Answers
Answer:
x = 240
Step-by-step explanation:
Using the Altitude- on- Hypotenuse theorem
(leg of large triangle)² = ( part of hypotenuse below it) × (whole hypotenuse)
x² = 144 × 400 = 57600 ( take the square root of both sides )
x = [tex]\sqrt{57600}[/tex] = 240
x = 240
Using Pythagoras' theorem on the 3 triangles of sides (as shown in the graphic - the 2 smaller inner triangles and the large main triangle) it can be shown that the height is the square root of the product of both segments of the baseline.
let's call the 2 segments p and q.
p+q = 400
p = 144
q = 400 - 144 = 256
so, as said before, height = sqrt(p×q) = sqrt(144×256) = 192
now the main Pythagoras with the smallest triangle to get x
x² = 192² + 144² = 36864 + 20736 = 57600
x = 240
now, FYI, why is that formula true ?
as we said, we called the segments of the long baseline p and q.
then we can the sides of the main triangle x and y.
and the height is simply h.
so, then we have for the main rectangular triangle
(p+q)² = x² + y²
and for the 2 smaller triangles
x² = p² + h²
y² = q² + h²
=>
p² +2pq + q² = p² + h² + q² + h²
2pq = 2h²
h² = pq
h = sqrt(pq)
and there you have it. just as simple as that.
Related Questions
Several days after a wedding, an outbreak of cyclosporiasis occurred among attendees. Of the 108 guests at the wedding, 76 were ill and met the case definition. 50 of the 76 who were ill ate the wedding cake. Three of those who were well ate the wedding cake. What is the attack rate for those who ate the wedding cake
Answers
Answer:
The answer is "94.3".
Step-by-step explanation:
Calculating the total numbers of cake eaters[tex]=50+3=53\\\\[/tex]
Calculating the total numbers of ill among them[tex]=50\\\\[/tex]
[tex]\therefore[/tex]
The attack rate for those who ate cake[tex]=\frac{50}{53}\times 100\%=94.3[/tex]
Does the verbal description c minus 12
Answers
Answer:
Yes.
Step-by-step explanation:
Minus and difference mean the same thing. To find the difference, you subtract or minus, so they are the same thing.
Cho tứ diện ABCD . Trên cạnh AB lấy điểm M , AC lấy N , trong tam giác BCD lấy điểm P tìm giao điểm
a, MP và (ACD)
b, AD và ( MNP)
c , BD và ( MNP)
Answers
Answer:
a. Trong mp (BCD), nối BP cắt CD tại E
Trong mp (ABP), nối MP cắt AE kéo dài tại F (trong trường hợp MP không song song AE)
⇒F=MP∩(ACD)⇒F=MP∩(ACD)
b. Nếu MN cắt BC, kéo dài MN cắt BC tại G
Nối GP cắt BD tại H
Trong mặt phẳng (ABD), nối MH cắt AD tại K (trong trường howph MH ko song song AD)
⇒K=AD∩(MNP)⇒K=AD∩(MNP)
c. H=BD∩(MNP)
Step-by-step explanation:
find the measure of x and y
Answers
Answer:
x = 94, y = 76
Step-by-step explanation:
The opposite angles of a cyclic quadrilateral sum to 180° , then
x + 86 = 180 ( subtract 86 from both sides )
x = 94
and
y + 104 = 180 ( subtract 104 from both sides )
y = 76
Given: overline LM cong overline ON and overline LO cong overline MN Prove : LMNO is a parallelogram
Answers
[tex]\overline {LM} \parallel \overline {ON} \ and \ \overline {LO} \parallel \overline {MN}[/tex] because they form congruent alternate interior angles with a common transversal, therefore, LMNO is a parallelogram because the opposite sides are parallel
The reason the above statement are correct is presented as follows:
The given parameters are;
[tex]\overline {LM}[/tex] is congruent to [tex]\overline {ON}[/tex] and [tex]\overline {LO}[/tex] is congruent to [tex]\overline {MN}[/tex]
Required:
To prove that LMNO (quadrilateral) is a parallelogram
Solution:
The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
[tex]\overline {LM} \cong \overline {ON}[/tex] [tex]{}[/tex] Given
[tex]\overline {LM} = \overline {ON}[/tex] [tex]{}[/tex] Definition of congruency
[tex]\overline {LO}[/tex] ≅ [tex]\overline {MN}[/tex] [tex]{}[/tex] Given
[tex]\overline {LO}[/tex] = [tex]\overline {MN}[/tex] [tex]{}[/tex] Definition of congruency
[tex]\overline{LN}[/tex] ≅
[tex]\overline{LN}[/tex] =
ΔLNO ≅ ΔLMN [tex]{}[/tex] Side Side Side (SSS) congruency postulate
∠NLM ≅ ∠LNO [tex]{}[/tex] Cong. Parts of Cong. Triangles are Cong. CPCTC
∠NLM and ∠LNO are alternate interior angles
[tex]\mathbf{\overline {LM} \parallel \overline {ON}}[/tex] [tex]{}[/tex] Alternate interior angles between parallel lines are congruent
∠MNL ≅ ∠NLO [tex]{}[/tex] CPCTC
∠MNL and ∠NLO are alternate interior angles
[tex]\mathbf{\overline {LO} \parallel \overline {MN}}[/tex] [tex]{}[/tex] Alternate interior angles formed between parallel lines are congruent
LMNO is a parallelogram because the opposite sides, [tex]\overline {LM} \parallel \overline {ON}[/tex] and [tex]\overline {LO} \parallel \overline {MN}[/tex] are parallel
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LMNO is a plane shape which has the properties of a parallelogram. The the explanations below, it has been proven to be a parallelogram.
A parallelogram is a quadrilateral which has some unique properties. These properties can be used to prove if a given shape is a parallelogram or not.
To prove that LMNO as given in the question is a parallelogram:
The opposite sides of a parallelogram are congruent.Thus,
/LM/ ≅ /ON/ (opposite side property)
/LO/ ≅ /MN/ (opposite side property)
The opposite sides are parallel to each other.i.e LM || ON and LO || MN
Consecutive angles are supplementary.i.e <MLO + <LMN = [tex]180^{o}[/tex]
also
<LON + <MNO = [tex]180^{o}[/tex]
The diagonals are at right angles to each other.LN ⊥ MO
Opposite angles are congruent.<LMN ≅ <LON and <MLO ≅ <MNO
Therefore the given quadrilateral LMNO has all the properties described above, then it is a parallelogram.
For more clarifications, visit: https://brainly.com/question/10988285
List pairs of congruent angles and the extended proportion that relates the corresponding sides for the similar polygons. Given ABDF ~ VXZT
** I NEED HELP I KEEP GETTING IT WRONG**
Answers
Given:
[tex]ABDF\sim VXZT[/tex]
To find:
The pairs of congruent angles and the extended proportion that relates the corresponding sides for the similar polygons.
Solution:
We have,
[tex]ABDF\sim VXZT[/tex]
The corresponding angles of similar polygons are congruent. So,
[tex]\angle A\cong \angle V[/tex]
[tex]\angle B\cong \angle X[/tex]
[tex]\angle D\cong \angle Z[/tex]
[tex]\angle F\cong \angle T[/tex]
The corresponding sides of similar polygons are proportional. So,
[tex]\dfrac{AB}{VX}=\dfrac{BD}{XZ}=\dfrac{DF}{ZT}=\dfrac{A F}{VT}[/tex]
Therefore, the required solutions are [tex]\angle A\cong \angle V,\angle B\cong \angle X,\angle D\cong \angle Z,\angle F\cong \angle T[/tex] and [tex]\dfrac{AB}{VX}=\dfrac{BD}{XZ}=\dfrac{DF}{ZT}=\dfrac{A F}{VT}[/tex].
can you help me find the slope intercept on the second one?
Answers
Answer:
y= 8x + 5
Step-by-step explanation:
y = 8x + b
5 = 8(0)+b
b = 5
Given m|n, find the value of x.
(6x-5)
(6x+5)
Answer:
Submit Answer
attempt
PLSSSS HELP
Answers
Answer:
x = 15
Step-by-step explanation:
The two angles form a straight line so they add to 180
6x-5+6x+5 = 180
Combine like terms
12x= 180
Divide by 12
12x/12 =180/12
x = 15
Translate the following into an expression 45% of a
Answers
Answer:
Step-by-step explanation:
ok so this is pretty simple,
Imagine a was the number 1
45% of 1, which would obviously be
45/100 * 1
Same thing here but for the variable a.
45/100 * a!
That would be the algebraic expression for 45% of a!
Cheers! I hope you can understand the problem better now.
What are the solutions of the following system?
Answers
Answer:
(0,-5) and (-4,3) are the points to the equations.
Step-by-step explanation:
Solution:
Step 1: Make an equation for y to substitute to the first equation.
x^2+y^2=25
y=-2x-5
Step 2: Substitute the y-value to the first equation.
x^2+(-2x-5)^2=25
x^2+4x^2+20x+25=25
Our x-values would be 0, and -4.
Step 3: Solve for the y-values by substituting 0 and -4 to the equation y=-2x-5.
y=-2(0)-5=-5 and makes the ordered pair (0,-5)
y=-2(-4)-5=3 and makes the ordered pair (-4,3)
Therefore our answers would be (0,-5) and (-4,3)
Answer:
(-4;3), (0;-5)
Step-by-step explanation:
pls pls pls pls help
Answers
Step-by-step explanation:
[tex]s = \pi \times {r}^{2} = \pi \times {6}^{2} = 36\pi[/tex]
[tex]h = 18 \times \sin(60) = 9 \sqrt{3} [/tex]
[tex]v = s \times h = 36\pi \times 9 \sqrt{3} = 324 \sqrt{3} \pi[/tex]
The slope (m) and the y-intercept (b) of the line 2x + 3y = 12 is:
Answers
Step-by-step explanation:
[tex]2x + 3y = 12 \\ 3y = - 2x + 12 \\ y = - \frac{2}{3} x + 4[/tex]
slope is -2/3
y intercept is 4
Answer:
The slope is -2/3 and the y intercept is 4
Step-by-step explanation:
2x + 3y = 12
Slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
2x + 3y = 12
Subtract 2x from each side
2x-2x+3y = -2x+12
3y = -2x+12
Divide by 3
3y/3 = -2x/3 +12/3
y = -2/3 x +4
The slope is -2/3 and the y intercept is 4
how do i solve this any one know pls help me
Answers
Answer: 5π OR 15.70796327
Step-by-step explanation:
Formula for circumference is C=2πr (radius) OR C=πd (diameter)
Our radius is 5 units, so our diameter is 10 units
C=10π
However, the question is only asking for length of semicircle
So you have to divide: 10π/2=5π
michael is making a square pyramid out of paper for a school project .he cuts a piece of paper with the dimensions shown to make the pyramid .what is the approximate surface area of the pyramid ?
Answers
Answer:
273.2
Step-by-step explanation:
Surface area of the pyramid=Area of square+4*area of triangle
Surface area of the pyramid=10^2+2*(8.66)*10
Surface area of the pyramid=100+173.2=273.2
What is the length of line segment SA
Answers
Answer:
slalalallalalalalalalalalallapapapqpqpq
The diagram above shows a plan for a park. ABCD is a rectangle.
APB and DQC are semicircles centred at X and Y.
Given AB = 7 cm and AC = 25 cm.
Calculate the perimeter of the park in cm.
Answers
Answer:
Perimeter of the park = 70 cm
Step-by-step explanation:
Perimeter of the park = perimeter of the 2 semicircles + 2(length of the rectangle)
Perimeter = 2πr + 2(BC)
✔️Perimeter of the 2 semicircles = 2πr
Where,
radius (r) = ½(AB) = ½(7)
r = 3.5 cm
Perimeter = 2*π*3.5 = 7*π
Perimeter of the two semicircles = 21.9911486 ≈ 22 cm
✔️Find BC using Pythagorean theorem:
Thus,
BC = √(AC² - AB²)
AC = 25
AB = 7
BC = √(25² - 7²) = √576
BC = 24
✔️Perimeter of the park = perimeter of the 2 semicircles + 2(length of the rectangle)
Perimeter of the park = 22 + 2(24)
= 22 + 48
= 70 cm
translate into an algebraic expression, find the number if 10% of it is m
Answers
Answer:
m/0.1
Step-by-step explanation:
--
we want to find it
-----
10%*x=m
OF means multiply
IT is any variable
IS is equal
10%*x=m
0.1*x=m
x=m/0.1 IN THE ANSWER DO NOT INCLUDE x
Martina is recording the percentages she earned on each quiz in her math class. Here are her results for the last 7 quizzes.
74, 64, 90, 74, 92, 68, 71
Find the range of the data set.
=___
Answers
Answer:
28
Step-by-step explanation:
Subtract highest number from lowest.
92-64 = 28
Identify the recursive formula for the sequence –3, 9, –27, 81, . . . .
Answers
Answer:
Hello,
Answer A
Step-by-step explanation:
[tex]a_n=(-3)*a_{n-1}\\a_1=-3\\Answer\ A[/tex]
Option A is correct -
[tex]f(n)=\left \{ {{f(1)=-3} \atop {f(n)=-3f(n-1)\;\;n > 1}} \right.[/tex]
We have a sequence : –3, 9, –27, 81, . . . .
We have to find the recursive formula for this sequence.
What is the formula to find the recursive of a Geometric sequence?The formula to find the recursive of geometric sequence is -
[tex]a_{n} =ra_{n-1} \;\;\;\;for\;n\geq 2[/tex]
We have the following sequence -
–3, 9, –27, 81, . . . .
First let's see if it is a geometric sequence or not. For a sequence to be a geometric sequence -
[tex]\frac{9}{-3} =\frac{-27}{9} =\frac{81}{-27}= -3=r[/tex]
Hence, it is a geometric sequence with r = -3.
Substituting the value of r in the formula of recursive, we get -
[tex]a_{n} = -3a_{n-1}[/tex] and [tex]a(1)=-3[/tex]
Hence, Option A is correct.
To solve more questions on finding the recursive of a sequence, visit the link below -
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Please help me fill in those couple blanks I’m really struggling
Answers
y = x^2 - 8x + 3
y - 3 = x^2 - 8x + 3 - 3
y - 3 = x^2 - 8x + ___
c = (8/2)^2 = 16
y - 3 + 16 = x^2 - 8x + 16
y + 13 = (x - 4)^2
y + 13 - 13 = (x - 4)^2 - 13
y = (x - 4)^2 - 13
Vertex: (4, -13)
Hope this helps!
9. Calculate the perimeter and the perimeter of a quadrant of a circle with radius 7 cm
correct to 3 significant figures.
Answers
Answer:
Circumference is 43.982 cm
Step-by-step explanation:
[tex]circumference = 2\pi r \\ = (2 \times 3.14 \times 7) \\ = 43.982 \: cm[/tex]
[tex]{ \underline{ \tt{ ‡†‡ \: \: trent008}}}[/tex]
HELP PLEASE BRAIN FOR CORRRECT
Answers
Answer:
1/6
Step-by-step explanation:
you divide y by x
y ÷ x
each column when you you divide y by x the answer is 1/6
(12, 9, 4) What is the area of the parallelogram shown below?
Answers
area of the parallelogram is: b x h
12 x 4 = 48 (d)
Identify the equation of the circle that has its center at (7, -24)
and passes through the origin.
Answers
Answer:
(x-7)²+(y+24)² = 625
Step-by-step explanation:
A circle with center (h, k) and radius r can be represented as
(x-h)²+(y-k)² = r²
We know the center and one point, and need to find the radius. The radius is equal to the distance from the center to any point on the circle. Therefore, we need to find the distance from the center to the point on the circle (in this case, the origin) to obtain the radius.
The distance formula for points (x₁, y₁) and (x₂, y₂) is √((x₁-x₂)²+(y₁-y₂)²). Note that x₁ and x₂ (as well as y₁ and y₂) are interchangeable but x₁ and y₁ or x₂ and y₂ are not.
Our distance between (7, -24) and the origin is
√((x₁-x₂)²+(y₁-y₂)²) = √((7-0)²+(-24-0)²)
= √625
= 25
Therefore, the radius is 25 and our equation is
(x-7)²+(y-(-24))² = (x-7)²+(y+24)² = 25² = 625
Convert
4 feet to inches
5 kilometers to meters
6 quarts to gallons, and
2,000 grams to kilograms
Answers
Answer:
1. 4ft=48inches
2. 5km=5,000m
3. 6 quarts=1,5 gallons
4. 2,000 grams=2km
Step-by-step explanation:
1. To convert feet to inches, multiply the number (4) by 12.
2. 1 Kilometer (km) is equal to 1000 meters (m). To convert kilometers to meters, multiply the kilometer value by 1000.
3. divide the volume value by 4
4. To convert grams to kilograms, you divide the number of grams you have by 1000
4 feet = 48 inches
5 kilometers = 5,000 meters
6 quarts = 1.5 US gallons
2,000 grams = 2 kilograms
find the ratio in which the point P(5,3) divides the line joining the points A(2,3) and B(7,3)
Answer should come 3:2 please help
Answers
9514 1404 393
Answer:
3 : 2
Step-by-step explanation:
We notice that P is on the horizontal line segment AB, so we can find the ratio by looking at the x-coordinates only.
AP : PB = (P -A) : (B -P)
= (5 -2) : (7 -5) = 3 : 2
In January Mr.Tan's students read 20 books. In February, they read 15 books. What is the percent increase or decrease in the number of books the read?
Answers
Answer:
there is a 25% decrease in books being read
Which linear equation fits this line?
a. O2 y - x = 2
b. O2 y = 2 + x
C. O2 y + x = 2
Answers
Answer:
c
Step-by-step explanation:
there are 32 students in a class and 20 of them own at least one pet what fraction of the class own pets
Answers
HOPE IT HELPS
PLEASE MARK BRAINLIEST
The fraction of the class that owns pets is 20/32, which can be simplified to 5/8.
To find the fraction of the class that owns pets, we divide the number of students who own pets by the total number of students in the class.
A fraction is a mathematical representation of a part-to-whole relationship. It is expressed as a numerical quantity written in the form of one number (the numerator) divided by another number (the denominator), separated by a horizontal line or slash (/).
The numerator represents the number of parts being considered or counted, while the denominator represents the total number of equal parts that make up the whole. Fractions can be used to describe a portion or share of something, as well as to compare quantities or perform mathematical operations.
Number of students who own pets: 20
Total number of students in the class: 32
Therefore, the fraction of the class that owns pets is 20/32, which can be simplified to 5/8.
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Please help!!! question b do as directed
Answers
Answer:
question b do as directed
Step-by-step explanation:
can you say again
