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3 years ago

Chau is riding his bicycle. He rides at a speed of 12.5 kilometers per hour for 5 hours. For how many kilometers does he ride?

Mathematics

2 answers:

Firlakuza [10]3 years ago

4 0

12.5 x 5 = 62.5km :)

PilotLPTM [1.2K]3 years ago

3 0

Answer: 62.5 kilometers

Step-by-step explanation:

12.5 and 5 should be multiplied to find out how many kilometers Chau rode within 5 hours. 12.5 * 5 = 62.5.

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A chord is 10cm from the centre of a circle of radius 15cm. Find the length of the chord.

almond37 [142]

Answer: 21.44 cm

Step-by-step explanation:

Given

Radius r=15 cm

distance of chord from the center is 10 cm

From the figure, the length of the chord is AC

Applying Pythagoras

$\Rightarrow AO^2=OB^2+AB^2\\\Rightarrow AB^2=15^2-10^2\\\Rightarrow AB^2=225-100=115\\\Rightarrow AB=\sqrt{115}=10.72\ cm$

The length of the chord is $AC=2AB=21.44\ cm$

5 0

3 years ago

What is the average rate of change of f(x) = -x2 + 3x + 6 over the interval –3

Rufina [12.5K]

Answer:

$\frac{\Delta y}{\Delta x} =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3$

Step-by-step explanation:

To find the average rate of change of a function over a given interval, basically you need to find the slope. The mathematical definition of the slope is very similar to the one we use every day. In mathematics, the slope is the relationship between the vertical and horizontal changes between two points on a surface or a line. In this sense, the slope can be found using the following expression:

$Average\hspace{3}rate\hspace{3}of\hspace{3}change=Slope=\frac{y_2-y_1}{x_2-x_1} =\frac{f(x_2)-f(x_1)}{x_2-x_1}$

So, the average rate of change of:

$f(x)=-x^2+3x+6$

Over the interval $-3$

Is:

$f(x_2)=f(3)=-(3)^2+3(3)+6=-9+9+6=6\\\\f(x_1)=f(-3)=-(-3)^2+3(-3)+6=-9-9+6=-12$

$\frac{\Delta y}{\Delta x} =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3$

Therefore, the average rate of change of this function over that interval is 3.

3 0

3 years ago

Sarah spends of her monthly take-home pay on rent, food, and clothing. If she earns $1,830 in take-home pay each month, how much

frosja888 [35]

Sarah spendings

We have that Sarah spends 2/3 of $1,830 in rent food and clothing

In order to find the money she spends, we just have to divide $1,830 in 3 and multiply the result by 2:

$\begin{gathered} \frac{1830}{3}=610 \\ 610\cdot2=1220 \end{gathered}$ <h2>Answer - D. $1,220</h2>

3 0

1 year ago

Graph the line whose y-intercept is -7 and whose x-intercept is 1

vesna_86 [32]

Answer:

$y=7x -7$

Step-by-step explanation:

We are given two points, the y - intercept and the x - intercept.

The y - intercept being: ( 0, -7 )

The x - intercept being: ( 1, 0 )

The equation of a line in slope - intercept form is:

y = mx + b, where m is the slope and b is the y - intercept.

We already have the y - intercept. So far we have:

y = mx - 7

What we're missing is the slope.

To find the slope, we can use this formula:

$\frac{y_{2}-y_{1} }{x_{2}-x_{1}}$ , where $x_{2}$ and $x_{1}$ are the x - coordinates of both points and $y_{2}$ and $x_{1}$ are the y - coordinates of both points.

$m=\frac{0-(-7)}{1-0} \\\\m=\frac{7}{1}\\m=7$

We now have the missing piece, the slope, so the equation now is:

$y=7x -7$

3 0

3 years ago

What is the y-coordinate of the solution for the system of equations? x−y=−11 y+7=−2x

ICE Princess25 [194]

Answer:

$y= 5$

Step-by-step explanation:

Given the system of equations:

$x-y=-11$

$y+7=-2x$

In order to find the y coordinate of the solution we must first find the solution to this system of equations. We first start by solving one of the given equations and then substitute the answer of that into the second equation and further solve to get the final answers.

$x=y=-11$