Answer:
Step-by-step explanation:
Triangles by definition have 3 sides. If the sides are corresponding then it is beneficial to us if they are the same length as well. If all 3 sides in one triangle are equal in length to the corresponding sides in another triangle, then the triangles are congruent by SSS (side-side-side). This is the case for us. Side EC is corresponding and congruent to side AC; side CD is corresponding and congruent to side CB; side ED is corresponding and congruent to side AB.
Triangles ΔABC ≅ ΔEDC by the property of SSS ( side side side).
Congruent TrianglesWhat do congruent triangles means?Triangles that are congruent share the same size and shape.
SSS Congruency:According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle.
How ΔABC ≅ ΔEDC by SSS?Consider ΔABC and ΔEDC,
As shown in the diagram,
ED = AB
DC = CB
EC = CA
Since, all the sides of both the triangles are equal , by SSS property
ΔABC ≅ ΔEDC
To know about SSS congruency for equilateral triangle, here
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1. Analyze the following pattern: 1, 2, 5, 10, 17,
Answer:
n² - 2n + 2
Step-by-step explanation:
The difference in the pattern are odd numbers.
2 - 1 = 1
5 - 2 = 3
10 - 5 = 5
17 - 10 = 7
So there is a -2n in the nth term.
If we subtract 1 on each term.
0, 1, 4, 9, 16
We get whole squares.
So there is a n² in the nth term.
(1)² - 2(1)+ c = 1
1 - 2 + c = 1
-1 + c = 1
c = 2
The nth term is:
n²-2n+2
Two points A (-2, 9) and B (4, 8) lie on a line l. (i) Find the slope of the line l. (2)marks (ii) Find the coordinates of the midpoint of the points A and B (iii) Find the distance between points A and B. (i). A line “t” is parallel to 3y = 6x + 9. Find the slope of this line “t”. (ii) Another line “r” is perpendicular to the line 3y = 6x + 9. Find the gradient of the line “r”.
Answer :
1 (i). [tex]slope \: = - \frac{1}{6} [/tex](ii). [tex]midpoints \: = (1 \: \: \frac{17}{2} )[/tex](iii) . [tex]distance \: = \sqrt{37} [/tex]2(i). [tex]slope \: = 2[/tex][tex]gradient \: = - \frac{1}{2} [/tex]I Hope it helps :)
Classify the triangle shown below. Check all that apply.
53
5
3
90°
37
4
O A. Equilateral
B. Isosceles
O C. Right
O D. Obtuse
E. Acute
O F. Scalene
Answer:
C. and F.
Step-by-step explanation:
A scalene triangle is a triangle in which all three sides have different lengths. Also the angles of a scalene triangle have different measures. Some right triangles can be a scalene triangle when the other two angles or the legs are not congruent. Right angle are 90 degrees
Answer:
C and F
Step-by-step explanation:
This triangle is not an equilateral triangle because their lengths are not equivalent to each other. It is not an isosceles triangle because no two lengths are equivalent to each other. It is a right triangle because it has one right angle(A 90 degrees angle.) It is not an obtuse triangle because there isn't an angle that is obtuse(More than 90 degrees but less than 180 degrees angle.) It isn't an acute triangle either because not all three angles are acute(Less than90 degrees angle.) Lastly, it is also a scalene triangle because none of the triangle lengths are equivalent to each other.
Write the following using algebraic notation, using the letter x for any
unknown numbers
I think of a number, add one, then double the result.
Answer:
x+1=x *x
Step-by-step explanation:
Answer:
x+1= x*x
Step-by-step explanation:
hope this helps
Which of the following is the solution to the following system of inequalities? Let the green region represent the answer region.
Answer:
Option (A)
Step-by-step explanation:
There are two inequalities drawn on a graph.
x + 2y ≤ 4 ------(1)
3x - y ≤ 2 -------(2)
Here solution set of the inequality (1) will be represented by the shaded area below the solid line (in blue) represented by "x + 2y = 4".
(Line x + 2y = 4 will have the slope slanting down and y-intercept as 2)
Second inequality will represent the shaded area on the left of the solid red line represented by "3x - y ≤ 2".
(Line 3x - y = 2 will have the slope upwards and y-intercept as -2)
Solution area of these inequalities will be the common area shaded in green.
Graph given in Option (A) will be the answer.
A triangle has vertices at (4.-2), (2.2), and (4.6). What are the vertices of the image of the triangle after applying the
translation (x, y)=(x - 1, y + 2)?
Answer:
see explanation
Step-by-step explanation:
The translation rule (x, y ) → (x - 1, y + 2 )
Means subtract 1 from the original x- coordinate and add 2 to the original y- coordinate, thus
(4, - 2 ) → (4 - 1, - 2 + 2 ) → (3, 0 )
(2, 2 ) → (2 - 1, 2 + 2 ) → (1, 4 )
(4, 6 ) → (4 - 1, 6 + 2 ) → (3, 8 )
Two similar triangles are shown below:
a
6
8
2
3
b
4
Which two sets of angles are corresponding angles?
O
O
O
O
Answer:
<a and <d; <b and <c.
Step-by-step explanation:
When two triangles are said to be similar, the ratio of the corresponding sides of both triangles is always the same, also, their corresponding angles are congruent. That is, they are equal.
The 2 set of angles that are corresponding angles of the two similar triangles given in the question above are:
<a and <d; <b and <c.
Both set of angles are congruent to each other. In other words, they are equal.
please help me in this because i am not able to understand this answer from any side
Answer:
7, 5929, 77
Step-by-step explanation:
The prime factorization of 847 is 7 · 11², therefore, to make it a perfect square you need to multiply it by 7 to make 5929 which has a square root of 7 · 11 = 77.
Speedy texting 3a: Lydia wants to text at least 8 characters per second, like James, then the equation would be 10r+4=8 could be used to model this situation. Solve this equation for R. 3b: Explain what the variable r represents in the equation given in question 3a.
Answer:
Speedy Texting
3a. In the equation, 10r + 4 = 8
r = 0.4 or 40%
3b. The variable r represents an independent variable in the equation. An independent variable is a variable that is not dependent on another variable, instead other variables depend on it. Whatever its value is changes the value of other variables in the equation.
Step-by-step explanation:
a) Solving the equation:
10r + 4 = 8
10r = 8 - 4
10r = 4
r = 4/10 = 0.4 or 40%
Haroldo, Xerxes, Regina, Shaindel, Murray, Norah, and Georgia are invited to a dinner party. They arrive in a random order and all arrive at different times. What is the probability that Xeres arrives first AND Regina arrives last?
Answer:
1/7
Step-by-step explanation:
There are seven people in all on person will arrive at a different time than others. Every single one of them arrives at different times so it's 1/7
Which of the following is a parent function?
Answer:
B
Step-by-step explanation:
A parent function is the simplest function that still satisfies the definition of a certain type of function. One of those functions is exponential, which is b.
Option (B) will be the correct option.
Definition of a parent function:A parent function is simplest function which represents the entire family of that kind of functions.
We will check each option given for the definition of a parent function.
Option (A)
[tex]f(x)=-2^{x+1}[/tex]
Parent function will be,
[tex]f(x)=2^x[/tex]
Option (B),
[tex]f(x)=4^x[/tex]
It's a simplest form of an exponential function.
Therefore, it's a parent function.
Option (C),
[tex]f(x)=e^{3x}-2[/tex]
Parent function → [tex]f(x)=e^{3x}[/tex]
Option (D),
[tex]f(x)=4x^2[/tex]
Parent function → [tex]f(x)=x^2[/tex]
Learn more about the parent function and the transformation here,
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identify the area of the trapezoid. options: 299cm^2 325cm^2 425cm^2 399cm^2
Answer:399
Step-by-step explanation:
((a+b)/2) * h
((13+25)/2) * 21
399
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The sum of the interior angles of a polygon is 9x². If x is 3 greater than the number of side of the polygon, how many sides does the polygon have?
Answer:
17
Step-by-step explanation:
This is a very neat problem -- for teachers.
Let the number of sides = y
The sum of the interior angles is 180*(y - 2)
We are told that this sum equals 9x^2
So far the equation is
(y - 2)*180 = 9x^2 Divide both sides by 9
(y - 2)*20 = x^2 Remove the brackets on the left.
20*y - 40 = x^2
We need another fact. We get that from the statement that x is three greater than the number of sides (y). Therefore y = x - 3
20*(x - 3) - 40 = x^2
20x - 60 - 40 = x^2 Combine like terms on the left
20x - 100 = x^2 Bring the left side to the right side.
0 = x^2 - 20x + 100 You have a quadratic.
a = 1
b = - 20
c = 100
When you solve the quadratic equation, you get
x = 20
Therefore the number of sides is 17.
Mr. Rifkin had 240 digital and manual cameras. After donating 82 digital cameras and 26 manual cameras, he had 3 times as many digital cameras as manual cameras left. How many digital cameras did he have at first?
Answer:
therefore, he had 181 digital cameras at first
Step-by-step explanation:
total=240
digital= 3x+82
manual= x+26
total= digital + manual
240= 3x+82+26+x
x= 240-108/4
x= 33
digital= 3×33+83
=181
Answer:
181
Step-by-step explanation:
Let d represent the number of digit cameras Mr. Rifkin had at first. Then 240-d is the number of manual cameras he had. The after-donation numbers are ...
(d -82) . . . digital cameras after donating 82
(240 -d) -26 . . . manual cameras after donating 26
These values are related by ...
(d -82) = 3((240 -d) -26)
4d = 724 . . . . . add 3d+82 and simplify
d = 181
Rifkin had 181 digital cameras at first.
_____
Check
Rifkin started with 181 digital cameras and 59 manual cameras. After donation, he had 99 digital cameras and 33 manual cameras, so 3 times as many digital as manual—as required.
Deb works 19.5 hours at a car wash every week. She makes $12.80 per hour. Each week, she puts 1 4 of her earnings into her savings account. How much money does Deb put into her savings account each week?
Answer:
She will save 62.40
Step-by-step explanation:
First find the total amount she makes
hours times hourly rate
19.5 * 12.80
249.60
She saves 1/4 of this, so multiply by 1/4
1/4 * 249.60
62.40
She will save 62.40
Answer:
62.40
Step-by-step explanation:
gregs gas tank is 1/3 full. after he buys 11 gallons of gas, it is 5/6 full. how many gallons can gregs tank hold
Explanation:
x = max number of gallons the tank can hold
Greg's car starts off 1/3 full, so (1/3)x = x/3 number gallons is in the car.
Add on 11 more gallons to get (x/3) + 11 = x/3+33/3 = (x+33)/3
The expression (x+33)/3 represents the number of gallons he has after buying 11 gallons of gas. This is equal to (5/6)x since this represents the idea of the tank being 5/6 full
The equation we need to solve is (x+33)/3 = (5/6)x
Let's do so to get...
(x+33)/3 = (5/6)x
(x+33)/3 = (5x)/6
6(x+33) = 3*5x
6x+198 = 15x
198 = 15x-6x
198 = 9x
9x = 198
x = 198/9
x = 22
His tank can hold up to 22 gallons.
I need help with this question
Answer:
y = -3x + 8
Step-by-step explanation:
You have to find the slope first using the formula [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
Insert any two points in the equation (1,5) and (2,2) and you get -3.
Then, you do any x value times the slope (1*-3 = -3) and add so that it equals the corresponding y value (8).
This makes it y = -3x + 8.
I NEED HELP PLEASE, THANKS! :)
Answer: [tex]\bold{b)\quad \dfrac{2\pi}{3},\dfrac{4\pi}{3},0}[/tex]
Step-by-step explanation:
Note the following identities: tan² x = sec²x - 1
[tex]\sec x=\dfrac{1}{\cos}[/tex]
tan² x + sec x = 1
(sec² x -1) + sec x = 1
sec² x + sec x - 2 = 0
(sec x + 2)(sec x - 1) = 0
sec x + 2 = 0 sec x - 1 = 0
sec x = -2 sec x = 1
[tex]\dfrac{1}{\cos x}=-2\qquad \dfrac{1}{\cos x}=1\\\\\cos x=-\dfrac{1}{2}\qquad \cos x=1\\\\x=\dfrac{2\pi}{3}, \dfrac{4\pi}{3}\qquad x=0[/tex]
Answer:
Option B
Step-by-step explanation:
We have tan^2( x ) + sec( x ) = 1.
First subtract 1 from either side, applying the identity tan^2( x ) = - 1 + sec^2( x ) = - 2 + sec( x ) + sec^2( x ) = 0
One key method that you should use to solve like problems, is to substitute a rather large value with a variable, such as say a. Let sec( x ) = a,
- 2 + a + a^2 = 0,
By the zero product property, a = 1, a = - 2. Substitute this value of a back into sec( x ) -
sec( x ) = 1, sec( x ) = - 2
From this we can create inequality( s ) as follows -
sec( x ) = 1, 0 ≤ x ≤ 2π, x = 0 and x = 2π
sec( x ) = - 2, 0 ≤ x ≤ 2π, x = 2π / 3 and x = 4π / 3
As you can see, x is the following solutions -
0, 2π, 2π / 3, 4π / 3
Eliminate 2π, and it should be that your solution is option B
The perimeter of a square is 80 minus 64 y units. Which expression can be used to show the side length of one side of the square? 16 (5 minus 4 y): Each side measures 5 minus 4 y units. 16 y (5 minus 4): Each side measures 5 minus 4 units. 4 (20 minus 16 y): Each side measures 20 minus 16 y units. 4 y (20 minus 16): Each side measures 20 minus 16 units.
Answer: 4 (20 minus 16 y): Each side measures 20 minus 16 y units.
Step-by-step explanation:
Hi, to answer this question we have to know the formula of the perimeter of a square:
Perimeter = side length x 4
Since:
p = 80-64y = s x 4
Solving for s (side length)
80-64y /4 = s
s = 20- 16 y
So, the correct option is:
4 (20 minus 16 y): Each side measures 20 minus 16 y units.
Feel free to ask for more if needed or if you did not understand something.
Answer:
i believe its C
Step-by-step explanation:
Abel’s age in 2019 will be equal to the sum of the digits of his year of birth. If Abel is an adult, how old is Abel now?
Answer:
23
Step-by-step explanation:
If Abel was born in 1994, in 2019 he would be 23.
1+9+9+4=23
Hi someone please help me I'm not sure how to do thissss
If the longer base of triangle XYZ is three times the length of the shorter base, a, what is the length of the hypotenuse in terms of the shorter base?
Answer: (√10)*a
Step-by-step explanation:
In a triangle rectangle, we have 3 sides, in this case, the shorter base, a, the longer base, b and the hypotenuse h.
And the hypotenuse can be found with the Pythagorean's theorem.
a^2 + b^2 = h^2
now, we know that b = 3a, then we can replace it in the above equation:
a^2 + (3*a)^2 = h^2
a^2 + 9*a^2 = h^2
10*a^2 = h^2
now we can apply the square root to both sides and get:
√(10*a^2) = √h^2
(√10)*a = h
Then we have found the length of the hypotenuse in terms of the shorter side a.
Mathematical Statement Justification
4(x + 5) = 2x + 2 Given
4x + 20 = 2x + 2
2x + 20 = 2
2x = -18
x = -9
Fill in the missing justifications in the correct order.
Answer:
Look at the explanation
Step-by-step explanation:
after the second line (4x-2x) +20= 2
--------------
after the 3rd line
2x=2-20=-18
-------------------
after 4th line x=-18/2
-----------------------------------------------------------------------------
At the end
4(-9+5)=2(-9)+2
-36+20=-18+2
-16=-16 so it is right
Construct the described data set. The entries in the data set cannot all be the same. The median and the mode are the same. What is the definition of median? A. The value that lies in the middle of the data when the data set is ordered. B. The sum of the data entries divided by the number of entries. C. The data entry that occurs with the greatest frequency. D. The data entry that is far removed from the other entries in the data set.
Answer:
Option A
Step-by-step explanation:
The median is the value that lies in the middle of the data when the data set is ordered.
It is also the value that separates the higher half of the dataset from the lower half of the dataset.
Answer:
B
Step-by-step explanation:
Find the value of x in each case:
Answer:
angle FGE = 36
angle GEL = 72
and angle GFH = 144
Step-by-step explanation:
well you know that angle GEF = 180 -2x
and that angle GFE = 180 -4x
so all the angles in triangle GEF must add to 180
so you have 180 = 180 -2x + 180 -4x + x
180 = 360 -5x
5x = 180
x = 36
so angle FGE = 36
angle GEL = 72
and angle GFH = 144
Describe the translation that maps the preimage to the image.
Answer:
the solution is A
Step-by-step explanation:
(x,y)==> (x-8, y)
(6-8, 4)==> (-2, 4)
At the city museum, child admission is $6.20 and adult admission is $9.50. On Friday, tickets were sold for a total sales of $1082.00. How many child tickets were sold that day?
Answer:
98child tickets were sold that day
Step by step Explanation:
Let the number of children= A of the number of adult
Then
6.20C + 9.50A = 1082.0
From the question it was said that four times as many adult tickets as child tickets were sold which implies that number of adult was FOUR times the children, then we can say
A= 4C
Then substitute into the above equation
6.20C + 9.50A = 1082.0
6.20C + 9.50(4C) = 1082.0
6.20C + 38C= 1082.0
44.2C =1082.0
C= 24.48
But we know that
A= 4C
A=4* 24.48
A= 97.9
Therefore ,98child tickets were sold that day
CaC(s) + H2O(l) > Ca(OH)2(s): triangle H = -65.2kJ
Answer:
Answer: 1) 155.65 kJ; 2) -59.0 kJ/mol; 3) a)
Step-by-step explanation:
Answer on Question # 55533 - Chemistry - General chemistry
Question:
1. Given the data. N2(g) + O2(g) = 2 NO(g) ΔH = +180.7 kJ; 2 NO(g) + O2(g) = 2 NO2(g) ΔH = −113.1
kJ; 2 N2O(g) = 2 N2(g) + O2(g) ΔH = − 163.2 kJ; Use Hess’s Law to calculate ΔH for the reaction
N2O(g) + NO2(g) = 3 NO(g); Show your work.
2. Calcium carbide (CaC2) reacts with water to form acetylene (C2H2) and Ca(OH)2. From the
following enthalpy of reaction data and data in Appendix C in textbook, calculate ΔHf° for CaC2(s):
CaC2(s) + 2 H2O(l) Ca(OH)2(s) + C2H2 (g) ΔH = −127.2kJ
3. Using average bond enthalpies, predict which of the following reactions will be most
exothermic: a) C(g) + 2 F2(g) CF4(g) b) CO(g) +3 F2(g) CF4(g) + OF2(g) c) CO2(g) + 4 F2(g) CF4(g) +
2 OF2(g)
Solution
1)
N2(g) + O2(g) = 2 NO(g) ΔH1 = +180.7 kJ x(+2)
2 NO(g) + O2(g) = 2 NO2(g) ΔH2 = −113.1 kJ x(-1)
2 N2O(g) = 2 N2(g) + O2(g) ΔH3 = − 163.2 kJ x(+1)
2N2O(g) + 2NO2(g) = 6 NO(g) ΔH = (ΔH3 + 2ΔH1 – ΔH2)
N2O(g) + NO2(g) = 3 NO(g) ΔH = (ΔH3 + 2ΔH1 – ΔH2)/2 = 155.65 kJ
2)
CaC2(s) + 2 H2O(l) = Ca(OH)2(s) + C2H2 (g) ΔHrxn = −127.2kJ
ΔHrxn = ΔHf°(C2H2) + ΔHf°(Ca(OH)2) - 2ΔHf°(H2O) - ΔHf°(CaC2);
ΔHf°(CaC2) = ΔHf°(C2H2) + ΔHf°(Ca(OH)2) - 2ΔHf°(H2O) – ΔHrxn
ΔHf°(C2H2) = 227.4 kJ/mol
ΔHf°(Ca(OH)2) = -985.2 kJ/mol
ΔHf°(H2O) = -285.8 kJ/mol
ΔHf°(CaC2) =227.4 - 985.2 + 2x285.8 + 127.2 = -59.0 kJ/mol
3)
a) C(g) + 2 F2(g) = CF4(g)
b) CO(g) +3 F2(g) = CF4(g) + OF2(g)
c) CO2(g) + 4 F2(g) = CF4(g) + 2 OF2(g)
C-F bond enthalpy 440 kJ/mol
C=O bond enthalpy in carbon dioxide 805 kJ/mol
C=O bond enthalpy in carbon monoxide 1077 kJ/mol
O-F bond enthalpy 184 kJ/mol
F-F bond enthalpy 153 kJ/mol
a) ΔHrxn = 2x153 - 4x440 = -1454 kJ – the most exothermic
b) ΔHrxn = 1077 + 3x152 - 2x184 - 4x440 = -595 kJ
c) ΔHrxn =805x2 + 4x153 - 4x440 – 2x2x184 = -274 kJ
if f(x)=kx^3-1 and f^-1 (15)= 2, find k
Answer:
k = 2
Step-by-step explanation:
Okay, the first thing we need to do here is find the inverse of the equation given.
f(x) = kx^3 -1
Let f(x) = m
m = kx^3 -1
m + 1 = kx^3
(m+1)/k = x^3
x = 3x√(m+1)/k
Thus, the inverse is;
f^-1(x) = 3x√(x + 1)/k
now let’s make the substitution for f^-1(15)
2 = 3x√(15+1)/k
2 = 3x√(16/k
Cube both sides
2^3 = 16/k
8 = 16/k
8k = 16
k = 16/8 = 2
3. Two-thirds of a number plus 4 is 76. What is the number?
Answer:
108
Step-by-step explanation:
2/3x+4=76
2/3x=72
x=72*3/2
x=108
Answer:
Do the opposite of what they say
76 - 4 = 72
72 / 2/3 = 72 x 3 / 2 = 216 / 2 = 108
108 is the number
now to double check
108 x 2/3 = 216 / 3 = 72
72 + 4 = 76
108 is the number
Hope this helps
Step-by-step explanation:
Find the volume of the prism
Answer:
152.4
Step-by-step explanation: