What is the range of this function?

Answer:

k≥12

Step-by-step explanation:

If k must be equal to or greater than 12, it can be expressed as k≥12. This is because the sign ≥ shows that k can both be 12 and could be higher than 12.

I hoped that helped!

:)

Answer:

c

Step-by-step explanation:

it says above

Answer:

Point B coordinates' are: (3.2, 1.6)

Step-by-step explanation:

Since this is a rhomboid the diagonals AC and OB, must be perpendicular to each other. Then we can find first the equation of the line where segment AC lies, seeing that this line will cross the y axis at the point (0,4), and the x axis at the point (2, 0). The line can then be obtained by calculating the slope of the segment that joins the two points, and then using that the line's y-intercept must be at the point (0, 4):

[tex]slope=\frac{0-4}{2-0} =-2[/tex]

then the equation of the line for segment AC must be:

[tex]y=-2x+4[/tex]

Next, we calculate the equation of a perpendicular line to the previous one, and that passes through the point (0, 0) to determine the equation of the line that contains the segment OB. Recall that the perpendicular line to one of slope m must have a slope given by: -1/m (the opposite of the reciprocal of "m". Then this new perpendicular line passing through (0, 0) must be given by:

[tex]y=\frac{1}{2} x+0\\y=\frac{1}{2} x[/tex]

Now we can find the point at which both lines intersect:

[tex]\frac{1}{2} x=-2x+4\\\frac{1}{2} x+2x=4\\\frac{5}{2} x = 4\\x=\frac{8}{5}[/tex]

and therefore the y value of the intersection point can be calculated via:

[tex]y=\frac{1}{2} x\\y=\frac{1}{2} (\frac{8}{5} )\\y=\frac{4}{5}[/tex]

Then, point point B must be located at an x value that doubles the x value of the intersecting point, and similarly the y value of point B must be at the double of the value of the intersection point we just calculated. That is:

Point B = [tex](2\,*\frac{8}{5} ,\,2\,*\frac{4}{5} )=(\frac{16}{5} ,\frac{8}{5}) =(3.2,1.6)[/tex]

We can see the coordinates of point B and the lines we just generated in the attached image.

Answer:

0.075

Step-by-step explanation:

To represent 7 1/2 as a decimal, it would be 0.075 since there are 7 hundredths and half a hundredth.

Answer:

a) Pop

b) 30

c) 230

Step-by-step explanation:

Step-by-step explanation:

(4x² + 3y) by (3x² - 4y)

(4(1)² + 3(2)) by (3(1)² - 4(2))

(4 + 6) and (3 - 8)

10 x (-5) = -50 or 50 if negatives aren't an option

Answer:

22

Step-by-step explanation:

(4×1²+3×2) × (3×1²-4×2)

(16+6)×(9-8)

22×1=22

Answer:

-10

-5

5

Step-by-step explanation:

From the answers given, you probably mean f(x) = x^3 + 10x2 – 25x – 250

The Remainder Theorem is going to take a bit to solve.

You have to try the factors of 250. One way to make your life a lot easier is to graph the equation. That will give you the roots.

The graph appears below. Since the y intercept is -250 the graph goes down quite a bit and if you show the y intercept then it will not be easy to see the roots.

However just to get the roots, the graph shows that

x = -10

x = - 5

x = 5

The last answer is the right one. To use the remainder theorem, you could show none of the answers will give 0s except the last one. For example, the second one will give

f((10) = 10^3 + 10*10^2 - 25*10 - 250

f(10) = 1000 + 1000 - 250 - 250

f(10) = 2000 - 500

f(10) = 1500 which is  not 0.

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

f(1) = (1)^3 + 10*(1)^2 - 25(1) - 250

f(1) = 1 + 10 - 25 - 250

f(1) = -264 which again is not zero

Answer:

yes its true

Step-by-step explanation:

just took the test

Answer:

y = x-4

Step-by-step explanation:

The first thing we need here is to find the slope m of the line passing through the two points.

Mathematically;

m = y2-y1/(x2-x1)

Where (x1,y1) = (0,-4) and (x2,y2) = (5,1)

Thus; m = (1-(-4))/(5-0) = 5/5 =0

The standard form of the equation is;

y = mx + c

where m is the slope and c is the intercept. We already calculated m to be 1, so the equation of the line would be;

y = x + c

To get c, what we need to do is to use any of the points and substitute the values of x and y to get c

Let’s use (5,1)

1 = 5 + c

c = 1-5

c = -4

So the line would be

y = x -4

Answer:

  8/15 acres per hour

Step-by-step explanation:

To find acres per hour, divide acres by hours:

  (2/5 ac)/(3/4 h) = (2/5)(4/3) ac/h = 8/15 ac/h

Derek can cover 8/15 acres per hour.

Answer:

Step-by-step explanation: so you calculate how many people ate chicken, beef, fish or are vegetarian then you will add it all together

chicken=128

beef= 80

fish=32

vegetarian=112

128+80+32+112= 352 people ate at the restaurant

Answer:

Altogether, 88 people went to the restaurant.

Step-by-step explanation:

Answer:

The volume of the composite figure is 162.7 in^3

Step-by-step explanation:

Here, we have a cylinder placed over a cube

The volume of the cube is L^3

With L being the length of its side = 5

The volume of the cube is 5^3 = 125 in^3

The volume of the cylinder is pi * r^2 * h

with r = 2 in and h = 3 in

The volume of the cylinder = 22/7 * 2^2 * 3 = 37.699 = 37.7 in*3

Total volume is thus;

37.7 + 125 = 162.7 in^3

Answer:

Option (3)

Step-by-step explanation:

Inequality n < -2 will be represented on a number line as,

A ray starting form -2 with a hollow circle directing towards -5.

Similarly, other inequality n ≥ 4 will be represented by a ray heading towards positive integers with a staring point 4 marked with a dark circle.

By combining these inequalities on a number line we get Option (3) as a correct option.

Answer: A para B

Step-by-step explanation: Me no a little espanol, y i think A par B, gracias hasta luego, mucho gusto!!

Answer:

I hope it will help you.....

Answer:

The solution is the triplet: (a, b, c) = (-3, 0, 0)

Step-by-step explanation:

Let's start with the second equation, and solving for "a":

a - b = -3

a = b - 3

Now replace this expression for a in the third equation:

2 a + b = -6

2 (b - 3) +b = -6

2 b - 6 +b = -6

3 b = -6 +6

3 b = 0

b = 0

So if b = 0 then a = 0 - 3 = -3

now we can replace a= -3, and b = 0  in the first equation and solve for c:

2 a - b + c = -6

2 ( -3) - 0 + c = -6

-6+ c = -6

c = -6 + 6

c = 0

Our solution is a = -3, b= 0 , and c = 0 which can be expressed as (-3, 0, 0)

Answer:

9

Step-by-step explanation:

Answer:

9m

Step-by-step explanation:

Let x be the length of the rectangle and P the perimeter

P= 4*2+ 2x

26= 8+2x

18= 2x

x= 9 m

Answer:

the nth term of the sequence is 3n+5.

now, 5th term=5×3+5=20

6th term = 6×3+5=23

is your answer...

Answer:

h = 1/2

Step-by-step explanation:

Step 1: Write equation

2.4(5h + 10) - 3 = 27

Step 2: Distribute

12h + 24 - 3 = 27

Step 3: Combine like terms

12h + 21 = 27

Step 4: Subtract 21 on both sides

12h = 6

Step 5: Divide both sides by 12

h = 6/12

Step 6: Simplify

h = 1/2

Answer:

From the attached graph, the x-intercept is (13, 0)

Step-by-step explanation:

The question equation is y = x³ + 11·x² - 312·x

To graph the equation, we find the value of y for a given value of x and we plot the values on a graph as follows;

x,              y

13,            0

14,            532

15,            1170

16,            1920

17,            2788

18,           3780

19,           4902

20,           6160

21,           7560

22,          9108

23,          10810

24,          12672

25,          14700

From the graph, the x-intercept can be found at at x = 13.

The x-intercept can also be obtained by equating the right hand side of the equation to 0 (y = 0 is the x -intercept) as follows;

0 = x³ + 11·x² - 312·x

Therefore, x = 0 is one of the x-intercepts

By dividing by x, we have

x² + 11·x - 312 = 0

By completing the square we have

x² + 11·x + (11/2)² = 312+(11/2)²

(x + 11/2)² = 1369/4

x + 11/2 = ±37/2

x = 37/2 - 11/2 = 13 or x = -37/2 - 11/2 = -24

Which gives the x-intercept as (13, 0).

Answer:

since 3x^2-7x+4=0 is in the form ax^2+bx+c=0, a=3, b=-7, c=4

Answer:

 I think its D?

         Hope this helped!

We can use the points (-4, 3) and (3, 1) to solve.

Slope formula: y2-y1/x2-x1

1-3/3-(-4)

-2/7

Therefore, the answer is C

Best of Luck!

Answer:

-2/7

Step-by-step explanation:

To find the slope we use the formula

( -4,3) and ( 3,1) are two points on the line

m = ( y2-y1)/(x2-x1)

    = ( 1-3)/( 3 - -4)

    ( 1-3) /(3+4)

     -2/7

Answer:

  x = 20%

Step-by-step explanation:

The area is the product of side lengths. If the original side is "a", then the one increased by 25% is ...

  a + 0.25·a = 1.25a

The one decreased by x is ...

  a -x·a = a(1 -x)

We want the area of the square to be the same as that of the rectangle, so we write an equation that says that, then solve for x.

  square area = rectangle area

  a^2 = (1.25a)(a)(1-x)

  1 = 1.25 -1.25x . . . . divide by a^2, eliminate parentheses

  1.25x = 0.25 . . . . . add 1.25x -1

  x = 0.25/1.25 = 0.20

  x = 20% . . . . . . expressed as a percentage

Answer:

When two vectors are parallel, it's because the angles of inclination are equivalent. They are defined by

[tex]\theta = tan^{-1}(\frac{y}{x} )[/tex]

So, we just need to find the angle for each vector and see if they are equivalent.

We have vectors [tex](3,1)[/tex] and [tex](-13,-1)[/tex]. You already can deduce that these vectors are not parallel, because, their divisions are not equivalent.

[tex]\frac{1}{3} \neq \frac{-1}{-13}[/tex]

Which will give different angles in the end.

Let's try the other pair of vectors [tex](2,3)[/tex] and [tex](-3.-2)[/tex]. Their division would be

[tex]\frac{3}{2} \neq \frac{-2}{-3}\\ 1.5 \neq 0.67[/tex]

As you can observe, their divisions are not equivalent, which means their tangents are not equivalent.

Therefore, those vectors are not parallel, because they don't have equivalent angles of inclination, not matter if they are pointing to the same or different direction.

Answer:

64.44cm^2

Step-by-step explanation:

11×7 -pi ×2^2=77-31.4×4=77-12.56= 64.44 cm^2

Answer:

Hello!

`~~~~~~~~~~~~~~~~~~~~~

Your answer would be (C)  10x2 + 18x+ 30

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

Hope this helped you!

P . S I would've put the explaintion but it's to long.

Answer:

C: 38 units

hope this helps!!

Answer:

hello the data is missing but it is included in the explanation below

missing data = 9, 6, 2, 1, 2, 5, 5, 1, 2, 6, 8, 10, 6, 6, 1, 5, 1, 3, 4, 4, 4, 5, 10, 9, 1, 6

Answer :

A) range = 9 , variance = 8.3015,  standard deviation = 2.8812

B)  The results cannot be a representative of the variation of attractiveness among the population of adult males

Step-by-step explanation:

A ) calculate the Range, variance and standard deviation

The given data = 9, 6, 2, 1, 2, 5, 5, 1, 2, 6, 8, 10, 6, 6, 1, 5, 1, 3, 4, 4, 4, 5, 10, 9, 1, 6

i) Range = difference between largest and smallest values

              = 10 -1 = 9

ii) variance = summation of ; (xi − x)^2/n-1

                   = 207.5385/26−1   ≈ 8.3015

iii) standard deviation = [tex]\sqrt{variance}[/tex]

                                    = [tex]\sqrt{8.3015}[/tex] = 2.8812

B) The results cannot be a representative of the variation of attractiveness among the population of adult males

Answer:

Child's dosage=60 milligram

Step-by-step explanation:

The correct formula is below

C= a/(a+12) ∙ A

Where,

C = child’s dosage in milligrams

a = age of the child

A = adult dosage in milligrams

a=6 year old

A=180 milligrams

C= a/(a+12) ∙ A

=6/(6+12)*180

=6/18*180

=1/3*180

=60

Child's dosage in milligram=60 milligram

Answer:

150  cans

Step-by-step explanation: