In a hockey club there are 5% more boys than there are girls. If there is a total of
246 members in the club, what is the number of boys and the number of girls?
HOW WOULD I WORK THIS OUT

To simplify expressions, one needs to apply rules correctly, such as combining like terms and using exponentiation rules. The process includes correctly applying the rule that simplifies multiplications of the same base by adding their exponents. Cubing exponentials involves multiplying the original exponent by 3.

To simplify mathematical expressions, it's crucial to follow the correct rules and operations. In this case, the example provided shows the exponentiation and multiplication rules. Specifically, when dealing with expressions like 3².3⁵, this is equivalent to multiplying 3 x 3 and then taking that result and multiplying it by 3 five more times. According to the rule xPx9 = x(p+q), where x is the base and p and q are the exponents, it simplifies to adding the exponents when the base number is the same and multiplied together.

The process of simplifying expressions involves several steps:

Additionally, when cubing exponentials, one should cube the digit normally and multiply the existing exponent by 3, a rule demonstrated in squaring operations as well.

Answer: First option is correct.

Step-by-step explanation:

Since we have given that

There is a geometric sequence:

where a₁ = 2

r = √2

We need to find a₉:

As we know the formula for "nth term ":

[tex]a_n=ar^{n-1}\\\\a_9=ar^{9-1}\\\\a_9=ar^8\\\\a_9=2\times (\sqrt{2})^8\\\\a_9=32[/tex]

Hence, First option is correct.

Answer:

[tex]1\frac{2}{5}[/tex] gallon of milk is needed to make one gallon of ice cream

Step-by-step explanation:

Using unitary method,  

Unitary method is a method use to find the value of a unit quantity.

[tex]6\frac{3} {10}[/tex] gallon of milk needed to make [tex]4\frac{1}{2}[/tex] gallon of milk

[tex]\frac{63}{10}[/tex] gallon of milk needed to make [tex]\frac{9}{2}[/tex] gallon of ice cream

One gallon of ice cream needed = [tex]\frac{63}{10} \times \frac{2}{9}[/tex] gallon of milk

                                                        = [tex]\frac{7}{5}[/tex] gallon of milk

                                                         = [tex]1\frac{2}{5}[/tex] gallon of milk

Thus, [tex]1\frac{2}{5}[/tex] gallon of milk is needed to make one gallon of ice cream.

factor X + 1 is the answer

Answer:

(x+2)(x+4)

Step-by-step explanation:

central angle theta (in radians) = arc length / radius

So theta = 5.6/8 = 0.7 radians

The central angle measure for a circle with an 8 cm radius and a 5.6 cm intercepted arc length is 0.7 radians.

The question asks to find the measure in radians for the central angle of a circle with a radius of 8 cm and an intercepted arc length of 5.6 cm. To calculate the central angle in radians, we use the formula θ = [tex]\frac{l}{r}[/tex], where θ is the central angle in radians, l is the arc length, and r is the radius of the circle. Substituting the given values, we get θ =  [tex]\frac{5.6}{8}[/tex]

Through calculation, θ = 0.7 radians. So, the measure of the central angle that intercepts an arc length of 5.6 cm in a circle with a radius of 8 cm is 0.7 radians.

All the given expressions are binomials except the expression in (i) which is a trinomial.

What are binomials in expressions?

Binomials can be defined as the expression that contains two variables that are different in terms.

ii.) 5x³* 2x²- 10x⁴+3x⁵+ 3x * (-2)x⁴

= 10x⁵-10x⁴+3x⁵-6x⁵

= 7x⁵+10x⁴ (this is an example of a binominal)

iii.) (t+2)²- 4t = t²+ 4t+4-4t = t²+4(binomial)

iv.) 5(a-1)-10(a-1)+100(a-1)

= 5a-5-10a+10+100a-100

= 95a - 95 (binomials)

v.) (2πr-πr²)r-(2πr-πr²)2r

= 2πr²-πr³-4πr²+2πr³

= -2πr²+πr³(binomials)

Answer:

Step-by-step explanation:

11.4

Answer:

Your answer is D :)

Step-by-step explanation:

No explanation :) <3

Answer:

The answer is 72 degrees

Step-by-step explanation:

The picture that Helpmetnx showed does work. But they made a mistake and assumed that the diagonal is a angle bisector, and it's not.

1. rectangle ABCD, BD & AC are the diagonals. ∠ABD =36 degrees

2. ∠ABD= ∠BDC = 36 - alternate interior angles

3. ∠DBC = 90 - 36 = 54. ∠DBC =∠ADB = ∠BCA = 54

4. Now we know that the triangle formed between the two diagonals is a isosceles triangle because of base angle theorem.

5. 180 - 54*2 = 72 degrees

I hope this helps!

Answer: The answer is actually 6.

Step-by-step explanation:

The value of x is 6, rounded to the nearest whole number.

To solve for x given the conditions:

1. Define the variables based on the problem:

  - Length of the rectangle [tex](\( L \)) = \( x + 2 \)[/tex]

  - Width of the rectangle [tex](\( W \)) = \( 2x - 5 \)[/tex]

2. Write the equation for the area of the rectangle:

  - Area [tex](\( A \)) = \( L \times W \)[/tex]

  - Given that the area is 56 cm², we have:

[tex]\[ (x + 2)(2x - 5) = 56 \][/tex]

3. Expand the equation:

[tex]\[ (x + 2)(2x - 5) = 2x^2 - 5x + 4x - 10 = 2x^2 - x - 10 \][/tex]

4. Set up the equation:

[tex]\[ 2x^2 - x - 10 = 56 \][/tex]

5. Move all terms to one side of the equation to set it to zero:

[tex]\[ 2x^2 - x - 10 - 56 = 0 \] \[ 2x^2 - x - 66 = 0 \][/tex]

6. Solve the quadratic equation using the quadratic formula:

[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]\\ where \( a = 2 \), \( b = -1 \), and \( c = -66 \).[/tex]

7. Calculate the discriminant:

[tex]\[ \Delta = b^2 - 4ac = (-1)^2 - 4(2)(-66) = 1 + 528 = 529 \][/tex]

8. Calculate the roots:

[tex]\[ x = \frac{-(-1) \pm \sqrt{529}}{2(2)} = \frac{1 \pm 23}{4} \][/tex]

So, the solutions are:

[tex]\[ x = \frac{1 + 23}{4} = \frac{24}{4} = 6 \][/tex]

and

[tex]\[ x = \frac{1 - 23}{4} = \frac{-22}{4} = -5.5 \][/tex]

Since x must be a positive value in the context of this problem, we have: x = 6

9. Verify the solution:

Length L = x + 2 = 6 + 2 = 8 cm

Width W = 2x - 5 = 2(6) - 5 = 12 - 5 = 7  cm

Area = [tex]\( 8 \times 7 = 56 \)[/tex] cm², which matches the given area.

Therefore, ( x = 6).