Answers
3(4t) (multiplication form)
these are two forms you can use to get your answer
answer: 12t
hope this helps
and
perimeter = 4t * 3
Related Questions
which algebraic expression shows the average melting point of helium hydrogen and neon if h represent melting point of helium, j represent the melting point of hydrogen and K represent the melting point of neon
Answers
Answer:
Which algebraic expression shows the average melting points of helium, hydrogen, and neon if h represents the melting point of helium, j represents the melting point of hydrogen, and k represents the melting point of neon?
Step-by-step explanation:
5x+14-2x=9-(4x+2) can someone help
Answers
3x+14=9-4x-2
3x+14=7-4x
7x+14=7
7x=-7
x=-1
Final answer: x=-1
Katie is buying souvenir.gifts for her big family back home. She wants to buy everyone either a key chain or a magnet. The magnets are on sale for 60 cents each and the key chains cost $2 each. She must purchase at least 36.gifts but has to spend less than $40. Let x represent the amount of key chains and y represent the amount of magnets. Model the scenario with a system of inequalities.
Answers
2x + 0.6y < 40
Answer:
[tex]x+y\geq 36[/tex]
[tex]2x+0.6y<40[/tex]
Step-by-step explanation:
The magnets are on sale for 60 cents each.
The key chains cost $2 each.
Katie must purchase at least 36 gifts but has to spend less than $40.
Now let x represent the amount of key chains.
Let y represent the amount of magnets.
So, the system of inequalities that form are:
[tex]x+y\geq 36[/tex]
And
[tex]2x+0.6y<40[/tex]
Miriam’s study group received test scores of 96, 81, 82, 99, 94, 92, 95, 82, and 80. Find the mean and median scores.
Answers
Answer:
The mean is
✔ 89
The median is
✔ 92
The mean of Miriam's test scores is 89 and the median is 92.
What is mean?"It is the average of a data set. "
What is median?"It is the middle value in a list ordered from smallest to largest."
For given question,
Total number of test scores = 9
The sum of all the test scores would be,
96 + 81 + 82 + 99 + 94 + 92 + 95 + 82 + 80 = 801
So, the mean would be,
[tex]\bar{X}=\frac{801}{9} \\\\\bar{X}=89[/tex]
So, the mean of Miriam's test scores is 89.
If we arrange the test scores in ascending order then it would be,
80, 81, 82, 82, 92, 94, 95, 96, 99
The middle value is 92
So, the median is 92.
Therefore, the mean of Miriam's test scores is 89 and the median is 92.
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A map of Brasilia has a scale of 1 inch to 5 miles. If the city is 2 7/16 inches across on the map, what is the distance across the actual city? a.) 10 1/2 mi b.) 8 3/16 mi c.) 12 3/16 mi d.) 8 1/4 mi
Answers
Answer:
[tex]12\frac{3}{16} \text{inches}[/tex]
Step-by-step explanation:
Given : The city is [tex]2 \frac{7}{16}[/tex] inches across on the map
To Find:On the map, what is the distance across the actual city?
Solution:
Distance on map = [tex]2 \frac{7}{16}=\frac{39}{16} inches[/tex]
Scale: 1 inch = 5 miles
So, [tex]\frac{39}{16} inches=\frac{39}{16} \times 5[/tex]
[tex]\frac{39}{16} inches=\frac{195}{16} =12\frac{3}{16} [/tex]
Thus ,the distance across the actual city is [tex]12\frac{3}{16} inches[/tex]
So, option C is correct.
You are planning a study and are considering taking an srs of either 300 or 700 observations. explain how the sampling distribution would differ for these two scenarios.
Answers
This question has following choices to choose the answer from:
The larger sample would have a center closer to the true population parameter.
The larger sample would have less sampling variability.
The smaller sample would have less sampling variability.
The statistics of the smaller sample have more chance for bias than those of the larger sample.
I believe that the correct answer from the 4 choices would be the last one:
"The statistics of the smaller sample have more chance for bias than those of the larger sample."
This is because in a smaller sample, there is a high probability that not all parts or portion of the sample population is represented hence resulting in bias. This is especially true for distribution types of data wherein extreme values exist. Following that bias would already be effect on the center and the sampling variability. So bias always comes first.
pie =????????????????????.??
Answers
I can assume you mean "Pi".
Pi is an irrational number that has an infinity decimal, also known as a terminating decimal, which means to repeat infinitely.
The summarized form of Pi is 3.14, but since you have multiple units, I can assume you want the extended form.
Here it is:
3.14159265359
I hope this helps!
An employment agency specializing in temporary construction help pays heavy equipment operators $ 134 per day and general laborers $ 92 per day. If thirty-eight people were hired and the payroll was $ 4756 , how many heavy equipment operators were employed? How many laborers?
Answers
x=heavy equipment
y= general labor
x+y=38
x=38-y
134x + 92y=4756
134(38-y)+92y =4756
5092-134y+92y=4756
-42y = -336
y = -336/-42 = 8
x=38-8=30
check 30*134 =4020
8*92 = 736
4020+736 = 4756
8 general laborers
30 heavy equipment operators
How much do you need to invest in an account earning an annual interest rate of 2.938% compounded weekly, so that your money will grow to $7,880.00 in 50 weeks?
Answers
however, the maturity term in years, is just 50/52, since is 50weeks from 52 in a year, so is 50/52 years, which is just a fraction of a year
[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\to &\$7,880\\ P=\textit{original amount deposited}\\ r=rate\to 2.938\%\to \frac{2.938}{100}\to &0.02938\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus fifty two} \end{array}\to &52\\ t=years\to \frac{50}{52}\to &\frac{25}{26} \end{cases} \\\\\\ 7880=P\left(1+\frac{0.02938}{52}\right)^{52\cdot \frac{25}{26}}[/tex]
solve for P
30% of the 70 buttons had holes how many did not have holes
Answers
70 - 21 = 59.
Answer: 59 buttons
Please help. Find the cube root of -27 that graphs in the first quadrant.
3(cos?+isin?) Use degree measure.
Answers
Now find r and theta for -27
[tex]-27 = 27(-1 +0i) = 27(cos 180 + i sin 180)[/tex]
r = 27 , theta = 180
[tex]\sqrt[3]{-27} = \sqrt[3]{27} (cos \frac{180 +360k}{3} +i sin \frac{180 +360k}{3} ) [/tex]
[tex]= 3(cos 60 + i sin 60) , k =0 \\ \\ = 3 (cos 180 + i sin 180) , k =1 \\ \\ =3(cos 300+i sin 300), k =2[/tex]
The cube root of -27 is -3, which cannot be graphed in the first quadrant of the complex plane. When considering complex roots, the angles of these roots do not lie in the first quadrant either, contradicting the given requirement.
Explanation:The cube root of -27 that graphs in the first quadrant in complex form can be represented as 3(cos Θ + i sin Θ), where Θ is the angle in degrees. To find a cube root that lies in the first quadrant, we look for an angle Θ whose cosine is positive and sine is positive, which corresponds to angles between 0° and 90°. However, the cube root of -27 is actually a negative real number, which is -3.
Since we cannot graph a negative real number (-3) in the first quadrant of the complex plane, which only contains positive real and imaginary numbers, the question seems to be a bit contradictory. Nonetheless, if we interpret the cube root in terms of complex numbers, we find that the complex roots of -27 are -3, 3ε², and 3ε⁴, where ε² = e²πi/3 and ε⁴ = e⁴πi/3, correspond to angles of 120° and 240° respectively, which do not lie in the first quadrant.
By what factor will the rate of the reaction change if the ph decreases from 5.50 to 2.00? express your answer numerically using two significant figures.
Answers
a. Rate law expression: [tex]\(\text{rate} = kxyz\)[/tex]
b. [tex]\[ \text{Rate factor} \approx 3.16 \times 10^3 \][/tex]
**Part A: Rate Law Expression**
Given that the reaction is first order in [tex]\( (IO_3)^- \)[/tex], first order in [tex]\( (SO_3)^{2-} \)[/tex], and first order in [tex]\( H^+ \)[/tex], the rate law for the reaction can be expressed as:
[tex]\[ \text{rate} = k \cdot [(IO_3)^-]^1 \cdot [(SO_3)^{2-}]^1 \cdot [H^+]^1 \][/tex]
Simplifying this, we get:
[tex]\[ \text{rate} = kxyz \][/tex]
Here, [tex]\( x \), \( y \), and \( z \)[/tex] are the concentrations of [tex]\( (IO_3)^- \), \( (SO_3)^{2-} \), and \( H^+ \)[/tex], respectively. [tex]\( k \)[/tex] is the rate constant.
**Part B: Rate Change with pH**
The pH of a solution is a measure of its hydrogen ion concentration [tex](\( [H^+] \))[/tex]. As the reaction is first order in [tex]\( H^+ \)[/tex], a change in pH will directly impact the rate. The relationship between pH and [tex]\( [H^+] \)[/tex] is logarithmic:
[tex]\[ \text{pH} = -\log[H^+] \][/tex]
To calculate the rate change factor when the pH decreases from 5.50 to 2.00, we need to consider the relationship between pH and [tex]\( [H^+] \)[/tex]:
[tex]\[ \text{pH} = -\log[H^+] \][/tex]
1. **At pH 5.50:**
[tex]\[ [H^+] = 10^{-\text{pH}} = 10^{-5.50} \][/tex]
2. **At pH 2.00:**
[tex]\[ [H^+] = 10^{-\text{pH}} = 10^{-2.00} \][/tex]
Now, calculate the rate factor:
[tex]\[ \text{Rate factor} = \frac{\text{rate at pH 2.00}}{\text{rate at pH 5.50}} = \frac{[H^+]_{\text{pH 2.00}}}{[H^+]_{\text{pH 5.50}}}\][/tex]
[tex]\[ \text{Rate factor} = \frac{10^{-2.00}}{10^{-5.50}} \][/tex]
[tex]\[ \text{Rate factor} \approx \frac{0.01}{3.16 \times 10^{-6}} \][/tex]
[tex]\[ \text{Rate factor} \approx 3.16 \times 10^3 \][/tex]
Expressing the answer numerically using two significant figures, the rate change factor is approximately [tex]\(3.2 \times 10^3\).[/tex]
The question probable maybe:
Part A:
The reaction is found to be first order in [tex](IO_3)^-[/tex], first order in [tex](SO_3)^2^-[/tex], and first order in H^+.
If [[tex](IO_3)^-[/tex]] = x, [[tex](SO_3)^2^-[/tex]] = y and [[tex]H^+[/tex]]=z, what is the rate law for the reaction in terms of x, y, and z and the rate constant k?
Express the rate in terms of k, x, y, and (e.g., kxy^3z^2).
▸ View Available Hint(s)
rate= kx^1y^1z
Part B:
By what factor will the rate of the reaction change if the ph decreases from 5.50 to 2.00? express your answer numerically using two significant figures.
36 % of women consider themselves fans of professional baseball. You randomly select six women and ask each if she considers herself a fan of professional baseball. Complete parts (a) through (c) below.
(a) Construct a binomial distribution using
n equals 6n=6 and
p=0.36.
x
P(x)
0
nothing
1
nothing
2
nothing
3
nothing
4
nothing
5
nothing
6
nothing
(Round to the nearest thousandth as
Answers
The binomial distribution of the number of women (out of six) who could be an interest in baseball is found by using the binomial probability formula. Probabilities range from 0.027 for zero women interested, to 0.002 for all six women interested.
Explanation:In this problem, we are constructing a binomial distribution for the number of women (out of six) who might consider themselves fans of professional baseball. This involves using the formula for a binomial probability, which is: P(x) = nCx * [tex](p^x) * ((1-p)^(^n^-^x^)[/tex]). Here, n represents the number of trials (in this case, 6 women), p represents the probability of success (here, a woman being a baseball fan, which is 0.36 or 36%), and x represents the number of successful outcomes we're interested in.
Each of these values rounds to the thousandth place
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To construct a binomial distribution, we use the formula P(x) = nCx * p^x * (1-p)^(n-x), where n is the number of trials, p is the probability of success, x is the number of successes, and nCx is the combination formula.
Explanation:To construct a binomial distribution, we use the formula P(x) = nCx * p^x * (1-p)^(n-x), where n is the number of trials, p is the probability of success, x is the number of successes, and nCx is the combination formula.
X = number of women who consider themselves fans of professional baseballn = 6 (randomly selected women)p' = 0.36 (probability of a woman considering herself a fan)The random variables X and P' represent the number of women who consider themselves fans of professional baseball and the probability of a woman considering herself a fan, respectively.
We should use the binomial distribution for this problem.
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EASY 5 POINTS!!!! You have a basketball trophy in your room. The ball on the trophy has a diameter of 9 inches. What is the volume of the ball? Use 3.14 for pi.
Answers
volume = (4/3) x pi x r^3
diameter = 9 so radius = 9/2 = 4.5
V =(4/3) x 3.14 x 4.5^3 = 381.51 cubic inches
99 33 11 3 2/3 what comes next
Answers
99/3=33
33/3=11
11/3= 3 2/3
Divide the last number by 3 to get the next number.
Divide fractions by multiplying by the reciprocal of the second number.
11/3*1/3= 11/9
11/9= 1 2/9
Final answer: 1 2/9
Also can be written as 11/9 (Improper fraction)
Find the decimal notation for 84.3%
Answers
to turn a percent into a decimal, move the decimal point 2 places to the left
84.3% = 0.843
Example 3 find the local maximum and minimum values and saddle points of f(x, y) = x4 + y4 − 4xy + 1. solution we first locate the critical points:
Answers
[tex]\begin{cases}f_x=4x^3-4y\\f_y=4y^3-4x\end{cases}[/tex]
We have critical points whenever both partial derivatives vanish:
[tex]4x^3-4y=0\implies x^3=y\implies x=y^{1/3}[/tex]
[tex]4y^3-4x=0\implies y^3=x=y^{1/3}\implies y^6=y\implies y=0,y=-1,y=1[/tex]
[tex]\begin{cases}y=0\implies x=0\\y=-1\implies x=-1\\y=1\implies x=1\end{cases}[/tex]
The Hessian is
[tex]\mathbf H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}12x^2&-4\\-4&12y^2\end{bmatrix}[/tex]
[tex]\det\mathbf H(x,y)=(12xy)^2-16[/tex]
At (0,0), we have [tex]\det\mathbf H(0,0)=-16<0[/tex], so (0,0) is a saddle point.
At (-1, -1), we have [tex]\det\mathbf H(-1,-1)=128>0[/tex] and [tex]f_{xx}(-1,-1)=12>0[/tex], so (-1, -1) is a local minimum.
At (1, 1), we have [tex]\det\mathbf H(1,1)=128>0[/tex] and [tex]f_{xx}(1,1)=12>0[/tex], so (1, 1) is also a local minimum.
At (1,1) and (-1,-1) there is minimum value and at (0,0) is the saddle point.
Given-
Given function is-
[tex]f(x,y)=x^4+y^4-4xy+1[/tex]
Locate the critical points,(use the derivation with respect to x and y)
[tex]f'(x)=4x^3-4y\\\\f'(y)=4y^3-4x[/tex]
Equate the above partial derivatives to the zero, we get.]
[tex]4x^3-4y=0\\\\x^3=y[/tex]
The value of x is obtained. Solve the equation two and put this value of x in that equation, we get,
[tex]4y^3-4x=0\\y^3-x=0[/tex]
Put the value of x, we get,
[tex]x^9-x=0[/tex]
[tex]x(x^8-1)=0[/tex]
from above equation we get one value of [tex]x[/tex] is zero.
[tex]x^8-1=0[/tex]
To the above equation we can rewrite,
[tex]x^2-1=0[/tex]
[tex](x-1)(x+1)=0[/tex]
hence we get three values of the [tex]x[/tex] (0,1,-1)
From the equation of partial derivative equation, we get that
[tex]x=0; y=0[/tex]
[tex]x=1;y=1[/tex]
[tex]x=-1;y=-1[/tex]
Thus three critical points are (0,0),(1,1) nd(-1,-1). Now calculate second partial derivative and D(x,y).
[tex]f"(x)=12x^2-0[/tex]
[tex]f'(xy)=-4[/tex]
[tex]f"(y)=12y^2-1[/tex]
[tex]D(x,y)=f"(x)f"(y)-f'(xy)^2[/tex]
[tex]D(x,y)=144x^2y^2-16[/tex]
Check at critical points,
[tex]D(0,0)=-16<0[/tex]
thus no local minima or maxima at point (0,0). this is the saddle point.
[tex]D(1,1)=12>0[/tex]
so (1, 1) is a local minimum.
[tex]D(-1,-1)=12>0[/tex]
so (-1, -1) is a local minimum.
Hence at (1,1) and (-1,-1) there is minimum value and at (0,0) is the saddle point.
For more about the maxima and minima follow the link given below-
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tanya set a goal to swim 30 miles over the summer. she plans to swim 3/4 mile per day until she reaches her goal. how many days will it take tanya to reach her goal?
Answers
30/.75=40
It will take Tanya 40 days to reach her goal.
By dividing Tanya's swimming goal of 30 miles by her daily swimming rate of 3/4 mile, we find that it will take her 40 days to reach her goal.
To calculate how many days it will take Tanya to reach her goal of swimming 30 miles by swimming 3/4 mile per day, we need to divide the total goal distance by the daily swimming distance. Therefore, the calculation is as follows:
Divide 30 miles by 3/4 mile.
Since dividing by a fraction is equivalent to multiplying by its reciprocal, we multiply 30 miles by 4/3.
30 miles * 4/3 = 120/3 = 40 days.
Hence, it will take Tanya 40 days to reach her goal of swimming 30 miles if she swims 3/4 mile each day
estimate 36.61 + 35.907 + 37.2
Answers
2ax+1=ax+5 solve for x
Answers
If you need a better understanding just ask
Mrs white wants to crochet beach hits and baby afghans for a church fund raising bazaar. she needs 7 hours to make a hat and 4 hours to make an Afghan and she has 68 hours available. she wants to make no more than 14 items and no more than 11 afghans. the bazaar will sell hats for $21 each and the afphans for $9 each. How many of each should she make to maximize the income for the bazaar?
Answers
In this problem, we represent x as the number of hats made, and y as the number of Afghans made by Mrs White.
Equation 1 relating to the time it takes to make these is expressed:
7x + 4y = 68
Another equation that represents inequality to the number of hats and Afghans respectively is expressed:
x<= 14
y<=11
the third equation expresses the income from selling these items expressed as
P = 21 x + 9y
we subtitute 1 to 3
P = 9(68-7x)/4 + 21x = 153-15.75x + 21 x = 153 -5.25x
So by trial and errror, x and y should be integers, we get two cases of which x and y should be
1) x = 4 ; y = 10
2) x = 8 ; y = 3
Subsituting to 3, P1 = 174$ while P2is equal to $195, Answer then is 8 hats and 3 Afghans in total.
The value of y is inversely proportional to the value of x. When y=24, x=4. What is the value of y when x=6?
Answers
When y=24, x=4
y= kx
24 = 4k
k = 24/4
k = 6
when x=6
y = kx
y = 6 (6)
y = 36
answer
y = 36 when x = 6
The value of [tex]\( y \)[/tex] when x = 6 is 16.
Given that [tex]\( y \)[/tex] is inversely proportional to [tex]\( x \)[/tex], we can write the relationship as:
[tex]\[ y = \frac{k}{x} \][/tex]
where [tex]\( k \)[/tex] is the constant of proportionality.
First, we need to determine the value of [tex]\( k \)[/tex]. We are given that [tex]\( y = 24 \)[/tex] when [tex]\( x = 4 \)[/tex].
[tex]\[ 24 = \frac{k}{4} \][/tex]
Solving for k:
[tex]\[ k = 24 \times 4 = 96 \][/tex]
Now that we have the value of [tex]\( k \)[/tex], we can find the value of [tex]\( y \)[/tex] when [tex]\( x = 6 \)[/tex]:
[tex]\[ y = \frac{96}{6} \][/tex]
[tex]\[ y = 16 \][/tex]
The perimeter of a parallelogram is 72 meters. The width of and the the parallelogram is 4 meters less than its length. Find the length width of the parallelogram.
Answers
l-4=w
2w+2l=perimeter=72
Substituting l-4 for 2, we get 2(l-4)+2l=72 and 2l-8+2l=72. After that, we get 4l-8=72 and 4l=80, getting l=20. Since l-4=w, w=16
How would you use the Fundamental Theorem of Calculus to determine the value(s) of b if the area under the graph g(x)=4x between x=1 and x=b is equal to 240?
Answers
Answer:
[tex]\displaystyle b = 11[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Functions
Function NotationCalculus
Integration
IntegralsDefinite IntegralsIntegration Constant CIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
g(x) = 4x
Interval [1, b]
A = 240
Step 2: Solve for b
Substitute in variables [Area of a Region Formula]: [tex]\displaystyle \int\limits^b_1 {4x} \, dx = 240[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle 4\int\limits^b_1 {x} \, dx = 240[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle 4(\frac{x^2}{2}) \bigg| \limits^b_1 = 240[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle 4(\frac{b^2}{2} - \frac{1}{2}) = 240[/tex][Distributive Property] Distribute 4: [tex]\displaystyle 2b^2 - 2 = 240[/tex][Addition Property of Equality] Add 2 on both sides: [tex]\displaystyle 2b^2 = 242[/tex][Division Property of Equality] Divide 2 on both sides: [tex]\displaystyle b^2 = 121[/tex][Equality Property] Square root both sides: [tex]\displaystyle b = \pm 11[/tex]Choose: [tex]\displaystyle b = 11[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
The senate in a certain state is compromised of 58 republicans, 39 democrats, and 3 independents. How many committees can be formed if each committee must have 3Republicans and 2 Democrats?
Answers
there are
C(58,3) ways to choose 3 from 58 republicans,
and
C(39,2) ways to choose 2 from 39 democrats.
So the committee has
(C(58,3)*(C(39,2)) variants, or
58!/(3!55!) * 39!/(2!37!)
=30856*741
=22864296
**NEEDS TO BE ANSWERED ASAP**
Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted.
The following table contains data from a study of two airlines which fly to Small Town, USA.
If one of the 87 flights is randomly selected, find the probability that the flight selected is an Upstate Airlines flight which was on time.
a. 43/87
b. 43/76
c. 43/48
d. 11/76
Answers
Answer: a. [tex]\dfrac{43}{87}[/tex]
Step-by-step explanation:
From the given table , it can be seen that the total number of flights are given : 43+33+6+5=87
Also, the the number of Upstate Airlines flights on time = 43
Now if one of the 87 flights is randomly selected, the probability that the flight selected is an Upstate Airlines flight which was on time will be :-
[tex]\dfrac{\text{Number of Upstate Airlines flight on time}}{\text{Total flight}}\\\\=\dfrac{43}{87}[/tex]
Hence, the probability that the flight selected is an Upstate Airlines flight which was on time [tex]=\dfrac{43}{87}[/tex]
how do i solve this question
Answers
The length of the longer leg of a right triangle is 6cm more than twice the length of the shorter leg. The length of the hypotenuse is 9cm more than twice the length of the shorter leg. Find the side lengths of the triangle.
Length of the shorter leg:
cm
Length of the longer leg:
cm
Length of the hypotenuse:
cm
Answers
By defining the shorter leg of the triangle as 'x' and applying the Pythagorean Theorem to solve the given equations, we find that the shorter leg is 3cm, the longer leg is 12cm, and the hypotenuse is 15cm.
Explanation:Let's define the shorter leg of the triangle as 'x'. As given, the longer leg would be '2x + 6' and the hypotenuse would be '2x + 9'.
To solve for the lengths of the sides, let's use the Pythagorean Theorem, which says that the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, the equation would be (2x + 6)^2 + x^2 = (2x + 9)^2.
Solve this equation by expanding, collecting similar terms, and factoring. You'll end up with x = 3. Therefore, the shorter leg of the triangle is 3cm, the longer leg is 2x + 6 = 2*3 + 6 = 12cm, and the hypotenuse is 2x + 9 = 2*3 + 9 = 15cm.
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the sum of three consecutive numbers is 267.what is the largest number
Answers
x + x+1 + x+2 = 267 =>
3x+3 = 267
x = 264/3 = 88
So the numbers are 88+89+90. 90 is the largest number.
A two pound box of fruit snacks contains 24 packets. Find the unit rate in packets per pound
Answers
The unit rate is 12 packets per pound.
Hope this helps!
Answer:
12
Step-by-step explanation:
Given that a two pound box of fruit snacks contains 24 packets
We have to find the unit rate per pound
This is a question of direct variation.
[tex]2 pounds = 24 packets\\1 pount= 12 packet[/tex]
i.e. unit rate is 12 packets per pound