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3 years ago

13

Amaya wants to jog 8 miles this week.She jogged 2 1/2 miles on Monday and 3 2/5 miles on wednesday. How many miles does Amaya st

ill need to jog?

1 answer:

madam [21]3 years ago

3 0

Answer:

2 1/10 miles.

Step-by-step explanation:

8 - (2 1/2 + 3 2/5)

= 8 - (5/2 + 17/5)

= 8 - (25/10 + 34/10)

= 8 - 59/10

= 80/10 - 59/10

= 21/10

= 2 1/10 miles.

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What are the coordinates of the endpoints of the midsegment for △XYZ that is parallel to XZ⎯⎯⎯⎯⎯ ?

Ksenya-84 [330]

The coordinates of the endpoints of the mid-segment of Δ XYZ that parallel to XZ are (1 , 6) and (1 , 3)

Step-by-step explanation:

In a triangle the segment which joining the mid points of two sides:

Parallel to the 3rd side
Its length is equal half the length of the 3rd side
It's called the mid-segment of the triangle

In Δ XYZ

∵ Vertex X is (0 , 7)

∵ Vertex Y is (2 , 5)

∵ Vertex Z is (0 , 1)

∵ The mid-segment of Δ XYZ is parallel to XZ

- The mid-segment intersects the other two sides of the Δ

at their mid-points

∴ The mid-segment intersects XY and YZ at their midpoints

∴ The endpoints of the mid-segment are the midpoints of

XY and YZ

The mid point of a segments whose endpoints are $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

∵ X = (0 , 7) and Y = (2 , 5)

∴ $x_{1}$ = 0 and $x_{2}$ = 2

∴ $y_{1}$ = 7 and $y_{2}$ = 5

∵ The mid point of XY = $(\frac{0+2}{2},\frac{7+5}{2})$

∴ The mid point of XY = $(\frac{2}{2},\frac{12}{2})$

∴ The mid point of XY = (1 , 6)

∵ Z = (0 , 1) and Y = (2 , 5)

∴ $x_{1}$ = 0 and $x_{2}$ = 2

∴ $y_{1}$ = 1 and $y_{2}$ = 5

∵ The mid point of ZY = $(\frac{0+2}{2},\frac{1+5}{2})$

∴ The mid point of ZY = $(\frac{2}{2},\frac{6}{2})$

∴ The mid point of ZY = (1 , 3)

∵ The endpoints of the mid-segment are the midpoints of

XY and YZ

∴ The end points of the mid segments are (1 , 6) and (1 , 3)

The coordinates of the endpoints of the mid-segment of Δ XYZ that parallel to XZ are (1 , 6) and (1 , 3)

Learn more:

You can learn more about the mid-point in brainly.com/question/5223123

#LearnwithBrainly

7 0

2 years ago

2x^2+x-1=2^are^x=-3/2 or x=

jenyasd209 [6]

The second answer is x=1

4 0

3 years ago

Find the multiplicative inverse of 6 + 2i

Marina CMI [18]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2774989

________________

Find the multiplicative inverse of

$\mathsf{z=6+2i}$

________

The inverse multiplicative of $\mathsf{z=a+bi}$ is

$\mathsf{\dfrac{1}{z}}\\\\\\
=\mathsf{\dfrac{1}{a+bi}\qquad\quad(a\ne 0~~and~~b\ne 0)}\\\\\\
=\mathsf{\dfrac{1}{a+bi}\cdot \dfrac{a-bi}{a-bi}}\\\\\\
=\mathsf{\dfrac{1\cdot (a-bi)}{(a+bi)\cdot (a-bi)}}\\\\\\
=\mathsf{\dfrac{a-bi}{a^2-\,\diagup\hspace{-10}abi+\,\diagup\hspace{-10}abi-(bi)^2}}$

$=\mathsf{\dfrac{a-bi}{a^2-b^2\cdot i^2}}\\\\\\
=\mathsf{\dfrac{a-bi}{a^2-b^2\cdot (-1)}}\\\\\\
=\mathsf{\dfrac{a-bi}{a^2+b^2}}\\\\\\\\
\therefore~~\mathsf{\dfrac{1}{a+bi}=\dfrac{a}{a^2+b^2}-\dfrac{b}{a^2+b^2}\,i\qquad\quad\checkmark}$

________

For this question,

$\mathsf{z=6+2i}$

So,

$\mathsf{\dfrac{1}{z}}\\\\\\
=\mathsf{\dfrac{1}{6+2i}}\\\\\\
=\mathsf{\dfrac{6}{6^2+2^2}-\dfrac{2}{6^2+2^2}\,i}\\\\\\
=\mathsf{\dfrac{6}{36+4}-\dfrac{2}{36+4}\,i}\\\\\\
=\mathsf{\dfrac{6}{40}-\dfrac{2}{40}\,i}$

$\therefore~~\mathsf{\dfrac{1}{z}=\dfrac{3}{20}-\dfrac{1}{20}\,i}\quad\longleftarrow\quad\textsf{this is the answer.}$

I hope this helps. =)

6 0

3 years ago

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What is the surface area of this point

Kaylis [27]

Answer:

The answer is 30ft.

Step-by-step explanation:

To find the surface area of a rectangle, we use the formula L(2) + W(2) + H(2)

Our length is 7ft

Our Width 2ft

Our height is 6ft

Let's plug our numbers into our equation:

7(2) + 2(2) +6(2)

= 14 + 4 + 12

=30 ft.

7 0

3 years ago

Read 2 more answers

Use Newton’s Method with initial approximation x1=1 to find x4, the third

babymother [125]

Let $f(x) = x^3 + 3x + \sin(x) - 5$ . Using Newton's method to approximate a solution to $f(x) = 0$ , we consider the recurrence

$\begin{cases} x_1 = 1 \\ x_{n + 1} = x_n - \frac{f(x_n)}{f'(x_n)} & \text{for } n \ge 1 \end{cases}$

Differentiating $f(x)$ gives

$f'(x) = 3x^2 + 3 + \cos(x)$

Then

$x_2 = 1 - \dfrac{f(1)}{f'(1)} = 1 + \dfrac{1 - \sin(1)}{6 + \cos(1)} \approx 1.024238790$

$x_3 = x_2 - \dfrac{f(x_2)}{f'(x_2)} \approx 1.024009549$

$x_4 = x_3 - \dfrac{f(x_3)}{f'(x_3)} \approx \boxed{1.024009528}$

which agrees numerically with the actual root of $f(x)$ up to at least 9 digits after the decimal point.

3 0

1 year ago