ABC is a right angled triangle. if B = 90°, AC = 96 cm, C = 30°. find ab

What is the equation of the line that is perpendicular to the given line and has an x-intercept of -3?

Anvisha [2.4K]

Answer:

$y=-\frac{3}{2}x-\frac{9}{2}$

Step-by-step explanation:

Let the equation of the perpendicular line is,

y = mx + b

where m = slope of the line

b = y-intercept

From the graph, slope of the line passing through (0, -1) and (3, 1),

m' = $\frac{y_2-y_1}{x_2-x_1}$

m' = $\frac{1+1}{3-0}$

m' = $\frac{2}{3}$

To get the slope (m) of this line we will use the property of perpendicular lines,

m × m' = (-1)

m × $\frac{2}{3}$ = -1

m = $-\frac{3}{2}$

Equation of the perpendicular line will be,

$y=-\frac{3}{2}x+b$

x-intercept of the line is (-3) therefore, point on the line is (-3, 0)

0 = $-\frac{3}{2}(-3)+b$

b = $-\frac{9}{2}=-4.5$

Equation of the line will be,

$y=-\frac{3}{2}x-\frac{9}{2}$

3 0

3 years ago

Solve for x: two thirds(x − 2) = 4x.

Sveta_85 [38]

Answer:

$x = - 0.4$

Step-by-step explanation:

$\frac{2}{3} (x - 2) = 4x$

Expand with the distributive rule:

$\frac{2}{3} x - \frac{2}{3} \times 2 = 4x$

$\frac{2}{3} x - \frac{4}{3} = 4x$

Add 4/3 to both sides:

$\frac{2}{3} x = 4x + \frac{4}{3}$

Subtract 4x from both sides

$- \frac{10}{3} x = \frac{4}{3}$

$- 10x = 4$

$x = - 0.4$

5 0

2 years ago

2 2/5 multiplied by 2 multiplied by 3 1/5

goldfiish [28.3K]

Answer:

15 9/25

Step-by-step explanation:

1 Convert 2\frac{2}{5}2

5

2

to improper fraction. Use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

c

b

=

c

ac+b

.

\frac{2\times 5+2}{5}\times 2\times 3\frac{1}{5}

5

2×5+2

×2×3

5

1

2 Simplify 2\times 52×5 to 1010.

\frac{10+2}{5}\times 2\times 3\frac{1}{5}

5

10+2

×2×3

5

1

3 Simplify 10+210+2 to 1212.

\frac{12}{5}\times 2\times 3\frac{1}{5}

5

12

×2×3

5

1

4 Convert 3\frac{1}{5}3

5

1

to improper fraction. Use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

c

b

=

c

ac+b

.

\frac{12}{5}\times 2\times \frac{3\times 5+1}{5}

5

12

×2×

5

3×5+1

5 Simplify 3\times 53×5 to 1515.

\frac{12}{5}\times 2\times \frac{15+1}{5}

5

12

×2×

5

15+1

6 Simplify 15+115+1 to 1616.

\frac{12}{5}\times 2\times \frac{16}{5}

5

12

×2×

5

16

7 Use this rule: \frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}

b

a

×

d

c

=

bd

ac

.

\frac{12\times 2\times 16}{5\times 5}

5×5

12×2×16

8 Simplify 12\times 212×2 to 2424.

\frac{24\times 16}{5\times 5}

5×5

24×16

9 Simplify 24\times 1624×16 to 384384.

\frac{384}{5\times 5}

5×5

384

10 Simplify 5\times 55×5 to 2525.

\frac{384}{25}

25

384

11 Convert to mixed fraction.

15\frac{9}{25}

15 9/25

8 0

2 years ago

Read 2 more answers

The college that Dora attends is selling tickets to the annual

Ksenya-84 [330]

Answer:

The solution of the system of equations is (11, 12)

Step-by-step explanation:

∵ The price of each student ticket is $x

∵ The price of each adult ticket is $y

∵ They sold 3 student tickets and 3 adult tickets for a total of $69

∴ 3x + 3y = 69 ⇒ (1)

∵ they sold 5 student tickets and 3 adults tickets for a total of $91

∴ 5x + 3y = 91 ⇒ (2)

Let us solve the system of equations using the elimination method

→ Subtract equation (1) from equation (2)

∵ (5x - 3x) + (3y - 3y) = (91 - 69)

∴ 2x + 0 = 22

∴ 2x = 22

→ Divide both sides by 2 to find x

∵ $\frac{2x}{2}=\frac{22}{2}$

∴ x = 11

→ Substitute the value of x in equation (1) or (2) to find y

∵ 3(11) + 3y = 69

∴ 33 + 3y = 69

→ Subtract 33 from both sides

∵ 33 - 33 + 3y = 69 - 33

∴ 3y = 36

→ Divide both sides by 3

∵ $\frac{3y}{3}=\frac{36}{3}$

∴ y = 12

∴ The solution of the system of equations is (11, 12)

5 0

2 years ago

If you can run 4 laps in 5.25 minutes, how many laps can you run in 20 minutes?

mina [271]

i believe you would be able to run 15 laps

7 0

3 years ago

Read 2 more answers