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elena-14-01-66 [18.8K]
3 years ago
8

PLS AWNSER ASAP!!Which expression can be used to determine the length of segment ZY? On a coordinate plane, triangle X Y Z has p

oints (3, 1), (3, 4), (negative 5, 1). 8 squared + 3 squared StartRoot 8 squared + 3 squared EndRoot 8 squared minus 3 squared StartRoot 8 squared minus 3 squared EndRoot
Mathematics
1 answer:
MArishka [77]3 years ago
7 0
Sqrt(8^2 + 3^2)

Y is 3,4
Z is -5,1

3-(-5) = 8 (difference between x coords)
4-1 = 3 (difference between y coords)
Equation is: sqrt( (xdiff)^2 + (ydiff)^2 )
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| 9. The distance between Town A and Town B was 108 km. A car and a van left Town A at 12 00 for Town B. On reaching Town B, the
Westkost [7]

Answer:

a)  Time until both vehicles meet is 1.5 hours after starting at noon.  That makes it 1:30PM.

b)  Average speed of car is 84 km/h

Step-by-step explanation:

A -----------------------z------------B

          <u>Left</u>      <u>Speed(km/h)</u>      <u>Time</u>

Car:   12PM            X  

Van:   12PM           60

Car/Van

DistanceCar        AB + z

DistanceVan       Az

Ratio:                  (AB+z)/Az  = 7/5

Time until both meet = T (in hours)

Distance Car:            xT

Distance Van:           60T

====

  xT = AB + z

  60T = Az

---

(xT/60T)= (7/5)

x = 60(7/5)

x = 84 km/h

=====

Time for car to reach B is:    time (hr) = 108 km/(84 km/h)

                                                 time = 1.286 hours

Distance for at 1.289 hours is:    distance (km) = (60 km/h)*(1.286 h)

                                                   distance = 77.14 km

At 1.286 hours, the car reverses direction.  The van is (108 km - 77.14 km) or 30.86 km away.

Add the distances travelled by both vehicles after the car reverses direction at 1.286 hours.  The sum will be 30.86 km when they meet, at time of T.

Car Distance + Van Distance = 30.86 km

T(84 km/h) + t(60 km)

They meet when they are 0 km apart, which can be modeled with the following equation:

Van travel Distance - Car Travel Distance = 0 starting at 1.286 hr.

Let <u>t</u> be the time <u>after</u> 1.286 hours that both vehicles meet/collide.

t*(60 km/h)  +  t(84 km/h) = 30.86 km

t(60+84) = 30.86 km

t(144 km/h) = 30.86 km

t = 0.2143 hr

Total time until the car and van meet is 1.286 hr + 0.2143 hr for a total of 1.50 hours.

=================

a)  Time until both vehicles meet is 1.5 hours after starting at noon.  That makes it 1:30PM.

b)  Average speed of car is 84 km/h

==============

<u>CHECK</u>

Is the ratio of the distance travelled by the car and the van until they meet in the ratio of 7/5?

Car distance is (1.5 hr)(84 km/h) = 126 km

Van distance is (1.5 hr)(60 km/h) = 90.0 km

Ratio is 126/90 or 1.4

Ratio of 7/5 is 1.4

<u><em>YES</em></u>

     

3 0
2 years ago
Find the vertex of the function given below.<br> y = 3x2 + 6x +1
anastassius [24]

Answer: The coordinates of the vertex are : (-1,-2)

Step-by-step explanation: To find the x coordinate, we use the formula:

Xv = -b/2a = -6/(2.3) = -6/6 = -1

Replacing x by -1, we write:

y = 3. (-1)^2 + 6. (-1) +1 = 3 - 6 + 1 = -2

8 0
3 years ago
A $950 notebook computer is discounted 15%. What is the sale price of the notebook computer?
Amanda [17]

Answer:

$807.5

Step-by-step explanation:

If the cost of the notebook is 15% off, the new total price is 85% of the original. Then:

(85%) x ($950) = $807.5

4 0
3 years ago
Twelve jurors are randomly selected from a population of 4 million residents. Of these 4 million​ residents, it is known that 46
vekshin1

Answer:  a) 0.17, b) 0.0363

Step-by-step explanation:

Since we have given that

Number of jurors selected = 12

Number of minorities of jurors = 2

​(a) What proportion of the jury described is from a minority​ race? ​

\dfrac{2}{12}=\dfrac{1}{6}=0.166666\approx0.17

(b) If 12 jurors are randomly selected from a population where 46​% are​ minorities, what is the probability that 2 or fewer jurors will be​ minorities?

Let X be the number of jurors who are minorities.

Probability of getting minorities = 0.46

Probability of getting no minorities = 1-0.46 =0.54

P(X\leq 2)=^{12}C_0(0.54)^{12}+^{12}C_1(0.46)(0.54)^{11}+^{12}C_2(0.46)^2(0.54)^{10}\\\\P(X\leq 2)=0.0363

(c) What might the lawyer of a defendant from this minority race​ argue?

Since the number of minorities juror are high among the population.

Hence, a) 0.17, b) 0.0363

7 0
3 years ago
Can anyone help me expand this please?
White raven [17]
Any explain this to me a little bit morebetter
7 0
3 years ago
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