The required perimeter of the square is 48 units as of the given condition.
Given that,
The perimeter of a square with a side length of 5x -8 and a bottom length of 3x of a square is to be determined.
Perimeter is the measure of the figure on its circumference.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The length of all sides of the square is always remains equal,
5x - 8 = 3x
2x = 8
x = 4
Side length,
3x = 3(4) = 12
Now,
The perimeter of the square is 4-time sides,
Perimeter = 4 (12)
Perimeter = 48 units.
Thus, the required perimeter of the square is 48 units as of the given condition.
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Which graph best represents the solution to the system of equations shown below?
y = -2x + 14
y = 2x + 2
Answer:
solution is (3,8)
option A
Step-by-step explanation:
[tex]y = -2x + 14[/tex]
[tex]y = 2x + 2[/tex]
Lets graph each equation
Given equation is in the form of y=mx+b
LEts graph each equation using a table
[tex]y = -2x + 14[/tex]
x y
0 14
1 12 points are (0,14) and (1,12)
[tex]y = 2x + 2[/tex]
x y
0 2
1 4 points are (0,2) and (1,4)
Graph both the table
The graph is attached below. both graph intersects at (3,8)
The x-intercept of the graph of f(x)= 3log(x-5)+2 is:
Answer: [tex]\frac{1}{e^{\frac{2}{3}}}+5[/tex] or 5.51
Step-by-step explanation:
The given function : [tex]f(x)= 3\log(x-5)+2[/tex]
We know that , the x-intercept is the point on graph( basically intersection of graph and x-axis) where y coordinate is zero.
I.e. for x-intercept of function , f(x) =0
i.e. [tex]0= 3\log(x-5)+2[/tex]
[tex]\Rightarrow\ \log(x-5)=\dfrac{-2}{3}[/tex]
Taking exponent on both sides , we get
[tex]x-5=e^{\frac{-2}{3}}\\\\\Rightarrow\ x=e^{\frac{-2}{3}}+5\ \ or\ \ x=\dfrac{1}{e^{\frac{2}{3}}}+5[/tex]
On simplification , [tex]\frac{1}{e^{\frac{2}{3}}}+5\approx5.51[/tex].
Hence , the x-intercept of the graph f(x)= [tex]\dfrac{1}{e^{\frac{2}{3}}}+5[/tex] or 5.51.
Answer:
10^-2/3 +5
Step-by-step explanation:
A company makes triangular plates for individual slices of pizza. For each plate, the base is 7 inches and the height is 12 inches. The area of the top of the plate is ____ inches squared.
Answer:
42 Inches squared ( hope that helps) ;)
The area of the top of the plate will be 42 inches squared.
What is the area of the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
Assume 'h' is the height of the triangle and 'b' be the base of the triangle. Then the area of the triangle is given as,
A = (1/2) × h·b
A company makes triangular plates for individual slices of pizza. For each plate, the base is 7 inches and the height is 12 inches.
Then the area of the triangle is given as,
Area = 1/2 x 12 x 7
Area = 6 x 7
Area = 42 square inches
The area of the top of the plate will be 42 inches squared.
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Which of the following is the correct expanded form for the series below?
A. 1+1+1/2+1/6
B.1+1/2+1/6+1/24
C.1+2/3+1/2+2/5
D.4+2+2/3+1/6
Answer: Option A is correct that is [tex]1 +1+\frac{1}{2} +\frac{1}{6}[/tex]
Explanation:
we will substitute the values of n in given expression
[tex]\sum_{n=1}^{4}\frac{n}{n!}[/tex]
when substituting n=1 we get in [tex]\sum_{n=1}^{4}\frac{n}{n!}[/tex]=[tex]\frac{1}{1!}[/tex]
when n=2 we get [tex]\frac{2}{2!}[/tex]
when n =3 we get [tex]\frac{3}{3!}=\frac{3}{6}=\frac{1}{2}[/tex] ;3 factorial that is 3! = 3 *2*1 = 6
when n=4 we get [tex]\frac{4}{4!}=\frac{4}{24}=\frac{1}{6}[/tex];4! = 4*3*2*1 = 24
Note: factorial means the product of the terms getting multiplied till 1
suppose n! will be equal to n(n-1)(n-2)(n-3).......1
The correct expanded form for the series is Option B, which represents the sum of inverse factorials up to 1/3! The other options do not accurately depict the factorial series.
Explanation:The correct expanded form for the series given would be the option that correctly represents the sum of the factorial terms in the sequence. The series in the choices seems to depict a sum of inverse factorials. Factorials are mathematical expressions that involve multiplying a series of descending natural numbers. The factorial of a number n is represented as n! and is equal to n × (n-1) × (n-2) × … × 1. Therefore, 0! and 1! are both equal to 1, while 2! is equal to 2, 3! equals 6, and 4! equals 24, and so on.
By applying this logic to the options:
Option A is incorrect because 1/6 is equivalent to 1/3! not 1/4!.Option B, 1 + 1/2 + 1/6 + 1/24, correctly represents the sum 1/0! + 1/1! + 1/2! + 1/3!.Option C is incorrect as the sequence of numbers does not represent factorials.Option D is incorrect because the numbers do not follow the pattern of the inverse factorial sequence.Therefore, the correct answer is Option B.
4/101.78 do long divison for this problem
How much money will you have at the end of one year if interest is compounded semiannually at 10% on a $600 deposit? A. $661.50 B. $662.00 C. $660.00 D. $659.50
Compound interest on a principal of $600.00 at a rate of 10% per year compounded twice per year over a period of one year results in an accumulated total of $661.50 (principal plus interest).
What is compound interest rate?Compound interest is computed as interest on the principle of an account plus any accrued interest.
Compound interest can be calculated using the following formula:
A = P(1 + r/n[tex])^{nt}[/tex]
,where x = compound interest
P = principal (the initial deposit or loan amount)
r = annual interest rate
n = the number of compounding periods per unit of time
t = the number of time units the money is invested or borrowed for
Given:
P = principal (the initial deposit amount) = $600
r = annual interest rate = 10%
n = the number of compounding periods per unit of time = 2
t = 1
First, convert R as a percent to r as a decimal
r = R/100
r = 10/100
r = 0.1 rate per year,
Then solve the equation for A
A = P(1 + r/n[tex])^{nt}[/tex]
A = 600.00(1 + 0.1/2[tex])^{(2)(1)}[/tex]
A = 600.00(1 + 0.05[tex])^{(2)}[/tex]
A = $661.50
Therefore, the amount is $661.50.
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What is the volume of a right circular cone with a diameter of 21 centimeters and a height of 87 centimeters? Use 3.14 as an approximation for π. Round your answer to the nearest tenth.
To which real number subset(s) do the following real numbers belong?
-4, -2, 1, 3, 5
A. whole numbers
B. natural numbers
C. integers and rational numbers
D. natural and irrational numbers
reflecting over which line will map the rhombus onto itself
At maximum speed, an airplane travels 2460 miles against the wind in 6 hours. Flying with the wind, the plane can travel the same distance in 5 hours.
Let x the maximum speed of the plane and y be the speed of the wind. What is the speed of the plane with no wind?
The speed of the plane with no wind is 451 miles per hour.
Explanation:Let's solve this problem step-by-step:
We are given that the airplane travels 2460 miles against the wind in 6 hours at maximum speed. This means that the speed of the airplane relative to the ground is its maximum speed minus the speed of the wind. So, the equation is: x - y = 2460/6 or x - y = 410 (where x is the maximum speed of the plane and y is the speed of the wind). We are also given that the airplane can travel the same distance with the wind in 5 hours. This means that the speed of the airplane relative to the ground is its maximum speed plus the speed of the wind. So, the equation is: x + y = 2460/5 or x + y = 492. To find the speed of the plane with no wind, we can add the two equations: (x - y) + (x + y) = 410 + 492. This simplifies to: 2x = 902. Dividing both sides by 2, we get: x = 451. Therefore, the speed of the plane with no wind is 451 miles per hour.
PLEASE HELP!!! IMAGE ATTACHED FIND THE AREA OF THE FIGURE ABOVE
Answer:
231in
Step-by-step explanation:
A grab bag contains 8 football cards and 2 basketball cards. an experiment consists of taking one card out of the bag, replacing it, and then selecting another card. determine whether the events are independent or dependent. what is the probability of selecting a football card and then a basketball card? express your answer as a decimal.
Answer:
Independent - 0.16
Step-by-step explanation:
To the nearest hundredth, what is the circumference of a circle with a radius of 4 units.
A. 201.06
B. 50.27
C. 12.57
D. 25.13
Answer:
it Is D
Step-by-step explanation:
just did it
X+y/3 =5 solve for (x)
Question 3 (Essay Worth 10 points)
(03.06 MC)
Part A: Eveline rented a car at $180 for 4 days. If she rents the same car for 9 days, she has to pay a total rent of $325.
Write an equation in the standard form to represent the total rent (y) that Eveline has to pay for renting the car for x days. (4 points)
Part B: Write the equation obtained in Part A using function notation. (2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
How many distinguishable 7 letter "words" can be formed using the letters in alabamaalabama?
Final answer:
The number of distinguishable 7-letter words that can be formed using the letters in alabamaalabama is 5040.
Explanation:
The number of distinguishable 7-letter words that can be formed using the letters in alabamaalabama can be calculated using permutations. In this case, we have 12 letters, but some of them are repeated. To calculate the total number of permutations, we need to divide the total number of permutations by the factorial of the number of times each repeated letter appears. The word alabamaalabama has 7 distinct letters, so there are no repeated letters in this case. Therefore, the number of distinguishable 7-letter words that can be formed is simply 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040.
Find the values of x and y. Show your work.
Answer:
the value of x and y are, 5 and 4
Step-by-step explanation:
SSS(Side Side Side) postulate states, that if three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.
In given triangle ABC and triangle CDE as shown in attachment , by above theorem ,we have
[tex]AB\cong BC[/tex]
⇒ [tex]7x-4=31[/tex]
[tex]7x=35[/tex]
∴ [tex]x=5[/tex]
also, [tex]BC\cong DE[/tex]
⇒ [tex]4y+8=24[/tex]
simplify:
[tex]4y=16[/tex]
∴ [tex]y=4[/tex]
Hence, the value of x=5 and y=4.
Use the properties of logarithmic functions to simplify the expression on the left side of the equation and determine the values of x and y. Then evaluate the simplified expression. The value of x is , and the value of y is. The value of the expression, rounded to nearest hundredth, is .
To simplify the equation using logarithmic functions, take the natural logarithm of both sides and use properties of logarithms to solve for x and y. Then substitute the values in the simplified expression to evaluate it.
Explanation:To simplify the expression on the left side of the equation using the properties of logarithmic functions, let's work step by step:
Take the natural logarithm (ln) of both sides of the equation. The natural logarithm cancels the exponential function.The natural logarithm of 5.6/16.0 is -1.050.Now, we have the equation ln(x) - ln(2y) = -1.050.Using the property of logarithms, subtracting the logarithms of two numbers is equivalent to dividing the numbers. So we have ln(x/2y) = -1.050.To find the value of x/2y, take the inverse natural logarithm (e^) of both sides.So we have x/2y = e^(-1.050).To solve for x, multiply both sides of the equation by 2y.Therefore, x = 2y * e^(-1.050).Once you have the values for x and y, substitute them into the simplified expression to find its value.Joo-Eun wants to draw a triangle with sides measuring 6 mm, 8 mm, and 11 mm. Which is true about Joo-Eun’s plan? Joo-Eun cannot draw a triangle with these side lengths. Joo-Eun can only draw one unique triangle with these side lengths. Joo-Eun can draw exactly two triangles with these side lengths. Joo-Eun can draw more than one triangle with these side lengths.
Answer:
Option 2 is correct .i.e., Joo-Eun can only draw one unique triangle with these side lengths.
Step-by-step explanation:
Measures of sides of triangles are 6 mm , 8 mm and 11 mm
We use a result which states that if sum of two sides of a triangle is greater than 3rd side then triangle with those measures exist.
here,
6 + 8 = 14 > 11
6 + 11 = 17 > 8
8 + 11 = 19 > 6
Therefore, triangle With given measures exist.
Now we use another result which says that a triangle with given measurement can only be drawn as one unique triangle and the angles would be unique for the particular triangle.
Therefore, Option 2 is correct .i.e., Joo-Eun can only draw one unique triangle with these side lengths.
The statement that is true about Joo-Eun’s plan is: Joo-Eun can only draw one unique triangle with these side lengths.
What is a Unique Triangle?A unique triangle is a congruent triangle that remains the same no matter how it is flipped.
The conditions for a unique triangle include;
The presence of three side lengths as is the case in the triangle Joo-Eun wants to draw, The presence of two angles and any side condition.The triangle in the above question meets the first condition.
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There are 4! (or 24) "words" that can be formed using each of the letters a, b, c and d once. if these "words" are alphabetized, which one is 17th?
A 12 foot ladder is leaning against a building. The ladder makes a 45 degree angle with the building. How far up the building does the ladder reach ?
A. 24√2
B.6√2
C. 6 feet
D.12√2
Answer:
The answer is B. 6 square root 2
Step-by-step explanation:
Given that jklm is a rhombus, find kjm.
a. 37°
c. 106°
b. 74°
d. 143°
Answer:
C.
Step-by-step explanation:
a) 7.02 is 10.4% of what number?
b) 152.5 is what percent of 61?
A television station would like to measure the ability of its weather forecaster. Past data have been collected that indicate the following:
Probability of sunshine on sunny days is 0.8
Probability of sunshine on rainy days is 0.4
Probability of a sunny day is 0.6
Find the probability of
(I)sunshine
(II)sunny given that the forecaster has predicted sunshine
Final answer:
The probability of sunshine on any given day is 0.64, and the probability that it is sunny given that sunshine has been forecasted is 0.75.
Explanation:
To address the question, we'll first define the given probabilities:
Probability of sunshine on sunny days (P(S|Sunny)) = 0.8Probability of sunshine on rainy days (P(S|Rainy)) = 0.4Probability of a sunny day (P(Sunny)) = 0.6Probability of a rainy day is the complement of a sunny day (P(Rainy)) = 0.4, since P(Sunny) + P(Rainy) = 1
Part I: Finding the probability of sunshine
To find the overall probability of sunshine, we use the law of total probability:
P(S) = P(S|Sunny) × P(Sunny) + P(S|Rainy) × P(Rainy)P(S) = 0.8 × 0.6 + 0.4 × 0.4 = 0.48 + 0.16 = 0.64Part II: Finding the probability of sunny given sunshine
To find the probability of sunny given that the forecaster has predicted sunshine, we use Bayes' theorem:
P(Sunny|S) = [P(S|Sunny) × P(Sunny)] / P(S) = (0.8 × 0.6) / 0.64 = 0.48 / 0.64 = 0.75A city’s annual rainfall totals are normally distributed, and the probability that the city gets more than 43.2 inches of rain in a year is given by P(z≥1.5)=0.0668. If the standard deviation of the city’s yearly rainfall totals is 1.8 inches, what is the city’s mean annual rainfall?
Answer: 40.5 inches
Step-by-step explanation:
Given: A city’s annual rainfall totals are normally distributed.
The probability that the city gets more than 43.2 inches of rain in a year is given by P(z≥1.5)=0.0668
Thus, X=43.2 inches
z=1.5
Standard deviation [tex]\sigma[/tex]=1.8 inches
We know that [tex]z=\frac{X-\mu}{\sigma}[/tex]
[tex]\Rightarrow\mu=X-z\sigma\\\Rightarrow\mu=43.2-1.5\times1.8\\\Rightarrow\mu=43.2-2.7\\\Rightarrow\mu=40.5\ inches[/tex]
Hence, the city’s mean annual rainfall is 40.5 inches.
How would you convert the repeating, nonterminating decimal into a fraction? Explain the process as you solve the problem. 0.1515
Answer:
5/33
Step-by-step explanation:
x = 0.1515
100 x = 15.1515
100 x - x = 15.1515 - 0.1515
99 x = 15
x = 15 / 99 = 3 ∙ 5 / 3 ∙ 33 = 5 / 33
0.15165 = 5 / 33
A model rocket is launched with an initial upward velocity of 67/ms. The rocket's height h (in meters) after t seconds is given by the following.
h= 67t-5t^2
Find all values of t for which the rocket's height is 30 meters.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Step-by-step explanation:
The rocket's height h (in meters) after t seconds is given by:
[tex]h=67t-5t^2[/tex]
67 m/s is the initial upward velocity of the rocket. We need to find the values of t for which the rocket's height is 30 meters. So equation (1) becomes :
[tex]67t-5t^2=30[/tex]
[tex]67t-5t^2-30=0[/tex]
The above equation is a quadratic equation. We need to find the value of t.After solving the quadratic equation, we get the values of t are :
t = 0.464 seconds = 0.46 seconds
or
t = 12.936 seconds = 12.94 seconds
Hence, this is the required solution.
The rocket's height is 30 meters at t = 3.79 seconds or t = 0.54 seconds after launch, when solved using the quadratic formula applied to the given equation.
Explanation:To find all values of t for which the rocket's height is 30 meters according to the given quadratic equation h = 67t - 5t2, we need to set the equation equal to 30:
30 = 67t - 5t2
Moving all terms to one side, we obtain:
0 = 5t2 - 67t + 30
Now, we can solve this quadratic equation using the quadratic formula:
t = (-b ± sqrt(b2 - 4ac)) / (2a)
Here, a = 5, b = -67, and c = 30. Plugging these values into the formula we get:
t = (67 ± sqrt(672 - 4 * 5 * 30)) / (10)
Calculating the discriminant and then computing the values for t:
t = 3.79 or t = 0.54
Therefore, the rocket is at 30 meters at approximately t = 3.79 seconds or t = 0.54 seconds after launch, rounded to the nearest hundredth.
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There are 36 students on the bus. There are 2 times as many girls than boys on the bus. On your paper, write a system of liner equations and solve for the number of girls and boys on bus. How many girls are on the bus. A-12 B-24 C-17 D-19
Final answer:
To find the number of girls and boys on the bus, create a system of linear equations and solve for the variables. In this case, there are 12 boys and 24 girls on the bus.
Explanation:
To solve for the number of girls and boys on the bus:
Let G represent the number of girls and B represent the number of boys.
From the problem, G = 2B and G + B = 36.
Substitute G = 2B into the second equation to get 2B + B = 36, which gives B = 12. Therefore, there are 12 boys and 24 girls on the bus.
What is 3/2 - 1 equal
The price of bananas is $6.50 for 5 pounds. What is the price as a unit rate?
$6.50/1lb
$1.30/1lb
$1/30/3lb
$1.05/1lb