What equation is the rule for the function illustrated by the table of values?

Answer:

A

Step-by-step explanation:

The velocity of a moving body is given by the equation:

[tex]v=t^2-5t+4 ,\, t\geq0[/tex]

Is the velocity is positive (v>0), then our object will be moving forwards.

And if the velocity is negative (v<0), then our object will be moving backwards.

We want to find between which interval(s) is the object moving backwards. Hence, the second condition. Therefore:

[tex]v<0[/tex]

By substitution:

[tex]t^2-5t+4<0[/tex]

Solve. To do so, we can first solve for t and then test values. By factoring:

[tex](t-4)(t-1)=0[/tex]

Zero Product Property:

[tex]t=1, \text{ and } t=4[/tex]

Now, by testing values for t<1, 1<t<4, and t>4, we see that:

[tex]v(0)=4>0,\, v(2)=-2<0,\,\text{ and } v(5)=4>0[/tex]

So, the (only) interval for which v is <0 is the second interval: 1<t<4.

Hence, our answer is A.

Answer:

this question is of high school or collage

Answer:

She has 20 items on the list

Step-by-step explanation:

Answer:

if she is 60% done shopping and has a total of 12 items, then the list will have 8 items left or 20 in total.

please friend complete your answer

Answer:

=10

Step-by-step explanation:

Answer:

Do we do all of them???

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

y = mx + b

m represents the slope, and as we can see in the equation, the number 4 is there instead of m, so therefore 4 is the slope

Answer:

5m = 5000 mm

Step-by-step explanation:

Answer:

Ms. Duncan should leave a $8.40. tip.

Answer:

f(x)=4784

f(13)= 0 because there is x value on the right hand side

Given:

X=number of hours

Y=number of tents made

Table of value.

To find:

The slope and its interpretation.

Solution:

Consider any two points from the table, i.e., (0,6) and (1,7).

The slope is

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{7-6}{1-0}[/tex]

[tex]m=\dfrac{1}{1}[/tex]

[tex]m=1[/tex]

Therefore, the slope is 1 and it represent that the number of tents made are increasing by 1 units in each hour.

Answer:

10

Step-by-step explanation:

PEMDAS MATH

Answer:

.06

Step-by-step explanation:

edg

Answer:

.06

Step-by-step explanation:

test on edg e

Answer:

Step-by-step explanation:

(1). [tex]\frac{1}{7}[/tex] x + y = 9 and y = - 7x ( Neither ) ; lines intersect.

(2). y = 3x - 3; 12x - 4y = 12 ( Neither ) ; Lines are overlapped or both equation are of the same line.

(3). 7y = 2x + 1; 14x + 4y = 12 ( Perpendicular ) ; [tex]m_{1}[/tex] = [tex]\frac{2}{7}[/tex] and [tex]m_{2}[/tex] = - [tex]\frac{7}{2}[/tex] , slopes are opposite reciprocals.

(4). x - 4y = 18; y = x + 4 ( Neither ) ; lines intersect.

(5). 3x - 4y = - 1; 3y = - 4x + 5 ( Perpendicular ) ; [tex]m_{1}[/tex] = [tex]\frac{3}{4}[/tex] and [tex]m_{2}[/tex] = - [tex]\frac{4}{3}[/tex] , slopes are opposite reciprocals.

Answer:

option A) Agree, because the solutions are the same is correct.

Step-by-step explanation:

FIRST SYSTEM

[tex]6x + y= 2[/tex]

[tex]-x-y=-3[/tex]

solving the system

[tex]\begin{bmatrix}6x+y=2\\ -x-y=-3\end{bmatrix}[/tex]

[tex]\mathrm{Multiply\:}-x-y=-3\mathrm{\:by\:}6\:\mathrm{:}\:\quad \:-6x-6y=-18[/tex]

[tex]\begin{bmatrix}6x+y=2\\ -6x-6y=-18\end{bmatrix}[/tex]

adding the equation

[tex]-6x-6y=-18[/tex]

[tex]+[/tex]

[tex]\underline{6x+y=2}[/tex]

[tex]-5y=-16[/tex]

so the system becomes

[tex]\begin{bmatrix}6x+y=2\\ -5y=-16\end{bmatrix}[/tex]

solve -5y for y

[tex]-5y=-16[/tex]

Divide both sides by -5

[tex]\frac{-5y}{-5}=\frac{-16}{-5}[/tex]

simplify

[tex]y=\frac{16}{5}[/tex]

[tex]\mathrm{For\:}6x+y=2\mathrm{\:plug\:in\:}y=\frac{16}{5}[/tex]

[tex]6x+\frac{16}{5}=2[/tex]

subtract 16/5 from both sides

[tex]6x+\frac{16}{5}-\frac{16}{5}=2-\frac{16}{5}[/tex]

[tex]6x=-\frac{6}{5}[/tex]

Divide both sides by 6

[tex]\frac{6x}{6}=\frac{-\frac{6}{5}}{6}[/tex]

[tex]x=-\frac{1}{5}[/tex]

Therefore, the solution to the FIRST SYSTEM is:

[tex]x=-\frac{1}{5},\:y=\frac{16}{5}[/tex]

SECOND SYSTEM

[tex]2x-3y = -10[/tex]

[tex]-x-y=-3[/tex]

solving the system

[tex]\begin{bmatrix}2x-3y=-10\\ -x-y=-3\end{bmatrix}[/tex]

[tex]\mathrm{Multiply\:}-x-y=-3\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-2x-2y=-6[/tex]

[tex]\begin{bmatrix}2x-3y=-10\\ -2x-2y=-6\end{bmatrix}[/tex]

[tex]-2x-2y=-6[/tex]

[tex]+[/tex]

[tex]\underline{2x-3y=-10}[/tex]

[tex]-5y=-16[/tex]

so the system of equations becomes

[tex]\begin{bmatrix}2x-3y=-10\\ -5y=-16\end{bmatrix}[/tex]

solve -5y for y

[tex]-5y=-16[/tex]

Divide both sides by -5

[tex]\frac{-5y}{-5}=\frac{-16}{-5}[/tex]

Simplify

[tex]y=\frac{16}{5}[/tex]

[tex]\mathrm{For\:}2x-3y=-10\mathrm{\:plug\:in\:}y=\frac{16}{5}[/tex]

[tex]2x-3\cdot \frac{16}{5}=-10[/tex]

[tex]2x=-\frac{2}{5}[/tex]

Divide both sides by 2

[tex]\frac{2x}{2}=\frac{-\frac{2}{5}}{2}[/tex]

Simplify

[tex]x=-\frac{1}{5}[/tex]

Therefore, the solution to the SECOND SYSTEM is:

[tex]x=-\frac{1}{5},\:y=\frac{16}{5}[/tex]

Conclusion:

As both systems of equations have the same solution.

Therefore, we conclude that Albert is right when says that the two systems of equations shown have the same solutions.

Hence, option A) Agree, because the solutions are the same is correct.

Answer:

endpoint for B is (10,-2)

Step-by-step explanation:

M={(x1+x2)/2,(y1+y2)/2}

(4,2)={-2+x2/2,6+y2/2)

By equating the x coordinates

4=-2+x2/2

8=-2+x2

8+2=x2

x2=10

By equating the y coordinates

2=6+y2/2

4=6+y2

4-6=y2

y2=-2

Therefore the endpoint for B is (10,-2)

Step-by-step explanation:

We have been given that a basketball team has 12 players and the coach wants to pick which 5 players will start today's game.

We will use combinations formula to solve our given problem. , where,

n = Number of total items,

r = Number of items being chosen at a time.

Upon substituting our given values in combinations formula we will get,

Therefore, the coach can choose from 792 combinations

Answer:

i) x = 2.8

ii) x = 2

Answer:

306

Step-by-step explanation:

18x17=306

The total number of matches played by the teams will be given by using permutation is 306.

A permutation is an act of arranging the objects or elements in order. Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.

There are 18 football teams in a league.

Each team plays two matches against each of the other teams.

Then the total number of matches played by the teams will be given by the permutation.

[tex]^{n}P_r = \dfrac{n!}{(n-r)!}[/tex]

We have

n = 18

r = 2

Then

[tex]\rm ^{18}P_2 = \dfrac{18!}{(18-2)!}\\\\\\^{18}P_2 = \dfrac{18!}{16!}\\\\\\^{18}P_2 = \dfrac{18 *17*16!}{16!}\\\\\\^{18}P_2 = 18*17\\\\\\^{18}P_2 = 306[/tex]

More about the permutation and the combination link is given below.

https://brainly.com/question/11732255

Answer:

a. days                         1        2        3     4       5

number of gallons    12      24     36    48    60

b.     g = 12d    (the number of days times 12)

c.    a person uses 84 gallons of water for showering each week.

Step-by-step explanation:

each day is 12 gallons so just multiply the number of days by 12 to get how many gallons that you use in a set number of days. for the last one, a week is 7 days so if you do 7 x 12 then you get how many gallons a person uses in a week.

Answer:

(6,9) and (7,9) - assuming the graph only has a single quadrant and the rectangle is vertical

Step-by-step explanation:

We know that the distance between (6,1) and (7,1) is one unit. Because a rectangle has 2 pairs of equal sides, we know that the distance between the 2 missing coordinates is equal to one. We then add these two units. Because the rectangle has a parameter of 18 units, we then have to subtract these 2 units from the total, leaving us with 16 units for both sides. We then divide 16 by 2 because there are 2 sides, leaving us with 8 units for each side. Assuming we are working with a coordinate graph (with only one quadrant instead of 4 on a coordinate plane), and assuming the rectangle is vertical, the missing coordinates should be 8 units above the coordinates you were given. Hope this helps! :)

Answer:

Step-by-step explanation:

9

3

4

Answer:

1. 9

2. 3

3. 4

Step-by-step explanation:

I have taken the test and got 100% on it so I hope this helped you!

Answer:

a 1/4 cuz perpendicular m × m original line is -1

Answer:

It's pretty simple. For example, if it says there is a percentage increase on something like there is a jacket for $25 and there was a 15% increase, you multiply 25 by 1.15 to see what the new price is. But say if the same $25 jacket is on sale for 15%, then you can multiply 25 by .15, then subtract that from 25 or originally subtract the 15% from 100 which is 85 and multiply 25x.85 and get the answer directly.

Hope this helps! But this would be easier to explain with an example

Answer:

y = 2x +4

Step-by-step explanation:

m = [tex]\frac{y_{2} -y_{1} }{x_{2} - x_{1} }[/tex]

y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )

~~~~~~~

(1, 6)

(- 3, - 2)

m = 2

y - 6 = 2 ( x - 1 ) <------ ( point-slope form )

y = 2x + 4  <------- ( slope-intercept form )

2x - y = - 4  <------ ( standard form )

Answer:

what is the y-coordinate for A?

Step-by-step explanation:

Answer:1.5

Step-by-step explanation: