A triangle has three sides 35cm 54 cm and 61 cm find its area Also find the smallest of its altitude
Answers
Answer:
Area of given triangle is 939.15cm² and smallest altitude is 30.8cm
Solution:We are given three sides of a triangle, Let the sides be :
( a ) = 35 cm( b ) = 54 cm( c ) = 61 cmWe can find the area of the triangle with its three sides using Heron's Formula
Heron's FormulaHeron's formula was founded by hero of Alexandria, for finding the area of triangle in terms of the length of its sides. Heron's formula can be written as:
[tex] \sf{ \pmb { \longrightarrow \: \sqrt{s(s - a)(s - b)(s - c)} }}[/tex]
where ( s ) :
[tex] \sf \longrightarrow s = \dfrac{a + b + c}{2} [/tex]
Therefore, for the given triangle first we will calculate ( s )
[tex] \begin {aligned}\quad & \quad \longmapsto \sf s = \dfrac{a + b + c}{2} \\ & \quad \longmapsto \sf s = \dfrac{35 + 54 + 61}{2} \\ & \quad \longmapsto \sf s = \dfrac{150}{2} \\ & \quad \longmapsto \sf s = 75cm \end{aligned}[/tex]
Now, Area of triangle will be:
[tex] \begin{aligned}&:\implies \sf\quad \sf \: A = \sqrt{s(s - a)(s - b)(s - c)} \\ &:\implies \sf\quad \sf \: A = \sqrt{75(75 - 35)(75 - 54)(75 - 61)} \\&:\implies \sf\quad \sf \: A = \sqrt{75 \times 40 \times 21 \times 14} \\ &:\implies \sf\quad \sf \: A = \sqrt{5 \times 5 \times 3 \times 3 \times 2 \times 2 \times 7 \times 7 \times 2 \times 2 \times 5} \\ &:\implies \sf\quad \sf \: A =5 \times 3 \times 2 \times 7 \times 2 \sqrt{5} \\ &:\implies \sf\quad \sf \: A =420 \times 2.23 \\ &:\implies \sf\quad \sf \boxed{ \pmb{ \sf A =939.15 {cm}^{2} }} \end{aligned}[/tex]
Also, we have to find the smallest altitude, and the smallest altitude will be on the longest side. So,
[tex] \begin{aligned}&:\implies \sf\quad \sf \: Area =939.15 \\ &:\implies \sf\quad \sf \: \dfrac{1}{2} \times b \times h =939.15 \\ &:\implies \sf\quad \sf \: \dfrac{1}{2} \times 61 \times h = 939.15 \\&:\implies \sf\quad \sf \: h =939.15 \times \dfrac{2}{61} \\&:\implies \sf\quad \sf \: h = \dfrac{1818.3}{61} \\ &:\implies \sf\quad \boxed{ \pmb{\sf \: h =30.79 \: (approx)}} \end{aligned}[/tex]
Answer:
Area = 939.15 cm² (2 d.p.)
Shortest Altitude = 30.79 cm (2 d.p.)
Step-by-step explanation:
Heron's Formula allows us to find the area of a triangle in terms its side lengths.
Heron's Formula
[tex]\sf Area = \sqrt{s(s-a)(s-b)(s-c)}[/tex]
where:
a, b and c are the side lengths of the triangles is half the perimeterGiven values:
a = 35 cmb = 54 cmc = 61 cmFind the value of s:
[tex]\sf \implies s=\dfrac{a+b+c}{2}=\dfrac{35+54+61}{2}=75\:cm[/tex]
Substitute the values into the formula and solve for area:
[tex]\begin{aligned}\implies \sf Area & =\sf \sqrt{75(75-35)(75-54)(75-61)}\\& = \sf \sqrt{75(40)(21)(14)}\\& = \sf \sqrt{882000}\\& = \sf \sqrt{176400 \cdot 5}\\& = \sf \sqrt{176400}\sqrt{5}\\& = \sf 420\sqrt{5}\\& = \sf 939.15\:\:cm^2\:\:(2\:d.p.)\end{aligned}[/tex]
The altitude of a triangle is a perpendicular line segment drawn from a vertex of the triangle to the side opposite to it.
The shortest altitude of a triangle is drawn to the longest side.
Therefore, the shortest altitude will be the height of the triangle when the longest side is the base:
[tex]\begin{aligned}\textsf{Area of a Triangle} & = \sf \dfrac{1}{2} \times base \times height\\\implies \sf 420\sqrt{5} & = \sf \dfrac{1}{2} \times 61 \times altitude \\\implies \sf Altitude & = \sf \frac{2 \cdot 420\sqrt{5}}{61}\\& = \sf \dfrac{840\sqrt{5}}{61}\\ & = \sf 30.79\:\:cm\:\:(2\:d.p.)\end{aligned}[/tex]
Related Questions
3) Write the inequality that
represents "owing $26.00 is
better than owing $147.00.”
6.NS.7b
Answers
Answer:
See belowStep-by-step explanation:
Owing represent a negative balance.
So the inequality for this case is:
- 26.00 > - 147.00The word owing is given which simply denotes to negative transaction
So here the inequality is
-26.00>-147.00Or
-147.00<-26.00V
Find the angle between v=i+2j+3k and w=4i-k.
:2
.
Answers
Answer:
86.28 degrees
Step-by-step explanation:
Angle between vectors is
[tex] \cos(x) = \frac{cross \: product}{magnitudes \: multiplied} [/tex]
The cross product is
[tex]4 + 0 - 3 = 1[/tex]
The magnitudes of first vector is
[tex] \sqrt{1 {}^{2} + 2 {}^{2} + 3 {}^{2} } = \sqrt{14} [/tex]
The second vector magnitude is
[tex] \sqrt{17} [/tex]
So the magnitudes multiplied is
[tex] \sqrt{14} \times \sqrt{17} = \sqrt{238} [/tex]
So our equation will be
[tex] \cos(x) = \frac{1}{ \sqrt{238} } [/tex]
[tex]x = \cos {}^{ - 1} ( \frac{1}{ \sqrt{238} } ) [/tex]
X is about 86.28 degrees
before tomorrow can I have a quick answer and maybe an explanation on how to answer these kinds of questions overall? need some help asap
Answers
Answer:
a) maximum; the parabola opens downward
b) positive; it must lie above the x-axis
c) x = 1.5
Step-by-step explanation:
The x-intercepts of a function are the points where the graph of the function crosses the x-axis. The y-values there are zero.
The "differences" of a function are related to the average slope between adjacent points. Second differences are related to the rate of change of the slope of the function. When second differences are negative, as here, the slope of the quadratic function is decreasing, becoming more negative. We say the curvature of the function is negatve, and that it opens downward.
__
a, b.If the graph of the parabola opens downward, and it crosses the x-axis, it must have a maximum that is a positive value of y.
__
c.The graph of a parabola is symmetrical about its vertex. That means points on the same horizontal line are the same distance from the line of symmetry, which must go through the vertex. The x-coordinate of the vertex will be the x-coordinate of the midpoint between the two x-intercepts:
x = (-2 +5)/2 = 3/2
The x-coordinate of the vertex is x = 1.5.
______
Additional comment
The attachment shows a table with three evenly-spaced points on the curve. The calculations show first differences (d1) and second differences (d2). You can see that the sign of the second diffference is negative, in agreement with the given conditions.
Suppose that at some future time every telephone in the
world is assigned a number that contains a country code
1 to 3 digits long, that is, of the form X, XX, or XXX,
followed by a 10-digit telephone number of the form
NXX-NXX-XXXX (as described in Example 8). How
many different telephone numbers would be available
worldwide under this numbering plan?
Answers
Using the Fundamental Counting Theorem, it is found that [tex]1.11 \times 10^{13}[/tex] different telephone numbers would be avaiable worldwide.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem:
For the code, considering that for each digit there are 10 possible outcomes, the number of options is [tex]n_1 = 10 + 10^2 + 10^3 = 1110 = 1.11 \times 10^3[/tex].For the number, there are 10 digits, each with 10 options, hence the number of options is [tex]n_2 = 10^{10}[/tex].Hence, the number of different telephone numbers that would be avaiable is given by:
[tex]N = n_1n_2 = 1.11 \times 10^3 \times 10^{10} = 1.11 \times 10^{13}[/tex]
[tex]1.11 \times 10^{13}[/tex] different telephone numbers would be avaiable worldwide.
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866
If Jyoti has 266 followers in 160 post's so how much followers should he gain in 1 post
Answers
Step-by-step explanation:
160 posts = 266 followers
then,
1 posts = 266/160
= 2.50 followers
PLEASE HELP!! WILL MARK BRAINLIEST!!!
Set up the triple integral for the volume of the sphere ρ=4 in spherical coordinates.
Answers
In Cartesian coordinates, the volume is
[tex]\displaystyle \iiint_R \mathrm dV[/tex]
where R is the set
[tex]R = \left\{(x,y,z) \, : \, -4\le x\le4 \text{ and } -\sqrt{16-x^2} \le y \le \sqrt{16-x^2} \text{ and }\right. \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~\left.-\sqrt{16-x^2-y^2} \le z \le \sqrt{16-x^2-y^2} \right\}[/tex]
Converting to spherical coordinates, we take
[tex]\begin{cases}x=\rho\cos(\theta)\sin(\phi) \\ y=\rho\sin(\theta)\sin(\phi) \\ z = \rho\cos(\phi)\end{cases}[/tex]
and we can compute the Jacobian to find
[tex]dV = dx\,dy\,dz = \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi[/tex]
and the set R transforms to
[tex]R' = \left\{(\rho,\theta,\phi) \,:\, 0\le \rho\le4 \text{ and }0\le\theta\le2\pi \text{ and } 0\le\phi\le\pi\right\}[/tex]
The new integral and hence the volume is then
[tex]\displaystyle \iiint_R \mathrm dV = \iiint_{R'} \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi \\\\ = \boxed{\int_0^\pi \int_0^{2\pi} \int_0^4 \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi}[/tex]
HI I am 10 years old and I need help with my math homework, here's what I need help with:
Pls help me it is do today
Answers
Answer:
1 1/4
Step-by-step explanation:
Answer:
5/4 or 1 1/4
Step-by-step explanation:
1 3/4 - 2/4 = 1 1/4 or 5/4
Find the distance between the two points in simplest radical form (5,2)and (-3,-5)
Answers
Answer:
[tex]\sqrt{113}\\[/tex]
Step-by-step explanation:
[tex]distance= \sqrt{(5-[-3])^2+(2-[-5])^2}\\\\distance= \sqrt{(8)^2+(7)^2}\\\\distance= \sqrt{64+49}\\\\distance= \sqrt{113}\\[/tex]
Create a table, chart, or diagram that you can use to help you decide which hypothesis test you need to use (selecting from: population proportion, a population mean, two proportions from independent samples, two means from dependent samples, and two means from independent samples). Explain your table, chart, or diagram so that someone new to statistics could use it to select the appropriate hypothesis test.
Answers
A hypothesis testing is a statistical inference that uses data from a sample to draw conclusions.
What is hypothesis testing?It should be noted that hypothesis testing simply means a statistical act where an assumption is made regarding a parameter.
In this case, a hypothesis testing is a statistical inference that uses data from a sample to draw conclusions. The null hypothesis predicts no effect while the alternative hypothesis states the research predictions.
Learn more about hypothesis on:
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42.
If y = x2, then y' – 2x =
A.
2x
B.
4x
C.
00
D.
01
Answers
Answer:
C. 00
Step-by-step explanation:
Using power rule....
y = x²
y' = 2x
Solving for y' - 2x......
y' - 2x
2x - 2x
0
I hope this helps!
A rectangle is graphed on a coordinate plane. The
coordinates for two of the vertices of the rectangle are
(-5, 8) and (-5, -6). What is the distance between
the two vertices?
Answers
The two vertices (-5, 8) and (-5, -6) of the rectangle have the same x-coordinates
The distance between the two vertices is 14 units
How to determine the distance between the two vertices?The vertices are given as:
(-5, 8) and (-5, -6)
The distance between the two vertices is calculated using:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
So, we have:
d = √[(-5 + 5)^2 + (8 + 6)^2]
Evaluate the sum
d = √196
Evaluate the square root
d = 14
Hence, the distance between the two vertices is 14 units
Read more about distance at:
https://brainly.com/question/7243416
Answer: 14
Step-by-step explanation:
Can someone pls help me with this.
Joe and Charmaine walk around a track.Joe walks each lap in 12 minutes. Charmaine walks each lap in 8 minutes.The two of them begin at the starting line at the same time. They walk until they meet again.
How much time does it take for them to meet again at the starting line?
How many laps does Joe complete
How many laps does Charmaine complete?
Answers
Answer:
[A] It will take 24 minutes for Joe and Charmaine to meet again at the starting line.
[B] Joe will complete 2 laps
[C] Charmaine will complete 3 laps.
Step-by-step explanation:
Factor two numbers 12 and 8:
12 = 2×2×3
8 = 2×2×2
Find LCM of 12 and 8:
Lcm of 12 and 8 - 2×2×3×2 = 24
Therefore,
[A] How much time does it take for them to meet again at the starting line?
It will take 24 minutes for Joe and Charmaine to meet again at the starting line.
[B] How many laps does Joe complete
Joe will complete 2 laps
[C] How many laps does Charmaine complete?
Charmaine will complete 3 laps.
~lenvy~
Find the solutions to the equation below.
Check all that apply.
2x^2 + 7x + 3 = 0
A. x = 4
B. x = -1/2
C. x = 2
D. x = 7
E. x = 3
F. x = -3
Answers
Answer:
B and F.
Step-by-step explanation:
2x^2 + 7x + 3 = 0
2x^2 + 6x + x + 3 = 0
2x(x + 3) + 1(x + 3) = 0
(2x + 1)(x + 3) = 0
x = -1/2, -3.
I NEED HELP ASAP!!!!!
Answers
2= not polynomial
3= polynomial
4= polynomial
5= not polynomial
6= polynomial
please help me.. no links pls
Answers
Answer:27
Step-by-step explanation:
Its pretty simple. Perimeter is the addition of all the sides. Add 4+9+8+6 to get 27.
The following figure shows a cube. Which expression represents the surface area of the cube?
Answers
Answer:
6 ⋅ 16
This is the sum of the areas of the 6 square faces.
The surface area of the cube in the figure given is 96 squared units
What is surface area of a cube?The surface area of a cube is calculated by finding the total area of all six faces. Since all sides of a cube are equal in length, you can use the formula:
Surface area of a cube = 6 × (side length)²
In other words, you square the length of one side of the cube and then multiply it by 6 to get the total surface area.
Let's say the side length of the cube is "s," then the formula becomes:
Surface area of a cube = 6 × s²
In the question given, we can calculate the surface area of this cube as;
Surface area = 6 * s²
s = 4
Surface area = 6 * 4²
Surface area = 6 * 16 = 96 unit²
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https://brainly.com/question/410493
#SPJ2
The Window has the shape of a kite. How many square meters of glass were used to make the Window
Answers
The window that has the shape of a kite has the area of the glass as 648 centimetre squared.
What is area of a figure?Area can be defined as the space occupied by a flat shape or the surface of an object. Therefore,
The window is the shape of a kite. Therefore, the square meters of the glass used for the window is the area of the window(kite).
Therefore,
area of kite = ab / 2
where
a and b are the length of the diagonalTherefore,
a = 18 + 18 = 36 cm
b = 15 + 21 = 36 cm
area of the window = 36 × 36 / 2 = 1296 / 2 = 648 cm²
learn more on area here:https://brainly.com/question/2494000
in a certain urban area, the relationship between number of students, x in thousands, and the umber of schools, y , has an x-intercept of -4 and a y-intercept of 3. Write an equation for this relationship in standard form
Answers
Answer:
[tex]\sf -3x+4y=12[/tex]
Step-by-step explanation:
x-intercept is when y = 0 → (-4, 0)
y-intercept is when x = 0 → (0, 3)
[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{3-0}{0-(-4)}=\dfrac34[/tex]
Substitute one of the points and the found slope into the point-slope form of a linear equation:
[tex]\implies \sf y-y_1=m(x-x_1)[/tex]
[tex]\implies \sf y-0=\dfrac34(x-(-4))[/tex]
[tex]\implies \sf y=\dfrac34(x+4)[/tex]
[tex]\implies \sf 4y=3(x+4)[/tex]
[tex]\implies \sf 4y=3x+12[/tex]
[tex]\implies \sf -3x+4y=12[/tex]
Solve the following quadratic equation by factorin
x - 12x + 35 = 0
2
x? -
The solution set is {}.
(Simplify your answer. Type each solution only
Answers
Answer:
(x - 5)(x - 7x)
Step-by-step explanation:
x - 12x + 35 = 0
x - 12x + 35 = 0
x - 5x - 7x + 35= 0
x ( x - 5) -7x(x + 5)
(x - 5)(x - 7x)
What is the mean of the data set? 66, 71, 75, 83, 88, 89, 90, 91
A. 88
B. 85.5
C. 80
D. 81.625
Answer: D
Answers
Answer:
D
Step-by-step explanation:
Raphael buys one raffle ticket.
a total of 250 raffle tickets are sold.
One of these tickets will win the raffle.
Each ticket has an equal chance of winning the raffle.
(a) Write down the probability that Raphael's ticket will win the raffle
(b) Write down the probability that Raphael's ticket will not win the raffle
Answers
Answer:
There is a 1/250 chance that his ticket will be chosen
There is a 249/250 chance that his ticket will not be chosen
Step-by-step explanation:
Hope that helps!
plsss help ill give briliantest
Answers
Answer:
The answer is 310
Step-by-step explanation:
Example of distributive property of division
The 1,860 is broken down into 1800 & 60
1800 divided by 6 + 60 divided by 6
1800 divided by 6 = 300 + 60 divided by 6 = 10
300 + 10 = 310
Help. Please asap rn.
Answers
Answer:
Area = 12 + 6.25π ft², Perimeter = 6 + 5π ft
Step-by-step explanation:
Area:
So I would break this shape into a triangle and a circle (the two semi-circles make a full circle).
Formula for Area of a Triangle: base · height ÷ 2
6 · 4 ÷ 2 = 24 ÷ 2 = 12
Formula for area of a circle: π · radius²
π · (5/2)² = 6.25π
Area of entire shape: Triangle + Circle
Area = 12 + 6.25π ft²
Perimeter:
So the perimeter is made up of the base of the triangle plus the circumference of the circle.
Base of Triangle: 6
Formula for circumference: 2rπ
5 · π = 5π
Perimeter = 12 + 5π ft
Pls answerrrrrrrrrrrrrrrrrrrrrr
Answers
Answer:
13
Step-by-step explanation:
the two lines with y in them are the same length
6y = y+65
5y = 65
y = 13
pls help me i will mark as brilliant
Answers
Step-by-step explanation:
total number of student = 900number of girls = 3001) to find the number of boys
number of boys = total no. of students - no. of girls
= 900 - 300
= 600
2) to find the ratio of boys and girls
ratio of boys and girls = no. of boys : no. of girls
= 600 : 300
= 200
3) ratio of boys and total no. of students
= 600 : 900
= 200: 300
= 2:3
4) ratio of girls and total no. of students= 300 : 900
= 1:3
5)ratio of girls and boys= 300 : 600
= 1:2You are the head seamstress at a boutique that specializes in making prom dresses. You are supervising the construction of a new style of dress that will take 180 hours of work to complete. Twenty percent of this time is for beading. Thirty-five percent of this time is for adding ruffles. The remaining time is divided equally between embroidery and sewing. When pricing this style, hourly labor and material costs are $40 for beading, $35 for ruffles, $20 for embroidery, and $18 for sewing. The dress is then sold in the showroom for 25% more than the cost of labor and materials. How much will this dress sell for in the boutique?
Answers
The amount at which the dress will sell for in the boutique is $6716.25.
What is the sellig price of the dress?The total cost of beading = 180 x 25% x $40 = $1800
The total cost of ruffles = 35% x 180 x $35 = 2205
Time left for making embroidery and sewing = (100% - 35% - 25%)/2 = 20%
The total cost of embroidery = 20% x 180 x $20 = $720
The total cost of sewing = 20% x 180 x $18 = $648
Total cost = 5373
Selling price = 1.25 x 5373 = $6716.25
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A credit card had an APR of 25.67% all of last year and compounded interest daily. What was the credit card's effective interest rate last year?
a
28.25%
b
29.25%
c
28.92%
d
27.32%
Answers
Answer:
The answer is 29.25%.
Step-by-step explanation:
Hope this is right!!!
Use the order of operations to find the value of the expression. 12
÷
2
×
3
−
(
7
−
5
) HELP KME OUT
Answers
Answer:
16
Step-by-step explanation:
12 divided by 2 x 3 - (7 - 5)
6 x 3 - 2
18 - 2
16
Answer:
answer 16
Step-by-step explanation:
12 ÷ 2 x 3 - ( 7 - 5 ) is it right?
---------------------------------------------
Solving from left to right
12 ÷ 2 x 3 - ( 7 - 5 )
6 x 3 - (+2)
18 - 2
16
Xan and Katie are twins. Xan weighs 666 pounds 999 ounces, and Katie weighs 888 pounds 111 ounce.
What is the difference, in ounces, between Xan and Katie's weight?
Answers
Answer:
Difference in weight is 24 once
Step-by-step explanation:
got it right
What is the measure of the angle x?
Answers
Answer:
40
Step-by-step explanation:
angle AOB= 2x=80
x=80/2
x=40
