Question in a nutshell

Woman goes into store every 8 days

Dude goes into store every 10 days

How many days will until they shop at the same time

We will prove both of the identities by expanding the exponents, only in the first one we need to use a little trick that is multiplying by (-1)^2 = 1.

Let's start with the first one:

(a + b)^2 = (- a - b)^2

We can start with the left side and write:

(a + b)^2 = (a + b)*(a + b)

Now, remember the rule of signs:

(-1)*(-1) = 1

So we can multiply by one the expression above and get:

(a + b)*(a + b) =  (a + b)*(a + b)*1 =  (a + b)*(a + b)*(-1)*(-1)

Now we can reorder the product to get:

(a + b)*(a + b)*(-1)*(-1) = (-1)*(a + b)*(-1)*(a + b) = (-a - b)*(-a - b) = (-a - b)^2

So we proved the first part, now the second one:

(a - b)^2

Let's just expand this:

(a - b)^2 = (a - b)*(a - b) = a*a + a*(-b) + (-b)*a + (-b)*(-b) = a^2 - 2ab - b^2

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Alternate interior angles are congruent if the two parallel lines are intersected by the transversal.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.

The parallel lines in the diagram has two red arrows on it.

The transversal line is the one that cut the other two parallel lines.

The angles formed are 9x + 5 and 10x - 5.

Therefore, if the two parallel lines are intersected by the transversal then alternate interior  angles are congruent.

Hence,

9x + 5 = 10x - 5

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Answer:

add a picture

Step-by-step explanation:

In case whereby the factors of 45= 3x3x5  and 75=3x3x5 given the factors, that both 45 and 75 share are 3, 5 , which are two factors

The factors of the two given numbers 45 and 75 can be seen as those whole numbers that when it is been used to divide the numbers 45 and 75 will have no remainders.

For instance , if we divide 45 by 3 then we will have 15 which do no have any remainder, same with when we divide 45 by 5 , it will have no remainder, same thing can be done to 75, we can divide it by 3 as wel as 5 without getting any remainder.

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Answer:

9.

he washes 9 cars on Tuesday.

Step-by-step explanation:

28 * 7 = 196.

448 - 196 = 252

252 / 28 = 9

On solving the linear equation  28x + 196 = 448, we get that Craig washed 9 cars on Tuesday.

Linear equation is an equation containing one unknown variable with power one and constants.

The standard form of an linear equation in one variable x is :

ax + b = 0 , where a, b are constants

x= -b/ a is solution if this equation or we can solve this equation by adding or subtracting , multiplying or dividing same number to both sides.

Given that Craig washes cars and earns $ 28 for each car . He washed 7 cars on Monday.

Let on Tuesday he washed x cars

Total money earned on Tuesday and Monday by Craig = $448

Money earned on Monday = $ 7× 28 = $ 196

Money earned on Tuesday  = $ x×28 = $ 28x

⇒ 28x + 196 = 448

Subtracting 196 from both sides we get

⇒ 28x + 196 -196 = 448 - 196

⇒ 28 x = 252

Dividing both sides by 28

⇒ x = 252/28 = 9

Therefore, Craig washed 9 cars on Tuesday.

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Answer:

50

Step-by-step explanation:

          i^2 = -1

First simplify the radicals. Then use FOIL method

[tex]\sf (3 + \sqrt{-16})(6-\sqrt{-64}) = (3 +\sqrt{i^2*4^2})(6-\sqrt{i^2*8^2})[/tex]

                                     = ( 3 + 4i)(6 -8i)

                                     = 3*6 - 3*8i + 4i*6 - 4i*8i

                                     = 18 - 24i + 24i - 32i^2

                                      = 18 - 24i + 24i - 32*(-1)

                                       = 18 - 24i +24i + 32

                                       = 18 + 32 - 24i + 24i

Combine like terms,

                                       = 50

 x = 5 is the value of x in exterior angle.

Why is this term "exterior angle" used?

∠QRS is exterior angle .

apply exterior angle theorem in ΔPQR

So, ∠QRS = ∠PQR + ∠RPQ

     8x - 9° = 3x + 12° + 3x - 11°

     8x - 9 = 6x + 1

       8x - 6x = 1 + 9

         2x = 10

            x = 10/2

            x = 5

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Answer:

assuming the percents are out of 100 the order is

14.8 then 15% then 154/5 then 1450%

if thats not the case let me know and i'll correct it

Step-by-step explanation:

15% of 100 = 15

154/5 = 30.8

1450% of 100 = 1450

[tex] - 2x + 2 = 180 \\ - 2x = 180 - 2 \\ - 2x = 178 \\ \frac{ - 2x}{ - 2} = \frac{178}{ - 2} \\ x = - 89[/tex]

ATTACHED IS THE SOLUTION of X

Step-by-step explanation:

this is very roughly converted from the original question, I bet. no punctuation marks and, and ...

what I understood of the important information is :

there are 23 boxes of books with 12 books in each.

there are 4 teachers dividing the books evenly among themselves for their cells (classes ?) of students.

so, we need to divide the books by 4 to distribute them evenly into 4 parts.

23×12/4 = 23×3 = 69

each teacher got 69 books.

The equations that could be used to determine the number of associates assigned to the case and the number of partners assigned to the case is: 800 x + 1800 y = 17600.

Let variable x =represent the number of associates, assigned to the case

Let variable y represent number of partners assigned to the case.

The system of equations re:

800 x + 1800 y = 17600

y = x + 2

Plug equation 2 in equation 1, we get,

800 x + 1800(x+ 2) = 17600

2600 x + 3600 = 17,600

Collect like terms

2400 x = 14,000

Divide both side by 2400x

x = 14,000 / 2400

x = 5.8

x = 6 (Approximately)

So,

y = x + 2

y = 5.8 +3

y = 7.8

y = 8 (Approximately)

Therefore the number of associates assigned to the case were 6, and the number of partners associated to the case were 8.

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Answer:

September2020

13outcomes

Zach’s gross income was $79,500.

Given:

Zach's salary = $75,000

His interest income from a CD = $4,500  

Expenses = $5,000

Contribution to an IRA = $4,000

Standard deduction = $5700

Exemption rate = $3,650

Zach’s gross income =  Salary + interest income

                                  = $75,000 + $4,500

                                  = $79,500

Therefore, Zach’s gross income was $79,500.

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Answer: No Solution

Step-by-step explanation:

||3x - 1| + 5| <1  ⇒

[tex]\left \{ {{|3x - 1| + 5 < 1} \atop {|3x - 1| + 5 > -1 }} \right.[/tex]    ⇒

[tex]\left \{ {{|3x - 1| < -4} \atop {|3x - 1| > -6} \right.[/tex]        ⇒

The first equation does not make sense because absolute value and as it is a system of equations, the whole system does not have a solution.

Answer:

Property of Equality

Step-by-step explanation:

B=D and D=B so they are the same value so its a property of equality

Answer: 4AB

Step-by-step explanation:

[tex](A+B)^2-(A-B)^2=\\((A+B)+(A-B))((A+B)-(A-B))=\\(A+B+A-B)(A+B-A+B)=\\(2A)(2B)=\\4AB[/tex]

The equation of the polynomial is P(x) = (x - 4)(x - 6)(x + 3)²

Polynomial expressions are mathematical statements that are represented by variables, coefficients and operators

The given parameters are

The sum of multiplicities of the polynomial equation must be equal to the degree.

This means that the multiplicity of the zeros 4 and 6 is 1

The equation of the polynomial is then calculated as

P(x) = (x - zero)^ multiplicity

So, we have

P(x) = (x - (-3))² * (x - 4) * (x - 6)

This gives

P(x) = (x - 4)(x - 6)(x + 3)²

Hence, the equation is P(x) = (x - 4)(x - 6)(x + 3)²

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The cube of the number five is written in these following forms:

The cube of a number n is equivalent to multiplying the number n by itself three times.

Hence, in expanded form, the cube of a number n is written as follows:

n x n x n.

In exponential form, the cube of a number n is written as follows:

n³.

In this problem, the number of interest is the number five, hence:

The result of the expression, which is the evaluation, is given by:

5 x 5 x 5 = 25 x 5 = 125.

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Answer:

6.25

Step-by-step explanation:

a quarter=1/4 which is 0.25; 0.25 for each person is 0.25(25)=6.25

Answer:

INVALID or 16

Step-by-step explanation:

The answer would be invalid due to the double addition signs.

However, if you meant to put a 2 in between those signs, it would be:

4+2+2+2+2+2+2

6+2+2+2+2+2

8+2+2+2+2

10+2+2+2

12+2+2

14+2

16

Answer:

Step-by-step explanation:

14

Answer:

D.   [tex]x^4-x^3+x^2-x+1-\frac{6}{5x+5}[/tex]

Step-by-step explanation:

Volume of a rectangular box = Base Area x Height

V = Ah

Here we are give V and h and asked to compute A

From the equation for V, dividing both sides by h gives
V/h = A

A = V/h

V = 5x⁵ - 1
h = 5x + 5

[tex]V = \dfrac{5x^5-1}{5x + 5}[/tex]

The simplified result is [tex]x^4-x^3+x^2-x+1-\frac{6}{5x+5}[/tex]

I solved this using synthetic division and can provide the steps if you want

Answer: B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

let the 2 consecutive odd numbers be x and x + 2 , then the sum is

x + x + 2 = 72 , that is

2x + 2 = 72 → B

subtract 2 from both sides

2x = 70 ( divide both sides by 2 )

x = 35

x + 2 = 35 + 2 = 37

the 2 consecutive odd numbers are 35 and 37

Answer: Slope 0.5298 ± 0.2372

Y-intercept 1.429 ± 1.198

X-intercept -2.697

Step-by-step explanation: I hope that helped

The the coordinates of endpoint J on line segment JL with a midpoint of (-2, 6) is ( -3,15 ).

A midpoint is simply a point that divides a line segment into two equal halves.

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2

Given the data in the question;

Midpoint K(-2, 6)

Point L(-1, -3).

Point J

To determine the coordinate of point J, plug the given points into the midpoint formula above and simplify.

First, we get the x-coordinate of point J

x = (x₁+x₂)/2

2x = x₁ + x₂

2( -2 ) = x₁ + ( -1 )

-4 = x₁ - 1

x₁ = -4 + 1

x₁ = -3

Next, we get the y-coordinate of point J

y = (y₁+y₂)/2

2y = y₁ + y₂

2(6) = y₁ + (-3)

12 = y₁ - 3

y₁ = 12 + 3

y₁ = 15

Therefore, the coordinates (x₁,y₁) of the endpoint point J is ( -3,15).

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Incomplete question.No requirement of question

The equation of the line in the point-slope form is y + 3 = 1/2(x - 5)

From the question, we are to determine the equation of the given line in point-slope form

First, we will determine the slope of the line

Using the points (1, -5) and (3, -4)

From the formula,

Slope = (y₂ - y₁) / (x₂ - x₁)

Slope = (-4 - -5) / (3 - 1)

Slope = ( -4 + 5) / 2

Slope = 1/2

Now,

For the point-slope form of the line

Using the point-slope form of the equation of a straight line,

y - y₁ = m(x - x₁)

Where m is the slope

The given point is (5, -3)

Thus,

The point-slope form of the line is  

y - -3 = 1/2(x - 5)

y + 3 = 1/2(x - 5)

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Answer:

1 5/7

Step-by-step explanation:

12/7 x 5/5 = 60/35 or 1 5/7

The weight of a person in Venus who weighs 210 pounds on Earth is 185.5 pounds.

It is given in the question that weight of a person on Venus varies directly with his or her weight on Earth. Also, a person weighing 120 pounds on Earth weighs 106 pounds on Venus.

We have to find the weight of the person in Venus who weighs 210 pounds on Earth.

Let weight on Earth be e and,

weight on Venus be v.

From the data given in the question, we can write,

e ∝ v

e = kv

Where k is the constant of proportionality

120 = k*106

k = 120/106 = 60/53

Hence, we can write,

210 = (60/53)*v

(210*53)/60 = v

v = 185.5 pounds

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Answer:

Exact form: x= -1 ± √2

Decimal Form: x= 0.41421356..., -2.41421356...

Step-by-step explanation:

The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros) replace  with 0 and solve for x.

Answer: 5<x<35

Step-by-step explanation:

An acute angle ranges from 0 to 90 degrees.

[tex]0 < 3x-15 < 90\\\\15 < 3x < 105\\\\5 < x < 35[/tex]