In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulas for the area of a triangle, such as half the base times the height. Use Heron's formula to find the area, in square feet, of ΔABC.
Options:
A)
7.385
B)
8.270
C)
6.495
D)
5.591
Answers
Answer:
C) [tex] 6.495\: ft^2 [/tex]
Step-by-step explanation:
a = 7 ft, b = 3 ft, c = 5 ft (Given)
Therefore, a + b + c = 7 + 3 + 5 = 15 ft
Let's calculate semi Perimeter of the triangle which is given by s
[tex] s =\frac{a+b+c}{2}=\frac{15}{2} = 7.5 \: ft[/tex]
Now, by Heron's formula, area of triangle ABC is given as:
[tex] A(\triangle ABC) =\sqrt{s(s-a) (s-b)(s-c)} [/tex]
[tex]\therefore A(\triangle ABC) =\sqrt{7.5(7.5-7) (7.5-3)(7.5-5)} [/tex]
[tex]\therefore A(\triangle ABC) =\sqrt{7.5(0.5) (4.5)(2.5)} [/tex]
[tex]\therefore A(\triangle ABC) =\sqrt{42.1875} [/tex]
[tex]\therefore A(\triangle ABC) =6.49519053 [/tex]
[tex]\therefore A(\triangle ABC) =6.495\: ft^2 [/tex]
Related Questions
Find the y-intercept of the line: 9x + 3y = -18
(0,-6)
(0,6)
(-2,0)
(3,9)
Answers
Answer:
(0,-6)
Step-by-step explanation:
9x + 3y = -18
Solve for y to get equation in slope intercept form
( y = mx + b )
9x + 3y = -18
Subtract 9x from both sides
9x - 9x + 3y = -18 - 9x
3y = -9x - 18
Divide both sides by 3
3y/3 = y
-9x - 18 / 3 = -3x - 6
We're left with y = -3x - 6
The equation is now in y intercept form
y = mx + b where b = y intercept
-6 takes the spot of b therefore the y intercept would be at (0,-6)
help asap please ----------------
Answers
Answer:
-1 Not in domain
0 In domain
1 In domain
Step-by-step explanation:
The domain for the square root function is all positive numbers including (0). The domain is the set of real numbers which when substituted into the function will produce a real result. While one can substitute a negative number into the square root function and get a result, however, the result will be imaginary. Therefore, the domain for the square root function is all positive numbers. It can simply be expressed with the following inequality:
[tex]x\geq0[/tex]
Therefore, one can state the following about the given numbers. Evaluate if the number is greater than or equal to zero, if it is, then it is a part of the domain;
-1 => less than zero; Not in domain
0 => equal to zero; In domain
1 => greater than zero: In domain
The following figures are not drawn to scale but AB and CD are straight lines. Find x.
Answers
Answer:
x=60
Step-by-step explanation:
solve, 180-(90+x) = 180-(30+2x)
Find the measure of the missing angle using the triangle angle sum theorm.
Answers
Which polynomial function has a leading coefficient of 3 and roots 4, I, and 2, all with multiplicity 1? Of(x) = 3(x + 4)(x - 1)(x - 2) O f(x) = (x - 3)(x + 4)(x - 1)(x - 2) f(x) = (x - 3)(x + 4)(x - 1)(x + 1)(x - 2) O f(x) = 3(x + 4)(x - 1)(x + 1)(x - 2) N
Answers
Note: There must be -4 instead of 4 otherwise all options are incorrect.
Given:
A polynomial function has a leading coefficient of 3 and roots -4, 1, and 2, all with multiplicity 1.
To find:
The polynomial function.
Solution:
The general polynomial function is defined as:
[tex]P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}[/tex]
Where, a is the leading coefficient, [tex]c_1,c_2,...,c_n[/tex] are the zeros with multiplicity [tex]m_1,m_2,...,m_n[/tex] respectively.
It is given that a polynomial function has a leading coefficient of 3 and roots 4, 1, and 2, all with multiplicity 1. So, the polynomial function is defined as:
[tex]P(x)=3(x-(-4))^1(x-1)^1(x-2)^1[/tex]
[tex]P(x)=3(x+4)(x-1)(x-2)[/tex]
Therefore, the correct option is A.
The math club sold 15 novelty erasers and made a profit of
$7. After another week, the club had sold a total of 25
erasers and made a profit of $15. Which equation models
the total profit, y, based on the number of erasers sold, X?
A. y - 15 = 0.8(x - 7)
B. y - 15 = 1.25(x - 7)
C. y - 7 = 0.8(x - 15)
D. y - 7 = 1.25(x - 15)
Answers
15 novelty eraser and a profit of $7
It means that x=15 and y=7
=> C and D is correct
Sold 25 erasers and a profit of $15
It means that x=25 and y=15
=> only C is right.
$975, and there is 7 percent sales tax on the purchase.
How much is the sales tax?
Answers
Answer:
$68.25
Step-by-step explanation:
To get the sales tax, you must notice that the sales tax is 7% of 975.
That is equal to:
975 × 0.07
0.07 is equal to 7%, or [tex]\frac{7}{100}[/tex].
The answer to the equation is 68.25.
Doug split a magic cards so that he and his friends each got 6 cards.if there were 24 cards in the pack how many friends did Doug share the cards with
Answers
Answer:
Doug share the cards with his three other friends.
Step-by-step explanation:
If there were 24 cards and each person was suppose to get 6
24 ÷ 6 = 4
The cards were shared among 4 people including Doug himself.
Have a nice day :)
Neeeeed helpppppppppp
Answers
Answer:
The answer is x = -3.
Step-by-step explanation:
To solve for (x), start by realizing that line segment IJ and line segment JK sum up to line segment IK, which equals 5. These line segments can then be turned into an equation, and the equation will look like [tex]7+x+2x+7=5[/tex].
Next, begin to solve the equation by combining like terms, which will look like [tex]3x+14=5[/tex]. Then, subtract 14 from both sides of the equation, which will look like [tex]3x=-9[/tex], and divide both sides by 3 and simplify, which will look like [tex]x=-3[/tex]. The final answer is x = -3.
identify the unit rate shown in the graph
Choices:
A. 1/3 mile per hour
B. 3 hours per mile
C. 3 miles per hour
D. 4 miles per hour
Answers
The answer is C or 3 miles per hour
how is it 3?:
there is a point at 6 and another at 3 all we do is 6 - 3 = 3
A(3,4) and B(-3,2) are pointd on a coordinate plane. find the coordinate of a points C on the x axis such that AC=BC
Answers
Answer:
Step-by-step explanation:
Here's the game plan. In order to find a point on the x-axis that makes AC = BC, we need to find the midpoint of AB and the slope of AB. From there, we can find the equation of the line that is perpendicular to AB so we can then fit a 0 in for y and solve for x. This final coordinate will be the answer you're looking for. First and foremost, the midpoint of AB:
and
Now for the slope of AB:
and
So if the slope of AB is 1/3, then the slope of a line perpendicular to that line is -3. What we are finding now is the equation of the line perpendicular to AB and going through (0, 3):
and filling in:
y - 3 = -3(x - 0) and
y - 3 = -3x + 0 and
y - 3 = -3x so
y = -3x + 3. Filling in a 0 for y will give us the coordinate we want for the x-intercept (the point where this line goes through the x-axis):
0 = -3x + 3 and
-3 = -3x so
x = 1
The coordinate on the x-axis such that AC = BC is (1, 0)
the first 4 questions
Answers
Answer:
(3)(4)(4)(2)Step-by-step explanation:
1.
7 > 0.7 > 0.07 > 0.007
2.
5h - 15hg
taking 5h common
5h (1 - 3g)
3.
5(2x- 1) = 35
dividing both sides by 5
2x - 1 = 7
2x = 7 + 1
2x = 8
x = 4
4.
if x is an odd number x + 2 will also be odd.
for example
11 is an odd number
on adding 2 we get 13 which is also an odd number.
Can any one help me with all these 3 questions? Thank you if you helped :)
Answers
Answer: Answer already been answered credits to that person give that person brainliest
Step-by-step explanation:
Can like someone help me I'm lost-
Answers
Answer:
the first graph
Answer:
1st option
Step-by-step explanation:
If the rate of change is constant, then it's always a straight line, so the 1st option, and if you see the graph, you'll see the line is going down at a rate of 1/4, so the slope is 1/4. So the answer to your question will be the 1st option.
Answered by GAUTHMATH
Write functions for each of the following transformations using function notation. Choose a different letter to represent each function. For example, you can use R to represent rotations. Assume that a positive rotation occurs in the counterclockwise direction.
• translation of a units to the right and b units up reflection across the y-axis
• reflection across the x-axis rotation of 90 degrees counterclockwise about the origin, point o
• rotation of 180 degrees counterclockwise about the origin, point o
• rotation of 270 degrees counterclockwise about the origin, point o
Answers
Answer:
1) [tex]T_{(a, \, b)}[/tex] = f(x - a) + b
Coordinate change
(x, y) → (x + a, y + b)
2) RFy(x, y) = f(-x)
Coordinate change
(x, y) → (-x, y)
3) RFx(x, y) = -f(x)
Coordinate change
(x, y) → (-y, x)
4) RCCW90(x, y) = f⁻¹(-x)
Coordinate change
(x, y) → (-y, x)
5) RCCW180(x, y) = -(f(-x))
Coordinate change
(x, y) → (-x, -y)
6) A 270 degrees counterclockwise rotation gives;
RCCW270(x, y) = -(f⁻¹(x))
Coordinate change
(x, y) → (y, -x)
Step-by-step explanation:
1) Horizontal translation a units right = f(x - a)
The vertical translation b units up = f(x) + b
Therefore, we get; [tex]T_{(a, \, b)}[/tex] = f(x - a) + b
The coordinate change
(x, y) → (x + a, y + b)
2) A reflection across the y-axis = RFy(x, y) = f(-x)
The coordinate change
(x, y) → (-x, y)
3) A reflection across the x-axis gives RFx(x, y) → (x, -y)
Therefore, in function notation, we get;
RFx(x, y) = -f(x)
4) A 90 degrees rotation counterclockwise, we get RotCCW90(x, y) → (-y, x)
In function notation RotCCW90(x, y) = INVf(-x) = f⁻¹(-x)
5) A 180 degrees counterclockwise rotation about the origin gives;
(x, y) → (-x, -y)
Therefore, we get;
In function notation RotCCW180(x, y) = -(f(-x))
6) A 270 degrees counterclockwise rotation gives RotCCW270(x, y) → (y, -x)
In function notation RotCCW270(x, y) = -(f⁻¹(x))
Which answer represents the range of the logarithmic function given below?
F(x) = log0.6^x
Answers
prime factor of 8 and prime factor of 12
Answers
Answer:
2
Step-by-step explanation:
a prime factor is a factor that is a prime number
a prime number is a number that will have a fraction in the quotient if it's divided by any number other than itself
2 is the only prime factor shared between 8 and 12
help pls!!
2xy + 3xt - 7yt = 0
In the equation above, x and y are positive and
x< y. What is t in terms of x and y?
A) t= 1/2
B) t= 2xy / 3x - 7y
C) t= 2xy / 7y - 3x
D) t= xy / 2(y-x)
Answers
Answer:
B
Step-by-step explanation:
[tex]2xy + 3xt - 7yt = 0[/tex]
[tex]3xt - 7yt = - 2xy[/tex]
Factor out t
[tex]t(3x - 7y) = - 2xy[/tex]
Divide by 3x-7y
[tex]t = - \frac{2xy}{3x - 7y} [/tex]
But since x and y are positive, the answer is positive
[tex]t = \frac{2xy}{3x - 7y} [/tex]
Find the volume - leave answer in terms of π
Answers
Answer:
144[tex]\pi[/tex]
Step-by-step explanation:
Volume of a Sphere :
V = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
V = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]6^{3}[/tex]
V = [tex]\frac{4}{3}[/tex](216)[tex]\pi[/tex] (216 times 4, divided by 3)
V = 288[tex]\pi[/tex]
Now divide by 2, it's only half of a sphere.
Match the measures of each angle
Answers
the question is on the image
Answers
Answer:
€3,551.05
Step-by-step explanation:
31*29=899
899*3.65=€3,551.05
the school will get an estimate of €3,551.05
Integrate with respect to x
-2/3√((2-5x)^3)
Answers
Hello,
[tex]\displaystyle \int {-\dfrac{2}{3} \sqrt{(2-5x)^3}} \, dx \\\\\displaystyle=-\dfrac{2}{3}*\dfrac{-1}{5} \int {-5*(2-5x)^{\frac{3}{2} }} \, dx \\\\\displaystyle=\dfrac{4}{3}*(2-5x)^{\frac{5}{2} }+C[/tex]
Help me with this problem
Answers
Answer:
Angle A is F Angle A = 57. 52+71=123. 180-123=57
3x-4y=-24
Identify the x- and y-intercept of the graph of each question
Answers
Answer:
x = -8 and y = 6
Step-by-step explanation:
3x - 4y = -24
Solve for y - intercept
3x - 4y = -24
To find y intercept , substitute x = 0
3 × 0 - 4y = -24
Any expression multiplied by 0 equals 0.
0 - 4y = -24
-4y = -24
Divide both sides by -4
-4y / -4 = -24/-4
y = 6
Similarly, Solve for x-intercept
3x - 4y = -24
To find x- intercept , susbtitute y = 0
3x - 4 × 0 = -24
Any expression multiplied by 0 equals 0.
3x - 0 = -24
3x = -24
Divide both sides by 3
3x / 3 = -24 / 3
x = -8
Therefore, y = 6 and x = -8
what is 9.7 as a fraction ?
Answers
Answer:
Step-by-step explanation:
9.7 = [tex]\frac{97}{10}[/tex]
Count the number of places in the decimal number after the decimal point.
Here , there is only one place.
So, multiply and divide by 10. 9.7 *10/1*10 = 97/10
Find the value of y...........
Answers
Answer:
y=0
Step-by-step explanation:
9514 1404 393
Answer:
y = 0
Step-by-step explanation:
Factor out 3^y:
3^(2y-1) +2(3^(y-1)) = 1 . . . . . . given
(3^y)^2(3^-1) +2(3^y)(3^-1) = 1 . . . . factor out 3^y
(3^y)^2 +2(3^y) -3 = 0 . . . . . . . . . . subtract 1, multiply by 3
Let x = 3^y. Substituting, we have ...
x^2 +2x -3 = 0
(x -1)(x +3) = 0
x = 1 or x = -3 . . . . . values of x that satisfy this equation
Then the corresponding values of y are ...
x = 3^y . . . . . . . . . . . . relation of x and y
log(x) = y·log(3) . . . . . take logs to solve for y
y = log(x)/log(3) . . . . . divide by the coefficient of y
For x = 1, this is y = log(1)/log(3) = 0
For x = -3, this is y = log(-3)/log(3) . . . . no real solutions
The only real solution is y = 0.
_____
The attachment shows the solution of f(x) = 0, where ...
[tex]f(x)=3^{2x-1}+2\times3^{x-1}-1[/tex]
That solution is x=0. This means the (real) solution to the given equation is y=0.
Find the surface area or volume of each rectangular prism. (Show work pls)
Answers
Answer:
496 in.²
346 mm²
880 in.²
168 cm³
960 m³
420 yd³
Step-by-step explanation:
SA = 2(wl + hl + hw)
SA = 2 · (8 · 16 + 5 · 16 + 5 · 8)
SA = 496
SA = 2(wl + hl + hw)
SA = 2 · (5 · 13 + 6 · 13 + 6 · 5)
SA = 346
SA = 2(wl + hl + hw)
SA = 2 · (4 · 20 + 15 · 20 + 15 · 4)
SA = 880
V = whl
V = 4 · 7 · 6
V = 168
V = whl
V = 10 · 8 · 12
V = 960
V = whl
V = 14 · 3 · 10
V = 420
Find the volume of this cylinder. Use 3 for .
V = 7r2h
14 cm
2
V = T[?]?
28 cm
Hint: Plug in the value of the
radius for r. The radius is shown
directly in the diagram.
Answers
Step-by-step explanation:
V = πr²h
V = 3 × 14² × 28
v = 16464cm³
Need help ASAP.
Consider the given functions.
Which graph represents the given function?
Answers
Please help! will give brainly
Answers
Answer:
5/6
Step-by-step explanation:
first form numerator you will multiply by π it means 3.14 multiply 11
the answer equals 34.54 ..and then you will use √ it means square root....so the answer is 5
the annwer is
5/6
Answer:
Step-by-step explanation:
[tex]\frac{11\pi }{6}[/tex] = 11 × [tex]\frac{\pi }{6}[/tex] = (12 - 1) × [tex]\frac{\pi }{6}[/tex]
The terminal point located in IV quarter ⇒ x-coordinate is positive and y-coordinate is negative.
(x, y) = ( [tex]\frac{\sqrt{3} }{2}[/tex] , - [tex]\frac{1}{2}[/tex] )
