Answer:
Yes.
Step-by-step explanation:
No x value is used twice.
Jim has to choose between two gym membership plans. Plan A: $50 monthly membership fee and $10 per visit. Plan B: $25 one time membership fee and $15 per visit. How many visits must Jim make to make Plan A the cheaper option?
How many visits for them to cost the same
If you answer the visits, I will give branliest
The number or visits that Jim must make to make Plan A the cheaper option is more than 5 visits
How to illustrate the equation?An equation is the statement that illustrates the variables given. Jim has to choose between two gym membership plans.
For Plan A: $50 monthly membership fee and $10 per visit. This will be:
50 + 10v
Plan B: $25 one time membership fee and $15 per visit. This will be:
= 25 + 15v
Let v = number of visit
This will be illustrated as:
50 + 10v = 25 + 15v
Collect like terms
15v - 10v = 50 - 25
5v = 25
Divide
v = 25 / 5
v = 5
There will be more than 5 visits for a cheaper option.
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is melissa correct that m(
Answer:
no melissa isn't correct she has made 3 mistakes
Step-by-step explanation:
Construct a confidence interval for p₁ -P2 at the given level of confidence.
x₁ = 355, n₁ = 536, x₂ =438, n₂ = 598, 99% confidence
The researchers are confident the difference between the two population proportions, p₁ - P₂, is between
(Use ascending order. Type an integer or decimal rounded to three decimal places as needed.)
Using confidence interval concepts, it is found that the correct options are:A. With 99% confidence, the mean width of all widgets is between 14.3 and 30.4.
Find the solution ?There is a 99% chance that the mean of the population is between 14.3 and 30.4.
The interpretation of a x% confidence interval is that we are x% sure that the population mean is in the interval.
In this problem, 99% confidence interval for widget width is between 14.3 and 30.4, hence we are 99% sure that the population mean, that is, the mean width of all widgets is between 14.3 and 30.4, hence options A and C are correct.
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How much would you need to deposit in an account now in order to have $5,000.00 in the account in 1633 days?
Assume the account earns 42% simple interest.
You would need to deposit ___
in your account now.
You would need to deposit $2,500 in order to have $5,000.00 in the account in 1633 days.
1st method: This can be found by using the simple interest formula I=PRT. In this case, I=5000, P=2500, R=.42, and T=1633. Solving for I gives you the answer.
2nd Method: If you deposit $2,500 in an account now, you will have $5,000 in the account in 1633 days. $2,500 * 1.42 = $3,550 $3,550 + $2,500 = $6,050 $6,050 / 2 = $3,025
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What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Here are the dimensions of two designs for a sandbox for the primary playground. Each sandbox is a rectangular prism. One design is 3 m by 3 m by 30 cm.
A second design is 3.25 m by 3.25 m by 25 cm.
a) Sketcheachsandbox.Includeitsdimensions.
b) Compare the designs. For each design, calculate the area
of material needed to build it and the volume of sand
it will hold.
c) Whichsandboxshouldbebuilt?Justifyyouranswer.
The volume of the first and second designs are 2.7 m³ and 2.64 m³ so, the second design will hold more sand.
What is volume?
The capacity occupied by a three-dimensional solid shape is known as volume. It is difficult to visualize in any shape, yet it may be compared among shapes. For instance, a compass box has a larger volume than an eraser placed inside of it.
Given:
One design is 3 m by 3 m by 30 cm,
A second design is 3.25 m by 3.25 m by 25 cm,
Calculate the volume for the first design as shown below,
Volume of first design = 3 × 3 × 30/ 100 (1 m = 100 cm),
The volume of the first design = 270 / 100
The volume of the first design = 2.7 m³
Calculate the volume of the second design as shown below,
The volume of the second design = 3.25 × 3.25 × 25 / 100
The volume of the second design = 264.06 / 100
The volume of the second design = 2.64 m³
The difference in the volume of both designs = The volume of the first design - The volume of the second design
The difference in the volume of both designs = 2.7 - 2.64
The difference in the volume of both designs =0.06 m³
Thus, the first design will hold more volume of sand.
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Write an equation to match this graph.
The equation that matches the graph is 7x-30y=-275
How to find the equation of a line?We should know that an equation is a mathematical expression in which two sides are equal.
The equation of a line is the equation formed with the slope of the straight line
The slope of the of the is determined taking the points
[tex]M=\frac{Y_{2}-Y_{1} }{X_{2}-X_{1} }[/tex]
Slope=(7-1)÷(35-5)
m=1/5
The equation of the line is
1/5 = (y-1)÷(x-35)
Cross multiplying the equation
7x-245=30y-30
Rearrange,
7x-30y=-30-245
7x-30y=-275
In conclusion the equation to match the graph is 7x-30y=-275
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Assume that a company makes only one product, maintains no beginning or ending inventories, and uses a standard costing system. The standard cost card for that product is shown below:
Standard Quantity or Hours Standard Price or Rate Standard Cost
Direct materials 3 pounds $ 13.00 per pound $ 39.00
Direct labor 2 hours $ 16.00 per hour $ 32.00
Fixed manufacturing overhead 2 hours $ 8.00 per hour $ 16.00
The company purchased 22,000 pounds of direct materials from its supplier at a cost of $12.50 per pound. The company used 22,000 pounds of direct material to start and complete 7,800 units of finished goods during the period. Its direct laborers worked 16,000 hours and were paid a total of $248,000. Based on this information, the total increase recorded in the Work in Process account related to direct labor would be:
Garrison 17e Rechecks 2020-09-29
Multiple Choice
$241,800.
$256,000.
$248,000.
$249,600.
Group Ends
Since the company paid a total of $248,000 in direct labor costs during the period, there is no difference between the standard and actual costs of direct labor.
How to calculate labor cost ?To determine the total increase recorded in the Work in Process account related to direct labor, we need to first calculate the total standard cost of direct labor for the period and then compare it to the actual cost of direct labor.
According to the standard cost card, each unit of the product requires 2 hours of direct labor at a rate of $16.00 per hour.
This means that the total standard cost of direct labor for the period is 2 * $16.00 * 7,800 = $248,000.
Since the company paid a total of $248,000 in direct labor costs during the period, there is no difference between the standard and actual costs of direct labor. Therefore, the total increase recorded in the Work in Process account related to direct labor would be $0.
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My sister is 8 years older than I am. The sum of our ages is 28. Find our ages.
I am years old. My sister is years old.
Answer:
My sister is
18
years old.
Step-by-step explanation:
s = m + 8 Eq. 1
s + m = 28 Eq. 2
s = my sister age
m = my age
Replacing Eq. 1 in Eq. 2:
(m+8) + m = 28
2m + 8 = 28
2m = 28 - 8
2m = 20
m = 20/2
m = 10
From Eq. 1:
s = m + 8
s = 10 + 8
s = 18
Check:
from Eq. 2:
s + m = 28
18 + 10 = 28
100 points for this one
Answer:
C) x < - 11 or x > 8---------------------------------------
First, solve the inequality:
|2x + 3| > 192x + 3 > 19 or 2x + 3 < - 192x > 16 or 2x < - 22x > 8 or x < - 11This is option C (you have chosen it correctly).
Now, graph it:
Mark points - 11 and 8 on the number line with open circle, then shade to the left from point - 11 and to the right from point 8.Answer:
x < -11 or x > 8
Step-by-step explanation:
Given absolute value inequality:
[tex]|2x+3| > 19[/tex]
[tex]\boxed{\begin{minipage}{7.1 cm}\underline{Absolute rule}\\\\If\;\;$|u| > a,\;a > 0$\;\;then\;\;$u < -a$\;\;or\;\;$u > a$\\ \end{minipage}}[/tex]
Apply the absolute rule:
[tex]\underline{\sf Case\;1}\\\begin{aligned}2x+3& < -19\\2x& < -22\\x& < -11\end{aligned}[/tex] [tex]\underline{\sf Case\;2}\\\begin{aligned}2x+3& > 19\\2x& > 16\\x& > 8\end{aligned}[/tex]
To graph the solution:
Place open circles at -11 and 8.Shade to the left of the open circle at -11.Shade to the right of the open circle at 8.A new gaming chair costs $309.99. You have already saved $144.99 and earn $27.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
27.5w − 144.99 = 309.99; w = 17
27.5 + 144.99w = 309.99; w = 6
27.5w − 309.99 = 144.99; w = 17
27.5w + 144.99 = 309.99; w = 6
The linear equation we need to solve is:
$27.50*w = $309.99 - $144.99
And the solution is w = 6.
How to write and solve the equation?
We know that the cost of the gaming chair is $309.99.
To buy this, you already have saved $144.99, and save another $27.50 per week, then the amount you have after w weeks is:
f(w) = $144.99 + $27.50*w
So the linear equation we need to solve is:
$144.99 + $27.50*w = $309.99
To solve this we need to isolate w.
$144.99 + $27.50*w = $309.99
$27.50*w = $309.99 - $144.99
w = ($309.99 - $144.99)/$27.50 = 6
So they can buy the chair after 6 weeks.
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You give a test to 100 students and determine the median of the scores. After grading the test you realize that the 10 students with the highest scores did exceptionally well. You decide to award these 10 students a bonus of 5 more points each. The median of the new score distribution will be (less than, greater than or the same as) that of the original score distribution?
Answer:
R'>R
Step-by-step explanation:
To determine the range of the scores, we conduct a test of 100 students. After grading the test, we realized that the 10 students with the highest scores did exceptionally well. We decide to award these 10 students a bonus of 5 more points each. The range of the new score distribution will be greater than that of the original score distribution.
We know the range is defined by R
R = X(n) - X(1), where X(n) is the maximum value of the observed values, and X(1) is the minimum value of those observed values.
Here for this test study, we awarded 10 highest scorers extra 5 points each. Therefore our maximum observed value becomes X(n) + 5. So, our range also becomes
R = X(n) + 5 - X(1)
So, R'>R. Hence, the range of the new score will be greater than that of the original score distribution.
Test the claim that the two samples described below come from populations with the same mean. Assume that the samples are independent simple random samples. Use a significance level of alpha = 0.1 The degree of freedom is The test statistic is Determine the rejection region for the test of The final conclusion is
Final conclusion would be that the difference between the means of the two samples is not statistically significant.
What is Null Hypothesis?
The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.
It is not possible to test the claim that the two samples come from populations with the same mean without more information about the samples themselves. In order to test this claim, you need to have the sample data, the sample sizes, and the standard deviations of the samples. You can then use a t-test for independent samples to determine whether the difference between the means of the two samples is statistically significant.
The t-test is a statistical test that is used to compare the means of two samples. The test statistic for the t-test is the difference between the means of the two samples divided by the standard error of the difference. The degree of freedom for the t-test is the sum of the sample sizes minus 2. The significance level, alpha, is the probability of making a type I error, which is the probability of rejecting the null hypothesis when it is true. The rejection region for the t-test is the set of values of the test statistic for which the null hypothesis is rejected.
If the test statistic does not fall in the rejection region, you cannot reject the null hypothesis, and you must conclude that the difference between the means of the two samples is not statistically significant.
Final conclusion would be that the difference between the means of the two samples is not statistically significant.
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Let T(n) denote the nth term of a sequence t. if T(1) = 3, and T(n+1) = T(n) +5 for n>1, what are the first four terms of the sequence
Based on the given analysis where T(1) = 3, and T(n+1) = T(n) +5 for n>1, the first four terms of the sequence are 3, 7, 8, 9
What is the first four terms of the sequence?First term, T(1) = 3
nth term, T(n+1) = T(n) +5 for n>1
Second term, T2 = T(n) +5
= 2 + 5
= 7
Third term, T3 = T(n) +5
= 3 + 5
= 8
Fourth term, T3 = T(n) +5
= 4 + 5
= 9
Therefore, the first four terms of the sequence are 3, 7, 8, 9
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AOB is a sector of a circle, centre O and radius 12 cm. The length of arc AB is 15 cm. Find the area of the sector.
The formula to find the arc length of a circle = θ/360 ×2××r
The formula to find the area of a sector= θ/360××r²
The only thing missing is "θ"
The arc length is given to be 15cm so basically θ/360×2×3.14×12 = 15
θ= 360×15 ÷ 2×3.14×12 = 5400÷ 75.36= 71.65
now that we found "θ" we just continue with the formula to find the area of a sector (θ/360×r²)
=71.65×3.14×12²= 90cm
(it's a bit complicated but i hope this helped i tried to simplify it as much as i could)
Help ASAP FIRST ONE TO GIVE CORRECT ANSWER GET BRAINLYEST ANSWER Artists use different techniques to make their prints unique.
Which print displays the artist's use of the woodcut technique?
Answer:Printmaking is the process of creating artworks by the process of printing. It can be done on paper, brick, wood, and even metal.A lithographic is a planetographic process where the design is drawn into a flat stone and is prepared by use of metal. As per the paintings shows the artwork shows us the rhinosaruers. The painting is made from water and oil.Hence the painting B shows us the use of lithography.
The price of one gallon of milk has increased from $3.24 to $4.05. What is the percentage increase?
Answer:
the price of one gallon of milk has increased by 25%.
Step-by-step explanation:
The price of one gallon of milk has increased from $3.24 to $4.05, which is an increase of $4.05 - $3.24 = $0.81. To find the percentage increase, we can divide the amount of the increase by the original price and multiply by 100%. This gives us:
(0.81 / 3.24) * 100% = 25%
Therefore, the price of one gallon of milk has increased by 25%.
The solution is 25 %
The percentage increase in the price of one gallon of milk is given by the equation P = 25 %
What is Percentage Error?
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage error is the difference between the measured value and the true value , as a percentage of the true value
Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100
Given data ,
Let the original price of the milk be A = $ 3.24
Let the increased price of the milk be B = $ 4.05
Let the percentage increase in the price be = P
Now , the equation will be
Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100
Substituting the values in the equation , we get
Percentage increase P = [ ( 4.05 - 3.24 ) / 3.24 ] x 100
On simplifying the equation , we get
Percentage increase P = ( 0.81 / 3.24 ) x 100
Percentage increase P = 0.25 x 100
Percentage increase P = 25 %
Therefore , the value of P is 25 %
Hence , the percentage increase is 25 %
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Zendaya's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y=7.6x+60y=7.6x+60, where yy represents the expected quiz score and xx represents hours spent on homework that week. What is the meaning of the xx-value when y=100y=100?
For the quiz score of 100, the time will be equal to 5.26 hours.
What is an expression?Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols. They can also denote the operation order and other properties of the logical syntax.
The numerical variables and operations denoted by the addition, subtraction, multiplication, and division signs are combined in the mathematical expression.
Given that the relationship can be represented by the equation y=7.6x+60. Here x is the time and y is the score of the quiz.
At the score of the quiz of 100, the value of x will be calculated as,
y = 7.6x+60
100 = 7.6x + 60
40 = 7.6x
x = 40 / 7.6
x = 5.26 hours
The meaning of the value of x = 5.26 hours is that for scoring 100 on the quiz the time will be 5.26 hours.
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Jennie is making popcorn. The recipe calls for 1/2 cup of butter, 3 tablespoons of kernels, and 1 teaspoon of salt. If she uses 10 tablespoons of kernels, how much butter does she need? Round your answer to the nearest hundredth.
The required butter she needed is given as 1.67 cups of butter.
As given in the question, Jennie is making popcorn. The recipe calls for 1/2 cup of butter, 3 tablespoons of kernels, and 1 teaspoon of salt. If she uses 10 tablespoons of kernels,
What is the Ratio?The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
here,
Let the nutter need be x cups,
now,
Taking the ratio o butter to kernels
[1 / 2] / 3 = x / 10
x = 10 / 6
x = 1.67
Thus, As of the given proportion, she requires 1.67 cups of butter.
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What is the discontinuity and zero of the function f of x equals x squared plus 5 times x minus 6 all over quantity x plus 6 end quantity question mark
a
Discontinuity at (−6, −7), zero at (−1, 0)
b
Discontinuity at (6, 5), zero at (−1, 0)
c
Discontinuity at (−6, −7), zero at (1, 0)
d
Discontinuity at (6, 5), zero at (1, 0)
The discontinuity of our given function is at point (-6, -7).
The zero of our given function is, (1, 0).
What is discontinuity and zero of the function?
A discontinuous function is a graph function that is not connected to any other functions. If the left-hand limit of f(x) and the right-hand limit of f(x) both exist but are not equal, then the function f(x) is said to have a discontinuity of the first kind at x = a.
The x-intercept(s) of the function's graph represent the real zero of the function.
Consider the given function,
[tex]f(x) = \frac{x^2+5x-6}{x+6}[/tex]
We know that a function is discontinuous, when its denominator is equal to zero.
To find the discontinuity for our given function, we will equate denominator to 0 as:
x + 6 = 0
x = -6
Now simplify the given function.
[tex]f(x) = \frac{x^2+5x - 6}{x+6}\\ f(x) = \frac{x^2 +6x - x - 6}{x+6}\\ f(x) = \frac{x(x+6)-1(x+6)}{x+6}\\ f(x) = \frac{(x-1)(x+6)}{x+6} \\f(x) = x-1[/tex]
Take y = x - 1
Since the denominator term is cancelled out, so our give function has a removable discontinuity.
Now, we will find value of y by substituting x = -6
⇒ y = -6 - 1
y = -7
Therefore, the discontinuity of our given function is at point (-6, -7).
Now, we will find zero of our given function by substituting f(x) = 0,as zero of the function is the point, where graph intersects x-axis and value of y is 0 at x-axis:
⇒ 0 = x - 1
x - 1 = 0
x = 1
Therefore, the zero of our given function is, (1, 0).
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draw a continuous region in a given region that is not a type 1 or type 2 region but can be split into one of eachDraw an example of a region that is(a) type I but not type II(b) type II but not type I
Type I regions- ∫∫R f(x,y)dA = ∫b x=a ∫h(x) y=g(x) f(x,y) dy dx
Type II regions- ∫∫R f(x,y)dA = ∫d y=c ∫h(y) x=g(y) f(x,y) dx dy
What is the type I and type II regions?Curves of type I can be described for yy in terms of xx and often "lay above and below" one another.
Type II curves, on the other hand, can be defined for xx in terms of yy and are more or less "left and right" of one another.
Type II regions can be divided into horizontal slices, but Type I regions can be divided into vertical slices.
When a location is simultaneously classified as Type I and Type II, you can choose to examine it in any manner.
Type I regions are regions that are bounded by vertical lines x=a and x=b, and curves y=g(x) and y=h(x), where we assume that g(x)<h(x) and a<b. Then we can integrate first over y and then over x:
∫∫R f(x,y)dA = ∫b x=a ∫h(x) y=g(x) f(x,y) dy dx
Type II regions are bounded by horizontal lines y=c and y=d, and curves x=g(y) and x=h(y), where we assume that g(y)<h(y) and c<d. Then we can integrate first over x and then over y:
∫∫R f(x,y)dA = ∫d y=c ∫h(y) x=g(y) f(x,y) dx dy
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A spinner is divided into four sections, each in a different color, as shown below. A spinner is divided into 4 unequal parts. Each part is labeled with a color. From largest to smallest: Blue takes up almost half of the spinner. Red takes up a little more than a quarter of the spinner. Green takes up a little less than a quarter of the spinner. Yellow takes up about half of a quarter of the spinner. After the spinner is spun, the arrow points to one of the colors. Which statement about possible outcomes is true?
The true statement regarding the probabilities on the spinner is given as follows:
The probability that the spinner will point to yellow is less than 1/4.
What is a probability?The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
Hence, for the spinner given in this problem, the probabilities are given by the fraction occupied by each area, as shown by the image given at the end of the answer.
From the text, these fractions, representing the probabilities, are given as follows:
Blue: around 1/2.Red: around 1/4.Green: around 1/4.Yellow: around 1/8.Missing InformationThe problem is given by the image shown at the end of the answer.
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Can you please help me
Answer:
the first option
Step-by-step explanation:
in an "and" statement both parts need to be true, so that the overall condition is true.
is x = 6 a valid solution ?
no, it violates both, x <= -8 and x <= 4
is a value between -8 and 4 a valid solution like x = -2 ?
no, it violates x <= -8, even though it is true for x <= 4.
only values that are smaller or equal to -8 (like -9) are true for both.
and therefore the first answer option is correct.
Choose the function whose graph is given by:
A. y=-3.5cos x
B. y=3.5sin x
C. y=sin(3x)
D. y=2.5sin x
The function plotted in the graph is given by - g(x) = 3.5 sin(x)
What is sine function? What is sine series? What is law of sines?In trigonometry, the sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle.Mathematically -[tex]$\sin \theta=\frac{a}{h}[/tex]
{θ} = angle theta
{a} = length of opposite side a
{h} = length of hypotenuse h
The sine series is given as follows -[tex]${\displaystyle {\begin{aligned}\sin(x)&=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots \;= \sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)!}}x^{2n+1}\\[8pt]\end{aligned}}}[/tex]
The law of sines states that for an arbitrary triangle with sides [a], [b] and [c] and angles opposite the sides [A], [B] and [C] -{sin(A) / a = sin(B) / b = sin(C) / c}
Given is a graph as shown in the image.
A sine function has its maximum value of [1] and the minimum value of [-1]. The given graph g(x), is a amplitude scaled version of the function f(x) given by -
f(x) = sin(x)
and
g(x) = Asin(x)
Here, [A] is equal to 3.5. So, the function g(x) is equal to -
g(x) = 3.5 sin(x)
Therefore, the function plotted in the graph is given by -
g(x) = 3.5 sin(x)
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How to set up the following question in the image below?
The expected number of students that pick soda is 80
How to determine the expected number of students that pick Soda?From the bar graph, we have the following parameters that can be used in our computation:
Ice cream = 40
Soda = 20
popsicle = 10
This means that the proportion of soda is
Soda = 20/(40 + 20 + 10)
Evaluate the sum
Soda = 20/70
So, we have
Soda = 2/7
For a group of 280 students, we have
Soda = 2/7 *280
Evaluate
Soda = 80
Hence, the number of students is 80
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Review the graph. Given z = -1 - i, which letter represents z3?
Answer:
C
Step-by-step explanation:
Multiply z times itself. Then multiply z times that first answer, to get z^3.
There's a formula for cubing a binomial but even if you don't remember it (like me) you can still find z^3.
But remember that i^2 = -1
This is related to sqrt(-1)= i, a definition for the imaginary number.
On the graph, go left or right for the real part and up or down for the imaginary part.
see image.
Which expression can be used to represent the volume of this prism?
Responses
3 × 9 × 9 units³
2 × 3 × 3 units³
2 × 3 × 9 units³
3 × 3 × 18 units³
The expression that represents the volume of the prism is
2 × 3 × 9 units³. That is option C.
What is a prism?Prism is defined as the type of polyhedron that has two polygonal faces lying in parallel planes and with the other faces parallelograms.
A prism can be of a regular shape or of an irregular shape. The volume of a regular shapes prism can be calculated using the formula stated below
volume of a prism = l × b × h
Length (l) = 9 units
Breath = 2 units
Height (h) = 3 units.
Therefore, the volume of the given prism can be calculated as 2 × 3 × 9 units³.
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a snail travels 5 meters in 20 minutes. He travels the same amount of time per meter. How long will it take him to travel 11 meters?
Answer:
Step-by-step explanation:rate = minute/meter => 20/5
so, 5/1 for rate
so for 11 meter, (5m/1min)(11)
The answer is 55 minutes
Find the length of BD. Use that length of BC. Round to the nearest tenth
By means of trigonometric functions, the length of side BC is approximately equal to 11.6 centimeters.
How to determine a missing length in a system of triangles by trigonometric functions
In this problem we find a geometric system formed by two right triangles, from which we need to determine the exact measure of side BC. This can be done by means of trigonometric functions, that represents relationships between two sides of a right triangle:
sin θ = y / r
cos θ = x / r
tan θ = y / x
cot θ = x / y
sec θ = r / x
csc θ = r / y
Where:
r - Hypotenusex - Leg adjacent to the angle.y - Leg opposite to the angle.First, obtain the length of side BD:
cos θ = BD / AB
BD = AB · cos θ
BD = 5 · cos 30°
BD = 5√3 / 2 cm
Second, calculate the length of side BC:
sin θ = BD / BC
BC = BD / sin θ
BC = 5√3 / 2 / sin 22°
BC ≈ 11.6 cm
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The length of a rectangle is 3 meters less than
twice its width. The area of the rectangle is
104 m²2. Find the dimensions of the rectangle.
Therefore, the length of a rectangle is 13m and width is 8m
What is area?A region's size on a planar or curved surface is described mathematically as its area. In contrast to a plane region or plane's area, which refers to a form or planar lamina, a surface area is the size of an open surface or the edge of a three-dimensional object.
Here,
width=x
length=2x-3
Area =l x w
104=(2x-3)(x)
104=2x^2-3x
52=x^2-3/2(x)
52+9/16=x^2-3/2(x)+9/16
841/16=(x-3/4)^2
29/4=x-3/4
x=32/4
x= 8m
Thus width = 8m
length = 2(8)-3 = 13m
Therefore the length of a rectangle is 13m and width is 8m
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