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Elena-2011 [213]
3 years ago
12

A cyclist bikes x distance at 10miles per hour and returns over the same path at 8miles per hour .what is the cyclists average r

ate for the round trip in miles per hour
Mathematics
1 answer:
algol [13]3 years ago
3 0
Average speed = total distance travelled / time taken
 in this case total distance = 2x miles

time taken for first half of the journey = x/10 hours and for second part its x / 8  hours

average speed = 2x / ( x/10 + x/8)  = 2 x /  (  4x + 5x / 40)
=  2x  * 40 / 9x =  80 / 9  mph 8.89 mph
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Applying the the properties of Congruence.
kolbaska11 [484]

Answer:

LM = 35cm and m \angle H = 98^o

Step-by-step explanation:

For this problem, it is critical to understand what the opening statement means.

Quadrilateral GHJK \cong quadrilateral LMNP means that each pair of <u>corresponding sides</u> between shapes are congruent (they have equal length), and each pair of <u>corresponding angles</u> between shapes are congruent (they have equal measure -- or same number of degrees when measured with a protractor).

So, it's important to be able to determine which pairs are the <u>corresponding</u> parts.  When the congruence is given like Quadrilateral GHJK \cong quadrilateral LMNP  the letters are in a particular order.  That order explains the order in which the shape is drawn out, and they put them in the same order for both shapes to mean that those are the letters that correspond with each other.

So, the first letter of each are a corresponding pair, the second letter of each are a corresponding pair, ... etc

In other words, point G and L correspond, point H and K correspond, etc.

<h3><u>Part 1 -- Find LM</u></h3>

To find the corresponding sides, the sides for these shapes are defined by a two adjacent letters (two letters next to each other in the name, or ... as it wraps around the end of the name... the first and last letter).

\overline{GH} \cong \overline{LM}\\ \overline{HJ} \cong \overline{MN} \\\overline{JK} \cong \overline{NP}\\\overline{KG} \cong \overline{PL}

While all of that is true, we only have a few sides with any information in them.  Notice that side GH in the first shape, and sides PL & LM in the second shape are the only sides with anything written.  So, we just need to determine which sides correspond (and thus, are congruent), so that we know how to move forward.  Looking at the list of congruent sides above, we see that  \overline{GH} \cong \overline{LM}

Since the sides (line segments) are congruent, their lengths are equal

GH = LM

...so we can substitute the expressions for each angle into the equation and solve for the unknown value "x"

GH = LM\\(4x+3)=(6x-13)

(4x+3)+13=(6x-13)+13\\4x+16=6x

(4x+16)-4x=(6x)-4x\\16=2x

divide both sides by 2

\frac{16}{2}=\frac{2x}{2}\\8=x

So, to find the length, LM, we just need to look back at the expression for LM:

LM = 6x-13\\LM = 6(8)-13\\LM = 48-13\\LM = 35

remembering that the lengths are measured in centimeters (as indicated on the diagram): LM = 35cm

<h3><u>Part 2 -- Find m∠H</u></h3>

To find the corresponding angles, the angles for these shapes are defined by a single letter, so since the points correspond in order, the names of the shapes tell which angles are congruent.

\angle G \cong \angle L\\\angle H \cong \angle M\\\angle J \cong \angle N\\\angle K \cong \angle P

While all of that is true, we only have a few angles with any information in them.  Notice that ∠H in the first shape, and ∠L & ∠M in the second shape are the only angles with anything written.  So, we just need to determine which angles correspond (and thus, are congruent), so that we know how to move forward.  Looking at the list of congruent angles above, we see that  

\angle H \cong \angle M

Since the angles are congruent, their measures are equal

m\angle H = m\angle M

...so we can substitute the expressions for each angle into the equation and solve for the unknown value "y"

m\angle H = m\angle M\\(9y+17)=(11y-1)

subtract 1 from both sides

(9y+17)+1=(11y-1)+1\\9y+18=11y

subtract 9y from both sides

\\(9y+18)-9y=(11y)-9y\\18=2y

divide both sides by 2

\frac{18}{2}=\frac{2y}{2}\\9=y

So, to find angle H, we just need to look back at the expression for the measure of angle H:

m\angle H = 9y+17\\m\angle H = 9(9)+17\\m\angle H = 81+17\\m\angle H = 98

remembering that the angle is measured in degrees (as indicated on the diagram): m \angle H = 98^o

6 0
2 years ago
If a line segment contains one endpoint at (2,3) and has a midpoint of (-2,6) what is the second endpoint of the line segment
olchik [2.2K]

Answer:

Step-by-step explanation:

The coordinates of the midpoint M are the average of the coordinates of the two endpoints:

M_x = \dfrac{2+x}{2},\quad M_y = \dfrac{3+y}{2}

Plug the known coordinates of the midpoint:

-2 = \dfrac{2+x}{2},\quad 6 = \dfrac{3+y}{2}

Solve for x and y:

-4 = 2+x,\quad 12 = 3+y

x=-6,\quad y = 9

4 0
3 years ago
Tamara rewrote the expression 0.2(4+1.4y - 2.1). Her steps are shown.
grin007 [14]

Answer:

Her first mistake was in Step 2. She added 0.2 to each term instead of multiplying by 0.2.

Step-by-step explanation:

CORRECT WAY:

0.2(4+1.4y - 2.1)

0.8 + 0.28y - 0.42

0.8 - 0.42 + 0.28y

0.38 + 0.28y

WHAT TAMARA DID:

0.2(4+1.4y - 2.1)

How she got 4.2: 0.2 + 4 = 4.2

How she got 1.6y: 0.2 + 1.4y = 1.6y

How she got -1.9: 0.2 + -2.1 = -1.9

WHAT SHE DID HERE IS WRONG. REMEMBER WHEN IT IS __( ______) IT MEANS THAT YOU NEED TO MULTIPLE NUMBER OUTSIDE THE PARATNESS TO EVERY NUMBER THAT IS INSIDE THE PARATNESS.

4 0
2 years ago
(1.16x10^-19)^2 square root
liubo4ka [24]
Is this the sqrt root of ((1.16x10^-19)^2)
6 0
3 years ago
Given the following two points find the slope. p1(-2,3)and p2(1,0)
Aloiza [94]

Answer

Slope(m) = -1


Step by step explanation

Slope (m) = (y2 - y1)/(x2 - x1)

Here p1 = (-2, 3) and p2 (1, 0)

x1 = -2, y1 = 3, x2 = 1, y2 = 0

Now plug in the values in the slope formula, we get

m = (0 - 3) / (1 - (-2))

m = -3/(1 + 2)

m = -3/3

m = -1

Therefore, slope = -1

Thank you.

8 0
3 years ago
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