A manager needs to buy chairs for his office. The price for one chair is$79.99. If the manager buys 2 or more chairs, he will receive a 40% discount on each chair. Approximately how much will the manager save on each chair if he buys 2 chairs?A.$32 B.$40 C.$48 D.$80

Option second [tex]\rm (w-2.5)(w+2.5)[/tex] and option fourth  [tex]\rm (-4v-9)(-4v+9)[/tex]  are the products that result in a difference in squares.

It is required to identify which products result in a difference in squares.

Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.

We know that:

[tex]\rm (a^2-b^2)=(a+b)(a-b)[/tex]

In option first:

[tex]\rm = (5z+3)(-5z-3)\\\rm = -(5z+3)(5z+3)\\\rm = -(5z+ 3)^2[/tex]

Which is not the difference between squares.

In option second:

[tex]\rm=(w-2.5)(w+2.5)\\\rm =(w^2-2.5^2)[/tex]By using [tex]\rm (a^2-b^2)=(a+b)(a-b)[/tex]

It is the difference between squares.

Similarly, in option third:

[tex]\rm =(8g+1)(8g+1)\\\rm =(8g+1)^2[/tex]

It is not the difference between squares.

Similarly, in option forth:

[tex]\rm = (-4v-9)(-4v+9)\\\rm = (4v+9)(4v-9)\\\rm = (4v)^2-9^2[/tex]

It is the difference between squares.

Similarly, in option fifth:

[tex]\rm = (6y+7)(7y-6)\\\rm = 42y^2+13y-42[/tex]

It is not the difference between squares.

Similarly, in option sixth:

[tex]\rm =(p-5)(p-5)\\\rm =(p-5)^2[/tex]

It is also not the difference between squares.

Thus, option second and option fourth are correct.

Learn more about polynomial here:

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Answer:

12 is the GFC.

Step-by-step explanation:

24 - 8, 3, 4, 6, 2, 12, 1, 24

60 - 10, 6, 2, 30, 20, 3, 5, 12, 4, 15

The greatest common factor of 24 and 60 is 12

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.

For us to find the greatest common factor we need to find the common factors between the numbers.

The factors of 24 = 1,2,3,4,6,8,12 and 24

The factors of 60 = 1,2,3,4,5,6,12,15,30 and 60.

The common factors are ;

1,2,3,4,6 and 12

And the greatest common factor is 12. because it is the highest factor.

learn more about greatest common factor from

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Answer:

the answer would be 3x+y-15

Veremos que el area del banderín es 930cm^2, entonces la opción correcta es A.

Luego de una pequeña busqueda online, pude ver que el banderin es un triangulo isósceles con base de 31cm y altura de 60 cm.

Recordar que para un triangulo de base b y altura h, el area es:

A = b*h/2

Entonces el area del banderín va a ser:

A = (31cm)*(60cm)/2 = 930cm^2

Entonces la opción correcta es A.

Sí quieres aprender más sobre triangulos, puedes leer:

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Answer:

Step-by-step explanation:

2: 4/2 is 2

3: 4/3 is 1 1/3

4: 4/4 is 1

5: 4/5 is .8

x                                       y                                       y/x

2                                      2                                      4/2

3                               1 1/3 or 1.333...                        4/3

4                                      1                                        4/4

5                                 4/5 or 0.8                              4/5

Hope this Helped! :)

-SGO

Answer:

1. 2c+9=m

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

it's just option B because it is only root

Answer:

the answer would be B. (2.5, -0.5)

plug the possibilities in and solve. just because it works for one, it doesn't mean that it will work for both.

3 (2.5) - (-0.5) = 7.5 + 0.5 = 8

(2.5) + (-0.5) = 2.5 - 0.5 = 2

i hope i helped. :)

Step-by-step explanation:

Read more about system of equations at:

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Answer:

Step-by-step explanation:

Yes

Answer:

A. Total area of Alaska is considerable larger than total area of Connecticut.

B. Population of California is considerably larger that population of Alaska.

Step-by-step explanation:

A. What is the difference in total area of Alaska and Connecticut?

According to the US government, total areas of Alaska and Connecticut are 663,268 square miles ([tex]6.633\times 10^{5}[/tex] square miles) and 5,567 square miles ([tex]5.567\times 10^{3}[/tex] square miles), respectively.

The difference between both quantities is:

[tex]x = 6.633\times 10^{5}\,mi^{2}-5.567\times 10^{3}\,mi^{2}[/tex]

[tex]x = 6.577\times 10^{5}\,mi^{2}[/tex]

Which means that total area of Alaska is considerable larger than total area of Connecticut.

B. What is the difference in total population of California and Alaska?

According to the US government, total populations of California and Alaska are 39,512,223 people ([tex]3.951\times 10^{7}[/tex] people) and 710,249 people ([tex]7.103\times 10^{5}[/tex] people), respectively.

The difference between both quantities is:

[tex]x = 3.951\times 10^{7}\,people - 7.103\times 10^{5}\,people[/tex]

[tex]x = 3.880\times 10^{7}\,people[/tex]

Which means that population of California is considerably larger that population of Alaska.

The quadratic polynomial 6x² – 7x + 2 has factors (3x – 2) and (2x – 1). Then the correct option is A.

It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.

The quadratic polynomial is 6x² – 7x + 2.

On factorization, we have

6x² – 7x + 2

6x² – (4 + 3)x + 2

6x² – 4x – 3x + 2

2x(3x – 2) –1(3x – 2)

(3x – 2)(2x – 1)

The factor is (3x – 2).

More about the factorization link is given below.

https://brainly.com/question/6810544

Answer:

8×7×7 diameters should be accurate

Answer:

c/d = 5x/3

Step-by-step explanation:

Given :-

c/d - a/b = x

a = 2c

b = 5d

To Find :-

Value of c/d in terms of x

Solving :-

Substitute value of a and b.

c/d - 2c/5d = x

3c/5d = x

c/d = 5x/3

Solution :-

c/d = 5x/3

Answer:

A=44 B=68

Step-by-step explanation:

There are two congruent sides, therefore the corresponding angles are also congruent.

Answer:

a and b both are 56 degree

Step-by-step explanation:

this is due to it's isosceles triangle. So, we take (180-68):2

Answer:

Given That:

[tex]{ \large\longrightarrow { \rm{z = {x}^{2} + {y}^{2} }}}[/tex]

Partial differentiating both sides with respect to x, we get:

[tex]{ \large\longrightarrow { \rm{ \frac{∂z}{∂x} = 2x}}}[/tex]

Partial differentiating again with respect to x, we get:

[tex]{ \large\longrightarrow {{ \rm{ \frac{ {∂}^{2}z }{∂ {x}^{2} } \: = 2 \: \: \: \: \quad -(i) }}}}[/tex]

Consider again:

[tex]{ \large\longrightarrow {{ \rm{ z = {x}^{2} + {y}^{2} }}}}[/tex]

Partial differentiating both sides with respect to y, we get:

[tex]{ \large\longrightarrow { { \rm{ \frac{∂z}{∂y} = 2y}}}}[/tex]

Now, partial differentiating both sides with respect to x, we get:

[tex]{ \large\longrightarrow{ \rm{ \frac{ {∂}^{2}z }{∂x \:∂y } = 0 \: \: \: \quad - (ii) }}}[/tex]

Consider again:

[tex]{ \large\longrightarrow { \rm{ \frac{∂z}{∂y} = 2y}}}[/tex]

Partial differentiating both sides with respect to y, we get:

[tex]{ \large\longrightarrow{ \rm{ \frac{ {∂}^{2}z }{∂ {y}^{2} } = 2 \: \: \: \: \: \quad - (iii) }}}[/tex]

Now, consider Left Hand Side, we get:

[tex]{ \large{ \rm{ \longrightarrow {x}^{2} \frac{ {∂}^{2}z }{∂ {x}^{2} } + 2xy \frac{ {∂}^{2} x}{∂x \:∂y } + {y}^{2} \frac{ {∂}^{2}z }{∂ {y}^{2} } }}}[/tex]

From Equation (i),(ii) and (iii), we can write:

[tex]\longrightarrow{ \large{ \rm{ {2x}^{2} + 0 + {2y}^{2} }}}[/tex]

[tex]\longrightarrow \: { \large{ \rm{2( {x}^{2} + {y}^{2} ) }}}[/tex]

[tex]\longrightarrow{ \large{ \rm{2z}}}[/tex]

Therefore,

[tex]{ \large{\longrightarrow \: { \rm{{x}^{2} \frac{ {∂}^{2} z}{∂ {x}^{2} } + 2xy \frac{ {∂}^{2}x }{∂x \:∂y } + {y}^{2} \frac{ {∂}^{2}z }{∂ {y}^{2} } = 2z }}}}[/tex]

Hence Proved!!

[tex] \: [/tex]

[tex]\boxed{\begin{array}{c|c}\bf f(x)&\bf\dfrac{d}{dx}f(x)\\ \\ \frac{\qquad\qquad}{}&\frac{\qquad\qquad}{}\\ \sf k&\sf0\\ \\ \sf sin(x)&\sf cos(x)\\ \\ \sf cos(x)&\sf-sin(x)\\ \\ \sf tan(x)&\sf{sec}^{2}(x)\\ \\ \sf cot(x)&\sf-{cosec}^{2}(x)\\ \\ \sf sec(x)&\sf sec(x)tan(x)\\ \\ \sf cosec(x)&\sf-cosec(x)cot(x)\\ \\ \sf\sqrt{x}&\sf\dfrac{1}{2\sqrt{x}}\\ \\ \sf log(x)&\sf\dfrac{1}{x}\\ \\ \sf{e}^{x}&\sf{e}^{x}\end{array}}[/tex]

Refer to the attachments for answer

Answer:

A

Step-by-step explanation:

Answer: 10 degrees

Step-by-step explanation:

-5+15=10

Answer:

slope: -1/2

y-int: 9/2

Step-by-step explanation:

rearrange 9-x=2y into slope-intercept form: y=mx+b (m being slope and b is y-intercept)

2y = -x + 9

divide both sides by 2 to isolate the y and get:

y = -x/2 + 9/2

m (slope) = -(1)/2

b (y-int) = 9/2

Answer:

37

Step-by-step explanation:

239-17=222

222/6=37

37

Answer:

32 is the values 21 is the integers

Step-by-step explanation:

that's may answer ty hope it's help

Complete question:

A project is graded on a scale of 1 to 5. If the random variable, X, is the project grade, what is the mean of the probability

distribution below?

Grade(X)_____ 1_____2_____3_____4_____5

Frequency____3 _____5____ 9 ____ 5 ____ 3

P(X) : _______ 0.1 ___0.2 ___0.4 ___ 0.2 __0.1

Answer:

3

Step-by-step explanation:

Given the probability distribution :

Grade(X)_____ 1_____2_____3_____4_____5

Frequency____3 _____5____ 9 ____ 5 ____ 3

P(X) : _______ 0.1 ___0.2 ___0.4 ___ 0.2 __0.1

The mean of the distribution :

Σ(X * P(X)) :

(1*0. 1) + (2 * 0.2) + (3 * 0.4) + (4 * 0.2) + (5 * 0.1)

0.1 + 0.4 + 1.2 + 0.8 + 0.5

= 3

Answer:

the mean is 3

answer choice D

Answer:

no

Step-by-step explanation:

17/8 = 2.125

1/2 = 0.5

Two ratios are proportional if they are equal.

17/8 and 1/2 are note equal, so they are not proportional.

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

Explanation:

For problem 1, we will plot a closed circle at x = -2 to include this value in the shaded solution set. We include it because of the "or equal to". The shading is to the right because of the "greater than". So we're describing all x values that are either equal to -2 or larger than -2. You could say "x is -2 or larger".

---------------------

In problem 2, we'll exclude the endpoint since we don't have "or equal to". We shade to the left to visually show all values smaller than 3.

---------------------

In problem 3, we follow the same idea as the last problem. We have an open hole to exclude the endpoint and shade to the right of 12 to describe all values larger than 12.

---------------------

With problem 4, we now include the endpoint again. This is similar to problem 1. We shade to the left to describe x values that are either -15 or smaller.

Answer:

Step-by-step explanation:

place a marker every mile along the race course. How

Answer:

Follow the steps shown below.

Step-by-step explanation:

12cos(30)+2tan(60)

[tex]12*\frac{\sqrt{3} }{2} + 2\sqrt{3}[/tex]

[tex]6\sqrt{3} + 2\sqrt{3}[/tex]

[tex]8\sqrt{3}[/tex]

[tex]\sqrt{64*3}[/tex]

[tex]\sqrt{192}[/tex]

Answer:

(1 - 2sinα)(1 + 2sinα)

Step-by-step explanation:

1 - 4sin²α ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

1 - 4sin²α

= 1² - (2sinα )²

= (1 - 2sinα)(1 + 2sinα)

Answer:

The value of the car today is $13,000, but will lose 11% of it's value each

Answer:

2474

Step-by-step explanation:

(725 x 2) + (512 x 2)

(1450)+(1024)

=2474

as a simplified fraction, the answer is 4/77

as a decimal it is about 0.0519480519480519