What is the coeficient of n in the following expression?
m+3n+5

Answer:

Let us take 'a' in the place of 'y' so the equation becomes

(y+x) (ax+b)

Step-by-step explanation:

Step 1:

(a + x) (ax + b)

Step 2: Proof

Checking polynomial identity.

(ax+b )(x+a) = FOIL

(ax+b)(x+a)

ax^2+a^2x is the First Term in the FOIL

ax^2 + a^2x + bx + ab

(ax+b)(x+a)+bx+ab is the Second Term in the FOIL

Add both expressions together from First and Second Term  

= ax^2 + a^2x + bx + ab

Step 3: Proof

(ax+b)(x+a) = ax^2 + a^2x + bx + ab

Identity is Found .

Trying with numbers now

(ax+b)(x+a) = ax^2 + a^2x + bx + ab

((2*5)+8)(5+2) =(2*5^2)+(2^2*5)+(8*5)+(2*8)

((10)+8)(7) =(2*25)+(4*5)+(40)+(16)

(18)(7) =(50)+(20)+(56)

126 =126

Answer:

6

Step-by-step explanation:

The given expression is,

[tex]\frac{5^{x+2}-5^x }{5^x\times4}[/tex]

Now, we know that,

[tex]a^{m+n} = a^m . a^n[/tex]

Then,

[tex]5^{x+2}=5^x . 5^2[/tex]

So,

[tex]\frac{5^{x+2}-5^x}{5^x\times4}=\frac{5^x.5^2-5^x}{5^x\times4}[/tex]

Now, taking [tex]5^{x}[/tex] common from the numerator of the given expression, then

[tex]\frac{5^{x+2}-5^x}{5^x\times4}=\frac{5^x(5^2-1)}{5^x\times4}[/tex]

[tex]\implies\frac{5^{x+2}-5^x }{5^x\times4}=\frac{5^2-1}{4}[/tex]

[tex]\implies\frac{5^{x+2}-5^x}{5^x\times4}=\frac{5\times5-1}{4}=\frac{25-1}{4}[/tex]

[tex]\implies\frac{5^{x+2}-5^x}{5^x\times4}=\frac{24}{4}=6[/tex]

So, the simplified form of the given expression gives the result 6.

Answer:

There are 126 $1 bills and 21 $5 bills.

Step-by-step explanation:

Given,

Total cash Amount = $231

Solution,

Let the number of $1 bill be 'x'.

And  the number of $5 bill be 'y'.

Now according to question, one-dollar bills is six times of five-dollar bills.

So, we can frame it in equation form as;

[tex]x=6y[/tex]   ⇒ equation 1

Again according to question, there is only one-dollar bills and five-dollar bills, and no change.

That means the total cash amount is in the form of $1 and $5.

So, we can frame the above sentence in equation form as;

[tex]1\times x+5\times y=231\\\\x+5y=231[/tex]⇒ equation 2

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

[tex]6y+5y=231\\\\11y=231\\\\y=\frac{231}{11}=21[/tex]

So, [tex]x=6y=6\times 21=126[/tex]

Hence There are 126 $1 bills and 21 $5 bills.

Answer:

0.56

Step-by-step explanation:

First, we need to look at the size of the image as a whole. It is 10x10, so it has 100 squares within it.

When counted, there are 56 shaded squares.

This gives us [tex]\frac{56}{100} =0.56[/tex]

the answer is 0.56, because there’s 56 shades squares.

Explanation: there’s 100 squares, 56 are shaded 56/100.

Answer:

2x + 45 = 6

Step-by-step explanation:

(2/9)x + 5 = 2/3                        Subtract 5 from both sides

(2/9)x +5-5=2/3-5

(2/9)x = - 4 1/3                          Multiply by 9

2x = -13/3 * 9

2x = -39

x = -19.5

==============

I see. You don't want it solved. Multiply by 9 to clear the fractions.

==============

2x + 45 = 6

==============

Solve it now. It should be easier.

2x = 6 - 45

2x = - 39

x = -19.5

Answer:

Rank 1 - plane.

Rank 2- line.

Rank 3- point.

Step-by-step explanation:

Here,  I have given the ranks based on what includes what.

Rank 1 is given to plane because infinite lines together makes a planes

and infinite points together makes a line.

so, Rank 1 includes both Rank 2 and Rank 3.

Now, Rank 2 is line because it consists of infinite number of points together

and is used to form a plane.

Rank 3 is point as it is the basic thing for any line or plane

See, it is simple, group of points make a line and group of lines make a plane.

visualize it this way,

When you zoom too in a plane, you see a line and when you zoom too in a line, you see a point.

For every 7 boys there are 5 girls.

Divide the number of boys by the ratio for boys: 28 / 7 = 4

Now multiply that by the ratio for girls:

4 x 5 = 20

There are 20 girls.

Answer: A

Step-by-step explanation:

The standard form of this complex number is A. 3/13 + 2/13i

=3+2i/9-4(-1)

=3+2i/9+4

=3+2i/13

Complex numbers in mathematics. Complex numbers are numbers expressed in the form of a + ib. Here, a and b are real numbers, and "i" is an imaginary number called "iota". The value of i = (√-1). For example, 2 + 3i is a complex number, 2 is a real number (Re), and 3i is an imaginary number.

Complex numbers are numbers that consist of two parts: real and imaginary. Complex numbers are more complex mathematical components such as algebra. They can be applied to many aspects of real life, especially electronics and electromagnetism.

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Answer:

-22.25

Step-by-step explanation:

-31.7+4.5(2.1)

-31.7+9.45

-22.25

Ahmed could have gained 61 rupees more, if had given had given in compound interest.

Solution:

Given that Ahmed lent amir Rs8000 at simple interest for 3 years at the rate of 5% per annum

Simple Interest calculation:

Principal = 8000

Rate of interest = 5%

Time = 3

Formula:

[tex]S.I=\frac{p\times n\times r}{100}[/tex]

Where , "p" is the principal and "n" is the number of years and "r" is the rate of interest

Substituting the values in formula,

[tex]S.I = \frac{8000 \times 3 \times 5}{100}\\\\S.I = 80 \times 3 \times 5 = 240 \times 5\\\\S.I = 1200[/tex]

Compound Interest calculation:

Principal = 8000

Rate of interest = 5% compounded annually

Time = 3

Formula:

[tex]C.I=P(1+\frac{R}{100})^n-P[/tex]

Substituting the values in formula,

[tex]\Rightarrow C.I=8000(1+\frac{5}{100})^3-8000\\\\\Rightarrow C.I=9261-8000\\\\\Rightarrow C.I=1261[/tex]

Therefore, the difference between the interests:

1261 - 1200 = 61

Thus he could have gained 61 rupees more, if had given had given in compound interest.

Answers:

x = 6

y = 6*sqrt(2)

=======================

Explanation:

To find these values, you can use the general template of a 45-45-90 triangle or you can use trig ratios

tan(45) = 1

tan(angle) = opposite/adjacent

tan(45) = x/6

1 = x/6

6*1 = x

x = 6

-------

sin(45) = 1/sqrt(2)

sin(angle) = opposite/hypotenuse

sin(45) = 6/y

1/sqrt(2) = 6/y

1*y = sqrt(2)*6

y = 6*sqrt(2)

Answer:

4.80 rounded

Step-by-step explanation:

Answer:

[tex]\large\boxed{A=6y+24}[/tex]

Step-by-step explanation:

[tex]\text{The formula of an area of a rectangle:}\\\\A=l\times w\\\\l-\text{length}\\w-\text{width}\\\\\text{We have:}\\\\l=6,\ w=y+4\\\\\text{Substitute:}\\\\A=6\times(y+4)\\\\\text{use the distributive property}:\ a(b+c)=ab+ac\\\\A=(6)(y)+(6)(4)\\\\A=6y+24[/tex]

Final answer:

To find the expression that represents the area of the rectangle, use the distributive property. The expression is 6y + 24.

Explanation:

To find the expression that represents the area of the rectangle, we can use the distributive property. The area of a rectangle is given by the formula A = length  imes width. So, for this rectangle, the length is 6 and the width is y + 4. To distribute the 6, we multiply it by both terms inside the parentheses: A = 6(y) + 6(4). This simplifies to A = 6y + 24, which is the expression that represents the area of the rectangle.

Answer:

The value of x in terms of b is (-3/b)

The value of x when b is 3 is -1

===============================

Step-by-step explanation:

The given function is :

-2 (bx - 5) = 16

Divide both sides by 2

bx - 5 = 16/(-2) = -8

Add 5 to both sides

bx = -8 + 5 = -3

Divide both sides by (b)

∴ x = -3/b

∴ The value of x in terms of b is (-3/b)

When b = 3 ⇒ ∴ x = -3/b = -3/3 = -1

Answer:

Two intersecting lines that form right angles (90 degree angles). All perpendicular line intersections will form .

Step-by-step explanation:

Answer: 90° angle

Step-by-step explanation: In the image provided, you can see that the 2 lines cross at a point so they're intersecting lines. However, notice the box that is used at the point where the lines meet. This box means that the lines meet at a 90° angle or a right angle and 2 lines that intersect at a right angle are called perpendicular lines which means that the lines are perpendicular.

The area calculated by them is 21.

Step-by-step explanation:

The given points are (-4,-2),(-3,-5),(3,-2) and (2,3).

The area of the quadrilateral:

A= [tex]\frac{(x1 y2+x2y3+x3y4+x4y1)-(x2y1+x3y2+x4y3+x1y4) }{2}[/tex].

From the given points,

A=[tex]\frac{(20+6+9-4)-(6-1-4-12) }{2}[/tex]

A=[tex]\frac{(31)-(-11) }{2}[/tex]

A= [tex]\frac{42}{2}[/tex]

The area of the quadrilateral = 21.

Answer:

The are is 28

Step-by-step explanation:

Given:

Point 1:  (– 4, – 2)

Point 2: (– 3, – 5)

Point 3: (3, – 2)  

Point 4: (2, 3)

then, the coordinates of the first point are x1 = -4, y1 = -2; of the second point x2 = -3, y2 = -5; and so on.

We can compute the area of the quadrilateral with the  shoelace formula as follows:

area = 1/2 * |x1*y2 + x2*y3 + x3*y4 + x4*y1 - x2*y1 - x3*y2 - x4*y3 - x1*y4 |

area = 1/2 * |(-4)*(-5) + (-3)*(-2) + 3*3 + 2*(-2) - (-3)*(-2) - 3*(-5) - 2*(-2) - (-4)*3 |

area = 1/2 * 56 = 28

Answer: 2x6x3=36 divided by 4=9+1=10.

The expression (2x6x3) ÷ 4 + 1 Grinch's plus two is solved using the order of operations, giving a result of 10 plus two Grinch's, symbolized as 10 + 2G.

The question is a basic arithmetic problem that involves both multiplication and addition within parentheses, followed by division and then more addition.

The order of operations, often abbreviated as PEMDAS - which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right) - must be followed to solve the expression correctly.

Let's solve the expression step by step:

The final answer is 10 plus two Grinch's, which we write as 10 + 2G.

Answer: The number is 6

Step-by-step explanation:

Let the number be x,

1/3 of the number is the same as 1/3 of x , so from the first statement , we have

16 + [tex]\frac{1}{3}[/tex]x = 3x

Multiplying the equation through by 3 , we have

48 + x = 9x

48 = 9x - x

48 = 8x

divide through by 8

therefore :

x = 6

Therefore : the number is 6

Answer:

2

Explanation:

Another way to write this is:

20 ÷ 10

2 whole tens go into 20.

20 ÷ 10 = 2

Answer: 2

This question is asking you to divide 20 by 10. This means:

20 ÷ 10=2

If 10 can go into a number 2 times, it means that 10•2=20. So, since we dont know how many times 10 goes into 20, we divide 20 by 10.

Below I have attached an image of the long division in case you need to do that as well.

Hope this helps comment below for more questions :)

1 box holds 9 so u divide 108 by 9 to get 12.

U can also multiply 3 and 27 until u get 108.  First divide 108 by 27 and get 4. so u then multiply 4 times 3 to get 12.

Answer:

Step-by-step explanation:

No of books that 3 boxes can hold = 27 books

No of boxes required =(3/27) * 108 = 3*108 / 27 =  3 *4 = 12

12 boxes are required

Answer:

The value of x will be an interger above or equal to 0. The value of y will be a interger equal or above 0.

Step-by-step explanation:

You can never buy a negative amount of books (x). You can only spend a positive amount of money. So even if she did not buy a book it would be 0, never under it.

Answer: it's the 2nd one

Step-by-step explanation: The value of x can be any real number greater than or equal to 0, and y will be a real number greater than or equal to 0

Answer:

Profit = $265.04.

Selling price = $1329.05

Step-by-step explanation:

Paul brought a Computer at a cost price of $1064.

Now ,

The marked price of the computer is given as $1399.

Also,

He is giving a total discount of 5% on  the marked price of the computer i.e., $1399.

So, The selling price of computer will become 95 percent of $ 1399 which equals  $1329.05.

Thus Paul sold the computer at a profit of $1329.05 - $1064

= $265.04.

Answer:

A) selling price of computer is $1329.05

B) Profit is $265.05

C) Profit percentage = 24.9%

Step-by-step explanation:

Given as :

The cost price of computer = c.p = $1064

The marked price of computer = m.p = $1399

The marked percentage discount = d = 5%

Let The selling price of computer = s.p

Now, According to question

discount% = [tex]\dfrac{m.p - s.p}{m.p}[/tex]

Or, d% =  [tex]\dfrac{m.p - s.p}{m.p}[/tex]

Or, 5% =  [tex]\dfrac{1399 - s.p}{1399}[/tex]

Or,  [tex]\dfrac{5}{100}[/tex] = 1 -  [tex]\dfrac{s.p}{1399}[/tex]

Or,  [tex]\dfrac{s.p}{1399}[/tex] = 1 - [tex]\dfrac{5}{100}[/tex]

Or,  [tex]\dfrac{s.p}{1399}[/tex] =  [tex]\dfrac{95}{100}[/tex]

∴  s.p = [tex]\dfrac{95}{100}[/tex] × 1399

Or, s.p = $1329.05

So,The selling price of computer = s.p = $1329.05

Now, Profit = selling price - cost price

or, p = s.p - c.p

Or, p = $1329.05 - $1064

∴ Profit = $265.05

Now, Profit % = [tex]\dfrac{\textrm profit}{c.p}[/tex]

Or, p% =  [tex]\dfrac{\textrm 265.05}{1064}[/tex]

∴  p% = 0.249

i.e p = 0.249 × 100

So, profit percentage = 24.9%

Hence, A) selling price of computer is $1329.05

B) Profit is $265.05

C) Profit percentage = 24.9%    Answer

Answer:

Total number of milkshakes sold on Monday = 300

Number of milkshakes without whipped cream = 90

Step-by-step explanation:

Given:

Adrienne adds whipped cream to 210 milk shakes which is 70% of the total milk shakes sold.

To find the total milkshakes sold.

Solution:

Let the total number of milkshakes sold on Monday be = [tex]x[/tex]

Percentage of milkshakes with whipped cream added to them = 70%

Number of milk shakes with added whipped cream can be given as:

⇒ [tex]70\% \textrm{ of the total number of milkshakes}[/tex]

⇒ [tex]70\% x[/tex]

⇒ [tex]\frac{70}{100}x[/tex]  [Representing percent in fraction form]

⇒ [tex]0.7x[/tex]  [evaluating in decimals]

We know that the number of milkshakes with whipped cream added to them = 210.

So, we have:

[tex]0.7x=210[/tex]

Solving for [tex]x[/tex]

Dividing both sides by  0.7

[tex]\frac{0.7x}{0.7}=\frac{210}{0.7}[/tex]

∴ [tex]x=300[/tex]

Thus, total number of milkshakes sold on Monday = 300

Number of milkshakes without whipped cream = [tex]300-210[/tex]= 90

Answer:

For the given equations the values of x and y by using substitution method are  [tex]x=1[/tex]  and [tex]y=\frac{13}{2}[/tex]

Step-by-step explanation:

Given system of equations are

[tex]-3x+2y=16\hfill (1)[/tex]

[tex]x-2y=-12\hfill (2)[/tex]

Solve the given equations by substitution method:

Now (2) implies

[tex]x-2y=-12[/tex]

[tex]x=-12+2y\hfill (3)[/tex]

Now substitute the x value in equation (1)

[tex]-3x+2y=16[/tex]

[tex]-3(-12+2y)+2y=16[/tex]

[tex]36-6y+2y=16[/tex]

[tex]36-4y=16[/tex]

[tex]-4y=16-36[/tex]

[tex]y=-(\frac{-26}{4})[/tex]

[tex]y=\frac{26}{4}[/tex]

Therefore  [tex]y=\frac{13}{2}[/tex]

Now substitute the y value in equation (3)

[tex]x=-12+2y[/tex]

[tex]x=-12+2\times \frac{13}{2}[/tex]

[tex]x=-12+13[/tex]

[tex]x=1[/tex]

Therefore [tex]x=1[/tex]  and [tex]y=\frac{13}{2}[/tex]

For this case we have that by definition, the equation of a line in its standard form is given by:

[tex]ax + by = c[/tex]

We have the following equation in the slope-intersection form:

[tex]y = -3x + 2[/tex]

Where:

-3: It's the slope

2: It is the cut-off point with the y axis.

We manipulate algebraically:

Adding 3x to both sides of the equation we have:

[tex]y + 3x = 2\\3x + y = 2[/tex]

Thus, the correct option is option B.

Answer:

Option B

Answer:

Part 1: 100

Part 2: 29.19 (Rounded)

Part 3: 20.96 (Rounded)

Step-by-step explanation:

Part 1: Triangle Sum Theorem (All angles of a triangle add up to 180 degrees)

45 + 35 + A = 180

80 + A = 180

Move the constant to the other side

80 + A = 180

-80          -80

A = 80°

Part 2: Law of sines

[tex]\frac{a}{sin(100)} = \frac{17}{sin(35)}[/tex]

Cross multiplication

sin(35)a = 16.7417318

Divide both sides by sin(35)

a = 29.18831866

Part 3: Law of cosines

[tex]b=29.19^{2}+17^{2}-2*29.19*17*cos(45)[/tex] = 439.2809039

Square root the answer

[tex]\sqrt{439.2809039}[/tex] =20.95902917

The value of angle A is 100 degrees and the measure of side a is 29.2 and b is 20.96.

A triangle is a polygon with three sides, angles, and vertices.

The triangle ABC, has AB = 17, angle ABC = 45 degree, angle ACB = 35 degree.

The measure of angle A can be determined by using the angle sum property.

45 + 35 + A = 180

80 + A = 180

A = 180-80

A = 100 degree.

Using the law of sines to find the length of side a,

a/ sin A = b/ sin B = c/sin C

a/ sin100 = 17/ sin 35

a = 17 * sin 100 / sin35

a = 29.2

Use the law of cosines to find the length of side b.

b² = c² +a² -2ac cos B

b² = (17)² + (29.2)² - 2* 17* 29.2 cos 45

b² = 439.23

b = 20.96

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Answer:

Let's begin by explaining the following:

The magnitude of any number (a charge in this particular case) is the distance this number has from 0 on the number line.

Now, since according physics a distance can never be negative, the magnitude of a number will always be positive. This means the magnitude of these given charges will always be positive, no matter if they are negative, positive or neutral.

Having this clarified, let's answer:

Element A has a charge of +5 and its magnitude is +5

Element B has a charge of -3 and its magnitude is +3

Element C has a charge of 10 and its magnitude is +10

Answer:

See explanation

Step-by-step explanation:

Consider triangles ABC and DEC. In these triangles,

Thus, by AAS postulate, triangles ABC and DEC are congruent. Congruent triangles have congeruent corresponding sides.

So,

[tex]BC\cong EC[/tex]

The Angle Angle Side postulate (AAS) states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.