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In the following diagram, BC is parallel to DE.
What is the measure of Zx?
Angles are not necessarily drawn to scale.
B
D
F
54°
105°
A
E
And please explain how I get the answer pls
Answers
The value of Angle DAF, x is 21°
Given,
Line BC parallel to line DE
The value of Angle ABC = 54°
The value of Angle BAC = 105°
We have to find the value of angle DAF
Here,
Angle DAF = x
Now,
Angle ABC = Angle DAB (Alternate interior angles)
So,
Angle DAB = 54°
Then,
Angle DAF, x = 180 - (105 + 54) (Linear pair of angles)
Linear Pair of Angles;
When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.
That is,
Angle DAF, x = 180 - 159
Angle DAF, x = 21°
Therefore,
The value of Angle DAF, x is 21°
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Related Questions
(12x)^1/2 in radical form
Answers
Answer: [tex]\sqrt{12x}[/tex]
Step-by-step explanation:
Fahima buys
2 packets of bread rolls costing £1.50 for each packet
1 bottle of ketchup costing £1.60
3 packets of sausages
Fahima pays with a £10 note
she gets 30p change
fahmia works out that one packet of sausages costs £2.30
is fahima right?
you must show how you get you answer
Answers
y= 3x + a / 2x -5
express x in terms of a and y
Answers
The equation y = 3x +a / 2x - 5 can be expressed in terms of a and y as x = (a - 5y) / (2y-3)
Given equation y = 3x + a / 2x - 5
= y(2x - 5) = 3x + a
= 2xy - 5y = 3x + a
= 2xy - 3x = a - 5y
= x(2y-3) = a - 5y
Hence, x = (a - 5y) / (2y - 3)
First, we will move the denominator 2x-5 and multiply it by y giving us 2xy-5y. Next, we will move all the terms which contain only a and y to one side and the rest remaining to another side, giving us 2xy - 3x = a - 5y. Since we need to express the equation in terms of x we take it as common from left-hand side of the equation and the remaining part we move to the right-hand side as the denominator. Hence we get our equation in terms of a and y as x = (a - 5y) / (2y - 3).
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A carpet installer measures three rectangular bedrooms for new carpeting how much carpet is needed for the three bedrooms bedroom a 3.1 m x 3.1 m bedroom be 2.9 m x 3.2 m bedroom c2.5 m x 3.4 m
Answers
The 27.4 m² of carpet is needed for three bedrooms.
Firstly we will calculate the area of each room.
Area of bedroom a = 3.1 × 3.1
Area of bedroom a = 9.61 m²
Area of bedroom b = 2.9 × 3.2
Performing multiplication on Right Hand Side of the equation
Area of bedroom b = 9.29 m²
Area of bedroom c = 2.5 × 3.4
Area of bedroom c = 8.5 m²
Total area of all the rooms = 9.61 + 9.29 + 8.5
Performing addition on Right Hand Side of the equation
Total area of all the rooms = 27.4 m²
Hence, 27.4 m² carpet is required for three bedrooms.
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i need help like immediately
1/4 (8x+4)=2x-4
Answers
Answer: the statement is false
Step-by-step explanation:
So the left side equals 2x+1
The multiply by the reciprocal (2x+1)*(2x-1)
(2x+1)*(2x-1) = 2x-4
Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Select three options.
y = –Two-fifthsx – 2
2x + 5y = −10
2x − 5y = −10
y + 4 = –Two-fifths(x – 5)
y – 4 = Five-halves(x + 5)
Answers
The equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4) is y = (-2/5)x + 2
The given equation of the line is
5x - 2y = -6
Ax + By = C1
Bx - Ay = C2
are perpendicular.
Then the perpendicular to the line 5x - 2y = -6 is 2x + 5y = C2
We have to find the value of C2
The line is passing through the point (5, -4)
Substitute the values in the equation and find the value of C2
2(5) + 5(-4) = C2
C2 = 10 -20
= -10
The equation will be 2x + 5y = -10
Rearrange the terms and make it slope intercept form
2x + 5y = -10
5y = -10 -2x
5y = -2x - 10
y = (-2/5)x - 2
Hence, equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4) is y = (-2/5)x + 2
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A shopkeeper buys a dress for 40$ she sells it for 48$
Workout the percentage increase in the price of the dress.
Please help now
Answers
b According to estimates, there are over 300 million people living in the Unite
States. How many Neyland Stadiums would it take to hold 300 million people
Answers
Answer:
it would take 3,000 neyland stadiums to take 300milion people is rounded i hope this helps
Step-by-step explanation:
Tyler bought a bowling ball for $80. Sales tax is 7%. What is the total cost of the bowling ball?
Answers
Answer:
Step-by-step explanation:
first multiply
80* 7% you can also do it as 80* (7/100)
=5.6
then,
add 80 and the ans of 80* (7/100)
80+5.6= 85.6
John climbs a cliff that is 128 feet high in 16 minutes. What is his average rate of ascent?
Answers
The answer is : 8 ft min
I took the test
A school had 1 200 students last year and only 1 080 students this year.
What was the percent decrease in the number of students?
Answers
Answer:The percentage decrease in the number of students is -10%.
Given that,
The school has 1,200 students last year.
And, this year it is 1,080.
Based on the above information, the calculation is as follows:
Therefore we can conclude that the percentage decrease in the number of students is -10%.
Step-by-step explanation: noice
need halp with the ques answer pls
Answers
The value of A rounded to the nearest hundredth is 0 and the value of A rounded to the nearest tenth is 10
From the given number line
The value of A = 7.51
The number line is defined as the straight line that consist of integers in equal intervals. We can also says that the number line is the pictorial representation of numbers on a horizontal line.
The rounding of a number is defined as a number is make it simple by keeping its value intact but closer to the next number. The closer to tenth, hundredth, thousand etc.
The value of A = 7.51
Rounding the rounder to nearest tenth = 10
Rounding the number to nearest hundredth = 0
Hence, the value of A rounded to the nearest hundredth is 0 and the value of A rounded to the nearest tenth is 10.
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One-third of a number decreased by six equals eight. What is the number?
Answers
Answer:
42
Step-by-step explanation:
6+8=14x3=42
42/3=14-6=8
Solve for the value of v.
123°
(2v+1)°
Answers
Step-by-step explanation:
the angles between 2 intersecting lines must be the same on both sides of either line, they are just left-right mirrored.
so,
123 = 2v + 1
2v = 122
v = 61
solve for the variable in 7/26=25/x
Answers
Answer:
x = 650/7
Step-by-step explanation:
7/26 = 25/x
7*x = 25*26
7x = 650
x = 650/7
Check:
7/26 = 25/(650/7)
7/26 = 25*7/650
7/26 = 175/65
7*650 = 26*175 = 4550
Y+2=1/4 x in standard form
Answers
Answer:
-[tex]\frac{1}{4}x[/tex] + y = -2
Step-by-step explanation:
Standard form: Ax + By = C
y + 2 = [tex]\frac{1}{4} x[/tex]
Rearrange terms:
1. Subtract 2 from both sides
y = [tex]\frac{1}{4} x[/tex] - 2
2. Subtract [tex]\frac{1}{4} x[/tex] from both sides
-[tex]\frac{1}{4}x[/tex] + y = -2
state: how heavy a load (in pounds) is needed to pull apart pieces of douglas fir 4 inches long and 1.5 inches square? data from students doing a laboratory exercise are given.
Answers
The range of the confidence interval for the mean load needed to separate the wood is (29,485.192 , 32,114.8).
Define confidence interval.In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. The size of a 90% confidence interval for a given estimate is one way to gauge how "excellent" it is; the greater the interval, the more care must be used when utilizing the estimate. Confidence intervals serve as a crucial reminder of the estimates' limits.
Given,
Data set: (33190, 31860, 32590, 26520, 33280, 32320, 33020, 32030, 30460, 32700, 23040, 30930, 32720, 33650, 32340, 24050, 30170, 28730, 31920)
The normal distribution's standard deviation, s = 3000 pounds
95% confidence interval
N = 20 observations were made.
Mean = 30,800
Margin of error :
z₇ × √3000².20
±1.314.8079
Confidence interval
= Mean + Margin of error
= 30,800 ±1.314.8079
= 29,485.192 , 32,114.8
The range of the confidence interval for the mean load needed to separate the wood is (29,485.192 , 32,114.8).
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According to a report for veterinarians in the united states, 36. 5 percent of households in the united states own dogs and 30. 4 percent of households in the united states own cats. If one household in the united states is selected at random, what is the probability that the selected household will own a dog or a cat?.
Answers
solve the inequality 2b + 5 <_ 30
Answers
The solution of the inequality 2b + 5 ≤ 30 is b ≤ 12.5
What are inequalities?Inequalities refers to some type of equations where the relationship between the left hand side and the right hand side of an equation is expressed in terms of symbols other than equal to
The symbols include
less thangreater thanless than or equal to greater than or equal toIn the problem given the symbol used is less than or equal to and the equation is solved by
2b + 5 ≤ 30
2b + 5 - 5 ≤ 30 - 5
2b ≤ 25
dividing through by 2
2b / 2 ≤ 30 / 2
b ≤ 12.5
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Consider the line y=-3/4x-9.
Find the equation of the line that is perpendicular to this line and passes through the point (-4, 2).
Find the equation of the line that is parallel to this line and passes through the point (-4, 2).
Equation of perpendicular line:
Equation of parallel line:
Answers
Answer:
Equation of Perpendicular Line: 4x-3y=22
Equation of parallel line:3x+4y+4=
A store manager instructs some new trainees that a barbecue grill priced at $700 winds up costing a customer $714 once the sales tax is included. What is the sales tax percentage?
Write your answer using a percent sign (%).
Answers
Answer:
0.02 or 2%
Step-by-step explanation:
$700(x)=$714
$700(0.02)=14
700+14=714
Please help !!! I don’t understand 25 points !
Answers
Answer: Triangle VUT:
84:70:42
Triangle RSQ:
30:25:15
Final simplified answer: 2.8:2.8:2.8
Scale factor of 2.8
Step-by-step explanation:
Each triangle's sides are a part of the ratio, then you divide each side by the corresponding one (84 by 30, and 70 by 25) to get your scale factor.
which multiplication table have 8 and 50
Answers
Answer:2
Step-by-step explanation:
2*4=8
2*25=50
a cashier cannot tell the difference between cilantro and parsley. customers would only buy either cilantro or parsley. he knows that 20% of his customers prefer parsley. these customers will buy parsley 40% of the time when shopping. otherwise, they wouldn't buy either herb. 40% of his customers prefer cilantro and will buy cilantro 15% of the time when shopping. otherwise, they wouldn't buy either herb. the other 40% of his customers don't prefer, and thus don't buy, either herb. given the next customer buys one of the two herbs, what is the probability it is parsley?
Answers
Probability that customer buy parsley given buy any of two herb
= 0.5714
What is probability in math?
Probability refers to potential. The subject of this area of mathematics is the occurrence of random events.The range of the value is 0 to 1. To forecast how likely events are to occur, probability has been introduced in mathematics.Parsley ( 0.4 , 0.6 )
buy = B ∩ P = 0.08
Don't buy = DB ∩ P = 0.12
Cilantro = ( 0.15 , 0.85 )
buy = B ∩ C = 0.06
Don't buy = DB ∩ C = 0.34
Don't buy anything = DB = 0.4
P( Buy anything ) = P(B∩P) + P( B ∩ C )
= 0.08 + 0.06 = 0.14
Now, P( P/B) = P( P ∩ B)/P(B)
= 0.08/0.14 = 4/7 = 0.5714
Hence, probability that customer buy parsley given buy any of two herb
= 0.5714
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Line ℓ has equation y=
–
x+5. Find the distance between ℓ and the point G(6,4).
Answers
Answer:
2.5√2 units
Step-by-step explanation:
The shortest distance between a point and a line is the length of the line segment perpendicular to the line and passes through the given point.
~~~~~~~~~~~~~~~~~~~~~
y = - x + 5 , slope m = - 1
Slope of perpendicular line is opposite reciprocal. In our case is 1 .
G ( 6 , 4 )
y - 4 = 1 × ( x - 6 )
y = x - 2
x - 2 = - x + 5 , x = 3.5
y = 1.5
Perpendicular line intersect the given line at the point O ( 3.5 , 1.5 )
OG = [tex]\sqrt{(6-3.5)^2 +(4-1.5)^2 }[/tex] = 2.5√2 units
Logan just became a personal trainer and is finalizing his pricing plans. One plan is to charge $18 for the initial consultation and then $88 per session. Another plan is to charge $39 for the consultation and $87 per session. Logan realizes that the two plans have the same cost for a certain number of sessions. What is that cost? How many sessions is that?
Answers
Answer: The 2 Plan will have same cost of $2149 after 64 sessions.
Let the Two plan be Plan A and Plan B.
Also let the number of session be
According to given detail
Plan A =
Plan B =
We need to find the value of when both are equal.
Plan A = Plan B
=
Solving above equation we get;
Number of session are 64.
Cost after 64 session will be,
Plan A =
Plan B =
Hence The 2 Plan will have same cost of $2149 after 64 sessions.
Step-by-step explanation:
it was 5 degrees above zero in the morning. By afternoon the temperature rose 27 degrees. How warm was it?
Answers
It was 33 degrees warm in the afternoon
How to determine how warm it was?From the question, we have the following parameters that can be used in our computation:
In the morning = 5 degrees above zero
Afternoon = Rise of 27 degrees
The degree of warmth in the afternoon is then calculated as
Degree of warmth = Temperature In the morning + Rise of the temperature
Substitute the known values in the above equation, so, we have the following representation
Degree of warmth = 5 + 27
Evaluate the sum
Degree of warmth = 33
Hence, the temperature is 33 degrees
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1 trillion = 1,000 billion
There are about 40 trillion cells in the human body.
Each cell consists of about 100 trillion atoms.
About how many atoms are there in the human body altogether?
Give your answer in standard form.
Answers
The number of atoms in standard form is 4 × 10²⁵ atoms
What is standard form?Standard form is number written in the form a × 10ⁿ where 1 ≤ a < 10 and n is an integer
How to find how many atoms are there in the human body altogether in standard form?Since there are about 40 trillion cells in the human body. and each cell consists of about 100 trillion atoms, we have that
40 trillion cells = 40 trillion × 1 cell
Also, 1 cell = 100 trillion atoms.
So, 40 trillion × 1 cell = 40 trillion × 100 trillion atoms.
Now, we know that 1 trillion = 1000 billion
So, Number of atoms = 40 trillion × 100 trillion atoms
= 40 × trillion × 100 × 1 trillion atoms.
= 40 × 1000 billion × 100 × 1000 billion atoms.
= 40 × 1000 × 100 × 1000 × 1 billion × 1 billion atoms.
We know that 1 billion = 1000000000
So,
= 40 × 1000 × 100 × 1000 × 1 billion × 1 billion atoms.
= 40 × 1000 × 100 × 1000 × 1000000000 × 1000000000 atoms
= 40000000000000000000000000
= 4 × 10000000000000000000000000
= 4 × 10²⁵ atoms
So, the number of atoms in standard form is 4 × 10²⁵ atoms
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What is the y-intercept for x^3+8x^2+11x-20? How many zeros are their in the graph?
Answers
Can you find the measure of the indicated angle and type the correct code? Please remember to type in ALL CAPS with no spaces,
Answers
Answer:
hey I need this answer and puzzle 4 and 5 you got these things?
Step-by-step explanation:
please
The measure of angles A, B , C and D°are 36°, 63°, 71° and 111° respectively
How to determine the measure of the indicated angle?
To find the measure of angles of A, B, C and D, you need to apply some of the angle geometry concepts as follows:
1. m<A
(x+24)° and A = 3x
Since alternate angles are equal, thus:
3x° = (x+24)°
3x -x = 24
2x = 24
x =24/2 = 12
Also, A = 3x = 3(12) = 36°
2. m<B
B = 10x-27 and 7x
Since corresponding angles are equal, thus:
10x -27 = 7x
10x -7x = 27
3x = 27
x = 27/3 = 9
Also, B = 10x -27 = 10(9) -27 = 90-27 = 63°
3. m<C
C = (5x+1)° and (6x-13)°
Since corresponding angles are equal, thus:
(5x+1)° = (6x-13)°
6x -5x = 13+1
x = 14
Also, C = 5x+1 = 5(14) + 1 = 70+1 = 71°
4. m<D
(6x+3)° and D = (4x+39)°
Since alternate angles are equal, thus:
6x+3 = 4x+39
6x-4x = 39-3
2x=36
x = 36/2 =18
Also, D = 4x+39 = 4(18) + 39 = 72+39 = 111°
Therefore, the m<A = 36°, m<B = 63°, m<C = 71° and m<D =111°. Since B, A, H and E correspond to m<A, m<B, m<C and m<D respectively, so type BAHE in the answer box
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