Which matrix represents the system of equations shown below? 2x-y=-6 and x-6y=13​

Answer:

Option 3.

Step-by-step explanation:

The given inequalities are

[tex]x-2y<4[/tex]

[tex]y>-2x-5[/tex]

If (a,b) is solution of given system of inequalities, then the above inequalities must be satisfy by the point (a,b).

For point (1,-4),

[tex](1)-2(-4)<4\Rightarrow 9<4[/tex] False

[tex]-4>-2(1)-5\Rightarrow -4>-7[/tex] True

Since, first inequality is false for (1,-4) point, therefore (1,-4) is not the solution.

For point (-8,2),

[tex](-8)-2(2)<4\Rightarrow -12<4[/tex] True

[tex]2>-2(-8)-5\Rightarrow 2>11[/tex] False

Since, second inequality is false for (-8,2) point, therefore (-8,2) is not the solution.

For point (0,0),

[tex](0)-2(0)<4\Rightarrow 0<4[/tex] True

[tex]0>-2(0)-5\Rightarrow 0>-5[/tex] True

Since, both of inequalities are true, therefore (0,0) is a the solution.

For point (-3,0),

[tex](-3)-2(0)<4\Rightarrow -3<4[/tex] True

[tex]0>-2(-3)-5\Rightarrow 0>-11[/tex] False

Since, second inequality is false for (-3,0) point, therefore (-3,0) is not the solution.

Hence, option 3 is correct.

Answer:

The length of the base is 11 meters.

Step-by-step explanation:

The diagram of the triangle is not shown; However, the given details are enough to solve this question.

Given

Shape: Triangle

Represent the height with h and the base with b

[tex]b = 3 + 2h[/tex]

[tex]Area = 22[/tex]

Required

Find the length of the base

The area of a triangle is calculated as thus;

[tex]Area = \frac{1}{2} * b * h[/tex]

Substitute 22 for Area and 3 + 2h for b

The formula becomes

[tex]22 = \frac{1}{2} * (3 + 2h) * h[/tex]

Multiply both sides by 2

[tex]2 * 22 = 2 * \frac{1}{2} * (3 + 2h) * h[/tex]

[tex]44 = (3 + 2h) * h[/tex]

Open the bracket

[tex]44 = 3 * h + 2h * h[/tex]

[tex]44 = 3h + 2h^2[/tex]

Subtract 44 from both sides

[tex]44 - 44 = 3h + 2h^2 - 44[/tex]

[tex]0 = 3h + 2h^2 - 44[/tex]

Rearrange

[tex]0 = 2h^2 +3h - 44[/tex]

[tex]2h^2 +3h - 44 = 0[/tex]

At this point, we have a quadratic equation; which is solved as follows:

[tex]2h^2 +3h - 44 = 0[/tex]

[tex]2h^2 + 11h - 8h - 44 = 0[/tex]

[tex]h(2h + 11) - 4(2h + 11) = 0[/tex]

[tex](h - 4)(2h + 11) = 0[/tex]

Split the above

[tex](h - 4) = 0\ or\ (2h + 11) = 0[/tex]

[tex]h - 4 = 0\ or\ 2h + 11 = 0[/tex]

Solve the above linear equations separately

[tex]h - 4 = 0[/tex]

Add 4 to both sides

[tex]h - 4 + 4 = 0 + 4[/tex]

[tex]h = 0 + 4[/tex]

[tex]h = 4[/tex] ---- First value of h

[tex]2h + 11 = 0[/tex]

Subtract 11 from both sides

[tex]2h + 11 - 11 = 0 - 11[/tex]

[tex]2h = 0 - 11[/tex]

[tex]2h = -11[/tex]

Divide both sides by 2

[tex]\frac{2h}{2} = -\frac{11}{2}[/tex]

[tex]h = -\frac{11}{2}[/tex] ------ Second value of h

Since height can be negative, we'll discard [tex]h = -\frac{11}{2}[/tex]

Hence, the usable value of height is [tex]h = 4[/tex]

Recall that [tex]b = 3 + 2h[/tex]

Substitute 4 for h

[tex]b = 3 + 2(4)[/tex]

[tex]b = 3 + 8[/tex]

[tex]b = 11[/tex]

Hence, the length of the base is 11 meters

Answer:

1402.5 Cubic Units

Step-by-step explanation:

Volume of a Triangular Prism: V = [tex]\frac{1}{2}bhl[/tex]

b - base

h - height

l - length  

15 is the height, 17 is the length, and 11 is the width  (assuming which is the base).

[tex]V=0.5 * (11 * 15 * 17) \\V=0.5*2085\\V=1402.5[/tex]

The volume of the prism should be 1402.5 cubic units.

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Answer:

The answer is option D.

All real numbers including zero

Hope this helps

Answer:

all non zero real numbers is the answer to the question.

this is because 0 cannot be a function of f of x because you would have undefined as an answer so therefore the answer is all non zero real numbers

Answer:

Total released water = 15,664,310,000 cubic feet

Total % of released water = 1.04%

Step-by-step explanation:

Given:

Water capacity = 1,500,000,000,000 cubic feet

Total seconds in a week = 7 × 24 × 60 × 60

Per seconds release amount = 25,900 cubic feet

Computation:

Total released water = 25,900 × 7 × 24 × 60 × 60

Total released water = 15,664,310,000 cubic feet

Total % of released water = 15,664,310,000 cubic feet / 1,500,000,000,000

Total % of released water = 0.0144

Total % of released water = 1.04%

Answer:

-1

Step-by-step explanation:

Move the +16 onto the other side. We now have 52 = -52x. Divide each side by 54 to get x = -1.

Answer:

-1=x

Step-by-step explanation:

68=-52x+16

Minus sixteen on both sides

52=-52x

Divide -52 on both sides which will equal to -1

-1=x

A solution is an assignment of values to the unknown variables that makes the equality in the equation true.

Answer:

what the variable is equal to

Step-by-step explanation:

for example, in a equation like 1x = 2x/2 the solution could be x=1

Answer:

They did pay at the same rate

Step-by-step explanation:

when dividing 47 by 3 you get 15.666... and when dividing 141 by 9 you also get 15.666... using this you can deduce that it is the same rate.

Answer:

Yes

Step-by-step explanation:

We can use ratios for this:

Diego:

47:3 tickets

Divide both sides by 3 so you get the price of one ticket

15.67: 1 ticket

Andre:

141: 9 tickets

Divide both sides by 9 so you get the price of one ticket

15.67: 1 ticket

Answer:

[tex]\frac{2x - 2}{x^2+3x-4}[/tex]

Step-by-step explanation:

In the figure attached, the question is shown. The function:

[tex]\frac{2x - 2}{x^2+3x-4}[/tex]

has a horizontal asymptote at y = 0 because the degree of the nominator polynomial is less than the degree of the denominator polynomial.

The roots of x² + 3x - 4 are -4 and 1

Then, x² + 3x - 4 = (x + 4)(x - 1)

The function has a vertical asymptote at x = -4 because it is a root of the denominator polynomial.

The function can be simplified as follows:

[tex]\frac{2(x - 1)}{(x+4)(x-1)}[/tex]

[tex]\frac{2}{x+4}[/tex]

Then, it has a removable discontinuity at x = 1

Answer:

D

Step-by-step explanation:

Answer: 74 Cups

Step-by-step explanation:

What is the question asking?

The question is asking for the minium number of cups Lauren needs to sell

Total in profits they need to make?

They need to make 183$ because 175 + 8 = 183

183 / 2.5 = 73.2

because we need to sell at least 183$ worth we need to sell 74 cups or else we will not be making it all the way there.

<!> Brainliest would be appreciated! <!>

[tex]

9y+18-5y+30=-4y-9 \\

8y+57=0 \\

y=-\frac{57}{8}=-7.125 \\

[/tex]

Hope this helps.

Answer:

[tex]y = -7 \frac{1}{8}[/tex]

Step-by-step explanation:

First off, Let's Simplify!

[tex]9y + 18 - 5y + 30 = -4y - 9[/tex]

Next, Let's Combine Like Terms!

[tex]9y - 5y + 18 + 30 = -4y - 9[/tex]

~~~~~~~~~~~~~~~~~~~~~~~

   [tex]4y + 48 = -4y - 9[/tex]

Now, Let's Isolate the Variable!

[tex]8y + 48 = -9[/tex]

[tex]8y = -57[/tex]

Final Answer:

[tex]y = -7 \frac{1}{8}[/tex]

Hope that helps and maybe earns a brainliest!

Answer:

5(x+11)/3(x+8) = 5x+55/3x+24

Step-by-step explanation:

The Answer Happens to be:

c

Answer:

process of elimination

Step-by-step explanation:

Answer:

The 1st step in problem solving is defining your variables.

Step-by-step explanation:

When you read the word problem, you have to make sure you know which variables are which, or else you will get lost. If you don't label your variables, then you will not be able to answer the question properly.

Answer:27.5

Step-by-step explanation:

Answer:

B. 27.5

Step-by-step explanation:

37 is the Q2, which is the median,

Q1 is 27 + 28 / 2 = 27.5

Answer: D

Step-by-step explanation:

All would add up to 241 instead of 2.41 because you are not using decimals for the constants (Example: 25q not .25q)

Answer: See below

Step-by-step explanation:

Make a table with first set of numbers as 1,3. Multiply both the numbers of this set sequentially by natural numbers to get the following table

1   2  3  4    5    6     7    8     9      10......

3  6  9  12  15    18   21   24   27    30......

We see that in each set of numbers the 2nd number is 3 times the first number.

If we plot these sets of numbers on a graph paper, we get a model depicting all the points which satisfy this ration requirement.

Answer:

361.25

Step-by-step explanation:

first subtract her sales

900 - 500 equals 400

next subtract her earnings

489-405= 85

next divide the remainder of her earnings by the remainder of her sales

85/400=.2125

finally multiply this by 1700

0.21 to 5 * 1700 equals 361.25

Answer:

(x-3)(x+i)(x-i)

Step-by-step explanation:

khan

The complete factorization of the polynomial is A = ( x + i ) ( x - i ) ( x - 3 )

Brackets should be expanded in the following ways to factorize an expression

For an expression of the form A = a ( b + c ) , the expanded version is given by A = ab + ac, i.e., multiply the term outside the bracket by everything inside the bracket

For an expression of the form A = ( a + b ) ( c + d ) , the expanded version is given by A = ac + ad + bc + bd, in other words everything in the first bracket should be multiplied by everything in the second.

Given data ,

Let the polynomial equation be represented as A

Now , the value of A is

A = x³ - 3x² + x - 3   be equation (1)

On simplifying , we get

A = ( x³ - 3x² ) + ( x - 3 )

Taking x² as the common term , we get

A = x² ( x - 3 ) + ( x - 3 )

Now , on factorizing the equation , we get

A = ( x² + 1 ) ( x - 3 )

where the value of ( x² + 1 ) = x² - i²

So , A = ( x² - i² ) ( x - 3 )

A = ( x + i ) ( x - i ) ( x - 3 )

Therefore , the value of A is ( x + i ) ( x - i ) ( x - 3 )

Hence , the factorized equation is A = ( x + i ) ( x - i ) ( x - 3 )

To learn more about factorizing click :

https://brainly.com/question/804076

#SPJ7

Answer:

You can verify if lines are parallel if they have the same slope and different y-intercepts and if they don't intersect each other. You can also graph the 2 equations to see if they ever intersect.

Step-by-step explanation:

Answer:

C. Check the intersecting lines with the corner of a piece of paper to ensure the lines create 90° angles. Took the test just now and got it right

Step-by-step explanation:

Answer: (6,-6)

Step-by-step explanation: so, the x coordinate before is 3, and traveling right is a positive number. So to find the x coordinate after, add 3 because it is going right 3 units, which is 6. The y coordinate was -2 before. Going down in terms for the y coordinate means negative, or to subtract, so the y coordinate after would be -6, because -2+4=-6

Hope you understand :)

Answer:

The coordinates of C are (2,2)

Answer:

Vertex: (0, 12)

Direction: Upwards

Step-by-step explanation:

Easiest way to do this is to graph it. When you do so you should be able to see that your vertex is at (0, 12) and that the graph opens upwards (a is not negative, so no reflection over the x-axis).

Answer:

Option A.

Step-by-step explanation:

Consider the below figure attached with this question.

Corresponding angles : If a transversal line intersect two parallel lines, then it makes 4 angles at each intersection point. The angles with same relative position at each intersection is know as corresponding angles.

From the clear figure it is clear that the pair of corresponding angles are:

[tex]\angle 1\text{ and }\angle 5[/tex]

[tex]\angle 2\text{ and }\angle 6[/tex]

[tex]\angle 3\text{ and }\angle 7[/tex]

[tex]\angle 4\text{ and }\angle 8[/tex]

Therefore, the correct option is A.

Answer:

a

Step-by-step explanation:

Answer:

price paid of speakers= £40.5

price paid of headphones=£ 5.6

price paid of book=£6.65

price paid of mobile phone=£42

price paid of mouse=£ 15.75

price paid of DVD=£11.05

solution,

1. Cost of speakers:

Discount percent=10 %

Marked price=£45

discount amount= discount % of MP

=10% of 45

=£4.5

Selling price= MP - discount amount

=£45-£4.5

=£ 40.5

2. cost of headphones:

discount amount= discount% of MP

=20% of 7

=£1.4

Selling price= MP- Discount amount

=£7-£1.4

=£ 5.6

3. cost of books:

discount amount= discount percent of MP

= 30% Of 9.50

=£ 2.85

selling price= MP- Discount amount

= £ 9.50-£2.85

=£ 6.65

4. cost of mobile phone:

discount amount= discount% of MP

=40% of 70

=£ 28

selling price= MP- Discount amount

=£70-£28

=£ 42

5. cost of mouse:

discount amount= discount% of MP

= 25% of 21

=£ 5.25

selling price= MP- Discount amount

=£21-£5.25

=£ 15.75

6. cost of DVD:

discount amount= discount % of MP

= 15% of 13

= £ 1.95

selling price= MP- discount amount

=£ 13 -£ 1.95

=£ 11.05

Hope this helps...

Good luck on your assignment..

Answer:

≈ 5.8

Step-by-step explanation:

Step 1: Round the fractions

29 1/5 = 146/5 = 29.2 ≈ 29

4 6/7 = 34/7 = 4.85714 ≈ 5

Step 2: Divide

29/5 = 5.8

The answer is under

Answer:

Step-by-step explanation:

y = 5900 - x

Simple interest = Prt

Simple interest on $x = x * 0.11 * 1 = 0.11x

Simple interest on $ (5900 - x) = (5900 - x) * 0.07 * 1

                                                   = (5900 - x) * 0.07

                                                   = 5900 * 0.07 - x * 0.07

                                                   = 413 - 0.07x

Return from tow investment =  $ 537

0.11x + 413 - 0.07x = 537  

Add the like terms

0.04x + 413 = 537

Subtract 413 for both sides

0.04x = 537 - 413

0.04x = 124

x = 124 /0.04

x = 3100

y = 5900 -  3100 = 2800

x = $ 3100

y = $ 2800  

Answer:

The answer is 3968

63 squared= 3969

3969-1 = 3968

Answer:

the answer is X<3

Step-by-step explanation:

Answer:

C

Step-by-step explanation: