Answers
BD, AB, BC for triangle ABC (angle B is a right-angle)
BD, AD are altitudes for triangle ABD
BD, DC are altitudes for triangle BDC
So in all, altitudes are
BD,AB, BC,AD,DC.
Using metric relations,
BD^2=AD*DC=5*7=35
=>
BD=sqrt(35)=5.916 (to 3 decimal places)
Hence the area of triangle ABC
Area=Base*Height/2 = (5+7)*sqrt(35)/2= 35.496 (to 3 decimal places)
Related Questions
What is the length of the base of a right triangle with an area of 15 m² and a height of 3 m?
Answers
Answer: 10
Answer:
10 m
Step-by-step explanation:
I did the test
What is the solution to the following system?
3x + 10y -12z = 40
x - 5y = 0
x- 4z = 0
--------------------------------------------------------------------
A.) (8, 40, 32)
B.) (10, 2, 3)
C.) (20, 4, 5)
D.) (40, 8, 10)
Answers
Answer: C.) (20, 4, 5)
Step-by-step explanation:
The given system is
[tex]3x + 10y-12z = 40.....................(1)\\x-5y =0..........................(2)\\x- 4z=0............................(3)[/tex]
From (2), we have
[tex]x=5y\\\Rightarrow\ y=\frac{x}{5}[/tex]
From (3)
[tex]x=4z\\\Rightarrow\ z=\frac{x}{4}[/tex]
Substitute the values of y and z in equation (1), we get
[tex]3x+10(\frac{x}{5})-12(\frac{x}{4})=40\\\\\Rightarrow\ 3x+2x-3x=40\\\\\Rightarrow\ 20x=40\\\\\Rightarrow\ x=5[/tex]
Then [tex]y=\frac{20}{5}=4[/tex]
and [tex]z=\frac{20}{4}=5[/tex]
Hence, the solution of the given system is (20,4,5)
What is the density of a cube with sides of 4 cm and a mass of 512g?
Answers
4 x 4 x 4 cube
To find the density
Density = mass/volume
The volume of this cube is
4*4*4 = 64
Density = mass / volume
density = 512g / 64cm^3
Density = 8 g/cm^3
Hope this helps
The density of the cube whose volume is 64 cm³ and mass is 512 g is given by the equation D = 8 g/cm³
What is the Volume of a Cube?
The formula of volume of the cube is given by:
Volume of Cube = a x a x a
Volume of Cube = a³
where a is the length of its sides or edges
Given data ,
Let the density of the cube be represented as D
Let the volume of the cube be represented as V
Now , the equation will be
The mass of the cube = 512 g
The side length of the cube a = 4 cm
So , Volume of Cube = a³
Substituting the values in the equation , we get
Volume of Cube V = 4 x 4 x 4
Volume of Cube V = 64 cm³
Now ,
The density of the cube D = mass of the cube / Volume of Cube
Substituting the values in the equation , we get
The density of the cube D = 512 / 64
The density of the cube D = 8 g/cm³
Therefore , the value of D is 8 g/cm³
Hence , the density of the cube is 8 g/cm³
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PLEASE HELP
8.02
1. Find the center, vertices, and foci of the ellipse with equation x squared divided by one hundred plus y squared divided by sixty four = 1.
A) Center: (0, 0); Vertices: (-10, 0), (10, 0); Foci: (-8, 0), (8, 0)
B) Center: (0, 0); Vertices: (0, -10), (0, 10); Foci: (0, -8), (0, 8)
C) Center: (0, 0); Vertices: (-10, 0), (10, 0); Foci: (-6, 0), (6, 0)
D) Center: (0, 0); Vertices: (0, -10), (0, 10); Foci: (0, -6), (0, 6)
2. Find the center, vertices, and foci of the ellipse with equation 2x2 + 6y2 = 12.
A) Center: (0, 0); Vertices: point negative square root of six comma zero and point square root of six comma zero ; Foci: (-2, 0), (2, 0)
B) Center: (0, 0); Vertices: (0, -6), (0, 6); Foci: Ordered pair zero comma negative four square root two and ordered pair zero comma four square root two ;
C) Center: (0, 0); Vertices: point zero comma negative square root of six and point zero comma square root of six ; Foci: (0, -2), (0, 2)
D) Center: (0, 0); Vertices: (-6, 0), (6, 0); Foci: Ordered pair negative four square root two comma zero and ordered pair four square root two comma zero
3. Graph the ellipse with equation x squared divided by twenty five plus y squared divided by four = 1.
A) A vertical ellipse is shown on the coordinate plane centered at, five, two, with vertices at, five, seven, and five, negative three and minor axis endpoints at three, two, and seven, two.
B) A horizontal ellipse is shown on the coordinate plane centered at five, two, with vertices at zero, two, and ten, two and minor axis endpoints at five, four and five, zero.
C) A vertical ellipse is shown on the coordinate plane centered at the origin with vertices at zero, five and zero, negative five and minor axis endpoints at, negative two, zero and two, zero.
D) A horizontal ellipse is shown on the coordinate plane centered at the origin with vertices at, negative five, zero and, five, zero and minor axis endpoints at, zero, two and zero, negative two.
4. Find an equation in standard form for the ellipse with the vertical major axis of length 6 and minor axis of length 4.
A) x squared divided by two plus y squared divided by three = 1
B) x squared divided by nine plus y squared divided by four = 1
C) x squared divided by three plus y squared divided by two = 1
D) x squared divided by four plus y squared divided by nine = 1
5. An elliptical riding path is to be built on a rectangular piece of property, as shown below.
A vertical ellipse is shown centered on the coordinate plane, surrounded by a rectangle of equal length and width.
The rectangular piece of property measures 8 mi by 6 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides.
Answers
Please, see the detailed solution in the attached files.
Thanks.
Cycle paths inc, makes bicycles,tricycles,and unicycles. last week they made 88 more bicycles than unicycles, and 5 times as many tricycles as unicycles. if they made 40 more bicycles than tricycles, how many unicycles did they make
Answers
x = bicycles
y = tricycles
z = unicycles
We write the following system of equations:
x = 88 + z
y = 5z
x = 40 + y
We solve the equation system for z:
1) x = 40 + y
2) y = 5z
3) x = 88 + z
Substituting x and y in equation 1:
88 + z = 40 + 5z
We cleared z:
4z = 88-40
z = 48/4
z = 12
Answer:
They did make 12 unicycles
PLEASE HELP! Two numbers have a sum of one and a product of -6 Use the quadratic equation -n squared plus n plus 6 equals 0 to determine the two numbers
Answers
so let one be x and one be y
you need to find the factors of -6 which is 1 and 6, and 2 and 3
the negative doesn't matter to which one.
only 3 and -2 add up to 1 and have a product of -6
the quadratic equation is ax² + bx + c
-n² + n + 6 = 0
( n + 3 ) ( n - 2 ) = 0
I hope this helps!
what is the constant of variation for the quadratic variation of x |2|3|4|5|6| fx |28|63|112|175|252|
Answers
You can find k using only the first point.
28 = k*2^2
7 = k
The constant of variation is 7.
The surface area of a sphere is found using the formula SA=4πr^2, where r is the radius. If the surface area of a sphere is 64π square feet, what is the radius, in feet? A. 3 B. 18 C. 1 D. 4
Answers
64pi=4pir^2
cancel the pi
64=4r^2
16=r^2
r=4
[tex]64 \pi = 4 \pi r^{2}[/tex]
[tex]16= r^{2}[/tex]
[tex]r^{2}=16[/tex]
[tex]r=4 [/tex] (Answer D)
Use the three steps to solve the problem. Betty has 10 more dimes than quarters. If she has $3.45, how many coins does she have?
Answers
Let
x-----------> number of dimes
y-----------> number of quarters
Step 2: set the equation and solve for the variable
we know that
0.10 x+0.25 y=3.45---------------> 10x+25y=345 equation (1)
x=y+10 equation (2)
substituting 2 in 1
10[y+10]+25y=345----> 10y+100+25y=345
35y=345-100-----------> y=245/35=7
x=y+10--------> x=7+10=17
Step 3: plug in the value of x and y from last step into the variables.
y=7--------> number of quarters coins
x=17-------> number of dimes coins
She has (7+17)=24 coins in total
Thus, 0.25x + 0.1(10+x) = 3.45
= 0.25x +1 +0.1 x = 3.45
= 0.35 x = 3.45 -1
= 0.35x = 2.45
x = 7
Therefore, the quarters are 7, while the dimes were 17,
Thus a total of 24 coins
Meg constructed triangle POQ and then used a compass and straightedge to accurately construct line segment OS, as shown in the figure below:
Which could be the measures of angle POS and angle POQ?
Measure of angle POS is 25 degrees, measure of angle POQ is 40 degrees
Measure of angle POS is 25 degrees, measure of angle POQ is 30 degrees
Measure of angle POS is 20 degrees, measure of angle POQ is 40 degrees
Measure of angle POS is 20 degrees, measure of angle POQ is 30 degrees
Answers
The correct answer is:
Measure of angle POS is 20 degrees, measure of angle POQ is 40 degrees
Explanation:
OS is an angle bisector of ∠POQ. This means it splits ∠POQ into two congruent pieces.
This tells us that ∠POS+∠SOQ = ∠POS+∠POS = ∠POQ.
If m∠POS = 20, this means that m∠POQ = 20+20 = 40°.
Wendy took a trip from one city to another, a distance of 580 mi. she traveled part of the way by bus, which arrived at the train station just in time for wendy to complete her journey by train. the bus averaged 40 mi/h, and the train averaged 80 mi/h. the entire trip took 9 1 2 h. how long did wendy spend on the train?
Answers
and therefore, she took (580-x) mi by train, thus the time taken with train was (580-x)/80 hours.
Hence, x/40 +(580-x)/80 = 9.5 hours
80(x/40) +80 (580-x)/80 = (9.5)80
= 2x + 580-x = 760
x= 760-580
x = 180
Thus the train covered a distance of (580-x) =580-180 = 400
Hence, Wendy took 400/80 = 5 hours on the train
Cary is 5 5 years older than dan. in 5 years the sum of their ages will be 81. find the age of each man now.
Answers
C - 55 = D
(C + 5) + (D + 5) = 81
C = D + 55
(D + 55 + 5) + (D + 5) = 81
(D + 60) + (D + 5) = 81
2D = 16
D = 8
C = 8 + 55 = 63
Cary is 63 years old, and Dan is 8 years old
y = x - 55
x + 5 + y + 5 = 81
Then,
x + 5 + x - 55 + 5 = 81
2x - 45 = 81
2x = 81 + 45
2x = 126
x = 126/2 = 63
Now, let's find y.
y = 63 - 55 = 8.
Therefore Cary is 63 years old and Dan is 8 years old.
Hope this helps !
Photon
-(-(-)(-)(-10x))=-5 solve for x
Answers
We need to cancel out the negatives, so we need to simplify this.
To make things a bit easier for you, we can begin by counting out how many negatives we have. After counting, you should have a negative number count of 5. However, one of the negatives is apart of (-10x) so we'll have 4 negatives and then an extra negative in with 10x.
Remember that "-" could also be looked at as "-1."
So, if we break this down into smaller parts and substitute "-" into "-1," then this'll look like this :
-1 × -1 × -1 × -1 × (-10x) = -5
Remember that a negative times a negative is always a positive.
So, since there are four negatives, then you just multiply it all together.
This results in 1 × (-10x) = -5
Simplify.
-10x = -5
Now, you simply divide both sides by -10.
-10x ÷ -10 = -5 ÷ -10
Simplify.
x = 1/2
~Hope I helped!~
If a right triangle has sides of length a, b and c and if c is the largest, then it is called the "hypotenuse" and its length is the square root of the sum of the squares of the lengths of the shorter sides (a and b). assume that variables a and b have been declared as doubles and that a and b contain the lengths of the shorter sides of a right triangle: write an expression for the length of the hypotenuse. submit
Answers
The expression for the length of the hypotenuse is c = [tex]\sqrt{a^2 + b^2}[/tex].
The length of the hypotenuse of a right triangle can be calculated using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse c is equal to the sum of the squares of the lengths of the other two sides a and b.
So, the expression for the length of the hypotenuse c is:
c = [tex]\sqrt{a^2 + b^2}[/tex]
This expression calculates the length of the hypotenuse given the lengths of the shorter sides a and b.
The hours of daylight,y, in Utica in days, x, from January 1, 2013 can be modeled by the equation y=3.06sin(0.017x-1.40) + 12.23. How many hours of daylight, to the nearest tenth,does this model predict for February 14, 2013?
(1) 9.4
(2) 10.4
(3)12.1
(4)12.2
Answers
Answer:
Option (4) 12.2
Step-by-step explanation:
Hours of daylight, y, in Utica in days, x, from January 1, 2013 can be modeled by the equation
y = 3.06 sin ( 0.017x - 1.40 ) + 12.23
We have to calculate the hours of daylight from the given equation for February 14, 2013.
From January 1, 2013 to February 14, 2013 number of days = 31 + 14 = 45 days.
Now we place x = 45 days in the equation
y = 3.06 sin (0.017 × 45 - 1.40) + 12.23
= 3.06 sin ( 0.765 - 1.40 ) + 12.23
= 3.06 sin ( - 0.635 ) + 12.23
= 3.06 ( - 0.0111) + 12.23
= -0.0339 + 12.23 = 12.196 = 12.20
Option (4) 12.2 is the correct answer.
The number of hours of daylight for the model for February 14 , 2013 is 12.2
Given data:
The function is represented as y=3.06sin(0.017x-1.40) + 12.23
To find the number of hours of daylight predicted by the model for February 14, 2013, substitute the corresponding value of x into the equation and evaluate it.
The total number of days , x = 31 days in January + 14 days in February
So, x = 45
Now, substitute x = 45 into the equation:
y = 3.06sin(0.017(45) - 1.40) + 12.23
Calculating the expression inside the sine function:
0.017(45) - 1.40 = -0.635
Substituting this value back into the equation:
y = 3.06sin(-0.635) + 12.23
The sine of -0.635 is approximately -0.593.
y = 3.06(-0.593) + 12.23
y ≈ 10.425
Rounding to the nearest tenth, the predicted number of hours of daylight for February 14, 2013, is 10.4.
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What is the domain of the graphed function?
A) y ≥ 4
B) x ≥ -2
C) y ≥ -2
D) x ≤ -2
Answers
1000p for an answer pleaseeeeee
Answers
but the 3 has a line above. which means repeated
Jennifer is calculating her gpa. if she uses "=(a1+a2+a3+a4)/4", this is an example of which type of entry?
Answers
(GPA) = Grade Point Average.
Effectively in a program like excel she can use:
GPA = (a1 + a2 + a3 + a4) / 4
Where,
ai = represents each of the notes (i: 1,2,3,4)
However, this is also an example of the following type of entry:
GPA = AVERAGE (a1: a4)
Answer:
Entry:
Formulas: are references of cells, names of cells or ranges, functions or operators that result in a value from other existing values.
Anybody have the answer to this?
Answers
one leg is 2.4 in
the other leg is 7.4/2=3.7 in (radius)
the hypotenuse is
c^2=a^2+b^2
c^2=5.76+13.69=19.45
c=sqrt 19.45=4.41 in
PLEASE HELP ASAP!!!!!!!!
Answers
Answer:
A. y = -2x + 4
Step-by-step explanation:
You are given the values of slope (m) and y-intercept (b). The slope-intercept form of the equation for the line is ...
y = mx + b
Putting m=-2 and b=4 into this form, you get ...
y = -2x + 4
Rewrite as a conditional statement.
2. The sprinkler was turned on this morning resulting in the grass getting wet.
Answers
Which statement best describes Marcos equation
Answers
Cosine function has period of 2[tex] \pi [/tex] because the function value will be same for variable that 2[tex] \pi [/tex] appart. In the problem, cos [tex]- \pi /2[/tex] and cos [tex] 3 \pi /2 [/tex] difference would be 4[tex] \pi [/tex], which is 2 * [tex] 2 \pi [/tex]. That means they both should have same value.
The area of a rectangular room is 120 square feet. The width is 10 feet. What is the length?
Answers
~Deceptiøn
The length of the rectangular room is 12 feet.
To find the length of a rectangular room when the area and width are known, you can use the formula:
Area = Length x Width
Given that the area is 120 square feet and the width is 10 feet,
we can substitute these values into the formula:
120 = Length x 10
Length = 120 / 10
Length = 12
Therefore, the length of the rectangular room is 12 feet.
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Marge wants to build a sidewalk of uniform width around a rectangular swimming pool that is 80 feet long and 50 feet wide.she has 2000 square feet of concrete to create the sidewalk.what should be the width of the sidewalk
Answers
We have then:
(80 + 2W) (50 + 2W) - 80 (50) = 2,000
Rewriting we have:
4000 + 160W + 100W + 4W ^ 2 - 4000 = 2000
4W ^ 2 + 260W - 2000 = 0
W1 = 6.949334595148748
W2 = -71.94933459514874 (ignore)
round:
W = 6.95
Answer:
the width of the sidewalk should be:
W = 6.95 feet
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle B?
Enter your answer in the box.
m∠B=
°
Answers
7x° = 180°-19°
7x° = 161°
x = 23°
m∠B = 6(23) + 19
= 157°
Answer:
∠B=157°
Step-by-step explanation:
It is given that Quadrilateral ABCD is inscribed in the circle.
Also, we know that if the Quadrilateral ABCD is inscribed in the circle, then the opposite angles of the quadrilateral are supplementary by the property of circles. Then,
∠B+∠D=180°
⇒[tex]x+6x+19=180[/tex]
⇒[tex]7x+19=180[/tex]
⇒[tex]7x=161[/tex]
⇒[tex]x=23^{{\circ}}[/tex]
Thus, the value of ∠B=6x+19=6(23)+19=138+19=157°.
A photographer is planning to enlarge a photograph by a scale factor of 1:5 . The original photograph has an area of 154 square inches.
What is the area of the new photograph?
_____in²
Answers
1^2/5^2 = 1/25
1/25 = 154/x
1x= 154 (25)
1x/1= 3850/1
x= 3850
A photographer is planning to enlarge a photograph by a scale factor of 1:5 . The original photograph has an area of 154 square inches.
Solution:
The photograph is being enlarged by a factor 5.
So, each dimension of the photograph is enlarged by 5
So, area is enlarged by [tex] 5^{2} [/tex]
Or, Area is enlarged by a factor=5*5=25
So, the Area of enlarged photograph=[tex] 5^{2} [/tex] *Area of original photograph
Area of enlarged photograph=25*Area of original photograph
Area of enlarged photograph=25*154
On multiplying 25 by 154 we get 3850
Area of enlarged photograph=3850[tex] inches^{2} [/tex]
Answer:
Area of new photograph=3850[tex] in^{2} [/tex]
Find the GCF of the following literal terms. m^7 n^4 p^3 and mn^12 p^5
m[]n[]p[]
Answers
Answer:
The GCF of following literal terms is [tex]m^1n^4p^3[/tex].
Step-by-step explanation:
The given literal terms are
[tex]m^7n^4p^3[/tex]
[tex]m^1n^{12}p^5[/tex]
The factored form of the given terms are
[tex]m^7n^4p^3=m\times m\times m\times m\times m\times m\times m\times n\times n\times n\times n\times p\times p\times p[/tex]
[tex]mn^{12}p^5=m\times n\times n\times n\times n\times n\times n\times n\times n\times n\times n\times n\times n\times p\times p\times p\times p\times p[/tex]
The common factors are m,n,n,n,n,p,p,p. So, the G.greatest common factors is
[tex]GCF=m\times n\times n\times n\times n\times p\times p\times p[/tex]
[tex]GCF=m^1n^4p^3[/tex]
Therefore the GCF of following literal terms is [tex]m^1n^4p^3[/tex].
A right triangle has an area of 33 mm 2 2 and a height of 11 mm. How long is the base of the triangle? Enter your answer in the box. mm
Answers
Area: 33/11
Area: 3
The answer is 3 millimeters
Describe a situation in which there would be a positive association between two variables.
Answers
.. number of miles driven
.. number of gallons of gas used
A cross-country travels 20 kilometers before she realizes that she has to cover at least 75 kilometers in order to qualify for the next race. If the racer travels at a rate of 10 kilometers per hour, how many whole hours will it take her to reach the 75-kilometer mark?