To participate in a competition, each team must follow the rules about the allowable number of adults and children on a team.



Let `x\ `represent the number of adults on the team. Let `y` represent the number of children on the team.



There has to be exactly one adult for every two students. Create an equation th

Answer:

1/2

Step-by-step explanation:

total marbles 6

white marbles 3

white marbles/ total = 3/6

simply 1/2

Step-by-step explanation:

total marbles 6

white marbles 3

white marbles/total =3/6

simply 1/2

let number be x

1/6x - 1/12x= 4

1/12x=4

cross multiply

x= 12 x 4

x= 48

If one-sixth of a certain number is four more than one-twelfth the number, the required number will be 48.

Let the unknown number be 'a'

One-sixth of the number is expressed as 1/6 a ..... 1

One-twelfth the number is also expressed as 1/12 a

Four more than one-twelfth the number will be written as:

1/12 a + 4 .... 2

Equating 1 and 2 will give:

1/6 a = 1/12 a + 4

a/6 = a/12 + 4

Collect the like terms

[tex]\frac{a}{6} - \frac{a}{12} = 4[/tex]

Find the LCM

[tex]\frac{2a-a}{12} = 4\\\frac{a}{12} = 4[/tex]

Cross multiply

a = 12×4

a = 48

This shows that the required number is 48

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Answer:

B and E

Step-by-step explanation:

To verify which are solutions, substitute the given values into the left side of the equation and if equal to the right side then they are solutions.

A

2(20)² + 18(20) = 800 + 360 = 1160 ≠ 20 ← not a solution

B

2(1)² + 18(1) = 2 + 18 = 20 ← solution

C

2(- 2)² + 18(- 2) = 2(4) - 36 = 8 - 36 = - 28 ≠ 20 ← not a solution

D

Is a repeat of C

E

2(- 10)² + 18(- 10) = 2(100) - 180 = 200 - 180 = 20 ← solution

F

2(- 1)² + 18(- 1) = 2(1) - 18 = 2 - 18 = - 16 ≈ 20 ← not a solution

Then B and E are solutions to the equation

[tex] \huge \mathrm{Answer࿐ }[/tex]

let's solve the quadratic equation :

So, there are two cases :

Case - 1 (when, 2x - 2 = 0)

Case - 2 (when, x + 10 = 0)

Therefore the required options will be :

Step-by-step explanation:

[tex] {2x}^{2} + 8x - 1 = 0 \\ {x}^{2} + 4x - \frac{1}{2} = 0 \\ {x}^{2} + 4x + {( \frac{1}{4} )}^{2} - \frac{1}{2} - { (\frac{1}{4} )}^{2} = 0 \\ {(x + \frac{1}{4}) }^{2} - \frac{9}{16} = 0 \\ {(x + \frac{1}{4}) }^{2} = \frac{9}{16} \\ x + \frac{1}{4} = ±( \frac{ 3}{4} ) \\ x = \frac{1}{2} \: or \: - 1[/tex]

Answer:

Step-by-step explanation:

divide each term by 2 to begin with x²

x² + 4x - 1/2 = 0

now add 1 to each side

x² + 4x = 1/2

now divide 4 in half and square the result and add it to each side

x² + 4x + 4 = 1/2 + 4

(x + 2)² = 9/2

Answer:

x=41

Step-by-step explanation:

so since this is a right triangle you can use the Pythagorean Theorem to find the missing side. the two sides you know are 'a' and 'b' and the missing side is 'c'. the theorem says that:

a^2+b^2=c^2

so:

9^2 +40^2=c^2

solve for the exponents:

81 +1600=c^2

1681=c^2

and now, since 1681 is the missing side's length squared, we must find the square root of 1681, which is 41

hope this helps :)

Answer:

[tex] {c}^{2} = {5}^{2} + {4}^{2} \\ {c}^{2} = 25 + 16 \\ {c}^{2} = 41 [/tex]

Answer:

The surface area of the parallelogram is;

2x^3 -6x^2 - 14x +24 squared centimeters

Step-by-step explanation:

To get the area of the parallelogram, we need to multiply the base length of the parallelogram by the height of the parallelogram

We have this as follows;

(x-4)(2x^2+2x-6)

= x(2x^2 + 2x-6) -4(2x^2 + 2x-6)

= 2x^3 + 2x^2 - 6x -8x^2 -8x + 24

= 2x^3 +2x^2 -8x^2 -6x-8x+24

= 2x^3 -6x^2 - 14x +24

Answer:

74-16 square root 10

Step-by-step explanation:

area = (length)^2

= (8- square root 10)^2

= 64- 16 square root 10 + 10

=74-16 square root 10

The area of the square is  [tex]74-16\sqrt{10}[/tex] inches².

Area of square

Let x be the length of square

then area = x²

How to find the square area?

Given the side length of a square is [tex]8-\sqrt{10}[/tex]  inches.

then the area of the square is [tex](8-\sqrt{10} )^{2}[/tex]

therefore,

[tex](8-\sqrt{10} )^{2}= 8^2+(\sqrt{10})^2-2(8)(\sqrt{10})[/tex]

                 [tex]=64+10-16\sqrt{10}[/tex]

                 [tex]=74-16\sqrt{10}[/tex]

Hence the area is [tex]74-16\sqrt{10}[/tex]  inches².

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Answer:

252

Step-by-step explanation:

Answer:

When the dimensions of the shape, such as radius, height, or length change, both surface area and volume also change. However, the volume of the object always changes more than the surface area for the same change in dimensions.

Answer:

(x-5)(x+1)

so x =5

Not a lot of steps involved cause I did it mentally

Hope that answers your question

Step-by-step explanation:

Answer:

c = 10

Step-by-step explanation:

3 is to 6 as 5 is to c:

 3       5

----- = -----

  6       c

Then 3c = 30, and c = 10

Answer:

as 1 mile = 1.609 km

so 5miles = 8.045 km

so 2/3 of the trail = 2/3 × 8.045 = 5.3633333 (ans)

Hope it helps

A trail is 5 miles long. Carlos walks 2/3 of the trail and runs the rest. Carlos walks 5.36 miles.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

A trail is 5 miles long. Carlos walks 2/3 of the trail and runs the rest.

we know that 1 mile = 1.609 km

then, 5 miles = 5 × 1.609

                      = 8.045 km

so, 2/3 of the trail = 2/3 × 8.045

                             = 5.3633

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Answer:

B

Step-by-step explanation:

Answer:

for the empty box in the -4 column put -8 and for the empty box in the 6x column put -18

Answer:

Ok

Explanation:

Step-by-step explanation:

$325x240acres

=$78000

Answer:

x=-1

Step-by-step explanation:

[tex] \frac{x ^{100} + 1 }{x + 1} [/tex]

[tex]x + 1 = 0[/tex]

[tex]x = - 1[/tex]

Answer:

[tex]\frac{10}{7}\cdot a^{3}\cdot y^{4} - \frac{1}{7}\cdot a^{4}\cdot y^{3} - \frac{5}{21}\cdot a^5\cdot y^{2}}[/tex]

Step-by-step explanation:

According to the statement, we have the algebraic equation[tex]\frac{2}{7}\cdot {a^{2}\cdot y^{2}}\cdot \left(5\cdot a\cdot y^{2} - \frac{1}{2}\cdot {a}^{2}\cdot y - \frac{5}{6}\cdot a^{3}\right)[/tex] and we must to rewrite it as a polynomial. Since there are two variables: [tex]a[/tex], [tex]y[/tex], we must observe the following definition of polynomial:

[tex]p(a, y) = \Sigma\limits_{i = 0}^{n} c_{i}\cdot a^{i}\cdot y^{n-i}[/tex] (1)

Where:

[tex]i[/tex] - Index.

[tex]c_{i}[/tex] - i-th Coefficient of the polynomial.

[tex]n[/tex] - Grade of the polynomial.

By means of algebraic handling, we have the following result:

1) [tex]\frac{2}{7}\cdot {a^{2}\cdot y^{2}}\cdot \left(5\cdot a\cdot y^{2} - \frac{1}{2}\cdot {a}^{2}\cdot y - \frac{5}{6}\cdot a^{3}\right)[/tex] Given

2) [tex]\left(\frac{2}{7}\cdot a^{2}\cdot y^{2} \right)\cdot \left(5\cdot a\cdot y^{2}\right) + \left(\frac{2}{7}\cdot a^{2}\cdot y^{2} \right) \cdot \left(-\frac{1}{2}\cdot a^{2}\cdot y \right) + \left(\frac{2}{7}\cdot a^{2}\cdot y^{2} \right)\cdot \left(-\frac{5}{6}\cdot a^{3}\right)[/tex] Associative and distributive properties/[tex](-a)\cdot b = -a\cdot b[/tex]

3) [tex]\frac{10}{7}\cdot a^{3}\cdot y^{4} - \frac{1}{7}\cdot a^{4}\cdot y^{3} - \frac{5}{21}\cdot a^5\cdot y^{2}}[/tex] Associative and commutative properties/[tex]\frac{a}{b}\times \frac{c}{d} = \frac{a\cdot c}{b\cdot d}[/tex]/[tex](-a)\cdot b = -a\cdot b[/tex]/Definition of subtraction/[tex]\frac{a\cdot c}{b\cdot c} = \frac{a}{b}[/tex]/Result

[tex]\huge{ \mathfrak{ \underline{ Answer }}}\: \: ✓ [/tex]

let's divide the figure into two parts :

_____________________________

Area of rectangular prism :

_____________________________

Area of triangular prism :

_____________________________

Volume of whole figure :

_____________________________

[tex]\mathrm{ \#TeeNForeveR}[/tex]

Answer:

maybe 2 minutes?

Step-by-step explanation:

not sure im so sorry!

Answer:

x=21.7

Step-by-step explanation:

cos ø=adjacent/hypotenuse

cos37°=17.3/hypotenuse

hypotenuse=17.3/cos 37°

hypotenuse=21.66

Answer:

C ≥ 9

Step-by-step explanation:

Since they have already spent 15 dollars, and they will spend more than 23, it should at least be 24, but can also be more than 24, so C is greater than or equal to 9 :D

0 solutions.

4x+2 is not = 4x+6

Therefore there will be Jo solutions

Answer:

no solutions

Step-by-step explanation:

Given the 2 equations

y = 4x + 2 → (1)

y = 4x + 6 → (2)

Substitute y = 4x + 2 into (2)

4x + 2 = 4x + 6 ( subtract 2 from both sides )

4x = 4x + 4 ( subtract 4x from both sides )

0 = 4 ← not possible

This indicates the system has no solution

Answer: C

Because if you put then in order(1,3,3,4,9) you will see that once you cross them off the last one will be 3 which would be the median and the answer.

Answer:

A

Step-by-step explanation: