In the following figure AEDC is a square, BA= BC and AE = AC. The area of AEDC is 25 cm² and angle B=90°, Calculate the length of AB.
Answers
A triangular prism is a prism which has both of its base sides as a rectangle. The length of side AB is 5/(√2) cm.
What is a triangular prism?Suppose you've got a triangle. Now, stretch it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.
Usually, when we talk about a triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.
The area of AEDC is 25 cm². Therefore,
AEDC = AC²
25 cm² = AC²
AC = 5 cm
In ΔABC,
AB² + BC² = AC²
Since AB=BC,
2(AB²) = AC²
AB² = 25/2
AB = 5/√2 cm
Hence, the length of side AB is 5/(√2) cm.
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Related Questions
The terminal side of angle θ intersects the unit circle in the first quadrant at (16/19,y). What are the exact values of sinθ and cosθ?
Answers
The exact value of sin θ and cos θ is: sinθ =(√105)/19 and cosθ =16/19
The terminal side of an angle is the angle at the standard position. The terminal side of an angle θ drawn in angle standard position is the side which isn't the initial side.
Given that the point of intersection of the terminal side of θ an the unit circle is:
(16/19,y)
The exact value of sin θ and cos θ is: sinθ =(√105)/19 and cosθ =16/19
The given parameters is represented by:
(16/19,y)
This means that :
(cosθ ,sinθ )=(16/19,y)
Using the following trigonometric identity:
cos²θ +sinθ =1
We have:
(16/19)²+y²=1
Expand fraction:
(256/361)+y²=1
Collect like terms:
y²=1-(256/361)
Take LCM:
y²=(361-256)/361
y²=105/361
Take square roots
y=(√105)/19
Substitute value for y in
(cosθ ,sinθ )=(16/19,y)
By comparison:
cosθ =16/19
sinθ =(√105)/19
So the exact value of sin θ and cos θ is: sinθ =(√105)/19 and cosθ =16/19
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Last year, about 2,400 people participated in a local event. This year, about 3,200 people participated. What was the approximate percent increase in participation?
Answers
Answer:
33 %
Step-by-step explanation:
3200 - 2400 = 800
800 / 2400 x 100
1 /3 x 100
100/ 3
33 %
Use the function below to find F(3).
Answers
Hello,
Answer: D
Step-by-step explanation:
F(x) = (1/5)ˣ
F(3) = (1/5)³ = 1³/5³ = 1/125
⇒ Answer D
Ten members of Balin’s soccer team ran warm ups for practice. Each member ran the same distance. Their combined distance was StartFraction 5 Over 6 EndFraction of a mile. To find the distance that each member ran, Balin wrote the expression below.
StartFraction 5 Over 6 EndFraction divided by 10
Which expression is equivalent to Balin’s expression?
Answers
The expression that is equivalent to Balin's expression is 5/6 x 1/10.
What is the equivalent expression?Division is the mathematical operation that is used to determine the quotient of a number.
In order to determine the distance ran by each member, divide the total distance ran by the total number of people.
5/6 ÷ 10
5/6 x 1/10
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The expression is equivalent to Balin’s expression is StartFraction 5 Over 6 EndFraction divided by 10
Division of fractionCombined distance = 5/6 mileNumber of Balin’s soccer team = 10Distance each member ran = Combined distance ÷ Number of Balin’s soccer team
= 5/6 ÷ 10
= 5/6 × 1/10
= 5/60
= 1/12 mile
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I need help with number 10,11 and 12 !
Answers
Answer:
10- I can't really help you with that one you have to just draw it on your own.
11- a triangle can only have 1 obtuse angle because the other 2 need to be acute to connect 3 sides.
12- x=20 degrees,y=64 degrees,z=116 degrees
Step-by-step explanation:
11- 1 obtuse angle because the other 2 need to be acute to connect 3 sides.
12- x=20 degrees because of the other 20 degree angle opposite to it. y=64 degrees because 180-(20+96)=64 (all angles in a triangle add to 180). z=116 degrees because supplementary angles add to 180 degrees and Y and Z are supplementary.
Help me please im trying to do this but dont understand it at all.
Answers
The attached graph represents the graph of the function g(x)
How to determine the function g(x)?The function f(x) is an absolute value function.
An absolute value function is represented as:
y = a|x - h| + k
Where
Vertex = (h, k)
From the graph, we have:
(h, k) = (-3, -2)
So, we have:
y = a|x + 3| - 2
Also, we have:
(x, y) = (-1, 0)
So, we have:
0 = a|-1 + 3| - 2
This gives
0 = 2a - 2
Solve for a
a = 1
Substitute a = 1 in y = a|x + 3| - 2
y = |x + 3| - 2
This means that
f(x) = |x + 3| - 2
We have:
g(x) = 2f(x)
This means that:
g(x) = 2(|x + 3| - 2)
So, we have:
g(x) = 2|x + 3| - 4
See attachment for the graph of g(x)
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Choose the most convenient method to graph the line y=−3.
Select the correct answer below:
Recognize the equation as that of a vertical line passing through the x-axis at −3
Recognize the equation as that of a horizontal line passing through the y-axis at −3
Identify the slope and y-intercept and then graph
Find the x- and y-intercepts and then graph
Answers
Answer:
Recognize the equation as that of a horizontal line passing through the y-axis at −3
Please help!!! Select the quadratic equation that has no real solution.
Answers
Answer:
2x² + 6x + 20
Step-by-step explanation:
See the picture
A television game show has 12 doors, of which the contestant must pick 3. Behind 3 of the doors are expensive cars, and behind the other 9 doors are consolation prizes. The contestant gets to keep the items behind the 3 doors she selects. Determine the probability that the contestant wins at least one car.
Answers
The probability that the contestant wins at least one car is 3/5.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
For 1 car, we consider two possible outcomes:
P(1 car) = 2/6 x 4/5 + 4/6 x 2/5
P(1 car) = 8/15
For no car in either door
P(no car) = 4/6 x 3/5
P(no car) = 2/5
The probability that the contestant wins at least one car is the sum of the probability of one car and the probability of two cars:
P(2 cars) = 2/6 x 1/5
= 1/15
P(1 car) + P(2 cars) = 8/15 + 1/15
= 3/5
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*insert prayer hands*
Answers
Step-by-step explanation:
ATTACHED IS THE SOLUTIONFind the volume of a rank 5cm long, breadth 5cm and height 5cm
Answers
Answer:
125cm³
Step-by-step explanation:
To find volume, we multiply length × width × height
(length × breadth × height)
here, we know our length to be 5cm, our width to be 5cm, and our height to be 5cm
length : 5cm
width/breadth: 5cm
height: 5cm
so, we can multiply our values together (we can plug in our known values to the volume formula of length × width × height)
length × width × height
5 × 5 × 5= 125
*note: we write volume as cubed (unit³)
So, we know our volume is 125cm³
hope this helps! have a lovely day :)
How would you limit the domain to
make this function one to one?
f(x) = 5-x²
Your answer will be the point to which you would
limit the function. So if you would restrict the
domain to either all x values greater than or equal
to two or all x values less than or equal to two, you
would simply enter 2.
Answers
Answer:
0
Step-by-step explanation:
You need to restrict the domain to one side of the axis of symmetry.
For the pair of
functions, f and g, determine the domain of f + g.
f(x) = 4x + 19, g(x) = 12x + 14
Answers
Answer: (-∞,∞)
Step-by-step explanation:
f(x)=4x+19
g(x)=12x+14
f + g= 4x +19 + 12x + 14 = 16x + 33
Domain of 16x + 33 = (-∞,∞)
Need answer ASAP. Giving Brainliest.
Answers
The inequality that represents the given graph is: D. y ≥ 2/3x + 2.
How to Determine the Equation of a Linear Inequality Graph?Using two points on the line, (0, 2) and (-3, 0), find the slope (m).
Slope (m) = change in y / change in x
Slope (m) = (2 - 0)/(0 - (-3))
Slope (m) = 2/3
The y-intercept (b) is the y-value of the point where the line intercepts the y-axis = 2.
Substitute m = 2/3 and b = 2 into y ≥ mx + b:
y ≥ 2/3x + 2
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Which inequality does the shaded region correspond to?
Answers
Answer:
y < x + 1
Step-by-step explanation:
identify 2 points along the line (-1,0) and (0,1)
gradient = [tex]\frac{0-1}{-1-0} =1\\\\the \ y \ intercept = 1\\\\y=x+1\\\\[/tex]
let us choose point (0,0) which is within our origin and substitute
0 = 0 +1
0 = 1
but we know 0 < 1
so the region is well represented by : y < x + 1
Answer:
y > x + 1
Step-by-step explanation:
→ As the line is upward sloping we can eliminate the 2 negative equations options
y < x + 1 or y > x + 1
→ As the region shaded is above the line y = x + 1, it must be y > x + 1
Write the expression as one
involving only sin x and cos x.
sin 2x + cos x
Answers
Answer:
sin 2x + cos x = 2 sin x cos x + cos x = (2 sin x + 1)cos x
Step-by-step explanation:
Given the expression: sin 2x + cos x,
then we can use the formula: sin 2x = 2 sin x cos x, which gives:
sin 2x + cos x = 2 sin x cos x + cos x = (2 sin x + 1)cos x
So there you have two expressions in terms of sin x and cos x, as requested. :D
MATH: GRAPHS AND FUNCTIONS PROBLEM 2
Answers
Answer:
Step-by-step explanation:
What are the domain and range of the function f of x is equal to the quantity x squared plus 5x plus 6 end quantity divided by the quantity x plus 2 end quantity?
A- D: {x ∊ ℝ | x ≠ 2}; R: {y ∊ ℝ | y ≠ −1}
B- D: {x ∊ ℝ | x ≠ − 3}; R: {y ∊ ℝ | y ≠ 0}
C- D: {x ∊ ℝ | x ≠ −2}; R: {y ∊ ℝ | y ≠ 1}
D- D: {x ∊ ℝ | x ≠ −2}; R: {y ∊ ℝ | y ≠ 0}
Answers
The domain and range of the function f of x are equal to : (C) D: {x ∊ ℝ | x ≠ −2}; R: {y ∊ ℝ | y ≠ 1}
Meaning domainA Domain can be defined as the values or numbers that are accepted or allowed in a particular function.
A domain is very important when dealing with a function.
In conclusion, The domain and range of the function f of x are equal to (C) D: {x ∊ ℝ | x ≠ −2}; R: {y ∊ ℝ | y ≠ 1}
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Which of the following rational expressions has the domain restrictions x = -6 amd x = 1?
Answers
Answer:
The answer is A)
Step-by-step explanation:
There is a domain restriction meaning the denominator should not equal to zero. If you substitute 6 and -1 into x for A) :
(1-1)(-6+6)=0
The Denominator can't be zero
Hope it helps!
Which relation is also a function
{(2,0),(3,2),(2,3)}
Answers
3,2
because each input only has one output and 2 has 0 and 3 so it is not a function that leaves 3,2.
What is the mean of the data set? Fifth Grade Jump Distance
2 |0
3 | 2 4 6
4 | 0 2 4 8
5 | 5
6 | 5
42
40
45
20
Answers
The mean of the data set is 42.
What is Mean?The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.
Given:
20, 32, 34, 36, 40, 42, 44, 48, 55, 65
Mean = 20+32+ 34+ 36+ 40+ 42+ 44+ 48+ 55+ 65/10
Mean = 416 / 10
Mean = 41.6
Mean = 42
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domain and range of the function f(x)=|x-5|+10
Answers
Answer:
Domain: (-infinity, infinity)
Range: [10, infinity)
Step-by-step explanation:
So the domain is easy to determine, because the only reason the domain would be restricted is in like logarithmic equations, radical equations, etc... So in this case the domain is all real number (-infinity, infinity) or all real numbers.
The range of this function is a bit different since it's an absolute function, so when the value inside the absolute values goes from -infinity to 0, it's actually decreasing, despite the value technically increasing. But there is a x-5 and that actually doesn't change the range, it simply shifts it to the right by 5 units, so the vertex is there, because that's when the value inside of it goes from being a negative to a positive number. the +10 does change the range, because normally an absolute value function has a vertex at (0, 0) and in this case it's slightly different since it has a vertex when x=5 since the x has 5 subtracted from it. But the +10 is moving that up. Since the lowest value of the absolute value will be 0, any negative number becomes positive. So the vertex is shifted up 10 units, thus the range is [10, infinity)
Range (10, infinity)
Jolene invests her savings in two bank accounts, one paying 6 percent and the other paying 8 percent simple interest per year. She puts twice as much in the lower-yielding account because it is less risky. Her annual interest is 2920 dollars. How much did she invest at each rate? Amount invested at 6 percent interest is $ Jolene invests her savings in two bank accounts , one paying 6 percent and the other paying 8 percent simple interest per year . She puts twice as much in the lower - yielding account because it is less risky . Her annual interest is 2920 dollars . How much did she invest at each rate ? Amount invested at 6 percent interest is $
Answers
Answer:
$14,600 at 8%$29,200 at 6%Step-by-step explanation:
The total amount of interest earned is the sum of the amounts of interest earned by each of the accounts.
SetupLet x represent the amount invested at 8%. Then 2x is the amount invested at the lower rate of 6%. The interest earned by each investment is the product of the amount and the interest rate. The total earned is ...
0.08x +0.06(2x) = 2920
SolutionWe can simplify this equation, then divide by the x-coefficient.
0.20x = 2920 . . . . . . . . . . . simplify
x = 14600 . . . . . . . . . . divide by 0.2
2x = 29200 . . . . . . . . multiply by 2
Jolene invested $29,200 at 6%, and $14,600 at 8%.
Identify the probability to the nearest hundredth that a point chosen randomly inside the rectangle is either in the circle or in the trapezoid.
Answers
The probability that a point is chosen randomly inside the rectangle is either in the circle or in the trapezoid is 0.23 option first is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
The area of the rectangle = 30×21 = 630 square m
The total outcomes = 630 square m
The favorable outcomes = area of the circle + area of the trapezoid
= π(5)² + [(11+15)/2]×5
= 78.53 + 65
= 143.53 square m
Probability(a point chosen randomly inside the rectangle is either in the circle or in the trapezoid):
= 143.53/630
= 0.227 ≈ 0.23
Thus, the probability that a point is chosen randomly inside the rectangle is either in the circle or in the trapezoid is 0.23 option first is correct.
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Answer:
0.13
Step-by-step explanation:
I guessed and got it correct. Sorry, I cant show work, I hope it helped!! <3
given the function f(c)=4|x-5|+3, for what values of x is f(x)=15?
Answers
15=4|x-5|+3 then solve for x
12=4|x-5|
3=|x-5|
3=x-5
-3=x-5
x=8, -2
Hope this helped :)
175g plus 0.4kg equal in grams
Answers
Answer:
575g
Step-by-step explanation:
Since we need the ans in grams first ensure that both values are in the same unit.
So convert 0.4 kg into grams by multiplying it with 1000grams.
This gives us 400g
175+400=575g
Chana and Josiah started skating at the same time in the same direction, but Josiah had a head start 10 meters past the starting line. Chana skated 3 meters per second and Josiah skated 2 meters per second. What does point I represent in this context?
CORRECT (SELECTED)
Chana's distance from the starting line at a time when she is behind Josiah.
Explanation: Point I is on line b, so it does represent Chana's distance at a certain time. Also, point I is below line a, so it represents a distance that is less than Josiah's distance.
Answers
The best representation for the point I is that Chana's distance from the starting line at a time when she is behind Josiah.
How to solve for the line BThe point I is the distance of Chana at a particular point in time. This distance is the line a.
At point a, the speed is more so below it, it shows a speed that is less than the distance which Josiah has covered.
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20) Sue had these expenditures for her car: April, $138.49; May, $356.75; June, $272.35; July, $417.28. What was
her average monthly expense for her car?
a.) $276.22
b.) $296.22
c.)$286.22
Answers
What is the slope of (6,0) and (1,3)
Answers
Answer:
- 3/5
Step-by-step explanation:
(y2-y1) / (x2-x1)
(6,0) & (1,3)
(3-0) / (1-6)
3/-5
- 3/5
On a coordinate plane, a line goes through points (negative 2, negative 2) and (4, 2).The graphed line can be expressed by which equation?
Answers
Answer:
y=⅔m-8 or 3y=2m-8
Step-by-step explanation:
put both equations in the form y=mx+c and solve simultaneously. when done, you will recive values for m and c. replace those values into y=mx+c