Answer: Olivia is 12 years old.
Step-by-step explanation
Tyler = T
Olivia = O
T=8
O=T*2-4
O=8*2-4
O=16-4
O=12
a rectangular storage container without a lid is to have a volume of 10 m3. the length of its base is twice the width. material for the base costs $15 per square meter. material for the sides costs $9 per square meter. let w denote the width of the base.
The total cost is $245.31.
Given,
Volume = 10[tex]m^{3}[/tex]
Width = w
Length = 2w
Base area = Length x Width = [tex]2w^{2}[/tex]
Cost of base = $15
Cost of sides = $9
Since the volume is 10[tex]m^{3}[/tex],
Volume = Base Area x Height
Height = [tex]\frac{10}{2w^{2} }[/tex] = [tex]\frac{5}{w^{2} }[/tex]
Cost of making such a container:
Cost of base = [tex]2w^{2}[/tex] x 15 = $[tex]30w^{2}[/tex]
Cost of sides = [(2 x 2w x [tex]\frac{5}{w^{2} }[/tex]) + (2 x w x [tex]\frac{5}{w^{2} }[/tex])] x $9 = $[tex]\frac{270}{w}[/tex]
Overall Cost = Cost of Base + Cost of Sides
f(x) = [tex]30w^{2} + \frac{270}{w}[/tex] = [tex]30(w^{2} + \frac{9}{w})[/tex]
To get the minimum cost, we will have to find the derivative of f(x) and equate it to zero.
d(f(x))/dx = 0
[tex]2w - \frac{9}{w^{2} } = 0\\w^{3} = 4.5 \\w = 1.651m[/tex]
Putting the value of w in f(x),
f(x) = $245.31 (after calculations)
Therefore, the final answer is $245.31.
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Write y+4=2(x-7) in standard form
[tex] \Large{\boxed{\sf 2x - y = 18}} [/tex]
[tex] \\ [/tex]
Explanation:We will try to write the given linear equation in standard form.
[tex] \Large{\left[ \begin{array}{c c c} \underline{\tt Standard \ Form \ of \ a \ linear \ equation \text{:}} \\ ~ \\ \tt Ax + By = C \end{array} \right] } [/tex]
Where:
A is a positive integer. (A ≠ 0)B and C are integers. (B ≠ 0)[tex] \\ [/tex]
Given linear equation:
[tex] \sf y + 4 = 2(x - 7) [/tex]
[tex] \\ [/tex]
First, expand the right side of the equation:
[tex] \sf y + 4 = 2 \cdot x + 2 \cdot (-7) \\ \\ \sf y + 4 = 2x - 14 [/tex]
[tex] \\ [/tex]
Subtract 2x from both sides of the equation:
[tex] \sf y + 4 - 2x = 2x - 14 - 2x \\ \\ \sf -2x + y + 4 = -14 [/tex]
[tex] \\ [/tex]
Subtract 4 from both sides of the equation:
[tex] \sf -2x + y + 4 - 4 = -14 - 4 \\ \\ \sf -2x + y = -18 [/tex]
[tex] \\ [/tex]
Since the coefficient of x (-2) has to be positive, multiply both sides of the equation by -1:
[tex] \sf -1 \cdot (-2x + y) = -1 \cdot (-18) \\ \\ \sf -1 \cdot (-2x) + (-1) \cdot y = 18 \\ \\ \boxed{\boxed{\sf 2x - y = 18 }} [/tex]
[tex] \\ [/tex]
[tex] \hrulefill [/tex]
[tex] \\ [/tex]
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natalie is the creator of better brain, a new mindfulness app for teens. the app currently has 1,262 downloads, and natalie has set a goal of doubling the downloads every month. write an exponential equation in the form y
Answer:
1262(2)^x
Step-by-step explanation:
What is the domain of this function?
f(x) = ²x - 3| + 1 ?
Answer: A.
Step-by-step explanation:
Most of the function f(x) has a domain (- infinity, positive infinity), and the function in the picture is the same. So, the answer is A
(6)/(a^(2))+(5a^(-2))/(3^(-3))
Answer:
[tex]\frac{141}{a^{2} }[/tex]
Step-by-step explanation:
[tex]\frac{6}{a^{2} } + \frac{5a^{-2} }{3^{-3} }[/tex]
[tex]\frac{141}{a^{2} }[/tex]
Please help me respond these two questions!!
The score of the 60th percentile on the test is 84.
What is a percentile?The definition of percentile is the percentage that a certain percentage falls beneath. Ben is the fourth-tallest child in a group of 20 kids, whereas 80% of the kids are shorter than you.
Given:
58, 64, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96
Calculate the percentile of score 71 as shown below,
[tex]Percentile = n / N \times 100[/tex]
Here, n is the number of scores below the score of 60th percentile and N is the total number of scores,
60 = n / 15 × 100
n / 15 = 60 / 100
n = 0.6 × 15
n = 9
Thus, the 9th term = 84 is the score of the 60th percentile,
Therefore, the score of the 60th percentile on the test is 84.
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Find u•v where theta is the angle between u and v
Answer:
88√2 = 124.5 (nearest tenth)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Dot Product of two vectors}\\\\$a \cdot b=|a||b| \cos \theta$\\\\where:\\ \phantom{ww}$\bullet$ $|a|$ is the magnitude of vector a. \\ \phantom{ww}$\bullet$ $|b|$ is the magnitude of vector b. \\ \phantom{ww}$\bullet$ $\theta$ is the angle between $a$ and $b$. \\ \end{minipage}}[/tex]
Given:
[tex]|u| = 8[/tex][tex]|v| = 22[/tex][tex]\theta =\dfrac{\pi}{4}[/tex]Substitute the given values into the dot product formula:
[tex]\begin{aligned}\implies u \cdot v &=|u||v| \cos \theta\\\\&=8 \cdot 22 \cdot \cos \left(\dfrac{\pi}{4}\right)\\\\&=176 \cdot \dfrac{\sqrt{2}}{2}\right)\\\\&=88\sqrt{2}\\\\&=124.5\; \sf (nearest\;tenth)\end{aligned}[/tex]
Find the value of x. A B D E C i an irregular pentagon with parallel ide A B and C E. Angle A B D meaure 104 degree. Angle C E D meaure 28 degree. Angle B D E meaure x degree
Angle B D E measure 228 degrees in the irregular pentagon A B D E C.
Polygons that lack equal sides and angles are referred to as irregular polygons. Polygons that are irregular are not regular, in other words. Closed two-dimensional shapes known as polygons are created by connecting three or more line segments. Regular and irregular polygons are two different forms of polygons.
As we know, the Sum of the interior angles of an irregular polygon =
(n − 2) × 180°
{ 'n' = the number of sides of a polygon.}
As given, A B D E C is a pentagon, so
n= 5
The sum of interior angles=
3 X \180= 540
As AB and CE are parallel to each other:
angle BAC=y
angleECA= 180-y
=>the sum of interior angles:
104+x+28+180-y+y= 540
104+x+28+180=540
x+312=540
=> x=228
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the figure(figure 1) shows the acceleration graph for a particle that starts from rest at t = 0s.
a) The velocity of particle at t=2s is 5m/s
b) The velocity of particle at t=4s is 20m/s
To obtain the function of velocity from the graph we need to find the equation of accleration- time graph
so the equation of accleration is :
a= [tex]\frac{10-0}{4-0}[/tex]t
a= 5/2t
and we know that :
a= [tex]\frac{dv}{dt}[/tex]
=> dv= adt
=> dv= [tex]\frac{5}{2}[/tex] t dt
integrating both side we get:
v= [tex]\frac{5}{4}[/tex][tex]t^2[/tex] +c
where c is constant
it is given that at t=0s it starts from rest so
v=0 at t=0
=> 0 = 0+c
=>c=0
so v=[tex]\frac{5}{4}t^2[/tex] ---- (i)
a) as we have got the equation of velocity with respect to time
we have to find velocity at t=2s
putting t=2s we get
v = 5/4 *4
so velocity of particle at t=2s is 5m/s
b) as we have got the equation of velocity with respect to time
we have to find velocity at t=4s
putting t=4s we get
v = 5/4 *16
so velocity of particle at t=2s is 20m/s
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equation of simple straight line
Complete question:
the figure shows the acceleration graph for a particle given that particle starts from rest at t=0.
determine the velocity of partice at
a)2s
b)4s
Jayden’s family has completed 90% percent of the trip. They have traveled 75 miles. How far is the trip?
Answer:
[tex]83\frac{1}{3} miles[/tex]
Step-by-step explanation:
90/100=75/x
90x=100(75)
90x=7500
/90. /90
x=83 1/3 miles
Hopes this helps
In the figure to the right, AE + DC = 1 1/5 cm, AB = 1 3/4 cm, DE = 1 1/4 cm, and BC = 1 3/10 cm. Find the perimeter of the figure.
active attachment
The perimeter of the given composite figure is; 5¹/₂ cm
How to find the perimeter of the composite figure?
To get the perimeter of the given composite figure, what we will do is to dd up the given segment side lengths and we are given the following;
AE + DC = 1¹/₅ cm
AB = 1 ³/₄ cm
DE = 1 ¹/₄ cm
BC = 1 ³/₁₀ cm.
Thus, we can say that the Perimeter is;
Perimeter = AE + DE + DC + BC + AB
Perimeter = (AE + DC) + DE + BC + AB
= 1¹/₅ + 1 ¹/₄ + 1 ³/₁₀ + 1 ³/₄
= (1²/₁₀ + 1³/₁₀) +(1¹/₄ + 1³/₄)
= 2⁵/₁₀ + 3
= 5¹/₂ cm
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let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. find r'(1) and s'(4).
The value of r'(1) and s'(4) is 0 that can be interpreted with the help of the graph that is given in the question.
Derivative in mathematics, the rate of change of a characteristic with recognize to a variable. Derivatives are essential to the answer of troubles in calculus and differential equations. The essence of calculus is the by-product. The by-product is the immediately price of extrade of a characteristic with recognize to certainly considered one among its variables. This is equal to locating the slope of the tangent line to the characteristic at a point
[tex]r(x) = f(g(x))[/tex]therefore the derivative of r is given by [tex]r'(x) = f'g(x)\times g'(x)[/tex]
[tex]r'(1) = f'(g(1))\times g'(1)[/tex] from the graphs
r'(1) = f'4 \times g'1 = (5/4) \times(0) = 0
Similarly s'(1) = g'(f(1))\times f'(1) from the graphs
f(1)=1.5, f'(1)
=\dfrac{ (3-0)}{(0-2)}
= -3/2 , g'(3/2) = 0
s'(4) = g'(3/2) \times f'(4) = 0(-1.5) = 0
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Complete question:
let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. find r'(1) and s'(4).
The area of the square in the figure below is 16 square inches. Solve for "s", the length of one side. Explain
the solution.
▪️▪️▪️▪️
▪️▪️▪️▪️
▪️▪️▪️▪️
▪️▪️▪️▪️
Area = 16 in²
A=S²
A=16
s²=16
Answer:
4
Step-by-step explanation:
[tex]\sqrt{16}[/tex] = 4
The side lengths of the square is 4.
Area = Length times width
Area = 4 x 4
Are = 16
what is the entire surd for 8 root 2
what is the entire surd of 5 root 9
what is the entire surd of 6 root 5
what is the entire surd of 3 root 13
help its urgent!!
The entire surds are √128, √225,√180, √117 respectively
What is an entire surd?An entire surd is a surd in which the entire number is under the root sign.
Given here are 8√2,5√9,6√5,3√13
thus their entire roots are 8√2 =√2×64
= √128
again, 5√9 = √9×25
= √225
6√5=√5×36
= √180
Similarly 3√13= √117
Hence, the respective entire surds are √128, √225,√180, √117
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Pete was building a doghouse for his dog, Chip. He made the door 36 inches tall. The height of the door was twice the height of the window in the doghouse.
Write an equation to determine the height of the window.
36 = 2h
36 = 2 + h
36 = h − 2
36 equals h over 2
Answer:
36 = 2h
Step-by-step explanation:
Here h represents the heigh
We know that the height of the door was twice the height of the window so that the equation will be
36 = 2h
which of the following is a constant in a mathematical model? a) decision variable. b) parameter. c) objective function. d) constraint. e) none of the answer choices are correct.
Answer:
b). parameter
Step-by-step explanation:
A parameter is a fixed value in the model that is not a decision variable and is not changed during the optimization process. It is used to represent known quantities that are used in the model but are not being optimized. For example, in a linear programming model, the cost of a product may be represented by a parameter, as the cost is not a decision variable and is fixed.
the margin of error of a confidence interval is the error from biased sampling methods. t or f
False. The margin of error only accounts for sampling variability (the fact that my sample will be different that many other people's and therefore provide different statistics.
What are statistics and their various forms?Statistics is a technique for interpreting, analyzing, and summarizing data in mathematics. In light of these characteristics, the various statistical types are divided into: Statistics that are descriptive and inferential. We analyze and understand data based on how it is presented, such as through graphs, bar graphs, or tables.
What are the two primary statistical methods?Inferential statistics, which draws conclusions from information using statistical tests like the student's t-test, is one of the two main statistical methods used in data analysis. Descriptive statistics presents data using indices like mean and median.
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Wyatt' Ga Mileage
\text{Gallon (\(x\))}Gallon (x) \text{Mile (\(y\))}Mile (y)
55 153153
77 214. 2214. 2
1010 306306
1414 428. 4428. 4
How much farther can Camden' car travel on one gallon of ga than Wyatt' car?
Both automobiles' lines have the equation "y = 3x," and their respective gas mileage is 3 miles per gallon. Wyatt's automobile gets more miles per gallon of gas than Camden's vehicle does.
We must compute the mileage (the distance driven per gallon of fuel) for each automobile using the provided information to determine the difference between the ranges of travel for Camden's and Wyatt's vehicles.
We can determine the miles for Wyatt's automobile using the data points (5, 15) and (7, 21). The equation for the slope of the line connecting these two locations is
(y2 - y1) / (x2 - x1) = (21 - 15) / (7 - 5) = 6/2 = 3
"Y = mx + b" is the equation for the line connecting these two points, where m denotes the line's slope and b its y-intercept. We may determine the equation of the line by adding the values of m as well as the dimensions of one of the endpoints into this equation:
y = 3x + b
15 = 3(5) + b
15 = 15 + b
0 = b
"Y = 3x" is the equation for the line passing thru the points (5, 15) and (7, 21).
We can determine the miles for Camden's automobile using the data points (10, 30) and (14, 42). The equation for the slope of the line connecting these two locations is
(y2 - y1) / (x2 - x1) = (42 - 30) / (14 - 10) = 12/4 = 3
"Y = mx + b" is the equation for the line connecting these two points, where m denotes the line's slope and b its y-intercept. We may determine the equation of the line by incorporating the values of m as well as the dimensions of one of the endpoints into this equation:
y = 3x + b
30 = 3(10) + b
30 = 30 + b
0 = b
"Y = 3x" is the equation for the line passing through the points (10, 30) & (14, 42).
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The question is -
Computes the miles per gallon of your car via the miles traveled and the number of gallons used. Also, if you enter the cost per gallon and how many miles you drive a day, it will estimate your monthly and yearly gas expenses with data points (5, 15) and (7, 21).
sum of two numbers is -11/12 ,one of them is 9/2, find the other
pls answer fasttttttt!!!!
plssssssssssssssssssssssssssssss.
step by step
Answer:
- [tex]\frac{65}{12}[/tex]
Step-by-step explanation:
let the number to be found be n , then
n + [tex]\frac{9}{2}[/tex] = - [tex]\frac{11}{12}[/tex]
multiply through by 12 ( the LCM of 2 and 12 ) to clear rhe fractions
12n + 54 = - 11 ( subtract 54 from both sides )
12n = - 65 ( divide both sides by 12 )
n = - [tex]\frac{65}{12}[/tex]
Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D is bounded by y = 1 − x2 and y = 0; rho(x, y) = 7ky
The mass and center of mass of the lamina is [tex]\frac{8}{15} k, (0, \frac{4}{7} )[/tex]
The mass of a homogenous lamina is given by [tex]$m=\iint_R \delta(x, y) d A$[/tex]
We can rewrite the equation using the limits of integration as [tex]$$m=\int_a^b \int_c^d \delta(x, y) d y d x$,[/tex] where a ≤ x ≤ b and c ≤ y ≤ d.
The objective is to find the mass and center of mass of the lamina that occupies the region D.
From the given equations, we get the limits of integration as -1 ≤ x ≤ 1 and 0 ≤ x ≤ 1-[tex]x^{2}[/tex]. Substitute the known values in the equation.
[tex]$$\begin{aligned}& m=\int_{-1}^1 \int_0^{1-x^2} k y d y d x \\& =\int_{-1}^1 \frac{1}{2} k\left(1-x^2\right)^2 d x \\& =\frac{1}{2} k \int_{-1}^1\left(1+x^4-2 x^2\right) d x \\& =\frac{k}{2}\left[x+\frac{x^5}{5}-2 \frac{x^3}{3}\right]_{-1}^1 \\\\\end{aligned}$$[/tex]
[tex]& =\frac{k}{2}\left[1+\frac{1}{5}-\frac{2}{3}+1+\frac{1}{5}-\frac{2}{3}\right] \\\\& =\frac{k}{2}\left[\frac{16}{15}\right] \\\\& =\frac{8}{15} k[/tex]
Hence, the mass of the lamina as [tex]\frac{8}{15} k[/tex].
The center of mass of the lamina is given by[tex]$(\bar{x}, \bar{y})$[/tex], where [tex]$$\begin{gathered}\bar{x}=\frac{1}{m} \iint_R x \delta(x, y) d A \text { and } \\\bar{y}=\frac{1}{m} \iint_R y \delta(x, y) d A .\end{gathered}$$[/tex]
First, find [tex]$\bar{x}$[/tex] as follows:
[tex]$$\begin{aligned}\bar{x} & =\frac{1}{\frac{8}{15} \mathrm{k}} \int_{-1}^1 \int_0^{1-x^2} k x y d y d x \\& =\frac{1}{\frac{8}{15} \mathrm{k}} \int_{-1}^1 \frac{1}{2} k x\left(1-x^2\right)^2 d x \\= & \frac{15}{8 k} \cdot \frac{k}{2} \int_{-1}^1 x\left(1+x^4-2 x^2\right) d x \\= & \frac{15}{16}\left[\frac{x^2}{2}+\frac{x^6}{6}-2 \frac{x^4}{4}\right]_{-1}^1 \\= & 0\end{aligned}$$[/tex]
Thus, the [tex]$\bar{x}$[/tex]-coordinate of the center of gravity as 0 .
Now, evaluate [tex]$\bar{y}$[/tex].
[tex]& \bar{y}=\frac{1}{\frac{8}{15}} \int_{-1}^1 \int_0^{1-x^2} k y^2 d y d x \\\\& =\frac{1}{\frac{8}{15}} \int_{-1}^1 \frac{1}{3} k\left(1-x^2\right)^3 d x \\\\& =\frac{15}{8 k} \cdot \frac{k}{3} \int_{-1}^1\left(1-x^6-3 x^2+3 x^4\right) d x \\\\& =\frac{15}{24}\left[x-\frac{x^7}{7}-3 \frac{x^3}{3}+3 \frac{x^5}{5}\right]_{-1}^1 \\\\& =\frac{15}{24} \times \frac{32}{35} \\\\& =\frac{4}{7}[/tex]
Hence, the center of gravity of the lamina is ([tex]0, \frac{4}{7}[/tex]).
Therefore, the mass and center of mass of the lamina that occupies the region D is [tex]\frac{8}{15} k[/tex], [tex](0, \frac{4}{7} )[/tex]
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please help will give brainliest
The given polygon IJKL is a rectangle. Therefore, option C is the correct answer.
Given that, the polygon IJKL if IJ≅KL, JK≅LI, IJ⊥JK, JK⊥KL, KL⊥LI and LI⊥IJ.
What is a rectangle?A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.
Here, the opposite sides IJ and KL are equal and the opposite sides JK and LI are equal.
Since, all the sides are perpendicular to each other makes an angle 90°
The given polygon IJKL is a rectangle. Therefore, option C is the correct answer.
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This equation has one solution. 5(x – 1) 3x = 7(x 1) what is the solution?
Answer:
send the complete question . there are some missing signs .
What is 10 percent of 75
Answer:
7.5
Step-by-step explanation:
100% = 75
100% divided by 10 is 10%
75 divided by 10 is 7.5
Bob's gift shop sold a record number of cards for Mother's Day. One salesman sold 33 cards, which was 10% of the cards sold for Mother's Day. How many cards were sold for Mother's Day?
Answer:330
Step-by-step explanation:
Set up cross multiplication:
33/x 10/100
Cross multiply
10*x 100*33
Divide sums
3,300/10x
Answer:
330 total cards
How do I find the missing side of a triangle ?
Answer: 1. Given two sides
If leg a is the missing side, then transform the equation to the form where a is on one side and take a square root: a = √(c² - b²)
If leg b is unknown, then: b = √(c² - a²)
For hypotenuse c missing, the formula is: c = √(a² + b²)
A bag of marbles contains only yellow and purple marbles. The number of yellow marbles is five times as the purple marbles. The bag contains 138 total marbles. develop a system of equations to represent the situation, determine how many of each color of marble is in the bag
show how you checked your answers
Answer:
23 purple marbles
115 yellow marbles
Step-by-step explanation:
Let y represent the yellow marble
Let p represent the purple marbles
So, we have the equations
y = 5p
Therefore, y + p = 138
5p + p = 138
6p = 138
p = 23 marbles
Now let's put 23 in for the p in the equation to find the number of yellow marbles
y = 5(23)
y = 115 marbles
At her health clubs, Lauren uses a treadmill every 2 days and the weight machines every 8 days. She used a treadmill on march 2 and will use the weight machines on march 8. Lauren says that the first time she will use both a treadmill and the weight machines in march is march 16 because the lcm of 2 and 8 is 16. Does Lauren’s reasoning make sense? Use an example or a counterexample to explain your analysis
Lauren's reasoning does not make sense because the LCM of 2 and 8 is not 16, the LCM will be equal to 8.
What is LCM?The Least Common Multiple is the meaning of the acronym LCM. The smallest number that both numbers can divide by is known as the least frequent multiple (LCM) for two numbers.
It can also be computed for several different numbers.
As per the given information in the question,
Lauren says that the LCM of 2 and 8 is 16.
Now, let's check whether it is correct or not.
Let's make a factor of both numbers,
2 = 2 × 1
8 = 2 × 2 × 2
So, the LCM will be: 2 × 2 × 2 = 8
It means that the LCM of 2 and 8 is not 16, the LCM is 8.
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all the sides of a triangle are integers, and the perimeter is 12. how many different possible triangles are there
3 such difference triangle are possible when the perimeter of a triangle 12cm. if the lengths of the three sides are all integers (in cm).
Given that,
The perimeter of a triangle 12cm.if the lengths of the three sides are all integers (in cm).
We have to find how many such difference triangle are possible.
We know that,
Perimeter of the triangle is 12cm.
p=12
a+b+c=12
a+b≥c
b+c≥a
So,
a+b+c≥2c
12≥2c
c≤6
So,
a≤6,b≤6,c≤6
We get,
a=6,b=3,c=3
a=5,b=4,c=3
a=4,b=4,c=4
Therefore, 3 such difference triangle are possible when the perimeter of a triangle 12cm. if the lengths of the three sides are all integers (in cm).
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6th grade math IXL program
Answer:
1.5 groups.
Step-by-step explanation:
1 divided by 8/12 is 1.5
Answer:
1 1/2
Step-by-step explanation:
The figure shows a large rectangle that is divided into 12 parts of equal size.
Think of the entire rectangle as 1.
Each small rectangle is 1/12 of 1.
Now count 8 small rectangles starting at the left.
When you divide 1 by 8/12, you can fit 1 full 8/12 (8 small rectangles) and another half of 8/12 (another 4 small rectangles.
Since you can fit 1 1/2 groups of 8 small rectangles,the result is 1 1/2.
Answer: 1 ÷ 8/12 = 1 1/2
Pls helppp i dont get it at all
Answer:
Law of Sines
Step-by-step explanation: