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3 years ago

What is the domain of the function represented by the graph?

Mathematics

1 answer:

dezoksy [38]3 years ago

8 0

Answer: Choice C. $x \ge -3$

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

Explanation:

The domain is the set of all allowed x inputs.

Here we see that x = -3 is the smallest x value possible as it is from the left-most point. The graph goes on forever to the right, so there is no largest x value. Effectively infinity is the largest x value even though infinity is not a number.

We can say the domain is $-3 \le x < \infty$ which can be simplified to $-3 \le x$ or $x \ge -3$

In short: x can be -3 or larger.

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You and a friend start riding bikes toward

Setler [38]

Answer:

1.5 hours

I traveled farther

2 miles

Step-by-step explanation:

$\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}$

My speed

$\dfrac{2\dfrac{1}{6}}{\dfrac{1}{4}}=\dfrac{\dfrac{13}{6}}{\dfrac{1}{4}}=\dfrac{26}{3}\ \text{mph}$

Speed of my friend

$7\dfrac{1}{3}=\dfrac{22}{3}\ \text{mph}$

Time passed for both me and my friend will be equal if we start at the same time and the combined distance covered by both of us will be 24 miles. Let $t$ be the time taken to meet

$\text{Distance}=\text{Speed}\times\text{Time}$

$\dfrac{26}{3}t+\dfrac{22}{3}t=24\\\Rightarrow \dfrac{48}{3}t=24\\\Rightarrow 16t=24\\\Rightarrow t=\dfrac{24}{16}\\\Rightarrow t=1.5\ \text{hours}$

So, we meet each other after 1.5 hours.

Distance traveled by me

$\dfrac{26}{3}\times 1.5=13\ \text{miles}$

Distance traveled by my friend

$\dfrac{22}{3}\times 1.5=11\ \text{miles}$

So, I traveled farther by $13-11=2\ \text{miles}$ .

7 0

3 years ago

Re-write the equation in slope-intercept form: 5x + 4y = 20

Mazyrski [523]

Answer:

y=5-5/4x

Step-by-step explanation:

slope-intercept form: y=mx+b (m= slope, b= y-intercept)

5x + 4y = 20

4y=20-5x

simplify

y=5-5/4x

3 0

3 years ago

The coordinates below represent two linear equations. How many solutions does this system of equations have?

AlexFokin [52]

<span>find the equations of the lines in slope-intercept form which is y=mx+b where m=slope b=y intercept
the choices:
0 solutions: means the lines don't intercect at all, meaning same slope but different y intercept or they ar paralell
1 solution: lines intercect in 1 point
2 solutions: curvy line with a straight line thorugh middle
infinetly solutions: same line

to find slope you do
slope=(y1-y2)/(x1-x2)
first line is
(-4,8)
(4,6)
(x,y)
x1=-4
y1=8
x2=4
y2=6
subsitute
(8-6)/(-4-4)=2/-8=-1/4
slope=-1/4
subsitute
y=-1/4x+b
subsitute one of the points
(4,6)
x=4
y=6
6=-1/4(4)+b
6=-1+b
add 1 to both sides
7=b
y=-1/4+7

now solve for the other equation

(-1,1)
(3,5)
x1=-1
y1=1
x2=3
y2=5
subsitute
(1-5)/(-1-3)=(-4)/(-4)=4/4=1
y=1x+b
subsitute
(-1,1)
x=-1
y=1
1=1(-1)+b
1=-1+b
add 1
2=b
y=x+2

we have the lines
y=-1/4x+7 and
y=x+2
solve for a common solution
y=x+2 and y=-1/4x+7 therefor
x+2=-1/4x+7
subtract 7 from both sides
x-5=-1/4x
mulitply both sides by -4
-4x+20=x
add 4x to both sides
20=5x
divide both sides by 5
4=x
subsitute
y=x+2
y=4+2
y=6
the soluiton is (4,6)
there is only one solution
the answer is B</span>

8 0

3 years ago

This test is really hard for me in my opinion

pshichka [43]

Answer:13 x 10 (130)Step-by-step explanation:1 1/4 cups of milk make 10 servings. 16 cups make 1 gallon. 1 1/4 + 1 1/4= 2 2/4 + 1 1/4+ 3 3/4 + 1 1/4= 5 + 1 1/4 = 6 1/4 + 1 1/4= 7 2/4 + 1 1/4 + 8 3/4 + 1 1/4 + 10 + 1/4 = 11 1/4 + 1/4 = 12 2/4 + 1 1/4 = 13 3/4 + 1 1/4 = 15 = 1 1/4 = 16 1/4

8 0

2 years ago

Please help me, im not gonna beg, I just really need help? k?

kupik [55]

For the unit rate, you are looking for how much one unit of something costs. Looking at the table, you'll see that 3 bottles of fragrance A costs $78. What you want to figure out is how much one bottle costs.

You can do this by taking the price and dividing it by how many there are.

78 ÷ 3 = $26

156 ÷ 6 = $26

234 ÷ 9 = $26

You can see that each bottle of fragrance A costs $26.

Now looking at the graph, you'll see that the line only lines up perfectly at 2 points: (1, 24) and (2, 48). This tells us that for each bottle of fragrance B, it costs $24.

Comparing the two, fragrance A will have the greatest unit rate.

3 0

2 years ago