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Which step shows the result of applying the subtraction property of equality?
1/4 (12x+8)+4 = 3

3 x+2+4= 3
3x+6 = 3
3x= -3
X=-1​

Answer:

The first one should be right. Since the teacher is charging $15 per hour of the piano lesson then it can't be any of the answers of $100h. The answer can't be C, the third one, since you're adding the enrollment fee to the cost of every piano lesson it would be wrong to subtract the $100. Hope that helps!

Step-by-step explanation:

The answer will the answer on the top $25=$100+$15h over h

Answer: The number of hours is 10 hours.

Step-by-step explanation:

Since we have given that

Average cost of lessons = $25

let h be the number of hours a student spends in lessons.

Since each student has fee of $100 plus $15 per hour.

So, According to question, it becomes,

[tex]25=\dfrac{100+15h}{h}\\\\25h=100+15h\\\\25h-15h=100\\\\10h=100\\\\h=\dfrac{100}{10}\\\\h=10[/tex]

Hence, the number of hours is 10 hours.

Answer:

1) multiplicative inverse of i = -i

2) Multiplicative inverse of i^2 = -1

3) Multiplicative inverse of i^3 = i

4) Multiplicative inverse of i^4 = 1

Step-by-step explanation:

We have to find multiplicative inverse of each of the following.

1) i

The multiplicative inverse is 1/i

if i is in the denominator we find their conjugate

[tex]=1/i * i/i\\=i/i^2\\=We\,\, know\,\, that\,\, i^2 = -1\\=i/(-1)\\= -i[/tex]

So, multiplicative inverse of i = -i

2) i^2

The multiplicative inverse is 1/i^2

We know that i^2 = -1

1/-1 = -1

so, Multiplicative inverse of i^2 = -1

3) i^3

The multiplicative inverse is 1/i^3

We know that i^2 = -1

and i^3 = i.i^2

[tex]1/i^3\\=1/i.i^2 \\=1/i(-1)\\=-1/i * i/i\\=-i/i^2\\= -i/-1\\= i[/tex]

so, Multiplicative inverse of i^3 = i

4) i^4

The multiplicative inverse is 1/i^4

We know that i^2 = -1

and i^4 = i^2.i^2

[tex]=1/i^2.i^2\\=1/(-1)(-1)\\=1/1\\=1[/tex]

so, Multiplicative inverse of i^4 = 1

Answer:

8

Step-by-step explanation:

xy^2 =  k*k y^2            x = k * k so x has to be a perfect square.

xy is a perfect square which means that since x is a perfect square (see above) then y will have to be as well

There is nothing that prohibits x = 4 and y = 4 as being the answer where x = y.

I think the smallest possible value for x + y is 8.

This excludes any possibility of 1 or 0 in some combination, although I would look into 1.

Please see attached image for complete answer and steps in detail.

Answer:

The result is 150 + 1.5d

Step-by-step explanation:

We want to translate the wordings into algebraic expression.

Firstly, we increase 120 by d%

d% = d/100

So increasing 120 by d % means;

120 + (d/100 * 120)

= 120 + 1.2d

Then increase this by 25%

= (120 + 1.2d) + 25/100(120 + 1.2d)

= 120 + 1.2d + (120+1.2d)/4

= 120 + 1.2d + 30 + 0.3d

= 120 + 30 + 1.2d + 0.3d

= 150 + 1.5d

Note that if [tex]i^2=-1[/tex] than [tex]i=\sqrt{-1}[/tex],

Also note that [tex]\sqrt{ab}=\sqrt{a}\sqrt{b}[/tex]

So we have,

[tex]\sqrt{-49}=\sqrt{-1}\sqrt{49}=\boxed{7i}[/tex]

and,

[tex]\sqrt{-4}=\sqrt{-1}\sqrt{4}=\boxed{2i}[/tex]

Hope this helps.

r3t40

Answer:

The irrational number could be √30

Step-by-step explanation:

An irrational number is a number which can not be written as a ratio between two numbers and it can not be written as a simple fraction. In simple words we can not write it in p/q form.

Find an irrational number that is between 5.2 and 5.5.

Mostly irrational numbers are square root numbers.

So square the both numbers.

(5.2)^2 (5.5)^2.

27.04 , 30.25

It means that the number is between 27.04 and 30.25

We will pick number 30

Square root 30

√30 = 5.48

The irrational number could be √30

It is 5.48 to the hundredth....

Answer:

[tex]\large\boxed{y=-\dfrac{3}{4}x-3}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept

Parallel lines have the same slope.

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

We have the equation of the line: [tex]y=-\dfrac{3}{4}x-5[/tex]

The slope is [tex]m=-\dfrac{3}{4}[/tex].

Put the value of the slope and the coordinates of the point (4, -6) to an equation of a line:

[tex]-6=-\dfrac{3}{4}(4)+b[/tex]

[tex]-6=-3+b[/tex]           add 3 to both sides

[tex]-3=b\to b=-3[/tex]

Finally:

[tex]y=-\dfrac{3}{4}x-3[/tex]

Answer:

395

You are 100% right! You go!

Step-by-step explanation:

We are given f(x)=5x^2-2x+8 and are asked to find the value of the function at x=9.

So replace x with (9):

f(9)=5(9)^2-2(9)+8

f(9)=5(81)-18+8          I did the exponent 9^2 and 2(9) in this step:

f(9)=405-18+8           I did 5(81) in this step

f(9)=405-10               I did -18+8 in this step

f(9)=395

Answer:

1

Step-by-step explanation:

Your equation may be written as follows:

[tex]\frac{1}{5} +2n=3n-\frac{4}{5}[/tex]

Start by multiplying both sides by 5 to clear your fractions.

[tex]\frac{1}{5} +2n=3n-\frac{4}{5} \\1+10n=15n-4[/tex]

Next, subtract 10n from both sides.

[tex]1+10n=15n-4\\1=5n-4[/tex]

Add 4 to both sides.

[tex]1=5n-4\\5=5n[/tex]

Divide both sides by 5 to solve for n.

[tex]5=5n\\1=n[/tex]

Final answer:

By setting up an equation 1/5 + 2x = 3x - 4/5 and solving for x, we find that the number is 1.

Explanation:

The problem involves finding a number when given a relationship involving fractions and that number. The relationship is: the sum of 1/5 and twice a number is equal to 4/5 subtracted from three times the number. To find the number, we set up an equation and solve for the variable, which represents the number.

Let's denote the number as x. Our equation can be written as:

1/5 + 2x = 3x - 4/5

We bring all the x terms on one side and the constants on the other to solve for x:

2x - 3x = -4/5 - 1/5

-x = -1

x = 1

Answer:

let the integers be x, x+2, x+4 and x+6

therefore,

x + x+2 + x+4 + x+6 = -72

=> 4x + 12 = -72

=> 4x = -72 - 12

=> x = -84/4

=> x = -21

therefore the integers are: -21, -19, -17, -15

[tex]\huge\boxed{\text{-21, -19, -17, -15}}[/tex]

Represent this mathematically. [tex]x+(x+2)+(x+4)+(x+6)=-72[/tex]

Combine like terms. [tex]4x+12=-72[/tex]

Subtract 12 from both sides. [tex]4x=-84[/tex]

Divide both sides by 4. [tex]x=-21[/tex]

Find the numbers by adding 2 each time. [tex]-21, -19, -17, -15[/tex]

Answer:

[tex]\large\boxed{\dfrac{27}{80}}[/tex]

Step-by-step explanation:

Put x = 3, y = 2 and z = 5 to the given expression [tex]10x^3y^{-5}z^{-2}[/tex]:

[tex]10(3^3)(2^{-5})(5^{-2})\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{10(27)}{(2^5)(5^2)}=\dfrac{270}{(32)(25)}=\dfrac{270}{800}=\dfrac{27}{80}[/tex]

Answer:

Tanya is 20 years old

Step-by-step explanation:

Let the age of Vera = x years

The age of Linda is twice the age of Vera = 2x years

Tanya  is four less than four times the age of Linda = 4(2x)-4 = 8x-4

Total age of Vera, Linda and Tanya is:

x+2x+8x-4

Combine the like terms:

11x-4

But now their total age is two more than nine times the age of Vera:

11x-4 = 9x+2

Solve the expression

Combine the like terms:

11x-9x=2+4

2x=6

Divide both the sides by 2

2x/2 = 6/2

x= 3

Thus the age of Vera is 3 years.

The age of Linda is 2x= 2*3 = 6 years

The age of Tanya is 8x-4 = 8*3 - 4 = 24-4 = 20years....

Answer:

[tex]\large\boxed{\dfrac{a^{-3}}{a^{-2}b^{-5}}=a^{-1}b^5}[/tex]

Step-by-step explanation:

[tex]\dfrac{a^{-3}}{a^{-2}b^{-5}}=a^{-3}\cdot\dfrac{1}{a^{-2}}\cdot\dfrac{1}{b^{-5}}\qquad\text{use}\ x^{-n}=\dfrac{1}{x^n}\\\\=a^{-3}\cdot a^2\cdot b^5\qquad\text{use}\ x^n\cdot x^m=x^{n+m}\\\\=a^{-3+2}b^5=a^{-1}b^5[/tex]

Answer:

(g − f) ( 3 ) = 23

Step-by-step explanation:

( g − f ) ( x ) = g ( x ) − f ( x )

= 6 x − ( 4 − x 2 )

= x 2 + 6 x − 4

to evaluate ( g - f ) ( 3 ) substitute x = 3 into ( g − f ) ( x )

( g − f ) = ( 3 ) 2 + ( 6 x 3 ) - 4 =23

For this case we have the following functions:

[tex]f (x) = 4-x ^ 2\\g (x) = 6x[/tex]

By definition we have to:

[tex](f-g) (x) = f (x) -g (x)\\(g-f) (x) = g (x) -f (x)[/tex]

Then, we find [tex](f-g) (x):[/tex]

[tex]f (x) -g (x) = 4-x ^ 2-6x = -x ^ 2-6x 4[/tex]

We evaluate the function in 3:

[tex](f-g) (3) = - (3) ^ 2-6 (3) 4 = -9-18 4 = -27 4 = -23[/tex]

Now we find[tex](g-f) (x):[/tex]

[tex]g (x) -f (x) = 6x- (4-x ^ 2) = 6x-4 x ^ 2 = x ^ 2 6x-4[/tex]

We evaluate the function in 3

[tex](g-f) (3) = 3 ^ 2 6 (3) -4 = 9 18-4 = 23[/tex]

Answer:

[tex](f-g) (3) = - 23\\(g-f) (3) = 23[/tex]

Answer:

[tex]\large\boxed{y=-\dfrac{8}{5}x+\dfrac{31}{5}}[/tex]

Step-by-step explanation:

[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept[/tex]

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\--------------------------[/tex]

[tex]\text{We have:}\\\\y=\dfrac{5}{8}x-4\to m_1=\dfrac{5}{8}\\\\\text{The slope of a perpendicular line:}\ m_2=-\dfrac{1}{\frac{5}{8}}=-\dfrac{8}{5}\\\\\text{The equation:}\\\\y=-\dfrac{8}{5}x+b\\\\\text{Put the coordinates of the point (2, 3) to the equation:}\\\\3=-\dfrac{8}{5}(2)+b\qquad\text{solve for}\ b\\\\3=-\dfrac{16}{5}+b\qquad\text{add}\ \dfrac{16}{5}\ \text{to both sides}\\\\\dfrac{15}{5}+\dfrac{16}{5}=b\to b=\dfrac{31}{3}\\\\\text{Finally:}\\\\y=-\dfrac{8}{5}x+\dfrac{31}{5}[/tex]

Answer:

4x - 1 and x + 6 are the factors of given Trinomial

Step-by-step explanation:

The given Trinomial is:

[tex]4x^{2}+23x-6[/tex]

We can factorize this trinomial by mid-term splitting. The mid-term(23x) can be split up in two terms (24x and -x) such that their sum is 23x and their product(-24x²) is equal to the product of other two terms (4x² and -6)

So, the above expression can be written as:

[tex]4x^{2}+23x-6\\\\ =4x^{2}+24x-x-6\\\\\text{Taking out commons, we get}\\\\=4x(x+6)-1(x+6)\\\\ =(4x-1)(x+6)[/tex]

Therefore, 4x - 1 and x + 6 are the factors of given Trinomial

Answer: 4x-1 and x+6

Step-by-step explanation: a p e x

Choices A and C are both true statements.  

But C is trivial.  It's CALLED a perpendicular "bisector" of the chord, so OF COURSE it bisects the chord ... otherwise it would be silly to CALL it a "bisector".

The choice that's surprising but true is A .

The perpendicular bisector of a chord passes through the center of the circle.

A chord in plane geometry is a line segment that connects two points on a curve. A line segment whose endpoints are on a circle is frequently described using this phrase. A cycle chord of a graph cycle is an edge that is not in and whose endpoints are in, according to graph theory, which also uses the phrase.

To know more about chords refer to :

https://brainly.com/question/4470346

#SPJ2

Answer:

Option C.

Step-by-step explanation:

If k<0, the function g(x) = f(x) + k represents the function f(x) shifted k units downwards.

In this case, given that k=-3 (k<0). The graph was shifted 3 units down. Therefore, the correct option is Option C.

Answer:

d. 1134 inches squared

Step-by-step explanation:

The formula for the area of a circle is [tex]\pi r^2[/tex]

where r is the radius.

You are given r=19 here so replace r in [tex]\pi r^2[/tex] with 19 giving us:

[tex]\pi (19)^2[/tex]

Then it is to the calculator we go:

1134 inches squared

Final answer:

The width of the rectangle frame with a total area of 160 square inches, and expressions for length (2x + 8) and width (2x + 6), is found to be 10 inches.

Explanation:

To solve for the width of the rectangle frame with an area of 160 square inches, where the length is represented by 2x + 8 and the width by 2x + 6, we need to set up an equation using the formula for the area of a rectangle, which is length × width. With the given area of 160 square inches, the equation is:

(2x + 8)(2x + 6) = 160

Let's expand this and solve for x:

4x² + 12x + 16x + 48 = 160

4x² + 28x + 48 = 160

4x² + 28x - 112 = 0

Divide everything by 4 to simplify:

x²+ 7x - 28 = 0

Factor this quadratic equation:

(x + 14)(x - 2) = 0

x = -14 or x = 2

Since a width cannot be negative, x = 2

Now, to find the width, replace x in the width expression:

Width = 2x + 6

Width = 2(2) + 6 = 4 + 6 = 10 inches

Thus, the width of the rectangle frame is 10 inches.

Answer:

100/9

Step-by-step explanation:

(7*5*2/7*3)² * (5^0/2^-3)³ * 2^-9

Solution:

We know that any number with power 0 = 1

(7*5*2/7*3)² * (1/2^-3)³ * 2^-9

Now cancel out 2 by 2

= (7*5*2/7*3)² * (1/1^-3)³ * 1^-9

=(70/21)² * (1)³/(1^-3)³ * 1^-9

=(10/3)^2 * 1/1^-1 * 1/1^9

=100/9 *1 *1

=100/9....

Answer:2x-5

Step-by-step explanation:-(x+5)+3x

-x-5+3x=(3x-x) -5

=2x-5

Answer:

B. One of the sides, or legs, that make up the right  angle.

Step-by-step explanation:

The Pythagoras Theorem applies to the right-angled triangles. It is basically a relationship between the sizes of the all lengths of the triangle. The Pythagoras Theorem is given by:

C^2 = A^2 + B^2; where A and B are perpendicular and base respectively, and C is the hypotenuse. It is interesting to note that A can either be the perpendicular or the base of the right angled triangle. Same goes for B; it can be either the perpendicular or the base. Both the perpendicular and the base intersect at 90 degrees. But both cannot be the hypotenuse. Therefore, the variable A in the Pythagoras Theorem is one of the sides, or legs, that make up the right  angle, i.e. Option B is the correct answer!!!

Answer:

-√3 - i ⇒ (2 , 7/6 π)

Step-by-step explanation:

* Lets explain how to convert a point in Cartesian form to polar form

- Polar coordinates of a point is (r , θ).

- The origin is called the pole, and the x axis is called the polar axis,

 because every angle is dependent on it.

- The angle measurement θ can be expressed in radians or degrees.

- To convert from Cartesian Coordinates (x , y) to Polar

 Coordinates (r , θ)

1. r = √( x² + y² )

2. θ = tan^-1 (y/x)

* Lets solve the problem

∵ The point in the Cartesian form is z = -√3 - i, where -√3 is the real

   part and -i is the imaginary part

∴ The x-coordinate of the point is -√3

∴ The y-coordinate of the point is -1

∵ Both the coordinates are negative

∴ The point lies on the 3rd quadrant

- To convert it to the polar form find r and Ф

∵ [tex]r=\sqrt{x^{2}+y^{2}}[/tex]

∵ x = -√3 and y = -1

∴ [tex]r=\sqrt{(-\sqrt{3}) ^{2}+(-1)^{2}}=\sqrt{3+1}=\sqrt{4}=2[/tex]

∵ Ф = [tex]tan^{-1}\frac{y}{x}[/tex]

∴ Ф = [tex]\frac{-1}{-\sqrt{3}}=\frac{1}{\sqrt{3}}[/tex]

- The acute angle π/6 has tan^-1 (1/√3)

∵ The point is in the third quadrant

∴ Ф = π + π/6 = 7/6 π

- Lets write it in the polar form

∴ -√3 - i ⇒ (2 , 7/6 π)

Answer:

2cis 7pi/6

Step-by-step explanation:

Answer:

obtuse, isosceles

Step-by-step explanation:

We have two angles that have the same measure  - that means two sides are equal length.  That means the triangle is isosceles

We have one angle that is greater than 90 degrees  - that tells us the triangle is obtuse

Answer:

10,000 m/square

Step-by-step explanation:

we know that

A hectare is a unit of area equal to [tex]10,000\ m^{2}[/tex]

The symbol is Ha

Verify each case

case 1) 10,000 m/square

The option is true

case 2) 100 m/square

The option is false

case 3) 100,000 m/square​

The option is false

[tex]\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) \qquad \qquad a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^3-64\implies x^3-4^3\implies (x-4)(x^2+4x+4^2)\implies (x-4)(x^2+4x+16)[/tex]

Answer:

The break- even point is attained when n=75

Step-by-step explanation:

The break-even point is defined as the point where revenue is equal to cost.

We take the equation for revenue r=15n, and set it equal to the equation c=9n+450

15n=9n+450

Subtract 9n from both sides:

6n=450

Divide both sides by 6.

6n/6=450/6

n=75

The break- even point is attained when n=75....

Final answer:

To determine Amanda's store's break-even point, set the revenue equal to the cost function and solve for n to find 75 shirts.

Explanation:

To find the break-even point of Amanda's store:

Set the revenue function equal to the cost function: 15n = 9n + 450

Solve for n: n = 75

Therefore, the break-even point is when Amanda sells 75 graphic t-shirts.