On your paper, construct a rectangle on a coordinate plane that satisfies these criteria.
• The sides of the rectangle are either vertical or horizontal.
• The perimeter of the rectangle is 42 units.
• Each of the vertices lies in a different quadrant.
What are the coordinates of the vertices of your rectangle? Explain how you know the perimeter of your rectangle is
42 units
Answers
Answer:
[tex]A = (5,3)[/tex]
[tex]B = (-5,3)[/tex]
[tex]C = (-5,-8)[/tex]
[tex]D = (5,-8)[/tex]
Step-by-step explanation:
Required
[tex]Perimeter = 42[/tex]
Construct a rectangle whose perimeter is 42 units and satisfies the given conditions.
First, name the rectangle ABCD.
Such that:
[tex]A = (x_1,y_1)[/tex]
[tex]B = (x_2,y_2)[/tex]
[tex]C = (x_3,y_3)[/tex]
[tex]D = (x_4,y_4)[/tex]
For the rectangle to be either horizontal or vertical, then:
[tex]y_1 = y_2[/tex] and [tex]y_3 = y_4[/tex]
We have that:
[tex]Perimeter = 42[/tex]
Replace perimeter with its formula
[tex]2(AB + BC) = 42[/tex]
Divide both sides by 2
[tex]AB + BC = 21[/tex]
This implies that, the distance between adjacent sides (through the edges) must be equal to 21
Having said that: a set of coordinates that satisfy the given conditions are:
[tex]A = (5,3)[/tex] -- First quadrant
[tex]B = (-5,3)[/tex] -- Second quadrant
[tex]C = (-5,-8)[/tex] -- Third quadrant
[tex]D = (5,-8)[/tex] -- Fourth quadrant
The above quadrants satisfy the condition:
[tex]y_1 = y_2[/tex] and [tex]y_3 = y_4[/tex]
HOW TO KNOW THE PERIMETER IS 42
To do this, we simply calculate the distance between the edges and add them up
Distance is calculated as:
[tex]D = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2[/tex]
For AB
[tex]A = (5,3)[/tex]
[tex]B = (-5,3)[/tex]
[tex]D_1 = \sqrt{(5 - (-5))^2 + (3 - 3)^2}= \sqrt{(10)^2 + (0)^2} = \sqrt{100} = 10[/tex]
For BC
[tex]B = (-5,3)[/tex]
[tex]C = (-5,-8)[/tex]
[tex]D_2 = \sqrt{(-5 - (-5))^2 + (3 - (-8))^2}= \sqrt{(0)^2 + (11)^2} = \sqrt{121} = 11[/tex]
For CD
[tex]C = (-5,-8)[/tex]
[tex]D = (5,-8)[/tex]
[tex]D_3 = \sqrt{(-5 -5)^2 + (-8 - (-8))^2}= \sqrt{(-10)^2 + (0)^2} = \sqrt{100} = 10[/tex]
For DA
[tex]D = (5,-8)[/tex]
[tex]A = (5,3)[/tex]
[tex]D_4 = \sqrt{(5 -5)^2 + (-8 -3)^2}= \sqrt{(0)^2 + (11)^2} = \sqrt{121} = 11[/tex]
So, the perimeter is:
[tex]P = D_1 + D_2 + D_3 + D_4[/tex]
[tex]P = 10 + 11 + 10 +11[/tex]
[tex]P = 42[/tex]
See attachment for rectangle
Related Questions
can u give an answer
Answers
Answer: 0
Step-by-step explanation:
Put 0 in the front box.
this is because you cant divide 11 apples equally into 6 people; 11 isn't a multiple of 6
A researcher at a major clinic wishes to estimate the proportion of the adult population of the United States that has sleep deprivation. What size sample should be obtained in order to be 99 % confident that the sample proportion will not differ from the true proportion by more than 4%? Round up to the nearest whole number.
Answers
The sample size needed to be 99% confident that the sample proportion will not differ from the true proportion by more than 4% is given as follows:
n = 1037.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error is given as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
As we have no estimate, the parameter is given as follows:
[tex]\pi = 0.5[/tex]
Then the sample size for M = 0.04 is obtained as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.04\sqrt{n} = 2.575 \times 0.5[/tex]
[tex]\sqrt{n} = \frac{2.575 \times 0.5}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2[/tex]
n = 1037.
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Reacting with water in an acidic solution at a particular temperature, compound A decomposes into compounds B and C according to the law of uninhibited decay. An initial amount of 0.40 M of compound A decomposes to 0.37 M in 30 minutes. How much of compound A will remain after 2 hours? How long will it take until 0.10 M of compound A remains? After 2 hours, the amount of compound A remaining will be ? M. (Do not round until the final answer. Then round to thenearest hundredth as needed.)
Answers
The answers to all parts are shown below.
The law of uninhibited decay is a first-order chemical reaction, which means that the rate of the reaction is proportional to the concentration of compound A.
The rate law can be written as:
rate = k[A]
where k is the rate constant and [A] is the concentration of compound A.
From the given data, we can use the following equation to determine the rate constant:
ln([A]t/[A]0) = -kt
where [A]t is the concentration of compound A at time t, [A]0 is the initial concentration of compound A, k is the rate constant, and t is the time.
Using the given data:
[A]t = 0.37 M
[A]0 = 0.40 M
t = 30 minutes = 0.5 hours
ln(0.37/0.40) = -k(0.5)
k = 0.0486 h⁻¹
(a) How much of compound A will remain after 2 hours?
Using the same equation and substituting the known values:
ln([A]t/[A]0) = -kt
ln([A]t/0.40) = -0.0486 x 2
[A]t/0.40 = e⁻(⁹⁷² /¹⁰⁰⁰⁰)
[A]t = 0.25 M
Therefore, after 2 hours, 0.25 M of compound A will remain.
(b) How long will it take until 0.10 M of compound A remains?
Substituting the known values into the equation again:
ln([A]t/[A]0) = -kt
ln(0.10/0.40) = -0.0486t
t = 4.26 hours
Therefore, it will take approximately 4.26 hours until 0.10 M of compound A remains.
(c) After 2 hours, the amount of compound A remaining will be 0.25 M.
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you
cou
Recommendations
Florida's B.E.S.T. Standards: Grade 8 > GG.5 Make predictions 38C
thro
Skill plans
pieces of vanilla cake
You have prizes to reveall Go to
Passersby have taken 4 pieces of vanilla cake and 6 pieces of coconut cake from a
sample tray. Based on past data, of the next 30 samples taken, how many should you expect
to be pieces of vanilla cake?
Vid
Answers
Out of the following 30 samples, you may expect that about 12 will be portions of vanilla cake.
How to determine probability?To solve this problem, use the concept of probability and make a prediction based on the past data.
In this case, out of the 10 pieces of cake that have been taken, 4 are vanilla and 6 are coconut.
Therefore, the probability of selecting a piece of vanilla cake from the tray is 4/10, or 2/5.
To predict how many of the next 30 samples will be pieces of vanilla cake, multiply the probability of selecting a vanilla cake by the total number of samples:
(2/5) x 30 = 12
So expect that out of the next 30 samples taken, approximately 12 of them will be pieces of vanilla cake.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
Answer:
A
Step-by-step explanation:
i do this all the time math is my thing
I NEED YOUR HELP WITH STATISTICS
Answers
For a probability distribution to be represented, it is needed that P(X = 0) + P(X = 1) = 0.44. Hence one possible example is:
P(X = 0) = 0.40.
P(X = 1) = 0.04.
Discrete random variable to represent a probability distribution =
The sum of all the probabilities must be of 1, hence:
P(X = 0) + P(X = 1) + P(X = 3) + P(X = 4) + P(X = 5) = 1.
Then, considering the table:
P(X = 0) + P(X = 1) + 0.15 + 0.17 + 0.24 = 1
P(X = 0) + P(X = 1) + 0.56 = 1
P(X = 0) + P(X = 1) = 0.44.
Hence one possible value is:
P(X = 0) = 0.40.
P(X = 1) = 0.04.
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Help pleaseeeee guys
Answers
On performing , the "row-operation" 2R₁ + R₂ → R₂ on the matrix "M", the resulting new-matrix is [tex]\left[\begin{array}{ccc}5&1&-5\\10&0&-8\end{array}\right][/tex] .
The matrix "M" is given as : [tex]\left[\begin{array}{ccc}5&1&-5\\0&-2&2\end{array}\right][/tex],
We have to apply the Row-Operation : 2R₁ + R₂ → R₂, on the matrix "M",
Performing the row-operation "2R₁ + R₂ → R₂" on a matrix "M" means multiplying the first-row of "M" by 2, and then adding the resulting values to the second-row of "M" to produce a new value for each element in the second row.
This operation does not affect the first row of "M" and changes the values in the second row of "M".
⇒ [tex]\left[\begin{array}{ccc}5&1&-5\\2\times5+0&2\times 1-2&2\times(-5)+2\end{array}\right][/tex],
⇒ [tex]\left[\begin{array}{ccc}5&1&-5\\10+0&2-2&-10+2\end{array}\right][/tex],
⇒ [tex]\left[\begin{array}{ccc}5&1&-5\\10&0&-8\end{array}\right][/tex].
Therefore, the new-matrix is [tex]\left[\begin{array}{ccc}5&1&-5\\10&0&-8\end{array}\right][/tex].
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Groups 1 and 3 In a class of 42 students, 12 boys and 15 girls know how to read three-letter words in English. 19 boys and 17 girls know how to identify all letters of the alphabet. None of the students in the class can write a sentence of five words if dictated to them. There are 22 boys and 20 girls in the class.
•Using a Venn diagram, show how many boys and girls cannot read a letter or a three-letter word.
•If all students should know how to write a sentence of five words by the end of the academic year, how many groups will you need to form to focus on remedial/tutor support (to teach at the right level)?
• If by the end of the academic year, all students are able to identify all letters, read three-letter words, and write a five-word sentence, what would this Venn diagram look like?
Answers
There are 23 boys and 20 girls in the class who cannot read a letter or a three-letter word.
How to solveThe Venn diagram is drawn as shown in the attached image, and it shows that the number of boys and girls who cannot read a letter or a three-letter word is marked as (c+d) which represents 13 boys and 8 girls.
Given:
The class has 42 students.
12 boys and 15 girls are said to know how to read three-letter words in English.
19 boys and 17 girls are said to know how to identify all letters of the alphabet.
None of the students in the class is able to write a sentence of five words if dictated to them.
There are in total 22 boys and 20 girls in the class.
Read three-letter words |
|____________|______________|
| | |
| Boys (12) | Girls (15) | Can read three-letter words
|____________|______________|
| | |
| Boys (10) | Girls (13) | Cannot read three-letter words
_______|____________|______________|
| | |
| Boys (9) | Girls (13) | Can identify all letters
|____________|______________|
| | |
| Boys (13) | Girls (7) | Cannot identify all letters
|____________|______________|
To find the number of boys and girls who cannot read a letter or a three-letter word, we need to add up the numbers in the two bottom circles:
Boys who cannot read a letter or a three-letter word: 10 + 13 = 23
Girls who cannot read a letter or a three-letter word: 13 + 7 = 20
Therefore, there are 23 boys and 20 girls in the class who cannot read a letter or a three-letter word.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
Answer:
4x = 100, so x = 25
The correct answer is C.
When Grace opens and lays a shipping box out flat, she sees that the top and the bottom of the box
both measure 10 inches by 14 Inches, the sides of the box both measure 14 inches by 8 inches, and
the front and back of the box both measure 8 inches by 10 inches. What is the surface area of Grace's
strooing box?
Answers
The surface area of Grace's shipping box is 664 square inches.
We have,
The box can be divided into six rectangles, each of which represents the face of the box.
To find the surface area of the box, we need to find the area of each face and then add them all up.
The top and bottom of the box are both 10 inches by 14 inches, so the area of each of these faces is:
= 10 x 14
= 140 square inches
The sides of the box are both 14 inches by 8 inches, so the area of each of these faces is:
= 14 x 8
= 112 square inches
The front and back of the box are both 8 inches by 10 inches, so the area of each of these faces is:
8 x 10
= 80 square inches
To find the surface area of the whole box, we add up the areas of all six faces:
= 2(140) + 2(112) + 2(80)
= 280 + 224 + 160
= 664 square inches
Therefore,
The surface area of Grace's shipping box is 664 square inches.
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radius of 18 feet and a central angle of 52° is shown below. Which of the following is the closest to the length of the arc from point C to point D?
Answers
The closest length to the arc from point C to point D is 16.34 ft (option c).
To find the length of the arc from point C to point D, we need to calculate the circumference of the circle and then find the fraction of the circumference represented by the central angle.
The circumference of a circle can be calculated using the formula:
Circumference = 2 × π × radius
Given the radius of 18 feet, the circumference is:
Circumference = 2 × π × 18 = 36π feet
To find the length of the arc, we need to find the fraction of the circumference represented by the central angle of 52°. The fraction is calculated by dividing the central angle by 360° and then multiplying it by the circumference.
Length of the arc = (Central angle / 360°) * Circumference
Length of the arc = (52° / 360°) × 36π
Length of the arc = (13/90) × 36π
Length of the arc = 468π / 90
Length of the arc ≈ 16.41 ft
Among the given options, the closest length to the arc from point C to point D is 16.34 ft (option c).
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each sine or cosine value to its equivalent measure
Answers
The equivalent sine and cosine values are as follows:
cos(74°) = sin(16°)cos(57°) = sin(33°)sin(32°) = cos(58°)sin(43°) = cos(47°)What is the relationship between sine and cosine angles?The relationship between sine and cosine angles is:
sinθ = cos(90 - θ)
This equation is known as the complementary angle identity for sine and cosine. It states that the sine of an angle is equal to the cosine of its complementary angle (90 degrees minus the original angle).
For example, if we have an angle theta = 30 degrees, its complementary angle would be 90 - 30 = 60 degrees.
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Geometry problem (possible drop down answers are ellipse rectangle and circle) please help! Will give crown to first to give correct answer.
Answers
Answer:
ellipses
a pair of parallel straight
Step-by-step explanation:
What is an equation of the line that passes through the point
(
8
,
7
)
(8,−7) and is parallel to the line
x+2y=18?
Answers
s
Brendon finished an obstacle course in 22.5 minutes. Tobias finished the course 85 seconds after Brendon. How long did it take Tobias to finish?
Answers
Answer:
23.35 minutes
Step-by-step explanation:
Brendan finished in 22.5 minutes. Tobias finished 85 seconds after. Just add 85 seconds to 22.5 minutes. There are 100 second in 1 minute. Since Brendan is already at 22.5, there is only 0.5 left to get to 23. 0.5 in this case means 50 seconds. You do 85 - 50 = 35. Now, you are at 23 minutes. Add 35 seconds to that to get to 23.25 minutes.
The EPA fuel economy estimates for automobiles models tested recently found them to be
normally distributed with a mean of 24.8 mpg and a standard deviation of 6.2 mpg. What is
the percentile rank of an automobile that has a fuel economy of 35 mpg?
90th Percentile
O 5th Percentile
O 95th Percentile
10th Percentile
Answers
Step-by-step explanation:
(35-24.8) / 6.2 = z-score of + 1.645 corresponding to .9495 =
~ 95th percentile
Can anyone help me w tvis
Answers
The number of weeks that the puppies weigh the same amount will be A. 6 weeks.
The equation that has no solution is A. 13 - 7x = -7x + 13.
The option determined from the graph is B. The ordered pair (25, 6) is a solution to y = x + 40 and y = 3x + 15.
How to calculate the number of weeksPuppy A weighs 4 1/5 pounds at birth and gains 3/4 pound each week. Puppy B weighs 5 2/3pounds at birth and gains 1/2 pound each week.
After how many weeks will the puppies weigh the same amount will be calculated thus:
4 1/5 + 3/4x = 5 2/3 + 1/2x
4.2 + 0 75x = 5.67 + 0.5x
Collect the like terms
5.67 - 4.2 = 0.25x
Divide
x = 1.47 / 0.25
x = 6
Hence ,the number of weeks that the puppies weigh the same amount will be A. 6 weeks.
It should be noted that the equation that has no solution is A. 13 - 7x = -7x + 13. This is because the values gives 0 all through.
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Please help with that question
Answers
The value of function f (α + β) is determined as (3√3 + 1)/3, (2√2 - 3)/3.
What is the value of function f (α + β)?The value of f (α + β) is calculated by applying the following formula as follows;
The given functions;
for α: x² + y² = 4
y is given as -1, the value of x is calculated as;
x² + (-1)² = 4
x² + 1 = 4
x² = 3
x = √3
α = (√3, - 1)
for β: x² + y² = 1
x is given as ¹/₃, the value of y is calculated as;
(¹/₃)² + y² = 1
¹/₉ + y² = 1
y² = 1 - ¹/₉
y² = ⁸/₉
y = √ (8/9)
y = 2√2/3
β = (¹/₃, 2√2/3)
The value of function f (α + β) is calculated as;
f(α + β) = (√3, - 1) + (¹/₃, 2√2/3)
f(α + β) = (3√3 + 1)/3, (2√2 - 3)/3
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100 Points! Algebra question. Photo attached. Solve the equation. Please show as much work as possible. Thank you!
Answers
Answer:
[tex]3 {cos}^{2} x - {sin}^{2} x = 0[/tex]
[tex]3 - 3 {sin}^{2} x - {sin}^{2} x = 0[/tex]
[tex]3 - 4 {sin}^{2} x = 0[/tex]
[tex]4 {sin}^{2} x = 3[/tex]
[tex] {sin}^{2} x = \frac{3}{4} [/tex]
sin(x) = +(1/2)√3
x = π/3 + 2kπ or x = 2π/3 + 2kπ
x = -π/3 + 2kπ or x = -2π/3 + 2kπ
(k is an integer)
Can someone answer this question
Answers
The options 2nd and 3rd are the monomials with degree 2.
Given are the expressions we need to find the monomials with degree 2.
So,
The general form of a monomial with degree 2 is:
ax²
The highest exponent of a polynomial's variable(s) in any of its terms is referred to as the polynomial's degree in mathematics.
It controls the polynomial's behavior and complexity.
A non-negative integer is used to represent the degree.
And,
A monomial is a mathematical expression consisting of a single term. It is composed of a coefficient multiplied by one or more variables raised to non-negative integer exponents.
Here, the monomials can be 2x² and x²
Hence the options 2nd and 3rd are the monomials with degree 2.
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Shirley Garcia is a restaurant supplies salesperson and receives 8% of her total sales as commission. Her sales totalled $15,000 during a given week. Find her commission.
Answers
Answer:
8% of $15,000 = .08 × $15,000 = $1,200
I have not gone to school in a month for family reasons and I have to submit 39 math assignments before Friday HELP
Answers
Diego is correct as the number of groups result to 6/5 or 1 1/5.
We have to find the number of groups of 5/6 in 1.
So, we need to perform the division as
= 1/ (5/6)
= 1 x 6/5
= 6/5
= 1 1/5
Thus, Diego is correct as the number of groups result to 6/5 or 1 1/5.
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How many 1/3 inch cubes does it take to fill a box with a width of 2 2/3 inches, length of 3 1/3 inches with a height 2 1/3
Answers
The number of 1/3 inch cubes required to fill the box is 62.
Volume of boxVolume = length × width × height
Height = 7/3
Length = 10/3
width = 8/3
Hence ,
Volume = 7/3 × 10/3 × 8/3 = 560/27
Size of cube = 1/3
Number of cubes required = Volume of box / size of cube
Number of cubes = 560/27 × 3/1
Number of cubes = 1680/27 = 62.22
Therefore, it will take 62 1/3 cubes to fill the box
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if you walked 3 blocks north and then 8 blocks west and then 10 blocks south how far are you from your starting point it each block is 2/10 of a mile?
Answers
You are approximately 3.4 miles from your starting point.
We have,
To solve this problem, we need to use the Pythagorean theorem, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the length of the hypotenuse.
|\
8 | \
| \
|___\
3
We can see that the three blocks north and 10 blocks south cancel each other out, so we only need to consider the 8 blocks west.
Using the distance formula, we can find that the distance traveled west is:
8 blocks × 2/10 mile per block = 1.6 miles
Now we can use the Pythagorean theorem to find the distance from the starting point:
distance = √(3² + 1.6²)
distance ≈ 3.4 miles
Therefore,
You are approximately 3.4 miles from your starting point.
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What is the length of Arc LM? Use 3.14 as pi and round your answer to the nearest tenth. please show work, will mark brainliest.
Answers
To find the length of arc LM, we need to use the formula for the circumference of a circle:
C = 2πr
In this case, the arc LM is a portion of the circumference of the circle. To find the length of the arc, we need to determine the angle at the center of the circle that corresponds to the arc.
Looking at the image you provided, we can see that angle LOM is a right angle (90 degrees). The angle at the center of the circle, LOCM, is half of the right angle, which is 45 degrees.
To calculate the length of arc LM, we need to find the fraction of the total circumference represented by the central angle LOCM. The fraction is given by:
Fraction of circumference = Angle at center / 360 degrees
Fraction of circumference = 45 degrees / 360 degrees
Fraction of circumference = 1/8
Now, we can calculate the length of arc LM:
Length of arc LM = Fraction of circumference * Circumference
Length of arc LM = (1/8) * (2πr)
Since the radius (r) is not given in the image, we cannot calculate the exact length of arc LM. However, we can provide the formula for the length of arc LM in terms of the radius:
Length of arc LM = (1/8) * (2πr) = πr/4
So, the length of arc LM is πr/4, where r is the radius of the circle.
If you have the value of the radius, you can substitute it into the formula to find the specific length of arc LM.
100 Points! Algebra question. Photo attached. Sketch the angle. Then find its reference angle. Show your calculations. Thank you!
Answers
The reference angle of 13π/8 is 3π/8 and the sketch of the angle is attached
How to sketch the angle and find the reference angleFrom the question, we have the following parameters that can be used in our computation:
Angle = 13π/8
Rewrite as
θ = 13π/8
The above angle is in the fourth quadrant
So, we subtract it from 2π to calculate the reference angle
Using the above as a guide, we have the following:
Reference angle = 2π - 13π/8
Evaluate the difference
Reference angle = 3π/8
Hence, the reference angle is 3π/8 and the sketch of the angle is added as an attachment
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5. In AABC, ZA = 70°, ZB = 50°, and a = 15 cm. Solve ▲ABC.
Answers
In triangle ABC, side BC (a) is 15 cm, side AC (b) is 13.30 cm, and side AB (c) is 12.23 cm. Also angle A is 70°, B is 50°, and C is 60°
Understanding the Angles and Sides of TriangleUsing the Law of Sines and the fact that the sum of the angles in a triangle is 180 degrees.
The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. Using this, we can find the lengths of the other sides of triangle ABC.
Let's denote side AB as c, BC as a, side AC as b, and angle C as ∠C.
Using the Law of Sines, we have:
sin(∠A) / a = sin(∠B) / b
Substitute in the known values, we get:
sin(70°) / 15 = sin(50°) / b
Make b the subject of the formula:
b = (15 * sin(50°)) / sin(70°)
Using a calculator, we can find the value of b:
b = (15 * 0.766) / 0.9397
= 12.23 cm
Therefore side AC = b = 12.23 cm
Now, to find side AB (c), we can use the Law of Sines again:
sin(∠B) / b = sin(∠C) / c
But ∠C is unknown. To find ∠C, we apply the sum of angle in a triangle rule
∠A + ∠B + ∠C = 180
70 + 50 + ∠C = 180
∠C = 180 - 70 - 50
∠C = 60°
Substitute the values in the Sine rule equation
sin(50°) / 12.233 = sin(60) / c
Make c the subject of the formula
c = (12.233 * sin(60)) / sin(50°)
c = (12.233 * sin(60°)) / sin(50°)
= 13.30 cm
Therefore, the lengths of the sides of triangle ABC are:
Side AB = c = 12.23 cm
Side BC = a = 15 cm
Side AC = b = 13.30 cm
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Find the surface area of the prism. Round to the nearest tenth if necessary.
Regular pentagon base
B≈61.94 cm2
Base length=6cm
Lateral edge=5cm
A regular pentagonal prism is shown. The length of the side of the pentagon is six centimeters. The height of the prism is five centimeters.
Answers
The surface area of the prism is 248.88 cm²
What is surface area of prism?The area occupied by a three-dimensional object by its outer surface is called the surface area.
The surface area of a prism is expressed as;
SA = 2B + ph
where h is the height of the prism, B is the base area of the prism and P is the perimeter of the base.
Base area = 61.94 cm²
height = 5cm
perimeter = 5 × 5 = 25cm
SA = 2 × 61.94 + 25 × 5
SA = 123.88+ 125
SA = 248.88 cm²
Therefore the surface area of the prism is 258.88 cm²
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Can someone please answer and provide an explanation for these problems?
Answers
62. The slope of the line is 1/8. the equation of line is y = 1/8x - 3/8
63. It has an infinite slope. The equation of line is x = 3
64. The slope of the line is -5. The slope of the new line is 1/5. The equation of line is y = 1/5x - 1
65. The slope of the line is 2/9. The slope of the new line is -9/2. The equation of line is y = -9/2x - 4
How do we identify the slope and equation of line?62) through: (3,0), parallel to y = 1/8x - 3. If a line is parallel to another, they have the same slope. Therefore the slope is 1/8.
For line equation⇒ (y - y1 = m(x - x1))
Substituting (3,0) and slope 1/8 gives us:
(y = mx + b) ⇒ y - 0 = 1/8 × (x - 3)
First, substitute the point and the slope into the equation: 0 = 1/8×3 + b
Then solve for b, the y-intercept: b = -3/8
⇒ y = 1/8x - 3/8
63) through: (3,-1), parallel to x = 0. A line parallel to x = 0 is a vertical line. A vertical line has the equation x = a, where a is the x-coordinate of any point on the line. A line through (3, -1) and parallel to x = 0 would simply be x = 3 or y = -1
64) through: (5, 0), perp. to y= -5x - 4. If a line is perpendicular to another, their slopes are negative reciprocals. The slope of y = -5x - 4 is -5, so the slope of the line we are looking for is -1/(-5) = 1/5
65) through: (-2, 5), perp. to y=2/9x - 1. perpendicular line to y = 2/9x - 1 has the slope that is the negative reciprocal of 2/9, which is -9/2. y = -9/2x - 4.
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?? geometry question
Answers
The measure of angle BGF from the given parallel lines is 108°.
Given that, measure of angle BGF=4x+28 and the measure of angle EHD = 2x+32.
1) From the given figure, angle BGF and angle EHC are interior alternate angles.
Angle FHC and angle EGA are corresponding angles.
Angle FHC and angle EGA are exterior alternate angles.
2) angle BGF+angle EHD=180°
3) 4x+28+2x+32=180°
6x+60=180
6x=120
x=20
Angle BGF=4x+28=108 °
Angle EHD = 2x+32
= 112°
Angle FHD=180-112=68°
Angle EGB=180-108=72°
Therefore, the measure of angle BGF from the given parallel lines is 108°.
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