Answers
Given:
A figure.
To find:
The value of x and y.
Solution:
In triangle ADC, all angles are equal, so it is an equilateral triangle.
We know that, all sides of an equilateral triangle are equal.
[tex]AD=AC[/tex] ...(i)
[tex]3x-5=5y-4[/tex] ...(ii)
In triangle ABD,
[tex]\angle BAD=\angle ABD[/tex]
Base angles are equal, so triangle ABD is an isosceles triangle.
[tex]AD=BD[/tex] ...(iii)
Using (i) and (iii), we get
[tex]AC=BD[/tex]
[tex]5y-4=y+12[/tex]
[tex]5y-y=4+12[/tex]
[tex]4y=16[/tex]
Divide both sides by 4.
[tex]y=4[/tex]
Putting y=4 in (ii), we get
[tex]3x-5=5(4)-4[/tex]
[tex]3x-5=20-4[/tex]
[tex]3x-5=16[/tex]
Adding 5 on both sides, we get
[tex]3x=16+5[/tex]
[tex]3x=21[/tex]
Divide both sides by 3.
[tex]x=7/tex]
Therefore, the value of x is 7 and the value of y is 4.
Related Questions
Solve the following inequality algebraically.
x + 2 < 11
Answers
Answer:
x < 9
Step-by-step explanation:
Subtract 2 from both sides so you can isolate the variable on the left.
help please btw last part of d it is 6
Answers
Answer:
Ans is C
Step-by-step explanation:
Answer: the answer is b!
Step-by-step explanation: Hope this helps! Merry Christmas!
Mark takes out a $238,000 mortgage for 30 years. Instead of paying his monthly payment of $1,220.09, he decided to pay $1,420.09. This leads to Mark paying off the entire mortgage in 22 years and 5 months. Mark calculates the percent of the total loan he pays back in interest with and without the extra payments. What is the difference between Mark's calculated percentages?
Answers
Answer:
24.04%
Step-by-step explanation:
Given that:
Mortgage = $238,000
Number of years = 30
Monthly payment without extra payment= $1220.09
Monthly payment with extra payment = $1420.09
Total amount paid :
Number of months * monthly payment
12 months = 1year
30 years = (30 * 12) = 360 months (without extra payment)
22 years 5 months = (22 * 12) + 5 = 269 months (with extra payment)
Amount paid without extra payment :
$1220.09 * 360 = $439232.4
Percentage of total loan paid as interest :
((439232.4 - 238000) / 238000) * 100%
= 0.8455142 = 84.55%
Amount paid with extra payment :
$1420.09 * 269 = 382004.21
Percentage of total loan paid as interest :
((382004.21 - 238000) / 238000) * 100%
= 0.6050597 = 60.51%
Difference between percentages:
84.55% - 60.51% = 24.04%
What is the M.A.D for 5 10 15 20 25
Answers
Answer:
6
Step-by-step explanation:
Find mean
Find. Absolute deviation=[Xi-mean]
Find mean deviation
Which of the following is a perfect square ?
A. - 4
B. 1 over 4 over 19 (1/4/19)
C. 0.9
D. 100
Answers
Find the base angles of the figure below.
A.) 72°
B.) 108°
C.) 36°
D.) 54°
Answers
Answer:
36
Step-by-step explanation:
The angles of a triangle have a sum of 180 degrees. This is an isosceles triangle indicated by the red markers on sides ED and EF. This means that the sides and angles are congruent.
Subtract 108 from 180 and divide that by 2.
180-108 = 72
72/2 = 36
A computer that cost 1099 last year cost 9999 this year. What is the percent change in price rounded to the nearest tenth
1%
0.1%
9.1 %
10 %
Answers
Type into a calculator as 1098 • 0.1
if x= (4/5)^-2 divided by (1/4)^2,find the value of x^-1
Answers
Answer:
[tex]\displaystyle x^{-1}=\frac{1}{25}[/tex]
Step-by-step explanation:
We are given the value of x:
[tex]x= (4/5)^{-2}[/tex] divided by [tex](1/4)^2[/tex]
We need to find the reciprocal of x or:
[tex]\displaystyle x^{-1}=\frac{1}{x}=\frac{\frac{1}{4}^2}{\frac{4}{5}^{-2}}[/tex]
Operating:
[tex]\displaystyle x^{-1}=\frac{1}{4}^2*\frac{5}{4}^{-2}[/tex]
[tex]\displaystyle x^{-1}=\frac{1}{16}*\frac{16}{25}[/tex]
[tex]\mathbf{\displaystyle x^{-1}=\frac{1}{25}}[/tex]
What's the next number? 0 , 1/3 , 1/2 , 3/5 , 2/3
Answers
Answer:
The next number of the series 0, 1/3, 1/2, 3/5, and 2/3 is 5/7
Step-by-step explanation:
The given numbers are;
0, 1/3, 1/2, 3/5, and 2/3
The number sequence is formed adding [tex]\dfrac{1}{\left (\dfrac{n^2 + n}{2} \right ) }[/tex] to each (n - 1)th term to get the nth term number in the sequence, with the first term equal to 0, as follows;
For the 2nd term, the (n - 1)th term is 0, and n = 2, gives;
The
[tex]0 +\dfrac{1}{\left (\dfrac{2^2 + 2}{2} \right ) } = 0 + \dfrac{1}{3} = \dfrac{1}{3}[/tex]
For the 3rd term, the (n - 1)th term is 1/3, and n = 3, gives;
[tex]\dfrac{1}{3} +\dfrac{1}{\left (\dfrac{3^2 + 3}{2} \right ) } = \dfrac{1}{3} + \dfrac{1}{6} = \dfrac{1}{2}[/tex]
For the 4th term, the (n - 1)th term is 1/2, and n = 4, gives;
[tex]\dfrac{1}{2} +\dfrac{1}{\left (\dfrac{4^2 + 4}{2} \right ) } = \dfrac{1}{2} + \dfrac{1}{10} = \dfrac{3}{5}[/tex]
For the 5th term, the (n - 1)th term is 3/5, and n = 5, gives;
[tex]\dfrac{3}{5} +\dfrac{1}{\left (\dfrac{5^2 + 5}{2} \right ) } = \dfrac{3}{5} + \dfrac{1}{15} = \dfrac{2}{3}[/tex]
For the next or 6th term, the (n - 1)th term is 2/3, and n = 6, gives;
[tex]\dfrac{2}{3} +\dfrac{1}{\left (\dfrac{6^2 + 6}{2} \right ) } = \dfrac{2}{3} + \dfrac{1}{21} = \dfrac{15}{21} = \dfrac{5}{7}[/tex]
The next number of the series 0, 1/3, 1/2, 3/5, and 2/3 = 5/7.
Connor is driving on a long road trip. He currently has 9 gallons of gas in his car. Each hour that he drives, his car uses up 2 gallons of gas. How much gas would be in the tank after driving for 3 hours? How much gas would be left after t hours?
Answers
i think its 2 gallons
Write the expression as a single multiplication sentence without
parentheses.
11 × (15 + 5)
Answers
Answer:
11x20
Step-by-step explanation:
15=5 equals 20 so 11x20 is 220
Which of the following are the coordinates of a rectangle with a length of 4 units and a width of 3 units in the coordinate plane?
A- (−2, 1), (−2, −2), (2, 1), (2, −2)
B- (4, 3), (0, 3), (4, 7), (0, 7)
C- (1, −4), (−1, −4), (1, 0), (−1, 0)
D- (5, 6), (−3, 6), (5, 1), (−3, 1)
Answers
-2 and 2 are the x values of the coordinates which are 4 units apart, being 4 units in LENGTH
1 and -2 are 3 units apart and them being in the y part of the coordinate it’s 3 units wide
I have no idea how to do this
Solve 3 x < 6
Answers
Answer:
X < 2
If you need an explanation, feel free to leave a comment
Cheers! :)
Compare using >, <, or =,
64 ounces
4 pounds
Answers
Answer:
64 ounces = 4 pounds
Step-by-step explanation:
HELPPPPP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE IT IS URGENT!!
Answers
Answer:
15: B. 6
16. D. 12.5
17. B and D
Step-by-step explanation:
There are 30 students in the class and 270 apples. if the apples are divided equally among the students, how many does each student get?
Answers
Answer:
9
Step-by-step explanation:
270/30=9
1 pts
Identify the ordered pair (point) and the slope for the point-slope form Y-3 = 7(2 – 4).
[Type in integers only.]
Point:(
I
Slope:
« Previous
Next >
Answers
Point: (4,3)
Twenty seconds after a plane in the air show- dives, it is 300 feet from where it begin. At what rate is the plane diving
Answers
Answer:
15 feets per second
Step-by-step explanation:
Given that:
Distance traveled by plane = 300 feets
Time taken by plane to travel such distance = 20 seconds
Rate at which the plane is diving is obtained thus :
Distance / time
= 300 feets / 20 seconds
= 15 feets / second
Hence, the plane is diving at a rate of 15 feets per second.
I need not just the answer but the work written out
Answers
Answer:
A(3) = -6 + (3 - 1) (5)
-6 + (2)(5)
-6 + (10)
4
A(4) = -6 + (4 - 1) (5)
-6 + (3)(5)
-6 + 15
9
A(10) = -6 + (10 - 1) (5)
-6 + (9)(5)
-6 + 45
39
does this figure have symmetry?
A)
Yes, because if you fold it in half, both halves match up
b) No, because if you fold it in half, both halves do not match up.
c) No because if you rotate it 90 degrees, it does not carry onto itself.
D) Yes, because if you rotate it less than one full turn, the figure carries onto itself.
Answers
Hello! Can someone please help me with these 2 questions! thank you so much! (i’ll give brainlist)
Answers
Answer:
1) 4 2)1/5 X=10
Step-by-step explanation:
Small to large is a fraction
Large to small is a whole number
a A persen sold on article at a profit of 15% If he
sold it for Rs. 81 less, his loss would love been
12% Find the cost price of the article
Answers
Answer:
cost price (cp)=RS.300
Phoebe knit a hat for a friend. She started with 197 meters of yarn. When she finished, she had 8,200 centimeters of yarn left over. How much yarn did Phoebe use to knit the hat? Write your answer in centimeters.
Answers
Answer:
Phone used 11,500 centimeters of yarn
Step-by-step explanation:
So first we know that 1 meter is equivalent to of 100 centimeters
Now lets convert everything into centimeters
197*100=19700
And thats it
Now we know she started with 19700 centimeters of yarn and has 8200 centimeters left over.
We can make an equation
We can make “x” stand for amount of yarn used.
19700-x=8200
Minus x becuase thats how much she used and equal 8200 becuase Thats what was left over
Now use inver operations
-x=-11,500
Now divide - on both sides
x=11,500
She used 11,500 centimeters of yarn
Answer: 11,500 centimeters of yarn
Step-by-step explanation:
Find the unit price of each item, rounding answers to the nearest tenth of a cent. A) 4 lbs for $2.37 b) 15 lbs for $8.57 c) 25 lbs for $13.59 Which bag (4, 15, or 25) is the best deal?
Answers
Answer:
A. $0.59
B. $0.57
C. $0.54
The best deal is 25 lbs for $13.59
Step-by-step explanation:
A) 4 lbs for $2.37
Units price (price per lb) = $2.37 / 4
= $0.5925
Approximately $0.59
b) 15 lbs for $8.57
Price per lb = $8.57 / 15
= $0.5713
Approximately $0.57
c) 25 lbs for $13.59
Price per lb = $13.59 / 25
= $0.5436
Approximately $0.54
Which bag (4, 15, or 25) is the best deal?
The best deal is 25 lbs for $13.59
the perimeter of a triangle is 29cm. the three sides lengths (all measured in cm) of the triangle are 8, 12 and x. Write and solve an equation to find x.
Answers
Step-by-step explanation:
We have 8 + 12 + x = 29.
Solving, we get x + 20 = 29, x = 9.
Answer:
9 cm
Step-by-step explanation:
The perimeter of a polygon is the sum of the lengths of all the sides of the polygon.
If a polygon is a triangle, and its 3 sides have length a, b, and c, then the perimeter is the sum of a, b,, and c.
perimeter = a + b + c
Here, the perimeter = 29 cm
The lengths of the sides are a = 8 cm, b = 12 cm, c = x.
8 + 12 + x = 29
x + 20 = 29
x = 9
Answer: 9 cm
-4x+9-x<-3 can someone give me the answer olease
Answers
Answer:
Yes I will always help someone in need. Your answer is x= >12/5
Step-by-step explanation:
Add me and ask any question.Please give me Brainiest
A bakery made 360 cookies. Twenty percent of the cookies were chocolate chip. How many cookies were chocolate chip
Answers
Answer:
72
Step-by-step explanation:
To calculate how much 20% of 360 makes we multiply 360 with 20 then divide it with 100
360 × 20 ÷ 100 = 72
Item 18 Two times the greater of two consecutive integers is 9 less than three times the lesser integer. What are the integers? Item 18 Two times the greater of two consecutive integers is 9 less than three times the lesser integer. What are the integers?
Answers
Answer:
11 and 12
Step-by-step explanation:
Let the consecutive integers be x and x+1
The lesser integer = x
The greater integer = x+1
Two times the greater of two consecutive integers is expressed as;
2(x+1) = 2x+2.
9 less than three times the lesser integer is expressed as;
3x - 9
Equate both expression
2x+2 = 3x - 9
2x-3x = -9-2
-x = -11.
x = 11
The greater integer = x+1 = 11+1 = 12
Hence the integers are 11 and 12
Answer:
11 and 12
Step-by-step explanation:
credit:answer above me
In a theater, there are 20 seats in the first row. Each row has 3 more seats than the row
ahead of it. There are 35 rows in the theater.
a. Express the number of seats in the nth row of the theater in terms of n.
b. Use sigma notation to represent the number of seats in the theater.
Answers
Answer:
b. Use sigma notation to represent the number of seats in the theater.
Pls help me ill give brainliest.
Pls do all 3 to get brainliest
Answers
Answer:
5. 8(a-5)= -40
8a-40= -40
8a= -40+40
8a=0
a=0/8
a=0
option c is correct.
6. for d,
-1<d<1
I think the answer is option d , which is missing in the attachment.
the 4 question is missing.
so I am not able to answer that