help read the instructions ffirst

Two lines [tex]y_1,y_2[/tex] are perpendicular if their slopes are in a relation [tex]m_1=-\frac{1}{m_2}[/tex].

So we need to find slopes and if the above relation holds then we can claim the lines are perpendicular.

To find slopes, use slope formula

[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]

The first slope of a line passing through [tex]PQ[/tex] is

[tex]m_1=\frac{-13-(-9)}{6-2}=\frac{-4}{4}=-1[/tex]

The second slope of a line passing through [tex]RS[/tex] is

[tex]m_2=\frac{-1-(-5)}{5-1}=\frac{4}{4}=1[/tex]

Now check if [tex]m_1=-\frac{1}{m_2}[/tex] is true

[tex]-1=-\frac{1}{1}\implies -1=-1[/tex]

This means the two lines are perpendicular.

Hope this helps.

Answer:

Step-by-step explanation:

Let the ends of the given segment are A and B.

Coordinates of A → (8, 6)

Coordinates of B → (12, 12)

If a point (x, y) is dilated by a scale factor 'k' about the origin, rule to be followed,

(x, y) → (kx, ky)

If k = [tex]\frac{2}{3}[/tex]

(x, y) → [tex](\frac{2}{3}x, \frac{2}{3}y)[/tex]

By this rule coordinates of the image points of A and B will be,

A(8, 6) → [tex]A'(\frac{2\times 8}{3},\frac{2\times 6}{3})[/tex]

           → A'(5.3, 4)

B(12, 12) → [tex]B'(\frac{12\times 2}{3}, \frac{12\times 2}{3})[/tex]

             → B'(8, 8)

Now we can get the image of segment AB after dilation by a scale factor of [tex]\frac{2}{3}[/tex].

Answer:

Step-by-step explanation:

Step-by-step explanation:

2x³ - 10x² + 4x - 20

= 2x²(x - 5) + 4(x - 5)

= (2x² + 4)(x - 5).

Hence (2x³ - 10x² + 4x - 20) / (x - 5)

= [(2x² + 4)(x - 5)] / (x - 5) = 2x² + 4.

Answer:

2x²+4

Step-by-step explanation:

2x³-10x²+4x-20

2(x³-5x²+2x-10)

x-5

2(x²×(x-5)+2(x-5)

x-5

2(x-5)×(x²+2)

x-5

2(x²+2)

=2ײ+4

Answer: B

Step-by-step explanation:

Answer:

The value of n is the size of the sample, the number of customers selected.

The value of p is 0.48.

The value of q is 0.52.

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

48% of consumers are comfortable having drones deliver their purchases.

This means that [tex]p = 0.48, q = 1 - p = 1 - 0.48 = 0.52[/tex]

The value of n is the size of the sample, the number of customers selected.

Answer:

x-intercept: 7/30

y-intercept: −3

Step-by-step explanation:

Answer:

Step-by-step explanation:

For x-intercept:

Substitute y=0:

7x-10(0)=30

7x=30

x=30/7

For y-intercept:

Substitute x=0:

7(0)-10y=30

-10y=30

y=-30/10

y=-3

Answer:

f(2) = -2

Step-by-step explanation:

Substitute 2 everywhere you see an x so f(2) = -2([tex]2^{2}[/tex]) - 2(2) + 10 so

f(2) = -2(4) - 4 + 10, so f(2) = -8-4+10, f(2) = -12+10, f(2) = -2

What measurement do you need? For ft it's 15840

Answer:

I do not know

Step-by-step explanation:

I do not know

Answer:A-B-C-D

Step-by-step explanation:

Answer:

1234

Step-by-step explanation:

i took the test

Answer:

If the bag contained 20% of blue marbles and 50% of green marbles than that would mean the bag would contain 30% of red marbles. The probability of picking a red marble from the bag would be considered unlikely.

Step-by-step explanation:

Answer:

The stratigraphic relationships that are documented as a principal part of the record of the excavation form a fundamental part of the overall site record and underpin the relationships between the site's other recorded individual archaeological components.

Step-by-step explanation:

Answer:

358 student

Step-by-step explanation:

3.50×358=1252

Answer:

i dont know

Step-by-step explanation:

Answer: 12:35 hrs

Step-by-step explanation:

Marlon watches the lions feed in the morning which was at 11:30.

Each feeding session lasts 20 minutes:

= 11:30 + 20

= 11:50 am

Marlon then walks for three quarters of an hour - 45 minutes - before stopping.

= 11:50 + 45

= 12:35 hrs

Answer:

136

Step-by-step explanation:

Sum of 5 and 3: 8

Sum of 8 and 9: 17

17 * 8 is 136

Answer: The sum of 5 and 3 is 8 and the sum of 8 and 9 is 17.

Answer:

113.04

Step-by-step explanation:

Area of a circle is πr2

π = 3.14

r = 6

πr2 = 113.04

Answer:

[tex]36\pi[/tex]

Step-by-step explanation:

The diameter is:

The Euclidean distance between points (x1, y1) and (x2, y2) is:

sqrt((x1 - x2)^2 + (y1 - y2)^2)

Substitute (x1, y1) = (0, 4) and (x2, y2) = (0, -8):

= sqrt((-0 + 0)^2 + (-(-8) + 4)^2)

= sqrt(12^2)

 = 12

or simply:

diameter: 4-(-8)=12

The radius is:

12/2=6 units

The area of the circle:

[tex]\pi r^2=\pi(6^2)=36\pi[/tex]

Answer: 9.4

Step-by-step explanation:

Answer:

a. 85 m

b. 96 cm

Step-by-step explanation:

Work for (a.)

Work for (b.)

Answer:

A 72cm

Step-by-step explanation:

Area of a triangle = 1/2 base x height

= 1/2 × 8× 9 = 36cm2

area of triangle = area of square

36cm2 = 36cm2

area of square = length x breath

= x x x = 36cm3

square has all sides(4) equal

therefore: 36/ 2 = 18cm (one side)

(18 x 18= 36cm3, so area is correct)

hence perimeter = 18+ 18+18+18 = 72cm

Answer:

see explanation

Step-by-step explanation:

(1)

The angle of inclination is the angle between the horizontal and the ramp.

Using the sine ratio in the right triangle formed by the ground and the ramp

let x be the angle of inclination, then

sinx = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{0.7}{4.2}[/tex] , then

x = [tex]sin^{-1}[/tex] ([tex]\frac{0.7}{4.2}[/tex] ) ≈ 10° ( to the nearest degree )

(2)

Again there is a right triangle between the ground and the vertical height of the kite, with hypotenuse being length of string.

let y be the height of the kite and x the horizontal distance, then

sin27° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{176}[/tex] ( multiply both sides by 176 )

176 × sin27° = y , then

y ≈ 80m ( to the nearest metre ) ← height of kite

and

cos27° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{176}[/tex] ( multiply both sides by 176 )

176 × cos27° = x , then

x ≈ 157m ( to the nearest metre ) ← horizontal distance

Step-by-step explanation:

[tex]1)

The angle of inclination is the angle between the horizontal and the ramp.

Using the sine ratio in the right triangle formed by the ground and the ramp

let x be the angle of inclination, then

sinx = \frac{opposite}{hypotenuse}hypotenuseopposite = \frac{0.7}{4.2}4.20.7 , then

x = sin^{-1}sin−1 (\frac{0.7}{4.2}4.20.7 ) ≈ 10° ( to the nearest degree )

(2)

Again there is a right triangle between the ground and the vertical height of the kite, with hypotenuse being length of string.

let y be the height of the kite and x the horizontal distance, then

sin27° = \frac{opposite}{hypotenuse}hypotenuseopposite = \frac{y}{176}176y ( multiply both sides by 176 )

176 × sin27° = y , then

y ≈ 80m ( to the nearest metre ) ← height of kite

and

cos27° = \frac{adjacent}{hypotenuse}hypotenuseadjacent = \frac{x}{176}176x ( multiply both sides by 176 )

176 × cos27° = x , then

x ≈ 157m ( to the nearest metre ) ← horizontal distance

[/tex]

The length of the straw placed inside a rectangular box with 10 inches by 8 inches by 2 inches is 2√42 inches.

To find the length of the straw, we can use the Pythagorean theorem. The straw acts as the hypotenuse of a right-angled triangle formed by the three dimensions of the box (10 inches, 8 inches, and 2 inches).

Let the length of the straw be represented by 'l'.

According to the Pythagorean theorem:

[tex]l^2 = 10^2 + 8^2 + 2^2[/tex]

[tex]l^2 = 100 + 64 + 4[/tex]

[tex]l^2 = 168[/tex]

Take square root on both sides:

[tex]l = \sqrt{168}[/tex]

[tex]l = \sqrt{4 \times 42}[/tex]

[tex]l = 2 \times \sqrt{42}[/tex]

So, the length of the straw is 2√42 inches in simplest radical form.

To learn more on trigonometry click:

https://brainly.com/question/25122835

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Complete question:

A straw is placed inside a rectangular box that is 10 inches by 8 inches by 2 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.

Answer:

B.…….................

Answer:

✔ less than

Step-by-step explanation:

The measure of angle ACB is less than the measure of the angle AOB.

GIven,
Making the conjecture.
What would happen to the angle formed if the vertex of angle AOB was moved from the center to point C, which lies on the circle is to be justify.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r². where h, k is the coordinate of the circle's center on coordinate plane and r is the circle's radius.

Here, there is a property of pair of lines,
when two lines intersect each other they hold some angle of intersection with each other, when the angle of intersection increases, assuming a point says the point of intercession getting close to the points then angle of the intersection will increase. If the point of intersection gets far away from that point, the angle of the intersection will decrease.

Similarly, in the given problem point O is close to the arc AB than C. Implies Angle ACB is smaller than Angle AOB.

Thus, the measure of angle ACB is less than the measure of the angle AOB.

Learn more about circle here:

brainly.com/question/11833983

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Answer:

sry I don't know.

if someone answer tell me the answer I also want to know : )

Answer:

S(4) = 2

Step-by-step explanation:

S(n) = n(n - 3) / 2

S(4) = 4(4 - 3) / 2

= 4 x 1 / 2

= 4/2

= 2

Answer:

Danny

Step-by-step explanation:

Danny charges less because he only charges $30 for 3 hours of swimming lessons while Martin charges $38 for only 2 hours of swimming lessons.