Find the perimeter of a triangle that has the side lengths given below.
6 cm, 7√3 cm, √27cm
Give the answer as a radical expression in simplest form.
Answers
The perimeter of a triangle that has the side lengths is 6 + 10√3 cm
How to determine the perimeter?The side lengths are given as:
6 cm, 7√3 cm and √27 cm
The perimeter is the sum of the side lengths.
So, we have:
P = 6 + 7√3 + √27
Express 27 as 9 * 3
P = 6 + 7√3 + √(9 * 3)
Take the square root of 9
P = 6 + 7√3 + 3√3
Evaluate the sum
P = 6 + 10√3
Hence, the perimeter of a triangle that has the side lengths is 6 + 10√3 cm
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Related Questions
Is this polynomial, rational, logarithmic, or exponential?
Answers
Answer:
logarithmic
Step-by-step explanation:
Which two numbers have a 3 that is 10 times the value of the 3 in 1,249.35?
Answers
Answer:
see below
Step-by-step explanation:
will be of the form xxxx3.x '3' will be just to the left of the decimal point
For the function defined by y = StartFraction 1 Over x squared EndFraction, if x is doubled, what is the effect on y?
a.
y is quartered
c.
y stays the same
b.
y is doubled
d.
y is tripled
Please select the best answer from the choices provided
Answers
Answer:
a. y is quartered.
Step-by-step explanation:
y=1/x^2
when x is doubled, the equation becomes:
y=1/(2x)^2=1/(4x^2)
Answer:
If we double x, then the new value of x becomes 2x. So we can find the effect on y by substituting 2x for x in the given function.
y = 1/x^2
When x is replaced by 2x, we get:
y' = 1/(2x)^2
= 1/4x^2
Therefore, y' = (1/4)y
So, if x is doubled, then y is quartered (option a is the correct answer)
A nursing student works at a doctor's office for $15 per hour and tutors other students for $25 per hour.
The student cannot work more than 20 hours each week.
The student wants to earn at least $375 each week.
• Define two variables and write a system of inequalities that represents the given constraints.
Answers
The system of inequalities represents the given constraints will be x + y < 20 and 15x + 25y > 375.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
A nursing student works at a doctor's office for $15 per hour and tutors other students for $25 per hour.
Let x be the number of hours for the doctor's office and y be the number of hours for the tutor.
The student cannot work more than 20 hours each week.
x + y < 20 ...1
15x + 25y > 375 ...2
The system of inequalities represents the given constraints will be x + y < 20 and 15x + 25y > 375.
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A bag of 10 Marbles has the following composition: Red – 3 Green – 4 Blue – 2 Yellow – 1 What is the Compound Probability of reaching in at random and extracting a Yellow marble followed by a Blue marble with NO REPLACEMENT?
Answers
The probability of extracting a Yellow marble followed by a Blue marble is 2/45 if the bag of 10 Marbles has the following composition: Red – 3 Green – 4 Blue – 2 Yellow – 1
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.
Total number of marbles = 3+4+2+1 = 10
P(Yellow) = 1/10
P(Blue) = 4/9
Probability of extracting a Yellow marble followed by a Blue marble:
= (1/10)(4/9)
= 4/90
= 2/45
Thus, the probability of extracting a Yellow marble followed by a Blue marble is 2/45 if the bag of 10 Marbles has the following composition: Red – 3 Green – 4 Blue – 2 Yellow – 1
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write 1.86×10⁵ as an ordinary numbe
Answers
[tex]\boxed{\sf 186,000}\boxed[/tex]
Answer:
186,000
Step-by-step explanation:
1. Multiply 10 to the 5th power:
[tex]10^{5}[/tex] = 100,000
2. Multiply:
1.86 × 100,000 = 186,000
hope this helps :)
I need help with 3 and 4
Answers
Answer:
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
( 3 )
the given figure resembles a rectangle !
now ,
[tex]Area \: of \: rectangle = length \times breadth \\ \\ given \: - \: length = 12 \: ft \\ \therefore \:breadth = x \: ft \\ \\ Area = 108 \: ft {}^{2} \\ \\ \implies \: length \times breadth = 108 \: ft {}^{2} \\ \\ \implies \: x \times 12 = 108 \\ \\ \implies \: x = \cancel\frac{108}{12} \\ \\ \bold\red{\implies \: x = 9 \: ft}[/tex]
_____________________________
_____________________________
( 4 )
the given figure resembles a parallelogram!
[tex]Area \: of \: parallelogram = height \times base \\ \\ \implies \: height = x \: cm\\ \\ \implies \: base = 16 \: cm \\ \\ \: Area \: = 96 \: cm {}^{2} \\ \\ \implies \: x \times 16 = 96 \\ \\ \implies \: x = \cancel\frac{96}{16} \\ \\ \bold\red{\implies \: x = 6 \: cm}[/tex]
hope helpful :D
[tex]\huge \underbrace \mathfrak \red{Answer}[/tex]
To find :-
To get the value of 'di in figure 3 and 4.
Figure 3
According to the figure, we know that it is a quadrilateral. It's all sides are at 90°.So we can assume that it can be rectangle. In the figure, length of one side is given and area of figure is given and we have the length of another side.Solution :-
Area of rectangle = length × width
area = 108 ft², length = 12 ft, width = x
[tex]108 = 12 \times x \\ \frac{108}{12} = x \\ 9 = x[/tex]
Therefore, the value of x in this figure is 9 ft.[tex] \\ [/tex]
Figure 4
According to figure, we finds out that it is quadrilateral as it has 4 sides. It has all parallel sides. We can assume that it is parallelogram as the sides which are facing each other are parallels. And here value of one side is given which is base and area is given, we have to find here is height.Solution :-
Area of parallelogram = base × height
Area = 96 cm², base = 16 cm, height = x
[tex]96 = 16 \times x \\ \frac{96}{16} = x \\ 6 = x[/tex]
Therefore, the value of x is 6 cm.A pair of shoes is $50, plus 10% tax. What is the total amount you will pay?
Answers
Answer:
$55
Step-by-step explanation:
Given:
A pair of shoes is $50, plus 10% tax.
To Find:
What is the total amount you will pay?
Solve:
Tax = Increase - Add on
Thus,
$50 × 10% = 5
$50 + 5 = $55
Hence, the total amount you will pay is $55.
Kavinsky
Help help help help help help
Answers
Explanation:
7. f(x) = x^4 + 3x^3 - 6x^2 - 10x + 8
f(2) = 2^4 + 2^3 - 6^2 - 10(2) + 8
f(2) = 16 + 8 - 12 - 20 + 8
f(2) = 0
8. x^2 - 9 = (x - 3)(x + 3)
x ^2 + x - 6 = (x + 3)(x -2)
Thus, the common factor is x + 3
A bag contains 5 green and 3 white balls (the balls are identical in all respect except colour). A ball is drawn at random from the bag without looking into the bag. What is the probability of getting a green ball? Is it more or less than getting a white ball?
Answers
Answer:
Probability of getting a green ball is more than that of getting a white ball.
Step-by-step explanation:
There are in all (5+3= 8) outcomes of the experiment. There are 5 outcomes in favour of the event of getting a green ball as there are 5 identical green balls in the bag.
Therefore, P(a green ball) = 5/8
In the same way,P(a white ball) = 3/8
5/8 > 3/8Thus, clearly the probability of getting a green ball is more than that of getting a white ball.
Zahra gave out a survey to some students in her school about their favorite color. Students could choose between purple and red. 187 of those surveyed said their favorite color was purple. 45% of the students surveyed said their favorite color was red. How many students were surveyed in total?
Answers
Answer:
340 people did the survey in total.
What is Algebra?
Algebra is a branch of mathematics that deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they do not have predefined values.
These symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations in order to determine their values.
Given:
People who like the color purple = 187
Moreover, 45% of people prefer the color red.
Purple color enthusiasts = 100 - 45 = 55%
Let the total number of people polled be x.
So, 55% of x = 187
55/100x = 187
x= 18700/ 55
x= 340
Therefore, the answer is 340.
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please. Will give brainliest
Answers
Answer:
The answer is c
scince I am not student so I don't use book n pen sorry
which expression is equivalent (7x3)2(x8)1/2
Answers
Answer:
B. 49x^10
Step-by-step explanation:
(7x^3)^2 * (x^8)^1/2
multiply the exponents
49x^6 * x^4
add the exponents
49x^10
If v₁ = (3,7) and V₂ = (-2,4), then v₁v₂ is equal to which of the following?
A. (-6,28)
B. 34
C. 22
D. (-21,-8)
Answers
Hope this helps
NO LINKS!!!! Exponential Growth and Decay Part 3
Answers
Answer:
6. 14.9 years
7. 4.8 years
8. 28.91 years
Step-by-step explanation:
Exponential growth or decay is described by the function ...
y = a·b^t
where 'a' is the initial value, and 'b' is the growth (or decay) factor. The growth (or decay) factor is one added to the growth rate.
__
This equation can be solved for t to get ...
y/a = b^t . . . . . . . divide by a
log(y/a) = t·log(b) . . . . take logarithms
t = log(y/a)/log(b) . . . . divide by the coefficient of t
Note that the time period is in the same units as the growth rate. (If the growth rate is per quarter, then the value of t will be in quarters.)
__
6.The initial value is a=8000; the final value is y=35000; and the growth rate is 10%/4 = 0.025 per quarter. The above equation will give the time period in quarters.
t = log(35000/8000)/log(1+0.025) ≈ 59.77 . . . quarters
Anisha will have $35,000 after 59.77/4 = 14.9 years.
__
7.No loan payment period is given, so we assume that the $43000 represents the repayment of the entire loan. The growth rate is 6% per year. The time required for the loaned amount to accumulate to a value of $43,000 is ...
t = log(43,000/32,500)/log(1 +0.06) ≈ 4.80 . . . years
If the loan period is 4.80 years, Kevin will have paid 43,000 to pay it off.
__
8.The growth rate is 0.024/12 = 0.002 per month. The number of months to achieve the desired balance is ...
t = log(3200/1600)/log(1 +0.024/12) ≈ 346.92 . . . . months
The balance in the account will be $3200 after 346.92/12 = 28.91 years.
_____
Additional comment
As a crude check on the answers, the "rule of 72" can be used. It says the doubling time is approximately 72 divided by the growth rate in percent. That is, a 10% growth rate will cause the value to double in approximately 72/10 = 7.2 years.
In the first problem, the value grows from 8000 to 35000, which represents a little more than 2 doublings (8000 to 16000 and 16000 to 32000). So, it is reasonable to expect the time period to be near 2 times 7.2 years, or 14.4 years. The value of 14.9 years is not unreasonable.
Answer:
Compound interest formula
[tex]\Large \text{$ \sf A=P(1+\frac{r}{n})^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedQuestion 6Given:
A = $35,000P = $8,000r = 10% = 0.1n = 4t = time (in years)[tex]\begin{aligned}8000\left(1+\frac{0.1}{4}\right)^{4t} & = 35000\\(1.025)^{4t} & = \frac{35000}{8000}\\(1.025)^{4t} & = 4.375}\\\ln (1.025)^{4t} & = \ln 4.375\\4t \ln 1.025 & = \ln 4.375\\4t & = \frac{\ln 4.375}{\ln 1.025}\\t & = 0.25\left(\frac{\ln 4.375}{\ln 1.025}\right)\\t & = 14.9427947\end{aligned}[/tex]
Therefore, she will have $35,000 in 15 years.
Question 7Given:
A = $43,000P = $32,500r = 6% = 0.06n = 1t = time (in years)[tex]\begin{aligned}32500\left(1+\frac{0.06}{1}\right)^{1t} & = 43000\\32500(1.06)^{t} & = 43000\\(1.06)^{t} & = \frac{43000}{32500}\\(1.06)^{t} & = \frac{86}{65}\\\ln (1.06)^{t} & = \ln \left(\frac{86}{65}\right)\\t \ln 1.06 & = \ln \left(\frac{86}{65}\right)\\t & = \dfrac{\ln \left(\frac{86}{65}\right)}{\ln 1.06}\\t & = 4.804621116\end{aligned}[/tex]
Therefore, Kevin will have paid $43,000 on the loan in 4 years and 10 months.
Question 8Given:
A = $3,200P = $1,600r = 2.4% = 0.024n = 12t = time (in years)[tex]\begin{aligned}1600\left(1+\frac{0.024}{12}\right)^{12t} & = 3200\\1600(1.002)^{12t} & = 3200\\(1.002)^{12t} & = \frac{3200}{1600}\\(1.002)^{12t} & = 2\\\ln (1.002)^{12t} & = \ln 2\\12t \ln (1.002) & = \ln 2\\12t & = \dfrac{\ln 2}{\ln 1.002}\\t & = \frac{1}{12}\left(\dfrac{\ln 2}{\ln 1.002}\right)\\t & = 28.91000404\end{aligned}[/tex]
The balance of the account will be $3,200 in 28 years and 11 months.
what is the equation of the line that passes through the point (3,6) and has a slope of -1/3
ASAP PLS
Answers
[tex]\Large\texttt{Answer\::}[/tex]
Please consult the "Calculations" section of this ans .
[tex]\Large\texttt{Calculations\::}[/tex]
The information we're given is below :
slope : -1/3Point crossed by the line : (3, 6)As per given information , we can do the following :
Write the line's equation in point slope formPoint - slope form looks like so :
y-y₁=m(x-x₁)
y-6=-1/3(x-3)
y-6=-1/3x+1
y=-1/3x+1+7
y=-1/3x+6
↑ [tex]\small\textsc{EQUATION OF THE LINE}[/tex]
[tex]\small\textit{hope\:helpful~}[/tex]
Phu takes out a $2,400 discounted loan using a simple interest rate of 8% for a period of 18 months. What is the effective interest rate, re
Answers
Answer:
9.1
Step-by-step explanation:
To calculate the total interest payable, we use the formula
I=P0rt,
and substituting our values yields
I=$2,400×0.08×1812=$288.
Therefore the total amount he receives at loan drawdown is $2,400−$288=$2,112. To calculate the effective interest rate, we use to formula
A=P0(1+ret).
In this instance we have A=$2,400,P0=$2,112 (redefined from the value above) and t=1.5. We substitute into the formula to get
$2,400=$2,112(1+1.5re).
Solve for re.
24002112=1+1.5re
24002112−1=1.5re
24002112−11.5=re
This gives re=0.0909⋯=9.0909…%, which is 9.1%
A driver spent 45minutes to cover a distance of 120km. what is the speed of the driver in km per hour.
Answers
Answer:
The speed is 160 km /hStep-by-step explanation:
A driver spent 45minutes to cover a distance of 120km
Convert minutes to hour
45 min = 45 /60 hr = 3/4 hrUse the distance equation
d = tsFind the speed
s = d/tSubstitute the distance and time value and find the value of speed
s = 120 / (3/4) = 120 * 4/3 = 160 km /hHey guys may yall help please and thank you !!
Answers
Answer: 12? im pretty sure
Step-by-step explanation: 1/4 of a unit so 4 for 1 unit, 4 x 3 is 12 units for 3
If you dont know the answer or get it wrong i will report
Answers
Step-by-step explanation:
law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
extended Pythagoras :
c² = a² + b² - 2×a×b×cos(C)
and : the sum of all angles in a triangle is always 180°.
1.
b² = 42.1² + 37² - 2×42.1×37×cos(13) =
= 105.8575002...
b = 10.28870741...
b/sin(13) = 37/sin(C)
sin(C) = 37 × sin(13)/b = 0.808963525...
C = 53.99478824...° ≈ 54°
A = 180 - 13 - 54 ≈ 113°
2.
c² = 18² + 13² - 2×18×13×cos(115) = 690.7853465...
c = 26.28279564...
c/sin(115) = 18/sin(A)
sin(A) = 18 × sin(115)/c = 0.62069273...
A = 38.36673893...°
B = 180 - 115 - A = 26.63326107...°
3.
the length of b is missing.
this cannot be solved without the missing information
PLEASE HELP I NEED THIS FAST. Find the volume of each rectangular prism
Answers
2: 48
3:108
4:288
5: 24
6:18
Twelve subtracted from twelve times a number is -84. What is the number? A) Translate the statement above into an equation that you can solve to answer this question. Do not solve it yet. Use x as your variable. The equation is B) Solve your equation in part [A] for x. Answer: 0 =
Answers
Answer:
x=-6
Step-by-step explanation:
Let x be the number
A) 12x-12=-84
B) 12x=-72
x=-6
HELP ME ON THIS PLSS Kathy swims at least 6 laps everyday. Write an inequality to show how long Kathy swims each day.
Answers
Answer:
x ≥ 6.
Step-by-step explanation:
Given : Kathy swims at least 6 laps every day.
To find: Write an inequality to show how long Kathy swims each day.
Solution : We have given that Kathy swims at least 6 laps every day.
We can see from given statement Kathy can swim 6 laps or greater then 6 laps in a day.
Then we use greater than or equal to sign ( for at least)
Since x ≥ 6.
Therefore, x ≥ 6.
I will give Brainliest, please help!! See the attached photo! ^^
You can’t use the same number twice!
Answers
Answer:
Step-by-step explanation:
1/5 = 0.2
This is what I came up with, hopefully this helps!
A certain lake is 85 feet deep. After a hurricane,
the level of the lake rose to 88 feet. Find the
percent of change in the depth of the lake.
Round to the nearest tenth of a percent.
Answers
Answer:
3%
Step-by-step explanation:
Easy!
88 - 85 which is equivalent to 3.
Make the 3 a percentage
A = 3%
Find the sum of the first n terms using the formula a(1-r^n)/1-r $50 + $50(1.1) + 50(1.1)^2 + … (6 terms)
Answers
The sum of n terms is 500(1.1ⁿ - 1) and the sum of the 6th terms is 385.78
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have sequence:
50 + $50(1.1) + 50(1.1)^2 + …
The common ration r = 1.1
First term = 50
The sum of n terms:
[tex]\rm Sum = \dfrac{50(1.1^n-1)}{1.1-1}\\\\\rm Sum = \dfrac{50(1.1^n-1)}{0.1}\\\\\\\rm Sum = 500(1.1^n-1)[/tex]
If n = 6 terms
Sum = 385.78
Thus, the sum of n terms is 500(1.1ⁿ - 1) and the sum of the 6th terms is 385.78
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how many solutions does the following equation have? 3x+6 =3(x+2)
Answers
Answer:
Infinite solutions
Step-by-step explanation:
3x+6 = 3(x+2)
3x+6 = 3x+6
6 = 6
Alyssa has a points card for a movie theater. She receives 70 rewards points just for signing up. She earns 12.5 points for each visit to the movie theater. She needs 245 points for a free movie ticket. How many visits must Alyssa make to earn a free movie ticket?
Answers
let x be the amount of times she visited the movie theater
[tex]70+12.5x=245\\\\12.5x=175\\\\x=14[/tex]
Alyssa needs to make 14 visits to earn a free movie ticket.
This is our y intercept
Rate of pay=12.5This is our slope.
So our equation is
p=12.5v+70Here v is visits
245=12.5v+7012.5v=175v=14visitsSelect the correct expression.
Select the expression that is equivalent to the expression below.
Answers
Answer:
[tex]8\sqrt[3]{-8x^3y^6z^{13}}[/tex]
Step-by-step explanation:
[tex]8\sqrt[3]{-8x^3y^6z^{13}}\\\\=8\sqrt[3]{(-1)^3\cdot2^3\cdot x^3 \cdot y^6 \cdot z^{12} \cdot z}\\\\=8\left[(-1)^3\cdot2^3\cdot x^3 \cdot y^6 \cdot z^{12} \cdot z \right]^{\tfrac 13}\\\\=-8\cdot 2 \cdot x \cdot y^2 \cdot z^4 \cdot z^{\tfrac 13}\\\\=-16xy^2 z^4 \sqrt[3]z[/tex]
Harry buys 3 granola bars for $5. Sidnee buys
9 granola bars for $15. What is the constant of
proportionality?
Answers
Answer:
The constant of proportionality is 5/3
Step-by-step explanation:
3 * k = 5
k = 5/3
Check
9 * k = 15
9 * 5/3 = 15
3*5 = 15
15 =15
The constant of proportionality is 5/3
The ratio for both Harry and Sidnee is the same, which is 5/3.
So, the constant of proportionality (x) is 5/3.
To find the constant of proportionality between the number of granola bars and the cost, we can use the formula for direct proportionality:
Constant of Proportionality (k) = Cost / Number of Granola Bars
For Harry:
Number of granola bars = 3
Cost = $5
Constant of Proportionality (k) for Harry = 5 / 3
For Sidnee:
Number of granola bars = 9
Cost = $15
Constant of Proportionality (k) for Sidnee = 15 / 9
Since both Harry and Sidnee's values for the constant of proportionality are the same (both simplify to 5/3), we can conclude that the constant of proportionality is 5/3, which is approximately 1.67.
This means that for every granola bar purchased, the cost increases by $5/3 or about $1.67.
So, the constant of proportionality (x) is 5/3.
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