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Answer:

[tex]s = \sqrt{2a} [/tex]

Step-by-step explanation:

A = 0.5S^2

2A = S^2

Therefore,

[tex]s = \sqrt{2a} [/tex]

To express the length in terms of the area, is an illustration of change of subject of formula.

The equation that express S in terms of the area is: [tex]S =\sqrt{2A}[/tex]

Given that:

[tex]A = \frac 12S^2[/tex]

First, multiply both sides by 2

[tex]2 \times A = \frac 12S^2 \times 2[/tex]

[tex]2 \times A = S^2[/tex]

[tex]2A = S^2[/tex]

Take positive square roots of both sides

[tex]\sqrt{2A} = \sqrt{S^2[/tex]

[tex]\sqrt{2A} = S[/tex]

Rewrite the equation as:

[tex]S =\sqrt{2A}[/tex]

Hence, the equation that express S in terms of the area is: [tex]S =\sqrt{2A}[/tex]

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Answer:

1. 54

2.?

Step-by-step explanation:

:) Have a nice day

Answer:

-8

Step-by-step explanation:

Let n = the number.

A number decreased by twelve is twice the opposite of ten.

n - 12 = 2 * (-10)

n - 12 = -20

n = -8

Answer:

m > 6

Step-by-step explanation:

[tex]3/2m -4 > 4/5 + 7/10m​\\\\\frac{3}{2}m-4>\frac{4}{5}+\frac{7}{10}m\\\\\mathrm{Add\:}4\mathrm{\:to\:both\:sides}\\\frac{3}{2}m-4+4>\frac{4}{5}+\frac{7}{10}m+4\\\\Simplify\\\\\frac{3}{2}m>\frac{24}{5}+\frac{7}{10}m\\\\\mathrm{Subtract\:}\frac{7}{10}m\mathrm{\:from\:both\:sides}\\\\\frac{3}{2}m-\frac{7}{10}m>\frac{24}{5}+\frac{7}{10}m-\frac{7}{10}m\\\\Simplify\\\\\frac{4}{5}m>\frac{24}{5}\\\\\mathrm{Multiply\:both\:sides\:by\:}5\\\\5\times\frac{4}{5}m>\frac{24\times\:5}{5}\\\\Simplify\\\\4m>24[/tex]

[tex]4m>24\\\\\mathrm{Divide\:both\:sides\:by\:}4\\\frac{4m}{4}>\frac{24}{4}\\\\Simplify\\\\m> 6[/tex]

Answer:

The perimeter of the triangle in centimetres is (9.1p + 2.4q - 4.1) centimetres

Step-by-step explanation:

Let a, b and c be the sides off a triangle. Its perimeter P = a + b + c.

Now, the triangle has side lengths (5.3p+ 7.6) centimetres, (3.8p – 4.3) centimetres, and (2.4q - 7.4) centimetres.

Let a = (5.3p+ 7.6) cm , b = (3.8p – 4.3) cm and c = (2.4q - 7.4) cm

So the perimeter of the triangle is P = a + b + c

substituting the values of a, b and c, we have

P = (5.3p + 7.6) cm + (3.8p – 4.3) cm + (2.4q - 7.4) cm

opening the brackets and collecting like terms, we have

P = (5.3p + 3.8p + 2.4q + 7.6 - 4.3 - 7.4) cm

P = (9.1p + 2.4q - 4.1) centimetres

So the perimeter of the triangle in centimetres is (9.1p + 2.4q - 4.1) centimetres

Answer: P(x) has a constant rate of change, but A(x) does not

Step-by-step explanation:

Answer:

2x +  y = 11

a² + b = 9

Step-by-step explanation:

I solved these by using order of operations and subsitution.

Answer:

y=2/5x + 7

Step-by-step explanation:

First, you have to rewrite 2x-5y=15 to slop intercept form.

To do that you have to first subtract 2x from both side to cancel it out.

2x- 2x-5y= 15 -2x.    

-5y= -2x+15

Next, you divide 5 on both side to leave the y by itself.

y= -2x/-5 + 15/-5

Simplify

y= 2/5x + (-3)                     2/5 is our slope

Now that we found the slope, we need to the y-intercept of line b

y=2/5x + b

To find the y-intercept, we substitue x and y with the coordinates (-10,3)

3= 2/5(-10) +b

Now we just solve for b

3= -4 +b

3-(-4) = b

7=b

Now we have identified that 7 is the y intercept

The full equation is y= 2/5x +7

I hope this helped :)

Answer:

900 feet per hour

Step-by-step explanation:

225×4 = 900

15×4=60

the tortoise's rate of speed is 900 feet per hour

hope that helps.

Answer:

1.37 * 10^10 years.

Step-by-step explanation:

Billion = 9 zeroes

13.7 billion = 13.7 * 10^9 = 1.37 * 10^10.

Answer:

Their place values

Step-by-step explanation:

On eight is in thousands while the other is in hundreds

Answer:

"8" on the left is ten times the value of the "8" on the right

Step-by-step explanation:

I am going to assume that the comma " , " denotes divisions of "thousands" and not the European system where the comma represents a decimal point.

(refer to attached for definitions of place values)

we can see that for the number 8,809 :

1) the 8 on the left is in the thousands place and hence represents 8000.

2) the 8 on the right is in the hundreds place and hence represents 800.

in order to find the relative order of difference between the two digits, we simply we divide the value of the two digits:

8000 ÷ 800 = 10

Hence the "8" on the left is ten times the value of the "8" on the right

Answer:

There are 76 oatmeal raisen cookies altogether.

Step-by-step explanation:

4 + 11 = 15

285/15 = 19

19 * 4 = 76

Answer:

TC = 36t + 25

Step-by-step explanation:

The amount paid by Carla as a storage fee or fixed cost = $25

Monthly rent or variable cost = $36

Let the number of months = t

Now we have to find the expression that represents the total cost. Below is the formula to find the expression.

Total cost = Variable cost + Fixed cost

Total cost = 36t + 25

TC = 36t + 25

Answer:

27

Step-by-step explanation:

20=v-7

v=20+7

v=27

Hence, v equals to 27

[tex]\huge\mathbb\purple{EXPLAIN}[/tex]

[tex]20 = v - 7[/tex]

[tex]v = 20 + 7 = 27[/tex]

Answer:

Step-by-step explanation:

Answer:

[tex]1\frac{1}{15}[/tex]

Step-by-step explanation:

[tex]\frac{7}{5}+\frac{2}{3}-1\\[/tex]

Convertir elemento a fracción: 1 = 1/1

[tex]=-\frac{1}{1}+\frac{7}{5}+\frac{2}{3}[/tex]

Mínimo común múltiplo de 1,5,3 = 15

Ajustar fracciones según el mcm

[tex]=-\frac{15}{15}+\frac{21}{15}+\frac{10}{15}[/tex]

Dado que los denominadores son iguales, combine las fracciones:

[tex]\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\= \frac{-15+21+10}{15}\\\\[/tex]

Sumar Restar los números: -15 + 21 + 10 = 16

[tex]=\frac{16}{15}\\\\16\div 15 = 1 \: remainder 1\\\\=1\frac{1}{15}[/tex]

Answer:

yellow

Step-by-step explanation:

ITS YELLOW IM GOOD AT THIS TRUST ITS YELLOW

whats the answer 5(x-y+2)

Answer :

5x - 5y + 10

Step-by-step explanation:

5(x - y + 2)

5(x) + 5( - y) + 5(2)

5x - 5y + 10

[tex]\boxed{\boxed{\bold{THANKS}}} [/tex]

Answer:

(a). y = 5

(b). RS = 28

     ST = 19

     RT = 47

Step-by-step explanation:

(a). There are three points R, S and T on a number line.

Therefore, RT = RS + ST -------(1)

Since, RT = 10y - 3

RS = 5y + 3

ST = 3y + 4

By substituting these values in the equation (1)

10y - 3 = (5y + 3) + (3y + 4)

10y - 3 = 8y + 7

10y - 8y = 7 + 3

2y = 10

y = 5

(b). RS =  5y + 3

           = 25 + 3

           = 28

      ST = 3y + 4

           = 15 + 4

           = 19

      RT = 10y - 3

            = 50 -3

            = 47  

Answer:

y = x² + 2x - 48

Step-by-step explanation:

Given the roots of the polynomial are x = 6 and x = - 8 , then the corresponding factors are

(x - 6) and (x + 8) and the polynomial is the product of the factors, that is

y = (x - 6)(x + 8) ← expand using FOIL

y = x² + 2x - 48

Answer:

number of girls = 90

Number of boys = 125

Number of adults = 20

Step-by-step explanation:

Total people at the summer camp= 235

Let

number of girls=x

Number of boys = x + 35

Number of adults = x - 70

Total people at the summer camp= number of girls + Number of boys + Number of adults

235 = x + (x+35) + (x - 70)

235 = x + x + 35 + x - 70

235 = 3x - 35

Add 35 to both sides

235 + 35 = 3x

270 = 3x

Divide both sides by 3

x= 270/3

= 90

x = 90

number of girls= x = 90

Number of boys = x + 35

= 90 + 35

= 125

Number of adults = x - 70

= 90 - 70

= 20

Total = 90 + 125 + 20

= 235

Answer:

There are 90 girls, 125 boys, and 20 adults.

Step-by-step explanation:

Let x be the number of girls. How many boys were there?

x + 35

How many adults were there?

x - 70

We know that 235 people are at RSM summer camp. Use this to make an equation.

x + (x + 35) + (x - 70) = 235

x + x + 35 + x - 70 = 235

3x - 35 = 235

3x - 35 + 35 = 235 + 35

3x = 270

3x ÷ 3 = 270 ÷ 3

x = 90

x, x + 35, x - 70

90, 125, 20

Answer:

0.31 - 0.39

Step-by-step explanation:

3/10 = 0.3

2/5 = 0.4

All the values between 0.3 and 0.4 excluding 0.3 and 0.4 (can't be 0.3 or 0.4)

The decimal number that is greater than 3/10 and less than 2/5 will be;

⇒ 0.35

A decimal number is a number that consists of a whole and a fractional part.

Given that;

A decimal number is greater than 3/10 and less than 2/5.

Now,

Let a decimal number = x

So, We get;

⇒ 3/10 < x < 2/5

Since, We have;

⇒ 3/10 = 0.3

⇒ 2/5 = 0.4

Thus, The decimal number that is greater than 3/10 and less than 2/5 is 0.35.

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m₁ = 10/3

m₂ = 1/2

6m² - 23m + 10 = 0​

6m² - 2m - 20m + 10 = 0

3m(2m - 1) - 10(2m - 1) = 0

(3m - 10)(2m - 1) = 0

3m - 10 = 0 =>3m = 10 => m₁ = 10/3

2m - 1 = 0 => 2m = 1 => m₂ = 1/2

Answer:

y=3/5

Step-by-step explanation:

9y+6=9+2y+2y

9y+6=9+4y

9y-4y=9-6

5y=3y=3/5

Answer: function

Step-by-step explanation: To determine whether the relation shown here

is a function, remember that a relation is a function if each x term

corresponds to exactly one y term.

In the data set show, each x term, -2, 9, 1, 3, and 10 appears only once.

This means that each x term corresponds to exactly one y term.

So yes, the relation is a function.

Answer:

ED and EC

Step-by-step explanation:

If the two rays which extend in the opposite direction having same endpoint is said to be opposite rays.

From the picture attached,

Rays having same endpoint E but not in the opposite directions are ED and EC.

This pair of rays meet at point E having different directions.

Similarly EA and EB is the other pair of rays having same end point (at E) but not in opposite directions.