Which of the three runners have the fastest pace? Explain how you know.

Picture attached with question

Mariana [72]

The function is stretched vertically by a factor of 3.

The function shifts 2 to the right.

The function is moved 5 units up.

Explanation:

The parent function of the graph is $f(x)=\sqrt{x}$

The transformation for the parent function is given by $g(x)=3\sqrt{x-2} +5$

Thus, the transformed function is in the form of $y=a\sqrt{x-h} +k$

where a is the vertical compression/stretch,

h moves graph to left or right and

k moves the graph up or down.

Thus, from the transformed function $g(x)=3\sqrt{x-2} +5$ , we have,

$a=3, h=2 , k=5$

The attached graph below shows the transformation of the graph that the graph is stretched vertically by a factor of 3 and shifted 2 units to the right and moved 5 units up.

Hence, The function is stretched vertically by a factor of 3.

The function shifts 2 to the right.

The function is moved 5 units up.

6 0

3 years ago

What is the mode of the histogram?

LUCKY_DIMON [66]

The mode is 7.

Mode means most and 7 hours of sleep is the most frequent.

8 0

3 years ago

10x+2y=10 in slope intercept form

faust18 [17]

Slope-intercept form is Y = MX + B. This is in standard form, AX + BY = C. You have to move the X to the other side of the equation and simplify it. 
10x - 2y = 10 
- 10x - 10x Subtract 10x from both sides 
- 2y = - 10x + 10 Now everything is in the right place, but it still needs to be simplified. 
Divide each term by -2, in order to isolate the variable Y. 
- 2y/ - 2 = - 10x/ - 2 + 10/ - 2 
The answer is: y = 5x - 5

7 0

3 years ago

Read 2 more answers

Before a bag of flour can be sold, it must be 40 kilograms but can be within 0.5

Serjik [45]

Answer:

The minimum acceptable weight of the flour bag is 39.5 kg,

and its maximum acceptable weight is 40.5 kg

Step-by-step explanation:

Notice that the selling weight of the bag to be sold (x) needs to differ from 40 kg at most 0.5 kg. Therefore, we can write the following inequality:

$|x-40|\leq 0.5$

The inequality can be solve once we remove the absolute value symbol, and solve for the unknown "x". Recall that in order to solve it, we need to consider the two possible cases:

a) that the expression within the absolute value symbol is larger than or equal to zero, and b) that the expression is less than zero.

a) If $x-40\geq 0$ then its absolute value is equal to itself (x-40), and when we remove the absolute value symbols, we get:

$x-40\leq 0.5\\x\leq 0.5+40\\x\leq 40.5\,\,kg$

which means that the weigh "x" of the flour bag should be smaller or equal than 40.5 kg

b) If $x-40$ , then the absolute value of this is its opposite : -x+40, and the inequality becomes:

$-x+40\leq 0.5\\40\leq 0.5+x\\40-0.5\leq x\\39.5\leq x$

which means that the weight of the flour bag must be larger than or equal to 39.5 kg

So, the minimum acceptable weight of the flour bag is 39.5 kg, and the maximum acceptable weight is 40.5 kg

6 0

3 years ago

The cost of the tank and filter system is $280. The base of the tank is a square with a perimeter of 60 inches what is the side

Kaylis [27]

Answer:

The side length of of the base of the tank is 15 inches.

Step-by-step explanation:

We are given the following in the question:

Cost of the tank and filter system = $280

Perimeter of tank base = 60 inches

The perimeter of tank is in the shape of square.

We have to find the side length of the base of the tank.

Perimeter of tank base = Perimeter of square =

$P = 4a\\\text{where a is the side of square}\\60 = 4a\\\Rightarrow a = 15\text{ inches}$

Thus, the side length of of the base of the tank is 15 inches.

4 0

3 years ago