The perimeter of a triangle is 44cm. One side is 4cm shorter than the second side and twice as long as the third side. Find the length of each side of the triangle.
Answers
The 1st, 2nd, and 3rd sides of the triangle are 16, 20, and 8 respectively.
Given that the perimeter of the triangle is 44 cm.
Let us consider a side 's' which is 4 cm shorter than the second side.
That means the second side is 4 cm longer than s, hence the second side is s+4 cm in length.
We also have that the side of length s is of length twice as long as the third side.
Hence, the length of the third side is half that of s so, it is of length s/2.
Hence, at the end 44=s+(s+4)+(s/2)=s(2+1/2)+4
⇒ s(5/2)=40
⇒ s=8*2=16
So, the 1st, 2nd, and 3rd sides of the triangle are 16, 20, and 8 respectively.
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Related Questions
Suppose that the relation H is defined as follows.
H= = {(2, 7), (2, -1), (-8, -2)}
Give the domain and range of H.
Write your answers using set notation.
domain = = 0
range = 0
X
Answers
Answer:
Domain = {-8, 2}Range = {-2, -1, 7}Step-by-step explanation:
The domain is the set of x values, and the range is the set of y values.
please help me with math
Answers
The area of triangle BMN is 124.7 square centimeter.
What are similar triangles?Similar triangles are triangles that their corresponding angles are equal and the ratio of their corresponding lengths are equal. They are often similar When at least Two angles are equal or The ratio of any corresponding lengths are same.
Analysis:
AB = AC = BC = 50cm
AH = AC/2 = 50/2 = 25cm
From Δ ABH, using Pythagoras theorem to find BH.
[tex](BH)^{2}[/tex] = [tex](AB)^{2}[/tex] - [tex](AH)^{2}[/tex]
[tex](BH)^{2}[/tex] = [tex]50^{2}[/tex] - [tex]25^{2}[/tex]
[tex](BH)^{2}[/tex] = 2500 - 625
[tex](BH)^{2}[/tex] = 1875
BH = [tex]\sqrt{1875}[/tex] = 43.3cm
ΔBMN and BHC are similar,
so, BM/BH = MN/HC
BM/43.3 = 12/25
25BM = 12 X 43.3
BM = 519.6/25 = 20.78cm
Area of ΔBMN
= 1/2(MN)(BM) = 1/2 x 12 x 20.78 = 124.7 square centimeter
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Tiger Biscuits factory planing to produce 10,000 units in Month Standard time per 200 units is 8 hours! the Company pays. Rs. 40 per her.
Answers
The total cost or amount that Tiger Biscuits will pay will be Rs 16000.
How to calculate the cost?From the information given, the factory is planing to produce 10,000 units and the standard time per 200 units is 8 hours.
The time taken to produce 10000 units will be:
= (10000/200) × 8
= 400 hours.
The amount that the company will pay will be:
= 400 × Rs 40
= Rs 16000
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Jackrabbits are capable of reaching speeds up to 40 miles per hour. How fast is this in feet per second? (Round to the nearest whole number.)
Answers
Juan wants to change the shape of his vegetable garden from a square to a rectangle, but keep the same area so he can grow the same amount of vegetables. The rectangular garden will have a length that is 2 times the length of the square garden, and the width of the new garden will be 16 feet shorter than the old garden.
Answers
Answer:
The answer is 32
Step-by-step explanation:
Find the measure of the angles indicated
Answers
Both angles have a measure of 125°.
How to find the measure of the angles?
Assuming the two horizontal lines are parallel, we know that the measure of the two indicated angles must be the same one.
Then:
-1 + 14x = 12x + 17
Now we need to solve this for x:
14x - 12x = 17 + 1
2x = 18
x =18/2 = 9
Now that we know the value of x we can replace it in any of the expressions for the angles:
-1 + 14*9 = 125°
Both angles have a measure of 125°.
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What is the down payment for this vehicle: $37,850.00 at 7% down
Answers
Answer:
$2,649.50
Step-by-step explanation:
s
AB ≅ BC and AD ≅ CD
Triangles A B C and A D C share side A C. Line X is drawn from point B to point B to form 4 triangles.
What additional information would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem?
What additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem?
Answers
The additional information that would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem is that BD is perpendicular to AC.
How to illustrate the information?From the information, Triangles A B C and A D C share side A C. Line X is drawn from point B to point B to form 4 triangles.
In this case, the additional information that would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem is that BD is perpendicular to AC.
Also, the additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem is that AX and CX are congruent.
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Answer:
What additional information would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem?
✔ AC and BD are perpendicular.
What additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem?
✔ AX and CX are congruent.
Step-by-step explanation:
right on edge
linear slope help pls
Answers
A slope is also known as the gradient of a line. The slope of the given linear table is $250 per car.
What is Slope?A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
The slope of the linear table is,
m = ($4,000 - $2,500)/(12-6) = $250 per cars
Hence, the slope of the given linear table is $250 per car.
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The number y of objects a machine produces is proportional to the time x (in minutes) that the machine runs. The machine produces five objects in four minutes.
a. Write an equation that represents the situation.
Hellllppp me please!!!!!!!!!!!
Answers
The equation that represents the situation will be 4y = 5x.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The number y of objects a machine produces is proportional to the time x (in minutes) that the machine runs.
The machine produces five objects in four minutes.
Let y be the number of objects and x be the number of the minutes.
Then the equation that represents the situation will be
y = (5/4)x
4y = 5x
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In a class test containing 20 questions, 5 marks are given for every correct answers, ( -2 ) marks given for every incorrect answers and zero mark for question not attempted. Anju gets 9 correct answer and 11 incorrect answers. What is her total score?
Answers
Answer:
she has 23 points
Step-by-step explanation:
hope this helps and mark brainliest please
A student can pitch a fast ball at 65 miles per hour. Convert this
speed to yards per second.
O 95.33 yd/sec
O 132.95 yd/sec
O 31.77 yd/sec
O 21.67 yd/sec
Answers
Answer:
31.77 yd/sec
Step-by-step explanation:
Conversions:
1 mile = 1760 yards1 hour = 3600 secondsGiven:
[tex]\sf 65\:miles\:per\:hour=65\:miles/hour=\dfrac{65\:miles}{hour}[/tex]
Therefore, to convert 65 mph to yards per second:
[tex]\implies \sf \dfrac{65\:miles}{hour}=\dfrac{65 \times 1760\:yards}{3600\:seconds}=31.777...\:yd/s[/tex]
Answer:
c.) 31.77... yd/sec
Explanation:
Given: 1 hours → 65 miles
Conversions:
(i) 1 hour = 60 minutes = 3600 seconds
(ii) 1 miles = 1760 yards
Then,
1 hour = 3600 seconds65 miles = (1760 × 65) = 114400 yards Speed:⇒ distance/speed
⇒ 114400/3600
⇒ 31.77777...
⇒ 31.77 yd/sec
Please help me with this geometry question, Im pretty sure you need to use SAS congruence rule
Answers
Congruent triangles are two or more triangles with the same length of sides and measure of internal angles. Thus the required proof is as shown below:
From the given diagram, it can be observed that:
AB = AC (similar property of two lines)
AC = AE (similar property of two lines)
Also,
m<A is a common angle to ΔABC and ΔADE
So that it can be concluded that;
ΔABC ≅ ΔADE (Side-Angle-Side property)
Thus since ΔABC ≅ ΔADE are congruent, then;
BC = DE (corresponding sides of congruent triangles)
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See below for the proof that sides BC and DE are congruent
How to prove the side lengths?The given parameters are:
AC = AE
AB = AD
∠BAD = ∠EAC
By the definition of congruence, side lengths marked with I are congruent and side lengths marked with II are congruent
From the attached figure, we have the following marks:
In triangle ABC,
AB = I and AC = II
In triangle ADE,
AD = I and AE = II
This means that two corresponding sides of ABC and ADE are congruent.
Since both triangles have a congruent angle, then the last corresponding sides are also congruent
i.e. BC = DE
Hence, sides BC and DE are congruent
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What is the solution (a, b) to this system of linear equations? 3a 6b=45 2a-2b=-12 (-27, 6) (-1, 7) (1, 7) (27, -6)
Answers
The solution of the system of linear equation are (1, 7)
How to solve system of equation?3a + 6b = 45
2a - 2b = -12
multiply equation(ii) by 3
Therefore,
3a + 6b = 45
6a - 6b = -36
9a = 9
a = 1
Hence,
2(1) - 2b = -12
2 - 2b = -12
-2b = -12 - 2
- 2b = - 14
b = -14 / -2
b = 7
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5. Try It #5
If f(x) is a linear function, with f(2)=-11, and f(4)=-25, find an equation for the function in slope-intercept form.
Answers
The function in slope-intercept form is mathematically given as
f(x)=14x+154
What is an equation for the function in slope-intercept form.?
Parameters
f(2)=-11,
f(4)=-25
Generally, the equation for the slope is mathematically given as
[tex]m=\frac{-25+11}{2-}[/tex]
m=7
In conclusion, the line equation
y-2=7(x-+11)
y as subject
y=14x+154
f(x)=14x+154
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Five little girls taken in couples weigh 129 pounds, 125 pounds, 124 pounds, 123 pounds, 122 pounds, 121 pounds, 120 pound, 118 pounds, 116 pounds and 114 pounds on a weighing machine. What was the weight of each one of the five little girls if taken separately
Answers
The weight of each one of the five little girls if taken separately is 242.4 lb.
Weight of each girl when taken separatelyThe weight of each girl can be determined from the average weight of the girls.
Weight of each girl = (Total weight) / number of girls
W = (129 + 125 + 124 + 123 + 122 + 121 + 120 + 118 + 116 + 114)/5
W = 1,212/5
W = 242.4 lb
Thus, the weight of each one of the five little girls if taken separately is 242.4.
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I need help to find the justification for this problem!
Answers
The tangents that exists between the two given circles are not common tangents because they are not of the same size or circumference.
What is a tangent?A tangent can be defined as the plane line that touches a curved surface such as a circle but doesn't pass through the circle.
From the diagram given, the two circles are not of the same size, that is, they have different circumstances. This means that the point where the line meets the both circles are not the same.
Therefore, the tangents that exists between the two given circles are not common tangents.
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Prove that the triangles formed due to the diagonal of rectangle are congruent to one another
Answers
A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle.The triangles formed due to the diagonal of the rectangle are congruent to one another.
What is a rectangle?A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
For the given rectangle ABCD, the length of the diagonals AC and BD can be written as,
AC = √(x² + y²)
BD = √(x² + y²)
Now, the triangles formed due to the diagonals AC and BD are ΔABC and ΔBCD. Also, for ΔABC and ΔBCD we can write,
∠ABC = ∠BCD = 90°
AB = CD = x {Oppsite sides of the rectangle are equal}
BC = AD = y {Oppsite sides of the rectangle are equal}
Hence, the two triangles are equal. Therefore, the triangles formed due to the diagonal of the rectangle are congruent to one another.
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Did the population of Town C increase by at least 100 percent from the year 2000 to the year 2010 ? The population of Town C in 2000 was of the population in 2005. The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.
Answers
Yes, the population of Town C increased by at least 100 percent from the year 2000 to the year 2010
Statement 1: The population of Town C in 2000 was 2/3 of the population in 2005
This tells us the population change from 2000 to 2005 since we need to know the population change from 2000 to 2010, this statement is not sufficient.
Statement 2: The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.
Since statement 2 provides no information about the population change from 2000 to 2005, there is no to answer this question with certainty. thus, statement 2 is not sufficient
Statement 1 and Statement 2 combined:
Let X= the population in 2000
Let Y= the population in 2005
Let Z= the population in 2010
From statement 1, we can write: X=[tex]\frac{2}{3}[/tex]Y
Multiply both sides by 3 to get [tex]3X=2Y[/tex]
Divide both sides by 2 to get [tex]\frac{3}{2}X=Y[/tex]
=>[tex]Y=1.5X[/tex]
As per statement 2, let's first determine the increase in the number of people from 2000 to 2005
If [tex]Y=1.5X[/tex], we know
X= the population in 2000
1.5X= the population in 2005
[tex]1.5X-X=0.5X[/tex]
So, the population increased [tex]0.5X[/tex] from 2000 to 2005
So, from 2005 to 2010, the population increased at least 0.5X
1.5X= the population in 2005
[tex]1.5X+0.5X=2.0X[/tex]
So, the population in 2010 was at least 2.0X
In other words, the population at least doubled from 2000 to 2010
So, the answer to the target question is yes, the population of Town C increased by at least 100 percent from the year 2000 to the year 2010
Did the population of Town C increase by at least 100 percent from the year 2000 to the year 2010?
(1) The population of Town C in 2000 was 2/3 of the population in 2005.
(2) The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.
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Carissa pays $2.10 each day for lunch. her money is in an account that is deducted each time she buys a lunch. there are 6 days until the end of the school year and her account has $12.75 in it. how much money will she get back at the end of the year?
Answers
Answer:
15¢
Step-by-step explanation:
$12.75 - 6 × $2.10 = $12.75 - $12.60 = $0.15
Answer: 15 cents
HELP ASAP!!!
REASONS ONLY
Given: ABCD is a parallelogram, FC is congruent to EC, DE bisects BC and BF bisects DC Prove: ABCD is a rhombus
Answers
The above question is a mathematical proof of the relationship between Lines and angles related to a Rhombus. See the proof below.
What is a Rhombus?A Rhombus is a parallelogram with four sides (that is a quadrilateral). It's sides however are all of equal length.
What is the above proof?∠DEC ≅ ∠BFC Reason = All Right Angles with Equal dimensions are congruent.∠C ≅ ∠C Reason = It is the same angle for the two Right angles above which are congruent, hence Reflexive Property.Δ DEC ≅ Δ BFC Reason = Angle Angle Side. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.[tex]\overline {DC}[/tex] ≅ [tex]\overline {BC}[/tex] Reason = The corresponding parts of congruent triangles are congruent. Also, it is a parallelogram with all congruent sides.ABCD is a Rhombus Reason = Its sides are all congruent.Learn more about Rhombus at;
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What is the range of Y = l0g8X?
O all real numbers less than 0
O all real numbers greater than 0
O all real numbers not equal to 0
all real numbers
Answers
Step-by-step explanation:
all real numbers not equal to 0
all real numbers
Step-by-step explanation:
[tex]What \ is\ the \ range \ of \ y = log_8x?\\x > 0 \ or\ x\in(0;\infty).\\Answer: \ all \ real \ numbers \ greater\ than \ 0.[/tex]
Using a table of values, determine the solution to the equation below to the nearest fourth of a unit.
2-5x=2x - 3
=
OA. X 0.75
OB. x= -0.75
OC. x 1.25
OD. x= -1.25
2
Answers
The solution to the equation below to the nearest fourth of a unit is 0.75
Solving linear equationGiven the linear equation below expressed as:
2-5x=2x - 3
Collect the like terms
-5x - 2x = -3- 2
-7x = -5
Divide both sides by -7 to have:
-7x/-7 = -5/-7
x = 5/7
x = 0.75
Hence the solution to the equation below to the nearest fourth of a unit is 0.75
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Hassan wants to ride his bicycle 26.8 miles this week. He has already ridden 6 miles.
If he rides for 4 more days, what is the average number of miles he would have to ride
each day to meet his goal?
Answers
AnsTHE OTHER GUY GOT IT RIGHT SORRY I DID THE MATH WRONG :( Step-by-step explanation:
Answer:
5.2 miles
Step-by-step explanation:
Distance left to ride = 26.8miles - 6 miles = 20.8 miles
There are 4 days left, so on average,
Hassan has to ride:
[tex] \frac{20.8}{4} \\ = 5.2mi[/tex]
Given: 4x + 5 = −6x + 5
Prove: x = 0 using two column proof
Answers
1) [tex]4x+5=-6x+5[/tex] (given)
2) [tex]4x=-6x[/tex] (subtraction property of equality)
3) [tex]10x=0[/tex] (addition property of equality)
4) [tex]x=0[/tex] (division property of equality)
-8√147x simplify do you know how to answer this?
Answers
Answer:
-56√3x
Step-by-step explanation:
√147 = 7√3
-8(7√3x)
-56√3x
The train will take 1h, then the bus will take and a half hours. i need to allow half an hour to change between them. how long will the whole journey take?
Answers
Total time for whole journey would be 3 hours.
The total trip is divided into three intervals :-
Travelling by trainTravelling by busTime taken to change between themHence to find the total time of the trip we need time taken in each interval and just add them up.
The final expression would be :-
Total time taken = Time taken by bus + Time taken by train +
Time taken to change between them
Given:-
Time taken by bus = 1.5 hrsTime taken by train = 1 hrsTime taken to change between them = 0.5 hrsThus Total time for whole journey would be 3 hours.
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A recipe calls for 11 tablespoons of sugar and 22 teaspoons of salt. How many
teaspoons of salt are needed for just one tablespoon of sugar?
On the double number line below, fill in the given values, then use multiplication or
division to find the missing value:
Answers
It will require 2 tablespoons of salt for just 1 tablespoon of sugar for the combination.
What are word problems?Word problems are a systematic approach used in mathematics for solving real-life cases by determining unknown values.
From the given information:
If it takes 11 tablespoon + 22 teaspoon to make 1 recipe.i.e.
11 tablespoon of sugar + 22 teaspoon of salt = 1 recipe
Then it will require 2 tablespoons of salt for just 1 tablespoon of sugar.
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Which best explains whether a triangle with side lengths 2 in., 5 in., and 4 in. is an acute triangle?
The triangle is acute because 22 + 52 > 42.
The triangle is acute because 2 + 4 > 5.
The triangle is not acute because 22 + 42 < 52.
The triangle is not acute because 22 < 42 + 52.
Answers
Answer:
The triangle is not acute because 2² + 4² < 5².
Step-by-step explanation:
Answer:
The triangle is not acute because 2² + 4² < 5²
Step-by-step explanation:
got it correct on my quiz
Given: AD∥BC and AB∥CD
Prove: AD≅BC and AB≅CD
Answers
Answer:
BC || AD and AB || CD (given)
∠BCA ≅ ∠DAC 2. As alt.interior angles with parallel lines
∠BAC ≅ ∠DCA 3. As alt.interior angles with parallel lines
AC ≅ AC (identity)
△ABC ≅ △CDA (ASA)
AB = CD (CPCT C)