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3 years ago

What must the value of x be, so that a parallel to b, m∠2 = 70°, and m∠7=(3x + 10)°?

Mathematics

1 answer:

Ksju [112]3 years ago

5 0

70=3x+10
Subtract 10 from both sides
60=3x
Divide both sides by 3
20=x
x=20

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A person stands 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 meters

In-s [12.5K]

Answer:

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

Step-by-step explanation:

Given that,

A person stand 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 m/s.

From Pythagorean Theorem,

(The distance between car and person)²= (The distance of the car from intersection)²+ (The distance of the person from intersection)²+

Assume that the distance of the car from the intersection and from the person be x and y at any time t respectively.

∴y²= x²+10²

$\Rightarrow y=\sqrt{x^2+100}$

Differentiating with respect to t

$\frac{dy}{dt}=\frac{1}{2\sqrt{x^2+100}}. 2x\frac{dx}{dt}$

$\Rightarrow \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}. \frac{dx}{dt}$

Since the car driving towards the intersection at 13 m/s.

so, $\frac{dx}{dt}=-13$

$\therefore \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}.(-13)$

Now

$\therefore \frac{dy}{dt}|_{x=24}=\frac{24}{\sqrt{24^2+100}}.(-13)$

$=\frac{24\times (-13)}{\sqrt{676}}$

$=\frac{24\times (-13)}{26}$

= -12 m/s

Negative sign denotes the distance between the car and the person decrease.

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

8 0

3 years ago

You are playing the game "Hidden Treasure" and your hint is that the treasure is 9 spaces away from the point (0, 0). Which of t

olganol [36]

Answer:

9,0 0,9 -9,0 0,-9

Step-by-step explanation:

up down left right

7 0

3 years ago

Use distributive property to write an expression that is equivalent to 6(u+12)

nirvana33 [79]

Answer:

6u + 72

Step-by-step explanation:

6(u + 12)

Distribute 6 to u and 12

6(u) + 6(12)

6u + 72

6 0

3 years ago

To find the area of a trapezoid with those numbers

Yuliya22 [10]

Area=14.6

To find a trapezoid

Top +Bottom /2 multiplied by height

So 2.5+ 4.8= 7.3

7.3/2= 3.65

3.65x4=14.6

3 0

4 years ago

What times what equals 120 and When you add the two numbers they equal 26?

Alona [7]

6 times 20 equals 120 and equals 26 when added together

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3 years ago