Given: ABCD is a trapezoid, AC ⊥ CD AB = CD, AC=the square root of 75 , AB = 5 Find: AABCD
Answers
In this attached picture according to the conditions of the problem we have an isosceles trapezoid and since we know that legs are equal (AD=BC=5 cm), we have to calculate bases and height in order to find the area. Working with the triangle BCD, we apply Pythagoras theorem and find that CD = [tex] \sqrt{75+25} [/tex] = 10 cm. Since BDC is a right triangle, applying theorem for the area of triangles, we find that [tex] \frac{1}{2} * BF = \frac{1}{2} * 5 * \sqrt{75} [/tex] and BF= [tex] 0.5\sqrt{75} [/tex]. Since ABCD is an isosceles trapezoid, triangles ADE and BFC are congruent with Angle Side Angle theorem. Then, DE=FC and with the help of Pythagoras theorem, DE=FC=2.5 cm. Then, AB=EF=5 cm and the area of the trapezoid is [tex]A= BF * \frac{AB+CD}{2} = 0.5 \sqrt{75} * \frac{5+10}{2} = 18.75 \sqrt{3} cm^{2} [/tex]
The area of the given trapezoid will be [tex]\frac{75}{4} \sqrt{3}[/tex].
It is given that
In trapezoid ABCD
AE ⊥ CD
AC = √75
AD=BC =5
AB =5
In the triangle ADC
From Pythagoras theorem
AC²+AD²=DC²
(√75)² +5² = DC²
DC=10
Let DE=CF=x (Isosceles trapezoid)
What is isosceles Trapezoid?
Trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal.
AB=EF= DC-2x
5 = DC-2x
x=5/2
AE = [tex]\sqrt({5^{2} } -(5/2)^2)\\\\[/tex]
AE = [tex]\sqrt{75} /2[/tex]
So, the area of the trapezoid ABCD = [tex]\frac{1}{2} *(AB+CD)*AE[/tex]
Area of the trapezoid ABCD = [tex]\frac{1}{2} *(5+10)*\frac{\sqrt{75} }{2}[/tex]
Area of the trapezoid ABCD = [tex]\frac{75}{4} \sqrt{3}[/tex]
Therefore, The area of the given trapezoid ABCD will be [tex]\frac{75}{4} \sqrt{3}[/tex].
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Related Questions
A farmer planted corn in a square field.one side of the field measures 36 yards. what is the area of the cornfield
Answers
Answer: 296 yd²
Answer:
1,296 ik im late but yeah
Step-by-step explanation:
help please
Sammy is planning a trip to Nashville. He knows the hotel costs $125 per night and the round trip flight is $159. He has a budget of $900 to spend on his trip. Which of the following inequalities represents his budget to determine how many nights he can stay in Nashville?
125n + 159 ≥ 900
125n + 159 ≤ 900
159n + 125 ≤ 900
159n + 125 ≥ 900
Answers
In short, the second option is correct. Hope this helps!
Find the equation for the line that passes through the point (−4,−2), and that is perpendicular to the line with the equation y−1=34(x+2).
Answers
y−1=34(x+2)
the equation above can be written in the form of y=ax+b, as follows:
y-1=34x+68
y=34x+69
the slope of the line is a=34
the slope of the perpendicular line will be:
m=-1/34
thus the equation of the perpendicular line cutting through (-4,-2) will be:
m(x-x1)=y-y1
thus
-1/34(x-(-4))=y-(-2)
-1/34x-4/34=y+2
y=-1/34x-36/17
Answer: y=-1/34x-36/17
Find the equation for the line that passes through the point (−4,−2), and that is perpendicular to the line with the equation y−1=34(x+2).
Jack Watkins earns a base salary of $1500 a month, plus a 4% commission on the sales he makes. What is his gross pay of his sales for the month are $8000.
A. 1520
B. 1532
C. 1700
D. 1820
Answers
solution:
Gross pay=(salary)+(commissions)
base salary=$1500
commission=4%
monthly sales=$8000
commissions earned in cash
=4/100×8000
=$320
thus
Gross salary=320+1500=$1820
Solve the equation. Check for extraneous solutions
please help!!!
Answers
!4x+3!=9+2x
1) 4x+3=9+2x
Solving for x:
4x+3-3-2x=9+2x-3-2x
2x=6
2x/2=6/2
x=3
Checking for extraneous solution:
!4x+3!=9+2x
x=3→!4(3)+3!=9+2(3)
!12+3!=9+6
!15!=15
15=15 Ok, then x=3 is not a extraneous solution
2) 4x+3=-(9+2x)
Solving for x:
4x+3=-9-2x
4x+3-3+2x=-9-2x-3+2x
6x=-12
6x/6=-12/6
x=-2
Checking for extraneous solution:
!4x+3!=9+2x
x=-2→!4(-2)+3!=9+2(-2)
!-8+3!=9-4
!-5!=5
5=5 Ok, then x=-2 is not a extraneous solution
Answer:
x = -2 or 3
What is -1 3/5 x -2/3 as a mixed number?
Answers
-8 -2
--- * ----- = 16/15 (an improper fraction), or 1 1/15 (a mixed number)
5 3
1 3/5=8/5x2/3=16/15=1 1/15
A tunnel is in the shape of a parabola. The maximum height is 16 m and it is 16 m wide at the base, as shown below.
A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 16 meters and its width from left to right is 16 meters.
What is the vertical clearance 7 m from the edge of the tunnel?
15.4 m
0.3 m
15.7 m
0.6 m
Answers
Width: w=16
x=w/2→x=16/2→x=8
x=8, y=-16→y=ax^2→-16=a(8)^2→-16=a(64)→-16/64=a(64)/64→-1/4=a→a=-1/4
y=ax^2→y=-(1/4)x^2
7 m from the edge of the tunnel → x=w/2-7=8 m-7 m→x=1 m
x=1→y=-(1/4)x^2=-(1/4)(1)^2=-(1/4)(1)→y=-1/4
Vertical clearance: 16-1/4=16-0.25→Vertical clearance=15.75 m
Please, see the attached file.
Answer: Third option 15.75 m
y -k= 4a (x-h)^2
Solving for this, the vertical clearance 7m forom the edge of the tunnel must be
15.7m
Hope this helps! Goodluck!
find the volume of the composite figure. round your answer to the nearest hundredth
Answers
Be sure to treat the two shapes as completely different figures, then add their totals together
The correct answer is 590.77mm3.
A laptop company has discovered their cost and revenue functions for each day: c(x) = 3x2 − 10x + 200 and r(x) = −2x2 + 100x + 50. if they want to make a profit, what is the range of laptops per day that they should produce? round to the nearest number which would generate profit.
Answers
c(x) = 3x2 − 10x + 200
and
r(x)=−2x2 + 100x + 50
Profit is given by:
P(x)=r(x)-c(x)
P(x)=(−2x2 + 100x + 50)-(3x2 − 10x + 200)
P(x)=-5x^2+110x-150
thus:
at maximum profit P'(x)=0
thus:
P'(x)=-10x+110=0
hence:
x=11
thus the number of units required for one to make profit is 11 units
The sides of a rectangle are in a 3:4 ratio. What is the length of the shorter sides of the rectangle if it's perimeter is 42cm
Answers
Given a rectangle with sides in a 3:4 ratio and a perimeter of 42 cm, the length of the shortest side is 9 cm.
Explanation:We are given that the sides of the rectangle are in a 3:4 ratio and that the perimeter is 42 cm. The rectangular perimeter is calculated by the formula 2*(length + width). In this case, because the sides are in a 3:4 ratio, we can say 2*(3x + 4x) = 42, where 'x' represents the length of the shortest side.
Solve this equation, 2*(7x) = 42, we find that 'x' is 3. So the length of the shorter side, 3x, is 9 cm. Applying the same 3:4 ratio, the longer side, 4x, is 12 cm.
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To find the length of the shorter side of a rectangle with sides in a 3:4 ratio and a perimeter of 42cm, we set up an equation using the ratio values as coefficients and the known perimeter. Solving this equation shows that a unit in the ratio equals 3cm and the shorter side is 9cm.
Explanation:In this mathematics problem, we are trying to find the length of the shorter side of a rectangle, knowing that the sides are in a 3:4 ratio and that the perimeter is 42cm. The perimeter of a rectangle can be found by using the equation [tex]P=2L+2W[/tex] (Perimeter equals twice the length plus twice the width).
If we represent the shorter side as 3x and longer side as 4x, we can establish the following equation based on the given perimeter:[tex]2*(3x)+2*(4x)=42c[/tex]m. Simplifying this equation gives 14x=42cm. Solving for 'x', we find x=3. Therefore, each unit in the ratio corresponds to 3cm, and the length of the shorter side, represented by 3x, is [tex]3*3=9[/tex]cm.
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What is the length of AC?
Answers
[tex]\bf \cfrac{small}{large}\qquad \cfrac{DE}{BA}=\cfrac{EC}{CA}\implies \cfrac{7}{84}=\cfrac{x}{156-x}\implies 1092-7x=84x \\\\\\ 1092=91x\implies \cfrac{1092}{91}=x\implies 12=x\qquad \quad \qquad \boxed{AC=156-12}[/tex]
Compare the functions shown below:
f(x)
cosine graph with points at 0, negative 1 and pi over 2, 1 and pi, 3 and 3 pi over 2, 1 and 2 pi, negative 1
g(x)
x y
−6 −11
−5 −6
−4 −3
−3 −2
−2 −3
−1 −6
0 −11
h(x) = 2 cos x + 1
Which function has the greatest maximum y-value?
a. f(x)
b. g(x)
c. g(x) and h(x)
d. f(x) and h(x)
Answers
Given an arbitrary function '[tex]f(x)[/tex]' we find the point of slope 0 by taking its first derivative and equaling to 0 ('[tex] \frac{d}{dx}f(x)=0 [/tex]').
Lets, first, find the local extremes of the first function:
[tex]f(x)=cos(x)[/tex]
[tex] \frac{d}{dx} f(x)=\frac{d}{dx}cos(x)=-sin(x)=0[/tex]
[tex]x=sin^{-1} (0)=0[/tex]
So our first function has a maxima at '[tex]x=0[/tex]' or at '[tex]y=f(0)=cos(0)=1[/tex]'.
Now we get the extremes for the second function:
[tex]h(x)=2cos(x)+1[/tex]
[tex]\frac{d}{dx} h(x)=\frac{d}{dx}[2cos(x)+1]=-2sin(x)=0[/tex]
[tex]x=0[/tex]
So our second function has a maxima at '[tex]x=0[/tex]' or at '[tex]y=h(0)=2cos(0)+1=3[/tex]'.
Clearly, '[tex]h(0)=3\ \textgreater \ f(0)=1[/tex]', this means the second function '[tex]h(x)[/tex]' has the largest maxima -y value-.
Answer:
f(x) and h(x)
Step-by-step explanation:
f(x) and h(x) have the greatest maximum y-value because if you graph out all the equations you can determine by graph which ones have the greatest y-value. When you graph the equations you find that f(x) and h(x) both have a greatest y-value of 3! While g(x) has a greatest y-value of -2.
*Please note that it is looking for the greatest y-VALUE not the greatest y-INTERCEPT.
A crowd of 50,000 fans is expected to attend the homecoming football game. if the typical vendor can serve 1,500 customers per hour and the game will last for four hours, how many vendors are needed to ensure that each fan can be served during the game? (round to the nearest whole number.) a) 9 b) 10 c) 8 d) 1
Answers
Since every hour, a vendor sells to 1500 customers, we multiply by hours, like this:
1500 * 4 = 6000.
Then we divide 50000/6000, and that would give us 8.33333333, and we round that to the next number which is 9, and that's the answer.
Answer: 9 vendors.
Hope this helped! c:
Using Multiplication, There are 9 vendors are needed to ensure that each fan can be served during the game.
What is Multiplication?Multiplication is to "increase a number by the number of times mentioned".
According to the question,
Number of fans expected to attend a football game = 50,000
Number of customer to be served = 1,500per hour
To find number of customer to be served for 50,000 fans
The game has to be last for 4 hours.
Formula : 1 vendor is to sell 1,500 customer per hour
4*1500 = 6000
A vendor has to sell 6000 customers in 4 hours.
In order to find the number of vendors have to sell 50,000 customers in 4 hours
Let 'x' be the number of vendors
To find the number of vendors only if we divide 50,000 by 6000
=[tex]\frac{50,000}{6000}[/tex] = 8.333 ≈ 9
Hence, there are 9 vendors are needed to ensure that each fan can be served during the game.
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Find 2 numbers that have... a product of 49 and a sum of 14
Answers
Express answer in exact form.
A regular hexagon with sides of 3" is inscribed in a circle. Find the area of a segment formed by a side of the hexagon and the circle.
(Hint: remember Corollary 1--the area of an equilateral triangle is 1/4 s2 √3.)
Answers
the regular hexagon can be divided into 6 equilateral triangles
area of one equilateral triangle=s²*√3/4
for s=3 in
area of one equilateral triangle=9*√3/4 in²
area of a circle=pi*r²
in this problem the radius is equal to the side of a regular hexagon
r=3 in
area of the circle=pi*3²-----> 9*pi in²
we divide that area into 6 equal parts------> 9*pi/6----> 3*pi/2 in²
the area of a segment formed by a side of the hexagon and the circle is equal to 1/6 of the area of the circle minus the area of 1 equilateral triangle
so
[ (3/2)*pi in²-(9/4)*√3 in²]
the answer is
[ (3/2)*pi in²-(9/4)*√3 in²]
What are the coordinates of the image of vertex P after a reflection of rx-axis(x, y)? P'( , )
Answers
Answer: (-7, 4)
Step-by-step explanation:
MANY POINTS!!
When adding fractions, make sure the ______ are the same, and then add the _______.
Answers
I hope this helps :)
Express 0.0037 as a power of 10.
Answers
To express 0.0037 as a power of 10, we move the decimal point 3 places to the right, resulting in 3.7 × 10⁻³.
Explanation:To express 0.0037 as a power of 10, we need to count the number of places we have to move the decimal point to get a number between 1 and 10. In this case, we have to move the decimal point 3 places to the right, so the power of 10 is -3.
0.0037 = 3.7 × 10-3
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Which of the following steps could be used as a shortcut method to multiply 12 by 50
Answers
Which of the following shows that polynomials are closed under subtraction when polynomial 5x − 6 is subtracted from 3x2 − 6x + 2?
3x2 − 11x + 8 may or may not be a polynomial
3x2 − 11x + 8 will be a polynomial
3x2 − x + 4 may or may not be a polynomial
3x2 − x + 4 will be a polynomial
Tip: Every 2 after 3x is an exponent.. so it would be 3x^2
Answers
Simply because polynomials have solutions. 3x2 − 11x + 8 does have 2 solutions.
Two triangles have side lengths 3, 4, 5 and 6, _____, 10, respectively. The triangles are similar to each other.
9
7
8
6.6
Answers
You have to find out happened between triangles
6 / 3 = 2
10 / 5 = 2
They multiplied the first triangle by 2 to get the second
Apply this to find the missing side
4 * 2 = 8
The answer is 8
Hope this helps!
Answer:
The correct option is: 8
Step-by-step explanation:
Suppose, the missing side length in second triangle is [tex]x[/tex]
So, the side lengths of first triangle: [tex]3, 4, 5[/tex]
and the side lengths of second triangle: [tex]6, x, 10[/tex]
As two triangles are similar, that means their corresponding side lengths will be proportional.
So,
[tex]\frac{3}{6}=\frac{4}{x}\\ \\ 3x= 4*6\\ \\ 3x= 24\\ \\ x=\frac{24}{3}=8[/tex]
So, the missing side length in second triangle is 8.
Can someone help me solve this ??
Answers
The external angle at the intersection of two secants is half the difference of the intercepted arcs. That is
∠E = (1/2)(4x° -2x°) = x°
The given measure of arc AB tells you
... 4x° = 56°
... x° = 14°
The appropriate choice is ...
... B. 14°
The hypotenuse of a right triangle is 5 m long. The longer leg is 1 m longer than the shorter leg. Find the side lengths of the triangle.
Answers
The Pythagorean theorem is used to determine the lengths of a right triangle's sides. When we know the hypotenuse length and the fact that one leg is 1m longer than the other, we can solve for the lengths to be approximately 3m and 4m.
Explanation:The subject of your question is related to the geometric concept of right triangles and the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².
In this problem, we know the hypotenuse = 5m and the longer leg is 1m longer than the shorter leg. Let's denote the shorter leg as 'x' m. Consequently, the longer leg is 'x+1' m. Applying the Pythagorean theorem, we get: (x)² + (x+1)² = 5².
Solving this equation, we find x~3m (shorter leg) and x+1~4m (longer leg). These are the lengths of the sides of your right triangle.
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f(x) = cos(x)
f'(x) = -sin(x)
f'(π/2) = -sin(π/2)
f'(π/2) = -1
My answer to this question is A. -1, but I am posting it here because several students got B. +1 as their answer. Can anyone confirm the answer as A?
Answers
A. -1
For confirmation, check a graph of cos(x) at π/2. It has negative slope at that point.
in the box below, enter the value that missing from the table.
Answers
d = v * t
Where,
d: distance
v: speed
t: time
Clearing the time we have:
t = d / v
Rewriting:
t = d * (1 / v)
We look for the value of d:
For t = 1, v = 75 we have:
1 = d * (1/75)
d = 75
Then, v = 15 we have:
t = 75 * (1/15)
t = 5 hours
Answer:
The value that is missing from the table is:
t = 5 hours
plz help
(4+3.2)×[(9−2)+2.5]
Answers
7.2((9 - 2) + 2.5)
Subtract the numbers in the parenthesis found inside the other parenthesis.
7.2(7 + 2.5)
Add the numbers in the parenthesis.
7.2(9.5)
Now multiply the two numbers together to get your final answer.
68.4
This means the expression (4 + 3.2) × ((9 − 2) + 2.5)is equal to 68.4.
Let me know if you have any further questions.
:)
Based on the graph, which statement BEST describes what is happening to the temperature over time?
A.The temperature rises 10 degrees over 3 hours.
B.The temperature rises 10 degrees over 6 hours.
C.The temperature rises 40 degrees over 3 hours.
D.The temperature rises 50 degrees over 6 hours.
Answers
Consider the equation x^2 + 12x + c = 0. If c = -28, list the steps to solve the equation by completing the square, and give the solution or solutions.
Answers
(x-2)(x+14)
Solve for x
x-2=0
x=2
x+14=0
x=-14
The solutions of the equation x² + 12x - 28 = 0 are x = 2 or x = -14.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
To solve the equation x² + 12x + c = 0, where c = -28, by completing the square.
Substitute c = -28 into the equation to get x² + 12x - 28 = 0.
x² + 12x = 28
Complete the square by adding the square of half the coefficient of x to both sides of the equation:
x² + 12x + (12/2)² = 28 + (12/2)²
x² + 12x + 36 = 64
(x + 6)² = 64
Take the square root of both sides of the equation.
x + 6 = ±8
x=8-6=2
x=-8-6=-14
Hence, the solutions of the equation x² + 12x - 28 = 0 are x = 2 or x = -14.
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The baseball team has sold tickets to a spaghetti dinner. forty-eight student tickets have been sold at $1.50 each. if the baseball team has made $149 total from the sale of all tickets, and adult tickets cost $3.50, how many adult tickets were sold?
Answers
number of students is 48
Amount collected from students=48*(1.5)=$72
Amount collected from adults=3.5*x=3.5x
Total amount collected will be:
72+3.5x=149
solving for x we have:
3.5x=149-72
3.5x=77
thus
x=77/3.5
x=22
thus the number of adults was x =22
Find the sum or difference: 2.8 - -5.1
Answers
-(-5.1)=5.1
2.8+5.1= 7.9
Is this what you were asking?
2.8 - (-5.1) = 2.8 + (+5.1) = 2.8 + 5.1 = 7.9