Is the line through points P(2,-9) and Q(6, -13) perpendicular to the line through points R(5,-1) and
S(1,-5)?
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.
A boat travels 336 miles in 22hours (with a constant speed). How far can it travel in 8 hours (with the same speed)?
Answer:
122.18 miles.
Step-by-step explanation:
336miles/22hours × x miles/8hours
336 × 8 ÷ 8 = 122.18miles
good luck, i hope this helps :)
help me i need help pls pls pls
Answer:
B.…….................
An experiment consists of tossing a die and then flipping a coin once if the number on the die is even. If the number on the die is odd, the coin is flipped twice. Using the notation 4HH, for example, to denote the outcome that the die comes up 4 and then the coin comes up heads, and 3HTHT to denote the outcome that the die comes up 3 followed by a head and then a tail on the coin, construct a tree diagram to show the 18 elements of the sample space SS.
For the sample space SS
(a) list the elements corresponding to the event AA that a number less than 3 occurs on the die;
(b) list the elements corresponding to the event BB that two tails occur;
(c) list the elements corresponding to the event A′A ′;
(d) list the elements corresponding to the event A′∩BA ′ ∩B;
(e) list the elements corresponding to the event A∪BA∪B.
Answer:
Kindly check attached picture for sample space.
Step-by-step explanation:
Sample space, S
S = {1HH, 1HT, 1TT, 1TH, 2H, 2T, 3HH, 3HT, 3TT, 3TH, 4H, 4T, 5HH, 5HT, 5TH, 5TT, 6H, 6T}
The tree diagram for all 18 elements in the sample space can be found in the picture attached below :
a.)
Event A ; number on die < 3
A = {1HH, 1HT, 1TT, 1TH, 2H, 2T}
b.)
Event B ; 2 tails occur :
B = {1TT, 3TT, 5TT}
QUESTIONS B, C and E are not well formatted
can someone help plz?.
SOMEONE PLEASE HELP AND MARK AS BRAINLIEST
A hailstone falls from a cloud at a height of 1,600 ft. If the equation for height as a function of time is h(t) = -16t2 + initial height where t is time in seconds and h(t) is height in feet, how many seconds will it take for the hailstone to hit the ground? [?] seconds
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:
Explain why an archaeological matrix is important in archeology
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:
Find dy/dx by implicit differentiation.
cot(y) = 9x – 7y
dy/dx = ?
Answer:
Step-by-step explanation:
I need help
A square and a triangle have equal area. If the triangle has a height of 8 cm and a base of 9 cm, what is the perimeter of the square?
A:
72 cm
B:
6 cm
C:
24 cm
D:
18 cm
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
Draw the image of the following segment after a dilation centered at the origin with a scale factor of 2/3
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].
Use intercepts to graph the linear equation –2x + 6y =18
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
Tom buys 4 tickets for a concert. The total cost is $85,60. How much does he pay
for each ticket?
Answer:
$21.40 for each ticket
Step-by-step explanation:
Answer:
$21.1
Step-by-step explanation:
The table shows the feeding times of some animals in a zoo. Each feeding session lasts for 20 minutes.
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
si hay 3/4 de nieve de chocolate y vainilla el resto y el resto de es de fresa qué fracción total de la nieve es de fresa?
La fraccio total de nieve de fresa es de ¼.
A circle has a diameter with endpoints at (0, 4) and (0, –8). What is the approximate area of the circle?
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]
classify the triangle by its sides, and then by angles
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:
What's the difference between an opened circle on a number line and a closed circle. ( Pls give an example)
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.
Determine the x-intercept points of the function h(x) = (x – 5)(x – 6).
Question 4 options:
A)
(5,0) and (6,0)
B)
(–5,0) and (–6,0)
C)
(5,0) and (–6,0)
D)
(–5,0) and (–6,0)
How many cubes with side lengths of 1/3 cm does it take to fill the prism
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!
Simplify completely"""
Answer:
[tex]\displaystyle \frac{2(x + 2)}{x - 10}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Terms/CoefficientsFactoringStep-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{2x^2 + 20x + 32}{x^2 - 2x - 80}[/tex]
Step 2: Simplify
[Fraction] Factor numerator: [tex]\displaystyle \frac{2(x + 2)(x + 8)}{x^2 - 2x - 80}[/tex][Fraction] Factor denominator: [tex]\displaystyle \frac{2(x + 2)(x + 8)}{(x - 10)(x + 8)}[/tex][Fraction] Divide: [tex]\displaystyle \frac{2(x + 2)}{x - 10}[/tex]f(x)=-12x^3-14x^2+6x
translate into algebraic expression four divided by the sum of x and three
[tex]\frac{4}{x+3}[/tex]
sum is addition
If x = 4 units, y = 8 units, and h = 7 units, find the area of the parallelogram shown above using decomposition. A. 28 square units B. 56 square units C. 84 square units D. 112 square units
Answer:
a
Step-by-step explanation:
area of parallelogram is equal to base times height 7 * 4
the relationship described is linear or expor
Mandy is training for a half marathon.
She runs 4 miles this weekend. For the
next several weeks she plans to increase
her distance by 10% each weekend.
Answer:
Kasi
Step-by-step explanation:
kasi mapiti itlog ko
Evaluate the formula for the perimeter of a parallelogram to solve the problem. Then check all that apply.
First, write the formula for the perimeter of a parallelogram, P = 2l + 2w.
Next, use parentheses when you substitute 8 for l and 6 for w.
After multiplying, add 16 and 12.
Sulio needs 28 feet of fencing.
Sulio needs 48 feet of fencing.
Answer:A-B-C-D
Step-by-step explanation:
Answer:
1234
Step-by-step explanation:
i took the test
When the following inequality is graphed, what will it look like?
2 > f
Answer:
Step-by-step explanation:
Why is the value of x to the nearest tenth?
Answer: 9.4
Step-by-step explanation:
5 km
5 km
7 km
Find the surface area
Answer:
190km
Step-by-step explanation:
2(wl + hl + hw)
2 · (5 · 7 + 5 · 7 + 5 · 5) = 190
good luck, i hope this helps :)
owrite down the name of each of these triangles
Answer:
sry I don't know.
if someone answer tell me the answer I also want to know : )