The area of a rectangular carpet is 252 square feet. The length is nine feet more than the width. Find the length and the width of the carpet.

Answer:

y= -x-7

Step-by-step explanation:

Slope intercept form: y = mx + b

m = slope

b = y intercept

The first thing you must do is isolate y so that it is by itself on the left side of the equation:

-x = y + 7

Subtract 7 to both sides:

-x - 7 = y + 7 - 7

-x - 7 = y

Flip:

y = -x - 7

-x = y + 7 in slope intercept form is y = -x - 7

This means the slope is -1 and the y-intercept of the equation is (0, -7)

Answer:

-20

2(xy-7)=-20 with x=-1 y=3

Step-by-step explanation:

2(xy-7)=?

When variables are connected such as xy, this means to multiply.

x=-1

y=3

Multiply the x and the y together.

-1*3=-3. Plug that into the equation.

2(-3-7)=?

Subtract the inside the parenthesis.

2(-10)=?

Multiply. Remember when multiplying a positive and a negative the answer will always be a negative.

2(-10)=-20

This means that 2(xy-7)=-20 with the x=-1 and y=3.

Hope this helps!

If not, I am sorry.

Solution: 8p+44

Detailed explanation:

First we can "expand" by multiplying 6 times the parentheses and then 2 times the other set of parentheses.

[tex]--\mapsto\boldsymbol{6(p+6)+2(p+4)}\\\\---\mapsto\boldsymbol{6p+36+2p+8}[/tex]

To make life easier let's just put the p's next to each other.

[tex]--\mapsto\boldsymbol{6p+2p+36+8}[/tex]

Now let's add the p's

[tex]---\mapsto\boldsymbol{8p+44}[/tex]

Voila! There's our answer!

__________________

Hope I helped! Best wishes.

Reach far. Aim high. Dream big.

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Answer:

y = 7/6x - 62/3

Step-by-step explanation:

The equation for slope:

y = mx + b

m is the slope and b is the y-intercept

y = 7/6x + b

-9 = 7/6(10) + b

-9 = 35/3 + b

-62/3 = b

Answer:

( 8x - 4 ) ( x - 2 )

Step-by-step explanation:

8x² - 12x - 8

8x² - 16x + 4x - 8

8x ( x - 2 ) - 4 ( x - 2 )

( 8x - 4 ) ( x - 2 )

Answer:

⇒ [tex]4(x-2)(2x+1)[/tex]

Step-by-step explanation:

1) Common factor

⇒ [tex]8x^2-12x-8\\[/tex]

⇒ [tex]4(2x^2-3x-2)[/tex]

2) Use the sum-product pattern

⇒ [tex]4(2x^2-3x-2)[/tex]

⇒ [tex]4(2x^2+x-4x-2)[/tex]

3) Common factor from the two pairs

⇒ [tex]4(2x^2+x-4x-2)[/tex]

⇒ [tex]4(x(2x+1)-2(2x+1))[/tex]

4) Rewrite in factored form

⇒ [tex]4(x(2x+1)-2(2x+1))[/tex]

⇒ [tex]4(x-2)(2x+1)[/tex]

Answer:

2.5 gallons of the 20% solution must be replaced by the 36% solution.

Step-by-step explanation:

[tex].12(20 - x) + .36x = 20(.15)[/tex]

[tex]2.4 - .12x + .36x = 3[/tex]

[tex]2.4 - .24x = 3[/tex]

[tex] - .24x = - .6[/tex]

[tex].24x = .6[/tex]

[tex]x = 2.5[/tex]

Compare the quantity in Column A with the quantity in Column B.

Column A Column B, The two quantities are equal.

Generally, the surface that has one end or side that is higher than the other (or vice versa); is a surface that slopes up or down.

In conclusion, Compare the number in Column A with the number in Column B.

The two amounts are identical in Columns A and B.

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The statements that describe a triangular prism are:

A triangular prism is a three-dimensional object that is made up of one base that has the shape of a triangle and three lateral sides that have the shape of a rectangle. A triangular prism has 5 faces, 9 edges and 6 vertices.

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The area of the square is 16 square inches and its perimeter is 16 inches.

What is Area of square ?

A square is a two-dimensional geometric shape with four equal sides and four right angles. The area of a square is the measure of the region enclosed by the square. The area is expressed in square units, such as square inches, square meters, or square feet.

The area of a square is given by the formula:

A = s²

where A is the area and s is the length of a side.

If the side length of the square is 4 inches, the area can be calculated as:

A = 4² = 16 square inches.

The perimeter of a square is given by the formula:

P = 4s

where P is the perimeter and s is the length of a side.

If the side length of the square is 4 inches, the perimeter can be calculated as:

P = 4 x 4 = 16 inches.

Therefore, the area of the square is 16 square inches and its perimeter is 16 inches.

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Answer:

the answer to that is B. 5 cells

Answer:

jjxfzhfxjgjhzjjjtxjxjxktxjtxjtxtxh

We will apply the Pythagoras theorem to find the measure of the unknown leg in a triangle when one leg and the hypotenuse are provided dimensions.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometric function.

According to Pythagoras, the sum of the squares of two sides equals the square of the longest side.

[tex]\rm h^2 = p^2+ b^2[/tex]

Where,

h is the hypotenuse

p is the perpendicular

b is the base

If any of the two is given the third side will be obtained using the  Pythagoras theorem.

In a triangle with given measurements for one leg and the hypotenuse, we will determine the measure of the unknown leg by the Pythagoras theorem.

Hence we willl apply the pythogorous theorem for finding the unknown side.

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Answer:

$15,539.67

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=11000\left(1+\frac{0.058}{4}\right)^{(4 \times 6)}[/tex]

[tex]\implies \sf A=11000(1.0145)^{24}[/tex]

[tex]\implies \sf A=15539.67451...[/tex]

Therefore, the value of the investment after 6 years will be $15,539.67 to the nearest cent.

Answer:

See below ~

Step-by-step explanation:

Linear pairs add up to 180 degrees.

⇒ 4x - 10 + 3x + 43 = 180

⇒ 7x + 33 = 180

⇒ 7x = 147

⇒ x = 21

∠A = 4(21) - 10

∠A = 84 - 10

∠A = 74°

∠B = 3(21) + 43

∠B = 63 + 43

∠B = 106°

Answer:

3 ÷ y

Step-by-step explanation:

Quotient refers to the division of two values, in this case 3 and y.

Answer:

3/y

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

median basically means the number which is in the middle so 8,8,9, 5 ,10,4,9

the median is 5 because left and right middle is 5 that's why it is median

The expression which represents the other factor, or factors, of the given polynomial is option (C) (2x-1)(x+1)

A cubic equation in algebra is a one-variable equation of the form ax3+bx2+cx+d=0 where an is nonzero. The roots of the cubic function defined by the left side of this equation are the solutions to this equation.

Given expression 2x³-3x²-3x+2 whose one of factor is (x-2)

We have to find second factor of given equation

First we will be rational root theorem to given expression so will get following expression:

[tex]\left(x+1\right)\frac{2x^3-3x^2-3x+2}{x+1}[/tex]

So one factor is (x-1) and now simplifying [tex]\frac{2x^3-3x^2-3x+2}{x+1}[/tex]  we get              2x² - 5x +2 and the factor of 2x² - 5x +2 will be (2x-1)(x-2)

Hence the expression which represents the other factor, or factors, of the given polynomial is option (C) (2x-1)(x+1)

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Answer:

xhdvuvzxvzvkkzv jzh jhj,

Step-by-step explanation:

Placing the equations under the correct solution, we get

x = 3                                      x ≠ 3

-14x = -42                              -5 + x = -9

[tex]-\frac{3}{5} +x = \frac{12}{5}[/tex]                          [tex]\frac{x}{3} =9[/tex]

[tex]\frac{x}{4} =\frac{6}{8}[/tex]                                    

x -5 = -2            

From the question, we are to place the equations under the correct solution

To do this, we will solve the equations one after the other

x = -42/-14

x = 3

x = -9 + 5

x = -4

∴ x ≠ 3

[tex]x = \frac{12}{5} +\frac{3}{5}[/tex]

[tex]x = \frac{12+3}{5}[/tex]

[tex]x = \frac{15}{5}[/tex]

x = 3

[tex]x=\frac{6\times 4}{8}[/tex]

[tex]x=\frac{24}{8}[/tex]

x = 3

x = 3 × 9

x = 27

∴ x ≠ 3

x = -2 + 5

x = 3

Hence, placing the equations under the correct solution, we get

x = 3                                      x ≠ 3

-14x = -42                              -5 + x = -9

[tex]-\frac{3}{5} +x = \frac{12}{5}[/tex]                          [tex]\frac{x}{3} =9[/tex]

[tex]\frac{x}{4} =\frac{6}{8}[/tex]                                    

x -5 = -2            

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Δ DGC is right angled triangle because Line E G is perpendicular-to CC', Option D is the correct answer.

Triangle is a polygon with three sides , angles and vertices.

It is given that the there are two Triangles , ABC and A'B'C' as an image of the ABC

* Line segment AA' has a midpoint at point F

*D is the mid point of the line joining BB' .*

The figure is attached with the answer.

the line of reflection of the object is always perpendicular to the object and the image.

it is also given that CGF is a right angle.

Therefore triangle DGC is right angled triangle , (the option given in the question is incorrect ) ,  Line E G is perpendicular-to CC'.

Option D is the correct answer.

Please Refer to the image for correct coordinates.

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Answer:

1073

Step-by-step explanation:

it's simple addition

The sum of the triangular numbers is [tex]\frac{n(n+1)(n+2)}{6}[/tex]

According to the question, the series of triangular numbers is given as in the form of the number of dots constituting the equilateral triangles i.e.
1, 3, 6, 10, 15 . . . . .n

triangular number are the sequence and series of the numbers and each number represents and constitute in visualization of  series of  equilateral triangle.

given series in the figure
1, 3, 6, 10, 15, . . . . . .  ., n
each number represents the number of dots containing in triangle
now the series can be given by
[tex]S = \frac{n(n+1)}{2}[/tex]  for n = 1, 2, 3, 4,. . . . .n
now , according to the question the sum of the series can be given as
⇒  ∑S
⇒   ∑[tex]\frac{n^2+n}{2}[/tex]
⇒  [tex]\frac{1}{2}[\sum n^2+\sum n]\\\frac{1}{2}[\frac{n(n+1)(2n+1)}{6}+\frac{n(n+1)}{2}] \\\frac{n(n+1)}{4}[\frac{(2n+1)}{3}+1] \\\frac{n(n+1)}{4}[\frac{(2n+1+3)}{3}] \\\frac{n(n+1)}{4}[\frac{(2n+4)}{3}] \\\frac{n(n+1)}{4}2[\frac{(n+2)}{3}]\\\frac{n(n+1)(n+2)}{6}[/tex]

Thus, the sum of the triangular number is given by [tex]\frac{n(n+1)(n+2)}{6}[/tex]

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Step-by-step explanation:

[tex] = (f + g)(4)[/tex]

[tex] = f(4) + g(4)[/tex]

The answer is A.

Answer:

183

Step-by-step explanation:

The absolute value of a number is the number's distance from zero, which will always be a positive value. To find the absolute value of a number, drop the negative sign if there is one to make the number positive.

Answer: 183 ✅

Step-by-step explanation:

Hii, do you need to know the absolute value of "-183"? No problem! (:

The absolute value of a number is that number's distance from zero.

That's why absolute value is always positive, because negative distances don't exist.

That's why the absolute value of a number is always positive.

| | denotes absolute value

[tex]\large\boldsymbol{\therefore,\;the\;absolute\;value\;of\;-183\;is\;183}}[/tex]

Voila! There's our answer, cheers! (:

Hope that this helped! Best wishes.      

[tex]\bigstar\underbrace[/tex]

Answer:

x = 4  &  x = -2

Step-by-step explanation:

For rational functions (functions which themselves are a fraction, with polynomial pieces in the numerator and polynomial pieces in the denominator), these functions have "discontinuities" anywhere the denominator is equal to zero.  Usually, those discontinuities are "vertical asymptotes".  Occasionally, those discontinuities are "holes".

A discontinuity is a "hole," only if both the numerator AND the denominator are zero for that same value of x.  If that value of x doesn't make the numerator zero (it only makes the denominator zero), the discontinuity is just a vertical asymptote.

To find the discontinuities, we'll be making an entirely separate equation.  It's not the function, it's not using algebra to change both sides of the equation/function we started with ... it's pretty much just like scratch work to figure out something that you can use later (although, your teacher may want to see your work on how you found them).

The equation we need for this is the denominator of our rational function set equal to zero:

[tex](x-4)(x+2)=0[/tex]

Note, this equation doesn't have a denominator.  It's not the original function.  It's like scratch work.  This equation is designed as if we want the denominator of our function to be zero, and to find the values of x that will make us divide by zero in the original function.

There are many ways to solve this equation.  The easiest is remembering the zero product property.  The Zero Product property states that if the product of two things is equal to zero, then at least one of the original things had to be zero:  [tex]\text{If }a*b=0,\text{ then }a=0\text{ or }b=0 \text{ (or both)}[/tex]

Noting that our equation is a product of two things, and is equal to zero, the zero product property allows us to separate our equation into two equations:

[tex]x-4=0, \text{ or } x+2=0[/tex]

Solving each equation by isolating x, by adding or subtracting the relevant number from both sides of the equations:

[tex]x=4, \text{ or } x=-2[/tex]

So these values of x will make the denominator of the original function zero.  These are both discontinuities of the function, so while when we were solving for values of x that would make the denominator zero, it was appropriate to say "or", we know that both of these values are discontinuities and now we list them both saying "and":

Discontinuities: [tex]x=4 \text{ and } x=-2[/tex]

But wait!  Are they holes, or are they just vertical asymptotes?  Do we have one of each?

Testing to see if the discontinuities are asymptotes:

To test and see if the discontinuities we've found are holes, we need to substitute them into the numerator of the original function, and see the result.... but just the numerator (we already know they will make the denominator zero, and we can't divide by zero)

Since the numerator is just x, we're checking to see if 4=0, or if -2=0.  They don't.  So, for this function, both of the discontinuities are vertical asymptotes.

Listing the asymptotes

Vertical asymptotes at [tex]x=4 \text{ and } x=-2[/tex]

The correct answer is option B which is P ( A|B) will be ( 4 / 9 ).

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Given that:-

The total sample will have 9 numbers

S = { 1,2,3,4,5,6,7,8,9} = 9

Even Number = { 2,4,6,8} = 4

Odd Number  = { 1,3,5,7,9} = 5

P ( A ) = ( 4 / 9 )

P ( B ) = ( 5 / 9 )

The probability will be calculated as:-

P( A:B ) = [tex]\dfrac{P(A)\times P(B)}{P(B)}[/tex]

P( A:B ) =[tex]\dfrac{( 5/9 ) ( 4/9 )}{5 / 9 }[/tex]

P( A:B ) = 4 / 9

Therefore the correct answer is option B which is P ( A|B) will be ( 4 / 9 ).

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Answer:

The group that is most likely able to have a lower mean age of painting students is Group A

Step-by-step explanation:

mean = sum of all terms divided by total number of terms

Looking at the graph data you have provided you can see that group A's students are a younger than students in Group B.

Which means when you calculate the mean the group which would give you the lower ratio with the same denominator of K (let there is K number of students in the class) will have lower mean age

here group A students are younger therefore their ratio will be lower

hence lower mean age

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