Answers
Answer:
48
Step-by-step explanation:
Remark
Use a^2 + b^2 = c^2 to solve for the height.
Givens
c = 10
b = 6
h = ?
Solution
b^2 + h^2 = c^2
6^2 + h^2 = 10^2
36 + h^2 = 100 Subtract 36
h^2 = 100 - 36
h^2 = 64 Take the square root of both sides
sqrt(h^2) = sqrt(64)
h = 8
The height = 8
Area = 1/2 * b * h
Area = 1/2 *12 * 8
Area = 48
Comment
You might wonder where the 12 came from. It wasn't given The base is the whole line across the bottom. 1/2 of it is six. The whole base = 12
Related Questions
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.
Can someone help meee
Answers
Answer:
A= 90 (right angel )
E= 90 - 67 = 23
I hope im right!!
using the commutative property, what would be the equivalent expression for 5+6= ?
Answers
Find the surface area of the rectangular prism.
2 in
2 in
4 in
Answers
Answer:
40 in
Step-by-step explanation:
I HAVE THE POWER OF GOD AND ANIME ON MY SIDE
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
5x^2-4x=6 help!!! Thank you in advance !
Answers
Answer:
x = 2 ± √34/5
Step-by-step explanation:
Move terms to the left side.
5x^2 - 4x = 6
5x^2 - 4x -6 = 0
Identify a, b, and c before plugging them into the quadratic formula.
a = 5
b = -4
c = -6
x = -(-4) ± √(-4)^2 - 4 * 5(-6)/2 * 5
Then simplify.
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]
Learn more about ellipse:
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what is the value? when r equals 0
Answers
Answer:
I do not know the answer to this question
Step-by-step explanation:
find the perimeter of the shape below
Answers
Answer:
It doesn't show the whole picture
Step-by-step explanation:
HELP I WILL GIVE BRAINLIEST
A mathematical phrase represented by numbers, variables, and operations is a(n) expression
equation
substitution
exponent
Answers
substitution- an operation is a expression
exponent- variables
Answer:
expression
Step-by-step explanation:
It is expression because it is a algebraic expression.
Y=-1|x-2|+1 how to solve
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
PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA 40 POINTS** !! DONT SKIP :((
Answers
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
16x - 16y = 16(x - y) = 16( 3 - 2) = 16*1 = 16
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:
What is 54288 divided by 6.24
Answers
Geometry
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
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
200 - 80 = 120
(80 x 0.25) + (120 x 0.1) = X
20 + 12 = X
32 = X
Thus, Joel had 120 dimes and 80 quarters.
Prove (triangle)ABC is congruent to (triangle) DEF using ASA
Answers
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:
Which trigonometric ratios are correct for triangle
ABC? Select three options.
Answers
Answer:
Options (1), (3) and (4)
Step-by-step explanation:
From ΔABC given in the picture,
By Pythagoras theorem
Hypotenuse² = (Leg 1)² + (Leg 2)²
BC² = AB² + AC²
(18)² = 9² + AC²
AC = [tex]\sqrt{324-81}[/tex]
AC = [tex]9\sqrt{3}[/tex] cm
sin(C) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{AB}{BC}[/tex]
= [tex]\frac{9\sqrt{3}}{18}[/tex]
sin(C) = [tex]\frac{\sqrt{3} }{2}[/tex]
sin(B) = [tex]\frac{AC}{BC}[/tex]
= [tex]\frac{9}{18}[/tex]
= [tex]\frac{1}{2}[/tex]
cos(B) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{9\sqrt{3}}{18}[/tex]
= [tex]\frac{\sqrt{3} }{2}[/tex]
tan(B) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{AC}{AB}[/tex]
= [tex]\frac{9}{9\sqrt{3} }[/tex]
= [tex]\frac{1}{\sqrt{3} }[/tex]
tan(C) = [tex]\frac{AB}{AC}[/tex]
= [tex]\frac{9\sqrt{3}}{9}[/tex]
= [tex]\sqrt{3}[/tex]
Therefore, Options (1), (3) and (4) are the correct options.
Answer:
Options (1), (3) and (4)
Step-by-step explanation:
From ΔABC given in the picture,
By Pythagoras theorem
Hypotenuse² = (Leg 1)² + (Leg 2)²
BC² = AB² + AC²
(18)² = 9² + AC²
AC =
AC = cm
sin(C) =
=
=
sin(C) =
sin(B) =
=
=
cos(B) =
=
=
tan(B) =
=
=
=
tan(C) =
=
=
Therefore, Options (1), (3) and (4) are the correct options.Step-by-step explanation:
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 measure of an angle is 72 degrees what is the measure of its conplementary angle
Answers
Answer:
18
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.
To learn more about the taxable income vsit:
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#SPJ2
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??
Answers
Step-by-step explanation:
12/15 in a calculator
0.8
Can someone please help me on this
Answers
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
46.32 + 3.474 + 9.264 = X
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
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? *
Answers
4.7 x 5
6.8 x 3
subtract the difference
3.1
The area of the parallelogram is___ cm2
Answers
Answer:
98 cm squared
Step-by-step explanation:
Can someone please help me!!
Answers
Answer:
the third option
Step-by-step explanation:
9(7/4)-2= what in fraction form ? Can someone please help ?
Answers
Answer:
55/4
Step-by-step explanation:
Determine whether the relation is a function. Explain.
(-1, 6), (1, 4), (-1, 2), (1, 6), (-1, 5)
Answers
Answer:
The relation is not a function.
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
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
V = 0.125 cubic feet
The cubic feet of slime that would fit in the container is 0.125.
QUICK ITS TIMED PLS HELP QUICK!!!!!
How is the product of 3 and -2 shown using integer tiles?
Answers
Answer:
The first one . +++ --
Step-by-step explanation: