Choose the equivalent system of linear equations that will produce the same solution as the one given below 4x-y=-11 2x+3y=5

Answer:

a) CD = 41 m

b) 77.32°

c) 1380 square metres

Step-by-step explanation:

We can divide the trapezium as shown in the diagram below.

a) To find CD, we use Pythagoras Rule:

[tex]CD^2 = 9^2 + 40^2[/tex]

[tex]CD^2 = 81 + 1600\\\\CD^2 = 1681\\\\=> CD = 41 m[/tex]

b) To find <BCD, we use trigonometric function SOHCAHTOA:

sin(BCD) = opp / hyp

sin(BCD) = 40 / 41

sin(BCD) = 0.9756

=> <BCD = 77.32°

c) The area of a trapezium is given as:

A = 1/2 (a + b) * h

where h = height = 40 m

a = top length = 30 m

b = bottom length = 39 m

A = 1/2 * (30 + 39) * 40

A = 1/2 * 69 * 40

A = 1380 square metres

Answer:

p < 2

Step-by-step explanation:

9p + 23 < 41

p < 2

Answer:

p < 2

Step-by-step explanation:

9p + 23 < 41

9p < 18

p < 2

Answer: The number of points added for r right answers is 12r. The number of points taken away for w wrong answers is 4w, so Olga's total points will be

... 12r -4w

To win, she needs this number to be more than 400. Your inequality is ...

... 12r -4w > 400

Answer:12r -4w > 400

Step-by-step explanation:

Answer:

1. 31.67 degrees

2. 38 degrees

3.

PNQ  = 117 degrees

LKQ =  102 degrees

4. XYV = 120 degrees

Step-by-step explanation:

1. Using sum of angles of a triangle = 180

angle ACB = 180 - 55.14 - 93.19 = 31.67

2.

FDE = 180-GDE = 180 - 135.11 = 44.89   [angles on a line are supplementary]

FED = HEJ = 97.11         [vertical angles]

DFE = 180-FDE-FED = 180 - 44.89 - 97.11 = 38 degrees

3.

MLN = 180 - 82 = 98   [angles on a line are supplementary]

PNQ = 360 - 67 - 78 - 98 = 117  [sum of exterior angles of a polygon = 360]

LKQ = 180 - 78 = 102  [angles on a line are supplementary]

4.

WXY+YXZ = 180 [angles on a line are supplementary]

=>

3x + x = 180

=>

x = 180/4 = 45

Now solve for XYV

XYV = 360 - 135 - 60 - 45 = 120  [sum of interior angles of quadrilateral = 360]

Note: In the future, please limit the number of problems per question to three.

Answer:

165

Step-by-step explanation:

we solve this by sum over the possible symmetry groups of the colorings.

1.If the board has 90 degree rotational symmetry, then all four squares are the same color. There are 5 such boards.

2. If the board has 180 degree rotational symmetry (but not 90 degree), then it has to be a 2-color checkerboard pattern. There are ⁵c₂=10 such boards.

All the remaining boards have no rotational symmetry. We can count these boards by taking all possible colorings, subtracting the ones counted above, and dividing by four (since each of these boards corresponds to four colorings). The result is (54−2×10−5)÷4=600÷4=150.

so, total number of boards= 5+10+150= 165.

Answer: 148.5

Step-by-step explanation:

To find the area of this shape, comprised of a rectangle and a triangle, we can find the area of each shape and add them together.

The area of a triangle is 12⋅b⋅h. We are given the triangle's height, 13. The base of the triangle will be the same as the width of the rectangle, which we also know: 11. Now we can calculate the area of the triangle:

A = 1/2⋅b⋅h

A = 12⋅11⋅13

A = 71.5

Now we can find the area of the rectangle, which is l⋅w. The width of the rectangle is 11, which is the same as the base of the triangle; the length is 7:

A =l⋅w

A = 7⋅11

A = 77

Finally, we can add together the area of the triangle and the rectangle to find the total area:

A = 71.5 + 77 = 148.5

The total area of the front of a house will be 148.5.

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

A rectangle has a width = 11

The triangle's height = 13

The rectangle's height = 7

Now,

Since, The base of the triangle will be the same as the width of the rectangle.

Hence, The area of rectangle = 7 x 11

                                              = 77

And, The area of triangle = 1/2 x 11 x 13

                                      = 71.5

Thus, The total area of the front of a house = 77 + 71.5

                                                                  = 148.5

Therefore, The total area of the front of a house will be 148.5.

Learn more about the rectangle visit:

https://brainly.com/question/398984

#SPJ2

Answer:

3/4

Step-by-step explanation:

Explanation:

List out the total number of outcomes = {1,2,3,4,5,6,7,8,9,10,11,12}

We have 12 items in this list.

From this list, highlight the outcomes that are less than 9. So we will have this smaller list of {1,2,3,4,5,6,7,8} which has 8 items in it.

There are 8 ways to get what we want (a number less than 9) out of 12 outcomes total

The probability is therefore 8/12 = 2/3

Answer:

-2

Step-by-step explanation:

Hello,

First of all, let's check the denominator.

[tex]x^2-x-6 \ \ \text{ *** How to factorise it ...? ***}\\\\\text{*** The product of the roots is -6=-2*3 and their sum is 1 ***}\\\\x^2-x-6=x^2-3x+2x-6=x(x-3)+2(x-3)=(x+2)(x-3)[/tex]

Now, let's see the numerator.

[tex]x^2+8x+4 \ \text{ *** -2 is not a zero as ***}\\\\(-2)^2+8*(-2)+4=4-16+8=-4\\\\\text{*** 3 is not a zero as ***}\\\\3^2+8*3+4=9+24+4=37\\[/tex]

So we cannot factorise the numerator with (x+2) or (x-3)

Then, -2 and 3 are the the discontinuities of the expression.

There is only -2 in the list, this is the correct answer.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

146

Step-by-step explanation:

Given:

[tex]x - \dfrac{1}{x} = 12[/tex]

To Find:

[tex] \sf \: The \: value \: of \: {x}^{2} + \dfrac{1}{ {x}^{2} } [/tex]

How to find:

Just square both side, Solve as a equation and get the answer. Simple, Isn't it?

Solution:

See in attachment.

Answer:

146

Step-by-step explanation:

The answer of this question id 146 .

you can do this type of numericals by above process.

Answer:

The second answer

Step-by-step explanation:

Remember rise over run since this is a negative line go down 4 and over to the right 3. Now you found your slope which is -4/3. To find the y intercept simply look at the y axis and look at where the line passes through it

Answer:

Graphs 1, 2, and 3 are not functions. Graph 4 is a function.

Step-by-step explanation:

Use the vertical line test.

Imagine a vertical line moving from left to right.

If in any position of the vertical line, it intersects more than one point on the graph, then it is not a function.

In graphs 1 and 2 it is clear that there are many vertical lines than would intersect the graph at more than one point.

In graphs 3, a vertical line would intersect the vertical parts of the graph at more than 1 point, so graph 3 is not a function.

The only function is graph 4.

The relations given in options 1, 2, and 3 are not functions only Graph 4 is a function.

A function is an expression, or rule that defined the relation between two variables.

If we use the vertical line test.

Imagine a vertical line moving from left to right.

If in any position of the vertical line, it intersects more than one point on the graph, then it is not a function.

In graphs 1 and 2 it is clear that there are many vertical lines than would intersect the graph at more than one point.

In graph 3, a vertical line would intersect the vertical parts of the graph at more than 1 point, so graph 3 is not a function.

Learn more about function here;

https://brainly.com/question/21145944

Since he needs beans to sell. The common sense constraints would be that both x and y need to be equal to or greater than 0, otherwise he wouldn’t have anything to sell.

The answer is the last choice

Answer:

x>=0, and

y>=0

Step-by-step explanation:

Let

x = pounds of house blend he sells/makes every day

y = pounds of exoted blend he makes/sells every day

constraint for costa rican beans

x/2 + y/4 <= 200 ...............(1)

constraint for Ethiopian beans

x/2 + 3y/4 <=330..................(2)

Total weight per day

x+y <= 200+330 = 530............(3)

common sense constraints, cannot have negative weight for coffee

x>=0, and

y>=0

Answer:

The area of △ABC is equal to the area of △DEF

Step-by-step explanation:

On a coordinate plane, triangles A B C and D E F are shown. Triangle A B C has points (4, 2), (7, 2), (4, 6). Triangle D E F has points (negative 2, negative 1), (4, negative 3), and (4, negative 1).

How do the areas of triangle ABC and DEF compare? The area of △ABC is 1 square unit less than the area of △DEF. The area of △ABC is equal to the area of △DEF. The area of △ABC is 1 square unit greater than the area of △DEF. The area of △ABC is 2 square units greater than the area of △DEF.

Answer: The length of the sides of the triangle ABC are given below:

[tex]AB=\sqrt{(7-4)^2+(2-2)^2} =3\ unit\\\\BC=\sqrt{(4-7)^2+(6-2)^2} =5\ unit\\\\AC=\sqrt{(4-4)^2+(6-2)^2} =4\ unit[/tex]

The area of triangle ABC is given as:

Area = 1/2 × base × height = 1/2 × 3 × 4 = 6 unit²

The length of the sides of the triangle DEF are given below:

[tex]DE=\sqrt{(4-(-2))^2+(-3-(-1))^2} =\sqrt{40} \ unit\\\\EF=\sqrt{(4-2)^2+(-1-(-3))^2} =2 \ unit\\\\DF=\sqrt{(4-(-2))^2+(-1-(-1))^2} =6 \ unit[/tex]

The area of triangle DEF is given as:

Area = 1/2 × base × height = 1/2 × 2 × 6 = 6 unit²

The area of triangle ABC is equal to 6 unit² and the area of triangle DEF is equal to 6 unit² , therefore The area of △ABC is equal to the area of △DEF

Answer:

b

Step-by-step explanation:

edge exam

Answer:

(x,y) = Any point on the line

m = the slope of the line

(x₁, y₁) = A given point on the line

Step-by-step explanation:

the equation of a straight line is;

y = mx + c

where;

x and y are any point on the line

m is the slope of the line

c is the intercept on the y axis

And a given point on (x,y) can be written as (x₁, y₁)

Therefore, for the case above;

(x,y) = Any point on the line

m = the slope of the line

(x₁, y₁) = A given point on the line

Answer:

20 miles

Step-by-step explanation:

Given that :

When the car traveling north 'N' had gone 15 miles, the distance between the cars was 5 miles more than the distance traveled by the car heading east

Let the distance moved by the east bound car be e,

therefore, distance between the cars when the northbound car had traveled a distance of 15 miles = e + 5

Using Pythagoras rule:

(Hypotenus)^2 = (adjacent)^2 + (Opposite)^2

(e+5)^2 = 15^2 + e^2

(e+5)(e+5) = 225 + e^2

e^2 + 5e + 5e + 25 = 225 + e^2

e^2 + 10e + 25 = 225 + e^2

e^2 - e^2 + 10e = 225 - 25

10e = 200

e = 200 / 10

e = 20 miles

Check attached picture for solution diagram

Answer:

3.6hours

Step-by-step explanation:

kevin-6hrs

so he gets 1/6 called in 1 minute

Anne-9 hrs

so she gets 1/9 called in 1 minute

together

1/6+1/9=5/18 called in one minute

so what about all which are 18/18

you get 3.6 hrs I guess

Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the y intercept rewrite the equation in the above form

That's

4x - 2y =- 12

2y = 4x + 12

Divide both sides by 2

y = 2x + 6

comparing with the above formula the y intercept is 6

That's

(0 , 6)

The x intercept of a line the x coordinate on the line when y = 0

To find the x intercept let y = 0

That's

2x + 6 = 0

2x = - 6

Divide both sides by 2

x = - 3

The x intercept is - 3

That's

(- 3 , 0)

Hope this helps you

Answer:

the answer is x=-3 and y=6 so that means it is B.

4x-2y=-12

then; plug in 0 for x and then solve;

y=6

then do the same for the other side. plug in 0 for y and then solve.

x=-3

Hope this helps!

Answer:

x = 3.25

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

...and is the order of operation.

First, subtract 3 from both sides of the equation:

4x + 3 = 16

4x + 3 (-3) = 16 (-3)

4x = 16 -3

4x = 13

Next, dvide 4 from both sides:

(4x)/4 = (13)/4

x = 13/4

x = 3.25

x = 3.25 is your answer.

~

Answer:

x = 3.25

Step-by-step explanation:

4x + 3 = 16

4x + 3 - 3 = 16 - 3

4x = 13

4x/4 = 13/4

x = 3.25

Answer:

a) 20 students

b) 20 students

Step-by-step explanation:

a) From the given frequency table, we have to check the number of students that scored above 73.5 and add them up.

Therefore, the number of students that have grades above 73.5 are:

14 + 4 + 2 = 20 students

b) 75 falls in between 74 - 76 and we do not have the individual frequencies of the grades (74, 75, 76).

However, we can use the data we have from the table to make an assumption.

The number of students that have grades below 75 will be:

13 + 5 + 2 = 20 students

Answer:

s= 14

Step-by-step explanation:

The missing side is s

sin 30° = 7/s        switch s and sin 30°

s = 7/sin 30°

sin 30° is 0.5

so :

Answer:Domain is (-infiniti,infiniti) and Range is (-infiniti,10.45)

Step-by-step explanation:

Answer:  18954

Step-by-step explanation:

The given format for password :  Each password will have one digit, followed by one letter, followed by two digits. The digit 7 will not be used. So, there are 26 letters and 9 digits that will be used.

We assume that the digits can be repeated.

Then by using fundamental principle of counting,

Number of passwords can be created =  (Number of digits) x (Number of letters) x (Number of digits)x(Number of digits)    

= 9 x 26 x 9 x 9

=  18954

Hence, Number of passwords can be created=  18954

Answer:

(0, –2)

Step-by-step explanation:

I am assuming that point 'B' is (-5 , 0).

The translation rule is: [tex](x,y)\rightarrow(x+5,y-2)[/tex].

Apply the rule to point 'B':

[tex]\frac{(-5,0)\rightarrow(-5+5,0-2)}{(x,y)\rightarrow(x+5,y-2)}\rightarrow\boxed{(0,-2)}[/tex]

B' should be (0, -2).

Answer:

Guy above me might be right but Im not sure. Im on the cumulative exam on edge.

Step-by-step explanation:

Answer:

Axis of Symmetry: x = 3

Vertex: (3, 5)

Step-by-step explanation:

Use a graphing calc.

Answer:

3

Step-by-step explanation:

Answer:6/16 or 3/8

Step-by-step explanation:

I did it

Answer: 3/16

Step-by-step explanation:

Answer:

b)

Step-by-step explanation:

Surface area of a cube = 6a²   , here a is the side of cube

When side is halved, side = a/2

Now, the surface area of new cube = 6* (a/2)²

                                                           = [tex]6*\frac{a^{2}}{4}=\frac{1}{4}*6a^{2}\\[/tex]

                                                            = one fourth of the cube

Answer: 15 teams

Step-by-step explanation:

Total number of games played in the tournament = 105

Number of participating teams = p

Each team plays against every other team , then the total number of games played by each team = (p - 1) , since a team can't play itself

To obtain total number of games played =

(Number of teams × number of games played) [p × (p-1)]

However, the teams played against each other only once :

Therefore, total number of games played:

[p × (p-1)] / 2

Since we've been given the total number of games played :

[p × (p-1)] / 2 = 105

p × (p-1) = 105 × 2

p × (p-1) = 210

p^2 - p = 210

p^2 - p - 210 = 0

p^2 - 15p + 14p - 210 = 0

p(p - 15) +14(p-15) = 0

(p - 15) = 0 or (p + 14) = 0

p = 15 or p = - 14

Number of teams can't be negative

Therefore p = 15

Number of teams = 15

Answer:

2,280

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

20 + (75% × 20) =

20 + 75% × 20 =

(1 + 75%) × 20 =

(100% + 75%) × 20 =

175% × 20 =

175 ÷ 100 × 20 =

175 × 20 ÷ 100 =

3,500 ÷ 100 =

35;