5+7}\implies \cfrac{\stackrel{\downarrow }{12}}{1-5+7} \\\\\\ \cfrac{12}{\stackrel{\downarrow }{-4}+7}\implies \cfrac{12}{\stackrel{\downarrow }{3}}\implies 4[/tex]

Answer:

Step-by-step explanation:

1. Due to the stretchiness of shirt fabric and the waste involved in cutting pattern pieces, it is unrealistic to require that the length of the fabric be specified to a hundredth of a centimeter. Measurement to the nearest half-centimeter is sufficiently accurate for the purpose. The appropriate choice is the measurement with a precision of 1 cm:

  232 cm

__

2. The most appropriate choice is the one that shows cubing 6^(1/3) will result in 6, just as cubing ∛6 will result in 6.

First you must distribute the 3 to the numbers in the parentheses

(3*m) + (3 * -5) + m

3m + (-15) + m

3m - 15 + m

Combine like terms (3m and m)

4m - 15

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

3m - 15 + m

Step-by-step explanation:

Multiply (m - 5) by 3.

m * 3 = 3m

-5 * 3 = -15

This doesn't apply with +m.

So this leaves it as 3m - 15 + m.

Hope this helps! :)

Answer:

Step-by-step explanation:

x(7x^2+4x) can be expanded by multiplying each of the two terms inside the parentheses by x:

x(7x^2+4x) = 7x^3 + 4x^2

Answer:

The numbers between 30 and 40 whose only factors are one and themselves, also called prime numbers, are 31 and 37.  :)

Answer:

It is 31 and 37

Numbers that have only one and itself as a factor are called prime numbers.

Answer:

Add 8 to both sides of the equation

Step-by-step explanation:

We have been given the quadratic equation;

x^2 - 14x +41 = 0

we are required to complete the square in order to express it in the form;

(x - p)^2 = q

In order to do this we need to find a constant c, such that;

[tex]c=(\frac{b}{2})^{2}[/tex]

where b is the coefficient of x in the quadratic equation. In our case b = -14. Therefore,

[tex]c=(\frac{-14}{2})^{2}=49[/tex]

Therefore, for us to complete the square, the left hand side of the quadratic equation should be;

x^2 - 14x +49

Since we already have 41, we can simply add 8 to make it 49. Thus, the first correct step to write the above equation in the form (x - p)2 = 9, where p and q are integers is to Add 8 to both sides of the equation

Answer:

The length of side AB is 5 units

Step-by-step explanation:

* Lets revise how to find the distance between two points

- If there are two points their coordinates are (x1 , y1) and (x2 , y2),

 then we can find the distance between them by this rule:

 d = √[(x2 - x1)² + (y2 - y1)²]

- Now lets solve the problem

∵ A = (4 , -5)

∵ B = (7 , -9)

- To find the length of AB use the rule of the distance above

- Let point A is (x1 , y1) and point B is (x2 , y2)

∵ x1 = 4 and x2 = 7

∵ y1 = -5 and y2 = -9

∴ AB = √[(7 - 4)² + (-9 - -5)²]

∴ AB = √[(3)² + (-4)²]

∴ AB = √[9 + 16] = √25 = 5

* The length of side AB is 5 units

Answer:

15

Step-by-step explanation:

if you have 2/5 lengths each time, if you divide that by 6 it gives 15.

Or if you go 2/5 to 4/5 to 6/5 until you have 30/5 because that is how long 6 feet is.

Answer:

Step-by-step explanation:

6+2 = 8 your welcome or 4 x 2 = 8 :)

I have no idea about the part A, but part b, all you have to do is get all the numbers of the fans, and put them in least to greatest. Then you count how fans are from 0-9, then you count how much fans are from 10 - 19, and so on. Im sorry that i couldn't answer it completely but i hope this helps.

Answer:

Step-by-step explanation:

First we will arrange the ages of fans of the basketball game in the increasing order.

9, 11, 14, 14, 16, 25, 25, 27, 28 30, 33, 35, 35, 37, 38, 39, 42, 46, 47, 60

Part A. Now we will make stem-and-leaf plot

0  |  9

1   |  1, 4, 4, 6

2  |  5, 5, 7, 8

3  |  0, 3, 5, 5, 7, 8, 9

4  |  2, 6, 7

5  |

6  |  0

Part B.

Frequency table

Age           Number of Fans

0 - 9                  1

10 - 19               4

20 - 29             4

30 - 39             7

40 - 49             3

50 - 59             0

60 - 69             1

Answer:

1 out of 5

Step-by-step explanation:

There are 5 answer choices total and you're supposed to choose 1 answer so 1 outta 5.

The probability that Peter will choose the correct answer by chance is 1/5 or 0.2 (or 20%).

If Peter has no knowledge about the correct answer to question number 4 on a multiple-choice test with 5 answer choices, the probability of him randomly selecting the correct answer is 1 out of 5.

This probability can be calculated by dividing the number of favorable outcomes (1, since there is only one correct answer) by the total number of possible outcomes (5, since there are 5 answer choices).

Mathematically, it can be represented as 1/5. Thus, the probability that Peter will choose the correct answer by chance is 1/5 or 0.2 (or 20%). This means that, on average, he would be expected to choose the correct answer 20% of the time if he were to guess without any knowledge or information.

To know more about probability:

https://brainly.com/question/32117953

#SPJ2

Answer:

[tex]r^2=4\sec 2\theta}[/tex]

Step-by-step explanation:

The given equation is:

[tex]x^2-y^2=4[/tex]

We substitute [tex]x=r\cos (\theta)[/tex] and [tex]y=r\sin (\theta)[/tex] to obtain:

[tex]r^2\cos^2\theta-r^2\sin^2\theta=4[/tex]

This implies that:

[tex]r^2(\cos^2\theta-\sin^2\theta)=4[/tex]

Apply double angle identity to obtain:

[tex]r^2\cos 2\theta=4[/tex]

This implies that:

[tex]r^2=\frac{4}{\cos 2\theta}[/tex]

This simplifies to:

[tex]r^2=4\sec 2\theta}[/tex]

You are basically just working this problem backwards; the way you would find the zeros of the function.

Therefore, to start, make each equal to zero and do the opposite (+ or -) to each side.

-2=x and 2/3=x

0=x+2 and 0=x-2/3

In a function like this, we are usually given an equation like (x+#)(x+#) then we would set these to zero. However, since we are working backwards we are trying to get it in that (x+#)(x+#) form.

(x+2)(x-2/3)

2+2/3 = 2 2/3 or 2.667

2 x 2/3 = 4/3 or 1.334

Your quadratic function is now x^2+2.67x+1.334

or x^2+2 2/3x+4/3.

Hope I helped!

Answer: [tex]x=-5[/tex]

Step-by-step explanation:

You need to find the value of the variable "x".

Solve for "x":

Subtract [tex]\frac{5}{6}x[/tex] from both sides of the equation:

[tex]\frac{2}{3}x-\frac{1}{2}-\frac{5}{6}x}=\frac{1}{3}+\frac{5}{6}x\\\\-\frac{1}{6}x-\frac{1}{2} =\frac{1}{3}[/tex]

Add  [tex]\frac{1}{2}[/tex]  to both sides of the equation:

[tex]-\frac{1}{6}x-\frac{1}{2}+\frac{1}{2} =\frac{1}{3}+\frac{1}{2}\\\\-\frac{1}{6}x=\frac{5}{6}[/tex]

Multiply both sides of the equation by -6:

[tex](-\frac{1}{6}x)(-6)=(\frac{5}{6})(-6)\\\\x=-5[/tex]

Separate the kite into two triangles.

The base of the triangles would be 6 ( half the width is given as 3, so the full width would be 3 x 2 = 6).

The height of the bottom triangle is given as 10.

The area of a triangle is 1/2 x base x height.

Bottom triangle = 1/2 x 10 x 6 = 30 square units.

For the top triangle you need to find the height using the Pythagorean theorem.

Height = √(5^2 - 3^2) = √(25-9) = √16 = 4

Now the area of the top triangle is 1/2 x 4 x 6 = 12 square units.

Total area = Bottom + top = 30 + 12 = 42 square units.

The distribution is very simple. Using FOIL.

It states that [tex](a+b)(c+d)=ac+ad+bc+bd[/tex].

Also note that when multiplying expressions we multiply variables and values differently. If we have variables like [tex]x[/tex] their exponents will add. If we have values like 3 we multiply them normally.

For example your practise 3.

[tex](x+3)(2x^2+4)=2x^2\cdot x+4x+3\cdot2x^2+3\cdot4 \\

\underline{2x^3+4x+6x^2+12}

[/tex]

Now just order the expressions from bigger exponent to smaller and than values. (Usual notation although no need).

And solution is:

[tex]\boxed{2x^3+6x^2+4x+12}[/tex]

Hope this helps.

r3t40

Answer:

See below

Step-by-step explanation:

[tex]a\cdot(b + c) = a\cdot b + a\cdot c[/tex]

3) Practice: Organizing information

[tex]\begin{array}{lll}\qquad \textbf{Steps} & \textbf{Problem: }(x + 3)(2x^{2} + 4) & \\\textbf{1. List variables} & a = x + 3 & \\ & b = 2x^{2} & \\ & c = 4 &\\\\\textbf{2. Distribute} & (x + 3)(2x^{2} + 4)& = (x + 3)(2x^{2}) + (x + 3)(4)\\\\\textbf{3. Redistribute} & (x + 3)(2x^{2})& (x + 3)(4)\\& a = 2x^{2} & a = 4\\& b = x & b = x\\& c = 3 & c = 3\\& 2x^{3} + 6x^{2} & 4x + 12\\\textbf{4. Combine}& & \\\qquad\textbf{terms} & 2x^{3} + 6x^{2}+ 4x + 12 & \\\end{array}[/tex]

4. Practice: Summarizing

[tex]\text{You can use the FOIL method to multiply two }\underline{\text{binomials}}.\\\text{The letters in FOIL stand for }\underline{\text{First, Outer, Inner, Last}}.\\\text{The FOIL method helps you to remember how to multiply each term in one }\\\underline{\text{binomial}} \text{ by each term in the other }\underline{\text{binomial}}.[/tex]

Answer:

36 watts.

Step-by-step explanation:

Power is calculated from

W = E^2/R

E = 24 volts.

R = 16 ohms

W = 24^2 / 16

W = 576 / 16

W = 36 watts.

Answer:

[tex]\left(a+3\right)\left(a-2\right)=a^2+a-6=[/tex]

Step-by-step explanation:

Given expression is [tex]\left(a+3\right)\left(a-2\right)[/tex].

Now we need to multiply this using FOIL.

F = First [tex]=\left(a\right)\left(a\right)= a^2[/tex]

O = Outside [tex]=\left(a\right)\left(-2\right)= -2a[/tex]

I = Inside [tex]=\left(3\right)\left(a\right)= 3a[/tex]

L = Last [tex]=\left(3\right)\left(-2\right)= -6[/tex]

Hence we get :

[tex]\left(a+3\right)\left(a-2\right)=a^2-2a+3a-6=a^2+a-6=[/tex]

Answer:

[tex](a+3)(a-2)=a^2+a-6[/tex]

Step-by-step explanation:

The given expression is:

[tex](a+3)(a-2)[/tex]

Using FOIL, we multiply the;

First terms:[tex]a\times a=a^2[/tex]

Outside terms: [tex]a\times -2=-2a[/tex]

Inner terms:[tex]3\times a=3a[/tex]

Last terms:[tex]3\times -2=-6[/tex]

Putting all together we have:

[tex](a+3)(a-2)=a^2-2a+3a-6[/tex]

This simplifies to [tex](a+3)(a-2)=a^2+a-6[/tex]

Answer:

410.5 yards cubed

Step-by-step explanation:

Volume of a cone is 1/3Bh

h is the height of the cone

B is the area of the base, which is a circle, so use πr^2 to find area of the circle

The radius is 7, so:

π7^2

π49(8)(1/3) = 410.5

Answer:

Step-by-step explanation:

Equation

Volume = (1/3) * pi * r^2 * h

Givens

pi = 3.14

r = 7 yd

h = 8 yd

Solution

V = (1/3) * 3.14 * 7^2 * 8

V = (1/3) * 3.14 * 49 * 8

V = (1/3) *  1231.5

V = 410.5 cubic yds.

The answer is 8x^4y^5.It has the highest degree and that is 4 in x and 5 in y.

Answer:

Step-by-step explanation:

Answer:

(9,-6)

Step-by-step explanation:

4x+3y=18

3x+4y=3

Multiply the first equation by 3

3(4x+3y)=18*3

12x+9y = 54

Multiply the second equation by -4

-4(3x+4y)=3*-4

-12x -16y = -12

Add these two new equations together to eliminate x

12x+9y = 54

-12x -16y = -12

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

    -7y = 42

Divide each side by -7

-7y/-7 = 42/-7

y = -6

Now we can find x

3x+4y =3

3x +4(-6) = 3

3x -24 =3

Add 24 to each side

3x-24+24 = 3+24

3x = 27

3x/3 = 27/3

x = 9

(9,-6)

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}4x+3y=18&(1)\\3x+4y=3&(2)\end{array}\right\\\\(1)\\4x+3y=18\qquad\text{subtract}\ 4x\ \text{from both sides}\\3y=-4x+18\qquad\text{divide both sides by 3}\\y=-\dfrac{4}{3}x+6\qquad\text{substitute it in (2):}\\\\3x+4\left(-\dfrac{4}{3}x+6\right)=3\qquad\text{use the distributive property}\\\\3x+(4)\left(-\dfrac{4}{3}x\right)+(4)(6)=3\\\\3x-\dfrac{16}{3}x+24=3\qquad\text{multiply both sides by 3}\\\\9x-16x+72=9\qquad\text{subtract 72 from both sides}\\\\-7x=-63\qquad\text{divide both sides by (-7)}\\\\\boxed{x=9}[/tex]

[tex]\text{Put the value of x to (1):}\\\\y=-\dfrac{4}{3}(9)+6\\\\y=(-4)(3)+6\\\\y=-12+6\\\\\boxed{y=-6}[/tex]

Answer:

Step-by-step explanation:

(x+3)^2=35+1

(x+3)^2=36

(x+3)^2=6^2

taking squareroot

x+3=+-6

x+3=6,-6

x=6-3=3

or x=-6-3=-9

Answer:

-13

Step-by-step explanation:

-4-8+3+6-10

Answer:-13

Step-by-step explanation:

When r varies inversely with x and r = -2 when x = 6, the value of r when x = -3 is 4.

r varies inversely with x, meaning that as one increases, the other decreases. Given r = -2 when x = 6, we can find the constant of variation by using the formula for inverse variation: r₁ * x₁ = r₂ * x₂. Plugging in the values, we have (-2) * 6 = r₂ * -3, which simplifies to r₂ = 4. Therefore, when x = -3, the value of r is 4. This demonstrates the relationship between variables in an inversely proportional scenario, elucidating the concept of variation in algebraic contexts.

Answer:

1/5 *3 = 15

You have to do Keep, Change, Flip. When you do that it becomes 1/5*3/1.

That equals 15.

Answer:

60

Step-by-step explanation:

124−4(3−5(17−14)+2(9+5))

=124−4(3−(5)(3)+2(9+5))

=124−4(3−15+2(9+5))

=124−4(−12+2(9+5))

=124−4(−12+(2)(14))

=124−4(−12+28)

=124−(4)(16)

=124−64

=60

Answer:

0.2

Step-by-step explanation:

2 divided by 10 gives you the decimal.

Answer:

∆AMN ≅ ∆NOA

Step-by-step explanation:

Given:

Quadrilateral AMNO

MN║AO

AM║ON

To prove:∆AMN ≅ ∆NOA

Lets first draw two diagonals represented by lines MO and AN inside the given quadrilateral AMNO

Now we know if lines are parallel then the alternate interior angles are congruent , hence

∠NMO≅∠AOM

∠MNA≅∠NAO

∠AMO≅∠NOM

∠MAN≅∠ANO

Also by Reflexive Property we have

NA≅NA

MO≅MO

From ASA congruence property of triangles that states that if two angles and a side of two triangles are congruent then the two triangle are said to be congruent, hence we have

ΔAMN≅ΔNOA

ΔMAO≅ΔONM  !

Answer:

∆AMN=∆NOA by rule SSS

Answer:

500000x4000000000000 = 2 x 10^18

Answer: [tex]2*10^{18}[/tex]  or  [tex]2,000,000,000,000,000,000[/tex]

Step-by-step explanation:

You can just make the multiplication indicated:

[tex]500,000*4,000,000,000,000=2,000,000,000,000,000,000[/tex]

You can rewrite the product in scientific notation form. This form is:

[tex]a*10^n[/tex]

Where "a" is a number between 1 and 10 but lesss than 10, and "n" is an integer.

In scientific notation, the decimal point must be after the first digit.

So, for the product [tex]2,000,000,000,000,000,000[/tex] the decimal point must be moved 18 places to the left.

Then, you get:

[tex]=2*10^{18}[/tex]