Consider the diagram and the proof below.
Given: In △ABC, AD ⊥ BC
Prove: StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction
Triangle A B C is shown. A perpendicular bisector is drawn from point A to point D on side C B forming a right angle. The length of A D is h, the length of C B is a, the length of C A is b, and the length of A B is c.
A 2-column table has 7 rows. The first column is labeled Statement with entries In triangle A B C line segment A D is perpendicular to line segment B C, In triangle A D B sine (uppercase B) = StartFraction h Over c EndFraction, c sine (uppercase B) = h, In triangle A C D, sine (uppercase C) = StartFraction h Over b EndFraction, b sine (uppercase C) = h, question mark, StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction. The second column is labeled Reason with entries given, definition of sine, multiplication property of equality, definition of sine, multiplication property of equality, substitution, and division property of equality.
What is the missing statement in Step 6?
b = c
StartFraction h Over b EndFraction = StartFraction h Over c EndFraction
csin(B) = bsin(C)
bsin(B) = csin(C)
Answers
Answer:
c- the right triangle altitude theorem
Step-by-step explanation:
i did it on edge! ; )
The missing statement in Step 6 is ,c- The right triangle altitude theorem.
We have given that,
In △ABC, AD ⊥ BC
Prove: StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction.
Triangle A B C is shown.
What is the right triangle altitude theorem?The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the hypotenuse in a right triangle and the two-line segments it creates on the hypotenuse
Therefore we have,
A perpendicular bisector is drawn from point A to point D on side C B forming a right angle.
The length of A D is h, the length of C B is a, the length of C A is b, and the length of A B is c.
So the missing statement in Step 6
b = c
c=The right triangle altitude theorem.
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Related Questions
Mona loves the ocean, so she was thrilled to visit the beach and collect some seashells. The function g(x) gives the number of seashells Mona found after x minutes of searching.
What does g(30)≥20 tell you?
Answers
The inequality g(30) ≥ 20 us that: D. Mona found no more than 20 seashells in the first 30 minutes.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values, numbers, and variables in an algebraic equation, especially based on any of the following inequality symbols:
Greater than or equal to (≥).Greater than (>).Less than (<).Less than or equal to (≤).How to determine the required function?Assuming the variable g represents the total number of seashells and the variable x represents the total number of time (minutes), an inequality which would model the situation is given by;
g(x) ≥ x
when x = 30, we have;
g(30) ≥ 20
Therefore, Mona found no more than (less than or equal to) 20 seashells in the first 30 minutes.
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Complete Question:
Mona loves the ocean, so she was thrilled to visit the beach and collect some seashells. The function g(x) gives the number of seashells Mona found after x minutes of searching.
What does g(30) ≥ 20 tell you?
It took at least 20 minutes for Mona to find 30 seashells.
Mona found at least 20 seashells in the first 30 minutes.
It took at least 30 minutes for Mona to find 20 seashells.
Mona found no more than 20 seashells in the first 30 minutes.
If LN = 6x - 5, LM = x + 7, and MN = 3x + 20, find MN
Answers
Answer:
68
Step-by-step explanation:
LM + MN = LN
x + 7 + 3x + 20 = 6x - 5
4x + 27 = 6x - 5
-4x -4x
27 = 2x - 5
+5 +5
32 = 2x
÷2 ÷2
16 = x
MN: 3x + 20
3(16) + 20
48 + 20
68
Like us, mice are warm-blooded creatures. Their bodies must maintain a constant
temperature of 37°C, regardless of the temperature of their environment. Doing so burns
calories. The more severe the temperature difference, the more calories the mouse must
burn to maintain its body temperature. Consulting the research literature, you found the
following model:
C = 0.37219T + 1,560
Where C is the number of calories an idle mouse burns each day and T is the temperature
of its environment in °C. What is the most comfortable temperature for an idle mouse?
(This is the temperature where it burns the least calories per day). How many calories will
it burn each day at that temperature?
Answers
At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.
According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.
To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.
To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:
dC/dT = 0.37219 = 0
Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.
Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.
For example, if we take a temperature of 20°C, we can calculate the calorie burn:
C = 0.37219 * 20 + 1,560
C = 7.4438 + 1,560
C ≈ 1,567.4438 calories per day
Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.
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Find the measure of ∠AED for m∠BEC = 36.
Answers
Hello!
∠AED and ∠BEC are opposite angles
so ∠AED = ∠BEC = 36°.
∠AED = 36°Nolan was given a box of assorted chocolates for his birthday. Each night, Nolan treated himself to some chocolates. There were originally 30 chocolates in the box and after 8 nights, there were 6 chocolates remaining in the box. Write an equation for
C
,
C, in terms of
t
,
t, representing the number of chocolates remaining in the box
t
t days after Nolan's birthday.
Answers
The equation of remaining chocolate C in terms of t is C = 30 - 3t.
What is an equation?A mathematical statement called an equation demonstrates the balance or equality of two expressions. It contains of variables, integers, and mathematical operations and is denoted by the equal symbol (=). Equations may be solved to determine unknown values and are used to express relationships between various quantities. To solve for x in the equation 2x + 3 = 7, for instance, remove 3 from both sides, which gives 2x = 4, then divide both sides by 2, which gives x = 2.
Given that,
Initial number of chocolates in box = 30
Also given that after 8 nights, number of remaining chocolates = 6
Implies that,
In 8 nights, 24 chocolates were treated.
In 1 night, 3 chocolates were treated.
The equation of remaining chocolate C in terms of t can be written as
C = 30 - 3t.
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A hospital sends an invoice to a patient. The patient schedules a payment plan in which she makes an initial payment of $1,451 the first month and then pays one-third of the previous month’s payment each of the following months until the invoice is paid in full. Approximately how much of the invoice will be paid after the fourth month?
$1,451.00
$2,095.89
$2,149.63
$2,167.54
Answers
Answer:
$2,149.63
Step-by-step explanation:
She makes an initial payment of $1,451 and pays one-third of the previous month's payment each of the following months.
1/3 × $1,451 = $483.67 (second month)
$483.67 + $1,451 = $1,934.67
1/3 × $483.67 = $161.22 (third month)
$161.22 + $1,934.67 = $2,095.89
1/3 × $161.22 = $53.74 (fourth month)
$53.74 + $2,095.89 = $2,149.63
$2,149.63 of the invoice will be paid after the fourth month.
Hope that helps.
Approximately $2,149.63 of the invoice will be paid after the fourth month.
Option C is the correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example: so
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The patient makes an initial payment of $1,451 in the first month.
In each subsequent month, the patient pays one-third of the previous month's payment.
Let P be the amount paid in the first month, and let M be the amount paid in each subsequent month.
Then we have:
P = $1,451
M = (1/3)P
So the amounts paid in each month are:
Month 1: $1,451
Month 2: (1/3)P = (1/3)($1,451) = $483.67
Month 3: (1/3)M = (1/3)($483.67) = $161.22
Month 4: (1/3)M = (1/3)($161.22) = $53.74
The total amount paid after four months.
= $1,451 + $483.67 + $161.22 + $53.74
= $2,149.63
Therefore,
Approximately $2,149.63 of the invoice will be paid after the fourth month.
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b. A number subtracted from five is the same as twice the number increased by eight.
Answers
Answer:
5-x = 2x +8
(subtracts 2x from both sides)
5-3x=8
(subtracts 5 from both sides)
-3x=3
(divides by -3 on both sides)
x= -1
The value of y varies jointly with x and z. If y = 2 when z = 110 and x = 11, find the approximate value of y when x = 13 and z = 195.
Answers
Answer:
y = 4Step-by-step explanation:
To find the approximate value of y when
x = 13 and z = 195 we must first find the relationship between them
The statement
y varies jointly with x and z is written as
y = kxzwhere k is the constant of proportionality
From the question
y = 2
x = 11
z = 110
We have
2 = 11(110)k
2 = 1210k
Divide both sides by 1210
\(k = \frac{1}{605} \)
So the formula for the variation is
\(y = \frac{1}{605} xz\)
When
x = 13
z = 195
y is
\(y = \frac{1}{605} (13)(195)\)
\(y = \frac{507}{121} \)
y = 4.1900
We have the final answer as
y = 4Hope this helps you
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 5 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 3.25 minutes.
Answers
The chance that a randomly chosen passenger will wait longer than 3.25 minutes is 0.35, or 35%.
What is probability?Probability is a way to gauge how likely something is to happen. It is a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty for the event.
According to question:Since the waiting times are uniformly distributed between 0 and 5 minutes, the probability density function (PDF) is:
f(x) = 1/5
for 0 ≤ x ≤ 5
f(x) = 0, otherwise
To find the probability that a randomly selected passenger has a waiting time greater than 3.25 minutes, we need to find the area under the PDF to the right of 3.25:
P(X > 3.25) = ∫\(3.25^5\) f(x) dx
= ∫\(3.25^5\) (1/5) dx
= [x/5]\(3.25^5\)
= (5 - 3.25) / 5
= 0.35
As a result, the chance that a randomly chosen passenger will wait longer than 3.25 minutes is 0.35, or 35%.
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Find x intercept
(0, 24) (4,0)
Answers
Answer:
bt.ly/d97sjdu8 there is your answer!
Step-by-step explanation:
Answer:
x-intercept is 0
Step-by-step explanation:
(0, 24) (4,0)
(x, y)
0/4=0
I will give Brainliest, please help!! See the attached photo! ^^
You can’t use the same number twice!
Answers
Find the area under the standard normal curve between z=0 and z=3. Round to four decimal places.
Answers
Z=0
Z=3
03
Simplify by combining like terms. X^2-2xy+Y^2+2xy=?
Answers
By combining like terms, x^2 and y^2 don’t have another like term, while 2xy is repeated twice, combine those by adding them together and they cancel eachother out, leaving the x^2 and y^2 by themselves
A goose is flying horizontally at an altitude of 300 ft and a speed of 50 ft/sec passes directly over a pond. Find the rate at which the distance from the goose to the pond is increasing when it is 500 ft away from the pond.
Answers
Answer:
The rate at which the distance from the goose to the pond is increasing is approximately 42.875 feet per second.
Step-by-step explanation:
We assume that goose is flying at constant velocity. After reading carefully the statement of the problem, we create the following geometrical diagram, which is included at the end of this explanation and represents the following Pythagorean identity:
\(x^{2}+y^{2} = r^{2}\) (Eq. 1)
Where:
\(x\) - Horizontal distance of the goose from pond, measured in feet.
\(y\) - Vertical distance of the goose from pond, measured in feet.
\(r\) - Resultant distance of the goose from pond, measured in feet.
We find the rate of change in time at which resultant distance is increasing by differentiating on (Eq. 1):
\(2\cdot x \cdot \dot x + 2\cdot y \cdot \dot y = 2\cdot r \cdot \dot r\)
\(x\cdot \dot x + y\cdot \dot y = r\cdot \dot r\)
\(\dot r = \frac{x\cdot \dot x + y\cdot \dot y}{\sqrt{x^{2}+y^{2}}}\) (Eq. 2)
Where:
\(\dot x\) - Rate of change of horizontal distance, measured in feet per second.
\(\dot y\) - Rate of change of vertical distance, measured in feet per second.
\(\dot r\) - Rate of change of resulting distance, measured in feet per second.
If we know that \(x = 500\,ft\), \(y = 300\,ft\), \(\dot x = 50\,\frac{ft}{s}\) and \(\dot y = 0\,\frac{ft}{s}\), the rate at which the distance from the goose to the pond is increasing is:
\(\dot r = \frac{(500\,ft)\cdot \left(50\,\frac{ft}{s}\right)+(300\,ft)\cdot \left(0\,\frac{ft}{s} \right) }{\sqrt{(500\,ft)^{2}+(300\,ft)^{2}}}\)
\(\dot r \approx 42.875\,\frac{ft}{s}\)
The rate at which the distance from the goose to the pond is increasing is approximately 42.875 feet per second.
Which one is greater?
1.74 × 0.84
OR
1.79 × 0.69
- NO LINKS DOCS OR FILES ETC
Answers
Answer:
1.75 * 0.84
Step-by-step explanation:
1.74 * 0.84 = 1.4616
1.79 * 0.69 = 1.2351
Answer:
1.74 x 0.84 is greater
Step-by-step explanation:
1.74 x 0.84 = 1.4616
while
1.79 x 0.69 = 1.23509
Drag the tiles to the correct boxes. Not all tiles will be used.
Match each equation with a value of x that satisfies it.
18
1
9
2
5
(x - 2) = 2
√²+7=4
V1-x
= -1
-3
Answers
For a given exponential expression, the determined value is x=3,0,6.
What are exponential expressions?A component of an exponential expression is an exponent. Powers can be expressed succinctly using exponential expressions. The exponent represents the number of times the base has been multiplied.Powers can be expressed succinctly using exponential expressions. The exponent represents the number of times the base has been multiplied. Exponential expressions or the representation of multiplication with exponents can be streamlined to produce the most efficient notation possible.Each exponential expression's x value is evaluated.
Therefore,
1. \($ \sqrt{x^2+7}=4 \\\)
\(&\left(x^2+7\right)=4^2 \\\)
\(&\left(x^2+7\right)=16 \\\)
simplifying the above equation, then we get
x² = 16 - 7 = 9
x = 3
2. \($\sqrt[2]{1-x}=-1$\)
(1 -x) = (-1)²
1 - x = 1
x = 0
3. \((x-2)^{\frac{1}{2}}=2 \\\)
(x - 2) = 2²
x - 2 = 4
x = 6
The determined value is x=3,0,6 for a given exponential expression.
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Diana has a tool box in the shape of a right rectangular prism. The volume of the tool box is 1.62 cubic feet. The height of the tool box is 0.75 feet, and the length is 1.8 feet. What is the width of Diana's tool box? Enter your answer as a decimal in the box. HURRY
Answers
Answer:
0.5 ft
Step-by-step explanation:
The applicable volume formula is ...
V = length · width · height
Filling in the given numbers, we can solve for the width.
0.375 ft^3 = (1.5 ft) · width · (0.5 ft)
Dividing by the coefficient of width, we have ...
0.375 ft^3/(0.75 ft^2) = width = 0.5 ft
The width of Deena's tool box is 0.5 ft.
Answer:
1.2
Step-by-step explanation:
According to a poll, 80% of Americans report being afflicted by stress. Suppose a random sample of 1,200 Americans is selected. Complete parts (a) through (d) below.
a. What percentage of the sample would we expect to report being afflicted by stress?
Answers
The percentage of the sample selected at random that would be expected to be afflicted by stress would also be = 80%
How to calculate the percentage afflicted by stress?The percentage of a data set is when part of the data is represented per 100 with a symbol of %.
It was stated in the question that 80% of Americans report being afflicted by stress.
Therefore when a sample is randomly selected from an American population, the percentage that is expected to be afflicted by stress should also be 80%.
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solve similar triangles (advanced)
solve for x
Answers
Answer:
27/2 =x
Step-by-step explanation:
We can write a ratio to solve
3 2
----- = ---------
3+x 11
Using cross products
3*11 = 2(3+x)
33 = 6+2x
Subtract 6 from each side
33-6 = 6+2x-6
27 = 2x
27/2 = 2x/2
27/2 =x
3/4x-3=5/8 without fractions or decimals
Answers
Answer:
x = 4 5/6
Step-by-step explanation:
The fractions have denominators of 4 and 8. The least common multiple of these is 8, so we can eliminate fractions by multiplying both sides of the equation by 8.
8(3/4x -3) = 8(5/8)
6x -24 = 5 . . . . . . . . . eliminate parentheses
6x = 29 . . . . . . . . add 24
x = 29/6 = 4 5/6 . . . . divide by 6
The solution is x = 4 5/6.
__
Check
Substituting 26/6 for x, we get ...
(3/4)(29/6) -3 = 5/8
29/8 -3 = 5/8
(29 -24)/8 = 5/8 . . . . . true
Identfy the equation that translates Y= In(x) five units down.
y= In(x-5)
y= In(x)+5
y= In(x+5)
y= In(x)-5
Please please help me
Answers
Answer:
y= In(x)-5
Step-by-step explanation:
Kala made $35,000 in taxable income last year.
Suppose the income tax rate is 15% for the first $7000 plus 17% for the amount over $7000.
How much must Kala pay in income tax for last year?
Answers
Answer:
1040
Step-by-step explanation:
Aisha organized her books for 5 hour and her coin collection for 3 hour. 7 What is the best estimate for the total time Aisha spent organizing?
Answers
Answer:
about 8 hours
Step-by-step explanation:
8 hours. It is Five hours plus Three hours.
When solving a linear system of equations, you are looking for which of the following?
Answers
When solving a linear system of equations, you are looking for the points of intersection between the equations
How to determine the statement that completes the given statementFrom the question, we have the following parameters that can be used in our computation:
Solving a system of linear equations
Also, we have the following from the options
Slopey-interceptx-interceptPoints of intersectionThe general rile is that
Slope = rate of change
x and y intercepts = when y and x equals 0
points of intersection = solution to the system
Hence, you are looking for the points of intersection between the equations
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Question
When solving a linear system of equations, you are looking for which of the following?
Slope
y-intercept
x-intercept
Points of intersection
below
(3 - i)(3 + 1) =
Answers
Answer:
12-4i
Step-by-step explanation:
i means √-1
(3 - i)(3 + 1) =
3*3=9
3*1=3
-i*3= -3i
-i*1 = -i
9+3-3i-i=
12-4i <--- answer
(3 - i)(3 + i) =
3*3=9
3*i=3i
-i*3= -3i
-i*i = -(√-1)*(√-1) = -(-1) = 1
9+3i-3i+1 =
10 <--- answer
How many tenths make up 4 wholes?
Answers
Answer:
40
Step-by-step explanation:
Hope that helped have a nice day!
Compare -2.3 and -8/3 using symbols <, >, or =.
Answers
₋2.3 < ₋8/3 is the correct answer.
Given, we need to compare the terms.
₋8/3 = ₋2.67
therefore, 2.3 is less than 2.667
hence we form it as ₋2.3 < ₋2.67
we form: ₋2.3 < ₋8/3
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Explain why the mapping diagram below represents a function.
Answers
Answer:
Because there is only one out put for each domain this mapping diagram is a function.
Step-by-step explanation:
Two sets are involved. There is a directional property, the relation is defined from one set called the domain on to another set called the codomain. A function is a relation that has exactly one output for each input in the domain.
To be eligible for the swim team, the mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s). The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.
What is the maximum time (in seconds) that she can take on her last lap and still make the team?
Answers
52s is the maximum time that she can take on her last lap and still make the team.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that he mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s).
The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.
We need to find the maximum time (in seconds) that she can take on her last lap and still make the team
Let x be the maximum time (in seconds) that she can take on her last lap
60=(63+62+65+58+x)/5
300=63+62+65+58+x
300=248+x
Subtract 248 on both sides
300-248=x
x=52s
Hence, 52s is the maximum time that she can take on her last lap and still make the team.
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A thread was folded in half, and then it was folded again, forming a bundle. Then the thread was cut into pieces by a striaght cut through the enitre bundle. Ine of the pieces is 8 cm, and the longest piece is 18 cm. What is the longest possible length of the thread
Answers
The longest possible length of the thread is;
Length = 144 cm
Let the length of the thread be x cm.
Now, it is first folded in half. This means divided into 2. Thus, we now have length as x/2.
We are told it is folded again. This means the length after second folding is now; (x/2) ÷ 2 = x/4.We are told that there is now a straight cut through the entire bundle with one of the pieces being 8cm and the longer piece being 18 cm.This means the ratio is; 8:18
Since the new length after the final folding is x/4, then it means after cutting;longer length will be; \((\frac{18}{8 + 18})\) \(* (\frac{x}{4})\)
Thus, we now have;
18 = (18/26) × (x/4)
18 will cancel out to give; x = 26 × 4
x = 144 cm
Therefore the longest possible length of the thread = 144 cm
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I thought it was 144 but it is not