20 divided by 5 plus 4 • 2

What is the domain and range of the graph below in interval notation? If union is needed, use Capital U. If infinity is needed u

elena55 [62]

Answer:

DOMAIN: $(-\infty,1]\cup(2,\infty)$

RANGE: $(-\infty,\infty)$

Step-by-step explanation:

The domain of a graph is the span of x-values covered by the graph, while the range of a graph is the span of y-values covered by the graph.

DOMAIN:

From the graph, we can see that the x-values covers everything to the left of x=1. Then we stop and then continue beginning at x=2 all the way until positive infinity.

However, note that at x=1, the dot is a closed circle while at x=2, the dot is an open circle. Thus, we will include x=1 into our domain but not include x=2 into our domain.

So, our domain is all values greater than or less than 1, and all values greater than 2.

In interval notation, this is:

$(-\infty,1]\cup(2,\infty)$

We use brackets with the 1 because we include it in our domain and we use parentheses with the 2 since we do not.

RANGE:

Looking at the graph, it seems that all y-values are covered. The part of the graph on the left covers all y-values less than or equal to 3, while the part of the graph on the right covers all y-values greater than -1. Thus, all y-values are covered.

Our range is all real numbers.

In interval notation, this is:

$(-\infty,\infty)$

5 0

3 years ago

WILL GIVE BRAINLIEST<br><br> can someone tell me a few linear equations with one solution?

erastova [34]

X - 3 = 7 (only solution is 10)

2x + 5 = 11 (only solution is 3)

7x - 1 = 27 (only solution is 4)

4x + 2 = -6 (only solution is -2)

7 0

3 years ago

Barbara drives between Miami, Florida and West Palm Beach, Florida. she drives 45 miles in clear weather and then encounters a t

WINSTONCH [101]

Answer:

Barbara's speed in clear weather is $60mph$ and in the thunderstorm is $38mph$ .

Step-by-step explanation:

Let $v_1$ be the speed and $t_1$ be the time Barbara drives in clear weather, and let $v_2$ be the speed and $t_2$ be the time she drives in the thunderstorm.

Barbara drives 22 mph lower in the thunderstorm than in the clear weather; therefore,

(1). $v_2 = v_1 -22$

Also,

(2). $v_1t_1 = 45miles$

(3). $v_2 t_2 = 57$ ,

and

(4). $t_1+t_2 = 2.25hr$

From equations (2) and (3) we get:

$t_1 = \dfrac{45}{v_1}$

$t_2 =\dfrac{57}{v_2}$

putting these in equation (4) we get:

$\dfrac{45}{v_1}+\dfrac{57}{v_2}=2.25$

and substituting for $v_2$ from equation (1) we get:

$\dfrac{45}{v_1}+\dfrac{57}{v_1-22}=2.25$

This equation can be rewritten as

$2.25v_1^2-151.5v_1+990=0$

which has solutions

$v_1 = 60$

$v_1 = 7.33$

We take the first solution $v_1 =60$ because it gives a positive value for $v_2:$

$v_2 = v_1 -22$

$v_2 = 60 -22\\$

$v_2 = 38$ .

Thus, Barbara's speed in clear weather is $60mph$ and in the thunderstorm is $38mph$ .

4 0

4 years ago

How to answer this? A farmer had 455 ducks and chickens. He sold 2/5 of the ducks and bought another 104 chickens. As a result,

julia-pushkina [17]

Answer:

(a) 25

(b) $4816

Step-by-step explanation:

Let's say the starting amount of ducks is d, and the starting amount of chickens is c. Since there are only ducks and chickens, we can say that d + c= 455.

Next, the farmer sells 2/5 of the ducks, so we subtract 2/5 of the ducks so that the ending duck amount is d - (2/5)d = (3/5) d

After that, the farmer buys another 104 chickens, so we add 104 chickens to the current amount of chickens to get the ending chicken number as 104+c

Given the ending duck and chicken count, we can say that the ending farm animal count (we can represent this as a) is (3/5)d + 104 + c = a

The number of ducks is 2/3 the total number of animals at the end, so (3/5)d = (2/3)a

Let's list our equations out so it is easier to solve:

d+c = 455

(3/5)d + 104 + c = a

(3/5)d = (2/3)a

We have three equations and need to solve for three variables. One common variable in all three equations is d, so it might help if we put everything in terms of d.

Starting with d+c=455, if we subtract d from both sides, we get c=455-d. We can substitute this in the second equation to get

(3/5)d + 104 + 455 - d = a

-(2/5)d + 559 = a

(3/5)d = (2/3)a

Next, we can substitute for a. If we multiply both sides by 3 and then divide by 2 in (3/5)d = (2/3)a , we get

(9/10)d = a

Substitute that in to the second equation to get

-(2/5)d + 559 = (9/10) d

-(4/10)d + 559 = (9/10) d

add (4/10)d to both sides to isolate the variable and its coefficient

(13/10)d = 559

multiply both sides by (10/13) to isolate the coefficient

d = 430

Therefore, the starting number of ducks is 430 and the starting amount of chickens is 455-430 = 25

For (b), 2/5ths of the ducks are sold, so this is (430) * (2/5) = 172. Each duck is sold for 28 dollars, so this is 172*28=$4816 as the total price

7 0

3 years ago

Find the zeros of the polynomial p(x) 5-10x

Charra [1.4K]

Answer:

Step-by-step explanation:

The given polynomial is :

p(x) = 5-10x

We need to find the zeros of the above polynomial. To find it, put p(x) = 0

5-10x = 0

Subtract 5 from both sides

5-10x-5=0-5

-10x=-5

or

10x=5

Divide both sides by 10.

x = 0.5 = 1/2

Hence, the zeros of the polynomial is 1/2.

3 0

3 years ago