Answer:
Numbering the options, we have;
1) Side B'A' has a slope of −1 and is perpendicular to side BA.
2) Side B'A' has a slope of 1 and is parallel to side BA.
3) Side B'A' has a slope of 1 and is perpendicular to side BA.
4) Side B'A' has a slope of −1 and is parallel to side BA.
The correct option is;
1) Side B'A' has a slope of -1 and is perpendicular to side BA
Step-by-step explanation:
The given coordinates are;
A(3, 5) B(1, 3), C(5, -1) and D(7, 1)
The slope of BA is found as follows;
[tex]Slope \, of BA= \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}} =\dfrac{3-5}{1-3}= \dfrac{-2}{-2} = 1[/tex]
Rotation of a line through 90 degrees gives
(x, y) will be (y, -x)
Therefore, the coordinates of A' = (5, -3)
The coordinates of B' = (3, -1)
Then the slope is given as follows;
[tex]Slope \, of \, B'A' =\dfrac{-1 -(-3)}{3-5}= \dfrac{2}{-2} = -1[/tex]
Therefore side B'A' has a slope of -1 and is perpendicular to side BA.
Option (4) will be the correct option.
Coordinates of the vertices of rectangle ABCD are,
A(3, 5), B(1, 3), C(5, -1) and D()Slope of a segment with endpoints [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by the expression,
Slope 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, slope of segment BA (m₁) = [tex]\frac{3-5}{1-3}[/tex] = 1
If a point (h, k) is rotated 90° clockwise about the origin, rule to be followed,
(h, k) → (-k, h)
Following this rule,
B(1, 3) → B'(-3, 1)
A(3, 5)→ A'(-5, 3)
Slope of segment B'A' (m₂) = [tex]\frac{1-3}{-3+5}=-1[/tex]
Expression representing two segments with slopes [tex]m_1[/tex] and [tex]m_2[/tex] to be perpendicular,
[tex]m_1\times m_2=-1[/tex]
Since, slopes of two segments BA and B'A' are (1) and (-1).
(1) × (-1) = -1
Therefore, both the segments BA and B'A' will be perpendicular.
Option (4) will be the answer.
Learn more,
https://brainly.com/question/16949200
Using the slope and the yintercept, graph the line represented by the following equation. Then select the correct graph. 2y+4=0
2y/5y cube + 4y square + 6y
Answer:
here down is the answer
(2y/5y)^3+4y^2+6y
8y^3/125y^3 +16y^2+6y
8/125+16y^2+6y
8/125+16y^2+6y=0
16y^2+6y+8/125=0
it is in the form of quadratic equation
formula :
x=(-b+-square root of b^2-4ac) /2a
here a=16,b=6&c=8/125
x=(-b+-square root of b^2-4ac)/2a
x=(-6+-square root of 36-4.09)/2a here 4.09 came by calculation
x=(-6+-31.91)/2
so
x=(-6+31.91)/2 first (+);
x=25.91/2
x=12.955;
x=(-6-31.91)/2 then(-);
x=-37.91/2
x=-18.955 ;
ans is = 12.955&-18.955;
A rectangular prism has a length of 4 cm, a width of 6 cm, and a height of 3 cm. what is it’s volume
Answer:
72 cm³
Step-by-step explanation:
The formula for the volume of a rectangular prism is:
V = lwh
where l is the length, w is the width, and h is the height
Let's substitute the given values into this formula:
V = lwh
V = (4)(6)(3)
Solve:
V = (4)(6)(3)
V = (24)(3)
V = 72
Therefore, the volume is 72 cubic centimeters.
Answer:
The answer is 72 cm3
Step-by-step explanation:
4 times 6 times 3
24 times 3
72
;))))))
I will mark you brainliest!!! Identify the exponential function shown in the graph.
Answer:
Letter B.
Step-by-step explanation:
Look for where the line corsses the Y axis. that will tell you the most about this line and it corsses at 8 so that can be the only one correct.
What is $ 1.20 x 5 =? My brain is not working! LOL!
Answer:
6.25
Step-by-step explanation:
=1.20*5
=6.25
Answer:
6
Step-by-step explanation:
1.20 x 5 = 6
6/5 = 1.20
Guess my rule. PLS HELP ME I BEG
Answer:
12,22,2002, 4x, 5x
Step-by-step explanation:
The rule is x2 +2
Not sure on the last 4
Sorry I answered late.
Which equation represents the line that passes through (-8.11) and
(4,7/2)?
Answer:
[tex]y=-5/8x+6[/tex]
Step-by-step explanation:
[tex]m=\frac{7/2 - 11}{4--8}[/tex]
[tex]m=\frac{-15/2}{12}[/tex]
[tex]m=-5/8[/tex]
[tex]y=-5/8x+b[/tex]
[tex](-8,11)[/tex]
[tex]11=-5/8 \times -8+b[/tex]
[tex]b=11-(-5/8)(-8)[/tex]
[tex]b=6[/tex]
L+S = 17 3L + 2S=46
Please show your work
Answer:
S= 5, L= 12
Step-by-step explanation:
To find the value of L and S, we need to first label the 2 equations.
L +S= 17 -----(1)
3L +2S= 46 -----(2)
From (1):
L= 17 -S -----(3) (-S on both sides)
Subst. (3) into (2):
3(17-S) +2S= 46
3(17) -3S +2S= 46 (expand)
51 -S= 46
-S= 46 -51 (-51 on both sides)
-S= -5
S= 5 (divide by -1 throughout)
Subst. S=5 into (3):
L= 17 -5
L= 12
Kelsey received 9 birthday gifts from her friends. Three gifts were wrapped in yellow
paper, 3 gifts were wrapped in red paper, 2 gifts were wrapped in purple paper, and
1 gift was wrapped in orange paper. What is the probability that the first gift Kelsey
opened was wrapped in purple paper?
Answer: 2/9
Step-by-step explanation:
From the question, we are told that
Kelsey received 9 birthday gifts from her friends and that three of the gifts were wrapped in yellow
paper. Also, 3 gifts were wrapped in red paper, 2 gifts were wrapped in purple paper, while the remaining
1 gift was wrapped in orange paper.
The probability that the first gift will be in purple paper will be the number of gifts in purple paper divided by the total number of gifts. This will be:
= 2/9
Which value of f 3f+5=32 a true statement
Choose 1 answer
A
f=6
B
f=8
C
f=9
D
f=12
Answer:
C. f = 9
Step-by-step explanation:
→Subtract 5 from both sides:
3f + 5 = 32
- 5 - 5
_________
3f = 27
→Divide both sides by 3:
f = 9
Answer:
C f=9
Step-by-step explanation:
Trust me, I got the answer right.
Pleas help !!!
Choices
X= -1
Y = -1
X = 1
Y= 1
Answer:
x=-1
Step-by-step explanation:
The axis of symmetry is along the vertex
The vertex is at (-1,-2)
The x coordinate is -1
x=-1
a) The ratio 20 minutes to 1 hour can be written in the form 1:n.
Find the value of n.
n =
Answer:
n =3
Step-by-step explanation:
20 minutes to 1 hour can also be written as 20 minutes to 60 minutes.
when simplified, you get 1:3
Answer:
1:30
Step-by-step explanation:
minutes : hour
20 : 1
convert the hour into minutes
1 hr = 60 minds
20 : 60
it was simplified so that 20 = 1
so they did 20 divided by 20 to get it to equal to 1
1 : _____
u need to equalise it and do the same to the other side so 60 divided by 20 as well ( this equals 30)
now the ratio is:
1 : 30
Help please !!!!!!!!!!!!!!!!!!!!!!!
Answer:
∠J and ∠K form a linear pair.
Step-by-step explanation:
If angles J and K are supplementary and adjacent, then they form what is known as a linear pair.
"Definition: Two angles that are adjacent (share a leg) and supplementary (add up to 180°)" -mathopenref
attachment need help asap
Answer:
c because the x value is equal to the y value
Step-by-step explanation:
Answer:
x=y
Step-by-step explanation:
They are both opposite each other.
Parallel to each other
Please answer correctly !!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!
Answer:
$12 million
Step-by-step explanation:
Vertex form of a quadratic equation:
y=a(x-h)^2+k
where (h,k) is the vertex.
The vertex is (5,12), and it is a maximum since a is negative.
Therefore, the maximum value is $12 million.
A ball is tossed from an upper-story window of a building. The ball is given an initial velocity of 8.8 m/s at an angle of 23 SE from the window. It hits the ground 5s later. (A) how far horizontally from the building does the ball land on the ground? (B) find the height that the ball was thrown from
Answer:
a)40.5m
b)139.5m
Step-by-step explanation:
Considering downward as 'positive' y-direction
[tex]x_i=0\\y_i=0\\v_i=8.8m/s\\a_x=0\\a_y=g\\\theta = 23\degree\\t=5s[/tex]
First is to resolve initial velocity into x and y component:
[tex]v_x_i=v_icos\theta = 8.8 \times cos(23)= 8.1m/s\\v_y_i=v_isin\theta = 8.8 \times sin(23)= 3.4m/s\\[/tex]
a) in order to find horizontal position of the ball:
[tex]x_f=x_i+v_x_it+\frac{1}{2} a_xt^2[/tex]
[tex]x_f= 8.1\times5=40.5m[/tex]
b) To find the height that the ball was thrown from(vertical position):
[tex]y_f=y_i+v_y_it+\frac{1}{2} a_yt^2\\y_f=(3.4\times 5)+(\frac{1}{2} \times9.8\times5^2)\\y_f=139.5m[/tex]
Write the equation in standard form: 3x + 1 = 2y
3x + 2y = 1
3x + 2y = –1
3x – 2y = –1
3x – 2y = 1
Answer:
3x+2y=-1
Step-by-step explanation:
moving the numbers around, the outcome will have to be different
// have a great day //
Answer:
c) 3x - 2y = -1
Step-by-step explanation:
Given equation,
→ 3x + 1 = 2y
Conversion into standard form,
→ 3x + 1 = 2y
→ 3x + 1 - 2y = 0
→ 3x - 2y = -1
Hence, option (c) is correct.
El que responda bien 5 estrellas y un gracias 7u7
Answer: AB=12
Los triangulos BCD y ADE son iguales por tener dos lados y el angulo comprendido respectivamente iguales. por tanto AE=DC=4
Luego AB = AE+EB = 4+8 = 12
IF (-6, 4) is the endpoint of a line segment, and (-2, -1) is its midpoint, find the other endpoint.
A) (2,-6)
B) (-14, 14)
9 (-16, 12)
D) (2,9)
A midpoint has coordinates of [tex](-2, -1)[/tex] we will call them [tex](x_m, y_m)[/tex].
The coordinates of a midpoint are constructed from coordinates of enpoints [tex](x_1,y_1),(x_2,y_2)[/tex], namely as a divided sum.
[tex]
x_m=\frac{x_1+x_2}{2}\implies x_1=2x_m-x_2 \\
y_m=\frac{y_1+y_2}{2}\implies y_1=2y_m-y_2
[/tex]
Now insert the numbers.
[tex]
x_1=2(-2)-(-6)=2 \\
y_1=2(-1)-4=-6
[/tex]
The result is an endpoint at [tex](2,-6)[/tex].
which method can be used to solve 11x13
Answer:
Simple column method
Step-by-step explanation:
11
x 13
33
110
143
Answer:
Use the grid method, since it is the most obvious option. But, you may also use the distribution method.
Step-by-step explanation:
Distribution method:
divide 13 into 10 +3
then multiply 11 with 10 and 3 individually.
This can be written as 11(10+3) = 110+33 = 143
Please mark brainiest
Um homem estava indo para a Bahia com suas sete irmãs. Cada irmã carregava sete caixas, cada caixa tinha sete gatos,cada gato estava com sete filhotes. Quantos estavam indo para a Bahia?
Answer:
2,752
Step-by-step explanation:
English Translation
A man was going to Bahia with his seven sisters. Each sister carried seven boxes, each box had seven cats, each cat had seven puppies. How many were going to Bahia?
Solution
1 man was going to Bahia
With his 7 sisters.
Total nunber of humans = 1 + 7 = 8 humans
Each of the 7 sisters carried 7 boxes.
Each of the 49 boxes had 7 cats
Total number of cats = 7 × 7 × 7 = 343 cats
Each of the 343 cats had 7 puppies
Total number of puppies = 7 × 343 = 2401 puppies.
Total number of living things going to Bahia
8 humans + 343 cats + 2401 puppies
= 2,752
Hope this Helps!!!
Escribe una ecuación en la forma pendiente interceptó para la línea descrita
Ejemplo 1: pendiente 1.5 , pasa por (0,5)
fórmula y=mx+b
Ayuden por favor
Answer:
Pendiente-Intercepto:
pendiente = 1.5, intercepto = 5
Ecuacion: y = 1.5x+5
the transformation shown is a rotation
true or false
Answer:
True
Step-by-step explanation:
Which two equations represent parallel lines?
A. Y=2x-5
B. Y=-1 over 2x +5
C. Y=1over2x-5
D. Y=2x+ 5
And why?
Answer:
A&D
Step-by-step explanation:
Lines with the same slope are parallel. 2x-5 and 2x+5 have the same slope
Answer:
A and D are parallel.
Step-by-step explanation:
Refer to the slope-intercept equation (y = mx + b).
M = the slope
If the slopes are equal, then the lines are parallel.
The slope for line A is 2, and so is the slope for line D.
Line A and line D are parallel.
Un cazador se encuentra en la parte mas alta de un arbol. Para averiguar a que altura se encuentra, deja caer una bola, observando que demora 4 segundos. Encuentra el alto del arbol (g=10m/s2)
Answer:
80 m
Step-by-step explanation:
La velocidad inicial de la pelota es 0 m/s.
La altura del árbol es s.
El tiempo necesario es de 4 segundos.
Podemos aplicar una de las ecuaciones de movimiento de Newton:
[tex]s = ut + \frac{1}{2}gt^2[/tex]
donde u = velocidad inicial
t = tiempo empleado
g = aceleración debido a la gravedad
Por lo tanto:
[tex]s = 0 * 4 + (1/2 * 10 * 4^2)\\\\s = 0 + 80 \\\\s = 80 m[/tex]
El árbol tiene 80 metros de altura.
please I really need help
Answer:
-8
Step-by-step explanation:
m∠3 + m∠5 = 180 (interior angles are supplementary)
-4x + 5 + (-13x + 39) = 180
-4x + 5 -13x +39 = 180
-17x = 180 - 5 - 39
-17x = 136
x = 136/(-17) = -8
Only need answer A answered please
HEY MATE HERE IS UR ANSWER
The graph of the function is the set of all points (x,y) in the plane that satisfies the equation y=f(x) y = f ( x ) . ... A vertical line includes all points with a particular x value. The y value of a point where a vertical line intersects a graph represents an output for that input x value.
FOLLOW ME AND MARK AS BRAINLIEST AND CHAT INBOX
An ice cream truck that plays loud music is circling Bulans neighborhood. C(t) models the volume of the music in dB that Bulan hears, t minutes after the truck arrives in her neighborhood. Here T is entered in radians C(t)=-15cos(2pi/15t)+65 how many minutes after te truck arrives does the volume reach 75
Answer:
5.5 minutes
Step-by-step explanation:
Fill in the given information and solve for t.
75 = -15cos(2πt/15) +65
-10/15 = cos(2πt/15)
t = 15/(2π)arccos(-2/3) ≈ 5.492
The volume reaches 75 dB about 5.5 minutes after the truck arrives.
Jernel has to figure out the area of her square garage. she knows that one side of the garage is equal to the length of her rabbit pen. the dimensions of the rectangular rabbit pen are 14 by 10. what is the area of the garage?
Answer: 196
Step-by-step explanation:
Just answered this...
14x14=196
PLEASE HELP! Suppose the hypotenuse of a right triangle is 24 cm and one of the legs is 11 cm. Use the Pythagorean Theorem to find the measure of the triangle’s other leg. Round the measure to the nearest tenth if needed.
Answer:
The other leg is about 21.3 cm
Step-by-step explanation:
Pythagorean Theorem: a²+b²=c²
11²+b²=24²
121+b²=576
Subtract 121 from both sides
b²=455
b=[tex]\sqrt{455}[/tex]
b≈21.3
Answer:
21.3 cm
Step-by-step explanation:
We need to apply the Pythagorean Theorem.
The Pythagorean Theorem is an equation that can only be applied to right triangles. It states that for a right triangle with legs (two shorter sides) a and b and hypotenuse (longest side) c:
a² + b² = c²
Here, we know the hypotenuse is 24 cm and that one of the legs is 11 cm. We can hence say that c = 24 and a = 11 (or b = 11, but it doesn't really matter). Plug these values into the equation to find the other leg length:
a² + b² = c²
11² + b² = 24²
121 + b² = 576
b² = 576 - 121 = 455
b = √(455) ≈ 21.3 cm
Thus, the answer is 21.3 cm.
~ an aesthetics lover
