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sergeinik [125]
3 years ago
5

I need to know the answer to this please ASAP

Mathematics
1 answer:
Ghella [55]3 years ago
5 0
Y = x - 1
because the gradient is 1 and the y-intercept is -1
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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.
konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

BC^2=BD\cdot AB.

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.

Take positive value x. You get

AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.

2. According to the previous theorem,

AC^2=AD\cdot AB.

Then

AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

Answer: AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0
3 years ago
Read 2 more answers
14) y = x – 4<br> 4<br> A) 1<br> B)<br> 3<br> C)<br> D) -1<br> 3
denis23 [38]

Answer:

the answer is a

Step-by-step explanation:

7 0
3 years ago
Solve the equation. 11 6 = n + 7 9 6 11 ​ =n+ 9 7 ​ start fraction, 11, divided by, 6, end fraction, equals, n, plus, start frac
belka [17]

Answer:

n = 19/18

Step-by-step explanation:

Given:

11/6 = n + 7/9

Find n

11/6 = n + 7/9

Subtract 7/9 from both sides of the equation

11/6 - 7/9 = n + 7/9 - 7/9

11/6 - 7/9 = n

(99-42) / 54 = n

n = 57/54

n = 19/18

4 0
3 years ago
There are two balance beams at the gym.one is 15 feet long ,theother is 162 inches long.which beam is longer?
Oduvanchick [21]
12 inches = 1 foot

Let x=length of 2nd balance beam in feet

by ratio and proportion

1/12 = x/162

multiply noth sides by 162 to isolate x

(1/12)(162) = (x/162)(162)

162/12 = x

13.5 = x

Source -->https://socratic.org/questions/at-the-gym-one-balance-beam-is-15-feet-long-while-the-other-is-162-in...<--

can you help me? brainly.com/question/3131429 
7 0
3 years ago
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A boat is 2000m from a cliff. If the angle of depression from the top of the cliff to the boat is 10 degrees, how tall is the cl
lubasha [3.4K]

Answer:

Let AB is the height of the cliff = H and p is the posit ion of the boat.Angle of depression= angle of elevation= 15 degrees therefore angle APB= 15 degrees tan 15=AB=h/1,000 h=(1,000)*tan 15=(1,000)(0.26794919243112)=268.94919243112 meters or

Simply: 268meters..........Ans

6 0
3 years ago
Read 2 more answers
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