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4 years ago

Two lines are perpendicular, and neither line is horizontal. Which of the following is not necessarily true of the lines?

1 answer:

7 0

I think the correct answer from the choices listed above is option C. Two lines are perpendicular, and neither line is horizontal so it must be that the slopes of the lines are opposite reciprocals, one slope is positive and the other has a negative slope. Having different slopes so they should intersect the y-axis at different values.

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In the given figures find x and y

11Alexandr11 [23.1K]

Answer:

1) x = 40° & y = 50°

2) x = 100° & y = 80°

Step-by-step explanation:

ABCD is a cyclic quadrilateral (∵ all the vertices of the quadrilateral are touching on the circle). As it is a cyclic quadrilateral , sum of it's opposite angles will be 180°.

⇒ ∠ADC + ∠ABC = 180°

⇒ 130° + y = 180°

⇒ y = 180 - 130 = 50°

In ΔABC ,

∠ACB = 90° (∵ AB is the diameter of the circle and a diameter subtends an angle of 90° on any point on circle.)

Using angle sum property of triangle ,

∠ABC + ∠ACB + ∠CAB = 180°

⇒ y + 90° + x = 180°

⇒ x + 50° + 90° = 180°

⇒ x + 140° = 180°

⇒ x = 180 - 140 = 40°

ΔABC is an isosceles triangle (∵AB = AC). As it is an isosceles triangle , it's base angles will be equal. So , ∠ABC = ∠ACB = 50°

Using angle sum property of triangle ,

∠ABC + ∠ACB + ∠BAC = 180°

⇒ 50° + 50° + y = 180°

⇒ y + 100° = 180°

⇒ y = 180 - 100 = 80°

ABEC is a cyclic quadrilateral (∵ all the vertices of the quadrilateral are on the circle.). As it is a cyclic quadrilateral , sum of it's opposite angles will be 180°.

⇒ ∠BAC + ∠BEC = 180°

⇒ y + x = 180°

⇒ x + 80° = 180°

⇒ x = 180 - 80 = 100°

5 0

3 years ago

How do you know if an equation has no solution or infinite solutions

shutvik [7]

Answer:

If an equation has no solution, then it means it can't be solved.

If an equation has infinite solutions, it means that the answers are too large to be defined.

Step-by-step explanation:

An equation has no solution if for instance there is an error in that equation.

An equation has infinite solutions or undefined answers if for instance a number is divided by zero.

5 0

4 years ago

Read 2 more answers

Type true or false for each situation. 1. 2. 3. 4.

zaharov [31]

Answer:

-true

-false

-true

6 0

3 years ago

Read 2 more answers

The cost of renting a landscaping tractor is a $100 base fee plus the hourly rate.

agasfer [191]

Answer:

a. f(h) = 100 + mh and g(h) = 100 + 2mh

b. The slope of g(h) is double of slope of f(h).

c. f(x) = 100 + mx.

Step-by-step explanation:

The cost of renting a landscaping tractor is a $100 base fee plus the hourly rate.

a. If the hourly rate is $m per hour, then the function f(h) represents the cost of renting the tractor for h hours, then

f(h) = 100 + mh .......... (1)

If the hourly rate is doubled i.e. 2m, then the function g(h) represents the cost of renting the tractor for h hours, then

g(h) = 100 + 2mh ........... (2)

b. If we graph the function f(h) then the slope of the equation will be m and the y-intercept will be 100.

If we graph the function g(h) then the slope of the equation will be 2m and the y-intercept will be 100.

Therefore, in the case of g(h), the slope will be double the slope of f(h).

c. If the tractor is rented for x hours, then the function f(h) will be

f(x) = 100 + mx. (Answer)

7 0

4 years ago

Help with this pleaseee

Savatey [412]

Answer:

Sum of 100 terms of the sequence = 15050

Step-by-step explanation:

Given expression which represents a sequence is,

$\sum_{r=1}^{100}(3r-1)$

So the sequence will be,

2, 5, 8, 11, 14..........

So, the given sequence is an arithmetic sequence with,

First term of the sequence 'a' = 2

Common difference 'd' = 5 - 2 = 3

Sum of 'n' terms of an arithmetic sequence is given by,

$S_n=\frac{n}{2}[2a+(n-1)d]$

Here, n = number of terms

a = first term

d = common difference

$S_{100}$ = $\frac{100}{2}[2(2)+(100-1)(3)]$

= 50[4 + 297]

= 15050

Therefore, sum of 100 terms of the sequence = 15050

3 0

3 years ago