Could these triangles be congruent?
B
E
O yes,
O yes, if AB - DE
s, if BC = 7
O yes, if AB EF
O no, because the hypotenuses must have different
lengths
A
7
С
D
7
F
Answers
Answer:
yes, if AB ≅ DE
Step-by-step explanation:
Triangles are said to be congruent if they have the same sides and the same angles.
The following measures are used to determine if triangles are congruent:
1) Angle-side-angle: If two angles and a side of a triangle is equal to two angles and corresponding side of another triangle, then they are congruent.
2) Side-side-side: If all three sides of a triangle is equal to three sides of another triangle, then the two triangles are congruent.
3) Side angle side: If two sides and an included angle of a triangle is equal to the two sides and corresponding angle of another triangle, then they are congruent.
4) Hypotenuse - leg: If the hypotenuse and one leg of a triangle is equal to the hypotenuse and leg of another triangle then they are congruent.
From the triangles DEF and ABC, already, they already have one equal triangle that is ∠F = ∠B and an equal side i.e DF = AC.
To satisfy congruence, two sides and an angle have to be equal, therefore if AB = DE then the two triangles would be congruent
Answer:
D). no, because the hypotenuses must have different lengths
Step-by-step explanation:
I just did the assignment on Edge and it's 100% correct.
Hope this helps!! Also heart and rate if you found this answer helpful!! :)
Related Questions
Line A has an x-intercept of -4 and a y-intercept of 8. What is its slope?
Answers
Answer:
Step-by-step explanation:
We can use the intercept form of the equation of a line, then solve for y.
Intercept form
x/(x-intercept) +y/(y-intercept) = 1
x/-4 +y/8 = 1
__
Solving for y, we have ...
-2x +y = 8 . . . . multiply by 8
y = 2x +8 . . . . add 2x
The coefficient of x is 2, so the slope is 2.
__
The graph shows you the rise is 8 for a run of 4, so ...
slope = rise/run = 8/4
slope = 2
How many distinct triangles can be formed for which mzA
= 75°, a = 2, and b = 3?
O No triangles can be formed.
One triangle can be formed where angle B is about 15°.
One triangle can be formed where angle B is about 40°.
Two triangles can be formed where angle B is 40° or
140°
Answers
We are given
m∠A = 75 deg
a = 2
b = 3
Apply the Law of Sines.
sin(B)/b = sin(A)/a
sin(B)/3 = sin(75)/2
sin(B) = (3*sin(75))/2 = 1.45
The value of the sin function cannot exceed 1.
This means that the triangle cannot exist.
Answer: No distinct triangles
Answer: A no triangles can be formed
Step-by-step explanation:
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match the circle equations in general form with their corresponding equations in standard form. x2 + y2 − 4x + 12y − 20 = 0
(x − 6)2 + (y − 4)2 = 56
x2 + y2 + 6x − 8y − 10 = 0
(x − 2)2 + (y + 6)2 = 60
3x2 + 3y2 + 12x + 18y − 15 = 0
(x + 2)2 + (y + 3)2 = 18
5x2 + 5y2 − 10x + 20y − 30 = 0
(x + 1)2 + (y − 6)2 = 46
2x2 + 2y2 − 24x − 16y − 8 = 0
x2 + y2 + 2x − 12y − 9 = 0
Answers
Answer:
1) For [tex]x^2 + y^2 - 4x + 12y - 20 = 0[/tex], the standard form is [tex](x-2)^2 + (y+6)^2 = 60\\[/tex]
2) For [tex]x^2 + y^2 + 6x - 8y - 10 = 0[/tex], the standard form is [tex](x + 3)^2 + (y - 4)^2 = 35\\[/tex]
3) For [tex]3x^2 + 3y^2 + 12x + 18y - 15 = 0[/tex], the standard form is [tex](x + 2)^2 + (y+ 3)^2 = 18\\[/tex]
4) For [tex]5x^2 + 5y^2 - 10x + 20y - 30 = 0[/tex], the standard form is [tex](x - 1)^2 + (y+ 2)^2 = 11\\[/tex]
5) For [tex]2x^2 + 2y^2 - 24x - 16y - 8 = 0[/tex], the standard form is [tex](x - 6)^2 + (y+ 4)^2 = 56\\[/tex]
6) For[tex]x^2 + y^2 + 2x - 12y - 9 = 0[/tex], the standard form is [tex](x+1)^2 + (y-6)^2 = 46\\\\[/tex]
Step-by-step explanation:
This can be done using the completing the square method.
The standard equation of a circle is given by [tex](x - a)^2 + (y-b)^2 = r^2[/tex]
1) For [tex]x^2 + y^2 - 4x + 12y - 20 = 0[/tex]
[tex]x^2 - 4x + y^2 + 12y = 20\\x^2 - 4x + 2^2 + y^2 + 12y + 6^2 = 20 + 4 + 36\\(x-2)^2 + (y+6)^2 = 60\\[/tex]
Therefore, for [tex]x^2 + y^2 - 4x + 12y - 20 = 0[/tex], the standard form is [tex](x-2)^2 + (y+6)^2 = 60\\[/tex]
2) For [tex]x^2 + y^2 + 6x - 8y - 10 = 0[/tex]
[tex]x^2 + 6x + y^2 - 8y = 10\\x^2 + 6x + 3^2 + y^2 - 8y + 4^2 = 10 + 9 + 16\\(x + 3)^2 + (y- 4)^2 = 35\\[/tex]
Therefore, for [tex]x^2 + y^2 + 6x - 8y - 10 = 0[/tex], the standard form is [tex](x + 3)^2 + (y - 4)^2 = 35\\[/tex]
3) For [tex]3x^2 + 3y^2 + 12x + 18y - 15 = 0[/tex]
Divide through by 3
[tex]x^2 + y^2 + 4x + 6y = 5[/tex]
[tex]x^2 + y^2 + 4x + 6y = 5\\x^2 + 4x + 2^2 + y^2 + 6y + 3^2 = 5 + 4 + 9\\(x + 2)^2 + (y+ 3)^2 = 18\\[/tex]
Therefore, for [tex]3x^2 + 3y^2 + 12x + 18y - 15 = 0[/tex], the standard form is [tex](x + 2)^2 + (y+ 3)^2 = 18\\[/tex]
4) For [tex]5x^2 + 5y^2 - 10x + 20y - 30 = 0[/tex]
Divide through by 5
[tex]x^2 + y^2 - 2x + 4y = 6[/tex]
[tex]x^2 + y^2 -2x + 4y = 6\\x^2 - 2x + 1^2 + y^2 + 4y + 2^2 = 6 + 1 + 4\\(x - 1)^2 + (y+ 2)^2 = 11\\[/tex]
Therefore, for [tex]5x^2 + 5y^2 - 10x + 20y - 30 = 0[/tex], the standard form is [tex](x - 1)^2 + (y+ 2)^2 = 11\\[/tex]
5) For [tex]2x^2 + 2y^2 - 24x - 16y - 8 = 0[/tex]
Divide through by 2
[tex]x^2 + y^2 - 12x - 8y = 4[/tex]
[tex]x^2 + y^2 - 12x - 8y = 4\\x^2 - 12x + 6^2 + y^2 - 8y + 4^2 = 4 + 36 + 16\\(x - 6)^2 + (y+ 4)^2 = 56\\[/tex]
Therefore, for [tex]2x^2 + 2y^2 - 24x - 16y - 8 = 0[/tex], the standard form is [tex](x - 6)^2 + (y+ 4)^2 = 56\\[/tex]
6) For [tex]x^2 + y^2 + 2x - 12y - 9 = 0[/tex]
[tex]x^2 + 2x + y^2 - 12y = 9\\x^2 + 2x + 1^2 + y^2 - 12y + 6^2 = 9 + 1 + 36\\(x+1)^2 + (y-6)^2 = 46\\[/tex]
Therefore, for[tex]x^2 + y^2 + 2x - 12y - 9 = 0[/tex], the standard form is [tex](x+1)^2 + (y-6)^2 = 46\\\\[/tex]
For Plato / Edmentum
Just to the test and got it right ✅
Factor completely [tex]3x^3-3x^2-18x[/tex].
A - 3x(x + 3)(x + 2)
B - 3x(x + 3)(x − 2)
C - 3x(x − 3)(x + 2)
D - 3x(x − 3)(x − 2)
Will give Brainliest!
Answers
Answer:
The answer is 3x(x - 3)(x + 2)
Step-by-step explanation:
3x³ - 3x² - 18x
Factor out 3x from the expression
We have
3x ( x² - x - 6)
Solve the terms in the bracket
We have
3x ( x² + 2x - 3x - 6)
Factor out x the expression in the bracket
We have
3x ( x ( x + 2) - 3( x + 2) )
Factor out x + 2 from the expression in the bracket
We have the final answer as
3x ( x - 3) (x + 2)Hope this helps you.
Which polynomial identity will prove that 35 = 27 + 8?
Answers
please solve it 90 POINTS please help- PLEASE HELP its Identify the following for the quadratic relations please slove it all please if you can save the picture and do it on the page -
i Will give brainliest
Answers
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
2)
a) elimination method
b) substitution method
c) substitution method
For the first part we can elimate the y variable by subtracting the equations. We can then find the value of x.
For the second part we can substitute y as 2x+5 in the second equation and solve for x.
For the third part we can substitute y as 4x+3 in the first equation and solve for x.
3)
[tex]\boxed{\mathrm{view \: attachment}}[/tex]
Find the total surface area of this cylinder. Give your answer to one decimal place PLEASE HELP THANK YOUUUU
Answers
Answer:
Step-by-step explanation:
surface area of cylinder=2 πr²+2πrh
=2πr(r+h)
=2π×12(12+18)
=24π×30
=720π
≈2261.9 cm²
I NEED HELP PLEASE, THANKS! :)
A gear of radius 6.1 cm turns at 11 revolutions per second. What is the linear velocity of the gear in meters per second?
v = linear velocity, d = distance traveled, and t = time.
Answers
Answer:
Velocity = 4.22 m/s
Step-by-step explanation:
Time = 1 second
Radius = 6.1 cm
Diameter = 12.2 cm = 0.122 m
Displacement = Revolution × π × Diameter
Displacement = 11 × 3.14 × 0.122
Displacement = 4.22 m
Now, Linear velocity:
Velocity = displacement / Time
Velocity = 4.22 / 1
Velocity = 4.22 m/s
Answer: 4.216 meters per second
Step-by-step explanation:
Notes: Use the following conversions:
1 revolution = 2π
100 cm = 1 meter
and the following formula: v = ωr/t where v is in meters per second
[tex]\dfrac{11\ revolutions\times 6.1\ cm}{1\ second}\times \dfrac{2\pi}{1\ revolution}\times \dfrac{1\ meter}{100\ cm}=\dfrac{1.342\pi\ meters}{second}\\\\\\=\large\boxed{\dfrac{4.216\ meters}{second}}}[/tex]
which of the following angles is coterminal with 5pi/3? pi/3, 2pi/3, 4pi/3, 5pi/3
Answers
Answer:
5pi/3
Step-by-step explanation:
For two angles to be co-terminal, one must differ from the other by a multiple of 2pi.
The angle of consideration is 5pi/3
Let us consider the options one by one and see if they differ from the angle of consideration by a multiple of 2pi.
5pi/3 - pi/3 = 4pi/3
5pi/3 - 2pi/3 = 3pi/3 = pi
5pi/3 - 4pi/3 = pi/3
5pi/3 - 5pi/3 = 0 = 0(2pi)
5pi/3 is co-terminal with itself
Which of the following is the correct factored form of the given equation? 6x^2 -13x - 8 = 0
Answers
Answer:
the 2nd
Step-by-step explanation:
The y-intercept in the linear equation −2y−4x−6=0 is _[blank]_. will give brainliest
Answers
Answer:
-3 is the value of the location where the line crosses the y-axis,and is commonly referred in the slope-intercept form of a line "the intercept". Now it may be your teacher expects you to answer this as the point on the plane where the y-intercept occurs, and that should be the point (0, -3). Make sure you follow your teacher's notation.
Step-by-step explanation:
Re-write the equation given in slope=intercept form by isolating the variable "y" on one side of the equation and expressing the rest in slope*x + y-intercet form:
[tex]-2y-4x-6=0\\-4x-6=2y\\y=-2x-3\\[/tex]
which tells us that the slope of the line is -2 and it y-intercept is "-3".
Now, watch out because you may be asked to write the actual coordinates of the y-intercept, which are: (0, -3)
giving the x-coordinate 0 and the y-value where the line crosses the y-axis.
Answer:
-3.
Step-by-step explanation:
-2y - 4x - 6 = 0
-2y = 4x + 6
y = -2x - 3
So, the y-intercept is (0, -3).
Hope this helps!
if AB is 3/4 and CD is 8/-6 are the parallel, perpendicular or niether
Answers
Answer:
neither
Step-by-step explanation:
parallel lines have the same slope, perpendicular lines' slopes are the negative inverse of eachother.
PLEASE HELP Which of the sets of ordered pairs represents a function? A = {(2, −2), (5, −5), (−2, 2), (−5, 5)} B = {(4, 2), (4, −2), (9, 3), (9, −3)} a. Only A b. Only B c. Both A and B Incorrect d. Neither A nor B
Answers
Answer: A. Only A
Step-by-step explanation:
A has exactly one output for every input but B has different outputs for an input.
Explication: If there is no repeated numbers in the x axis and the y axis it is a function you can also figure this out by doing the line test if you draw a horizontal line across your function and there is no repeated numbers on the x axis or y axis it is a function
Francis surveyed a random sample of 70 students at Franklin High School about their favorite season. Of the students surveyed, 18 chose fall as their favorite season. There are 1816 students at Franklin High School.
Answers
Complete question is;
Francis surveyed a random sample of 70 students at Franklin High School about their favorite season. Of the students surveyed, 18 chose fall as their favorite season. There are 1816 students at Franklin High School. Based on the data, what is the most reasonable estimate for the number of students at Franklin High School whose favorite season is fall?
Answer:
467
Step-by-step explanation:
We are told that 18 out of 70 of the surveyed students' favorite season is fall. This when expressed in fraction, gives; 18/70.
Now we need to multiply this fraction by the total number of Franklin High School students in order to get the estimate for the number of students at Franklin High School whose favorite season is fall. Total number of students = 1816. Thus, estimate is;
1816 × 18/70 = 467
Thus, the most reasonable estimate for the number of students at Franklin High School whose favorite season is fall would be 467.
A shop advertises 25% off its prices in a sale.
A dress is £90 in the sale.
How much was it before the price reduction?
Answers
Answer:
it's 22.5
Step-by-step explanation:
You do 25% of 90 =22.5
Answer:
£120
Step-by-step explanation:
A reduction of 25% of the price, means the price of the dress in sale is 75%.
⇒ £90 →75%
X→100%
⇒ the price before the reduction= X=(90×100)÷75=£120
The graph below shows the price of different numbers of beach balls at a store: Which equation can be used to determine p, the cost of b beach balls? b = 5.50p p = 5.50b p = 11b b = 11p
Answers
Answer:
p = 5.50b
Step-by-step explanation:
2 beach balls cost 11
4 beach balls cost 22
6 beach balls cost 33
So each (1) ball b costs 5.50 ($) p
how many millimeters are in a meter
Answers
Answer:
There are 1000 millimeters in a meter.
Step-by-step explanation:
I really hope this helps in any way.
Answer:
1,000
Step-by-step explanation:
The word millimeter has the prefix of 'milli-'.
'Milli-' means a thousand.
Applying the prefix meaning to the word, a millimeter would be a thousandth of a meter.
There are 1,000 millimeters in a meter.
Brainilest Appreciated.
Soon Yi loves to bake, and she is making flaky pastry. Soon Yi starts with a layer of dough 2 22 millimeters ( mm ) (mm)left parenthesis, start text, m, m, end text, right parenthesis thick. The baking process then involves repeatedly rolling out and folding the dough to make layers. Each time Soon Yi rolls and folds the dough, the thickness increases by 8 % 8%8, percent. What is the smallest number of times Soon Yi will have to roll and fold the dough so that the resulting dough is at least 2.5 mm 2.5mm2, point, 5, start text, m, m, end text thick
Answers
Answer:
3times
Step-by-step explanation:
Baking Process: repeatedly rolling out and folding the dough to make layers
Soon Yi starts with a layer of dough = 2millimeters
Each time Soon Yi rolls and folds the dough, the thickness increases by 8 % = 1 + 8 %
When time = 1
Thickness = 2(1 + 8 %) = 2(1+0.08)
= 2(1.08) = 2.16
For time = n
Thickness = 2(1 + 8 %)^n = 2(1.08)^n
When thickness ≥ 2.5mm, n= ?
2.5 = 2(1.08)^n
2.5/2 = (1.08)^n
1.25 = (1.08)^n
Since the numbers are close (1.25 and 1.08), we can compute by multiplying 1.08 by itself till we get 2.5.
1.08 ×1.08× 1.08 = 1.259712
(1.08)³ is a bit above 1.25
2(1.08)³ satisfies the thickness of at least 2.5mm
Let's check our answer using the formula:
When n = 3
2(1.08)³ = 2 × 1.259712 = 2.519424
This satisfies the thickness of at least 2.5mm
Therefore, the smallest number of times Soon Yi will have to roll and fold the dough so that the resulting dough is at least 2.5 mm = 3
Find w please help me
Answers
Answer:
w = 77°
Step-by-step explanation:
From the picture attached,
WXYZ is a quadrilateral having 4 interior angles,
m∠y = 90°
Therefore, (2x - 10) = 90°
2x = 90 + 10
2x = 100
x = 50
Now, m∠z = (x + 15)° = 65°
m∠x = (3x - 22)° = 150 - 22
= 128°
Sum of interior angles of a polygon = (n - 2)×180°
where n = Number of sides of the polygon
If n = 4,
m∠u + m∠x + m∠y + m∠z = (4 - 2) × 180°
w + 128 + 90 + 65 = 360
w = 360 - 283
w = 77°
Therefore, measure of w = 77°
Juan hiked to the top of a 3,000-foot mountain and back down without taking a break. Which graph best represents Juan's distance from the top of the mountain during the entire hike?
Answers
Answer:
Top left graph.
Step-by-step explanation:
If Juan didn't take a break, there is no plateau/flat line. And if he started hiking up and then down, then the graph should be an upside-down V shape.
Answer:
Graph A is the most acuurate
A large stand of fir trees occupies 24 hectares. The trees have an average density of 1 tree per 20m squared. A forester estimates that each tree will yield 300 board-feet. Estimate the yield of the stand if one-tenth of the trees are cut.
Answers
Answer:
The yield of the stand if one-tenth of the trees are cut is 360000 board-feet.
Step-by-step explanation:
First, let is find the total amount of fir trees that occupies the area of 24 hectares. (1 hectare = 10000 square meters)
[tex]n = \sigma \cdot A[/tex]
Where:
[tex]\sigma[/tex] - Surface density, measured in trees per square meter.
[tex]A[/tex] - Total area, measured in square meters.
Given that [tex]\sigma = \frac{1}{20}\,\frac{tree}{m^{2}}[/tex] and [tex]A = 24\,h[/tex], the total amount of fir trees is:
[tex]n = \left(\frac{1}{20}\,\frac{trees}{m^{2}} \right)\cdot (24\,h)\cdot \left(10000\,\frac{m^{2}}{h} \right)[/tex]
[tex]n = 12000\,trees[/tex]
It is known that one-tenth of the tress are cut, whose amount is:
[tex]n_{c} = 0.1 \cdot n[/tex]
[tex]n_{c} = 0.1 \cdot (12000\,trees)[/tex]
[tex]n_{c} = 1200\,trees[/tex]
If each tree will yield 300 board-feet, then the yield related to the trees that are cut is:
[tex]y = S\cdot n_{c}[/tex]
Where:
[tex]S[/tex] - Yield of the tress, measured in board-feet per tree.
[tex]n_{c}[/tex] - Amount of trees that will be cut, measured in trees.
If [tex]n_{c} = 1200\,trees[/tex] and [tex]S = 300\,\frac{b-ft}{tree}[/tex], then:
[tex]y = \left(300\,\frac{b-ft}{tree} \right)\cdot (1200\,trees)[/tex]
[tex]y = 360000\,b-ft[/tex]
The yield of the stand if one-tenth of the trees are cut is 360000 board-feet.
convert the decimal to a simplified fraction 0.8=
Answers
Answer:
4/5
Step-by-step explanation:
You know 0.8 x 10 = 8, so 8/10 is the fraction.
Now, simplify 8/10.
8/10 = 4/5
Answer:
4/5
Step-by-step explanation:
Step 1: Convert decimal to fraction
0.8= 8/10
Step 2:Simplify
8/10=4/5
A restaurant offers 6 choices of appetizer, 8 choices of main meal, and 5 choices of dessert. A customer can choose to eat just one course, or two different courses, or all three courses. Assuming all choices are available, how many different possible meals does the restaurant offer?
Answers
Step-by-step explanation:
For one course:
6+8+5=
Two courses with appetizers and main meals (* means times)
6*8
Two courses with appetizers and dessert
6*5
Two courses with main meals and dessert
8*5
Write a two-column proof. Given: <2 is congruent to <5; Segment AB is congruent to Segment DE Prove: Segment BC is congruent to Segment EC
Answers
Answer:
proof
Step-by-step explanation:
Statements
Reasons
<2 is congruent to <5; Segment AB is congruent to Segment DE
Given
<3≅<4
Vertical angle theorem
ΔCDB≅ΔCAE
AAS
Segment BC is congruent to Segment EC
CPCTC
The segment BC is congruent to segment EC and this can be proven by using the properties of a triangle and the given data.
Given :
Angle 2 is congruent to angle 5.Segment AB is congruent to Segment DE.The following steps can be used in order to prove that segment BC is congruent to segment EC:
Step 1 - Using the triangle properties it can be proven that segment BC is congruent to segment EC.
Step 2 - According to the vertical angle theorem, angle 3 is congruent to angle 4.
Step 3 - Now, according to the AAS (Angle Angle Side) postulate, triangle CDB is similar to triangle CAE.
Step 4 - So, according to the CPCTC, segment BC is congruent to segment EC.
For more information, refer to the link given below:
https://brainly.com/question/25813512
trig and picture pls help
Answers
Answer:
Im pretty sure that the answer is 32.
Step-by-step explanation:
Hope this helps
Which expression represents a difference of squares ?
Answers
Answer:
first and last options
Step-by-step explanation:
Difference of squares are in the form a² - b². The only choices that satisfy this are 25x² - 36 and 1 - 16x².
Answer:
1 and 4
Step-by-step explanation:
A winter recreational rental company is fencing in a new storage area. They have two options. They can set it up at the back corner of the property and fence it in on four sides. Or, they can attach it to the back of their building and fence it in on three sides. The rental company has decided that the storage area needs to be 100 m2 if it is in the back corner or 98 m2 if it is attached to the back of the building. Determine the optimal design for each situation.
Answers
Answer:
Rectangular area attached to the back of the building
two sides of legth 7 m and one side of 14 m
Step-by-step explanation:
We need to compare quantity of fencing material to be used in both cases
1.Option
A = 100 m² dimensions of storage area "x" and "y"
x*y = 100 y = 100/x
The perimeter of the storage area is
p = 2*x + 2*y ⇒ p = 2*x + 2*100/x
p(x) = 2*x + 200/x
Taking drivatives on both sides of the equation
p´(x) = 2 - 200/x²
p´(x) = 0 ⇒ 2 - 200/x² = 0
2*x² - 200 = 0 x² = 100
x = 10 m
and y = 100/10
y = 10 m
Required fencing material in first option
2*10 + 2*10 = 40 m
2.-Option
Following the same procedure
A = 98 m² y = A/x y = 98/x
p = 2*x + y p(x) = 2*x + 98/x
p´(x) = 2 - 98/x² p ´(x) = 0
2 - 98/x² = 0
2*x² = 98 x² = 49
x = 7 m and y = 98/ 7 y = 14 m
Total quantity of fencing material
p = 2* 7 + 14 p = 28
Therefore option 2 is more convinient from economic point of view
Optimal design rectangular storage area with two sides of 7 m and one side of 14 m
There is a bag filled with 5 blue, 6 red and 2 green marbles. A marble is taken at random from the bag, the colour is noted and then it is not replaced. Another marble is taken at random. What is the probability of getting 2 blues?
Answers
Answer:
Step-by-step explanation:
Total marbles = 5 + 6 + 2 = 13
P( getting blue ball from first draw) = 5/13
The marble is not replaced. So, Now total marbles will be 12 & number blue marbles will be 4
P( getting blue ball from second draw) = 4/12 = 1/3
P(getting two blues) = [tex]\frac{5}{13}*\frac{1}{3}\\[/tex]
= 5/39
What do the Nineteenth Amendment and the Indian Citizenship Act of 1924
have in common?
O A. They both affected American Indians directly.
O B. They both allowed certain Americans to own property.
O C. They both permitted free expression with some restrictions.
O D. They both provided suffrage to a group of Americans.
Answers
Answer:
D
Step-by-step explanation:
Suffrage is the right to vote, and the nineteenth amendment gave women the right to vote, and the indian citizenship act of 1924 gave native americans the right to vote
Which triangle results from a reflection across the line x = 1?
Answers
Answer:
Correct answer is option D.
Step-by-step explanation:
Given that [tex]\triangle ABC[/tex] in the image 1 attached.
If we have a look at the image attached, the coordinates are:
[tex]A(1,1)\\B(2,5)\ and\\C(4,1)[/tex]
To find reflection of a point across any line, the distance of points from the line must be same.
Point A(1,1) lies on the line x = 1, so its reflection A' will be at the same point A'(1,1).
Point C(2,5) is at a distance 1 from x = 1 on right side, so C' will be 1 distance on the left side of x = 1 i.e. 1 will be subtracted from its x coordinate.
i.e. C'(1 - 1, 5)
C'(0, 5)
Point B(4, 1) is at a distance 3 from x = 1 on right side, so B' will be 3 distance on the left side of x = 1 i.e. 3 will be subtracted from its x coordinate.
i.e. B'(1 - 3, 1)
B'(-2, 1)
When we plot the above point A', B' and C', we get the option D as correct.
The vertices of the triangle after reflection across the line x = 1 are:
A'(1, 1),
B'(-2, 1),
and C'(0, 6).
The correct option is D.
Given information:
As per the diagram,
The vertices of the triangle are:
A(1, 1),
B(4, 1),
and C(2, 6).
To find the reflection of the triangle across the line x = 1, we can apply the reflection transformation.
The line x = 1 acts as the mirror or reflection axis. To reflect a point across this line, we can imagine folding the image over the line so that the distance between the point and the line is preserved, but the point is now on the other side of the line.
Let's reflect each vertex of the triangle across the line x = 1:
Reflecting point A(1, 1):
The distance between point A and the line x = 1 is 0 since A lies on the line itself. Therefore, the reflection of point A will also be (1, 1).
Reflecting point B(4, 1):
The distance between point B and the line x = 1 is 3 units. Reflecting across the line x = 1 will place B 3 units to the left of the line, resulting in the point (1 - 3, 1), which simplifies to (-2, 1).
Reflecting point C(2, 6):
The distance between point C and the line x = 1 is 1 unit. Reflecting across the line x = 1 will place C 1 unit to the right of the line, resulting in the point (1 - 1, 6), which simplifies to (0, 6).
Therefore, the vertices of the triangle after reflection across the line x = 1 are:
A'(1, 1),
B'(-2, 1),
and C'(0, 6).
To learn more about the reflection;
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