In the figure below, there are three right trangles. Complete the following.
A
C
D
B
(a) Write a similiarity statement relating the three right triangles.
ACDA~A~A
(b) Complete each proportion.
BD
BC
BC
DA
DC
=
0
BD
X
5
Answers
Part (a)
Let one of the angles be [tex]\theta[/tex]. After solving for all of the other angles using the triangle sum theorem, we see that [tex]\triangle CDA \sim \triangle BDC \sim \triangle BCA[/tex].
Part (b)
[tex]\frac{BD}{BC}=\frac{BC}{CA}, \frac{DA}{DC}=\frac{DC}{DB}[/tex]
Related Questions
Luciana is adding water to a pool at a constant rate. Before she added any water the pool had 12. 000 gallons of water Luciana is adding 9 gallons of water each minuto Which equation roprosents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes? A m = Dw+ 12,000 B W = m + 12. 000 С W = 12,000m + 9 D W = 12. 000 - 9m
Answers
The equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.
What is a linear equation?
A linear equation is an equation that can be written in the form of
y = mx + b
Where x and y are variables and m and b are constants. This is also known as the slope-intercept form of a linear equation. The slope of the line (m) represents the steepness of the line and the y-intercept (b) represents the point where the line crosses the y-axis.
Luciana is adding water to the pool at a constant rate of 9 gallons per minute. So, for every minute that passes, the number of gallons in the pool increases by 9. This relationship can be represented by the equation W = 12,000 + 9m, where W is the total number of gallons in the pool and m is the number of minutes that have passed.
Hence, the equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.
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The equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.
Option (D) is correct.
What is a linear equation?
A linear equation is an equation that can be written in the form of
y = mx + b
Where x and y are variables and m and b are constants. This is also known as the slope-intercept form of a linear equation. The slope of the line (m) represents the steepness of the line and the y-intercept (b) represents the point where the line crosses the y-axis.
Luciana is adding water to the pool at a constant rate of 9 gallons per minute. So, for every minute that passes, the number of gallons in the pool increases by 9. This relationship can be represented by the equation W = 12,000 + 9m, where W is the total number of gallons in the pool and m is the number of minutes that have passed.
Hence, the equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.
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A researcher is following the growth of a particular type of flower. She writes the given equation to show the height of the flower g(n), in inches, after n days. When the researcher finished his study, the height of the flower was about 11.04 inches. What is a reasonable domain to plot the growth function
Answers
After solving, the possible domain in interval notation is (0, 7).
In the given question, a researcher is following the growth of a particular type of flower.
The equation to show the height of the plant f(n), in cm, after days (n) = 8(1.05)^n
According to the given information,
The height of the plant is modeled by the function= f(n)
The height of the plant is approximately 11.04cm when the number of days = 7
The days are started from n > 0 and n<=7
Hence the possible domain in interval notation = (0, 7)
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The complete question is:
A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after days (n) = 8(1.05)^n
Part A: When the scientist concluded his study, the height of the plant was approximately 11.26 cm What is a reasonable domain toplot the growth function?
Part B: What does the y-intercept of the graph of the function () represent?
Part C: What is the average rate of change of the function f(n) from n = 2 ton, and what does it represent?
PLEASE HELP I’LL GIVE BRAINLIST!!!!!!!!
An object in free fall is dropping using only the force of gravity. Let's assume that is the case with the Drop of Doom for a moment just for the sake of our calculations.
When using feet to measure the distance traveled over time, we can approximate the force of gravity as -16ft/sec^2. That means every second, the speed of the ride is increasing at a rate of 16 ft/sec down towards the ground (hence the negative sign).
Zumanjaro is said to be a 415-foot drop. We can represent this fall using the function: h(t)= -16t^2+415, where h is the height above the ground (or in this case the height above the stopping point of the ride) in feet and t is the time in seconds.
Using this function, how long does the ride take to complete its 415 drop?
Answers
A wood has pine, oak and ash trees.
The numbers of pine trees and oak trees are in the ratio 5:8.
The numbers of oak trees and ash trees are in the ratio 2:3
The total number of trees in the wood is 300. Find the number of ash trees.
Answers
The graph shows Miguel's savings over time. What is the slope of the line?
Answers
Answer:
3/4 x
Step-by-step explanation:
The rise is 3 and the run is 4, making the slope 3/4 x
The trait for a dimples (D) is dominant over the trait for no dimples (d). Two people with dimples (Dd x Dd)
got married. Complete the diagram below to show the genes of their children. What percentage of the
offspring will most likely have no dimples?
0%
25%
50%
75%
Answers
Answer:
25%
Step-by-step explanation:
Here is my punnett square:
D d <---parent 1
D DD Dd
d Dd dd
^
|
| parent 2
The results: DD, Dd, Dd, dd
DD, Dd: will have dimples because they have a dominant allele in their genotype. So in their phenotype, they will have dimples.
dd: will not have dimples because they do not have the dominant allele for dimples in their genotype. So in their phenotype, they will NOT have dimples.
3 cases (25% chance for DD, 50% chance for Dd, 25% chance for dd)
1/4 is DD is 25%
2/4 is Dd is 50%
and 1/4 is dd is 25%
answer: 25%
Have a nice day!
solve the system:
2x+5y=24.
x=y+5
(i need the answer completely with the problem, and without a link)
Answers
Substitute the given x equation into the first equation
2(y+5)+5y=24
Distribute
2y+10+5y=24
Combine like terms
7y+10=24
Subtract
7y=14
Divide by 7
Y=2
Substitute into the second equation
X=2+5
X=7
(7,2)
What are the x-intercept and the y intercept of the graph of 6x - 3y = 36?
Answers
The x-intercept and the y intercept of the graph of 6x - 3y = 36 are x = 6 and y = -12
How to determine the x-intercept and the y intercept of the graph?
From the question, we have the following parameters that can be used in our computation:
6x - 3y = 36
Set y to 0 to determine the x-intercept
So, we have the following representation
6x = 36
Divide by 6
x = 6
Set x to 0 to determine the y-intercept
-3y = 36
Divide by -3
y = -12
hence, the intercepts are x = 6 and y = -12
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Anthony throws a ball from a point of 40m above the ground. The height of the ball h, in meters, after t seconds is represented by the function h(t) = -5t2 + 40t.
What was the maximum height
of the football?
How many seconds did it take
for the football to hit the ground?
Answers
Answer:
maximum height is 80 feet
8 seconds until it hits ground
Step-by-step explanation:
-5t(t - 8) = 0
-5t= 0; t = 0 (this represents the beginning of the throw)
t-8=0; t = 8 (this represents the end of the throw)
To find maximum height, find the vertex of the graph,
you can use -b/2a to find 't' and then substitute that value back into the function to find h(t)
x = -40÷2(-5)
x = -40/-10
x = 4
h(4) = -5(4²)+40(4)
h(4) = -5(16) + 160 which is 160 - 80 = 80
A school has 2000 students a survey finds that 36 students out of a random sample of 80 student's are bilingual the margin of error for the survey is +4% find the interval in which the total number of bih Guam students is most likely to lie
Answers
Answer:
(820 ; 980)
Step-by-step explanation:
Given :
Sample size, n = 80
Number of bilingual from sample = 36
Sample proportion, phat = x / n = 36 / 80 = 0.45
Margin of Error = 4% = 0.04
Interval = sample proportion ± margin of error
0.45 ± 0.04
(0.41 ; 0.49)
(0.41 * 2000 ; 0.49 * 2000)
(820 ; 980)
can someone help me pls
Answers
Hope that helped my friend!! :D
Y=-1/2X+6 in standard form
Answers
The standard form of linear function y = - (1 / 2) · x + 6 is (1 / 12) · x + (1 / 6) · y = 1.
How to find the definition of a linear function in standard form
In this question we find a linear function in slope-intercept form:
y = m · x + b
Where:
m - Slopeb - InterceptFrom which we must obtain the linear function in standard form:
a · x + b · y = c
Where:
a, b - Depedent coefficients.c - Independent coefficient.We can derive the standard form of the linear equation by algebra properties:
y = m · x + b
(1 / b) · y = (m / b) · x + 1
- (m / b) · x + (1 / b) · y = 1
If we know that m = - 1 / 2 and b = 6, then the equation of the line in standard form is:
- [(- 1 / 2) / 6] · x + (1 / 6) · y = 1
(1 / 12) · x + (1 / 6) · y = 1
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Factor Completely
-3p^7+3p^3
Answers
Answer:
3p^3 (-p^4 + 1)
Step-by-step explanation:
The common factor of both -3p^7 and 3p^3 is 3p^3
Divide -3p^7 by 3p^3 and get -p^4
Divide 3p^3 by 3p^3 and get 1
So the factorisation is 3p^3 (-p^4 + 1)
(Please help)
I don't know what to do!
Answers
Kindly answer this one. Thank you.
Answers
Answer:
See below.
Step-by-step explanation:
I'm assuming these questions are about the Midline Theorem (segment AL joins the midpoints of the non-parallel sides.
♦ The midline's length is the average of the lengths of the top and bottom parallel sides.
[tex]AL=\frac{OR+CE}{2}[/tex]
Use this equation and substitute values given in each problem, then solve for the missing information.
1. AL = x, CE = 9, OR = 5
[tex]x=\frac{9+5}{2}=7[/tex]
2. AL = m - 4, CE = 15, OR = 17
[tex]m-4=\frac{15+17}{2}=16\\\\m-4=16\\\\\\m=20\\\\AL=20-4=16[/tex]
3. OR = y + 5, AL = 15, CE = 18
[tex]15=\frac{(y+5)+18}{2}\\\\15=\frac{y+23}{2}\\\\30=y+23\\\\7=y\\\\OR = 7+5=12[/tex]
Question 18 of 40
5
Simplify (4-2)5
Answers
Jina is running. The number of minutes she has run varies directly with the number of calories she has burned. See the graph below.
How many calories is Jina burning per minute ?
What is the slope of the graph ?
Answers
The number of calories Jina is burning per minute is 0.1 and the slope is 0.1
How many calories is Jina burning per minute?From the question, we have the following parameters that can be used in our computation:
Points, (x, y) = (0, 0) and (150, 15)
The burning rate per minute can then be calculated as
Burning rate per minute = (y₂ - y₁)/(x₂ - x₁)
Substitute the known values in the above equation, so, we have the following representation
Burning rate per minute = (15 - 0)/(150 - 0)
Evaluate the quotient
Burning rate per minute = 0.1
What is the slope of the graph?In (a), we have
Burning rate per minute = 0.1
This rate is the same as the slope
Hence, the slope is 0.1
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How do you write log2 in exponential form?
Answers
To change logarithmic form to exponential form, spot the logarithmic equation's base and move the base to another side to the equal sign. Moving the base will make the current number or variable into the exponent.
Do not move something but the base: the other numbers or value will not change sides, and the word "log" will be release.
Log Rules:
1. the first rule is logb(mn) = logb(m) + logb(n)
2. the second rule is logb(m/n) = logb(m) – logb(n)
3. the third rule is: log b (mn) = n · logb(m)
1. Multiplication can be turned outside the log into addition and vice versa can be turned.
2. Division can be spin outside the log into a subtraction, and vice versa.
3. An exponent can be proceeded as a multiplier outward on all within a log, and vice versa.
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What are the 3 types of translation?
Answers
When the state of an object is changed from one to another it is known as translation in mathematics and they are of three types.
The three types of translation in math are
horizontal translationvertical translationcompression translationWhen the object moves either from left to right or from right to left it is known as vertical translation.
The movement in up or downward direction of the graph is known as horizontal translation.
The domain of the function remains same in both the cases.
A translation in which the size of the object decreases or is compressed is known as the compression translation.
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Compare the ratios 9 to 12 and 4 to 6. One model has 12 sections. The second model has 6 sections. Which statement correctly compares the ratios? The ratio 9 to 12 is greater than 4 to 6. The ratio 9 to 12 is less than 4 to 6. The ratio 9 to 12 is equal to 4 to 6. The ratios cannot be compared.
Answers
Answer:
The ratio 9 to 12 is greater than 4 to 6.
9/12 = 3/4.
4/6 = 2/3.
3/4 is more.
Amy, Bodie, Claire, and Dejan are in the same math class. The locations of their desks in relation to each other are graphed on the coordinate plane below.
If the length of each square represents one foot, how far is it from Claire's desk to Dejan's desk?
A.
9 feet
B.
8 feet
C.
7 feet
D.
10 feet ?
Answers
Answer:10 ft
Step-by-step explanation:
How many blocks with dimensions of One-third times 1 times 1 can fit in a unit cube?
A block has a length of one-third, height of 1, and width of 1.
2
3
6
9
Answers
Given:
Dimensions of a block are [tex]\dfrac{1}{3}\times 1\times 1[/tex].
To find:
The number of block that can be fit in a unit cube.
Solution:
Volume of a cuboid is:
[tex]V=l\times b\times h[/tex]
Where, l is length, b is breadth or width and h is the height of the cuboid.
So, the volume of the given block is:
[tex]V_1=\dfrac{1}{3}\times 1\times 1[/tex]
[tex]V_1=\dfrac{1}{3}[/tex]
Dimensions of a unit cube are [tex]1\times 1\times 1[/tex]. So, the volume of the unit cube is:
[tex]V_2=1\times 1\times 1[/tex]
[tex]V_2=1[/tex]
We need to divide the volume of unit cube by the volume of a block to find the number of block that can be fit in a unit cube.
So, the number of blocks that fit in a unit cube is:
[tex]n=\dfrac{V_2}{V_1}[/tex]
[tex]n=\dfrac{1}{\dfrac{1}{3}}[/tex]
[tex]n=3[/tex]
Therefore, the correct option is B.
Answer:
the answer would be "b" 3 because its in 1/3 and the block is 1/3
What can you multiply to the first equation to eliminate the y's?
4x + y = 12
- 2x + 3y = 10
Answers
Answer:
I think this is how....
Step-by-step explanation:
4x + y = 12
4x + y -y = 12 - y
4x = 12
*divide by 4 on each side*
x = 3
What is the slope of a line that is parallel to the line with the following equation?
y=-2/3x+2
2/3
-4/3
4/3
-2/3
Answers
Answer:
D)
Step-by-step explanation:
we know that,
Parallel lines have the same slope
given equation is in the form given by
[tex] \displaystyle y = mx + b[/tex]
where m is know
as [tex]m_{parallel}=m[/tex], the answer is -⅔
Fill in the blank so that products unloaded and time are in a proportional relationship.
A conveyer belt unloads 48 products in 6 minutes. The same conveyor belt unloads
⬜ products in 1 minute.
Answers
Answer: 8 products in 1 minute
Step-by-step explanation:
6 min=48 products
48/6=8
1 min= 8 products
A teacher performing a demonstration finds that a piece of cork displaces 23.5 mL of water. The
piece of cork has a mass of 5.7 g. What is the density of the cork?
Answers
Answer:
0.243 g/mL
Step-by-step explanation:
Density is grams divided by mL. All you need to do for this is take your values and use them for the equation. Divide 5.7 grams by 23.5 mL
Irrelevant answers will be reported. DUE TODAY!!!
Answers
Answer:
C. Ferris wheel
Step-by-step explanation:
Circumference = pi x diameter
Take each of the entries from the diameter column and multiply by 3.14. They are all correct except for the Ferris wheel.
70.5 x 3.14 = 221.37
Help! How do I do this??
Answers
b=cos(48)x13=9
Answer:
a = 14.9; b = 11.1
Step-by-step explanation:
SOHCAHTOA:
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
[tex]cos48[/tex]° : adjacent is 10, and hypotenuse is a
[tex]cos48=10/a; a*cos48=10;a=10/cos48[/tex]
type 10/cos48 into calculator to get a = 14.9
[tex]sin48[/tex]° : opposite is b, and hypotenuse is a
[tex]sin48=b/a; sin48=b/14.9; b=14.9*sin48[/tex]
type 14.9*sin48 into calculator to get b = 11.1
What value of n makes the equation true? Show your work.
Answers
Answer:
5n
Step-by-step explanation:
(7^5 * 7^n) ^ 4 = (7^11/7^n)^3
7^(20 + 4n) = 4.7^15 / n^3
= 20/4 = 5n and 15/3 = 5n
Answer 5n
what is x and the measure of angle EHF
Answers
Answer:
x = 10, ∠ EHF = 110°
Step-by-step explanation:
7x and 11x are adjacent angles and sum to 180° , then
7x + 11x = 180
18x = 180 ( divide both sides by 18 )
x = 10
∠ EHF = 11x = 11(10) = 110°
Answer:
EHF = 110 deg
Step-by-step explanation:
From what it looks like 7x and 11x are being used as units of measurment. I can asssume a full circle adds up to 36x because 180deg adds up to 18deg.
If there were a number that was supposed to fill in for x it could be 0 because if the angles in this problem were 110 deg and 70 deg they would make 180 deg which is the straight line that the problem has.