Answer:
X=29°
Step-by-step explanation:
Since triangles ABC and DEC are congruent, Angle A = Angle D = 74°
Sum of all angles in a triangle is 180°
So, Angle A + Angle B + Angle C =180°
74°+2X+48°=180°
2X=180°-122°
2X=58°
X=29°
======================================================
Explanation:
When it comes to congruence statements like this, the order of the letters is important. This is so we pair up the letters properly.
ABC has A first, B second, C third
DEC has D first, E second, C third
So we have these pairings
A pairs with DB pairs with EC pairs with C (ie it pairs with itself)Which leads to
A = DB = EC = CDue to the fact that congruent triangles have congruent corresponding parts.
Since B = E and B = 2x, we can say that E = 2x by either substitution or the transitive property. Both effectively say the same thing.
---------------------------
Now focus on triangle CDE
The three angles we have are
C = 48D = 74E = 2xThose three angles add to 180. This is true for any triangle.
C+D+E = 180
48+74+2x = 180
122+2x = 180
2x = 180-122
2x = 58
2x = 58/2
x = 29
--------------------------------
Side note: since x = 29, this means angle B = 2x = 2*29 = 58, and this is the measure of angle E as well.
We can check the answer by doing C+D+E = 48+74+58 = 180. So we have confirmed the answer.
The perimeter of a triangular garden is 78 feet. Find the length of the three sides if the middle length side is 3 feet greater than twice the length of the smallest side, and the longest side is 3 feet less than 3 times the length of the smallest side.
Answer:
36, 29 and 13
Step-by-step explanation:
Let 'a' be the longest side.
Let 'b' be the middle side.
Let 'c' be the smallest side.
From the question given above,
The perimeter of a triangular garden is 78 feet. This can be written as:
Perimeter = a + b + c
78 = a + b + c ...... (1)
The middle length side is 3 feet greater than twice the length of the smallest side. This can be written as follow:
b = 2c + 3 ...... (2)
The longest side is 3 feet less than 3 times the length of the smallest side. This can be written as follow:
a = 3c – 3 ..... (3)
Summary:
78 = a + b + c ...... (1)
b = 2c + 3 ...... (2)
a = 3c – 3 ..... (3)
Substitute the value of a in equation
3 and the value of b in equation 2 into equation 1
78 = a + b + c
b = 2c + 3
a = 3c – 3
78 = (3c – 3) + (2c + 3) + c
78 = 3c – 3 + 2c + 3 + c
78 = 3c + 2c + c – 3 + 3
78 = 6c
Divide both side by 6
c = 78/6
c = 13
Substitute the value of c into equation 2 and 3 to obtain the value of b and a respectively
b = 2c + 3
c = 13
b = 2(13) + 3
b = 26 + 3
b = 29
a = 3c – 3
c = 13
a = 3(13) – 3
a = 39 – 3
a = 36
Therefore, the length of the three sides are: 36, 29 and 13
Write the inequality that best represents the relationship shown on this number line. Explain how you determined the inequality.
Answer:
x ≥ _
Step-by-step explanation:
I can't see the numbers, however the number under the closed dot would be the number to insert there. Leave x alone.
If John can drink 1 jug of water in 6 days and mary can drink one jug of water in 1w days how many days would it take them to drink it togethee
Answer:
1
Step-by-step explanation:
because mary can drink 1 jg in 7 days john can drink in six da7 if the drink it together itll go fatser
Help! Best answer will get brainiest
Answer:
x=20
Step-by-step explanation:
Complementary means =90 degrees, so with that being said, you need to write the equation as follows:
2x+10+x+20=90
Then add like terms:
3x+30=90
Subtract 30 from both sides (30 and 90)
3x=60
Divide both sides by 3
x=20
I hope this helps!!
Four types of hardware need to be distributed evenly
into boxes: 91 screws, 39 nuts, 39 bolts, and 143 nails.
How many boxes of hardware can be filled? How
many of each type of hardware will fill each box?
Answer:
I don't have an answer to this question but one tip is to try using GCF (greatest common factor)
it is a big help when I try to do math
All lines that are parallel to JC
OH MY GOD THEY JUST TOOK AWAY EVEN MORE HOW DO I REPORT ADMIN ABUSE
Answer:
oof i don't know if that's possible
maybe try emailing them
Step-by-step explanation:
Answer:
what?
Step-by-step explanation:
The sum of a lists of numbers is 624 and the mean is 52. How many numbers are in the set?
Answer:he sum of a lists of numbers is 624 and the mean is 52. How many numbers are in the set? Get the answers you need, now!
Step-by-step explanation:
Which statement describes the graph of this polynomial function?
f(x)= x4 + x3 - 2x2
Answer:
NOT c
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
The graph crosses the x-axis at x = 2 and x = –1 and touches the x-axis at x = 0.
The graph touches the x-axis at x = 2 and x = –1 and crosses the x-axis at x = 0.
The graph touches the x-axis at x = –2 and x = 1 and crosses the x-axis at x = 0.
I er uh need some assistance
Answer:
6
Step-by-step explanation:
16/2.5 = 6.4, but you have to round down because you cant chop a book into tenths, so 6
Yesterday, the temperature at noon was 8.7F. By midnight, the temperature had decreased by 20.6 degrees. What was the temperature at midnight
Answer:
-11.9 F
Step-by-step explanation:
While hiking, Sandra went up 120 meters. If Sandra started at 800 meters above sea
level, what is her elevation now?
The Answer:
If Sandra started at 800 meters and went up 120, the answer would be 920.
Step-by-step explanation:
First, simply add 800 meters, which is what she started with. Next, since she has gone up 120 meters since then, and the question is asking us what her elevation is NOW, you can add 800 + 120 to get 920. This question is solved by using addition.
Hope this helps!
Choose the correct correspondence.
B
U
т
6
8
A
1
2
3
4
D
7
5
7
R
C
S
A
2
3
4
A restaurant sells a coffee refill mug for $6.75. Each refill cost $.1.25. Last month, Keith spent $31.75 on a mug and the refills. How many refills did Keith purchase last month? Write and solve an equation to determine the number of refills, r, that Keith purchased.
Answer:
He purchase 20 times.
Step-by-step explanation:
1.25(r)+6.75
1.25(20)+6.75
25+6.75=$31.75
what is the answer? please
Answer:
cvvvvvvvvvvvvvvgfjgf
Step-by-step explanation:
cxvvvvvvvvvvvvvv
Imagine that your team has been assigned by a construction company to measure the dimensions of an empty lot in a subdivision. Briefly give examples of the 6 types/sources of errors described above and explain what you would do to minimize them.
Answer:
All explained below.
Step-by-step explanation:
The sources of errors are;
1) Instrumental Errors: This could be as a result of wrong calibration of equipment.
2) Observational Systematic errors: An example of this is parallax error while taking a reading.
3) Environmental random errors: In this type of error, a slight change in the temperature of humidity in the lot could possibly affect the accuracy of the measurement.
4) Observational random errors: This refers to errors gotten when the values are incorrectly read or incorrectly interpolated.
5) Environmental systematic errors: An example of this is that the current supplied to the instrument taking the reading may be low. Thus, this may affect effective reading.
6) Theoretical systematic errors: This could arise from over simplification of the experimental model. An example of this is that the experiment might require a totally frictionless surface which may not be achievable. And this will lead to wrong measurement.
Minimizing the errors:
1) Instrumental Errors can be minimized by ensuring proper calibration of equipment before use.
2)Observational Systematic errors can be minimized by ensuring readings are not taken at an angle.
3)Environmental random errors could be minimized by carrying out the experiment in a relatively good laboratory under fair weather conditions.
4)Observational random errors can be minimized by ensuring that the results from the readings are properly collated and the rightly interpolated as the case may be.
5)Environmental systematic errors can be minimized by ensuring stable power source to the instrument being used for the reading.
6)Theoretical systematic errors could be minimized by taking an average of at least 3 tests result to get a fair representation of the final result.
Hello please help willl give brainliest!
Answer:
It will take Wilson 50 minutes to paint this bookcase.
Step-by-step explanation:
40%=20 minutes
10%=5 minutes
100%=50 minutes
Hope this helped! :)
What set of transformations could be applied to rectangle ABCD to create A″B″C″D″?
'Rectangle formed by ordered pairs A at negative 4, 2, B at negative 4, 1, C at negative 1, 1, D at negative 1, 2. Second rectangle formed by ordered pairs A double prime at negative 4, negative 2, B double prime at negative 4, negative 1, C double prime at negative 1, negative 1, D double prime at negative 1, negative 2.
Reflected over the x‒axis and rotated 180°
Reflected over the y-axis and rotated 180°
Reflected over the x‒axis and rotated 90° counterclockwise
Reflected over the y-axis and rotated 90° counterclockwise
Answer:
B. Reflected over the y-axis and rotated 180°
Step-by-step explanation:
A(-4, 2) Reflected over the y-axis (x, y) → (-x, y) → A'(4, 2)
A'(4, 2) → rotated 180° (x, y) → (-x, -y) → A"(-4, -2)
The set of transformations that can be applied to ABCD, to create A″B″C″D″ is a reflection over the y-axis, followed by a rotation of 180°
What is composite transformation?"It is the production of the image of a figure through two or more transformation."
What is reflection?"It is a geometric transformation where all the points of an object are reflected on the line of reflection."
What is rotation?"It is a transformation in which the object is rotated about a fixed point."
For given question,
The rectangle ABCD is formed by ordered pairs A at (-4, 2) , B at (-4, 1), C at (-1, 1), D at (-1, 2)
The rectangle A″B″C″D″ is formed by ordered pairs A" at (-4, -2), B" at (-4, -1), C" at (-1, -1) , D" at (-1, -2)
We can observe that the coordinates of ABCD are of the form (-x, y) where x, and y, are positive numbers
The form of the ordered pair of the vertices of the A″B″C″D″ is (-x, -y)
The coordinates of the point (-x, y) after reflection over y-axis would be of the form (x, y)
And after rotation of 180° the coordinates would be (-x -y)
Therefore, the set of transformations that can be applied to ABCD, to create A″B″C″D″ is a reflection over the y-axis, followed by a rotation of 180°
Learn more about geometric transformations here:
brainly.com/question/15577335
#SPJ2
Х
Probability with discrete random variables
A furniture factory makes a 4-piece desk. Quality control at the factory has randomly sampled numerous desk
sets and determined the number of damaged pieces in each set.
The table below is a partially completed probability distribution for the random variable X, where X represents
the number of damaged pieces in a randomly selected desk set from this factory.
X
0
1
2
3
4
P(X) 0.75
0.14
0.07
0.03
?
What is the probability that a randomly selected desk set contains exactly 4 damaged pieces?
P ( X = 4) =
Show Calculator
Answer:
0.01
Step-by-step explanation:
On khan
X in the equation 4(x-2)-3=9.
Answer:
[tex]x=5[/tex]
Step-by-step explanation:
[tex]4\left(x-2\right)-3=9[/tex]
[tex]\mathrm{Add\:}3\mathrm{\:to\:both\:sides}[/tex]
[tex]4\left(x-2\right)-3+3=9+3[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]4\left(x-2\right)=12[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}4[/tex]
[tex]\frac{4\left(x-2\right)}{4}=\frac{12}{4}[/tex]
[tex]Simplify[/tex]
[tex]x-2=3[/tex]
[tex]\mathrm{Add\:}2\mathrm{\:to\:both\:sides}[/tex]
[tex]x-2+2=3+2[/tex]
[tex]Simplify[/tex]
[tex]x=5[/tex]
Use the diagram to answer the question. Fill in the blank for the letter given with the missing reason in the flow proof.
Please help me out :(
Answer:
a)M5=40º
b)M2=140º
c)M2 and M5 are supplementary angles
d)M2 and M5 are same side interior angles
e) A||B
Step-by-step explanation:
Remember that same side interior angles are the angles that are located on the same side of a straight line that cuts through two parallel lines, and these angles are supplementary, meaning that the sum of both of them will always be 180º. So by stating that M5 and M2 add up to 180º and they are on the same side of a straight line cutting through two straight lines we can prove that those two lines are parallel.
If m∠2 = 42 and m∠6 = 126, what is m∠4?
Answer:
D.) 138
Step-by-step explanation:
It cannot be the others because it is a big obtuse angle.
Answer:
D.) 138
Step-by-step explanation:
It cannot be the others because it is a big obtuse angle.
When dividing 8,164 by 78.5, what is the place value of the last digit in the quotient?
ones
Answer:
Ones
Step-by-step explanation:
The last digit will always be the ones place no matter what.
Answer:
ONES
Step-by-step explanation:
alfredo ha 3 coins in his pocket. the value of the coin is $0.31
what 3 coins are in his pocket?
Answer:
quarter, nickel, and a penny
Step-by-step explanation:
you need to add up to 31 but you can only use 3 coins so 25, 5, and 1 make 31.
75/1+15e^-0.4x=25 solve for x
Answer:
[tex]\frac{75}{1}+15e^-\cdot \:0.4x=25\quad :\quad x=-\frac{25}{3};\quad \ne \mathrm{True},\:e\ne \:0\quad \left(\mathrm{Decimal}:\quad x=-8.33333\dots \right)[/tex]
Step-by-step explanation:
[tex]\frac{75}{1}+15e^-\cdot \:0.4x=25[/tex]
[tex]\mathrm{Apply\:rule}\:\frac{a}{1}=a[/tex]
[tex]\frac{75}{1}=75[/tex]
[tex]75+15\cdot \:0.4e^-x=25[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:15\cdot \:0.4=6[/tex]
[tex]75+6e^-x=25[/tex]
[tex]\mathrm{Subtract\:}75\mathrm{\:from\:both\:sides}[/tex]
[tex]75+6e^-x-75=25-75[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]6e^-x=-50[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}6e^-;\quad \ne \mathrm{True}[/tex]
[tex]\frac{6e^-x}{6e^-}=\frac{-50}{6e^-};\quad \ne \mathrm{True}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]e^{ }x=-\frac{25}{3e^-};\quad \ne \mathrm{True}[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}e;\quad \ne \mathrm{True},\:e\ne \:0[/tex]
[tex]\frac{e^{ }x}{e}=\frac{-\frac{25}{3e^-}}{e};\quad \ne \mathrm{True},\:e\ne \:0[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]\frac{x}{e}=-\frac{25}{3e^1};\quad \ne \mathrm{True},\:e\ne \:0[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}e[/tex]
[tex]\frac{xe}{e}=\left(-\frac{25}{3e^1}\right)e;\quad \ne \mathrm{True},\:e\ne \:0[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x=-\frac{25}{3};\quad \ne \mathrm{True},\:e\ne \:0[/tex]
What is the equation of the axis of symmetry?
Easy please help
Answer:
[tex]-\frac{b}{2a}[/tex] is the equation for axis of symmetry.
Step-by-step explanation:
b is the second part of the quadratic equation and a is the first part.
For example, [tex]2x^{2} +6x + 4[/tex]
a is 2 and b is 6.
Plug in those values into the equation and then you get the axis of symmetry.
HELPPPPP MEEE PLEASESESESESESESES
1. Write an equation that represents the table.
Answer:
x=y-16
x=1 then y=44
x=2 y=28
x=3 y=12
x=3 y=-4
x=5 y=-20
the correct anserw is basalt promise me i even looked this up:)
Answer:
ok
Step-by-step explanation:
Answer:
Great job.
Step-by-step explanation:
Using the diagram to the right, which statement do you KNOW is true (E is between J and N)?
A JE = EN
B. JN = EJ - NU
C. JE-EN = JN D. JN + JE = EN
Answer:
5. Answer C is right for sure.
6. JN=JE+EN
Step-by-step explanation:
Find the explicit equation for the given sequence:
-21, -14, -7, 0, . . .
Answer:
7 mark above answer brilliant