TOPIC: simultaneous linear equations

p + 2q = 3,
p - 2q = 3​

Answer:

Sample response:

Both inequalities use the division property to isolate the variable, y. When you divide by a negative number, like –7, you must reverse the direction of the inequality sign. When you divide by a positive number, like 7, the inequality sign stays the same. The solution to the first inequality is y > -23, and the solution to the second inequality is y <>

We know that the area of a semicircle = 1/2(πr^2)

r = the radius

We also know that the area of a rectangle = xy

x = width

y = length

In our problem,

r = w

x = w

y = w + 5

A(w) = w(w + 5) - 1/2(πw^2)

Let's simplify the right side of the function.

A(w) = w^2 + 5w - 1/2πw^2

Answer:

[tex]f(x)=2x^{2}-3[/tex]

[tex]D=(-\infty,\infty)[/tex]

[tex]R=[-3,\infty)[/tex]

x-intercepts: [tex](\frac{\sqrt{6}}{2},0)[/tex] and [tex](-\frac{\sqrt{6}}{2},0)[/tex]

y-intercept: (0,-3)

f(3)=15

Step-by-step explanation:

A quadratic function is any polynomial function whose greatest power is a 2, so [tex]f(x)=2x^{2}-3[/tex] is a nice example of it.

For the domain, as a rule, polynomial functions that have positive whole degrees will be defined for all real  numbers, so:

[tex]D=(-\infty,\infty)[/tex]

When talking about quadratic functions, its range will happen from the lowest point (in this case the vertex) to it's highest point (in this case infinity)

In order to find the vertex, we can use the following formula:

[tex]x=-\frac{b}{2a}[/tex]

which is used for quadratic equations in standard form:

[tex]y=ax^{2}+bx+c[/tex]

In this case a=2, b=0 and c=-3, so we get:

[tex]x=-\frac{0}{2(2)}=0[/tex]

Now we know that the range will happen at x=0, so we substitute:

[tex]f(0)=2(0)^{2}-3=-3[/tex]

so the range will be:

[tex]R=[-3,\infty)[/tex]

For the x-intercepts we need to set the given function equal to zero so we get:

[tex]2x^2-3=0[/tex]

and solve for x:

[tex]2x^{2}=3[/tex]

[tex]x^{2}=\frac{3}{2}[/tex]

[tex]x=\pm \sqrt{\frac{3}{2}}[/tex]

which can be rationalized to:

[tex]x=\frac{\sqrt{6}}{2}[/tex] and [tex]x=-\frac{\sqrt{6}}{2}[/tex]

so the x-intercepts are located at:

[tex](\frac{\sqrt{6}}{2},0)[/tex] and [tex](-\frac{\sqrt{6}}{2},0)[/tex]

For the y-intercept, we need to set x=0 so we get:

[tex]f(0)=2(0)^{2}-3[/tex]

[tex]f(0)=-3[/tex]

So the y-intercept is located at:

(0,-3)

and finally, in order to get f(3) we must substitute x for 3 so we get:

[tex]f(3)=2(3)^{2}-3[/tex]

f(3)=15

Answer:

[tex]-2^{2}[/tex] * [tex]7^{5}[/tex]

Step-by-step explanation:

-2 is shown two times in the equation, and 7 is shown 5 times. That is why the answer is [tex]-2^{2}[/tex] * [tex]7^{5}[/tex]

Hope this helps!

Answer:

The answer is "K= 102"

Step-by-step explanation:

Given:

Number of employees = 7128

sample size =70

k=?

Formula:

[tex]\to K= \frac{\text{Number of employees}}{\text{sample size}} \\\\[/tex]

        [tex]= \frac{7148}{70} \\\\= 102.11\ \ \ \ or \ \ \ 102[/tex]

Answer:

The answer for this question is 1e+110

Answer:

A counterclockwise rotation of 270º about the origin is equivalent to a clockwise rotation of 90º about the origin. Given a point (4, 5), the x-value, i.e. 4 and the y-value, i.e. 5 are positive, hence the point is in the 1st quadrant of the xy-plane.

Step-by-step explanation:

Answer:

2 miles

Step-by-step explanation:

3.3 kilometers to miles is 2.0505. I'm not sure if this question want you to round, but if it does, the answer would be 2 miles.

To get your approximate answer, multiply 3.3 (kilometers) by 0.62 (miles).

You get 2.046 if you multiply it by 0.62 like the question says to do.

Answer:

8x^3/5

Step-by-step explanation:

Evaluate the exponent

16x^3/10

Factor 2 out of 16x^3

2(8x^3)/10

Cancel the common factors

Factor 2 out of 10

2(8x^3)/2(5)

Cancel the common factor

(8x^3)/5

Rewrite the expression

8x^3/5

I hope this helps! :)

Answer:

Step-by-step explanation:

x + 3•(+1) = 2•x + 4•(-1)

x + 3  =  2x - 4

  -3         -3

 x  =  2x - 7

-2x      -2x

- x  =  -7

÷(-1)     ÷(-1)

  x = 7

Answer:

add ans subtract like normal

Step-by-step explanation:

Step-by-step explanation:

To add decimals, follow these steps: Write down the numbers, one under the other, with the decimal points lined up. Put in zeros so the numbers have the same length .Then add, using column addition, remembering to put the decimal point in the answer.

subtraction also in the same way only place the large no up and small down and do subtraction.

I hope this helps....

Answer:

224 meters

I took the test, and got it right.

Answer:

224 meters

Step-by-step explanation:

Have a great day!

Answer:

225 feet

Step-by-step explanation:

-245 plus -83 then add 103

Answer:

The answer is

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

[tex]M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )[/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(12,-7) and (-6,15)

The midpoint is

[tex]M = ( \frac{12 - 6}{2} , \: \frac{ - 7 + 15}{2} ) \\ = ( \frac{6}{2} \: , \: \frac{8}{2} )[/tex]

We have the final answer as

Hope this helps you

Answer:

4 km

Step-by-step explanation:

T = time

D = distance

S = speed

the forumla to find the distance is

T * S = D

manipulate the equation for this problem:

D/S = T

Plug-in the known values

D = 12.5 km

S = 50kph

12.5km/50kph

cancel units and simplify

4 km

Answer:

d

Step-by-step explanation:

527 / 17 = 31

The number line that shows the points −12/5 and –2.8 is Option A.

Integers are arranged at equal intervals along horizontal straight lines called number lines. A number line can be used to represent every number in a series. The endpoints of this line go on forever. Some will have a defined beginning and end. It refers to those as closed number lines. Number lines might be alternatively left empty or blank. A number ladder is a vertical number line.

The given numbers are: −12/5 and –2.8

As we can re-write -12/5 in decimal form= -2.4

Now, we need to mark the number on the number line.

As the number -2.4 lies between -2 and -3 on the left side of zero.

and, -2.4 lies between -the numbers 2.5 and -3.0 on the left side of zero.

Learn more about number line here:

brainly.com/question/13425491

#SPJ2

Answer:

7/2 = x

Step-by-step explanation:

2(x + 4) = 3(2x - 2)

Distribute

2x+8 = 6x -6

Subtract 2x from each side

2x-2x+8 = 6x-2x -6

8 = 4x -6

Add 6 to each side

Add 6 to each side

8+6 = 4x-6+6

14 = 4x

14/4 = 4x/4

7/2 = x

Answer:

x= 7/2

Step-by-step explanation:

2x + 8 = 6x - 6

2x - 6x = -6 - 8

- 4x = -14

x = 7/2

Answer:

7.1 cm

Step-by-step explanation:

The diagonal of a cube connects two opposite corners.

You can use the diagonal of a cube in a right triangle in which it is the hypotenuse. The legs of the triangle are a diagonal of a face and an edge.

Let the length of the edge be s.

a^2 + b^2 = c^2

[tex] s^2 + 10^2 = (\sqrt{150})^2 [/tex]

[tex] s^2 + 100 = 150 [/tex]

[tex] s^2 = 50 [/tex]

[tex] s = \sqrt{50} [/tex]

[tex] s = 5\sqrt{2} [/tex]

s = 7.1

Answer: 7.1 cm

Answer:

182

Step-by-step explanation:

You add all of them together and you will get the same answer if you would simplify it i simplified it

Answer:

A

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

b = y - mx

Step-by-step explanation:

Given

y = mx + b ( subtract mx from both sides )

y - mx = b

Answer:

-1

Step-by-step explanation:

Step-by-step explanation:

Ax − B = C

Dy + E = F

Solve for x and y:

x = (B + C) / A

y = (F − E) / D

So the sum of x and y is:

x + y = (B + C) / A + (F − E) / D

For x + y to be as large as possible, A, E and D must be small, and B, C, and F must be large.  With some trial and error:

x + y = (9 + 8) / 1 + (7 − 3) / 2

x + y = 17 + 2

x + y = 19

For x + y to be as small as possible, we want the first term to be a small fraction, and the second term to be as negative as possible.  So A must be large, B + C must be small, F must be less than E, and D must be small.

x + y = (3 + 4) / 8 + (2 − 9) / 1

x + y = ⅞ − 7

x + y = -6⅛

Step-by-step explanation:

Hey there!!

It 's so simple.

You remember common property of triangle. (i.e sum of interior angle of a triangle is 180°)

So,

77° + 31° + x = 180°

x + 108° = 180°

x = 180° - 108°

Therefore the measure of angle x is 72°.

Hope it helps....

Answer:

Step-by-step explanation:

Amari ran 3/4 distance Mary ran

A = 3/4  M

Amari ran 12 miles

12 = 3/4 M                Multiply by 4

12 * 4 = 3*M              Combine    

48 = 3M                   Divide by 3

48/3 = M

M = 16

So Mary ran 16 miles.  

Answer:

-3

Step-by-step explanation:

16/4=4, so seven less than that is -3

Answer:

x ≈ 10.6

Step-by-step explanation:

Given

[tex]\frac{13}{11}[/tex] = [tex]\frac{x}{9}[/tex] ( cross- multiply )

11x = 117 ( divide both sides by 11 )

x ≈ 10.6 ( to the nearest tenth )

We can write a ratio:

15/5 = 36/x

Let "x" equal the unknown part of the triangle.

Solution:

15/5 = 36/x

~Cross multiply

15x = 180

~Divide 15 to both sides

x = 12

Best of Luck!