Antti entered a -kilometer race. His goal is to finish in one hour. He starts off sprinting, and completes the first kilometers of the race at an average speed of kilometers per hour.

To achieve his goal of a one-hour finish time, what average speed (in kilometers per hour) must Antti maintain for the last kilometers of the race?

Enter your answer as a number in decimal form, without units.Hint(s):

6 0

3 years ago

A motorboat can travel 35mph in still water. If the boat can travel 7 miles downstream at the same time it takes to travel 3 mil

LenaWriter [7]

Answer: the rate of the river's current is 14 mph.

Step-by-step explanation:

Let x represent the rate of the river's current.

The speed of the motor boat in still water is 35 mph.

Since the boat travelled more miles downstream than upstream at the same time, it means that while going downstream, it moved in the direction of the current and while going upstream, it moved against the direction of the current. The total speed downstream would be

(35 + x) mph and the total speed upstream would be (35 - x) mph.

Time = distance/speed

If the boat can travel 7 miles downstream, the time spent travelling downstream is

7/(35 + x)

At the same time it takes to travel 3 miles upstream, the time spent travelling upstream is

3/(35 - x)

Since the time is the same, then

7/(35 + x) = 3/(35 - x)

Cross multiplying, it becomes

7(35 - x) = 3(35 + x)

245 - 7x = 105 + 3x

3x + 7x = 245 - 105

10x = 140

x = 140/10

x = 14

6 0

3 years ago

Which linear inequality is represented by the graph?

Genrish500 [490]

answer is y ≤ $\frac{1}{3}x (-4)$

Given that,

Area of shaded inequality below solid line is positive

and y-intercept of the solid line is equal to - 4

therefore,

The inequality must be

y ≤ $\frac{1}{3}x (-4)$

In Mathematics, inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.

A system of linear inequalities in two variables includes at least two linear inequalities in the identical variables. When we solve linear inequality then we get an ordered pair. So basically, in a system, the solution to all inequalities and the graph of the linear inequality is the graph displaying all solutions of the system. Let us see an example to understand it.

the Linear inequality: 2x – y >1, x – 2y < – 1

The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.

here is given step to easily find the value of inequality:

Step 1: The inequality is already in the form that we want. That is, the variable y y is isolated on the left side of the inequality.

Step 2: Change inequality to equality. Therefore, y > x + 1y>x+1 becomes y = x + 1y=x+1.

Step 3: Now graph the y = x + 1y=x+1. Use the method that you prefer when graphing a line. In addition, since the original inequality is strictly greater than symbol, \Large{>}>, we will graph the boundary line as a dotted line.

Step 4: The original inequality is y > x + 1y>x+1. The greater than symbol implies that we are going to shade the top area or region.

learn more about linear inequality here : brainly.com/question/21857626

SPJ9

7 0

1 year ago