What is the definition of a lateral area? Please show me an example too, so I understand what to do with it.
Answers
Answer:
• Lateral area is the area of the sides of a 3-dimensional object, excluding the top and bottom bases. (Those bases are generally parallel to each other.) In the case of a cone or cylinder, it is the area of the curved surface. In the case of a pyramid, it is generally the area of the triangular faces. In the case of a cuboid, it is the area of the sides, excluding the top and bottom.
• Some examples are shown in the first attachment. An ambiguous case is shown in the second attachment. (For the ambiguous case, you would need to talk to the poser of the question to see what area they intend by "lateral area.")
Step-by-step explanation:
The total surface area of an object is the total area you would paint if you were to paint all surfaces of the object. The lateral area is the area you would paint if you did not paint the top or bottom surfaces (bases) of the object. For a pyramid or cone, the top base is a point, so has no area.
Some formulas are used for lateral area:
LA = πrs . . . . . cone with base radius r and slant-height s
LA = 2πrh . . . . cylinder with base radius r and height h
LA = Ph . . . . . . prism with base perimeter P and height h
LA = 1/2Ps . . . . pyramid with base perimeter P and slant height s
___
About the ambiguous case in the second attachment
Generally, we take the "lateral area" of a pyramid to be the total area of its triangular faces. Here, the figure appears to be resting on one of its triangular faces, and the square base is uncovered at the side. This orientation suggests that the "lateral area" should include the area of the square, and exclude the area of one of the triangles.
Further adding to the ambiguity is the fact that the top flat surface might also be considered a "base" and excluded from the area calculation.
I don't have a definitive answer for this situation except to say that whoever posed the problem certainly had something in mind when they asked for the "lateral area" of this figure. They should be consulted as to their intent. (When this question was answered on Brainly, the square was included and one triangle was excluded. No feedback was provided to indicate whether that choice was "correct.") Personally, I might say this is a square pyramid and its lateral area is that of the four triangles: 352 m².
Final answer:
The lateral area is the sum of the areas of all the sides of a 3D geometric figure excluding the base(s). For example, the lateral area of a cylinder with height h and radius r is calculated as 2πrh. To understand the concept further, comparing the areas of two squares and using scale for area measurements were demonstrated.
Explanation:
The term lateral area refers to the surface area of the sides of a three-dimensional geometric figure, excluding the area of its bases (top and bottom faces). In other words, it is the sum of the areas of all the faces of the figure that are not its base(s).
To illustrate, let's consider a cylinder as an example. If the cylinder has a height (h) and the radius of its base (r), the lateral area (Alateral) is calculated by the formula Alateral = 2πrh. This is because the lateral surface of a cylinder is essentially a rectangle wrapped around the circular base, the length of the rectangle being the circumference of the base (2πr) and the width being the height (h).
Now let's compare two areas. Suppose you have two squares, one with a side length twice the size of the other. If the smaller square has a side length of 's', then its area is s². The larger square, with sides twice as long, will have an area of (2s)², which equals 4s². The ratio of their areas is therefore 4s² to s², which simplifies to 4:1, showing that the larger square has four times the area of the smaller one.
Similarly, we can use a scale to find the area of a space. By determining the length and width, we can perform the necessary calculations to find the area. When we have two areas to compare, proportions are used to compare their sizes. The area is computed using the dimensional formula L² (length times width for rectangles or 2πr for the circumference and πr² for the area of a circle).
Related Questions
Find the equation of the line that is perpendicular to the line 4x + 2y = 1 and passes through the point (−4, 3).
A) y=2x+5
B) y=2x+2
C) y=1/2x+2
D) y=1/2x+5
Answers
Answer:
y=1/2x+5 or d
Step-by-step explanation:
Answer is D
Step-by-step explanation:
Jessica has some markers. She has 5 more black markers than blue markers. She has 4 times as many red markers as black markers. She has 8 blue markers. How many markers does Jessica have altogether? asap 60 points
Answers
Answer:
73 markers
Step-by-step explanation:
let b = blue markers
black markers = b+5
red markers = 4* black markers
= 4 * (b+5)
= 4b+20
The total markers is blue + black + red
b + b+5 + 4b+20 = 6b+25
We know she has 8 blue markers
black markers = b+5 = 8+5 = 13
red markers = 4b +20 = 4*8 +20 = 32+20 = 52
The total markers =6b+25= 6(8) + 25 = 48+25 = 73
Which is not a correct way to name the angle?
Answers
Answer:
The third one (QRP)
Step-by-step explanation:
it indicates that the angle is at point R, which it isn't! The letter in the middle shows where the angle is
Option C is not a correct way to name the angle. This is obtained by understanding the correct ways of naming an angle.
What are the correct ways of naming an angle?The correct ways of naming an angle are,
By its vertexBy three points (the middle point must be the vertex)By using numbersIn the given question,
Option A has three points and the middle point is the vertex.Option B is the vertex.Option C has three points but the middle point is not the vertex.Hence option C is not a correct way to name the angle.
Learn more about naming a triangle here:
brainly.com/question/26038114
#SPJ2
Please help I've failed this many times
Answers
Answer:
x-intercept (9, 0)y-intercept (0, 17.5)Step-by-step explanation:
You can compute the slope from two of the points, then write the point-slope form of the equation of the line.
slope = (change in y)/(change in x)
= (15 -20)/(3 -1) = -5/2
Then the equation of the line, using the first point) is ...
y = m(x -h) +k . . . . . . for slope m through point (h, k)
y = -5/2(x -1) +20
The x-intercept is the value of x where y=0:
0 = -5/2(x -1) +20 . . .put 0 where y is in the equation, then solve for x
0 = (x -1) -8 . . . . . . . . multiply by -2/5 (the inverse of the x-coefficient)
9 = x . . . . . . . . . . . . . simplify, add 9
The x-intercept is (9, 0).
__
The y-intercept is the value of y where x=0:
y = -5/2(0 -1) +20 . . . . . . put 0 where x is in the equation, then solve for y.
y = -2.5 +20 = 17.5
The y-intercept is (0, 17.5).
_____
Comment on the problem
Your question page seems to offer both lesson and video help. Either or both may be better than the written solution here.
The prism is 7 cubes wide, 10 cubes high, and 4 cubes deep. Each cube is 0.5 inch wide. What is the volume of the prism in cubic inches?
Answers
35 cubic in.
7/2=3.5
10*4=20/2=10
10*3.5=35
98 POINTS!! PLS HELP!
2 Plain, 3 Cinnamon raisin, 4 Poppy seed, 2 French toast, 1 Wheat.
1. Whats the probability of (Not Cinnamon raisin) Explain.
1b. Probability of (Plain, Wheat, or Poppy) Explain how you got this answer.
Show work
Answers
1. 9/12 because all of them added together is 12 but cinnamon raisin is 3 so 12-3 gives u 9 and the total is 12 so 9/12
1b. Plain(2) wheat(1) poppy(4) 2+1+4=7. The total is again 12 so 7/12
What is the area of a cylindrical ring where the diameter of the cross section is 6.3 in and the center line has a length of 48 in
Answers
Answer:
The area of cylinder 949.536 in²
Step-by-step explanation:
Points to remember
Curved surface area of cylinder = 2πrh
Where r - radius of cylinder
h - Height of cylinder
To find the area of cylinder
Here r = diameter/2 = 6.3/2 = 3.15 in
h = 48 in
Area = 2πrh
= 2 * 3.14 * 3.15 * 48
= 949.536 in²
Therefore area of cylinder 949.536 in²
What is the length of the third side of the window frame below?
(Figure is not drawn to scale.)
A picture of a right triangular window frame is shown. The longest side has length labeled as 39 inches. The height of the frame is labeled as 36 inches.
15 inches
27 inches
25 inches
32 inches
Answers
Answer:
15 inches
Step-by-step explanation:
The longest side of the right triangular window frame is 39 inches
The height is 36 inches
Let the base of the window frame be x inches
So according to Pythagoras theorem,
x² + 36² = 39²
x² = 39² - 36² = 225
x = [tex]\sqrt{225}[/tex] = 15 inches
The third side of the window frame is therefore equal to 15 inches.
The length of the third side of the window frame will be 15 inches. Then the correct option is A.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The longest side has a length labeled as 39 inches. The height of the frame is labeled as 36 inches.
Let x be the length of the third side of the window frame. Then we have
39² = x² + 36²
x² = 39² - 36²
x² = 1521 - 1296
x² = 225
x = 15 inches
Then the correct option is A.
More about the Pythagoras theorem link is given below.
https://brainly.com/question/343682
#SPJ2
Some states are running out of license plate numbers. Delaware currently uses six-digit numbers in its license plate numbering system. The state of Washington recently stated that it needs to explore options to replace their current system of three numerical digits followed by three letters. New Jersey currently uses a system of one letter, two numerical digits, then three letters. How many license plate numbers can Delaware assign under their system?
a. 100,000 plate numbers
b. 101,000 plate numbers
c. 1,000,000 plate numbers
d. 110, 000 plate numbers
Answers
Answer:
c. 1,000,000 plate numbers
Step-by-step explanation:
Each of the 6 digits of a Delaware plate can take on any of 10 values, so there are ...
10×10×10×10×10×10 = 1,000,000
possible plate numbers.
Delaware can assign 1,000,000 license plate numbers under its six-digit numbering system, as each of the six places can have any digit from 0 to 9 giving 10^6 or one million possible combinations.
The question asks how many license plate numbers Delaware can assign under their six-digit numbering system. To find the number of possible combinations for a six-digit number where each digit can be any number from 0 to 9, we need to calculate 10 possibilities for each position (including the leading zero) multiplied together.
Therefore, the calculation follows this pattern: 10 imes 10 imes 10 imes 10 imes 10 imes 10, which equals 1,000,000 possible combinations. This is because each of the six places in the license plate number can have any of the ten digits from 0 to 9. So the answer to how many license plate numbers Delaware can assign under their system is 1,000,000 plate numbers.
(5x^3-6-15x) / (10+5x)?
I need help please...
Answers
Answer:
(x^2 -2x +1) -16/(5x+10)
Step-by-step explanation:
The quotient and remainder can be found by polynomial long division or by synthetic division.
___
For synthetic division, it is recommended to divide the dividend and divisor by the leading coefficient of the divisor (5), so the divisor coefficient is 1. This results in a divisor of (x+2) and a remainder of -16/5. The simplified remainder becomes ...
(-16/5)/(x+2) = -16/(5x +10)
See the attachments for the various methods of computing the quotient.
An architect created the blueprints for the Chin's house. The scale factor is 1 inch: 40 inches. The length and width of the living room on the blueprint are 4 inches and 8 inches respectively. WHat is the area of the actual living room?
Answers
Step 1: Find the area of the living room on the blueprint with the formula Area = length x height
A = 4 x 8
A = 32
Step 2: We now know that the area of the living room on the blueprint is 32 inches, but we have to convert it into the actual answer. To do this multiply 32 by 40 (you have to do this because 1 inch is 40 inch in reality meaning that each inch in the 32 inches is times 40 <<< Does that make sense?), so...
40 x 32 = 1,280
Hope this helped!
Answer:
The measurements for the actual room are, in inches, 160 x 320
Step-by-step explanation:
If you want the computed area, then multiply those numbers together since A=bh. I assumed you were just looking for the measurements of the actual room. Set up a ratio for the scale first, the model info in the numerator and the actual room info in the denominator:
[tex]\frac{m}{a}: \frac{1}{40}[/tex]
Here, the m is the model on paper and the a is the actual room. So if the length of the room on paper is 4 inches, that will go on top with the model stuff and we will solve for the missing equivalent length of the actual room:
[tex]\frac{m}{a} :\frac{1}{40} =\frac{4}{x}[/tex]
Cross multiply to get that the length of the actual room is 160 inches long. Divide by 12 if you need that number in feet.
Doing the same with the width:
[tex]\frac{m}{a} :\frac{1}{40}=\frac{8}{y}[/tex]
Cross multiply to get that the width of the actual room is 320 inches. Again, if you need that in feet, divide by 12.
What are the vertical and horizontal asymptotes for the function f(x)= x^2+x-6/x^3-1?
a) vertical asymptote: x = 1
horizontal asymptote: none
b) vertical asymptote: x = 1
horizontal asymptote: y = 0
c) vertical asymptote: x = –2, x = 3
horizontal asymptote: y = 0
d) vertical asymptote: x = –2, x = –3
horizontal asymptote: none
Answers
Answer:
Option B
Step-by-step explanation:
Given
f(x)= (x^2+x-2)/(x^3-1)
For vertical asymptotes we have to put the denominator of the function equal to zero:
x^3-1=0
x^3=1
So,
x=1
As the degree of denominator is greater than the degree of numerator, there will be only horizontal asymptote which will be y=0 because all the y values will be dragged down to the x-axis.
So the horizontal asymptote: y=0
And Vertical asymptote: x =1
Answer:
b
Step-by-step explanation:
the club's total number of members will grow exponentially each month. She uses the given expression to model the number of club members, in hundreds, after advertising for t months.
1.8(1.02)^12t
What does the value 1.8 represent?
Answers
Answer:
1.8 represents the initial number of the club members in hundreds.
Step-by-step explanation:
* Lets revise the exponential grows
- If a quantity grows by a fixed percent at regular intervals,
the pattern can be depicted by this function.
- The function of the exponential growth is:
y = a(1 + r)^x
# a = initial value (the amount before measuring growth)
# r = growth rate (most often represented as a percentage and
expressed as a decimal)
# x = number of time intervals that have passed
* Now Lets study the problem to solve it
- The club's total number of members will grow exponentially
each month
- The expression to model the number of club members, in
hundreds, after advertising for t months is
1.8(1.02)^12t
* Lets compare between this model and the function above
# a = 1.8 ⇒ initial number of members in hundreds
# r = 1.02 - 1 = 0.02 ⇒ growth rate
# x = 12t ⇒ number of time intervals
* 1.8 represents the initial number of the club members in hundreds.
if g(x)= 2x -1 then g(4)=
Answers
g(4)=2×4_1
8-1
=9
hence the answer is 9
hope it helps you!!!!!!!!!
Answer:
g(4) = 7
Step-by-step explanation:
To evaluate g(4) substitute x = 4 into g(x), that is
g(4) = (2 × 4) - 1 = 8 - 1 = 7
Can someone help and explain this problem to me? I’m stuck
a. 2 units
b. 3 units
c. 8 units
d. 9 units
Answers
Answer:
c. 8 units
Step-by-step explanation:
You are to find the y-intercepts of the two functions given, then report the difference between them. The y-intercept is the y-value when x=0.
For f(x), we have ...
f(0) = 3·2^0 = 3·1 = 3
__
For the table, we can see that x=0 is halfway between x=-2 and x=2, so the y-intercept can be expected to be halfway between y=3 and y=-13. That value for y is ...
g(0) = (3 + (-13))/2 = -10/2 = -5
That is, the y-intercept of g(x) is -5.
__
The difference between f(0) and g(0) is ...
f(0) -g(0) = 3 -(-5) = 8 . . . . units
Which of the following points is a solution of the inequality y < -|x|?
A. (1,-2)
B. (1,-1)
C. (1,0 )
Answers
ANSWER
The correct choice is A
EXPLANATION
The given inequality is
y < -|x|
We substitute each point into the inequality to determine which one is a solution.
Option A
-2 < -|1|
-2 < -1.
This statement is true.
Hence (1,-2) is a solution.
Option B.
-1 < -|1|
-1 < -1.
This statement is false.
Option C
0 < -|1|
0 < -1.
This statement is also false.
what is the discriminant of the polynomial below 4x^2-20x +25
Answers
Answer:
The discriminant D=0
Step-by-step explanation:
For the duadratic polynomial [tex]ax^2+bx+c[/tex] the discriminant is
[tex]D=b^2-4ac.[/tex]
In your case, for the polynomial [tex]4x^2-20x+25,[/tex]
[tex]a=4;[/tex][tex]b=-20;[/tex][tex]c=25;[/tex][tex]D=(-20)^2-4\cdot 4\cdot 25=400-400=0.[/tex]Answer:
The answer is 0 D
*algebra* What is (f−g)(x)?
Answers
Answer:
x^3 -6x^2 +18x-10
Step-by-step explanation:
f-g (x) = f(x) -g(x)
f(x) = x^3 -2x^2 +12x-6
g(x) =4x^2 -6x +4
f(x) -g(x) =x^3 -2x^2 +12x-6 - (4x^2 -6x +4)
Distribute the minus sign
x^3 -2x^2 +12x-6 - 4x^2 +6x -4
Combine like terms
x^3 -2x^2- 4x^2 +12x+6x-6 -4
x^3 -6x^2 +18x-10
Decimal Calculations (Multiplication). An employee earns a salary of $380 for a 40-hour work week. If the employee worked 40 hours plus 14 hours of overtime at the overtime rate of 12.50 for each hour overtime worked, find her total income for the week.
Answers
Answer:
$ 555
Step-by-step explanation:
Salary for a 40-hour work week = $380
Total income for the week will be = Salary of regular 40 hours + Salary of 14 hours overtime
Salary per hour for the overtime work = $ 12.50
So,
The salary for 14 hours of overtime will be = $ 12.50 x 14 = $ 175
Therefore,
Total income for the week will be = $ 380 + $175 = $ 555
Thus, for a 40 hour work week and 14 hours of overtime the total income of the week will be $ 555
The municipal swimming pool in Chandler, Arizona has three different ways of paying for individual open swimming. Sam, Jane, and Suzy are trying to decide which way to pay.
• Early Pay: Pay $45.00 before Memorial Day; swim any number of days
• Deposit Plus: $12.00 deposit plus $4.00 per day
• Daily Pay: $6.00 per day
1. Write an equation for each method of payment. Write your equations in slope-intercept form so that x is the number of days and y is the cost.
a. Early Pay:
b. Deposit Plus:
c. Daily Pay:
2. If Sam goes swimming 4 times, what would he need to pay with each payment plan? Which is the best payment method for him?
3. If Sam goes swimming 8 times, what would he need to pay with each payment plan? Which is the best payment method for him?
4. If Sam goes swimming 12 times, what would he need to pay with each payment plan? Which is the best payment method for him?
5. Jane and Suzy decide to look at the different options available for individual open swimming. Jane enjoys swimming and would like to go to the pool on most days, but Suzy doesn’t know how many times she will go swimming this summer as she doesn’t really enjoy the summer heat and the pool atmosphere. Please explain in paragraph form which option would be best for Jane and which option would be best for Suzy. Explain your answer.
Any help would be greatly appreciated, I've been doing work all day and my mind is blank when I look at these questions. Thank you in advance.
Answers
1. a Early Pay: y = 45
b. Deposit Plus: y = 12.00 + 4.00x
c. Daily Pay: y = 6.00x
2. Early pay = $25
Deposit Plus = 12.00 + 4.00(4) = 12.00 + 16.00 = $28.00
Daily Pay = 6.00(4) = $24.00
Daily Pay is the cheapest one.
3. Early Pay = $45
Deposit Plus = 12.00 + 4.00(8) = 12.00 + 32.00 = $44.00
Daily Pay = 6.00(8) = $48.00
Deposit Plus is the cheapest one.
4. Early Pay = $45
Deposit Plus = 12.00 + 4.00(12) = 12.00 + 48.00 = $60.00
Daily Pay = 6.00(12) = $72.00
Early Pay is the cheapest one.
5. Since Jane likes to swim most days, it would be cheaper for her to do the Early pay option, because the price is a one time fee and she can swim every day.
Since Suzy doesn't really like to go swimming and might only go a couple times, it would be best for her to do the daily pay, that way she didn't spend any money up front if she doesn't swim at all.
Mrs. Robinson, an insurance agent, earns a salary of $4,800 per year plus a 3% commission on her sales. The average price of a policy she sells is $6,100.
Write an inequality to find how many policies Mrs. Robinson must sell to make an annual income of at least $8,000.
4800+183x<(line under the arrow)=8000
4800+183x=8000
4800+183x>=8000
4800+186>(ine under the arrow)=8000
Answers
Answer:
[tex]4800+183x\geq 8000[/tex]
She must sell at least 18 policies to make an annual income of at least $8,000
Step-by-step explanation:
Let [tex]x[/tex] be the number of policies Mrs. Robinson must sell
We know that Mrs. Robins makes 3% on commission for each policy sold. We also know that the average price of a policy is $6,100, so she makes 3% of $6,100 per policy sold. To find the 3% of $6,100 we just need to multiply 3% and $6,100; then dive the result by 100%:
[tex]\frac{3*6,100}{100} =183[/tex]
Now we know that she makes $183 per policy sold. Since [tex]x[/tex] is the number of policies sold, [tex]183x[/tex] is her total commission for selling [tex]x[/tex] policies.
We also know that She makes $4,800 per year, so her total annual income is her salary plus her commissions, in other words:
[tex]4800+183x[/tex]
Finally, we know that she wants to make at least $8,000, so her salary plus her commissions must be greater or equal than $8,000:
[tex]4800+183x\geq 8000[/tex]
Let's solve the inequality:
1. Subtract 4800 from both sides
[tex]4800-4800+183x\geq 8000-4800[/tex]
[tex]183x\geq 3200[/tex]
2. Divide both sides by 183
[tex]\frac{183x}{183} \geq \frac{3200}{183}[/tex]
[tex]x\geq 17.48[/tex]
Since she can't sell a fraction of a policy, we must round the result to the next integer:
[tex]x\geq 18[/tex]
We can conclude that she must sell 18 policies to make an annual income of at least $8,000.
What is the point of maximum growth rate? Round to the nearest tenth.
Answers
Answer:
(x, f(x)) ≈ (5.5, 4)
Step-by-step explanation:
You can go to the trouble to find the point where the second derivative is zero (the derivative has a maximum), or you can realize the function is symmetrical about y=4, which is where the point of inflection is. The x-value there is ...
4 = 8/(1 +3e^(-0.2x))
1 +3e^(-0.2x) = 8/4 = 2
e^(-0.2x) = 1/3
x = ln(1/3)/-0.2 = 5ln(3) ≈ 5.493 ≈ 5.5
We already know the value of f(x) is 4 there.
The point of maximum growth is about (5.5, 4).
The mean average of the following 4 math marks will become your report card marks 97,78,84, and 86 what will your report card mark be ?
Answers
Answer:
86.25
Step-by-step explanation:
97+84+78+86=345 then u divide by 4 which is 86.25
Consider the function f(x) = sin(x) and the function g(x) shown below.
Answers
Answer:
C
Step-by-step explanation:
g(x) = f(x - π/3), so g(x) is f(x) shifted to the right π/3 units.
Answer C.
MATH GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG
Answers
Answer:
Option C is correct.
Step-by-step explanation:
The equation used to represent the slop-intercept form is
y= mx + b
where m is the slope
and b is the y-intercept.
So, in the given question y-intercept = (0,8)
b= 8 and
slope =m= 1/2
the equation will be:
y = mx + b
y= (1/2)x + 8
So, Option C is correct.
Find the solution set for the equation, given the replacement set.
5x + 2y = –3; {(–2, 9.5), (–3, 11.5), (–4, 8.5), (–5, 6.5)}
a.
{(–2, 9.5), (–3, 11.5)}
c.
{(–4, 8.5)}
b.
{(–3, 11.5)}
d.
{(–4, 8.5), (–5, 6.5)}
Answers
Answer:
c. {(–4, 8.5)}
Step-by-step explanation:
A plot of the equation and the offered points is attached.
__
It might be helpful to put the equation into slope-intercept form.
2y = -5x -3
y = -5/2x -3/2
This shows you that y will be an odd multiple of 1/2 only for even values of x. So, we only need to check the points (-2, 9.5) and (-4, 8.5).
At x=-2, y = -5/2(-2) -3/2 = 5 -3/2 < 9.5 . . . . . (-2, 9.5) is not a solution
At x=-4, y = -5/2(-4) -3/2 = 10 -3/2 = 8.5 . . . . (-4, 8.5) is a solution
Of the offered choices, the only one in the solution set is (-4, 8.5).
GEOMETRY!!! 15 PTSSSSS
Answers
Answer:
23) option c
JL ≈ 9.3
25) option c
y ≈ 9.6
Step-by-step explanation:
25)Given in the question that,
cos(21°) = 9 / y
y = 9/cos(21°)
y = 9.64
y ≈ 9.6(nearest tenth)
23)Given in the question that the hypotenuse of right angle triangle = 12
To find,
height of the right angle triangle
angle k = 39°
so by using trigonometry identity
cos(39) = opp/hypo
cos(39) = JL / KL
JL = cos(39)(12)
JL = 9.32
JL ≈ 9.3
Answer:
Q 23. Last option 7.6
Q 25 Third option
Step-by-step explanation:
To solve Q 23
From the figure we can write,
Sin 39 = Opposite side/Adjacent side
= JL/KL
= JL/12
JL= 12 * Sin 39
= 12 * 0.629 = 7.55
= 7.6
To solve Q 25
Cos 21 = 9/y
y = 9/Cos 21 = 9/0.9335
= 9.64
= 9.6
Law of sines: sin(A)/a=sin(B)/b=sin(C)/c How many distinct
Answers
Answer:
According to the given question if one of the angle of the triangle is 75 degree and the other two sides are of length 2 and 3 units respectively then option C is correct. Only One triangle can be formed where Angle B will be 40 degree. You can figure it out from the steps mentioned below first of all draw an Arc with the length either 3cm or 2 cm that will be the base of a triangle and then from the ending point again cut an arc then after from the starting point that is the point draw an angle of 75 degree with the help of protactor and extend it to meet the Arc finally you can get the 40 degree.
Hope this helps. Name me brainliest please
What is the x-intercept and the y-intercept of the line in the graph
Answers
Answer:
x intercept= 3
y=-2
Step-by-step explanation:
the intercept is the point when the line crosses the axis
a rectangle is 6 meters longer than it is wide. The area of the rectangle is 315 square meters. find the length
Answers
Answer:
The length is 21 meters
Step-by-step explanation:
* Lets use variable to represent the dimensions of the rectangle
- The length of the rectangle is 6 meters longer than its width
# Let the width of the rectangle = x meters
∴ The length of the rectangle = x + 6 meters
- The area of the rectangle = Length × width
∵ The area of the rectangle = 315 meters²
∵ The length of the rectangle = x + 6
∵ The width of the rectangle = x
∴ x(x + 6) = 315 ⇒ open the brackets to solve the equation
∴ x² + 6x = 315 ⇒ subtract 315 from both sides
∴ x² + 6x - 315 = 0
- Lets factorize the quadratic equation to find the value of x
∵ The last term of the quadratic is negative
∴ The brackets have different sign
# x² = x × x ⇒ 1st terms in the two brackets
# -315 = -15 × 21 ⇒ 2nd terms in the two brackets
# x × -15 = -15x ⇒ 1st term in the first bracket and 2nd term in
the second bracket
# x × 21 = 21x ⇒ 1st term in the second bracket and 2nd term
in the first bracket
# 21x - 15 x = 6x ⇒ the middle term of the quadratic equation
∴ The factoriz of x² + 6x - 315 = 0 is
(x + 21)(x - 15) = 0
∴ x + 21 = 0 OR x - 15 = 0
# x + 21 = 0 ⇒ subtract 21 from both sides
∴ x = -21 ⇒ neglect this answer because there is no negative
value for the dimensions
# x - 15 = 0 ⇒ add 15 to both sides
∴ x = 15
- The value of the width is x
∴ The width = 15 meters
- The value of the length is x + 6
∴ The length = 15 + 6 = 21 meters