Two shapes are shown below, one isosceles triangle and one rectangle. The dimensions can be represented by algebraic expressions, as shown in the diagram below. They both have the same area. Find the numerical value of the perimeter of the isosceles triangle. show full calculations please
Answers
Answer:
Perimeter of Isosceles Triangle = 16 units
Step-by-step explanation:
Area of rectangle is given by the formula;
Area = 1/2 × base × height
From the diagram, base = 6x - 6 and height = 6x - 8
Thus,Area = 1/2 × (6x - 6) × (6x - 8)
Area = (3x - 3)(6x - 8) = 18x² - 42x + 24
Secondly, area of rectangle is given by;
Area = length x breadth
So, area of rectangle in question = (6x - 9)(3x - 2) = 18x² - 39x + 18
We are told both the area of the triangle and the rectangle are the same, so let's equate both areas;
18x² - 42x + 24 = 18x² - 39x + 18
18x² will cancel out and rearranging, we have;
24 - 18 = 42x - 39x
6 = 3x
x = 6/3
x = 2
Plugging 2 for x for the height and base of the triangle, we have;
base = 6(2) - 6 and height = 6(2) - 8
Base = 6 and height = 4
So,let's find the slant height of the isosceles triangle.
Dividing the base by 2,we have; 6/2 = 3
So,using Pythagoras theorem, let the slant height be h, so we have;
h² = 3² + 4²
h² = 9 + 16
h² = 25
h = √25
h = 5
2 slant sides of isosceles triangle are the same. So perimeter = 5 + 5 + 6 = 16 units
Related Questions
The side of one square is equal to 3m and its diagonal is equal to the side of a second square. Find the diagonal of the second square.
Answers
Answer:
6m
Step-by-step explanation:
the side of first square = 3 m
area of first square = 3^2= 9 m^2
let the side of second square = x m
since diagonal of first square = x m as per the question
in a square each angle is 90 degree
therefore by applying pythagorus theorem ,
diagonal ^2 = side^2 + side ^2
diagonal^2 = 3^2+3^2=9+9
DIAGONAL= square root of 18
diagonal= 3[tex]\sqrt{2}[/tex] m = side of second square
therefore in second square ,
one angle is 90 degree , therefore by applying pythagorue theorem
diaqonal^2 = side ^2 + side ^2 = (3[tex]\sqrt{2}[/tex])^2 + ( 3[tex]\sqrt{2}[/tex])^2
diagonal ^2 = 18 + 18
diagonal = square root of 36
therefore diagonal of second square is 6m
hope it helps you... please mark me as the brainliest..
Answer:
6m explained it all hope it helps
Sadie's Road Paving Company used 750 tons of cement to pave 4 miles of roadway. How much cement, on average, did the company use per mile? Write your answer as a decimal.
Answers
Answer: 187.5 tons of cement
Step-by-step explanation:
From the question, Sadie's Road Paving Company used 750 tons of cement to pave 4 miles of roadway. To calculate the number of cement on average that the company use per mile, we divide 750 tons of cement by 4 miles. This will be:
= 750 tons of cement/4
= 187.5 tons of cement
The company used 187.5 tons of cement per mile.
Answer: The company used 187.5 tons per mile.
Step-by-step explanation:
Hi, to answer this question we simply have to divide the amount of cement used (750 tons) by the miles that the company pavemented (4 miles):
Mathematically speaking:
750 t / 4 m = 187.5 tons per mile
The company used 187.5 tons per mile.
Feel free to ask for more if needed or if you did not understand something.
A patient was
given
medicine. She took 5 ml of
medicine 3 times in one day. How much medicine did
she take in total that day?
Answers
In the diagram below, P and Q are points on a circle with centre O.
PQT is a tangent to the circle.
Angle OPQ=18∘
Work out the size of angle PQT.
Answers
Answer:
∠PQT = 72°Step-by-step explanation:
According to the diagram shown, ∠OPQ = ∠OQP = 18°. If PQT is a tangent to the circle, it can be inferred that line OQ is perpendicular to line QT. Ths shows that ∠OQT = 90°.
Also from the diagram, ∠OQP + ∠PQT = ∠OQT;
∠PQT = ∠OQT - ∠OQP
Given ∠OQP = 18° and ∠OQT = 90°
∠PQT = 90°-18°
∠PQT = 72°
The smallest of three consecutive odd is numbers is n. If their sum is 27,find the three numbers
Answers
Answer:
Therefore the sum of three odd numbers is always an odd number. Hence Proved. Let the number is 15,13 and 3 then 15=2*7+1 13=2*6+1 3=2*1+1 where 1,6 and 7 now 15+13+3=2*7+1+2*6+1+281+11 =2(7+6+1)+3 =2*14+3(24 is our 'm') and 2*14≠30. OR 15+13+3≠30
Step-by-step explanation:
The question is that you cannot get 30 by adding any three odd numbers because addition of 3 odd numbers always give another odd number and hence 30 which is an even number cannot be achieved. 2n-1 where n is a natural number.
Find the interquartile range (IQR) of the data in the dot plot below. cavities
Answers
Answer:
It is 4 cavities
Step-by-step explanation:
The interquartile range (IQR) of the data in the dot plot is 4
Calculating interquartile rangeFrom the question, we are to determine the interquartile range (IQR) of the data
From the diagram, we can produce the data set
0, 0, 0, 1, 1, 3, 3, 4, 7, 7
Now, we will determine the interquartile range of this data set.
The interquartile range is the difference in value between the upper quartile and lower quartile.
The upper quartile (Q3), is the value under which 75% of data points are found when arranged in increasing order.
The lower quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order.
∴ IQR = Q3 - Q1
From the data set
0, 0, 0, 1, 1, 3, 3, 4, 7, 7
Upper quartile (Q3) = 4
and
Lower quartile (Q1) = 0
∴ Interquartile range (IQR) = 4 - 0
IQR = 4
Hence, the interquartile range (IQR) of the data in the dot plot is 4
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On a road trip you see a sign “350 km to Indianapolis”. About how many hours will it take you to drive to Indianapolis if you are traveling at 72 mi/h (1 mile\approx≈1.61 km). Round your answer to the nearest hundredth.
Answers
Answer:
3.019 hours.
Step-by-step explanation:
In this case they ask us to calculate the time in hours that are in those distances, for this we have the speed and the distance, we know that speed is equal to:
v = d / t
therefore the time would be:
t = d / t
we must pass the distance that is in kilometers to miles, like this:
350 km * 1 mile / 1.61 km = 217.4 mi
Now if replacing:
t = 217.4 / 72 = 3.019
Therefore, the time would be 3.019 hours.
Find the 98th term of the arithmetic sequence 8, 24, 40,...
Answers
Answer:
Step-by-step explanation:
AP = 8, 24 , 40....
a = 8 , d =16 , n =98 , An = ?
an= a +(n-1)d
an = 8+97*16
an=8+1552
an=1560
hope it helps you..
The 98th term of the arithmetic sequence ( 8, 24, 40, . . . ) is 1560 ( One thousand five hundred and sixty ).
What is an arithmetic sequence?An arithmetic sequence is simply a sequence of numbers in which the difference between the consecutive terms is constant.
The nth term is an arithmetic sequence is expressed as;
aₙ = a₁ + ( n - 1 )d
Where aₙ is the nth term, a₁ is the first term in the sequence and d is the the common difference between terms.
Given the data in the question;
n = 98a₁ = 8d = 24 - 8 or 40 - 24 = 1698th term of the arithmetic sequence a₉₈ = ?We substitute our given values into the expression above.
aₙ = a₁ + ( n - 1 )d
a₉₈ = 8 + ( 98 - 1 )16
a₉₈ = 8 + ( 97 )16
a₉₈ = 8 + 1552
a₉₈ = 1560
Therefore, the 98th term of the arithmetic sequence ( 8, 24, 40, . . . ) is 1560 ( One thousand five hundred and sixty ).
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Dos hermanos juntaron su dinero para comprar un regalo a su papa entre los dos reunieron 864 que cantidad aporto cada uno si paco dio 5 pesos por cada 7 que dio juan
Answers
Answer:
Paco contributed = 360pesos
Juan contributed = 504pesos
Question:
Two brothers gathered their money to buy a gift for their dad. Between them they gathered 864, which amount each contributed if Paco gave 5 pesos for every 7 that Juan gave.
Step-by-step explanation:
Let the common factor between each brother = p
Paco gave = 5×common factor = 5p
Juan gave = 7×common factor = 7p
Total money contributed by both brothers = 864
Total money contributed by both brothers = 5p + 7p
5p + 7p = 864
12p = 864
p = 864/12
p = 72
Paco contributed = 5p = 5×72 = 360pesos
Juan contributed = 7p = 7×72 = 504pesos
Find two positive consecutive odd integers whose products is 99.
Answers
Answer:
9,11
Step-by-step explanation:
let the numbers be x, x+2 (since consecutive odd integers have a difference of 2)
therefore;
x(x+2)= 99
x²+2x=99
I usually solve the sum like this,
we need to find the nearest square number ( number smaller than the number on the R.H.S)
here, it is 81, whose square root is 9. therefore the solution is 9
verification:
(9)²+2*9=99
81+18=99
99=99
hence, 9 is the solution. therefore the positive odd consecutive integers are
x=9
x+2=9+2= 11
verification:
9*11=99
99=99
L.H.S=R.H.S
A teacher Buys tickets for each of my students to visit a museum each student and $6.50 and she spent a total of $182 how many students tickets did you buy
Answers
Answer:
The ticket is bought for 28 students.
Step-by-step explanation:
It is given that the teacher is going to buy museum ticket for each students.
Total money spent = $182
Price of each ticket = $6.50
Let total number of tickets bought = [tex]x[/tex]
We know that to find the total amount of money spent on ticket, we can add price of each ticket (i.e. $6.50) [tex]x[/tex] number of times.
OR
In other words, simply multiply the number of tickets with price of each ticket to find the total money spent.
Total money spent = [tex]x \times 6.50[/tex]
We know that total money spent is $182.
[tex]\Rightarrow x \times 6.50 = 182\\\Rightarrow x = \dfrac{182}{6.50}\\\Rightarrow x = 28[/tex]
The ticket is bought for 28 students
5x+7/2=3/2x-14 please help me with this
Answers
Answer:
x = 5
Step-by-step explanation:
5x + 7/2 = 3/2x - 14
like terms together;
5x - 3/2x = -14 - 7/2
7/2x = 35/2
divide both sides by the reciprocal of the fraction next to the unknown
divide by 2/7
x = 5
Triangle DEF is reflected over the y-axis, and then translated
down 4 units and right 3 units. Which congruency statement
describes the figures?
O ADEF – ASUR
O ADEF - ASRU
O ADEF - ARSU
O ADEF – ARUS
Answers
Answer:
B. ΔDEF ≅ ΔSRU
Step-by-step explanation:
Hope this helps!
The congruence statement is [tex]\triangle D EF \cong \triangle SRU[/tex]
The pre-image of the triangle is triangle DEF.
When reflected over the y-axis, and then translated down 4 units and right 3 units, the image of the triangle is SRU
Translation and reflection are rigid transformations.
Hence, the congruence statement is [tex]\triangle D EF \cong \triangle SRU[/tex]
Read more about transformation at:
https://brainly.com/question/4289712
What is the measure of
Answers
Answer:
B= 55°
Step-by-step explanation:
A+B+C= 180°
90°+B+35°=180°
B= 55°
Please answer CORRECTLY !!!!!! Will mark Brainliest !!!!!!!!!!!!!!!!
Answers
Answer:
4 amperes
Step-by-step explanation:
I graphed the function on the graph below to find the maximum value of c.
As an estimation we are told 5 miles is 8 km.
Convert 72 km to miles.
Answers
Answer:
45 miles
Step-by-step explanation:
5 miles = 8 km
72 km = 9 * 8 km
Since 8 km = 5 miles, replace 8 km with 5 miles
72 km = 9 * 8 km = 9 * 5 miles = 45 miles
Describe the graph the inequality on a number line: -7 ≥ g - 21 I need help on this its due today and ill give large sum of points for anybody to help me. I don't understand
Answers
Answer:
Step-by-step explanation:
Jonathan collects postcards and stamps. The number of postcards in his collection is 12 more than the number of stamps. He has 39 postcards in all. If Jonathan has x stamps, which equation represents this situation and how many stamps does he have?
Answers
x = 39 - 12
x = 27 (this is the number of stamps he collected)
The measure of an angle is 159
degrees.
What is the measure of its
supplementary angle?
Answers
Answer:
21°
Step-by-step explanation:
Supplementary is defined as two angles whose sum is 180. These angles must therefore be on a straight line cut by a transversal and must be less than 180 by themselves.
If one angle is 159, then we can simply subtract it from 180 to get the other angle.
A more algebraic way is to set up the equation, 159 + x = 180. Subtract 159 from 180 to find x.
The Measure of supplementary angle is 21⁰.
What are supplementary angle?The pair of angles that always add up to 180 degrees are referred to as supplementary angles. The term "supplements of each other" refers to these two angles. The Latin words "Supplere" and "Plere" are the source of the word "supplementary." "Supplere" means "supply," while "Plere" means "fill." Thus, "something when supplied to complete a thing" is the definition of "supplementary."
Given an angle 159⁰
and according to supplementary angles property,
when sum of two angles is 180⁰ are supplementary
∠A + ∠B = 180⁰ (angles are supplementary)
Let the another angle be x
159 + x = 180
x = 180 - 159
x = 21⁰
Hence the supplementary angle is 21⁰.
Learn more about supplementary angle;
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How many minutes are in 130 seconds?
Answers
Answer:
2 minutes 10 seconds!!!!!
Look at these equations.
9 = 7 + a
a + 8 = b + 5
Use both equations to work out the value of b.
Answers
Answer:
9=7+a....................equation 1
a+8=b+5................equation 2
equation 1
9=7+a
9-7=a
2=a
a=2
put equation 1 into equation 2
2+8=b+5
10= b+5
10-5= b
5=b
b=5
meaning value of b=5
The value of b is 5 for the given equations 9 = 7 + a and a + 8 = b+5.
What is substitution method?
The substitution method is the algebraic method to solve simultaneous linear equations. In this method, the value of one variable from one equation is substituted in the other equation.
According to the given question we have , two equations
[tex]9 = 7+a...(i)[/tex]
and [tex]a + 8 = b + 5...(ii)[/tex]
From equation (i)
9 = 7 + a
⇒ a = 9 -7
⇒ a = 2
Substitute the value of a in equation (ii)
⇒ 2 + 8 = b + 5
⇒ 10 = b + 5
⇒ b = 10 -5
⇒ b = 5
Hence, the value of b is 5 for the given equations 9 = 7 + a and a + 8 = b+5.
Learn more about substitution method here:
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what is the inverse of the statement “if i like art class, then i like painting” ?
Answers
Answer:
If I do not like art class, then I do not like painting.
Step-by-step explanation:
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Step-by-step explanation:
If an^2 =b then in terms of a and b , n=?
Answers
Answer:
√b/a
Step-by-step explanation:
an^2 =bn^2=b/an=√b/aAnswer:
n = ± [tex]\sqrt{\frac{b}{a} }[/tex]
Step-by-step explanation:
Given
an² = b ( divide both sides by a )
n² = [tex]\frac{b}{a}[/tex] ( take the square root of both sides )
n = ± [tex]\sqrt{\frac{b}{a} }[/tex]
Solve for r.
–5 ≥ 5 (r+5)
Answers
Answer:
-6 ≥ r
Step-by-step explanation:
–5 ≥ 5 (r+5)
Divide each side by 5
–5/5 ≥ 5/5 (r+5)
–1 ≥ (r+5)
Subtract 5 from each side
-1-5 ≥ r+5-5
-6 ≥ r
Please help me find the area
Answers
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Find the area of the big rectangle first:
14 x 11 = 154
Fine the area of the small rectangle:
5 x 3 = 15
Use πr^2
π(4)^2 = 16π
Divide this by 4 as it is only a quarter of the circle:
16π / 4 = 4π
Add all the values together:
4π + 154 + 15 = 181.5663709
Round this off as needed.
To 2 d.p. it is 181.57 in^2
Have A Nice Day ❤
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- Ally ✧
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An expression is given: x(-1.8-6y) Use the distributive property to expand the expression.
Answers
Answer: x(-1.8-6y) = -1.8*x -6*y*x
Step-by-step explanation:
The distributive property says that if we have:
A*(B + C) where A, B and C can be any numbers, we can expand the equation as:
A*(B + C) = A*B + A*C.
So, in this case, we have the equation:
x*(-1.8 - 6y)
so we can expand this as:
x*(-1.8 - 6y) = x*(-1.8) + x*(-6*y) = -1.8*x -6*y*x
How many different combinations of three books can be selected from 40 books?
Answers
Answer:
1600
Step-by-step explanation:
40x40
How many distinct diagonals does an undecagon have?
-39
-45
-47
-44
-None of these answers are correct.
Answers
Answer:
-45
Step-by-step explanation:
Is 20, 101, and 99 a Pythagorean triple
Answers
Answer:
yes
Step-by-step explanation:
Using the Pythagorean Theorem, we should get 20² + 99² = 101² and we need to check if this is a true statement.
400 + 9801 = 10201
10201 = 10201 so yes, it is.
someone please help, this is my last question!
Answers
Answer:
9.5
Step-by-step explanation:
