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Goryan [66]
2 years ago
13

If AB=7x, CB=5x+8 and BD AC what is the length of CB

Mathematics
1 answer:
seropon [69]2 years ago
8 0

Answer:

x = 4

CB = 28

Step-by-step explanation:

In triangle ABC,

AB = CB..... (given)

Therefore,

7x = 5x + 8

7x - 5x = 8

2x = 8

x = 8/2

x = 4

CB = 5x + 8 = 5*4 + 8 = 20 + 8 = 28

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Ipatiy [6.2K]
First notice that the triangle with sides x,y,a and the triangle with sides z,a+b,x are similar. This is true because the angle between sides x,y in the smaller triangle is clearly 30^\circ, while the angle between sides y,z in the larger triangle is clearly 60^\circ. So the triangles are similar with sides x,y,a corresponding to a+b,z,x, respectively.

Now both triangles are 30^\circ-60^\circ-90^\circ, which means there's a convenient ratio between its sides. If the length of the shortest leg is \ell_1, then the length of the longer leg is \ell_2=\sqrt3\ell_1 and the hypotenuse has length \ell_3=\sqrt{{\ell_1}^2+{\ell_2}^2}=2\ell_1.

Since x is the shortest leg in the larger triangle, it follows that a+b=2x, so a+b=15=2x\implies x=\dfrac{15}2
4 0
3 years ago
Ted brought a cooler containing 7.5 liters of water to a picnic. If 500 milliliters of water are served to each person, how many
bekas [8.4K]
Answers:
k = 13The smallest zero or root is x = -10
===============================
Work Shown:
note: you can write "x^2" to mean "x squared"
f(x) = x^2+3x-10
f(x+5) = (x+5)^2+3(x+5)-10 ... replace every x with x+5
f(x+5) = (x^2+10x+25)+3(x+5)-10
f(x+5) = x^2+10x+25+3x+15-10
f(x+5) = x^2+13x+30
Compare this with x^2+kx+30 and we see that k = 13
Factor and solve the equation below
x^2+13x+30 = 0
(x+10)(x+3) = 0
x+10 = 0 or x+3 = 0
x = -10 or x = -3
The smallest zero is x = -10 as its the left-most value on a number line.
7 0
3 years ago
Subtract 8+7i from 4-16i​
White raven [17]

Answer:

-4 -23i

Step-by-step explanation:

(4-16i) - (8+7i)

Distribute the minus sign

4-16i -8-7i

Combine like terms

4-8   -16i -7i

-4 -23i

8 0
3 years ago
Read 2 more answers
Joseph tweets 13 times a day. define each variable and write an algebraic expression to describe the number of post after any gi
notka56 [123]

13 •X= # of tweets

X= number of days

3 0
3 years ago
Will mark brainliest help!
kakasveta [241]

Answer:

52.5

Step-by-step explanation:

Since ED ≈ AD, ∆AED is a isosceles triangle where <EAD and <AED has same angle measurement

Now, m<B = 105°, since ABCD is a parallelogram, <B = <D

so, m<ADC = 105° so, m<ADE = 180°-105° = 75°

Now, m<EAD+m<AED+m<ADE = 180°

or, m<AED+m<AED+m<ADE = 180°

or, x+x+75°=180°

or, 2x=180+75°

or, 2x=105°

or, x=52.5°

3 0
2 years ago
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