Dr. Ballard refers to Earth as a ‘living breathing creature’- do you think he meant for us to take this literally?

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:

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:

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:

Answer:48 cubes

You could fit 48 cubes with side lengths of 1/3 cm inside a rectangular prism with dimensions of 1 cm X 2 2/3 cm X 2/3 cm.

I hope it's helpful!

Answer:

i dont know

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:

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: 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:

$21.40 for each ticket

Step-by-step explanation:

Answer:

$21.1

Step-by-step explanation:

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:

Open circle: used for < (less than) or > (greater than) because the number is not part of the solution.

Closed circle: used for ≥ (greater than or equal to) or ≤ (less than or equal to) because the number is part of the solution.

Shading:

Shade to the right for > or ≥

Shade to the left for < or ≤

Step-by-step explanation:

2 < x < 5

Place a open circle on 2 with shading to the left and a open circle on 5 with shading to the right.

4 ≤ x ≤ 10

Place a closed circle on 4 with shading to the left and a closed circle on 10 with shading to the right.

Answer:

B.…….................

Answer:

First, you solve for y, then you graph the equation.

See picture for how to solve for y (aka put in slope intercept form) and graph.

1/3 is the slope and 3 is the y intercept

Step-by-step explanation:

see photos

Answer:

a

Step-by-step explanation:

area of parallelogram is equal to base times height 7 * 4

La fraccio total de nieve de fresa es de ¼.

Answer:

Step-by-step explanation:

[tex]\frac{4}{x+3}[/tex]

sum is addition

Answer:

10 seconds

Step-by-step explanation:

The function is

[tex]h(t)=-16t^2+\text{Initial height}[/tex]

Initial height = 1600 ft

t = Time taken

[tex]0=-16t^2+1600[/tex]

[tex]\Rightarrow -16t^2=-1600[/tex]

[tex]\Rightarrow t^2=\dfrac{1600}{16}[/tex]

[tex]\Rightarrow t^2=100\\\Rightarrow t=\pm 10[/tex]

So, time taken by the hailstone to reach the ground is [tex]10\ \text{seconds}[/tex].

Answer:

10 seconds

Step-by-step explanation:

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:

190km

Step-by-step explanation:

2(wl + hl + hw)

2 · (5 · 7 + 5 · 7 + 5 · 5) = 190

good luck, i hope this helps :)

Answer: 9.4

Step-by-step explanation:

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

#SPJ12

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:

riangles can be classified by their sides and by their angles. ... If no sides are the same length, then it is a scalene triangle. If two sides are the same length, then it is an isosceles triangle. If all three sides are the same length, then it is an equilateral triangle.

Step-by-step explanation:

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]

Answer:

sry I don't know.

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

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:A-B-C-D

Step-by-step explanation:

Answer:

1234

Step-by-step explanation:

i took the test