What is the solution set of the system of inequalities 5x<8+4y and 2y≤6?

Answer:

2794 m^2

Step-by-step explanation:

Area of Triangle - Area of Circle

1/2bh - piR^2

4050 - 1256

= 2794

The approximate area of the shaded region is, 2794 m²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given a right triangle with a circle cut out of it,

Area of circle = π*Radius²

Area of triangle = 1/2*base*height

Area of circle = π*20² = 1256 m²

Area of triangle = 1/2*90*90 = 4050 m²

Area of the shaded region = Area of triangle - Area of circle

Area of the shaded region = 4050 - 1256 = 2794 m²

Hence, The approximate area of the shaded region is, 2794 m²

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The value of k that makes the polynomial k^2x^3 - 6kz + 9 divisible by x-1 is 3. This is found using the Remainder Theorem and substituting x=1 into the polynomial and solving the resulting equation.

The question asks for the value of k such that the polynomial k2x3 - 6kz + 9 is divisible by x-1. To find the value of k, we use the Remainder Theorem, which states: if a polynomial f(x) is divisible by x-c, then f(c) = 0.

Applying this theorem, we set x=1 and solve for k:

Therefore, the value of k that makes the polynomial divisible by x-1 is 3.

Answer:

Step-by-step explanation:

4x² - 8x= 0​

4x(x -2) = 0

: 4x = 0 or x - 2 = 0

4x = 0

Dividing by 4

x = 0/4

x = 0

And

x - 2 = 0

x = 2

Answer:

Therefore the maximum number of video games that we can purchase  

is 6.

Step-by-step explanation:

i) Let us say the number of video game system we can buy that costs $185

 is x and the number of video games of cost $14.95 is y.

ii) The total amount we can spend on the purchase of the video game

   system is $280.

iii) Now with the amount of $280 mentioned in ii) we can see that the

   number  of game systems that can be bought is 1.

 Therefore x = 1.

 Therefore the equation we can write to equate the number of video

  games  and video game system is given by $185 + $14.95 × y ≤ 280

  Therefore 14.95 × y ≤ 280 - 185 = 95

  Therefore y ≤   95 ÷ 14.95 = 6.355

  Therefore the maximum number of video games that we can purchase  

   is 6.

Answer:

slope = 3

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (4, 11)

m = [tex]\frac{11-2}{4-1}[/tex] = [tex]\frac{9}{3}[/tex] = 3

Answer:

3

Step-by-step explanation:

y2 - y1/ X2 - X1

11 - 2/ 4-1

9/3

= 3

Answer:

Step-by-step explanation:

Since both points have their y coordinate as -6, and this is a line,

Then your answer would be y = -6

The question is about finding the number of ways to choose 2 items without replacement from a set of 3 items using combinatorics, and there are 3 different ways to do so.

The question deals with the concept of combinations in probability and combinatorics. When choosing 2 objects from a set of 3 items (a pencil, an eraser, and a desk) without replacement, we can use the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of items and k is the number of items to choose.

In this case, we have 3 items and we want to choose 2, so we plug the values into the formula to get the number of combinations without replacement.

Using the combination formula, C(3, 2) = 3! / (2! × (3-2)!) = 3.

Therefore, there are 3 different ways to choose 2 objects from the set of a pencil, an eraser, and a desk.

Answer:

Step-by-step explanation:

F(x) = 2x + 6

G(x) = - 5x - 9

product of F and G .....the product is the result of multiplication

(2x + 6)(-5x - 9) =

-10x^2 - 18x - 30x - 54 =

-10x^2 - 48x - 54 <====

Answer:

Therefore the change in water level over the course of 9 months is a drop in level of 3.4 cm (=  -3.4 cm)

Step-by-step explanation:

i) change in water level over the course of 9 months =

   [tex]- \frac{5}{8} - 0.4 - 0.4 - 6 - 2.9 + 3.2 + 6\frac{5}{8} - 3.2 + 0.3[/tex]

 = [tex]-0.625 - 0.4 - 0.4 - 6 - 2.9 + 3.2 + 6.625 - 3.2 + 0.3[/tex]

= -3.4

Therefore the change in water level over the course of 9 months is a drop in level of 3.4 cm (= - 3.4 cm)

Answer:

Step-by-step explanation:

1 liter = 1000 ml....so 2 liters and 450 ml = (2* 1000) + 450) = 2450 ml

5 liters = (5 * 1000) = 5000 ml

5000 ml - 2450 ml = 2550 ml or 2 liters and 550 ml <== this is how much is left

so he used 2450 ml in 1 month....and he has 5000 ml

5000/2450 ≈ 2.04 months <===  it will be all used up

Answer:

Step-by-step explanation:

1 litre = 1000 ml

5 liter = 5 * 1000 = 5000 ml

2 liter 450 ml = 2 liter + 450 ml = 2000 ml + 450 ml = 2450 ml

Oil left = 5000 - 2450 = 2550 ml

2550 - 2450 = 100 ml

4 liter 900ml is used in two months and 100 ml will be left over

Answer:

n = 17.6

Step-by-step explanation:

Cross-multiply and you have:

5 * n = 11 * 8

5n = 88

n = 88/5 = 17.6

Answer:

It can be a parallelogram, a square, a rectangle and rhombus too.

Answer:

There are many special types of quadrilateral.

A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel .

A parallelogram also has the following properties:

Opposite angles are congruent;

Opposite sides are congruent;

Adjacent angles are supplementary;

The diagonals bisect each other.

A rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals. On the other hand, not all quadrilaterals and parallelograms are rectangles.

A rectangle has all the properties of a parallelogram, plus the following:

The diagonals are congruent.

A rhombus is a parallelogram with four congruent sides. The plural of rhombus is rhombi . (I love that word.)

A rhombus has all the properties of a parallelogram, plus the following:

The diagonals intersect at right angles.

A square can be defined as a rhombus which is also a rectangle – in other words, a parallelogram with four congruent sides and four right angles.

A trapezoid is a quadrilateral with exactly one pair of parallel sides. (There may be some confusion about this word depending on which country you're in. In India and Britain, they say trapezium ; in America, trapezium usually means a quadrilateral with no parallel sides.)

Step-by-step explanation:

you should be able to find your answer in this i rlly hope it helps you

Answer:

6

Step-by-step explanation:

hold up hold up so you are saying 60 less than what quotient I'm guessing 68 divided by 12 so the answer would be 6

Answer:

Option A: 12.5

Step-by-step explanation:

We use trigonometric ratios on this right angled triangle.

[tex]$ cos \hspace{1mm} \theta = \frac{adj}{hyp} $[/tex]

we get:

[tex]$ cos \hspace{1mm} 28^{\circ} = \frac{11}{x} $[/tex]

Also cos 28° = 0.88

Therefore, x = [tex]$ \frac{11}{0.88} $[/tex]

[tex]$ = \frac{100}{8} =\textbf{12.5} $[/tex]

OPTION A is the answer.

Answer:

x=5 y=9

Step-by-step explanation:

hope this helps :) have a nice day :) :) :)

Answer:

m=-7

Step-by-step explanation:

The slope intercept form is y=mx+b.

So, the variable that represents slope is x.

If your plug your equation in, -7 would be the slope.

Answer:

Step-by-step explanation:

6 1/2 + 2 3/4=M

M=9 1/4

Answer:

The smaller number is 22

The larger number is 30

Step-by-step explanation:

L + S = 52

L = S + 8

Set both equations equal to L.

S + 8 = -S + 52

+S        +S

2S + 8 = 52

     - 8    - 8

2S = 44

S = 22

To find the larger number, plug 22 in as S into the equations.

L = 30

Final answer:

The two numbers are 22 and 30, with the smaller number being 22 and the larger one being 30 (which is 8 more than the smaller number).

Explanation:

The sum of two numbers is 52, and the larger number is 8 more than the smaller number. Let's denote the smaller number as x and the larger number as x + 8. The equation to represent their sum is:

x + (x + 8) = 52

By combining like terms, the equation simplifies to:

2x + 8 = 52

Subtract 8 from both sides of the equation to isolate the term with x:

2x = 44

Divide by 2 to solve for x:

x = 22

Now that we have the value of the smaller number, we can find the larger number:

x + 8 = 22 + 8 = 30

So, the two numbers are 22 and 30.

Answer:

12

Step-by-step explanation:

I calbvkjy

The answer is 3 :)

Have a nice day!

Answer:

D) 12

Step-by-step explanation:

3x+x=2x+24

4x=2x+24

4x-2x=24

2x=24

x=24/2

x=12

Answer:

18 cm

Step-by-step explanation:

The circumference (C) of a circle is calculated as

C = 2πr ← r is the radius

Given

C = 36π, then

2πr = 36π ( divide both sides by 2π )

r = [tex]\frac{36\pi }{2\pi }[/tex] = 18

Answer:

[tex]\large\boxed{x=\dfrac{5}{4},\ y=\dfrac{15}{16}}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=\dfrac{3}{4}x&(1)\\\dfrac{5}{2}x+2y=5&(2)\end{array}\right\\\\\text{Substitute}\ (1)\ \text{to}\ (2):\\\\\dfrac{5}{2}x+2\left(\dfrac{3}{4}x\right)=5\\\\\dfrac{5}{2}x+\dfrac{3}{2}x=5\\\\\dfrac{5+3}{2}x=5\\\\\dfrac{8}{2}x=5\\\\4x=5\qquad\text{divide both sides by 4}\\\\x=\dfrac{5}{4}[/tex]

[tex]\text{Put the value of}\ x\ \text{to (1)}\\\\y=\dfrac{3}{4}\cdot\dfrac{5}{4}\\\\y=\dfrac{15}{16}[/tex]

Answer:

Step-by-step explanation:

y = 3x/4 .........(1)

5x/2 + 2y = 5 .......(2)

Putting (1) into (2)

5x/2 + 2(3x/4) = 5

5x/2 + 3x/2 = 5

Multiply each term by 2

5x + 3x = 10

8x = 10

x = 10/8

x = 5/4

x = 1 1/4

And y = 3x/4

y = 3(5/4) ÷ 4

y = 15/4 ÷ 4

y = 15/(4×4)

y = 15/16

Answer:

x = 111

Step-by-step explanation:

Sum of interior angles= (n-2)*180= (7-2)*180 = 5*180 = 900

x + 139 + 121 + 125 + 126 + 158 + 120 = 900

x + 789 = 900

x = 900 - 789 = 111

x = 111

The transformed function after reflecting f(x)=|x| across the x-axis, moving it 2 units to the right, and 7 units down is f(x)=-|x-2|-7.

The original function is f(x)=|x|.

When the graph of the function is reflected across the x-axis, it changes the sign of the output or y-coordinate.

Thus, the absolute value function becomes f(x)=-|x|.

When this function is moved 2 units to the right, it results in a shift in the coordinate of x within the function, thus becoming f(x)=-|x-2|.

Lastly, when the function is moved 7 units down, 7 is subtracted from the function, resulting in the final equation of f(x)=-|x-2|-7.

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This is an equation representing the ellipse

Explanation:

Answer:

x-20

Step-by-step explanation:

x+4=y+24

x=y+24-4

x=y+20

y=x-20

The value of the variable number x will be 1.25.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

Let x be the number. Then the Five times a number is written as 5x. Then the expression will be

⇒ 10 - 5x

The triple number is written as 3x. Then the equation is given below.

10 - 5x = 3x

Simplify the equation, then we have

10 = 3x + 5x

10 = 8x

x = 10 / 8

x = 1.25

The value of the variable number x will be 1.25.

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Final answer:

The algebraic equation set up from the problem 10 - 5x = 3x leads us to find that x = 1.25. Thus, the number in question is 1.25.

Explanation:

The question describes an algebraic problem where we are trying to find a particular number. According to the problem, five times this number, when subtracted from ten, equals three times the number. To find the number, we set up the equation based on the given information:

10 - 5x = 3x

Where x is the number we are trying to find. Now, we will solve for x:

Add 5x to both sides of the equation to get all x terms on one side:

10 = 3x + 5x

Combine like terms on the right side:

10 = 8x

Divide both sides by 8 to solve for x:

x = 10/8

Simplify the fraction:

x = 1.25

So, the number we were seeking is 1.25.

Step-by-step explanation:

The slope is described by the the initial and final value of one quantity over the difference between the initial and final of the other

Rate: for points on a Cartesian plane,(x1, y1) and (x2, y2)

the slope, m= (y2 - y1)/(x2 - x1)

The rate of change on the other hand is mostly refers to how much a quantity is changing with time i.e the rate of change of y from y1 to y2 can be expressed as

rate = (y2 - y1)/(t2 - t1)...where t1 and t2 are the various time in y1 and y2 respectively...

Mikes repair shop $100 service charge plus $65 per hour Amys auto repair $40 service charge plus $80 per hour write an equation for each repair shop to represent the total cost of a car repair as a function of the number of hours worked let C = total cost to you let h = number of hours worked. Suppose you need to get the dent in your car repaired you see the ads above in the newspaper your father who knows a bit about cars said it would take no more than 3 hours for the repair person to fix your car how do you determine where you should take your car to get it repaired

-Mike Cost:: M(3) = 100 +65*3 = $295

-Amy Cost:: A(3) = 40 + 80*3 = $280

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

-Mike charges 100 dollars service charge plus 65 dollars per hour.

-Amy charges 40 dollars service charge plus 80 dollars per hour.

-The cost to repair from mike is 100 + 65 * x.

-The cost to repair from amy is 40 + 80 * x.

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

Let x = 3 and you get:

The cost to repair from mike is 100 + 65 * 3 = 295 dollars.

The cost to repaid from amy is 40 + 80 * 3 = 280 dollars.

As long as the time to repair is 3 hours or less, the cost to repair will be cheaper from Amy.

Answer:

$4200

Step-by-step explanation:

15 floor times 40 tiles

15 X 40 = 600 tiles

so 600 tiles times 7 dollars

600 X 7 = 4200 dollars

Final answer:

To find the total cost of floor tiles for 15 kitchen floors, multiply the total number of tiles by the cost per tile. The builder will need 600 tiles (15 floors × 40 tiles) and with each tile costing $7, the total cost comes to $4200.

Explanation:

The student is asking about the total cost of floor tiles needed for an apartment building project. To calculate this, we need to find the total number of tiles used and then multiply this by the cost per tile. There are 15 kitchen floors, with each floor using 40 tiles. Each tile costs $7.

First, let's find out how many tiles are needed in total:

Number of floors × Number of tiles per floor = Total number of tiles

15 floors × 40 tiles per floor = 600 tiles in total

Next, let's calculate the total cost:

Total number of tiles × Cost per tile = Total cost

600 tiles × $7 per tile = $4200

Therefore, the builder spends a total of $4200 on floor tiles for the 15 kitchen floors.