What is the solution to this system of equations?
y=1/3​x+4
y=1/6​x+3

The area of living room is (126 + 10.5x) square feet. The solution has been obtained by using area of rectangle.

What is area of rectangle?

The territory a rectangle occupies inside its four sides or limits is known as its area.

We are given that the length of the room is being expanded by x feet.

This means that the extended length of the room is (12 + x) feet

We are given width of the room to be 10.5 feet

We know that area of a rectangle = length * width

So,

⇒Area = (12 + x) * 10.5

⇒Area = (126 + 10.5x) square feet

Hence, the area of living room is (126 + 10.5x) square feet.

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Answer:

The relation is not a function

Step-by-step explanation:

First, it's important to know that for a relation to be a function, each input can only have one output. Since the input 3 has both the output 9 and 27, the relation can not be a function.

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The missing letter in this sequence is s.

The term called sequence in math of defined as as an arrangement of numbers in a particular order.

Here we know the following sequence from the question that can be written as,

g w m t _ q y

And we need to find the missing term in it.

When we number the alphabets then we get the the value for

=> g = 7

=> w = 23

=> m = 13

=> t = 20

Here the rule has been used is written as,

=> 7 x (n) + 6

where n refers the position of the letter.

Then the missing letter is calculated as,

=> 19.

Therefore option c is correct.

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Answer:

Step-by-step explanation:Answer: Quadralateral has 4 sides shape all of not 4 sides that is not quadralateral. Example of quadralateral: Parallelogram. Rectangle.

Answer:

nice

Step-by-step explanation:

Answer: [tex]g(f(x))=9x^2 -6x-3[/tex]

Step-by-step explanation:

[tex]g(f(x))=g(3x^2 -2x+4)=3(3x^2 -2x+4)-15=9x^2 -6x+12-15=9x^2 -6x-3[/tex]

Hello!

To solve the first problem:

Radii are lines that go from the center of a circle to the edge. There are three of these lines in this circle.

The radii for this circle are lines AD, AC, and AD.

The correct answer choice is answer choice C.

To solve the second problem:

We have two congruent triangles. This means that their sides and angles are identical. We need to find the angles that are equal to that of angles A and C in triangle one.

These would be angles D and F.

The correct answer choice is answer choice A.

Hope this helps!

The standard deviation of the distribution of price increases over this period is 0, and the modal price increase during this period is $2.

a) The standard deviation of the distribution of price increases over this five-year period can be calculated using the formula for the standard deviation of a population:

SD = √(Σ(x - μ)²/N)

Where x is each price increase, μ is the mean of the price increases, and N is the number of price increases.

First, we find the mean:

μ = (4 + 2 - 1 + 2 + 2) / 5 = 9/5

Next, we calculate the standard deviation:

SD = √(((4 - 9/5)^2 + (2 - 9/5)^2 + (-1 - 9/5)^2 + (2 - 9/5)^2 + (2 - 9/5)^2) / 5) = √(0 / 5)

= 0

b) The modal price increase during this period is the one that occurs most frequently. In this case, the modal price increase is $2, as it occurs thrice.

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The number of tiles that must be sold in a quarter for Belleterre Tile to earn $15,210 in quarterly operating profit is 138000 tiles .

To calculate the number of tiles needed to be sold in order to earn $15,210 in quarterly operating profit, you need to first find the unit variable cost (the cost of producing each tile),

The average variable cost per tile is = 357556/125900 = $2.84  ;

the average selling price per tile is = 463312/125900 = $3.68   ;

So , Average contribution margin per tile is = $3.68 - $2.84 = $0.84  ;

The Number of tiles to earn  earn $15,210 in quarterly operating profit is calculated as : (total fixed costs + profit) / (contribution margin)

⇒ (100800+15120)/0.84

⇒ 115920/0.84 = 138000 tiles .

Therefore , to earn $15,210 in quarterly operating profit , 138000 tiles should be sold .

The given question is incomplete , the complete question is

Belleterre Tile Revenue and Costs for Third Quarter is :

Total Revenue sold   : 125900 tiles  ;

Total revenue            : $462312   ;

Total Variable costs  : 357556    ;

Total Fixed Costs      : 100800  ;

The CFO tells you that the company owner have said that unless the quarterly operating profit exceeds $15210, they will liquidate the company. How many tiles would have to be sold in a quarter for Belleterre Tile to earn $15,210 in quarterly operating profit ?

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

Work Shown:

Solve the first equation for y.

3x+y = 0

y = -3x

Then substitute that into the other equation to solve for x.

x-6y = 19

x-6(-3x) = 19

x+18x = 19

19x = 19

x = 19/19

x = 1

Once we determine x, we can determine y.

3x+y = 0

3*1+y = 0

3+y = 0

y = -3

Or you could say:

x-6y = 19

1-6y = 19

-6y = 19-1

-6y = 18

y = 18/(-6)

y = -3

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

In summary we get x = 1 and y = -3 pairing up together.

The ordered pair solution is (x,y) = (1, -3)

To confirm the answer, plug the coordinates back into the original equations. Simplify both sides. You should get the same thing on both sides. I'll let you do these confirmation steps.

Visually you can use something like Desmos or GeoGebra to note that the two lines intersect at (1, -3)

Given:-

Multiply the given eqⁿ ( 1 ) to 6

now , add the eqⁿ ( 3 ) to eqⁿ ( 2 )

18x + 6y = 0

x - 6y = 19

————————

19x = 19

x = 19/19

x = 1

now , put the value of x = 1 in eqⁿ ( 1 )

━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

For the function  h (a) = In(t sint + 5)dt the decreasing interval is 14.322

The function h is a mathematical expression that relates a variable "a" to the result of an integral of another function.

In this specific case, the integral is calculated for the function "t sin t + 5" with respect to "t" from 1 to "a".

We can use differentiation to find the critical points of "t sin t + 5" and determine if it is increasing or decreasing over the interval.

We find that the function has a critical point at t = π/2, where it changes from increasing to decreasing. This means that the function h is decreasing over the interval (π/2, 7).

However, for values of "a" less than π/2, the function being integrated is increasing, meaning the function h is also increasing for those values of "a".

Therefore, option (c) is correct.

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Although part of your question is missing, you might be referring to this full question: On a map, the scale is inches/miles = 1/75. Going from home to the first destination is 1.5 inches, and then from there to the next destination is 2.25 inches. How many miles were travelled?

281.25 miles were travelled.

The distances travelled in inches need to be added.

1.5inches + 2.25inches = 3.75 inches

Let y be the number of miles. Thus, the proportion for the given situation is,

1/75 = 3.75/y

In the next step, it needs to be cross-multiplied,

1×y = 3.75×75

Thus,

y = 281.25

So, 281.25 miles were travelled.

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Answer:

A)  The perimeter of the figure is 19 units (nearest unit).

B)  The area of the figure is 23 square units (nearest square unit).

Step-by-step explanation:

The given figure is part of a circle and part of a square.

From inspection of the diagram, the circular part is a quarter circle.

Therefore, the length of the curved part of the figure is a quarter of the circumference of a circle (with radius 3 units).

[tex]\boxed{\begin{aligned}\textsf{Circumference of a circle}&=2 \pi r\\\\\implies \textsf{Circumference of a $\frac{1}{4}$ circle}&=\dfrac{1}{4} \cdot 2 \pi r\\\\&=\dfrac{1}{2}\pi r\end{aligned}}[/tex]

The perimeter of the figure is the sum of the length of the curved part and the measures of the straight edges.

[tex]\begin{aligned}\textsf{Perimeter}&=\dfrac{1}{2} \pi \cdot 3+2 \cdot 2+2 \cdot 5\\&=\dfrac{3}{2}\pi+4+10\\&=18.7123889...\\&=19\; \sf units\end{aligned}[/tex]

Therefore, the perimeter of the figure is 19 units to the nearest unit.

The area of the curved part of the figure is a quarter of the area of a circle (with radius 3 units).

[tex]\boxed{\begin{aligned}\textsf{Area of a circle}&=\pi r^2\\\\\implies \textsf{Area of a $\frac{1}{4}$ circle}&=\dfrac{1}{4} \pi r^2\end{aligned}}[/tex]

The area of the part of a square can be separated into two rectangles (see attachment).  The area of a rectangle is the product of its width and length.

The area of the figure is the sum of the area of the curved part and the two rectangles.

[tex]\begin{aligned}\textsf{Area}&=\dfrac{1}{4}\pi \cdot 3^2+3 \cdot 2+2 \cdot 5\\&=\dfrac{1}{4}\pi \cdot 9+6+10\\&=\dfrac{9}{4}\pi +6+10\\&=23.0685834...\\&=23\; \sf square\;units\end{aligned}[/tex]

Therefore, the area of the figure is 23 square units to the nearest square unit.

The perimeter of the figure, which is part circle and part square, can be found to be 18. 71 units.

The area of the figure would be 23. 07 units ².

The perimeter is the distance around the shape so we can add up the sides given and then find out the missing dimensions around the quarter circle.

The distance of that quarter circle is:

= ( Pi x Diameter ) / 4 quarters

= ( π x ( 3 + 3 )) / 4

= 4. 71 units

The perimeter then is:

= 2 + 5 + 5 + 2 + 4. 71

= 18. 71 units

To find the area, you can divide the figure into three shapes which would be two rectangles and one quarter circle.

The area of the rectangles would be:

= Length x Width                                                = 5 x 2

= 3 x 2                                                                 = 10 units ²

= 6 units ²

The area of the quarter circle would be:

= ( π x radius ² ) / 4

= ( π x 3 ² ) / 4

= 7. 07 units ²

Sum them all up:

= 6 + 10 + 7. 07

= 23. 07 units ²

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Answer:

[tex]f^{-1}(x)=\sqrt{x+6}[/tex]

Step-by-step explanation:

To find the inverse of a function you have to exchange the variables, the "x" become "y" and vice versa.

After doing that you must leave the y-value on the left side of the equation.

[tex]y = x^2 - 6\\\\x=y^2-6\\\\x+6=y^2\\\\y^2=x+6\\\\\sqrt{y^2}=\sqrt{x+6} \\\\y=\sqrt{x+6} \\\\f^{-1}(x)=\sqrt{x+6}[/tex]

A number line starting from 0 and directed to +30 represents  how long it took Courtney to run 3.1 miles

Given is that Alan ran 3.1 miles in 35 minutes and Courtney ran 3.1 miles 5 minutes faster than Alan.

It is given that Courtney ran 3.1 miles 5 minutes faster than Alan. This means that he runs 3.1 miles in (35 - 5) or 30 minutes.

Therefore, a number line starting from 0 and directed to +30 represents  how long it took Courtney to run 3.1 miles.

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Answer:

45%

Step-by-step explanation:

17 + 14 = 31 8th graders

14 divided by 31, times 100 = 45%

So, 45% of the 8th graders estimated they spend less than an hour a day on social media.

The correct expression is (x+9)/2, The smallest number is 0.104.

Compare all the digits in ascending order before the decimal, then all the digits in ascending order after the decimal, to find the smallest number.

Sort the following integers in ascending order: 0.1, 0.005, 1000, 1.001, 100, 0.05. The sequence is as follows:

0.005, 0.050, 0.1, 1.001, 100, 1000.

Because the 5 in 0.050 is in the hundredths place whereas the 5 in 0.005 is in the thousandths place, 0.005 is smaller than 0.050.

When we compared two decimal values in Example 1, we saw that 0.2 is greater than 0.15.

The smallest number is 0.104.

The correct expression is (x+9)/2

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Answer:

y = (1/6)x - 5/3

Step-by-step explanation:

Please find the attachment for detail

It is linear. The cost of mowing a lawn for Travis is directly proportional to the number of hours he works. For every hour he works, he charges $4 more. So the equation would be y = 4x + 10 (where y is the cost and x is the number of hours worked)

The expression (4/9) - (5/7)[(2/3) x (2/3)] in the simplified form will be 8/63.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ (4/9) - (5/7)[(2/3) x (2/3)]

Simplify the expression, then we have

⇒ (4/9) - (5/7)[(2/3) x (2/3)]

⇒ (4/9) - (5/7)(4/9)

⇒ (4/9) - (20/63)

⇒ (28 - 20) / 63

⇒ 8 / 63

The expression (4/9) - (5/7)[(2/3) x (2/3)] in the simplified form will be 8/63.

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The first six values of the recursive function  F(n+2) = 2F(n) + F(n+1) are 0, 1, 1, 3, 5, and 11.

We are given a recursive function:

                            F(0) = 0, F(1) = 1

                        F(n+2) = 2F(n) + F(n+1)    , n ≥ 0

For n = 0:

                     F(0+2) = 2F(0) + F(0+1)

                         F(2) = 2(0) + 1    

                         F(2) = 1      

For n = 1:

                     F(1+2) = 2F(1) + F(1+1)

                         F(3) = 2(1) + 1    

                         F(3) = 3

For n = 2:

                     F(2+2) = 2F(2) + F(2+1)

                         F(4) = 2(1) + 3    

                         F(4) = 5    

For n = 3:

                     F(3+2) = 2F(3) + F(3+1)

                         F(5) = 2(3) + 5    

                         F(5) = 11        

Hence, F(0) = 0, F(1) = 1, F(2) = 1, F(3) = 3, F(4) = 5, F(5) = 11.

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On solving the provided question, we can say that in the quadrilateral BD = 11, BC = 8, DC = 8 and perimeter of ABCD is = 38

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

in the quadrilateral

BD = 11 ( equal angle have equal sides)

BC = 8

DC = 8

perimeter of ABCD is = 38

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The equation has one solution at (0, -2) for the system of linear equations represented in the graph.

The points where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. In other words, the set of all possible values for the variables that satisfy the specified linear equation constitutes the solution set of the system of linear equations.

Given the graph,

and the line passes from (0, -2) and (4, 0)

since the line passes from  (0, -2) and (4, 0),

so one of the solutions is at (0, -2),

and another solution is at (4, 0).

according to the options equation has  (0, -2) as one of the solutions.

Hence option B is correct.

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The second order differential equation:-

[tex]\frac{d^2y}{dx^2}+P(x)\frac{dy}{dx}+Q(x)y[/tex].

Now, According to the question:

A differential equation is an equation that consists of a function and its derivative. A differential equation that consists of a function and its second-order derivative is called a second order differential equation. Mathematically, it is written as y'' + p(x)y' + q(x)y = f(x), which is a non-homogeneous second order differential equation if f(x) is not equal to the zero function and p(x), q(x) are functions of x. It can also be written as F(x, y, y', y'') = 0. Further, let us explore the definitions of the different types of the second order differential equation.

Hence, The second order differential equation.

[tex]\frac{d^2y}{dx^2}+P(x)\frac{dy}{dx}+Q(x)y[/tex].

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The measure of the angles p  for the given set of angles of triangle is found as: p = 60°.

Supplementary  of  110° = 180° - 110°

Supplementary  of  110° = 70°

Similarly,

Supplementary  of  130° = 180° - 130°

Supplementary  of  130° = 50°

Using angle sum property of triangles:

70° +  50° + p = 180

p =  180 - 120

p = 60°

Thus, the measure of the angles p  for the given set of angles of the triangle is found as: p = 60°.

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Answer:

A

Step-by-step explanation:

Group like-terms, that is move the numbers to one side of the sign.

Then, divide both sides by 2

Answer:

x = 1/156

Step-by-step explanation:

3x+1/52 = 0

3x = 1/52

x = 1/52/3

x = 1/156

Answer:

[tex]x=-\frac{1}{3}[/tex]

Step-by-step explanation:

[tex]\frac{3x+1}{52} = 0[/tex]

Multiply both sides by 52, and you get:

[tex]\frac{3x+1}{52}*52\\[/tex] [tex]=3x+1[/tex]

[tex]0*52=0[/tex]

So, [tex]3x+1=0[/tex]

[tex]3x+1=0[/tex]

     [tex]-1[/tex]    [tex]-1[/tex]

[tex]3x=-1[/tex]

Divide both sides by 3:

3x/3 = x

-1/3 = -1/3

[tex]x=-\frac{1}{3}[/tex]

Answer:

Perimeter = 85.5cm, Area = 3163.5cm

Step-by-step explanation:

To find the perimeter of a shape, you need to add all of the sides together.

In this case, you need to add 3 sides together.

38cm + 37cm + x.

To find x, you need to subtract 81.1 from 98.7 and divide by two. (98.7 - x - x = 81.1)

(98.7 - 81.1) / 2 = 8.8.

The perimeter is: 8.8cm + 38cm + 29cm = 85.5cm

To find the area of the trapezoid (shape on the right of the triangle), you need to use the formula, (length of top + length of bottom)/2 * height.

Length of the top base: 81.1cm

Length of bottom base: 98.7 - 8.8 = 89.9cm

Height = 37

(81.1 + 89.9) / 2 * 37 = 3163.5cm

Answer:  40 divided  by 2 (half) = 20+16 = 36

Step-by-step explanation:

Answer:

Ответ:

Пошаговое объяснение:

Ответ : Пошаговое объяснение : - 1