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2 years ago

In the diagram triangles ABE and ACD are similar.

Mathematics

1 answer:

jolli1 [7]2 years ago

3 0

Answer:

p = 7.2

q = 6.4

Step-by-step explanation:

if the triangles are similar then the side lengths must be proportional :

AC/BA = CD/BE

9/5 = p/4 cross multiply expressions

5p = 36 divide both sides by 5

p = 7.2

same goes for q

9/5 = (q+8)/8 cross multiply expressions

72 = 5(q+8) divide both sides by 5

14.4 = q+8 subtract 8 from both sides

6.4 = q

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3 years ago

3. 'a' and 'b' are the intercepts made

Julli [10]

Given:

'a' and 'b' are the intercepts made by a straight-line with the co- ordinate axes.

3a = b and the line pass through the point (1, 3).

To find:

The equation of the line.

Solution:

The intercept form of a line is

$\dfrac{x}{a}+\dfrac{y}{b}=1$ ...(i)

where, a is x-intercept and b is y-intercept.

We have, 3a=b.

$\dfrac{x}{a}+\dfrac{y}{3a}=1$ ...(ii)

The line pass through the point (1, 3). So, putting x=1 and y=3, we get

$\dfrac{1}{a}+\dfrac{3}{3a}=1$

$\dfrac{1}{a}+\dfrac{1}{a}=1$

$\dfrac{2}{a}=1$

Multiply both sides by a.

$2=a$

The value of a is 2. So, x-intercept is 2.

Putting a=2 in $b=3a$ , we get

$b=3(2)$

$b=6$

The value of b is 6. So, y-intercept is 6.

Putting a=2 and b=6 in (i), we get

$\dfrac{x}{2}+\dfrac{y}{6}=1$

Therefore, the equation of the required line in intercept form is $\dfrac{x}{2}+\dfrac{y}{6}=1$ .

5 0

2 years ago

PLZ HELP ASAP AND SHOW UR WORK!!!! THE ≤. WITHOUT THE LINE IN THE BOTTOM

Marina86 [1]

Answer:

Step-by-step explanation:

$\frac{2}{3}x +6$

subtract 6 from both sides

$\frac{2}{3}x$

divide by 2/3(or multiply by 3/2)

$x$

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3 0

3 years ago

Consider equation of circle x2-2x+y2-4y-4=0,if line 2x-y+a=0 is its diameter then find value of a

g100num [7]

Answer:

Step-by-step explanation:

x² - 2x + y² - 4y - 4 = 0

x² - 2x + y² - 4y = 4

complete the squares

(x² - 2x + x₀) + (y² - 4y + y₀) = 4

the unknown number will be the square of half of the x¹ coefficient

(x² - 2x + 1) + (y² - 4y + 4) = 4 + 1 + 4

(x - 1)² + (y - 2)² = 9

This tells us that the circle is centered on (1, 2)

Which is also a point on the diameter

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a = y - 2x

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4 0

2 years ago

Write the equation of the line given the slope and the y-intercept. Type your answer in the box without skipping any spaces. m =

Over [174]

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m(x-x₁) = (y-y₁)

∴equation of line with m = 2 and y-intercept = (0,3) =

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= 2x - 0 = y - 3

making y the subject obtains y = 2x + 3.

so, equation of the line: y = 2x + 3.

7 0

3 years ago