Use Heron's Area Formula to find the area of the triangle. (Round your answer to two decimal places.) A = 79°, b = 77, c = 43
Answers
Answer:
1549.5
Step-by-step explanation:
Hello There!
Heron's area formula is
[tex]A=\frac{(a)(b)sin(c)}{2}[/tex]
all we have to do is plug in the values
so
[tex]A=\frac{77*41sin79}{2} \\77*41=3157\\3157sin79=3098.997018\\\frac{3098.997018}{2} =1549.498509[/tex]
so the area of the triangle is 1549.498509
our final step is to round to the nearest hundredth
the answer would be 1549.5
Answer:
1610.289units²
Step-by-step explanation:
a=79
b=77
c=43
s=(79+77+43)/2=99.5
by using heron's formula
area of triangle=√{s(s-a)(s-b)(s-c)}
=√{99.5(99.5-79)(99.5-77)(99.5-43)} =1610.289units²
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9(7/4)-2= what in fraction form ? Can someone please help ?
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Answer:
55/4
Step-by-step explanation:
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Prove (triangle)ABC is congruent to (triangle) DEF using ASA
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Answer/Step-by-step explanation:
Two triangles can be proven to be congruent to each other if two angles and an included side of one triangle is congruent to the corresponding two angles and included side of the other triangle.
Two angles (<C and <A) in ∆ABC, are congruent to two angles (<D and <F) in ∆DEF. Also, the included side (AC) in ∆ABC is congruent to the included side (DF) in ∆DEF.
Therefore, based on the Angle-Side-Angle Congruence Theorem, ∆ABC is congruent to ∆DEF.
Answer:
Answer/Step-by-step explanation:
Two triangles can be proven to be congruent to each other if two angles and an included side of one triangle is congruent to the corresponding two angles and included side of the other triangle.
Two angles (<C and <A) in ∆ABC, are congruent to two angles (<D and <F) in ∆DEF. Also, the included side (AC) in ∆ABC is congruent to the included side (DF) in ∆DEF.
Therefore, based on the Angle-Side-Angle Congruence Theorem, ∆ABC is congruent to ∆DEF.
Step-by-step explanation:
Find the surface area of the rectangular prism.
2 in
2 in
4 in
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Answer:
40 in
Step-by-step explanation:
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A person invested $540 in an account growing at a rate allowing the money to double
every 9 years. How much money would be in the account after 21 years, to the nearest
dollar?
Answers
Answer:2721
Step-by-step explanation:
The long side of a right triangle is called the hypotenuse. The hypotenuse
is always opposite the right angle of the triangle. The two shorter sides are
called legs. Though other triangles can have a longest side, it is only called
the hypotenuse in a right triangle.
Where can you find the hypotenuse in a right triangle?
А
It is opposite the right angle.
B
It is opposite the acute angle.
C
It is the shortest leg.
D
It is the obtuse angle.
Answers
Answer:
b
Step-by-step explanation:
A part time seamstress made $8881.93 last year. If she claimed herself as an exemption for $3650 and had a $5700 standard deduction, what was her taxable income last year?
A: $3181.93
B: $468.07
C: $0
D: $5231.93
Answers
Answer:
c
Step-by-step explanation:
A part-time seamstress made $8881.93 last year. The taxable income is $0.
We have given that,
A part-time seamstress made $8881.93 last year. If she claimed herself as an exemption for $3650 and had a $5700 standard deduction.
We have to determine, what was her taxable income last year.
What is the taxable income?
Taxable income is the portion of your gross income used to calculate how much tax you owe in a given tax year.
Therefore the taxable income is $0.
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Part 3: Write the equation of and graph an ellipse.
Given the foci and vertices of an ellipse, complete the following steps.
Vertices at (4, -6 +-9)
Foci at (4, -6 +-5sqrt2)
a) What is the center of the ellipse? Explain how to determine this from the given points.
b) Write the standard equation of the ellipse. (3 points
c) What are the lengths of the major and minor axes? (2 points)
Major Axis:
Minor Axis:
d) Sketch a graph of the ellipse and label the center, foci, and the major and minor axes. (4 points)
Answers
Answer:
Step-by-step explanation:
The center is halfway between vertices, at (4, -6).
It is also halfway between foci.
:::::
The vertices are vertically aligned, so the parabola is vertical.
General equation for a vertical ellipse:
(y-k)²/a² + (x-h)²/b² = 1
with
center (h,k)
vertices (h,k±a)
co-vertices (h±b,k)
foci (h,k±c), c² = a²-b²
Apply your data and solve for h, k, a, and b.
center (h,k) = (4, -6)
h = 4
k = -6
vertices (4,-6±a) = (4,-6±9)
a = 9
foci (4,-6±c) = (4,-6±5√2)
b² = a² - c² = 9² - (5√2)² = 31
b = √31
The equation becomes
(y+6)²/81 + (x-4)²/31 = 1
:::::
length of major axis = 2a = 18
length of minor axis = 2b = 2√31
The various parts of the question needs to be answered.
Center: (4,-6)
Standard equation: [tex]\dfrac{(x-4)^2}{\sqrt{31}^2}+\dfrac{(y+6)^2}{9^2}=1[/tex]
Length of major axis: 18 units
Length of minor axis: [tex]2\sqrt{31}\ \text{units}[/tex]
Graph is attached.
EllipseThe Vertices are of the form
[tex](h,k\pm a)=(4,-6\pm 9)[/tex]
This means that the ellipse is symmetrical to the y axis.
The center of an ellipse is given by [tex](h,k)[/tex]
So, here the center is [tex](4,-6)[/tex]
[tex]a=\pm 9[/tex]
The foci are of the form
[tex](h,k\pm c)=(4,-6\pm 5\sqrt{2})[/tex]
So, [tex]c=\pm 5\sqrt{2}[/tex]
[tex]b=\sqrt{a^2-c^2}\\\Rightarrow b=\sqrt{9^2-(5\sqrt{2})^2}\\\Rightarrow b=\pm\sqrt{31}[/tex]
The standard equation for major axis being parallel to y axis is given by
[tex]\dfrac{(x-h)^2}{b^2}+\dfrac{(y-k)^2}{a^2}=1\\\Rightarrow \dfrac{(x-4)^2}{\sqrt{31}^2}+\dfrac{(y+6)^2}{9^2}=1[/tex]
Length of major axis is
[tex]2a=2\times 9\\ =18\ \text{units}[/tex]
Length of minor axis is
[tex]2b=2\sqrt{31}\ \text{units}[/tex]
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Answers
Answer:
if x ≥ 2, then y = x - 1
if x < 2, then y = -x + 3
Step-by-step explanation:
y = 1* |x - 2| + 1
y = |x-2| + 1
*** The rule on absolute value: |a| =a, if a ≥ 0; |a| = -a, if a < 0
If x-2 ≥ 0, then |x-2| = x-2, so y = (x - 2) + 1 = x - 1; y = x - 1
So if x ≥ 2, then y = x - 1
If x-2 < 0, then |x-2| = -(x-2) = -x + 2, so y = {-x + 2} + 1 = -x + 3; y = -x + 3
So if x < 2, then y = -x + 3
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How is the product of 3 and -2 shown using integer tiles?
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Answer:
The first one . +++ --
Step-by-step explanation:
Paulo missed three out of 15 questions on a quiz, or 3/15. Write the fraction of questions Paula answered correctly as a decimal. What is the answer??
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Step-by-step explanation:
12/15 in a calculator
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The measure of an angle is 72 degrees what is the measure of its conplementary angle
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Answer:
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Step-by-step explanation:
Eber bought a new pair of baseball cleats for $64.95. The sales
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Answer:
Yes
Step-by-step explanation:
(3, 2) is a solution to the given system of linear equations.
x - 8y = 3 - 8*2 = 3 - 16 = - 13
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Joel had 200 coins,
which were dimes and quarters. The total value is $32.
Answers
Answer:
Joel had 120 dimes and 80 quarters.
Step-by-step explanation:
Given that Joel had 200 coins, which were dimes and quarters, and the total value was $ 32, to determine how many coins of each type he had, the following calculation must be performed:
0.25 - 0.10 = 0.15
200 x 0.10 = 20
32 - 20 = 12
12 / 0.15 = 80
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What is 54288 divided by 6.24
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Jeremy makes $4.70 every time he mows a lawn but it costs him $6.80 to refill his lawn mower with gas. If Jeremy mows 5 lawns using 3 tanks of gas, how much did he profit? *
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The area of the parallelogram is___ cm2
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
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Olive has a plastic container shaped like a cube to put slime in. She measures one side and finds that it’s 0.5 foot long. Use the formula V = s3 to determine how many cubic feet of slime will fit in her container. PLEASE HELP!
Answers
Answer:
0.125 cubic feet
Step-by-step explanation:
Since the container has a shape of a cube with a measure of its side 0.5 ft, then;
Volume of the container, V = [tex]s^{2}[/tex]
where s is the measure of its side.
s = 0.5 ft, then;
V = [tex](0.5)^{3}[/tex]
= 0.125
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You have a restaurant bill of $46.32. If you are taxed 7 1/2 and decide to tip your server 20%, how much is your total?
a.
$59.75
b.
$59.05
c.
$58.92
d.
$58.87
Answers
Answer:
The correct answer is B. $59.05.
Step-by-step explanation:
Given that I have a restaurant bill of $ 46.32, if I am taxed 7 1/2 and decide to tip my server 20%, to determine how much is my total, the following calculation must be performed:
1/2 = 0.5
46.32 + (46.32 x 0.075) + (46.32 x 0.2) = X
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49.79 + 9.26 = X
59.05 = X
Thus, the total amount that I must pay is $ 59.05.
Answer:
b
Step-by-step explanation:
trust
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Answer:
A= 90 (right angel )
E= 90 - 67 = 23
I hope im right!!
What is the area of the triangle?
Answers
9514 1404 393
Answer:
7 square units
Step-by-step explanation:
There are several ways the area of triangle EBD can be found.
find the lengths EB, BD, DE and use Heron's formula (messy due to roots of roots being involved).define point G at the lower left corner and subtract the areas of ∆DEG and BCD from trapezoid BCGE.figure the area from the coordinates of the vertices.use Pick's theorem and count the dots.We choose the latter.
__
Pick's theorem says the area of a polygon can be found as ...
A = i + b/2 -1
where i is the number of grid intersection points interior to the polygon, b is the number of grid points intersected by the border.
The attached figure shows the lines EB, BD, and DE intersect one point in addition to the vertices. So, b=4. A count of the red dots reveals 6 interior points (i=6). So, the area is ...
A = 6 + (4/2) -1 = 7
The area of ∆EBD is 7 square units.
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Answers
Answer:
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Step-by-step explanation:
The x-values of the relation are repetitive, making it not a function.
Answer:
Not a function
Step-by-step explanation:
-1 is used more than once
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please help if you can!
picture included
Answers
Answer:
x = 12.5
Step-by-step explanation:
Based on the interesting chords theorem, we would have the following:
2*x = 5*5
2x = 25
Divide both sides by 2
x = 25/2
x = 12.5
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Answer:
expression
Step-by-step explanation:
It is expression because it is a algebraic expression.
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
Move terms to the left side.
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Answer:
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Step-by-step explanation: