Tell whether the ratios form a proportion. 3/7 , 12/21

Answer:

[tex]6\sqrt{7}[/tex]

Step-by-step explanation:

If you bring 252 to its prime numbers, its 2, 2, 3, 3, and 7. Just multiply 2 and 3 and you get 6 root 7.

The expression equivalent to the square root of 252 is 6[tex]\sqrt{7}[/tex].

That number which can be divided by itself or 1 only. eg. 2, 3, 5, 7, 11, 13 etc.

Given value,

252

Expressed in prime numbers as:

252 = 2x2x3x3x7 or [tex]2^{2}[/tex] x [tex]3^{2}[/tex] x 7

∴ [tex]\sqrt{252}[/tex] = 2x3 [tex]\sqrt{7}[/tex] = 6 [tex]\sqrt{7}[/tex]

Hence [tex]\sqrt{252}[/tex] can be expressed as 6 [tex]\sqrt{7}[/tex]. Similarly any real number can be represented as the product of prime numbers.  

To learn more about prime numbers, refer to the link:

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Answer:

45, 46, 33, 0, 6

Step-by-step explanation:

Answer:

vertical

Step-by-step explanation:

Answer:

If 30 unicorns out of 300 walk away then it will be 300-30=270 unicorns left.

If 50 dragons fly away out of 200 then it will be 200-50=150.

Therefore there are 270 unicorns and 150 dragons left.

I hope this helps you...Thank you...

Answer:

x = 5, y = -2

Step-by-step explanation:

Given equations:

From the first equation we get:

Substitute x in the second equation, find y:

Find x:

Answer:

The dimensions of the field is 185 yards by 48 yards

Step-by-step explanation:

Here, we are interested in calculating the dimensions of the field.

Let the width of the field be x yards

From the question, we are made to know that the length of the field is 7 yards less than quadruple ( 4 times) the width

So mathematically, the length of the field will be ;

(4x -7) yards

The perimeter of the field mathematically is:

2(l + b)

Thus;

2(x + 4x- 7) = 466

2(5x -7) = 466

divide both side by 2

5x - 7 = 466/2

5x - 7 = 233

5x = 233 + 7

5x = 240

x = 240/5

x = 48 yards

Length of field is; 4x -7 = 4(48) -7 = 192 - 7 = 185 yards

Answer:

(2,5) and (5,8)

Step-by-step explanation:

you can just plug in the numbers to get your answer and if two numbers aren't the same then its not a solution

example: (2,5)

5 = 2 + 3

5 = 5

5 does equal 5 making it a solution because it makes sense right?

example: (4,6)

6 = 4 + 3

6 = 7

this isn't a solution because six doesn't equal 7

Answer:

[see below]

Step-by-step explanation:

[tex]y=x+3[/tex]

The ordered pair is a solution.

The ordered pair is not a solution.

The ordered pair is a solution.

[tex]7=3+3\\\\\boxed{7\neq 6}[/tex]

The ordered pair is not a solution.

Hope this helps.

Nope

Step-by-step explanation:

Pi is an irrational number because it can not be expressed by a simple fraction.

Answer: No it's a rational number

Step-by-step explanation:

Answer:

The number of ducks Old Mc Donald raises are 23 and the number of cows Old Mc Donald raises are 77.

Step-by-step explanation:

We are given that Old Mc Donald raises ducks and cows. The animals have a total of 100 heads and 354 feet.

Let the number of ducks Old Mc Donald raises be 'x' and the number of cows Old Mc Donald raises be 'y'.

So, according to the question;

                                   [tex]x+y=100[/tex]

                                    [tex]x=100-y[/tex]  -------------------- [equation 1]

{because one head of a duck and one head of cow}

                                   [tex]2x+4y=354[/tex]

                                   [tex]x+2y=177[/tex]   --------------- [equation 2]

{because there are two feet of a duck and four feet of cow}

Now, putting the value of x in equation 2 we get;

                                  [tex]100-y+2y=177[/tex]

                                  [tex]y=177-100[/tex]

                                    y = 77 cows

Putting this value of y in equation 1 we get;

                                 x = 100 - y

                                 x = 100 - 77 = 23 ducks

Hence, the number of ducks Old Mc Donald raises are 23 and the number of cows Old Mc Donald raises are 77.

Answer:

The answer is -7

5k=-30-5.

5k=-35.

k= -7.

Hi there! Hopefully this helps!

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[tex]-30=5k+5[/tex]

Swap sides so that all variable terms are on the left hand side.

[tex]5k+5=-30[/tex]

Subtract 5 from both sides.

[tex]5k=-30-5[/tex]

Subtract 5 from −30 to get −35.

[tex]5k=-35[/tex]

Divide both sides by 5.

[tex]k=\frac{-35}{5}[/tex]

You can also do "5(-7) + 5 = ??" For proof.

Answer:

(D) ab + bc =ad

    ab-ad = -bc

    a(b-d) =bc

     a = bc / b-d

(e) The Pythagoras Theorem states that in a Right angled triangle the {hypotenuse}^2 = {opposite}^2 + {adjacent}^2

Step-by-step explanation:

Answer:

x-6 = -4

Step-by-step explanation:

3x - 8= -2

Add 8 to each side

3x - 8+8= -2+8

3x = 6

Divide by 3

3x/3 = 6/2

x =2

We want to find x-6

2-6 = -4

Answer: - 4

Step-by-step explanation:

3x - 8 = -2

3x = -2 + 8

3x = 6

x = 6/3

x = 2

so, therefore x - 6 => 2 - 6 = -4

Answer:

$7

Step-by-step explanation:

t = ticket price

We know the total cost of the ticket and snacks was $15, and just the snacks were $8 so:

t + $8 = $15

To find the amount of the ticket, subtract $8 from each side

t + $8 - $8 = $15 - $8

The $8 cancels and you're left with

t = $7

So the ticket costs $7

The remaining cost after the snack cost is the cost of the movie ticket and it is $7.

To subtract in mathematics is to take something away from a group or a number of objects.

In a different sense, subtraction refers to a mathematical procedure where two values will be subtracted to produce a new value.

Total spent = cost of snacks + cost of a movie ticket

Given that,

Total spent = $15

Cost of snacks = $8

So,

15 = 8 + cost of movie ticket

Cost of movie ticket = 15 - 8 = $7

Hence "The remaining cost after the snack cost is the cost of the movie ticket and it is $7".

For more about subtraction,

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Answer:

A rational number is a number able to be put into a fraction, an irrational number is not able to be. Therefore, when adding the two, the rational and the irrational will be irrational. For example, 2 is a rational number, and 1.8903 is irrational. If you add the two, you will get 3.18903, which is unable to be put into a fraction.

Answer:

a

Step-by-step explanation:

Since we have a negative slope, that means the correlation for the scatter plot also has to be negative.

Since the only scatter plot that has a negative correlation is graph A, a is our answer.

Answer: (-0.5, 4)

Step-by-step explanation:

Midpoint formula: [tex](\frac{x1+x2}{2} ,\frac{y1+y2}{2} )[/tex]

(x1, x2)=(2, -3)

(y1, y2)=(2, 6)

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

 [tex](\frac{x1+x2}{2} ,\frac{y1+y2}{2} )[/tex]

=[tex](\frac{2-3}{2} ,\frac{2+6}{2} )[/tex]

=[tex](\frac{-1}{2} ,\frac{8}{2} )[/tex]

=[tex](-0.5, 4)[/tex]

Hope this helps!! :)

Please let me know if you have any question or need further explanation

Answer:

[tex]M=(-\frac{1}{2},4)[/tex]

Step-by-step explanation:

The midpoint formula is given by:

[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Let (2,2) be x₁ and y₁ and let (-3,6) be x₂ and y₂. Therefore:

[tex]M=(\frac{2+-3}{2},\frac{2+6}{2})[/tex]

Simplify:

[tex]M=(-\frac{1}{2},\frac{8}{2})\\M=(-\frac{1}{2},4)[/tex]

Answer:

x≤-4

Step-by-step explanation:

There is one very important exception to the rule that multiplying or dividing an inequality is the same as multiplying or dividing an equation. Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign.

8x≤-32

1. Divide both sides by 8

Answer: I am pretty sure it is a rational number!

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

AB = 3x + 4 and AC which is twice of AB is equal to 11x - 17

2 (3x + 4) = 11x - 17

6x + 8 = 11x - 17

8 + 17 = 11x - 6x

25 = 5x

5 = x

AC = CD = 11x - 17 ➡ 11×5 - 17 = 38

CD = 38 and DE = 49 - 38 = 11

Answer:

D,

Step-by-step explanation:

that's because you only factorise when you have a common factor, ax-3b cannot be factorised because they have nothing in common so it is wrong to use x to factorise it. If you want to be sure that it is not factorisable, try expanding it and you'll see that you will not get the same answer.

Answer:112

Step-by-step explanation: Line SW is 180 degrees since it is a straight line. Subtract angle TBU 18 and angle UBW 50 from line SW 180 to get angle SBU which is 112.

Answer:

10^(-1)

Step-by-step explanation:

Recall that a value that is multiplied by a number that is between 0 and 1 will result in a number that is smaller than the original number.

the first 3 are all greater than 1, hence will result in a greater value if when multiplied with another number.

The last one is 10^(-1) = 0.1

Anything multiplied by 0.1 will result in a value that is 1/10th of the original value.

Hence this is the answer.

Answer:

10/\-1 is correct

Step-by-step explanation:

Answer: (2 1/2, 0) (the last option)

Step-by-step explanation:

I guess the function is:

f(x) = (2  1/2) - (3  1/2)*x

now, the rule for f-1(x) that we know is:

f-1( f(x) ) = x.

So if we want to find the x-intercept of f-1(x), we must evaluate it in f(0)

f-1(f(0)) = 0.

And we have that f(0) = (2  1/2) - (3  1/3)*x = 2  1/2

This means that the x-intercept of f-1(x) will be when x= 2  1/2, so the intercept is:

(2 1/2, 0)

Answer:

5/8

Step-by-step explanation:

1 man, 4 women out of 8 people total

Answer:

k=6

Step-by-step explanation:

25=19+k

Subtract 19 from each side

25-19=19-19+k

6 = k

Answer:

k = 6

Explanation:

to find the value of k in the equation provided, you must subtract nineteen from both sides. this will isolate the variable.

25 = 19 + k

25 - 19 = 19 - 19 + k

6 = k

k = 6

therefore, the value of the variable k in 25 = 19 + k is 6.

Answer:

Step-by-step explanation:

Given the incomplete quadratic equation [tex]\[x^2 + \dfrac{4}{5}x + \underline{~~~~}\][/tex], we are to complete it so that the result will be the square of a binomial. To do that, we will use the completing the square method.

Completing the square method is a way of completing a quadratic equation by solving for a constant to add that will make the quadratic equation a perfect square of a binomial.

To get the constant term using the method, we will take the square of the alf of the coefficient of x in the equation given.  

Coefficient of x = 4/5

half of the coefficient of x = 1/2(4/5)

half of the coefficient of x = 4/10 = 2/5

Square of the half of the coefficient of x = (2/5)²

Square of the half of the coefficient of x = 4/25

Hence the constant that we will use to complete the equation to make if a square of a binomial is 4/25

The equation will become:

[tex]= \[x^2 + \dfrac{4}{5}x +\dfrac{4}{25} \\\\= \[x^2 + \dfrac{4}{5}x +(\dfrac{2}{5})^2\\\\= (x +\dfrac{2}{5})^2[/tex]

Hence the constant value that will make the resulting quadratic the square of a binomial is 4/25

Answer:

4/25

Step-by-step explanation:

Suppose the quadratic is the square of the binomial $x+c.$ We have $(x+c)^2 = x^2+2cx + c^2.$ Comparing the linear term of $x^2 + 2cx+c^2$ to the linear term of $x^2 + \frac{4}{5}x + \underline{~~~~},$ we have $2c = \dfrac{4}{5},$ so $c = \dfrac{2}{5}.$ Therefore, the constant term is

\[c^2  = \left(\dfrac{2}{5}\right)^2 = \boxed{\frac{4}{25}}.\]

Answer:

19.84 Miles

give or take

Step-by-step explanation:

1 km is .62 miles

.62 x 32 = 19.84

Answer:

19.88 miles

Step-by-step explanation: