Determine the length of CD.
Question 13 options:
A)
10.77 units
B)
3.74 units
C)
6.32 units
D)
9.17 units
Answers
Answer:
The answer is 6.32
Step-by-step explanation:
According to the Altitude Geometric Mean Theorem, the length of the altitude of a triangle is the geometric mean of the lengths of the 2 segments is divides the hypotenuse into.
CD= Altitude
CD^2= 4 times 10
or
CD= The square root of 4 times 10
Square root of 4 times 10 is 6.3245553203
Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. The length of CD is 6.32 units. The correct option is C.
What are Similar figures?Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".
In ΔBDC and ΔABC, the two angles are given,
∠D = ∠C = 90°
∠B = ∠B {Common}
Therefore, the two triangles are similar triangles, thus, the ratio of the sides can be written as,
CB / AB = CD / AC = DB / CB
Now, the ratio can be solved as,
CB / AB = DB / CB
CB / 14 = 10 / CB
CB² = 14 × 10
CB = √140
Further, in triangle ABC using the Pythagorean theorem, we can write,
AB² = CB² + AC²
14² = (√140)² + AC²
196 - 140 = AC²
AC = √56
Again, using the ratio of the similar triangle, we can write,
CD / AC = DB / CB
CD / √56 = 10 / √140
CD = (√56 × 10)/√140
CD = 6.32 units
Hence, the length of CD is 6.32 units.
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Related Questions
A teacher asks her students to write down the number of hours studied, rounded to the nearest half hour. She compiles the results and develops the probability distribution below for a randomly selected student. What is the mean of the probability distribution?
Probability Distribution
Hours Studied: X
Probability: P(X)
0.5
0.07
1
0.2
1.5
0.46
2
0.2
2.5
0.07
Answers
Answer:1.50
Step-by-step explanation:None
Answer: the answer is d
Step-by-step explanation:
Find the sum of the first four terms of the geometric series 100 + 50 + 25 + ...
Answers
Answer:
Decimal:
100 + 50 + 25 + 12.5 + 6.25 + 3.125 + 1.5625
Fraction:
[tex]100 +50+25 + 12\frac{1}{2}+6\frac{1}{4}+3\frac{1}{8}+1\frac{9}{16}[/tex]
Can someone help me please
Answers
A triangle has side lengths of
[tex] \sqrt{125} [/tex]
[tex] \sqrt{5} [/tex]
[tex] \sqrt{20} [/tex]
What is the perimeter of the triangle?
[tex]4 \sqrt{5} [/tex]
[tex]6 \sqrt{5} [/tex]
[tex]8 \sqrt{5} [/tex]
none of the answers are correct
Answers
Answer:
3 is the right one
Step-by-step explanation:
Simple math you know
10
Select the correct answer from the drop-down menu.
The solution set for 6a2 - a -5 = 0 is
Reset
Next
Answers
Answer:
a = {-5/6 , 1}
Step-by-step explanation:
6a² - a -5 = 0
Factor
(6a + 5)(a - 1) = 0
Root 1
6a + 5 = 0
6a = -5
a = -5/6
Root 2
a - 1 = 0
a = 1
Solution set
a = {-5/6 , 1)
Wat is the Ans?
Got the question
Answers
Answer:
C
Step-by-step explanation:
C= 2* pi*r = 2* pi* 5 ≈ 31.4 cm
A car rental company charges $11 a day and 18 cents per mile to rent their cars. If the total charge for a 2-day rental was $61.60, how many miles were driven? Write and solve and equation.
Answers
Answer:
220 miles
Step-by-step explanation:
.18m + 11d = 61.60
d = 2
.18m + 22 = 61.60
Subtract 22 from both sides
.18m = 39.60
Divide both sides by .18
m = 220
Help me please i need to hand this in
Answers
Hope this helps
A small radio transmitter broadcasts in a 31 mile radius. If you drive along a straight line from a city 38 miles north of the transmitter to a second city 36 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter? Hint: assume that the transmitter is at the origin. Write the equations of the line and circle.
Answers
9514 1404 393
Answer:
63.7% or 33.35 miles
Step-by-step explanation:
The hint suggests that we find the points where the drive begins and ends picking up the transmitter. We suspect both of those points will have irrational coordinates, so finding the distance between them will involve dealing with squares and roots of irrational numbers. We want to see if there's an easier way.
The distance from the transmitter to the path being driven can be found using the "distance to a line" formula. First, we need the equation of the line in general form. In intercept form, it is ...
y/38 +x/36 = 1
19x +18y -684 = 0 . . . . . . multiply by LCM(36, 38) and subtract that amount
Then the distance from the origin to the line is ...
d = |19·0 +18·0 -684|/√(19² +18²) = 685/√685 ≈ 26.1243
The distance (x) along the line from the point where the transmitter is first picked up until the point of closest approach can be found from the Pythagorean theorem:
x² + (26.1243)² = 31²
x² = 31² -(684/√685)² = 190429/685
x ≈ 16.6733
The driving distance for which the transmitter is picked up is twice this, so is ...
2x = 2(16.6733) ≈ 33.3466 . . . miles
The total drive length is also given by the Pythagorean theorem:
drive length = √(36² +38²) = √2740 ≈ 52.3450 . . . miles
Then the fraction of the drive during which the signal is picked up is ...
fraction = (33.3466 mi)/(52.3450 mi) ≈ 0.6371 ≈ 63.7%
__
The signal is picked up for 33.35 miles, about 63.7% of the drive.
______
The intercept-form equation for a line is ...
x/(x-intercept) +y/(y-intercept) = 1
The distance from (x, y) to line ax+by+c=0 is given by ...
d = |ax+by+c|/√(a²+b²)
The Pythagorean theorem relates legs a, b and hypotenuse c of a right triangle this way:
c² = a² +b²
Oscar is buying soil for his plants. He needs to fill one pot with 8 cups of soil and another pot with 3 gallons of soil. If
the price of soil is $2.50 per quart, how much, in dollars, will he pay in all? You may use the conversions to help you
answer the question
1 cup = 8 fluid Ounces
1 pint = 2 cups
1 quart = 2 pints
1 gallon = 4 quarts
1 gallon = 3.875 liters
Enter your answer in the space provided
Answers
Answer:
$35
Step-by-step explanation:
8 cups /2 = 4 pints
4/2 = 2 quarts = 5 dollars for first pot
3*4 = 12 quarts, = 30 dollars for second pot
is 0.45 greater than 0.5
Answers
Answer:
0.5
hope this helps
have a good day :)
Step-by-step explanation:
The sum of 4 and x
4 + x
4 - x
4x
Answers
Answer:
16
Step-by-step explanation:
ezz
Seeking help to solve the problem shown in the image.
Answers
9514 1404 393
Answer:
1340
Step-by-step explanation:
The perimeter of a rectangle of length L and width W is ...
P = 2(L+W)
The perimeter of the rectangle outline of the figure is ...
P = 2(315 +300) = 2·615 = 1230
That outline is the sum of all of the line segments making up the figure except for two lengths of 55 units each. Adding those, we find the perimeter of the figure to be ...
P = 1230 +2(55) = 1230 +110 = 1340 . . . units
_____
Additional comment
It can be convenient to consider the total of horizontal segments and the total of vertical segments. We have shown in the attachment that, except for the 55-unit "indent", the horizontal and vertical lengths are equivalent to those of an ordinary rectangle. Thinking about the problem in this way makes it unnecessary to do the tedious arithmetic necessary to find each segment length. (Here, there is not enough information to do that anyway.)
Find the number if 1/3 of it is 12?
Answers
Answer:
36
Step-by-step explanation:
If 1/3 of x is 12, we can make an equation.
x/3=12
So now we isolate x.
x=36
Answer:
36
Step-by-step explanation:
of means multiply and is means equals
1/3 * n = 12
Multiply each side by 3
3 * 1/3 n = 12 *3
n = 36
A = 7x2 - 3x + 10
B = -4x2 + 6x - 4
A - B =
Your answer should be a polynomial in standard form.
Answers
Answer:
A - B = 11x² -9x + 14
A - B = 11x² -9x + 14
given the following trigonometric ratio, enumerate the meaning ratio
Answers
Answer:
The trigonometric ratios are presented below:
[tex]\sin \theta = \frac{AC}{\sqrt{AC^{2} + BC^{2}}}[/tex]
[tex]\cos \theta = \frac{BC}{\sqrt{AC^{2} + BC^{2}}}[/tex]
[tex]\cot \theta = \frac{BC}{AC}[/tex]
[tex]\sec \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{BC}[/tex]
[tex]\csc \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{AC}[/tex]
Step-by-step explanation:
From Trigonometry we know the following definitions for each trigonometric ratio:
Sine
[tex]\sin \theta = \frac{y}{h}[/tex] (1)
Cosine
[tex]\cos \theta = \frac{x}{h}[/tex] (2)
Tangent
[tex]\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{y}{x}[/tex] (3)
Cotangent
[tex]\cot \theta = \frac{\cos \theta}{\sin \theta} = \frac{x}{y}[/tex] (4)
Secant
[tex]\sec \theta = \frac{1}{\cos \theta} = \frac{h}{x}[/tex] (5)
Cosecant
[tex]\csc \theta = \frac{1}{\sin \theta} = \frac{h}{y}[/tex] (6)
Where:
[tex]x[/tex] - Adjacent leg.
[tex]y[/tex] - Opposite leg.
[tex]h[/tex] - Hypotenuse.
The length of the hypotenuse is determined by the Pythagorean Theorem:
[tex]h = \sqrt{x^{2}+y^{2}}[/tex]
If [tex]y = AC[/tex] and [tex]x = BC[/tex], then the trigonometric ratios are presented below:
[tex]\sin \theta = \frac{AC}{\sqrt{AC^{2} + BC^{2}}}[/tex]
[tex]\cos \theta = \frac{BC}{\sqrt{AC^{2} + BC^{2}}}[/tex]
[tex]\cot \theta = \frac{BC}{AC}[/tex]
[tex]\sec \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{BC}[/tex]
[tex]\csc \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{AC}[/tex]
The following diagram shows part of the graph off with x-intercept (5,0) and y-intercept (0,8).
Find the y-intercept of the graph of f(x) + 3.
Answers
Step-by-step explanation:
By question , it's given that the X intercept is (5,0) and the y intercept is (0,8) . And we need to find the y-intercept of the graph of f(x) + 3 . For that , firstly let's find out the equation of the line.
We can use here two point form of the line .So that , the equation would be ,[tex]\sf\implies y- y_1 = \bigg(\dfrac{y_2-y_1}{x_2-x_1}\bigg) ( x - x_1) \\\\\sf\implies y - 0 = \bigg(\dfrac{0-8}{5-0}\bigg)( x - 5 ) \\\\\sf\implies y = \dfrac{-8}{5}( x - 5 ) \\\\\sf\implies 5y = -8x +40 \\\\\sf\implies 8x + 5y - 40 = 0 [/tex]
Let us say that this is f(x) :-
[tex]\\\\\sf\implies f(x) = 8x + 5y - 40 \\\\\sf\implies \boxed{\sf\red{ f(x)+3 = 8x +5y -37 }}[/tex]
Plot its graph :-
We can either convert it into intercept form but plotting a graph can also be done to find y intercept .
[tex]\implies \boxed{\pink{\sf y - intercept = 7.4}}[/tex]
Refer to attachment for graph .
Hence the y Intercept is 7.4 .
An archeologist is digging at a former lake and finds items at the following elevations.
Place the items in order from highest elevation to lowest
________________________________________________
Write the elevation where each item was found as a positive or negative integer:
Arrowhead = _______ feet
Fishbone = ______ feet
Fish Hook = _______ feet
Fossil = _______ feet
Pottery = _______ feet
Shell = ________ feet
Answers
Answer:
Fossil > Arrow Head > Pottery > Shell > Fishbone > Fish Hook
Step-by-step explanation:
Arrowhead = ___20___ feet
Fishbone = __-10___ feet
Fish Hook = ___-40__ feet
Fossil = __30___ feet
Pottery = ___10___ feet
Shell = ____0___ feet
If something is above sea level, it would have a positive elevation, and if below sea level, a negative elevation. And at sea level, you have 0 elevation.
After this, just put them in order of decreasing elevation. So, the highest elevation is 30ft with the fossil, then 20 with the arrow head, pottery at 10, shell at 0, fishbone at -10, fish hook at -40.
Find the circumference of a circle with a radius of 6 cm.
Hi besties i need. help ASAP please and. ty
Answers
Answer:
37.7
Step-by-step explanation:
Circumference = [tex]2\pi r[/tex]
Circumference = [tex](2)(\pi )(6)[/tex]
Circumference = 37.69911184 / 37.7
Therefore, circumference of the circle with the radius 6 cm is 37.7.
Answer:
37.7
Step-by-step explanation:
formula for circumference of a circle=2πr
2×π×6=37.7cm
Verify the identity:
sin(AB)
sin(A B
tan(A) | tan(B)
tan(A) =tan(B)
Answers
Answer:
Step-by-step explanation:
Right side =
sin A / cos A + sinB/ cosB (sinAcosB + sinB cos A ) * cosA cosB
------------------------------------- = cosA cosB (sinAcosB - snBcosA ) sinA/cosA - sinB/cos B
= Left side.
The trigonometry identity [tex]\frac{sin(A+B)}{sin(A-B)}[/tex] is equals to [tex]\frac{tan(A)+tan(B)}{tan(A)-tan(B)}[/tex].
What is trigonometric identity?Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.
According to the given question.
We have a trigonometric identity.
[tex]\frac{sin(A+B)}{sin(A-B)} =\frac{tan(A)+tan(B)}{tan(A)-tan(B)}[/tex]
To prove the above trigonometric identity we will show L.H.S = R.H.S
[tex]L.H.S=\frac{sin(A+B)}{sin(A-B)}[/tex]
⇒ [tex]L.H.S = \frac{cosBsinA-sinBcosA}{sinAcosB-cosAsinB}[/tex]
⇒ [tex]L.H.S = \frac{\frac{sinAcosB}{cosAcosB} + \frac{sinBsinA}{cosBcosA} }{\frac{sinAcosB}{cosAcosB}-\frac{cosAsinB}{cosAcosB} }[/tex] (dividing the numerator and denominator by [tex]cosAcosB[/tex] )
⇒ [tex]L.H.S = \frac{\frac{sinA}{cosA} +\frac{sinB}{cosB} }{\frac{sinA}{cosA}-\frac{sinB}{cosB} }[/tex]
⇒ [tex]L.H.S = \frac{tanA+tanB}{tanA- tanB}= R.H.S[/tex]
Hence, L.H.S = R.H.S
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The graph shows a linear function.
아이가
10!
8
6
4
2
-10-8-6-4
-3
24
10
-6
-104
Which table of values has a smaller rate of change than the function in the graph?
y
-6
X
-6
-7
y
3
4
5
6
OA.
Ос.
0
1
5
1
2
16
0
3
9
х
B.
E-6 -8
-4
03-5
2-4
81
- 2
0 2
3114
418
Answers
9514 1404 393
Answer:
table C
Step-by-step explanation:
The rates of change can be computed using the slope formula.
m = (y2 -y1)/(x2 -x1)
The points used and the resulting "rate of change" are shown in the attachment.
Table C shows a rate of change (1/3) that is less than that of the graph (1/2).
_____
I like to use a spreadsheet for repetitive calculations, especially ones involving negative numbers. This helps prevent errors (and tedium). The formula is entered only once.
The table of values which has a smaller rate of change than the function in the graph is C.
What is Slope?This is defined as the ratio of the vertical change to the horizontal change between any two distinct points on a line.
Slope formula.
m = (y2 -y1)/(x2 -x1)
For table C = 4 -3 / -3 - (-6)
= 1/3
Table C shows a rate of change of 1/3 which is less than that of the graph at 1/2 .
Read more about Slope here https://brainly.com/question/25722412
You have at most 8 hours to spend at a concert and at park. You want to spend at least 3 hours at the concert and more than 4 hours at the park.
Answers
Jill bought 3 boxes of ice pops. Each box contains 4 orange ice pops and some cherry ice pops. The number of cherry ice pops in each box was the same. Jill bought 36 ice pops in all. What are the 2 steps of this equation and how many cherry ice pops are in each box?
Answers
Answer: 9 cherry ice pops
Step-by-step explanation:
if you bought 3 boxes and there is four orange one in each pack the that is
12 and 36 divided by 4 is 9 so there is 9 cherry ice pops
Hi plz help, if you can ill mark you 5 starz! :)
Answers
Answer:
b and 288
Step-by-step explanation:
ywwwwwwwwwwww
Find the volume of this rectangular prism. 3 in 3 in 8 in
Answers
Answer: 72
Step-by-step explanation: LxWXH
3x3x8=72
find the surface area of the shape.
Answers
Answer:
268 m²
Step-by-step explanation:
8x26=208
3x10x2=60
208+60=268
In a class of 6 there are 4 students who are secretly robots
Answers
Answer:
then 2 are human
Step-by-step explanation:
because 4 are robots
Answer:
The rest are normal students.
6-4= 2 so that's how many normal students there are.
Please add a little bit more detail to the question please :)
a farmer estimates that 6% of his plants will be eaten by rabbits. if he has 550 plants, how many will be eaten by rabbits?
Answers
Answer:
33 plants
Step-by-step explanation:
6 x 550 = 3300
3300/100 = 33
Convert the following repeating decimal into a fraction in the simplest format .61
Answers
Answer: 61/100 would be the answer
Calculate the scale factor of ABC to DEF. Enter answer as a whole number or as a fraction in lowest terms, using the slash mark ( / ) for the fraction bar.
Answers
Answer:
3
Step-by-step explanation:
because 3x3= 9 and 4x3=12 and 5x3=15