There are thirty three students in the chess club. There are five more boys than girls in the club. Write and solve a system of equations to find the number of boys and girls in the chess club.

By applying algebra, radical and power properties, we find that the simplified form of (√5 + √6) · (√7 - √5) is equal to √35 + √42 - 5 - √30.

How to simplify a product of two binomials with radical numbers

Herein we need to apply algebra and radical and power properties to simplify the expression described in the statement, whose procedure is shown below:

(√5 + √6) · (√7 - √5)     Given

(√5 + √6) · √7 + (√5 + √6) · (- √5)     Distributive property

√7 · √5 + √6 · √7 + √5 · (- √5) + √6 · (- √5)     Distributive property

√35 + √42 - 5 - √30     (- a) · b = - a · b/ √a · √b = √a · b/Result

By applying algebra, radical and power properties, we find that the simplified form of (√5 + √6) · (√7 - √5) is equal to √35 + √42 - 5 - √30.

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The domain of the  f(x)=3x-2 form a graph is -∞ < x<∞. See the attached graph. The interval notation is given as (-∞, ∞)

It is to be noted that the domain of a function is the set of input or argument values for which the function is real and defined. Note from the graph that the function has no undefined points nor domain constraints. Hence, the domina is expressed as the notation:

-∞ < x < ∞.

If one were to solve for x,

Then

y = 3x -2

=

3x -2 = y [Flipping the eqation]
3x -2 + 2 = y + 2 {Added two to both sides]

Hence,

3x = y +2

Divide both sides by 3 to get:

3x/3 = (y+2)/3
x = [1/3y] + [2/3]

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The expression represents a polynomial with  two terms. The constant term is 1 ; leading terms is 7X^4 and leading coefficient is 7

Algebraic expressions that are made up of variables and coefficients are called Polynomials. Variables may be called indeterminates. Arithmetic operations such as addition, subtraction, multiplication can be performed for polynomial expressions but not division. As can be noticed, Polynomial is made up of two terms that are  Poly meaning “many” and nominal meaning “terms.”.

Term with the highest degree is the leading term of a polynomial therefore 7X^4

Coefficient of the leading term is the leading coefficient of a polynomial therefore 7

The expression has only two terms separated by "+" therefore two terms.

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Using  "if" and "only if" for the second definition of ligament gives:

A ligament is a bond of tissue if and only if, it connects bones or hold organs in place.

This is a term used to refer to a type o statement that brings two conditional statement together, Most of the times biconditional statements use if and only if to combine the two conditions.

In the given statement, the two conditions are

Biconditional statements ensures that the two statements are maintained for the statement to be valid.

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Answer:

h-4^10

Step-by-step explanation:

The difference of h and 4 is h-4

to the 10th power, is putting 10 as the exponent.

Answer:

£72.00

Step-by-step explanation:

60*20% (0.20) = 12
60 (original price) + 12 = 72
therefore, the original price of the bag was £72.00

Answer:

7

Step-by-step explanation:

A(3,2) is the element located at row 3, column 2 and that is 7

Answer: 7

Step-by-step explanation:

A₃₂ - the first index is a line, the second index is the column

Their intersection is this number

This number is 7

The values of x that will make this expression equal to 0 are -1 and 9

Given the expression;

(x-9)(x+1)

Let's take the following steps to determine the values

First, expand the bracket, we get;

x² + x - 9x - 9

x² + x - 9x - 9

equate the expression to zero, we have;

x² + x - 9x - 9 = 0

add or subtract the like terms, we get;

x² - 8x - 9 = 0

Factorize the values

x² - 9x + x - 9 = 0

Factor out the common terms in the equation, we get;

x(x - 9) + 1(x - 9) = 0

The equation are;

x + 1 = 0 and x - 9 = 0

Then,

x + 1 = 0

x = -1

x - 9 = 0

x = 9

Thus, the values are - 1 and 9

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The sum of exterior angles of a regular octagon

=360°

Each exterior angle of a regular octagon

=360°/8

=45°

Each interior angle of a regular octagon

=180°-45°=135°

Hope it helps you : )

The statements that are true if the given pairs of triangles are congruent are:

1. ∠A ≅ ∠T; AC ≅ QT; ∠C ≅ ∠Q; ∠ABC ≅ ∠QRT

2. ∠ATF ≅ ∠LYZ; FT ≅ YL

3. B

4. ∠TAW ≅ ∠ERS; AW ≅ ER; WT ≅ SE

5. ∠GER ≅ ∠WAC; GE ≅ AC; AW ≅ ER; RE ≅ WA

If two triangles are congruent to each other, every part of the triangles that corresponds to each other will have congruent or equal measures.

1. Triangle ABC and TRQ are congruent to each other, therefore, the statements that are true are:

2. Triangle FAT and LZY are congruent to each other, therefore, the statements that are true are:

3. Two triangles are congruent if and only if their corresponding parts are congruent, therefore, the answer is: B.

4. Triangle WAT and ERS are congruent to each other, therefore, the statements that are true are:

5. Triangle GRE and CWA are congruent to each other, therefore, the statements that are true are:

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a) Number of points the team has  is 18

b) Number of games lost by the team is  9

a) How many point does the team have?

Number of wins the team has  = W= 5

Number of draws the team has  = D= 3

Number of points of the team = P

The equation is given by,

P = 3W +D

P= 3*5 + 3

P = 15+3

P = 18

Number of points the team has 18 points

b) How many games has this team lost?

Number of points of the team =P = 50

Number of draws the team has = D= 14

Number of wins the team has  = W

Number of matches played by the team =T= 35

The equation is given by,

P = 3W +D

50 = 3W+ 14

3W = 50- 14

3W = 36

W = 12

Rewriting as equation,

Lost matches = Total matches - (Win matches+ Draw matches)

                      = T - (W+ D)

                      = 35 - (12+ 14)

                      =35 - 26

                      = 9

Number of games lost by the team = 9

What is an equation?

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Answer:

59.6°

Step-by-step explanation:

Answer:

[tex](x, y) \rightarrow (-x, y)[/tex]

(Option 3)

Step-by-step explanation:

Let's take into account ΔABC.

A(-2, -2) B(-1, 1) C(3, 2)

This process is entirely trial and error. Try out the different transformations and see which one results the image from the preimage.

In this case, our transformation is (-x, y). Let's put this into trial and error:

[tex]A(-2, -2) \rightarrow A'(2, -2)\\B(-1, 1) \rightarrow B'(1, 1)\\C(3, 2) \rightarrow C'(-3, 2)[/tex]

Simply, the values we got for the image is the same as provided in the question. So we know that option 3 is the right answer.

Answer:

Mackenzie the answer is the 3rd option:)

Step-by-step explanation:

Answer:

a=41

Step-by-step explanation:

Answer:

a = 49

Step-by-step explanation:

41 + a + 90 = 180

solve for a

hope this helped

have a good day ^^

For given data y varies directly with x and the constant of variation is 2.

And the equation is y = 2x

In this question, we have been given some values of x and y.

we need to determine whether y varies directly with x.

If so, find the constant of variation and write the equation.

x = -2, -4, -16

y = -4, -8, -32

Consider the ratio y/x

-4/-2 = 2

-8/-4 = 2

-32 / -16 = 2

As y/x ratio is constant, y varies directly with x.

and the constant of variation is 2.

Also, the equation from given x, y values would be,

y = 2x

Therefore, for given data y varies directly with x and the constant of variation is 2.

And the equation is y = 2x

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Answer:

16

Step-by-step explanation:

Divide to find this answer.

If you're allowed to use a calculator, divide 80÷5 or

80/5 This will give you the answer 16.

If you are not permitted to use a calculator, see attached image for an example of a long division

Answer:

lol its 2x your afh

Step-by-step explanation:

Answer:

4.08.

Step-by-step explanation:

8/100

= 0.08

Answer:

Option 1, 4

Step-by-step explanation:

[tex]\frac{108}{8}=\frac{27}{4}=6.75 \\ \\ 169<170<196 \implies 13<\sqrt{170}<14 \\ \\ \therefore \frac{108}{8}<\sqrt{170}[/tex]

I WILL USE THE REASONS CORRESPONDING ANGLES AND ANGLES ON THE STRAIGHT LINE. SINCE THE DIAGRAM LACKS FULL LABELLING THAT MAKES ME UNABLE TO EXPLAIN MORE USING DEMONSTRATION

[tex]3x - 3 + (4x - 6) = 180 \\ 3x + 4x - 3 - 6 =180 \\ 7x - 9 = 180 \\ 7x = 180 + 9 \\ 7x = 189 \\ \frac{7x}{7} = \frac{189}{7} \\ x = 27[/tex]

ATTACHED IS THE SOLUTION x=27°

Answer:

x = 27

Step-by-step explanation:

3x - 3 and 4x - 6 are same- side exterior angles and sum to 180° , that is

3x - 3 + 4x - 6 = 180

7x - 9 = 180 ( add 9 to both sides )

7x = 189 ( divide both sides by 7 )

x = 27

$ 807.76    is the balance after 3 years by compound interest.

What is compound interest with example?

Given

Principal , P = $675

Rate , r = 6% = 0.06

Time = t years

n = 12             (compounded monthly)

(a)

Balance after t years is given as,

A = P(1 + r/n)nt

A = 675(1 + 0.06/12)12t

A = 675(1.005)12t

Balance after t years =  675(1.005)12t              

(b)

Balance after 3 years =  675(1.005)12*3

= 675(1.005)36

= 675*1.19668

=807.7593 \approx 807.76

Balance after 3 years = $ 807.76          

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The rational numbers are represented by P, Q, R, and S is mathematically given as

This is further explained below.

We make use of the idea of a number line, which displays the actual numbers in ascending order from left to right and from left to right to left.

One unit represents the distance between point U and point T.

It is separated into three sections that are all the same size.

Generally, the equation for TR is mathematically given as

TR = RS = SU

Therefore

TR = RS = SU = 1/3

[tex]R = -1 - (1/3)\\ R= -4/3\\\\S = -1 - (2/3) \\S= -5/3[/tex]

Considering the value of P

[tex]P = 2 + 1/3 = 6/3 + 1/3[/tex]

P= 7/3

Considering the value of Q

[tex]Q = 2 + 2/3 = 6/3 + 2/3[/tex]

Q = 8/3

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From the given statements, the statement which is true when comparing numbers using a number line is :

The number left is always the least.

The definition of a number line is a straight line that shows numbers arranged at equal distances.

A number line is often shown horizontally and can be extended indefinitely in any direction.

Moving right causes the numbers to increase (or become greatest), while moving left causes the numbers to decrease ( or becomes least).

Larger numerals on the number line are always to the left of smaller numbers. Positive numbers have a negative opposite, and negative numbers have a positive opposite. Because it is defined as the distance from zero (the origin) on a number line, the absolute value of any real number is always positive.

Hence the right statement is that the number left is always the least.

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D. The number left is always the least

Answer: Correct option is B)

Put x=3y=4

(3x+4y):(5x+6y)=(3×3+4×4):(5×3+6×4)

                                      =(9+16):(15+24)

                                      =25:39

Step-by-step explanation:

Using proportions, it is found that:

A proportion is a fraction of a total amount, and the measures in the context of a problem are found using basic arithmetic operations such as multiplication and division.

One application of proportions is for ratio problems, as fractions are built from the ratios to find the equivalent amounts.

Caleb noticed that for every 10 orders of cheese pizza there were 7 orders of pepperoni pizza, 5 orders of sausage pizza and 8 orders of mushroom pizza, hence the fraction of Pepperoni pizzas out of the total is given by:

Pepperoni = 7/(10 + 7 + 5 + 8) = 7/30 of the total.

If 35 pepperoni pizzas were ordered, the total number is found as follows:

7x/30 = 35

7x = 30 x 35

x = 30 x 5

x = 150 pizzas.

2 out of every 25 pizzas were burned, hence the number of burned pizzas is given by:

2/25 x 150 = 2 x 6 = 12 pizzas.

The cheese fraction is given by:

10/30.

Hence, out of 360 pizzas, the number is given by:

10/30 x 360 = 10 x 12 = 120 cheese pizzas

The mushroom fraction is given by:

8/30.

Hence, out of 360 pizzas, the number is given by:

8/30 x 360 = 8 x 12 = 96 mushroom pizzas

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the question does not have a solution.

a) graphing - the parabola never crosses the x-axis. When y = 0, what does x equal? none.

b) cannot factor/properly solve for zeros.

Answer:

b

Step-by-step explanation:

The graph was horizontally stretched by a factor of 2.

u vu h,j h j h jcuvugogjjvjccjcjcvk

FISRT RIGHT THEN EQUATION IN THE GENERAL FORM y=mx+c

y=-4-15x

In the y intercept the x coordinate in the axis is 0.

therefore we can plug in the value 0 in the place of x and solve for y

[tex]y = - 4 - 15(0) \\ y = - 4[/tex]

The y intercept is -4.