The rate of interest is 7.7 % if £9000 has a final value of £13102 in 5 years
When interest is compounding, it indicates that the balance as a whole, rather than just the principal, is taken into account when the following interest period begins.
For instance, after a year, a $100 loan with 5% annual compound interest will have a debt of $105 due. The interest will be applied to the entire $105, creating a new amount of $110.25 the next year, rather than being taken as 5% of $100.
The interest will be added to that $110.25 the following year, and so on throughout the loan.
This is distinct from simple interest, which is a periodic payment to the loan holder of a fixed sum of money derived from a percentage of the principal
We have given that the final amount is 13102 and the principal amount is 9000 and time n is 5 years we have to find the rate
We have the formula
[tex]A=p(1-\frac{r}{100})^n[/tex]
A= 13102
P=9000
n=5
r = ?
[tex]13102=9000(1-\frac{r}{100})^5\\\\1.455=(1-\frac{r}{100})^5\\\\1.077=1-\frac{r}{100}\\\\r=7.7[/tex]
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Which measurement is not equal to one mile
1 yard = 3 feet
6 yards = 18 feet
Truck = 20 feet
Difference = 2 feet = 24 inches
I need help I can't figure this out
Answer:
C
Step-by-step explanation:
It can't be A since you can't have a negative inside a square root
It can't be B [tex]-\sqrt{x+2}[/tex] since it would always be negative and the graph starts positive then turns negative at x=4
C makes since since the graph looks sort of like an upside down [tex]\sqrt{x}[/tex] and has an intercept at y=2
It can't be D since after x=2 the inside of the square root would become negative and you can't have a negative inside of a square root
Cole, a caterer, is investing some money in equipment and employees to help grow his business. Recently he spent $100 on equipment and hired a server who makes $16 per hour. Cole is hoping to make up these expense at the next job that is scheduled, which pays a base of $50 in addition to $18 per hour that the server works. In theory, this event could pay enough to cancel out Cole's expenditures. How much would the job pay?
Given f(x), find g(x) and h(x) such that f(x) = g(h(x)) and neither g(x) nor h(x) is solely x.
f(x)=√-2x³-4-4
The functions h(x) and g(x) are h(x) = -2x³ - 4 and g(x) = √x - 4
Let's work backwards from the given function f(x) to find g(x) and h(x).
f(x) = √(-2x³ - 4) - 4
We can start by letting h(x) = -2x³ - 4.
This means that g(x) must take the square root of its input and then subtract 4 from the result.
In other words:
g(x) = √x - 4
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cot (x + y)=
cotx coty-1/cotx+coty
Actually, the correct identity is: cot(x + y) = (cot x cot y - 1) / (cot x + cot y) This identity can be derived from the sum formulas for tangent and cotangent: tan(x + y) = (tan x + tan y) / (1 - tan x tan y) cot(x + y) = (cot x cot y - 1) / (cot x + cot y) We can start by substituting cot(x + y) with its equivalent expression: cot(x + y) = cot x cot y - 1 / (cot x + cot y) Multiplying both sides by (cot x + cot y), we get: cot(x + y) (cot x + cot y) = cot x cot y - 1 Expanding the left side, we get: cot x cot y + cot x cot
Recently, the top web browser had 51.85% of the market. In a random sample of 300 people, what is the probability that fewer than 129 did not use the top web browser? Round the final answer to at least 4 decimal places and intermediate z-value calculations to 2 decimal places.
Probability that fewer than 129 people in a random sample of 300 did not use the top web browser is approximately 0.0564 for z value.
We must use the normal approximation to the binomial distribution to determine the likelihood that less than 129 individuals in a random sample of 300 persons did not use the most popular web browser. The number of successes in a fixed number of independent trials with the same chance of success in each trial is modelled using the binomial distribution.
Secondly, based on the market share of 51.85%, we must determine the anticipated proportion of 300 participants who did not use the leading web browser:
Estimated percentage of users not using the most popular web browser: 300 * (1 - 0.5185) = 143.55
The standard deviation of the number of participants in a sample of 300 who didn't use the most popular web browser needs to be calculated next:
Standard deviation =[tex]\sqrt{(300 * 0.5185 * 0.4815)}[/tex] = 9.16
We must compute the z value for this value in order to determine the likelihood that fewer than 129 persons did not use the most popular web browser:
z = (129 - 143.55) / 9.16 = -1.59
The probability of a z-score smaller than -1.59 is 0.0564, according to a basic normal distribution table or calculator.
Hence, there is a 0.0564 percent chance that less than 129 out of 300 randomly selected participants did not utilize the most popular web browser.
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are the traiangles shown in the diagram at the right similar? Use angle relationships to explain how you know.
A<65
C< 70
B?
F<45
E<115
D< ?
The two triangles have similar angles, thus the two triangles are similar using the AA criteria.
What are congruent triangles?The dimensions of the sides and angles of two or more triangles determine whether they are congruent. A triangle's size and shape are determined by its three sides and three angles, respectively. If pairings of corresponding sides and corresponding angles are identical, two triangles are said to be congruent. These are the exact same size and form. Triangles can satisfy a wide variety of congruence requirements.
For the triangle ABC using the sum of interior angles of triangle we have:
A + B + C = 180
65 + 70 + B = 180
135 + B = 180
B = 45
Now, for triangle DEF we have:
F = 45.
E = 180 - 115 = 65
Thus, D = 70
The two triangles have similar angles, thus the two triangles are similar using the AA criteria.
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will mark brainliest
what is the value of csc(-176°) to the nearest thousandth?
Step-by-step explanation:
csc(x) = 1/sin(x)
We know that sin(-x) = -sin(x), so we can rewrite csc(-176°) as:
csc(-176°) = 1/sin(-176°) = -1/sin(176°)
Now, we need to find sin(176°) without a calculator. We can use the fact that the sine function has period 360°:
sin(x) = sin(x - 360°)
Therefore, we can subtract 360° from 176° until we get an angle between 0° and 360°:
176° - 360° = -184° + 360° = 176° - 360° = -184° + 360° = ...
We can continue this process until we get an angle between 0° and 360°. Notice that after each subtraction of 360°, the sine function is negated:
sin(176°) = -sin(-184°) = sin(176° - 360°) = -sin(-184° + 360°) = ...
We can continue this process until we get an angle between 0° and 360°:
sin(176°) = -sin(-184°) = sin(176° - 360°) = -sin(-184° + 360°) = sin(176° - 720°) = -sin(-544°) = sin(544°)
Now, we need to find the sine of 544°, which is equivalent to the sine of 544° - 360° - 360° = -176°. We know that sin(-x) = -sin(x), so:
sin(544°) = -sin(-176°) = sin(176°)
Therefore:
csc(-176°) = -1/sin(176°)
Now, we can use the fact that sin^2(x) + cos^2(x) = 1 to find cos(176°):
sin^2(176°) + cos^2(176°) = 1
cos^2(176°) = 1 - sin^2(176°)
cos(176°) = ±sqrt(1 - sin^2(176°))
Since 0° ≤ 176° ≤ 180°, the cosine function is negative:
cos(176°) = -sqrt(1 - sin^2(176°))
Substituting this into the formula for csc(-176°), we get:
csc(-176°) = -1/sin(176°) = -1/(-sqrt(1 - cos^2(176°))) ≈ -17.204
Therefore, the value of csc(-176°) to the nearest thousandth is -17.204.
If x = 3 and 6x(2y-3x) = 18, what is the value
of y?
(F) 2
(G) 4
(H) 5
(J) 6
(K) 9
Answer:
(H) 5
Step-by-step explanation:
[tex](6)(3)(2y-9)=18 \\ \\ 2y-9=1 \\ \\ 2y=10 \\ \\ y=5[/tex)
use sum of difference identity to find exact value
sin(-15 degrees)
Answer: We can use the fact that the sine function is an odd function, which means that:
sin(-x) = -sin(x)
So, we have:
sin(-15 degrees) = -sin(15 degrees)
We can use the sum and difference identity for sine, which states that:
sin(a - b) = sin(a)cos(b) - cos(a)sin(b)
Letting a = 45 degrees and b = 30 degrees, we get:
sin(45 degrees - 30 degrees) = sin(45 degrees)cos(30 degrees) - cos(45 degrees)sin(30 degrees)
We can use the fact that cos(45 degrees) = sin(45 degrees) = √2 / 2 and cos(30 degrees) = √3 / 2 and sin(30 degrees) = 1 / 2 to simplify:
sin(15 degrees) = (√2 / 2)(√3 / 2) - (√2 / 2)(1 / 2)
sin(15 degrees) = (√6 - √2) / 4
Therefore, we have:
sin(-15 degrees) = -sin(15 degrees) = -[(√6 - √2) / 4] = (-√6 + √2) / 4
So the exact value of sin(-15 degrees) is (-√6 + √2) / 4.
Step-by-step explanation:
Consider the two triangles.
15
C
20
Mark this and return
B
H.
12
G
To prove that the triangles are similar by the SAS
similarity theorem, it needs to be shown that
OZCZC
OZC=ZG
O
O
2/02/5
HI
BC
BC
HI
Save and Exit
Next
Submit
2log12 3 + 4log12 2 simplifying
Hello, I was happy to solve the problem. If you find a bug, post in the comments or click on the report, I will see it and try to fix it as soon as possible.
The answer to this problem: 2
A right triangular prism and its net are shown below.
(All lengths are in feet.)
Answer:
120ft²
Step-by-step explanation:
SA = 6(8) + (6+8+10) 3
= 48 + (24)(3)
= 48 + 72
= 120ft²
recently, alicia went on a trip. on the first part of the trip, she drove 260 miles to visit her grandparents. this distance is 4/5 of the total she traveled. what equation can you use to find d, the total length of her trip in miles
The equation we can use to find d, the total length of Alicia's trip in miles, is: 260 = (4/5)d
Calculating the equation of the total length of the tripLet d be the total length of Alicia's trip in miles. According to the problem, the distance she drove to visit her grandparents is 4/5 of the total distance, so we can write:
260 = (4/5)d
To find the total distance d, we can solve this equation for d. First, we can multiply both sides by 5/4 to isolate d:
260 x 5/4 = (4/5)d x 5/4
325 = d
Therefore, the equation we can use to find d, the total length of Alicia's trip in miles, is: 260 = (4/5)d and the distance is d = 325
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The mean age of 25 people in a cinema is 24 year-old. Another person arrives at the cinema and the mean age becomes 25 year-old. Determine the age of the new person.
According to the given information, the mean age of 25 people in the cinema is 24, which means the total age of all 25 people is:
25 people * 24 years = 600 years
When the new person arrives, the total age becomes:
26 people * 25 years = 650 years
The difference between the two totals is the age of the new person:
650 years - 600 years = 50 years
Therefore, the age of the new person is 50 years old.
If j || k, m angle 2 = (7x+13), and m angle 8 = (10x-44), find each angle measure
The angle of 2 = (7x+13) is ∠1 = 146°, ∠2= 34°, ∠3 =34° ∠4= 146°
and angle 8 = (10x-44) is ∠5 =146°, ∠6= 34°, ∠7 = 34°, ∠8= 146°
What are the various types of angles?Acute AnglesObtuse AnglesRight AnglesStraight AnglesReflex AnglesComplete angleWhat is an angle?An angle is a figure obtained from two lines or rays that have the same termination in plane geometry. The common terminal of the two rays is known as the vertex.
In the given question, ∠8= ∠5 = 10x-44
∠1=7x+13
As the corresponding angles on the same side of transversal are equal,
10x-44 = 7x+13
3x = 57
x = 19
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Find the area of the shaded region
The area of the shaded region is evaluated to be equal to the expression 24z² - 22z + 3
How to evaluate for the area of the shaded regionTo get the area of the shaded region, we subtract the area of the small square from the area of the bigger square as follows:
area of bigger square = (5z - 2)(5z - 2)
area of bigger square = 25z² - 20z + 4
area of small square = (z + 1)(z + 1)
area of bigger square = z² + 2z + 1
area of the shaded region = 25z² - 20z + 4 - (z² + 2z + 1)
area of the shaded region = 25z² - 20z + 4 - z² - 2z - 1
area of the shaded region = 24z² - 22z + 3
Therefore, the area of the shaded region is evaluated to be equal to the expression 24z² - 22z + 3
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it takes brian 2/3 of hour to wash his dog sport. if he washes him once a week how many hours will brian spend washing sport over 4 weeks
Answer: 2 hours 40 minutes
Step-by-step explanation: 2/3 x 4 = 8/3 simplified to 2 2/3
2 hours and 2/3 of an hour = 2 hours 40 minutes
The sum of 12 data values is 942. What is the average of the data values?
Answer:
To find the average (also known as the arithmetic mean) of the data values, we need to divide the sum of the values by the number of values. We are given the sum of 12 data values, which is 942. So:
Average = Sum of values / Number of values
Average = 942 / 12
We can simplify this by dividing both the numerator and denominator by their greatest common factor, which is 6:
Average = (942 ÷ 6) / (12 ÷ 6)
Average = 157 / 2
Average = 78.5
Therefore, the average of the 12 data values is 78.5.
Step-by-step explanation:
A jewelry store purchases a diamond ring from a wholesaler for $375.50. The store plans to mark up the ring by 175%. What will be the
selling price of the diamond ring? Round to the nearest cent.
Answer:
$1,033.13.
Step-by-step explanation:
To find the selling price of the diamond ring, we need to add the markup amount to the original cost.
Markup amount = 175% of $375.50
= 1.75 x $375.50
= $657.63
Selling price = Original cost + Markup amount
= $375.50 + $657.63
= $1,033.13
Therefore, the selling price of the diamond ring will be $1,033.13.
Answer:
$1031.63
Step-by-step explanation:
Mark-up refers to the amount or percentage added to the cost price of a product to determine its selling price. It represents the increase in price that a business applies to cover its expenses, generate profit, and account for other factors like overhead costs, operating expenses, and desired profit margin.
To calculate the selling price of the diamond ring, we need to add the mark-up amount to the cost price and round the result to the nearest cent.
To find the mark-up amount, multiply the cost price by the mark-up percentage:
[tex]\begin{aligned}\textsf{Mark-up amount}&=\textsf{Cost price} \times \textsf{Mark-up percentage}\\\\&=\$375.50 \times 175\%\\\\&=\$375.50 \times \dfrac{175}{100}\\\\&=\$375.50 \times 1.75\\\\&=\$657.125\end{aligned}[/tex]
Therefore, the ring will be marked-up by $657.125.
To find the selling price, add the mark-up amount to the cost price:
[tex]\begin{aligned}\textsf{Selling price}&=\textsf{Cost price} + \textsf{Mark-up amount}\\\\&=\$375.50 +\$657.125\\\\&=\$375.50 +\$657.125\\\\&=\$1032.625\end{aligned}[/tex]
Finally, round the selling price to the nearest cent:
[tex]\large\boxed{\textsf{Selling Price} = \$1031.63}[/tex]
Therefore, the selling price of the diamond ring will be $1031.63, rounded to the nearest cent.
PLEASE HELP ASAP!!!!
A cylinder with a diameter of 8 yards has a volume of 452.16 yd3. What is the height of the cylinder? Use 3.14 for π.
2 yards
8 yards
9 yards
18 yards
Answer:
The peak of the cylinder is about 9 yards.
Explanation:
From the above question,
They have given:
A cylinder with a diameter of 8 yards has a volume of 452.16 yd³.
Here we need to find what is the height of the cylinder
Here,
[tex]\pi = 3.14[/tex]. 44 yards 11 yards 8 yards 3 yards
To locate the radius of the cylinder, which is half of of the diameter.
[tex]\text{radius = 8 yards} \div \text{2}[/tex]
[tex]\text{radius} = 4 \ \text{yards}[/tex]
Then we can use the formulation for the quantity of a cylinder to locate the height:
[tex]\text{volume} = \pi \times \text{radius} \times \text{height}[/tex]
[tex]452.16 = 3.14 \times 4^2 \times\text{height}[/tex]
[tex]452.16 = 50.24 \times \text{height}[/tex]
[tex]\text{height} = 452.16 \div 50.24[/tex]
[tex]\text{height} = 9 \ \text{yards}[/tex]
Therefore, the peak of the cylinder is about 9 yards.
Answer: 9 yards
The first person to answer was correct.
Step-by-step explanation:
I took the quiz so you don't have to! <3
Solve the following quadratic equation by completing the square. If necessary, round to the nearest tenth. x2 + 16x = -15
Answer:
x=1, x=15
Step-by-step explanation:
[tex]x^2+16x=-15\\x^2+16x+(8)^2=-15+8^2\\x^2+16x+64=-15+64\\(x+8)^2=49\\\sqrt{(x+8)^2=49} \\x+8=+-7\\x=8-7 = 1\\x=8+7=15[/tex]
while calculating your quiz grades you noticed Mrs. McClellan wrote the following numbers at the top of your quizzes:. 8/10; 81%; 0.805. place scores in ascending order.
HELP PLEASE!!!!
Tell me what to shade in! And also tell me what word is formed
50 point reward!***
Answer:
7/8, 1/5, 1/3, 5/9, 11/12, 2/5, 3/5, 3/20, 9/25, 3/7, 3/8, 4/9, 8/15, 4/5, 5/7, 1/8, 7/12, 21/25, 1/6, 3/14, 1/4, 8/27, 3/4, 2/3, 5/6, 2/15, 27/40, 9/10, 5/12
the secret message spells "YES"
Step-by-step explanation:
you cant divide any of the numbers above by the same number and not get a decimal.
Answer: The word is yes
Step-by-step explanation:
Shade in 7/8, 1/5, 2/5, 3/7, 8/15, 3/14, 3/4, 5/9, 3/8, 4/5, 1/4, 2/3, 1/3, 3/5, 5/7, 1/8, 5/6, 2/15, 11/12, 3/20, 9/25, 4/9, 7/12, 21/25, 1/6, 8/27, 9/10, 27/40, and 5/12.
4. Oliver just got a new credit card and immediately made a purchase for $2500. The card offers a 0% APR for the first 90 days and a 17.99% APR afterward, compounded daily. Oliver doesn't expect to pay off the $2500 balance on the card for one year, nor does he expect to make any more purchases during the year. He wants to know how much money in interest the 0% APR for the first 90 days will save him. Help Oliver calculate the answer. Ignore any possible late payment fees.
Part II: What is the effective interest rate offered by Oliver's credit card? Round your answer to two decimal places.
Part III: How much will Oliver pay in interest on the $2500 purchase over the course of the year?
Part IV: What would the effective interest rate have been if the APR had been 17.99%, compounded daily, for the whole year? Round your answer to two decimal places.
Part V: How much would Oliver have paid in interest on the $2500 purchase over the course of the year with the effective interest rate from Part IV?
Part VI: How much money in interest will the 0% APR for the first 90 days save Oliver?
The solution to the interest rate problems from part I to part VI can be found below.
Interest rate calculationPart I:
Interest rate per day = 0.1799 / 365 = 0.00049342466Interest accrued during first 90 days = 2500 * (1 + 0.00049342466)^(90) - 2500 = $33.53Part II:
Effective annual interest rate = (1 + (APR / n))^n - 1Effective annual interest rate = (1 + (0.1799 / 365))^365 - 1 = 0.1974 or 19.74%Part III:
Interest = P * ((1 + r/n)^(n*t) - 1)
where P is the principal (in this case, $2500), r is the interest rate per year (0.1799), n is the number of times the interest is compounded per year (365), and t is the time in years (1).
Interest = 2500 * ((1 + 0.1799/365)^(365*1) - 1) = $449.23
Part IV:
If the APR had been 17.99%, compounded daily, for the whole year, the effective interest rate would be the same as the APR, since there is no introductory 0% period.
Effective annual interest rate = 17.99%
Part V:
Interest = P * ((1 + r/n)^(n*t) - 1)Interest = 2500 * ((1 + 0.1799/365)^(365*1) - 1) = $449.23Part VI:
As calculated in Part I, the interest Oliver would accrue during the first 90 days with the 17.99% APR is $33.53. Since the 0% APR for the first 90 days means he will not accrue any interest during that time, the 0% APR will save him $33.53 in interest.
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Considering only the values of θ for which the expression is defined, which of the following is equivalent to the expression below?
cos(−θ)⋅tan(−θ)⋅cscθ
Select the correct answer below:
−sinθ
1
sinθ
−1
The cos(θ) term cancels out and we are left with -1. Therefore, the equivalent expression is -1.
We can start by using the trigonometric identities:
cos(-θ) = cos(θ)
tan(-θ) = -tan(θ)
csc(θ) = 1/sin(θ)
Substituting these identities into the original expression, we get:
cos(θ) * (-tan(θ)) * (1/sin(θ))
Simplifying this expression, we can cancel out the cos(θ) and the sin(θ) terms:
-1 * cos(θ) * (1/(cos(θ))) The cos(θ) term cancels out and we are left with -1. Therefore, the equivalent expression is -1.
In other words, the original expression simplifies to -1 for all values of θ where it is defined (i.e. θ ≠ (2n + 1)π/2, where n is an integer). This means that as θ varies, the value of the expression will always be -1 when it is defined. Trigonometric identities are mathematical equations that involve trigonometric functions and are true for every possible value of the variables involved. There are various types of trigonometric identities, including:
Pythagorean Identities:
[tex]sin^2a + cos^2a= 1\\tan^2a + 1 = sec^2a\\1 + cot^2a = csc^2a[/tex]
Angle Sum and Difference Identities:
sin(α±β) = sin α cos β ± cos α sin β
cos(α±β) = cos α cos β ∓ sin α sin β
tan(α±β) = (tan α ± tan β) / (1 ∓ tan α tan β)
Double Angle Identities:
sin 2θ = 2 sin θ cos θ
cos 2θ =[tex]cos^2[/tex]θ - [tex]sin^2[/tex]θ = 2 [tex]cos^2[/tex]θ - 1 = 1 - 2[tex]sin^2[/tex]θ
tan 2θ = (2 tan θ) / (1 - [tex]tan^2[/tex]θ)
Half Angle Identities:
sin (θ/2) = ± √[(1 - cos θ) / 2]
cos (θ/2) = ± √[(1 + cos θ) / 2]
tan (θ/2) = ± √[(1 - cos θ) / (1 + cos θ)]
Product-to-Sum Identities:
sin α sin β = (1/2) [cos (α-β) - cos (α+β)]
cos α cos β = (1/2) [cos (α-β) + cos (α+β)]
sin α cos β = (1/2) [sin (α+β) + sin (α-β)]
Sum-to-Product Identities:
sin α + sin β = 2 sin [(α+β)/2] cos [(α-β)/2]
sin α - sin β = 2 cos [(α+β)/2] sin [(α-β)/2]
cos α + cos β = 2 cos [(α+β)/2] cos [(α-β)/2]
cos α - cos β = -2 sin [(α+β)/2] sin [(α-β)/2]
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For each pair of triangles below state whether the triangles are congruent not congruent or impossible to tell
Answer:
a) congruent
b) not congruent
c) congruent
Step-by-step explanation:
You want to know which sets of isosceles triangles are congruent.
Isosceles triangleAn isosceles triangle has two congruent sides and two congruent angles. If those sides and angles match corresponding sides and angles in another isosceles triangle, then the triangles will be congruent.
Unless the triangle is equilateral, the two congruent base angles will have different measures than the angle between the congruent sides. Once any of the angle measures is known, the others are determined—provided that we also know which angle it is that is known.
a) Third angle knownThe congruent side measures are the same, and the apex angle is the same. This triangle pair is congruent.
b) Angles givenThe base angle of one triangle is the same measure as the apex angle of the other. (Neither is 60°.) These triangles cannot be congruent.
c) Base angle knownThe congruent side measures are the same, and the base angles are the same. This triangle pair is congruent.
Unsure about this question! Please help me.
The factors of [tex]16x^2yz[/tex] are [tex]4xyz, xz, and 12.[/tex]yz, xz, and 12.
What is the expression?The factors of the given expression 16x^2yz are:
[tex]4xyz:[/tex]This is a valid factor of [tex]16x^2yz[/tex] because it contains all the variables x, y, and z, and the exponent of x is 1, the exponent of y is 1, and the exponent of z is 1. Additionally, it contains a numerical factor of 4.
[tex]2xy:[/tex]This is not a factor of 16x^2yz because it does not include the variable z, which is present in the given expression.
[tex]xz:[/tex] This is not a factor of [tex]16x^2yz[/tex] because it does not include the variable y, which is present in the given expression.
[tex]12:[/tex] This is not a factor of [tex]16x^2yz[/tex] because it is a numerical factor and does not contain any of the variables x, y, or z.
[tex]xyz:[/tex] This is not a factor of [tex]16x^2yz[/tex] because it does not contain any numerical factor. It only includes the variables x, y, and z without any exponents.
Therefore, the factors of [tex]16x^2yz[/tex] are [tex]4xyz, xz, and 12.[/tex]
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What is the justification for each step in the solution of the equation?
23x−13=2(x+2)
Select from the drop-down menus to correctly justify each step.
23x−13=2(x+2)
Given
2x−1=6(x+2)
1Combine like terms.
2x−1=6x+12
Distributive Property
2x=6x+13
2Distributive Property
−4x=13
Addition or Subtraction Property of Equality
x=−134
Justification for equation 23x−13=2(x+2) with Distributive Property, Addition or Subtraction Property of Equality, and Division Property of Equality. We also combined and isolated variable. The final solution is x = -1.1905.
Here is a step-by-step justification for each step in the solution of the equation 23x−13=2(x+2):
Step 1: Given
The equation 23x−13=2(x+2) is given as part of the problem statement.
Step 2: Distributive Property
We distribute the 2 on the right side of the equation by multiplying it by both terms inside the parentheses to get 2x + 4. This results in the equation 23x − 13 = 2x + 4.
Step 3: Combine like terms
We combine the like terms on the right side of the equation to get 6x + 12. This results in the equation 23x − 13 = 6x + 12.
Step 4: Distributive Property
We subtract 2x from both sides of the equation to isolate the variable on one side. This results in the equation 21x - 13 = 12.
Step 5: Addition or Subtraction Property of Equality
We add 13 to both sides of the equation to isolate the variable. This results in the equation 21x = 25.
Step 6: Division Property of Equality
We divide both sides of the equation by 21 to solve for x. This results in the solution x = 25/21 or x = -1.1905.
In conclusion, the Distributive Property, Addition or Subtraction Property of Equality, and Division Property of Equality were used to support each step in the solution of the problem 23x13=2(x+2). In order to make the equation simpler and isolate the variable on one side, we additionally combined like terms. x = -1.1905 is the solution's final form.
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What is the missing length?
Answer:
Using the Pythagorean theorem, we know that in a right-angle triangle, we have:
a^2 + b^2 = c^2
where c is the hypotenuse.
From the given information, we have:
ab = 11 - x
a = x
b = 11
c = 11 (given)
We can use the given values to eliminate a or b from the Pythagorean theorem:
a^2 + (11 - x)^2 = 11^2
Expanding and simplifying, we get:
a^2 + 121 - 22x + x^2 = 121
a^2 + x^2 - 22x = 0
Substituting a = x into the above equation, we get:
x^2 + x^2 - 22x = 0
2x^2 - 22x = 0
2x(x - 11) = 0
So, either x = 0 or x - 11 = 0.
Since x cannot be zero (as it represents a length), we have x - 11 = 0.
Therefore, x = 11.
Hence, the value of x in its simplest form with a rational denominator is 11/1 or just 11.
Answer:
[tex]x=11\sqrt{2}[/tex]
Step-by-step explanation:
The given right triangle is an isosceles right triangle since its legs are equal in length (denoted by the tick marks).
Side x is the hypotenuse of the isosceles right triangle.
Given both legs are 11 units in length, we can use Pythagoras Theorem to calculate the length of the hypotenuse.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
As a and b are the legs, and c is the hypotenuse, substitute the following values into the formula and solve for x:
a = 11b = 11c = xTherefore:
[tex]\implies 11^2+11^2=x^2[/tex]
[tex]\implies 121+121=x^2[/tex]
[tex]\implies 242=x^2[/tex]
[tex]\implies x^2=242[/tex]
[tex]\implies \sqrt{x^2}=\sqrt{242}[/tex]
[tex]\implies x=\sqrt{242}[/tex]
To simplify the radical, rewrite it as a product of prime numbers:
[tex]\implies x=\sqrt{11^2 \cdot 2}[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}[/tex]
[tex]\implies x=\sqrt{11^2}{\sqrt{2}[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]
[tex]\implies x=11\sqrt{2}[/tex]
Therefore, the length of side x in simplest radical form is 11√2.