given:m<6=m<8b l l cprove:a l l b

(120 + 10x) sq. feet or 10(12+x) sq. feet will be the combined area of the two rooms.

the given dimensions of the living room are given as follows,

length =12

width/breadth =10

thus the area of the living room will be,

length x breadth, i.e.

=12 x 10

=120 sq. feet

the given dimensions of the dining room are given as follows,

length= x

width/breadth=10

thus the area of the dining room can be calculated as

length x breadth

=10x sq. feet

Now, to calculate the combined area of both the rooms, we have to add the area of the dining room and the area of the living room,

that is,

(120 + 10x) sq. feet

What is area?

The area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

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Answer:

-286

Step-by-step explanation:

45(-6)-16

= -270 - 16

= -286

Step-by-step explanation:

45x - 16

x = -6

45(-6) - 16

-270 - 16

-286

Hope this helps! :)

Answer:

3x - 4

Step-by-step explanation:

"Difference" is a clue word that tells you to use subtraction. The other clue word is "times" but that means times, or multiplication and is pretty straight forward.

"Three times a number" means to multiply a number, but we don't know the number, so we use a variable (a letter). I put x but you could use n or c or almost any letter for the variable.

"the difference of ___ and ___" means to subtract those two things.

So we get 3x - 4

When we have a function and want to evalueate it for some "x", we just substitute every "x" with the value in parenthesis. So, to evaluate f(a + 2), we have x = a + 2, so we need to substitute every "x" in the function with a + 2:

Now, to simplify, we first need to use the distributive property on the second parenthesis and evaluate the binomial in the first:

Now, we group the like-terms and add them:

For yhe other one, Let's do each term and then make the substraction:

So:

To answer this question, we will use the next table (obtained from the Question Tab):

City -------- Number of restaurants

Carlsbad 489

Potter Valley 261

Little Heath 282

Edgbaston 216

Barrow 317

If we want to know how many more restaurants there are in Carlsbad than in Barrow, we need to subtract the number of restaurants in Barrow from Carlsbad as follows:

From the table, we have that in Carlsbad there are 489 restaurants, while there are 317 in Barrow.

We can check this as follows:

In summary, we can say that there are 172 more restaurants in Carlsbad than in Barrow.

Question 16

[tex](f(x), g(x))=x^2, (x-9)[/tex]

Question 17

[tex](f(x), g(x))=\sqrt{x}, 9+\sqrt{x}[/tex]

The values for first question are f(x) = x², g(x) = (x - 9) and for second question f(x) = √x, g(x) = 9 + √x.

A function may be defined as an expression in which for one value of input variable x there is only one value of output variable y. The input variable is called independent variable and output variable is called dependent variable. A composite function is the one which is written as a combination of two function. For two given functions f(x) and g(x) the composite functions are f(g(x)) and g(f(x)). In the first question the composite function is F(x) = (x - 9)². the parent functions will be f(x) = x² and g(x) = (x - 9).

in the second question the composite function is H(x) = √(9 + √x). The parent functions will be f(x) = √x and g(x) = 9 + √x.

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We know that the mean is 80, the median is 90, and the mode is 70. This means that the majority of students got an 80 on the test.

However, the median is 90, which means half of the class is below 90 where Tom's grade is placed.

Answer:

10 m

Step-by-step explanation:

Area of a square

[tex]A=s^2[/tex]

where s is the side length.

If the area of the floor is 6 m²:

[tex]\begin{aligned}A&=s^2\\\implies 6&=s^2\\\sqrt{6}&=\sqrt{s^2}\\s&=\sqrt{6}\end{aligned}[/tex]

Therefore, the side length of the square is √6 m.

Perimeter of a square

[tex]P=4s[/tex]

where s is the side length.

Substitute the found value for s into the formula to find the perimeter:

[tex]\begin{aligned}P&=4s\\\implies P&=4 \cdot \sqrt{6}\\P&=4 \sqrt{6}\\P&=9.79795897...\\ P&=10 \sf \;m\;(nearest\:integer)\end{aligned}[/tex]

Therefore, the perimeter is 10 m to the nearest integer.

1

Step

Multiple both numerator and both denominator

2

3

4

We are given the following equation:

In the first step we will use the distributive property on the left side:

In step 2, we will add like terms on the left side using associative properties of addition and subtraction and we will subtract 20 from both sides, we get:

Solving the operations we get:

In step 3 we will add 34x to both sides, this is the inverse additive inverse:

Solving the operations:

In step 4, we divide both sides by 17, this is the division property of equality:

Solving the operations:

The price that Misu can pay for a comforter based on the markup percentage is $103.57.

From the information, the Bedspread shop knows his customers will pay no more than $145 for a comforter Misu wants a 40 percent markup on selling price.

Let the selling price be represented as x. Based on the information given, this will be illustrated as:

x + (40% × x) = 145

x + 0.4x = 145

1.4x = 145

Divide

x = 145/1.4.

x = 103.57

The selling price will be $103.57.

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The product of  (7) (-16)(-7) (-1) is - 784 by using simple multiplication.

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. The symbols for multiplication are a cross (x), an asterisk (*), and dot (.). You seem to utilize the cross a lot when you write in your notebooks. In both algebra and computer languages, the asterisk and dot are symbols (higher mathematics).

7 × -16 = -112

-112 × -7 = 784

784 × -1 = -784

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Answer:

-42/7 and 42/-7

Explanation:

The absolute value of a number is represented by:

The lines represent absolute value of a number x, and what it does is that it makes everything into a positive number.

For example |-5|=5 and |5|=5, so we always have two options with an absolute value: that it comes from a negative number or that it comes from a positive number.

In this case we have that a number with an absolute value of 42 (it could be |-42|=42 or |42|=42) divided by a number with an absolute value of 7 (it could be |-7|=7 or |7|=7) the quotient is -6.

One possible numberic equation is:

Since this meets all the above conditions

Another possible numeric equation is:

Since this too meets all the above conditions.

The ordered pair that describes the location of N is (2,6)

Given:

N's coordinates are: (-2,-6)

Point N ′ is produced by reflecting point N over the y-axis.

By reflecting point N' over the x-axis, the final point N" is produced.

x , y = -x , y

N(-2 -6) = N'(2 6)

To locate the ordered pair describing where N" is located.

Point N's coordinates are (-2,-6). Point N ′ is produced by reflecting point N over the y-axis.

x , y = -x , y

N(-2 -6) = N'(2 6)

The resultant point N" is created by reflecting point N' over the x-axis.

The ordered pair for point N" is therefore (2,6) gives its location.

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Given the two sides measurement,

• Assuming that the other side represent x and the other side represent y,( 4cm;6cm) , and that we are drawing a right angle triangle .We can constuct a triangle as follows :

• We can find the value of side h by using Pythagorean theorem:

• Subsequently, we will find angle angle , as shown in the diagram above as follows:

• Since we have angle ,= 56.3 °, ,we can find, angle :

• + + 90° = 180 °,....(angles in a triangle adds up to 180°)

∴ = 180° -90° -56.3°

=33.7°

To answer this question, we will use the following diagram as reference:

To determine the tangent of θ, we have to find the value of x.

To find x, we use the Pythagorean theorem and get:

Therefore:

Therefore:

Answer:

Answer

Options A, F, G, N

The line segments include

QR

QS

QT

RS

RT

ST

Note that the segments only have a dash on top of them and not an arrow.

Explanation

A line segment is a region of a line bounded by two different endpoints and contains all the points on the line that are between the two endpoints.

From the attached image, we can see that there is a line with infinite length (the arrows at the two endpoints indicate that this line continues till infinity), has points Q, R, S and T.

So, the line segments will be any space from one endpoint to another. They'll include

QR

QS

QT

RS

RT

ST

Note that the segments only have a dash on top of them and not an arrow.

Hope this Helps!!!

Hi i hope this helps you out

Answer:

72.7% to nearest 10th percent would be 73%!

Step-by-step explanation:

Hope it helps! =D

Given:

Slope = 1/3

Contain the point = ( -3,-1 )

Find-:

The equation of a line.

Explanation-:

The general equation of a line is:

Where,

Given the slope is 1/3, then the equation of the line become.

The value of y-intercept is:

The point (-3,-1) contains the line so its satisfied the equation.

So equation of line become:

The final equation of line is:

The sectorial area of the circle is equal 31.3cm^2

The formula for the b of the sector of a circle is /360o (r2) where r is the radius of the circle and  is the angle of the sector.

Area of a Sector of Circle = (θ/360º) × πr^2, where, θ is the sector angle subtended by the arc at the center, in degrees, and 'r' is the radius of the circle.

Data;

The area of the sector can be calculated using the formula given

[tex]A = \frac{\theta }{360} * \pi r^2[/tex]

Substituting the values into the formula;

[tex]A = \frac{\theta }{360} * \pi r^2\\A = \frac{56}{360}* \pi * 8^2\\A = 31.27cm\\A = 31.3cm^2[/tex]

The area is equal 31.3cm^2

Translation:

The area of a circular sector of a circle with radius equal to 8cm and central angle equal to 56 degrees.

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Answer:

Part A: C(x) = 0.068x+0.8

Part B: 1.28

Part C: 9.76

Explanation:

Part A:

The cost C equals

cost = revenue - profit

which is

Part B:

The cost of producing 7 units is found by putting in x = 7 into the above equation. This gives

Hence, the cost of producing 7 items is 1,28 million dollars.

Part C:

To break even, the cost must equal the revenue

or

subtracting 0.068 from both sides gives

dividing both sides by 0.082 gives

which is the break-even point

We have to reflect the triangle across the y-axis.

If we have a point P = (x,y) and we reflect it across the y-axis, we will change the x-coordinate to its opposite value and and the y-coordinate is kept the same.

The image point then is P' = (-x,y).

Then, to reflect the triangle, we have to reflect the three vertices and then join the vertices.

We can then reflect the vertices as:

Answer: [tex]9x-4[/tex]

Step-by-step explanation:

Reflecting across the y-axis means [tex]f(x) \longrightarrow f(-x)[/tex].

[tex]g(x)=-9(-x)-4=9x-4[/tex]

Answer:
The sum of a sequence is known as a series. Thus means a harmonic series is infinite with no limit

The formula for the volume of a cone is a third of the product of pi, its height h and the square of its radius r. Then, it is:

Answer: C

ANSWER

EXPLANATION

We want to solve the given linear equation:

To do this, divide both sides of the equation by -6 to isolate u and simplify:

That is the solution to the linear equation.

The equation of the line 4x-20y = -160 in the slope intercept form is y = x/5 + 8 .

The equation of the line in slope intercept form is written as

y = mx + c ,

where m is the slope of the line , and c is the y intercept .

In the question ,

the equation of the line is given

equation of line is given as 4x-20y = -160

to convert the equation in slope intercept form , we rewrite it as

20y = 4x+160

dividing both sides by 20 ,

we get

20y/20 = 4x/20 + 160/20

y = x/5 + 8

hence ,the slope intercept form is y = x/5 + 8 , where 8 is the y intercept and 1/5 is the slope .

Therefore , the equation of the line 4x-20y = -160 in the slope intercept form is y = x/5 + 8 .

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A.

[tex]3n =19 - 1 \\ 3n = 18 \\ \frac{3n}{3} = \frac{18}{3} \\ n = 6[/tex]

B.

[tex]21 + 5 = - 2p \\ 2p = - 26 \\ \frac{2p}{2} = \frac{26}{2} \\ p = 13[/tex]

HOPE THIS HELPS.