Anna has a total of 36 goldfish in her aquarium, some are orange and some are black. The number of orange goldfish is 7 more than twice the number of black goldfish. Which system of equations below can be used to describe the number of black and orange goldfish in Anna's aquarium?

Answer:

The solutions are:

[tex]x=\frac{7-\sqrt{17}}{2},\:x=\frac{7+\sqrt{17}}{2}[/tex]

Step-by-step explanation:

Given the quadratic equation

-x² + 7x = 8

Solving using the quadratic formula

[tex]-x^2+7x=8[/tex]

Subtract 8 from both sides

[tex]-x^2+7x-8=8-8[/tex]

Simplify

[tex]-x^2+7x-8=0[/tex]

For a quadratic function of the form ax² + bx + c = 0, the solutions are:

[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

For a = -1, b = 7, c = -8

[tex]x_{1,\:2}=\frac{-7\pm \sqrt{7^2-4\left(-1\right)\left(-8\right)}}{2\left(-1\right)}[/tex]

[tex]x_{1,\:2}=\frac{-7\pm \:\sqrt{49-32}}{2\left(-1\right)}[/tex]

[tex]x_{1,\:2}=\frac{-7\pm \sqrt{17}}{2\left(-1\right)}[/tex]

Separate the solutions

[tex]x_1=\frac{-7+\sqrt{17}}{2\left(-1\right)},\:x_2=\frac{-7-\sqrt{17}}{2\left(-1\right)}v[/tex]

solving

[tex]x_1=\frac{-7+\sqrt{17}}{2\left(-1\right)}[/tex]

   [tex]=\frac{-7+\sqrt{17}}{-2}[/tex]

Apply the fraction rule:  [tex]\frac{-a}{-b}=\frac{a}{b}[/tex]

i.e. [tex]-7+\sqrt{17}=-\left(7-\sqrt{17}\right)[/tex]

so

     [tex]=\frac{7-\sqrt{17}}{2}[/tex]

Similarly solving

[tex]x_2=\frac{-7-\sqrt{17}}{2\left(-1\right)}[/tex]

    [tex]=\frac{-7-\sqrt{17}}{-2\cdot \:1}[/tex]

Apply the fraction rule:  [tex]\frac{-a}{-b}=\frac{a}{b}[/tex]

i.e. [tex]-7-\sqrt{17}=-\left(7+ \sqrt{17}\right)[/tex]

    [tex]=\frac{7+\sqrt{17}}{2}[/tex]

Therefore, the solutions are:

[tex]x=\frac{7-\sqrt{17}}{2},\:x=\frac{7+\sqrt{17}}{2}[/tex]

Hello there! ;)

1 is neither prime nor composite.

Prime numbers have 2 factors.

Composite numbers have 3 or more factors.

However, 1 has 1 factor.

Therefore, it's neither prime nor composite.

Hope this helps!

~Just a determined gal

#CarryOnLearning

[tex]MysteriousNature[/tex]

Answer:

The budget for dances is $380

Step-by-step explanation:

If we know that the ratio between student government budget for dance and charity event is 5:7 this means that there is some amount of money that fits 5 times into the student government budget for dance and 7 times into the budget for the charity events. So in order to find what is the value of that among we divide $532.00 by 7, and then multiply that amount by 5 to get the budget for the dance events. So we do........

$532.00 / 7 x 5 = $76 x 5 = $380

answer : 240

you do 24 x 10 :)

Answer:

the answer is: 3, 4

Step-by-step explanation:

those numbers meet in the circle where it supposed to go

Answer:

No its not

4km =4000m < 5000m

Step-by-step explanation:

hope it helps

Answer:

5000 meter>4km

Step-by-step explanation:

4km is= 4000meter so 5000 meters i greater than 4km

Answer:

Median is 31, if you are talking about the parallel line in between JK and and ML

Hey there!

Monte will need 9 packages of hot dogs.

To do this, we can first find the LCM.

To do this, first you find the prime factors of 20: 2 x 2 x 5

Then, you find the prime factors of 18: 2 x 3 x 3

Multiply each number by the greatest number it occurs:

2 x 2 x 3 x 3 x 5

And you get the LCM, 180. This means that you can get 180 total hot dogs and 180 total buns.

Then, divide that by the number of hot dogs in a package, to get the number of packages needed: 180/20 = 9

9 packages of hot dogs are needed.

Answer:

16

Step-by-step explanation:

128/8 = 16

n= 16

The value of n is equal to 16.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

WE are given an expression as;

8n = 128

We need to find the value of n.

8n = 128

n= 128/8 = 16

n= 16

Hence, the value of n is equal to 16.

To know more about an expression follow;

brainly.com/question/19876186

#SPJ2

Answer:

6/5

Step-by-step explanation:

120/100 =

12/10 =

6/5

Answer:

5) 6cm 6)J

Step-by-step explanation:

5) 30/7.5=4

24/4=6

6) J=P

K=Q

L=R

M=S

Answer:

The answer is 35

Step-by-step explanation:

It wants to know how many basketball and baseball players there are. If there are 20 basketball players and the ratio is 4:3 then you need to divide the number of basketball players by 4 then multiply by 3. Add 20 to that number and the answer is C

Answer:

35

Step-by-step explanation:

I came up with 35 because 20/4= 5, so we are multiplying players by 5. Similarly, 3x5=15 for baseball players. 20 basketball players plus 15 baseball players is 35. I hope this helps!

Answer:

720 sq ft

Step-by-step explanation:

Formula:

2 B + P x H

Answer:

720 sq ft

Step-by-step explanation:

fourmula

2b+p×h

Answer:

y = -2.5x

Step-by-step explanation:

The constant of variation = y/ x = 5/-2 = -2.5

Also -7.5 / 3 = -2.5

-10 /4 = -2.5 and so on

the answer is   -2/5 hope this helped

A. It will be twice as much as because the height is increased by 2

Answer:

b

why would you measure with something too big or too small?

Answer:

Ria earns 14.88 dollars each week

Step-by-step explanation:

Amount earned by peter every week = $12.40

If Ria earns 1.2 times as money per week as Peter, then;

Amount Ria earns = 1.2 * 12.40

Amount Ria earns = 14.88

Hence Ria earns 14.88 dollars each week

Answer:

10

Step-by-step explanation:

To obtain the length of the segment :

a² + b² = c²

a = 8 ; b = 6

8² + 6² = c²

64 + 36 = c²

100 = c²

Square root of both sides :

Sqrt(100) = sqrt(c²)

10 = c

Mistake in the solution is that 6² = 36 and not 12

Answer:

2/3

Step-by-step explanation:

16/24

4/6

2/3

Answer:

2/3

Step-by-step explanation:

16 ÷ 8 = 2

24 ÷ 8 =3

so the simplest form is 2/3

Answer:

The perimeter of the pentagon is;

29 units

Step-by-step explanation:

Let A, B, C, D, and E represent the vertices of the pentagon

The "x" and "y" coordinates of the vertices of the pentagon are given as follows;

A(-6, 2), B(-2, -2), C(5, -2), D(5, 2), E(-2, 5)

The length of the sides between each pair of coordinates can be found using the following formula;

[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]

Therefore, we have;

Length of segment AB = √((-2 - (2))² + (-2 - (-6))²) = 4·√2

Length of segment BC = √((-2 - (-2))² + (5 - (-2))²) = 7

Length of segment CD = √((5 - 5)² + (2 - (-2))²) = 4

Length of segment DE = √((5 - 2)² + (-2 - 5)²) = √58

Length of segment EA = √((5 - (2))² + (-2 - (-6))²) = 5

The length of the perimeter of the pentagon = 5+√58 + 4 + 7 + 4·√2 ≈ 29.2726273554 ≈ 29

The length of the perimeter of the pentagon ≈ 29.

Answer:

72 spheres are formed

Step-by-step explanation:

We start by calculating the volume of the metallic cylinder

Mathematically, we have this as;

V = pi * r^2 * h

V = pi * 21 * 14^2

V = 4116 π cm^3

The volume of each small sphere is;

V = 4/3 * pi * r^3

= 4/3 * π * 7/2^3 = 57.167 π cm^3

To get the number of small spheres, we simply divide the volumes

That will be 4116 pi / 57.167 pi = 72

Answer:

112

Step-by-step explanation:

234:2=117

117+5=122

--->234-122=112

Answer:

Abdullah is 46.8 years old.

Step-by-step explanation:

Umer is 5 years old and the product of their ages is 234 so that means Abdullah is 46.8 years old.

5*46.8 = 234