Answers
Answer:
6 square units
Step-by-step explanation:
The attachment shows the figure redrawn to scale, along with helpful semicircle O with diameter EB. Trig relations can be used to find the area of triangle ADB. The relation between an inscribed angle and its corresponding central angle is also helpful.
__
anglesAny right triangle can be inscribed in a semicircle whose diameter is the hypotenuse. Accordingly, we have constructed semicircle O whose center is the midpoint of EB. Hence its radius is EB/2 = 4/2 = 2.
Then angle EBD is an inscribed angle, hence half the measure of central angle EOD. Since ∠EOD is double the measure of ∠EBD, it is congruent to ∠EBC, which is also double the measure of ∠EBD. We have called the measure of this double angle θ. Its complement is the angle marked β.
segmentsThe fact that angles EOD and EBC are congruent means that segments OD and BC are parallel. Segment BC is the altitude of ΔADB with respect to base AD.
The tangent ratio is ...
Tan = Opposite/Adjacent
Applying that to angle β, we have
tan(β) = OD/AD [eqn 1]
tan(β) = BC/AC [eqn 2]
These two relations can be solved for the measures of AD and BC, which we need in order to find the area of ΔADB.
areaEquation [eqn 1] tells us ...
AD = OD/tan(β)
Equation [eqn 2] tells us ...
BC = AC·tan(β)
The area of ΔADB is ...
Area = 1/2bh
Area = 1/2(AD)(BC) = 1/2(OD/tan(β))·(AC·tan(β))
Area = 1/2(OD)(AC) . . . . . . factors tan(β) cancel
The length of AC is given as 6, and we know OD = 2, so the area is ...
Area = 1/2(2)(6) = 6
The area of triangle ADB is 6 square units.
Related Questions
Slope of (-4,-7) and (-2,-19)
Answers
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the slope of (-4, -7) and (-2, -19).
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Use the slope formula.Here's the slope formula:
[tex]\star~\boxed{\mathrm{\cfrac{y2-y1}{x2-x1}}}[/tex]
Where
y2 and y1 are y-coordinates
x2 and x1 are x-coordinates
Input the values, which are:
-19: y2
-2: x2
-7: y1
-4: x1
[tex]\star~\mathrm{\cfrac{-19-(-7)}{-2-(-4)}}[/tex]
[tex]\star~\mathrm{\cfrac{-19+7}{-2+4}}[/tex]
Simplify!
[tex]\star~\mathrm{\cfrac{-12}{2}}[/tex]
[tex]\star~\mathrm{-6}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students out :)
A square has side lengths of 1.9 centimeters. what's the area of square?
Answers
Answer:
3.61cm^2
Step-by-step explanation:
1.9 * 1.9 = 3.61
Which ratio is equivalent to Sun U?
(IMAGE ABOVE)
SOMEONE PLEASE HELP ME ILL GIVE YOU BRAINLIST ANSWER!!!!!
Answers
Answer:
(a) SV/VW
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationship between trig functions and sides in a right triangle. This problem also makes use of the properties of similar triangles:
corresponding sides are proportionalcorresponding angles are congruent__
sine ratioThe sine of angle U is given by ...
Sin = Opposite/Hypotenuse
The side opposite angle U in ΔTUS is ST. The hypotenuse of that right triangle is side TU. This means the desired ratio is ...
sin(U) = Opposite/Hypotenuse = ST/TU
corresponding ratioIn similar ΔVWS, angle W has the same measure as angle U. Its sine will be the ratio of the corresponding sides. The similarity statement ΔTUS~ΔVWS tells you that the side corresponding to ST is SV, and the side corresponding to TU is VW.
sin(U) = sin(W) = SV/VW
simplify 9+ (-2)^3 HELP PLEASE
Answers
Answer:
1
Step-by-step explanation:
Raise -2 to the power of 3 = -8
9-8= 1
Answer:
1
Step-by-step explanation:
A number raised to the 3rd power is equal to that number multiplied by itself twice. Below I have expanded the expression to visualize this process. If this makes it more confusing, the main way is just to go from line 1 to line 4.
9 + (-2)³ <---- Original expression
9 + (-2 x -2 x -2) <---- (-2)³ expanded
9 + (4 x -2) <---- -2 times -2
9 + (-8) <---- 4 x -2
1 <---- 9 - 8
which represents factorization of the trinomial 10x^2 + 11x + 3 ?
(5x+3)(2x+1)
(5x+1)(2x+3)
(5x+1)(3x+3)
(5x+2)(3x+1)
Answers
Answer:
[tex](5x+3)(2x+1)[/tex]
Step-by-step explanation:
- Sum-product method
For a polynomial of the form [tex]ax^2+bx+c[/tex]
We rewrite the middle term as a sum of two terms whose product is
[tex]a*c = 10*3 = 30[/tex] and whose sum is [tex]b = 11[/tex]
[tex]10x^2 + 11x + 3[/tex]
[tex]10x^2 + 6x + 5x + 3 -- > (3*10 = 6*5), (6+5 = 11)[/tex]
- Factor using the greatest common factors (GCF)
[tex]2x(5x + 3) + 1(5x + 3)[/tex]
- Final Answer
[tex]= (5x+3)(2x+1)[/tex]
Two different cross sections are taken parallel to the base of a three-dimensional figure. The two cross sections are the same shape, but are not congruent. Which could be the three-dimensional figure?.
Answers
The geometric figures which could be this three-dimensional figure are:
ConeTriangular pyramidSquare pyramidWhat is a cross section?A cross section can be defined as an exposed surface or shape that is formed when a cut is made through a three-dimensional figure.
In this scenario, the geometric figures which could be this three-dimensional figure are:
Cone: when cut horizontally, its cross section would always form a circle of different sizes.Triangular pyramid: when cut horizontally, its cross section would always form a triangle of different sizes.Square pyramid: when cut horizontally, its cross section would always form a square of different sizes.Read more on here: https://brainly.com/question/2459472
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Jennifer needs to use a ladder to clean a second floor window on a building. If the window is 13 ft above the ground and the base of the ladder is 4 ft from the building, which equation below can be
used to determine the length (x) of the ladder needed to reach the window? Draw a picture
Answers
By using the Pythagoras theorem, the length of the ladder will be 13.6 feet.
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
Jennifer needs to use a ladder to clean a second-floor window on a building.
If the window is 13 ft above the ground and the base of the ladder is 4 ft from the building.
Then the length of the ladder will be
H² = 13² + 4²
H² = 169 + 16
H² = 185
H = 13.6 ft
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Answer: 4^2+13^2=x^2
Step-by-step explanation:
trust
Daniel was offered a job after college earning a salary of $60,000. He will get a raise
of $4,000 after each year working for the company. Answer the questions below.
regarding the relationship between salary and the number of years working at the
company.
The independent variable, x, represents the
and the
dependent variable is the
because the
depends on the
A function relating these variables is M(x) =
So M (5) =
meaning 5
Answers
The independent variable represents the number of years that Daniel has worked.
The dependent variable is the total salary of Daniel. This is because it depends on the number of years worked.
M(5) is $80,000.
What is independent and dependent variable?
The independent variable is that is given. The dependent variable is the variable that is being determined. It is usually affected by the independent variable.
M(5) = $60,000 + (4000 X 5) = $80,000
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You are a pharmacy technician at costco. you are responsible for filling prescriptions for patients
that are ordered by the doctors.
you are looking over a pharmacy order. a doctor ordered 180 ml of prednisone 2 mg/1ml. you
checked, and do not have 180 ml of prednisone 2 mg/1ml. at the moment, you only have 10 mg
tablets in stock and cherry syrup.
you want to make this order for the patient, and in order to do this, you need to calculate how
many 10 mg tablets you will need to mix cherry syrup, in order to create 180 ml of 2mg/1ml.
now, just to make sure you understand the metric system well, can you describe what ml
measures and how it compares to the base unit? what does mg compare and how does it
compare to the base unit?
Answers
Answer:
36 tablets
Step-by-step explanation:
We are asked to find the number of tablets of a particular mass that are required to give a specific mass-to-volume ratio for a given volume of solution. The units used are all SI (metric) units.
__
metric unitsThe International System of units (abbreviated SI in all languages) defines seven base units and a number of derived units. The base unit for length is the meter. For mass, the base unit is the kilogram. The derived unit for volume is the liter, which is 1/1000 of a cubic meter.
Currently, there are 20 prefixes defined that signify powers of 10 ranging from 10^-24 to 10^24. These are used in front of the abbreviations for units. Useful here are the prefixes kilo- and milli-, standing for 10^3 and 10^-3, respectively. The relevant abbreviations are ...
m - meterg - graml or L - liter (often L is used in order to avoid confusion)k - kilom - milliIn this problem, the volume of syrup used is 180 ml, or 180×10^-3 liters. The mass of medicine in one tablet is 10 mg, or 10×10^-3 grams.
__
mass of medicineWe desire a solution with a concentration of 2 mg/ml. We want 180 ml of the solution, so the mass of medicine that needs to be incorporated is ...
(180 ml)×(2 mg/ml) = 360 mg
number of tablets
Each tablet supplies 10 mg of medicine. To get 360 mg of medicine, we need n tablets, such that ...
n(10 mg) = 360 mg
n = (360 mg)/(10 mg) = 36 . . . . tablets
36 tablets of 10 mg each are needed to mix with 180 ml of syrup to give 2 mg/ml.
Solve the inequality: 10+5≥25
A:≥2
B: ≥30
C: ≥3
D: ≥20
Answers
Answer:
no c is write
Step-by-step explanation:
10+5≥ 25
10-10+5≥ 25-10
0+5≥ 15
≥3 ans…
Answer: The correct answer choice A: ≥2
Step-by-step explanation:
10+5>25 is false
Let's solve your inequality step-by-step.
10x+5 ≥ 25
Subtract:
[tex]10x+5-5[/tex] ≥ [tex]25-5[/tex]
[tex]10x[/tex] ≥ [tex]20[/tex]
Divide:
[tex]\frac{10x}{10}[/tex] ≥ [tex]\frac{20}{10}[/tex]
[tex]x[/tex]≥[tex]2[/tex]
10+5≥25 is False: The left side 15 is less than the right side 25, which means that the given statement is false.
you may mean 10x+5≥25, if so your answer is A.
Calculate the surface area of the composite figure
Answers
Answer:
Below in bold.
Step-by-step explanation:
Total surface area = 1/2 * area of a sphere + area of the side o a cone
= 1/2 * 4 π r^2 + π r L
= 1/2 * 4 π 7^2 + π*7*25
= 307.876 + 549.779
= 857.65 in^2 to nearest hundredth.
When graphing f(x)=a sin(bx) you would determine the functions period using which of the following?
A. The period is 2pi/b
B. The period is a
C. The period is pi/b
Answers
Explanation:
The value of 'a' out front in y = a sin(bx) determines the amplitude.
The b term helps us compute the period, which is 2pi/b for sine, cosine, secant, and cosecant functions.
For example, y = 2sin(3x) has an amplitude of 2 and period of 2pi/3
For tangent and cotangent functions, the period would be pi/b.
Translate the shape A three squares right and three squares up.What are the coordinates of the vertices of the image?
Answers
Answer:
see explanation
Step-by-step explanation:
a translation of 3 squares right means add 3 to the x- coordinate
a translation of 3 squares up means add 3 to the y- coordinate
then
(1, 1 ) → (1 + 3, 1 + 3 ) → (4, 4 )
(3, 1 ) → (3 + 3, 1 + 3 ) → (6, 4 )
(1, 4 ) → (1 + 3, 4 + 3 ) → (4, 7 )
The Chang family is on their way home from a cross-country road trip. During the trip, the function D(t)=3260−55t can be used to model their distance, in miles, from home after t hours of driving.
part A:Find D(12) and interpret the meaning in the context of the problem.
part B: If D(t)=2490, find the value of t and interpret its meaning in the context of the problem.
Answers
Considering the given function, we have that:
a) D(12) = 2600, which means that after 12 hours of driving, the family is 2600 miles from home.
b) D(t) = 2490 when t = 14, which means that the family is 2490 miles from home after 14 hours of driving.
What is the function in this problem?The distance that the family is from home, after t hours of driving, is given by:
D(t) = 3260 - 55t.
Then, after 12 hours, the distance is given by D(12), that is:
D(12) = 3260 - 55 x 12 = 2600.
D(12) = 2600, which means that after 12 hours of driving, the family is 2600 miles from home.
D(t)=2490, hence:
3260 - 55t = 2490
55t = 770
t = 770/55
t = 14
D(t) = 2490 when t = 14, which means that the family is 2490 miles from home after 14 hours of driving.
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Question 3 of 10
What is the value of y?
210
y +10°
O
A. 40°
OB. 50°
O C. 60°
OD. 30°
50⁰
Answers
Answer:
y = 40 degrees
Step-by-step explanation:
All three interior angles of a triangle sum to 180 degrees.
2y + y+10 + 50 = 180
3y + 60 = 180
3y = 120
y = 40
1. You have a fair coin, flipping the coin has a 50% chance of showing a head. What is the probability of getting all heads when flip 10 times.
Answers
you’re welcome
Answer:
1 / 1024
Step-by-step explanation:
Each flipping has 1/2 chance
In ten flippings:
[tex](\frac{1}{2} )^{10} =\frac{1^{10} }{2^{10} } =\frac{1}{1024}[/tex]
Hope this helps
Two angles are supplementary.
measures (4x + 9)° and the other angle measures
(x + 1)°. What is the measure of the smaller
angle?
Answers
Answer:
35°
Step-by-step explanation:
If 2 angles are supplementary, that means they add up to 180 :
Now we make an equation and solve for x :
(4x+9) + (x+1) = 180
5x+10 = 180
5x = 170
x = 34
Now we find the measure of the smaller angle using our value of x :
x+1 = 34 +1
x+1 = 35
Hope this helped and have a good day
The value of the surface area of the rectangular prism is equal to the value of the volume of the rectangular prism. Write and solve an equation to find the value of x.
Answers
Answer:
Equation: 24x + 2(36) = 6(6x) or 24x + 72 = 36x Answer: x = 6
Step-by-step explanation:
24x + 72 = 36x
-24x -24x
72 = 12x
/12 /12
6 = x
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Problem 5.2
Here are three lines that intersect at
one point.
Determine the values of x, y, and z
Answers
Answer:
z=98 degrees
x=64 degrees
y=18 degrees
Step-by-step explanation:
y is congruent to 18 since theyre opposite of eachother, same with x and 64. find z by using the straight 180 line. (180=64+18+z, so z=98)
Which inequality represents all values of yfor which the product below is defined? √4x*√X+2
Answers
Use the law
√a√b=√ab
So
y=√4x(x+2)y=√4x²+8xGraph attached
Find the x-intercepts for the parabola defined
by this equation:
y = x² + 3x - 4
Write your answer as two ordered pairs
Answers
Answer:
(-4,1)
Step-by-step explanation:
Factoring, Guess and check.
2y = x + 10
3y = 3x + 15
Answers
2y=x+10
3y=3x+15
2y-10=x
3y=3(2y-10)+15
2y-10=x
3y=6y-30+15
2y-10=x
0=3y+15
2y-10=x
3y=15
x=2y-10
y=5
2y=x+10
2×5=x+10
x=0
x=0, y=5
What is a corresponding angle?
Answers
Answer:
the angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal
Answer:
I was taught like this.
Corresponding has emphasis on the word pond
Fish live in a pond
Therefore, it has to be an angle F
answer is 8.99, but how tho
Answers
Answer:
x ≈ 8.99
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationship between trig functions and sides in a right triangle. Here, the geometry of the problem can be modeled by a right triangle. We are given one side and want to find the difference in lengths of the other side for two different angles.
__
setupThe tower height is the side opposite the angle of elevation. The distance from the tower to the end of the shadow is the side adjacent to the angle of elevation, so the relevant trig relation is ...
Tan = Opposite/Adjacent
tan(angle of elevation) = (tower height)/(length of shadow)
Solving for the length of shadow, we have ...
length of shadow = (tower height)/tan(angle of elevation)
The difference in shadow lengths is 2x for the two different angles, so we have ...
2x = 24.57/tan(30°) -24.57/tan(45°)
__
solutionDividing by 2 and factoring out the tower height, we have ...
x = 12.285(1/tan(30°) -1/tan(45°)) = 12.285(√3 -1)
x ≈ 8.993244
The value of x is about 8.99.
Make this into an expression. the product of four and a number, divided by seven
Answers
Answer:
4x ÷ 7
Step-by-step explanation:
the product of 4 and a number (x)
would be 4x. Then you would divide by 7.
Find the area of the circle formed when a plane passes 7 cm from the center of a sphere with radius 8 cm. give your answer in terms of pi.
Answers
The area of the circle formed when the plane passes through the center of the given sphere is: 15π cm².
What is the Area of a Circle?Area of a circle = πr² (radius of the circle = r).
Given the following:
Radius of sphere = 8 cmDistance of the plane from the center of the sphere = 7 cmRadius of the circle = √((radius of sphere)² - (distance of the plane from the center of sphere²)) = √(8² - 7²)
Radius of the circle = 3.87 cm
Area of the circle = π(3.87²) ≈ 15π cm².
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What is the value of x in the solution to the system of linear equations? y=3x+2
y=x-4
Answers
{y=-7
What is the value of v? With working out please
Answers
Answer:
v = 130
Step-by-step explanation:
substitute the given values for u, a and t into the equation
v = 32 + ( 9.8 × 10) = 32 + 98 = 130
three consecutive odd integers have a sum of 51. what is the smallest integer
Answers
Answer:
15
Step-by-step explanation:
Let 2n+1 be the first odd integer.
Therefore, the consecutive odd integers will be 2n+3 and 2n+5
If the sum of the consecutive odd integers is 51 then:
⇒ 2n + 1 + 2n + 3 + 2n + 5 = 51
⇒ 6n + 9 = 51
⇒ 6n = 42
⇒ n = 7
To find the values of the integers, substitute the found value of n into the expressions:
First integer: 2(7) + 1 = 15Second integer: 2(7) + 3 = 17Third integer: 2(7) + 5 = 19Therefore, the three consecutive odd integers that sum to 51 are 15, 17 and 19. The smallest of which is 15.
The formula for the volume, V, of a cone having the radius, r, and the height, h, is shown below.
Write the formula to calculate the height, h.
Answers
The formula for calculating the height is h = 3V/πr²
Subject of the formulaThe formula given is the formula for calculating the volume of a cone
V = 1/3πr²h
where
h is the height
r is the radius
Make h the subject of the formula
Cross multiply
3V = πr²h
Divide both sides by πr²
3V/πr² = πr²h/πr²
h = 3V/πr²
Hence the formula for calculating the height is h = 3V/πr²
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