LL
F
C
9
5
D
2x+3
E
What is the value of x and the length of segment DE?
1 5
9
9
2x + 3
2. 10x+15=9(9)
Length of DE=
units
Answers
Answer:
[tex]x=\boxed{6.6}[/tex]
[tex]\overline{\sf DE}=\boxed{13.2}\:\:\sf units[/tex]
Step-by-step explanation:
Geometric Mean Theorem - Altitude Rule
The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of one segment to the altitude is equal to the ratio of the altitude to the other segment:
[tex]\sf \dfrac{segment\:1}{altitude}=\dfrac{altitude}{segment\:2}[/tex]
From inspection of the given diagram:
altitude = FD = 9segment 1 = CD = 5segment 2 = DE = [tex]2x+3[/tex][tex]\begin{aligned}\sf \dfrac{segment\:1}{altitude} & = \sf \dfrac{altitude}{segment\:2}\\\\\implies \dfrac{5}{9} & = \dfrac{9}{2x+3}\\\\5(2x+3) & = 81\\\\10x+15 & = 81\\\\10x & = 66\\\\ \implies x & = 6.6\end{aligned}[/tex]
Substitute the found value of x into the expression for DE:
[tex]\begin{aligned}\sf \overline{DE} & = 2x+3\\\implies \sf \overline{DE} & = 2(6.6)+3\\& = 13.2+3\\& =16.2\:\: \sf units\end{aligned}[/tex]
Related Questions
Land Area
City
Chicago
(in square miles)
227.635
468.670
Population
(in 2011)
2,707,120
Los Angeles
3,819,702
To the nearest tenth, by how many people per square mile is the population density of Chicago greater than the population density of
Los Angeles?
Answers
Population density=Total population/Total area
#Chicago
Population density
2707120/227.63511892.4#Los angeles
Population density
3819702/468.6708150.1Difference
11892.4-8150.13742.3The population density of Chicago is 3741.9 greater than Los Angele's population density.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the given information in the question,
The population density is the ratio of the total population to the total area.
Total population of Chicago = 2,707,120
The land area of Chicago = 227.635
Then, the population density of Chicago will be:
= 2,707,120/227.635
= 11892.37
Total population of Los Angeles = 3,819,702
The land area of Los Angeles = 468.670
Then, the population density of Los Angeles will be:
= 3,819,702/468.670
= 8150.08
Then, the difference between Chicago and Los Angeles will be:
= 11892.37 - 8150.08
= 3741.9
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Whatis the tigonemtric form of -3+4i
Answers
We calculate the module:
[tex]|z|\: = \: \sqrt{( - 3) ^{2} \: + \: {4}^{2} } [/tex]
[tex]|z| \: = \: \sqrt{9 \: + \: 16} [/tex]
[tex]|z| \: = \: \sqrt{25} [/tex]
[tex] \boxed{|z| \: = \: 5}[/tex]
We calculate the angle formed by "z":
[tex] \arctan( \frac{4}{ - 3} ) \: = \: \underline{0.92729521 \: \text{rad}}[/tex]
We pass it to degrees:
[tex]0.92729521 \: \times \: \frac{180}{\pi} [/tex]
[tex] \frac{166.91313924}{\pi} [/tex]
[tex] \frac{166.91313924}{3.14159265}[/tex]
[tex] \boxed{ 53.13°}[/tex]
Now we use this formula to transform it into a trigonometric form:
[tex] \boxed{z \: = \: |z| \times \: ( \cos( \alpha) \: + \: i \: \times \: \sin( \alpha))}[/tex]
We substitute the values already obtained:[tex] \boxed{ \bold{z \: = \: 5 \times \: ( \cos( 53.13°) \: + \: i \: \times \: \sin( 53.13°))}}[/tex]
Answer:[tex] \boxed{ \bold{z \: = \: 5 \times \: ( \cos( 53.13°) \: + \: i \: \times \: \sin( 53.13°))}}[/tex]
MissSpanishExpress your answer in simplest a+ bi form. (8+5i)(3+2i)-(4+i)(4-i)
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \:(8 + 5i)(3 + 2i) - (4 + i)(4 - i)[/tex]
[tex]\qquad \sf \dashrightarrow \:[( 8 \sdot3) + (8 \sdot2i) + (5i \sdot3) + (5i \sdot2i)] -[( 4 \sdot4) + (4 \sdot - i) + (i \sdot4) + (i \sdot - i)][/tex]
[tex]\qquad \sf \dashrightarrow \:[24+ 16i + 15i+ 10i {}^{2} ] -[16 - 4 i+ 4i - i {}^{2} ][/tex]
[tex]\qquad \sf \dashrightarrow \:[24+ 31i+ 10 {}{( - 1)} ] -[16 - ( - 1){}^{} ][/tex]
[tex]\qquad \sf \dashrightarrow \:[24+ 31i - 10 {}{} ] -[16 + 1{}^{} ][/tex]
[tex]\qquad \sf \dashrightarrow \:[14+ 31i {}{} ] -[17{}^{} ][/tex]
[tex]\qquad \sf \dashrightarrow \: - 3+ 31i {}{} [/tex]
I hope you understood the procedure ~
(b) A bag contains five red counters and 3 blue counters. One counter is taken at random from the bag. What is the probability of obtaining a red counter?
please can your help !!!!!
Answers
Answer:
p(obtaining a red counter) = 0.625Step-by-step explanation:
The total number of counters in the bag is 5 + 3 = 8.
and only 5 are red.
Then
the probability of obtaining a red counter is :
[tex]= \frac{5}{8} = 0.625[/tex]
Ayuda por fa es para hoy
Answers
Translation: please help it's due today
Would love to help but there is no question to answer
Question 15 of 25
What is the value of x in the diagram below?
49
LY
14
2
Answers
Is ab parallel to cd? explain.
yes, because both lines have a slope of 4/3.
yes, because both lines have a slope of 3/4
no, because the slopes of the lines are not equal.
no, because the slopes of the lines are not opposite reciprocals of each other.
don't copy answers off of sites, otherwise i'd report you
Answers
Both lines are parallel because: A. both lines have a slope of 4/3.
What is the Slope of a Line?The slope of a line = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].
The slope of parallel lines are the same, while the slope of perpendicular lines are negative reciprocals.
Slope of AB = 4 units/3 units = 4/3
Slope of CD = 4 units/3 units = 4/3
Both lines have the same slope, therefore, they are parallel to each other.
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In order to go on the field trip, you must accrue 75 positive
behavior points. you found out that you have 45% of the
points necessary to go. how many points do you have? use the
variable, p, for your equation.
what is the equation?
Answers
Answer:
Equation 75 X .45 = P
P = 33.75
Pythagorean Theorem
FIRST TO ASNWER WILL GET THANKS AND WILL BE MARKED BRAINLIEST
Answers
Answer:
b=17.75 ft
Step-by-step explanation:
We will answer this using Pythagorean Theorem.
Since the bottom of a ladder is 3 feet from the wall, and the ladder is 18 ft long, the ladder is the hypotenuse. Knowing pythagorean theorem (a^2+b^2=c^2), we can plug it in.
3^2 + b^2 = 18^2
9+b^2=324
b^2=315
b=17.75 ft
Combine like terms to create an equivalent expression.
Enter any coefficients as simplified proper or improper fractions or integers.
-\dfrac65-\dfrac23v+\dfrac{4}{15}+\dfrac13v−
5
6
−
3
2
v+
15
4
+
3
1
v
From khan academy
Answers
The equivalent expression of [tex]-\dfrac65-\dfrac23v+\dfrac{4}{15}+\dfrac13v[/tex] is [tex]-\dfrac{15}{15}-\dfrac{v}3[/tex]
How to determine the equivalent expression?The expression is given as:
[tex]-\dfrac65-\dfrac23v+\dfrac{4}{15}+\dfrac13v[/tex]
Collect like terms
[tex]-\dfrac65+\dfrac{4}{15}+\dfrac13v-\dfrac23v[/tex]
Evaluate the like terms (take LCM)
[tex]\dfrac{-6 * 3 + 4}{15}+\dfrac{v - 2v}3[/tex]
Evaluate the like expressions
[tex]-\dfrac{15}{15}-\dfrac{v}3[/tex]
Hence, the equivalent expression of [tex]-\dfrac65-\dfrac23v+\dfrac{4}{15}+\dfrac13v[/tex] is [tex]-\dfrac{15}{15}-\dfrac{v}3[/tex]
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Expand and simplify 5(3x+2)-2(4x-1)
Answers
5(3x+2)-2(4x-1)
= 15x+10-8x+2
= 7x+12
What is the area of the shaded region?
O 21 mm²
O24 mm²
O 42 mm²
48 mm²
Answers
Reasoning:
The area of the big triangle will be: (6+4+2)(5)(0.5). The answer will be equal to 30 mm^2. The area of the smaller triangle will be: (4)(3)(0.5). The answer will be 6 mm^2. Next, subtract the area of the larger triangle by the smaller triangle (30-6). The final answer will then be 24mm^2.
Sorry if this may have been confusing. I had to do this on my phone.
The sum of multiples of five from 10 to 75, inclusive.
Answers
The asked sum of multiples of five from 10 to 75, inclusive, is 595.
To find the sum of multiples of five from 10 to 75, inclusive, we can use the formula for the sum of an arithmetic series:
Sum = (n/2) * ([first term] + [last term])
Following the given case, the first term (a) is 10, the last term (l) is 75, and the common difference (d) between consecutive terms is 5 (since we are considering multiples of five).
The number of terms (n) can be calculated as:
n = (last term - first term) / common difference + 1
Let's calculate the number of terms first:
n = (75 - 10) / 5 + 1
n = 65 / 5 + 1
n = 13 + 1
n = 14
Now, we can determine the sum of the multiples of five:
Sum = (14/2) * (first term + last term)
Sum = 7 * (10 + 75)
Sum = 7 * 85
Sum = 595
Therefore, the asked sum of multiples of five from 10 to 75, inclusive, is 595.
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What is the probability that a person chosen at random from this group has brown or green eyes? startfraction 3 over 25 endfraction startfraction 7 over 25 endfraction startfraction 13 over 25 endfraction startfraction 17 over 25 endfraction
Answers
Using it's concept, it is found that the probability that a person chosen at random from this group has brown or green eyes is of [tex]\frac{13}{25}[/tex].
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Researching the problem on the internet, it is found that the group has 20 + 6 + 17 + 7 = 50 people, of which 20 + 6 = 26 have brown or green eyes, hence the probability is given by:
p = 26/50 = 13/25.
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( 12y + 2x) + 4y simplify the expression
Answers
Answer:
[tex]2x+16y[/tex]
Add [tex]12y[/tex] and [tex]4y[/tex].
[tex]2x+16y[/tex]
Answer:
2x + 16y
Step-by-step explanation:
The y terms can be added together. 12y + 4y is 16y. The 2x has to just stay the way it is because it could only be added to another x term and there aren't any. So you are left with 2x + 16y
What is the length of the diagonal from B to D of this rectangle? Round your answ
to the nearest tenth of a metre.
Answers
Answer: 19.7
Step-by-step explanation:
By the Pythagorean theorem,
[tex](BD)^{2}=8^{2}+18^{2}\\\\(BD)^{2}=388\\\\BD=\sqrt{388} \approx \boxed{19.7}[/tex]
What is the slope of the line shown below (3 9)(-4 2)
Answers
Answer:
slope = 1
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 9 ) and (x₂, y₂ ) = (- 4, 2 )
m = [tex]\frac{2-9}{-4-3}[/tex] = [tex]\frac{-7}{-7}[/tex] = 1
Which best describes a random sample?
A.) a sample in which the elements are chosen by chance
B.) a sample in which the chosen elements are predetermined
C.) a sample in which each element of the populations chose
D.) a sample in which the chosen elements are removed from the population once they are chisen
Answers
A random sample is a sample in which the chosen elements are removed from the population once they are chosen.
What is a random sample?A sample is a smaller group of the population that has the desired elements of the population. A sample is sometimes necessary because it might not be feasible or cost effective to access the whole population.
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What is the value of x in the figure below?
Answers
Answer:
The value of x in the figure is 3.5
Step-by-step explanation:
When we look at the figure, we see that AB and BC, are connected, to make a longer side of a triangle. We can also see that BC is dilated from AB. When dilating, we multiply or divide by a number, to get the extended or shortened length. (Just keep multiplication and division in mind) To get x, we can do the same that we did to get 2, from 4. From AB to BC it goes from 4 to 2.
To get 2 from 4, you must divide 4 by 2. So when we do the same thing to 7, we should get x.
7 / 2 = 3.5
The value of x in the figure is 3.5
[tex]\\ \rm\dashrightarrow \dfrac{4}{2}=\dfrac{7}{x}[/tex]
[tex]\\ \rm\dashrightarrow 2=\dfrac{7}{x}[/tex]
[tex]\\ \rm\dashrightarrow x=\dfrac{7}{2}[/tex]
[tex]\\ \rm\dashrightarrow x=3.5[/tex]
y=-8x+1 find the slope and y-intercept in this equation.
Answers
the slope is always the number in front of the x and the y intercept is always the number by itself
hope this helps!
In circle P, diameter QS measures 20 centimeters.
Circle P is shown. Line segment Q S is a diameter. Line segment R P is a radius. Angle R P S is 123 degrees.
What is the approximate length of arc QR? Round to the nearest tenth of a centimeter.
9.9 centimeters
19.9 centimeters
21.5 centimeters
43.0 centimeter
Answers
The approximate length of arc QR to nearest tenth is 9.9cm
Length of an arcThe formula for calculating the length of an arc is expressed as:
L = r theta
where
r is the radius of an arc = 20cm/2 = 10cm
theta = 180 - 123 = 57 degrees
Determine the length of an arc
L = 10(57π/180)
L = 57π/18
L = 9.94cm
Hence the approximate length of arc QR to nearest tenth is 9.9cm
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Answer:
9.9
Step-by-step explanation:
What is the greatest common factor of 12, 2, and 84?
Answers
Answer:
2
Step-by-step explanation:
2 can go into 12,2, and 84
To obtain the greatest common divisor of (g.c.d) we must do it in simultaneous decomposition.
This method consists of extracting the common and uncommon prime factors, then
[tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{12 \ \ \ 2 \ \ \ 84}\\ \ 6 \ \ \ 1 \ \ \ 42 \end{matrix}\right|\begin{matrix} 2\\ \: \end{matrix} \end{gathered}$}[/tex]
As we can see the number 2, is the only common prime number.
The greatest common factor of 12, 2, and 84 is 2.
The triangle and the trapezoid have the same area what is the base b of the triangle
Answers
Answer:
b =22
Step-by-step explanation:
The formula to calculate the area of a trapezoid:
1/2*(a+b)*h : (a: base, b: base, h: height)
The formula to calculate the area of a triangle:
1/2*a*h (a: base, h: height)
All inputs are given for trapezoid so let's first find the area of trapezoid then we can find the value of b:
1/2*(10+12)*7 = 77 cm^2 is the area of trapezoid
now for the area of triangle:
1/2*b*7 = 77 (it was given that the areas are equal)
first we multiply both sides by 2
7*b = 154 now divide both sides by 7
b = 22
solve pls brainliest
Answers
Answer:
The ans of first one is 0/8 = 0
and 6÷0 = undefined....hope this helps:)
1) 0/8 = 0
2) 6/0 = Undefined
Detailed Answer:
Zero divided by any number gives zero.
Diving any number by zero is undefined.
Question 9
Expand and simplify (2x-7)(3x-8).
Answers
Answer:
=> Expand by applying the FOIL method
[tex]2x\cdot \:3x+2x\left(-8\right)-7\cdot \:3x-7\left(-8\right)[/tex]
=> combine like terms
[tex]6x^2-37x+56[/tex]
how many solutions does 10x - 10= -10x + 10
Answers
If im wrong im so sorry!! ):
Which addition does the model below represent?
5 positive tiles and 3 negative tiles.
Answers
Any time we have a single positive tile pair up with a single negative tile, those two tiles cancel out.
Three positive tiles and three negative tiles will pair up and cancel out. We're left with two positive tiles only. This represents the number 2.
In other words, 5 + (-3) = 5 - 3 = 2
Bo is flying a kite, holding his hands a distance of 3.5 feet above the ground and
letting all the kite's string play out. He measures the angle of elevation from his hand
to the kite to be 29°. If the string from the kite to his hand is 110 feet long, how many
feet is the kite above the ground? Round your answer to the nearest tenth of a foot if
necessary.
Answers
The height of the kite will be 53.32 feet above the ground.
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
Given that:-
The boy is flying a kite, holding his hands a distance of 3.5 feet above the ground andletting all the kite's strings play out. He measures the angle of elevation from his hand to the kite to be 29°. If the string from the kite to his hand is 110 feet long, what is the total vertical height?The height of the kite above the ground will be calculated as:-
[tex]Sin\theta = \dfrac{perpendicular}{Hypotenuse}[/tex]
[tex]Sin(29)=\dfrac{H}{110}[/tex]
H = Sin(29) x 110
H = 53.32 feet
The hand of the boy is 3.5 above the ground so the total height H(t) of the kite above the ground will be:-
H(t) = 53.232 + 3.5
H(t) = 56.28 feet.
Therefore the height of the kite will be 53.32 feet above the ground.
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Answer:
Step-by-step explanation:
\text{What function uses the \color{green}{\textbf{O}PPOSITE} and the \color{#EB0000}{HYPOTENUSE}?}
What function uses the OPPOSITE and the HYPOTENUSE?
\text{\Large \underline{S}\color{green}{O}\color{#EB0000}{H}-CAH-TOA}
S
OH-CAH-TOA
\text{sin }\color{purple}{29}=\frac{\color{green}{\text{opposite}}}{\color{#EB0000}{\text{hypotenuse}}}=\frac{\color{green}{x}}{\color{#EB0000}{110}}
sin 29=
hypotenuse
opposite
=
110
x
\text{sin }29=
sin 29=
\,\,\frac{x}{110}
110
x
\frac{\text{sin }29}{1}=
1
sin 29
=
\,\,\frac{x}{110}
110
x
110\text{ sin }29=
110 sin 29=
\,\,x
x
Cross multiply.
x=53.329058...
x=53.329058...
Type into calculator.
\text{Add 3.5, the distance from the ground to his hand:}
Add 3.5, the distance from the ground to his hand:
53.329058...+3.5=
53.329058...+3.5=
\,\,56.829058...
56.829058...
\approx
≈
\,\,56.8
56.8
Round to the nearest tenth.
\text{The kite is 56.8 feet above the ground.}
The kite is 56.8 feet above the ground.
Help me I need the answer on paper help me now
Answers
Answer:
a) k = 10 b) k = 7.5
Step-by-step explanation:
a)
( 5k+ 20 ) + ( 7k + 40 ) = 180
12k + 60 = 180
12k = 120
k = 10
b)40 + ( 12k + 10) + 180 - ( 8k + 80 ) = 180
50 + 12k + 180 - 8k - 80 = 180
50 + 12k -8k - 80 = 0
50 + 4k - 80 = 0
30 = 4k
k = 7.5
hich represents the inverse of the function f(x) = 4x?
Oh(x)=x+4
Oh(x)=x-4
h(x) = ²x
h(x) = x
Answers
Answer:
[tex]h(x) = \frac{1}{4} x[/tex]
Step-by-step explanation:
To find the inverse of a function, the steps are:
Let y= f(x)Make x the subject of formulaReplace x with f⁻¹(x) and y with xIn this case, since h(x) is the inverse function of f(x), we can replace x with h(x) in step 3.
_____
f(x)= 4x
Let y= f(x) [tex]\textcolor{steelblue}{\text{ - step 1}}[/tex]
y= 4x
Divide both sides by 4:
[tex] \frac{1}{4} y = x[/tex]
[tex]x = \frac{1}{4} y \: \: \: \textcolor{steelblue}{\: \text{ - step 2}}[/tex]
Replace x with h(x) and y with x:
[tex]\bf{h(x) = \frac{1}{4} x} \: \: \: \textcolor{steelblue}{\: \text{ - step 3}}[/tex]
Additional:
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