5 Points
Rebecca is given two triangles, AABC and A DEF. At first glance, she thinks
that the triangles are congruent. How can she use what she knows about
rotations and triangle congruence to prove the triangle congruence?
Answers
Answer:
A
Step-by-step explanation:
Rotating ABC 90° will make segment AB parallel to segment DE, facilitating comparison of sides and angles. The triangles are marked with two angles and the side between them, so the appropriate theorem to use is the ASA theorem. (That theorem refers to a side (S) between two angles (A..A).)
She can use what she knows about rotations and triangle congruence to prove that triangle congruence as per option A.
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
As per the given figure, we have triangles in which two angles and one side are equal.
∠A = ∠E = 65° (angle)
BA = ED (side)
∠A = ∠E = 30° (angle)
By rotating ABC 90°, section AB becomes parallel to segment DE, allowing for easier comparison of sides and angles. Because the triangles are defined by two angles and the side between them, the ASA theorem is relevant. (This theorem is about a side (S) between two angles (AA).)
Thus, the correct answer is option A.
Learn more about congruent triangles here:
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Related Questions
Solve the inequality.
Answers
Answer:
1 1/5 [tex]\geq[/tex] x OR one and on fifth is greater than or equal to x.
Step-by-step explanation:
2/5 [tex]\geq[/tex] x - 4/5
To isolate x, we need to add 4/5 to each side:
6/5 [tex]\geq[/tex] x is what we get
We can simplify it to:
1 1/5 [tex]\geq[/tex] x
Add 4/5 to both sides
X <= 6/5
X <= 1 1/5
Last year, there were “x” students in the Math Club, but this year, there was a 40% increase in membership. Represent this year’s membership in terms of “x”.
Answers
Answer:
(x)1.4=Y
Step-by-step explanation:
40% increase of memeber so ita 140% of X
What is the image of the point (-5, 2) under the translation T3,-4?
Answers
Answer: (5,7)
Step-by-step explanation:
We want to find the image of a point after a given translation.
The image of the point (-5, 2) under the translation T(3, -4) is the point (-2, -2)
First, we can define how a general translation T(a, b) affects a general point (x, y).
It will add a units to the x-value and b units to the y-value, then we have:
T(a,b)[(x, y)] = (x + a, y + b).
Now we just need to apply the translation:
T(3, -4) to the point (-5, 2)
It gives:
T(3, -4)[(-5, 2)] = (-5 + 3, 2 + (-4)) = (-2, -2)
So the image of the point (-5, 2) under the translation T(3, -4) is the point (-2, -2)
If you want to learn more, you can read:
https://brainly.com/question/16874971
Find the surface area of the polyhedra
pls!! show how you got the surface area
Answers
Answer:
960cm^2
Step-by-step explanation:
surface area = sum of area of one sides
front + back = 336cm^2
side x 2 = 336cm^2
base + top = 288cm^2
sum = 960cm^2
Mark Brainiest, please
A hummingbird’s nest is 6 meters high in a tree. A flower is on the ground 14 meters away from the base of the tree. How far will the hummingbird need to fly to get from its nest to the flower if it takes a direct path?
Answers
Answer:
15.23 m
Step-by-step explanation:
The problem given describes the shape of a right angled triangle.
From the diagram below:
The height of the tree is the opposite = 6 m
The distance of the flower from the base of the tree = adjacent = 14 m
The distance the bird must fly to get from the nest to the flower = hypotenuse = h
According to Pythagoras rule:
[tex]hyp^2 = opp^2 + adj^2[/tex]
Therefore:
[tex]h^2 = 6^2 + 14^2\\\\h^2 = 36 + 196\\\\h^2 = 232\\\\h = \sqrt{232} \\\\h = 15.23 m[/tex]
The bird will have to fly 15.23 m to get from its nest to the flower in a direct path.
CAn someone please help
Answers
no. of squares=90
no. of toothpicks=(89*3)+4
=271
rule of patern = 4+3+3...
no. of toothpicks=1000
no. of squares= (996÷3)+1
= 333
What is the value of b in the equation b + 8 = 13? a 5 b 8 c 13 d 21
Answers
Answer:
a
Step-by-step explanation:
b+8=13.
first,you have to make b the subject of the formula (stand alone) and for that to happen +8 will have to cross the equality sign.when a positive sign crosses over the equality sign it changes to a negative sign.
so that would be b=13-8
Therefore,b=5(a)
What is 0.00245 in standard form
Answers
Answer:
2.45*10^-3
Step-by-step explanation:
The number 0.00245 expressed in standard form is; 2.45 × 10-³.
While expressing numbers in standard form;
We must ensure that only one significant digit appears before the decimal point.
As such; we have 2.45 × 10-³.The 10-³ term accounts for the shift of the decimal rightward in a bid to arrive at the first significant digit.
Read more:
https://brainly.com/question/11288844
Classify the quadrilateral whose vertices are: A(3, 2); B(0,5);
C(-3, 2); D(0, -1). Select all that apply.
A) square
B) rhombus
C) trapezoid
D) parallelogram
E) rectangle
F) none of these
Answers
Answer:
select answers: A), B), C), D), and E)
Step-by-step explanation:
Please see attached image with the figure obtained by joining the given points.
Notice that the figure is that of a square, and a square happens to be a very special case of a bunch of other figure definitions, like:
rectangle (four side figure with parallel sides and right angles at the vertices) So the square is a special type of rectangle.
Rhombus (four side figure with all sides of the same length) So the square is a special type of rhombus)
Trapezoid (four side figure with at least two parallel sides), So the square is a special type of trapezoid.
Parallelogram (four side figure with two pairs of parallel sides) So the square is a special type of parallelogram.
Therefore you need to select answers: A), B), C), D), and E)
PLEASE help, i will give brainliest<3
Please simplify then determine the value of the polynomial when n=3 and when n=2.
a) (5n^2 + 3n -4) + (-3n^2 + 4n -1)
b) (7n^2 - 5n - 2) - (-n^2 + 6n + 8)
Answers
Answer:
a. 34
b. 0
Step-by-step explanation:
you plug the n values as n
note when -n^2, you do this:
[tex]-(2)^{2}[/tex]= -4
so don't mistake it for +4
pay special attention to the signs to solve like:
+ times - is a negative!
Answer:
Simplified Expression a ) 2n^2 + 7n - 5,
Simplified Expression b ) 8n^2 - 11n - 10,
When n = 3 part a ) 34,
When n = 2 part a ) 17,
When n = 3 part b ) 29,
When n = 2 part a ) 0
Step-by-step explanation:
Consider the " simplification " process at hand;
[tex]a ) (5n^2 + 3n -4) + (-3n^2 + 4n -1),\\5n^2+3n-4-3n^2+4n-1,\\5n^2-3n^2+3n+4n-4-1,\\\\Simplified Expression = 2n^2+7n-5[/tex]
[tex]b ) (7n^2 - 5n - 2) - (-n^2 + 6n + 8),\\7n^2-5n-2+n^2-6n-8,\\\\Simplified Expression = 8n^2-11n-10[/tex]
For each part ( a and b ) I removed the ( ) and grouped like elements to receive the simplified expression;
Value of each polonomial;
[tex]a ) 2n^2 + 7n - 5,\\2 * ( 3 )^2 + 7 * ( 3 ) - 5,\\34\\\\2 * ( 2 )^2 + 7 * ( 2 ) - 5\\17[/tex]
[tex]b ) 8n^2 - 11n - 10,\\8 * ( 3 )^2 - 11 * ( 3 ) - 10,\\29\\\\8 * ( 2 )^2 - 11 * ( 2 ) - 10,\\0[/tex]
Each expression was solved through substitution and algebra.
" Simplified " Solution - See in answer above
* I hope the answer wasn't too confusing, for further information look through my response thoroughly
Simplify the following as much as possible:
6a – 3a + 9a
Answers
Answer: 12a
Step-by-step explanation:
All we need to do is combine the like terms. Which all of them have the common variable a so we can add and subtract them together.
6a - 3a + 9a
Working left to right according to pemdas we can subtract first.
3a + 9a
Now add.
12a
That is as far as we can simplify.
Find the value of x in the isosceles triangle shown below
Thank you!
Answers
solve for x. 7(x-3)+3(4-x)=-8
Answers
Answer:
x=1/4
Step-by-step explanation:
1.distribute the 7 and 3 into parentheses
2. combine like terms
3. add 9 on both sides
4. divide both sides by 4
x=1/4
hope this helped!
Answer:
x = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
7(x-3)+3(4-x)= -8
Expand 7(x-3) and 3(4-x)
i.e. 7x-21+12-3x= -8
4x-9=-8
Collect like terms
4x= -8+9
4x= 1
x = [tex]\frac{1}{4}[/tex]
Hope this helps!!!
Solve for x in the equation x squared minus 12 x + 59 = 0.
Answers
Answer:
4 11/12
Step-by-step explanation:
x2−4x−12<0
x2+10x−24<0
x−1=2y
x=−5912
Decimal Form:
x=−4.91¯6
Mixed Number Form:
x=−4 11/12
Answer:
There is no solution to this.
Step-by-step explanation:
Maybe check for a typo?
you would first need to calculate the discriminant, D= b^2-4 a c
D= (-12)^2 -4*1*59
Simplify
D=-92
Since D<0, the quadratic equation has no real solutions.
What are some words that relate to geometry but are difficult to precisely define
Answers
Answer:
the point the line the planeStep-by-step explanation:
:D
please help urgent ❤️❤️❤️❤️
Answers
Answer:
B,Friday
Step-by-step explanation:
4 to 9 is 5 hours,the total hours for the week is 32.5 hours
HELP! Which of the following are interior angles in the figure below? PLEASEEE!!!!! URGENT dont need to explain
Answers
f(n) = 65 - 4n; 29
determine which term produces the given number?
Answers
Answer:
9 th term
Step-by-step explanation:
Equate 65 - 4n to 29 and solve for n , that is
65 - 4n = 29 ( subtract 65 from both sides )
- 4n = - 36 ( divide both sides by - 4 )
n = 9
Which of the following are exterior angles? Check all that apply
Answers
Answer:
Options A, E
Step-by-step explanation:
If the angle doesn't lie inside this triangle, we can assume it is an exterior angle, provided it is between a side of this triangle and an adjacent side extended outward;
[tex]< 4 - Doesn't Lie In Triangle, - Exterior Angle,\\< 3 - Lies In Triangle, - Interior Angle,\\\\< 6 - Doesn't Lie In Triangle, Execption, - Neither Interior Nor Exterior,\\\\< 1 - Lies In Triangle - Interior Angle,\\< 5 - Doesn't Lie In Triangle - Exterior Angle\\\\< 2 - Lies in Triangle - Interior Angle[/tex]
Refer to Solution below;
A. Check!
E. Check!
Calcula: t15 + t25 Si se sabe que: 26; 31; 36; 41; …
Answers
Answer:
242
Step-by-step explanation:
Here, we want to calculate t15 + t25
Mathematically, nth term is
a + (n-1)d
here, a = 26 and d = 31-26 = 5
t15 = 26 + (15-1)5
t15 = 26 + 70
t15 = 96
t25 = 26 + (25-1)5
t25 = 26 + 120
t25 = 146
t15 + t25 = 96 + 146 = 242
What is the equation of the following line? Be sure to scroll down first to see all answer options.
Answers
Answer:
y = 9x
Step-by-step explanation:
The y intercept is zero since it goes through the point (0,0)
We need to find the slope
m = (y2-y1)/(x2-x1)
= (9-0)/(1-0)
= 9/1
Putting this into slope intercept form y = mx+b
y = 9x +0
y = 9x
13. Jane buys a set of 17 spiral notebooks. Each notebook has 95 pages. What is total number of pages?
Answers
Multiply number of notebooks by number of pages in each one.
17 x 95 = 1615
The answer is 1,615 total pages
Answer:
A. 1615
Step-by-step explanation:
Solve as shown:
17 books that each have 95 pages equals the total pages.
17(95)=?
17(95)=1615
i need to solve this wink wink 5-6+8*674/2
Answers
Answer: 2,695
Step-by-step explanation:
5-6+8*674/2
Multiply 8 and 674
5-6+5,392/2
Divide 5,392 by 2
5-6 + 2,696
Subtract 6 from 5
-1 + 2,696
Add
2,695
Step-by-step explanation:
5 - 6 = -1
-1 + 8 = 7
7 x 674 = 4,718
4,718 / 2 = 2,359
Write 0.245bar in the form p/q
Answers
Answer:
245/999
Step-by-step explanation:
0.245bar = n
1000 n - n = 245
999n = 245
n = 245/999
Which data set could be represented by the box plot shown below?
A horizontal boxplot is plotted along a horizontal axis marked from 0 to 20, in increments of 1. A left whisker extends from 1 to 6. The box extends from 6 to 16 and is divided into 2 parts by a vertical line segment at 12. The right whisker extends from 16 to 19. All values estimated.
Answers
Answer:
Any set of data that satisfies the 5-Number summary: 1,6,12,16 and 19 can be represented with the box plot.
Step-by-step explanation:
Interpreting Box Plots
A box plot is used to present the 5-Number summary of a set of data.
The 5-Number summary consists of the following in their order of appearance on the box plot.
Minimum ValueFirst Quartile, [tex]Q_1[/tex]Median, [tex]Q_2[/tex]Third Quartile, [tex]Q_3[/tex]Maximum ValueIn the box plot, the following rules applies
The whisker starts from the minimum value and ends at the first quartile.The box starts at the first quartile and ends at the third quartile. There is a vertical line inside the box which shows the median. The end whisker starts at the third quartile and ends at the maximum value.Using these, we interpret the given box plot
A left whisker extends from 1 to 6.
Minimum Value=1First Quartile =6The box extends from 6 to 16 and is divided into 2 parts by a vertical line segment at 12.
Median=12Thrid Quartile=16The right whisker extends from 16 to 19.
Maximum Value =19Therefore any set of data that satisfies the 5-Number summary: 1,6,12,16 and 19 can be represented with the box plot.
Dream Studio offers 5 music lessons for $60. Fox Studio offers 8 music lessons for $72. What is the cost per lesson at each studio? What studio offers a better deal? Why?
Answers
Dream Studio offers music lessons at $12 per lesson. Fox Studio offers music lessons at $9 per lesson. The better deal here would be Fox Studio. This is because Fox Studio offers cheaper lessons. For eight lessons at Dream Studio it costs $96, where as eight lessons at Fox Studio costs only $72.
Explanation:
Step 1 - Find the cost per lesson at Dream Studio
60 / 5 = 12
So, $12 per music lesson at Dream Studio.
Step 2 - Find the cost per lesson at Fox Studio
72 / 8 = 9
So, $9 per music lesson at Fox Studio.
Step 3 - Find out which offers a better deal
•Dream Studio = $96 for eight music lessons
• Fox Studio = $72 for eight music lessons
What’s the answer ??
Answers
Answer:
-5^x-3x-6
Step-by-step explanation:
(-5^x - 4 + g(x) ) (x)
(-5^x - 4 - 3x -2) simplified -5^x-3x-6
Answer:
-5^x -3x -6 = A[tex]f(x) = - {5}^{x} - 4 \\ g(x) = - 3x - 2 \\ (f + g)(x) = \\ ( - {5}^{x} - 4) + ( - 3x - 2)[/tex]
[tex]( - {5}^{x} - 4) + ( - 3x - 2) \\ - {5}^{x} - 4 - 3x - 2 \\ collect \: like \: terms \: \\ - {5}^{x} - 3x - 4 - 2 \\ [/tex]
[tex] - {5}^{x} - 3x - 6[/tex]
what is the slope of the equation y= 5/4c- 7/4
Answers
Answer:
5/4 is the slope
Step-by-step explanation:
y= 5/4c- 7/4
This is in the slope intercept form
y = mx+b where m is the slope and b is the y intercept
5/4 is the slope and -7/4 is the y intercept
Answer:
5/4
Step-by-step explanation:
This equation is in slope intercept form (y=mx=b) so when interpreting the information we see that the slope is 5/4.
y = y
m = slope
x = x or in this case they use c
b = y intercept
This equation represents a line that intercepts at -7/4 and has a slope of 5/4. This can be checked by plugging in any point on the line for x and y.
Hope this helps!
Varuns monthly income is 18000 he spends 1/5 of his income for house rent and 3/5 of his income on other expenditure how much does he save every month
Answers
Answer:
$3600
Step-by-step explanation:
Given:
Total income T = $18,000
Fraction of income spent on house rent f1 = 1/5
Fraction of income spent on other expenditures f2 = 3/5
Fraction of income saved is;
f = 1 - (1/5+3/5) = 1 - 4/5
f = 1/5
The Amount he save is A;
A = fraction saved × total amount = f × T
Substituting the values
A = 1/5 × $18,000
A = $3,600
The Amount he save is $3,600
Answer: Varun saves 3,600 every month
Step-by-step explanation: Varun's income in the first instance is fixed at 18000, and out of this amount he spends 1/5 on house rent. We shall now determine the amount represented by 1/5 as follows;
Total income = 18000
House rent = 1/5
Rent expense = 1/5 of 18000
Rent expense = 1/5 * 18000
Rent expense = 3600
he also spends 3/5 on other expenditure
Other expenditure = 3/5 of 18000
Other expenditure = 3/5 * 18000
Other expenditure = (3 * 18000)/5
Other expenditure = 54000/5
Other expenditure = 10800
His expenses therefore have been derived as
Total expenditure = 3600 + 10800
Total expenditure = 14400
His savings per month therefore is derived as;
Total income - total expenditure = savings
18000 - 14400 = savings
3600 = savings
Therefore, Varun saves 3,600 every month
An entry level programmer's annual pay is $58.916 based on 52 weeks per year. Due to the economy, his company is having to cut back on
the number of weeks that it employs its programmers. If the firm cuts the work year to 51 weeks but keeps the same rate of pay, how
much should the programmer expect his annual pay to decrease? Round your answer to the nearest dollar
Answers
Answer: $1133
Step-by-step explanation:
Programmer's pay for 51 weeks will be
(51 * 58916) / 52 = 57,783
Loss in salary
= 58916 - 57783 = 1133