Answers
ABC is a right triangle
AB is perpendicular to BC
If 2 lines are perpendicular, the product of slopes is -1
m1 x m2 = -1
mAB x mBC = -1
mAB = -1 / mBC
mAB = -1 / (1/2)
mAB = -2
Related Questions
What is an equation of the line that passes through the point (-4,-6)(−4,−6) and is perpendicular to the line 4x+5y=25?
Answers
First you put the equation into y=mx+b form:
1. move the 4x to the other side
5y=-4x+25
2. divide by 5 on both sides
y=(-4/5)x+5
Next, since the line has to be perpendicular, you take the negative reciprocal of the slope (flip the fraction and put the opposite sign)
1. 5/4
Now, find the y intercept (the b)
1. set up the equation
-6=(5/4)(-4)+b
2. multiply the 5/4 and -4
-6=-5+b
3. move the -5 to the other side (add it)
-1=b
Now, put all the elements together
1. y=(5/4)x-1
The rate of growth of a particular population is given by dP/dt=50t^2-100t^3/2, where P is population size and t is fine and years. Assume the initial population is 25,000. a) determine the population function, P(t)b) estimate to the nearest year how long it will take for the population to reach 50,000
Answers
SOLUTION
Step1: write out the giving equation
[tex]\frac{dp}{dt}=50t^2-100t^{\frac{3}{2}}[/tex]Step2: Integrate both sides of the equation above
[tex]\int \frac{dp}{dt}=\int 50t^2dt-\int 100t^{\frac{3}{2}}dt[/tex]Then simplify by integrating both sides
[tex]p(t)=\frac{50t^{2+1}}{2+1}-\frac{100t^{\frac{3}{2}+1}}{\frac{3}{2}+1}+c[/tex][tex]p(t)=\frac{50}{3}t^3-40t^{\frac{5}{2}}+c[/tex]since the initial value is 25,000, then
the Population function is
[tex]\begin{gathered} p(t)=\frac{50}{3}t^3-40t^{\frac{5}{2}}+25000\ldots\ldots..\ldots\text{.. is the population function} \\ \text{where t=time in years} \end{gathered}[/tex]b). For the population to reach 50,000 the time will be
[tex]\begin{gathered} 50000=\frac{50}{3}t^3-40t^{\frac{5}{2}}+2500 \\ 50000-25000=\frac{50}{3}t^3-40t^{\frac{5}{2}} \\ 25000=\frac{50}{3}t^3-40t^{\frac{5}{2}} \\ \text{Then} \\ \frac{50}{3}t^3-40t^{\frac{5}{2}}-25000=0 \\ \end{gathered}[/tex]Multiply the equation by 3, we have
[tex]\begin{gathered} 50t^3-120t^{\frac{5}{2}}-75000=0 \\ \end{gathered}[/tex]To solve this we rewrite the function as
[tex]14400t^5=\mleft(-50t^3+75000\mright)^2[/tex]The value of t becomes
[tex]\begin{gathered} t\approx\: 15.628,\: t\approx\: 9.443 \\ t=15.625\text{ satisfy the equation above } \end{gathered}[/tex]Then it will take approximately
[tex]16\text{years}[/tex]
The triangles formed by two ladders leaning against a wall are similar. How long is the shorter ladder?
Answers
To solve this problem we must use proportions
[tex]\begin{gathered} \text{ }\frac{x}{8}\text{ = }\frac{42}{24} \\ \text{ x = }\frac{8\text{ x 42}}{24} \\ \text{ x = }\frac{336}{24} \\ \text{ x = 14} \end{gathered}[/tex]The length of the shortest ladder is 14.
letter B is the correct answer.
NO LINKS!! Please help me with this probability question
Answers
Answer: B) 46.67% approximately
=================================================
Work Shown:
A = it will be cloudy tomorrow
B = it will be rainy tomorrow
P(A) = 0.30
P(B) = 0.15
P(A and B) = 0.14
Apply the conditional probability formula.
P(B given A) = P(A and B)/P(A)
P(B given A) = 0.14/0.30
P(B given A) = 0.4667 approximately
P(B given A) = 46.67% approximately
Answer:
b) About 46.67%.
Step-by-step explanation:
Let event A = being cloudy.
Let even B = being rainy.
Given probabilities:
Probability of being cloudy = 30%.Probability of being rainy = 15%.Probability of being cloudy and rainy = 14%.Therefore:
P(A) = 0.3P(B) = 0.15P(A ∩ B) = 0.14Conditional Probability Formula
[tex]\sf P(B|A)=\dfrac{P(A \cap B)}{P(A)}[/tex]
The probability of being rainy given it is cloudy = P(B | A).
Substitute the given values into the formula:
[tex]\implies \sf P(B|A)=\dfrac{0.14}{0.3}=0.46666...=46.67\%\;(2\;d.p.)[/tex]
Therefore, the probability of it being rainy if you know it will be cloudy is about 46.67%.
Let E be the event where the sum of two rolled dice is less than 9. List the outcomes in E^c
Answers
The Solution:
Let the outcomes when two dice are tossed be as summarized in the picture attached below:
What is the value of 10 1
Answers
10
10x1=10
Hope this helps
Graph the line y=1/4x+3 then name the slope and y-intercept by looking at the graph. How do I graph this what are my points and what is m= as well as what is b=?
Answers
Make graph line using the slope and the y-intercept or the point.
m=1/4 and b=3
What is graph ?
graph is a mathematical representation of a networks and it describes that the relationship between lines and points. A graph consists of some points and lines are between them. The length of the lines and position of the points do not matter.
Sol-as per the given question y=1/4x+3
The slope-intercept form y=mx+b where m is the slope and b is the y intercept
y=mx+b
Reorder terms
y=1/4x +3
Use the slope-intercept form to find the slope and y-intercept
Slope=1/4
y-intercept :(0,3)
Any line can be graphed using two points is Select two x
values, and plug them into the equation to find the corresponding Y values.
In record terms -y=1/4 x+3
The table of x and y values are-
X-0,4
Y-3,4
graph the line using the slope and the y-intercept, or the points.
Slope -1/4
y-intercept (0,3)
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A dwarf seahorse swims 3/4 inch in a minute. How many minutes would take the seahorse to swim 1/3 inch?
A. 1/3 divided by 3/4= 4/9
B. 1/3 times 3/4= 1/4
C. 3/4 divided by 1/3= 9/4
D. 3/4 + 1/3= 13/12
Answers
Answer:
A
Step-by-step explanation:
we have 3/4 in / minute.
so, we divide this by 3/4 to get the time for 1 inch.
and then we multiply by 1/3 to get the time for 1/3 inch.
that combination, dividing by 3/4 and multiplying by 1/3, can be done in any sequence (commutative property of multiplication).
therefore, this can be expressed as 1/3 divided by 3/4. and A is the correct answer.
A $40,000 is placed in a scholarship fund that earns an annual interest rate of 4.25% compounded daily find the value in dollars of the account after 2 years assume years have 365 days round your answer to the nearest cent
Answers
SOLUTION
From the question, we want to find the value in dollars of the account after 2 years.
We will usethe formula
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ Where\text{ A = value of the account, amount in dollars = ?} \\ P=principal\text{ money invested = 40,000 dollars } \\ r=annual\text{ interest rate = 4.25\% = }\frac{4.25}{100}=0.0425 \\ n=number\text{ of times compounded = daily = 365} \\ t=time\text{ in years = 2 years } \end{gathered}[/tex]Applying this, we have
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=40,000(1+\frac{0.0425}{365})^{365\times2} \\ A=40,000(1.000116438)^{730} \\ A=40,000\times1.0887116 \\ A=43,548.467179 \\ A=43,548.47\text{ dollars } \end{gathered}[/tex]Hence the answer is 43,548.47 to the nearest cent
I need help A. -3 B. 3 C. -2D. -10
Answers
The average rate of change can be calculated as the division of the output of the function on the interest interval by the size of the interval. To do that we have to find the value of "y" at the end of the interval and subtract it by the value of "y" at the beggining. This is shown as an expression below:
[tex]\text{average rate of change=}\frac{y_{\text{ final}}-y_{\text{ initial}}}{x_{\text{ final}}-x_{\text{ initial}}}[/tex]For this function the values of x are:
[tex]\begin{gathered} x_{\text{ initial}}=0 \\ x_{\text{ initial}}=3 \end{gathered}[/tex]The values for y are:
[tex]\begin{gathered} y_{\text{ initial}}=10 \\ y_{\text{ final}}=1 \end{gathered}[/tex]Using these values we can calculate the average rate of change:
[tex]\text{average rate of change=}\frac{1-10}{3-0}=\frac{-9}{3}=-3[/tex]The average rate of change for this function is approximately -3 for the given interval. The correct answer is A.
Which of the following is NOT an equation?1. 5(2x+1)=10x+52. 4x-13. 5+3=104. x/2+1=7
Answers
By definition, an equation is a statement that two mathematical expressions are equal.
Equations always contain the equal sign "="
Out of the 4 expressions listed, number 2. does not contain the equal sign, which means that this expression is not an equation.
All other expressions contain the equal sign, they can be considered equations.
Newton's Second Law, F=m.a, describes the relationship between an object's mass, a force acting on it, and the resulting acceleration, where: F is force, in Newtons m is mass, in kilograms a is acceleration, in meters per second squared A young boy and his tricycle have a combined mass of 30 kilograms. If the boy's sister gives him a push with a force of 60 Newtons, what is his acceleration? 1 2 meter per second squared 2 meters per second squared 30 meters per second squared 90 meters per second squared
Answers
Newton's Second Law, F=m.a, describes the relationship between an object's mass, a force acting on it, and the resulting acceleration, where: F is force, in Newtons m is mass, in kilograms a is acceleration, in meters per second squared A young boy and his tricycle have a combined mass of 30 kilograms. If the boy's sister gives him a push with a force of 60 Newtons, what is his acceleration? 1 2 meter per second squared 2 meters per second squared 30 meters per second squared 90 meters per second squared
we have that
F=m*a
we have
m=30 kg
F=60 N
substitute in the formula
60=30*a
solve for a
a=60/30
a=2 m/s^2
therefore
the answer is 2 meters per second squaredI don’t understand how to explain this question
Answers
The segments cannot be set equal since the constant terms 15 is greater than two. The variable x remains like a constant term in both sides of the point B. we say that 15x > 2x
What is inequality?In mathematics, the signs used inequality calculations are
greater thanless thangreater than or equal toless than or equal toUsing the picture as evidence the mark represented by B is not the midpoint hence the equality sign will not be used here. The sign to be used is the inequality sign.
In addition, the constants 15 and 2 shows that 15 is greater than 2. and there is no other addition to the variable x to help check the effect of the greatness of 15
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Look at this graph: у 10 9 8 7 6 5 3 2 1 0 1 2 3 4 5 6 7 8 9 10 What is the slope?
Answers
EXPLANATION
As we can see in the graph, we can calculate the slope with the following equation:
[tex]\text{Slope}=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]Let's consider any ordered pair, as (x1,y1)=(1,7) and (x2,y2)=(5,8), replacing this in the equation will give us:
[tex]\text{Slope}=\frac{(8-7)_{}}{(5-1)}=\frac{1}{4}[/tex]Answer: the slope is equal to 1/4.
Mr. Herman had $125, and Mr.Chandra had $80. After each of them had paid for a concert ticket, Mr. Herman had 6 times as much money as Mr. Chandra. how much money did Mr. Chandra have left?
Answers
We have
Let x = cost of the ticket
After paying for the tickets, Mr. Herman had 125 - x
and Mr Chandra had 80 - x
Then, the equation is:
[tex]125-x=6(80-x)[/tex]So, solve for x:
[tex]\begin{gathered} 125-x=480-6x \\ 125-x+6x=480-6x+6x \\ 125+5x=480 \\ 125+5x-125=480-125 \\ 5x=355 \\ \frac{5x}{5}=\frac{355}{5} \\ x=71 \end{gathered}[/tex]The concert ticket cost is $71
Therefore, Mr. Chandra have left:
[tex]80-71=9[/tex]Answer: $9
25. Brett wants to sound proof his studio, which is in the shape of a box. He will cover all 4 walls, the floor and the ceiling with the sound proof padding material. If the floor's dimensions are 15ft x 20ft and the height of the room is 10ft tall, how much will Brett spend on padding that costs $2.50 per square foot?
Answers
We have that the floor's dimensions are 15ft x 20ft and the height of the room is 10ft tall. This is
if we extended it we would have:
We want to find how many square foot Brett needs to cover. We just find the area of each side of the studio.
We find it just by multiplying both of its sides (they all are rectangles):
Wall 1
area = 10ft x 15 ft
area = 150 ft²
Wall 2
area = 10ft x 20 ft
area = 200 ft²
Wall 3
area = 10ft x 15 ft
area = 150 ft²
Wall 4
area = 10ft x 20 ft
area = 200 ft²
Floor
area = 15ft x 20 ft
area = 300 ft²
Ceiling
area = 15ft x 20 ft
area = 300 ft²
A condensed way....
TOTAL AREA
Now, we add all the areas found, this will be the total area Brett must cover:
Wall 1 + wall 2 + Wall 3 + Wall 4 + ceiling + floor = total area
150 ft² + 200 ft² + 150 ft² + 200 ft² + 300 ft² + 300 ft² = 1300 ft²
COST
Since the padding costs $2.50 per square foot, and there are 1300 square foot to cover. Brett will spend
$2.50 x 1300 = $3250
Answer: Brett spend on padding $3250
I
Three relationships are described below:
I. The amount of time needed to mow a yard increases as the size of the yard increases.
II. The amount of timeneeded to drive from city A to city B decreases as the speed you are driving increases.
III. The income of a worker who gets paid an hourly wage increases as the number of hours worked increases and
increases as the salary rate increases.
What type of variation describes each relationship?
Answers
The type of variation that describes each relationship include the following:
Direct variation: the amount of time needed to mow a yard increases as the size of the yard increases.Indirect variation: the amount of time needed to drive from city A to city B decreases as the speed you are driving increases.Joint variation: the income of a worker who gets paid an hourly wage increases as the number of hours worked increases and increases as the salary rate increases.What is an indirect variation?An indirect variation simply refers to a type of proportional relationship in which a variable is inversely proportional to another variable. This ultimately implies that, an indirect variation represents two variables that are inversely proportional to each other, which means as one variable increases, the other variable decreases and vice-versa.
What is direct variation?Direct variation refers to a type of proportional relationship in which a variable is directly proportional to another variable. This ultimately implies that, a direct variation represents two variables that are directly proportional to each other, which means as one variable increases, the other variable also increases and vice-versa.
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I have 4 questions I need help with This is first question number 2
Answers
We have the next function that models the Australian GDP since 1960 :
[tex]G(i)=1806x(1.037)^t[/tex]Where t is the number of years since 1960.
a)If we are in the year 1960, it means t=0
Therefore:
[tex]G(t)=1806x(1.037)^1[/tex][tex]G(0)=1806x(1.037)^0[/tex][tex]G(0)=1806[/tex]b)Now, we need to find the Australia capita in 1963.
This means t=3
Therefore:
[tex]G(t)=1806x(1.037)^t[/tex][tex]G(3)=1806x(1.037)^3[/tex][tex]G(3)=2013.974721[/tex]c) We need to find when the function is equal to 100,000.
Therefore we equal the function G(t)=100,000.
Then:
[tex]1806x(1.037)^t=1000000[/tex]Solve for t:
Divide both sides by 1806:
[tex]\frac{1806x(1.037)^t}{1806}=\frac{100000}{1806}[/tex][tex](1.037)^t=\frac{50000}{903}[/tex]Add Ln for each side:
[tex]\ln (1.037)^t=in(\frac{50000}{903})[/tex][tex]t\ln (1.037)=in(\frac{50000}{903})[/tex]Then:
[tex]t=\frac{in(\frac{50000}{903})}{\ln (1.037)}[/tex][tex]t=110.48286[/tex]Rounded to the nearest year:
[tex]t=110[/tex]Therefore: 1960 +110 = 2070
On 2070 the Austranlian GDP reaches 100,000 USD
If the correlation coefficient r is equal to 0.755, find the coefficient of determination and the coefficient of nondetermination.Question 10 options: The coefficient of determination is 0.430 and the coefficient of nondetermination is 0.570 The coefficient of determination is 0.869 and the coefficient of nondetermination is 0.131 The coefficient of determination is 0.570 and the coefficient of nondetermination is 0.430 The coefficient of determination is 0.131 and the coefficient of nondetermination is 0.869
Answers
Given the word problem, we can deduce the following information:
The correlation coefficient r is equal to 0.755.
To determine the coefficient of determination and the coefficient of nondetermination, we use the formulas below:
[tex]Coefficient\text{ }of\text{ }Determination=r^2[/tex][tex]Coefficient\text{ }of\text{ N}ondetermination=1-r^2[/tex]Now, we first plug in r=0.755 to get the coefficient of determination:
[tex]Coeff\imaginaryI c\imaginaryI ent\text{ o}f\text{ D}eterm\imaginaryI nat\imaginaryI on=r^2=(0.755)^2=0.57[/tex]Next, we get the coefficient of nondetermination:
[tex]\begin{gathered} Coeff\imaginaryI c\imaginaryI ent\text{ o}f\text{ N}ondeterm\imaginaryI nat\imaginaryI on=1-r^2=1-0.57=0.43 \\ \end{gathered}[/tex]Therefore, the answer is:
The coefficient of determination is 0.570 and the coefficient of nondetermination is 0.430
STATEMENTREASON1. DBC - RST1. Given2. ZABC - ZDBC+ ABD2. Angle addition therom3.3. Ifa=b+cand c>0,thena > b4. ABC > RST4. SubstitutionWhich of the following statements would complete the proof in line 3?O ZABC> ZABDO LABC> DBCO ZDBC> ZABD
Answers
Answer
Option B is correct.
Angle ABC > Angle DBC
Explanation
Since it's been proven that
Angle ABC = Angle ABD + Angle DBC
Since Angle ABD > 0,
Angle ABC > Angle DBC is the part that completes the proof that
Angle ABC > Angle RST
Hope this Helps!!!
Find the length of the missing side of the triangle using the Pythagorean theorem. (Type an integer or decimal rounded to the nearest tenth as needed.)
Answers
Pythagorean theorem
[tex]\begin{gathered} a^2=b^2+c^2,\text{ where a is the hypotenuse} \\ a^2=(6.5)^2+(4.9)^2 \\ a^2=42.25+24.01 \\ a^2=66.26 \\ a=\sqrt[]{66.26}=8.1^{\prime} \end{gathered}[/tex](Type an integer or decimal rounded to the nearest tenth as needed.)
Integer = 8'
decimal rounded to the nearest tenth as needed = 8.1'
Which ocean animal is closest to a depth of -0.7km?
Answers
Answer:
whales, walruses, porpoises, dolphins, seals, dugongs, manatees, and sea otters
Step-by-step explanation:
have good day
suppose that you have a savings account with 8500 in it. it pays 7% interest compound as shown below. find the value for the next 4 years
Answers
We want find the compound interest annualy for 4 years, $8500, at 7%'
The formula for the compound amount over one year is;
[tex]A=P(1+\frac{r}{100})[/tex]1st year:
[tex]\begin{gathered} A=8500(1+0.07) \\ A=\text{ \$9095} \end{gathered}[/tex]2nd year:
[tex]\begin{gathered} A=9095(1.07) \\ A=\text{ \$9731.65} \end{gathered}[/tex]3rd year:
[tex]\begin{gathered} A=9731.65(1.07) \\ A=\text{ \$10412.87} \end{gathered}[/tex]4th year:
[tex]\begin{gathered} A=10412.87(1.07) \\ A=\text{ \$11141.77} \end{gathered}[/tex]How do you solve this?
Answers
Answer: I thought you already asked this question.
Step-by-step explanation:
Carolina wants to find out how many different ways can she arrange the apps on her Iphone on the first row. The first row has space for 4 apps, and she has 12 apps to choose from
Answers
ANSWER
495 ways
EXPLANATION
Carolina has 12 apps to choose from and she only has space for 4 apps.
To find out how many ways she can do it, we will need to use combination.
That is:
[tex]^{12}C_4[/tex]Note: we use combination because the order of the apps is not a factor
So, we have that:
[tex]\begin{gathered} ^{12}C_4\text{ = }\frac{12!}{(12\text{ - 4)! 4!}}\text{ = }\frac{12!}{8!\text{ 4!}} \\ =\text{ 495 ways} \end{gathered}[/tex]She can arrange them in 495 ways.
given: S is the midpoint of BT ; BO || AT prove:
Answers
"S is the midpoint of BT": this is given.
BO || AT: this is given.
SB = ST: definition of midpoint.
alternate interior
vertical
ΔBOS = ΔTAS: SAS or ASA (both are right).
Question 2 (2 points)Find the value of x. If needed, round your answer to the nearest tenth.50°X5Not drawn to scaleX =
Answers
Solution
Find the value of x in the triangle shown below:
Calculate the value of x
Opposite = 5
adjacet = x
[tex]tan\theta=\frac{opp}{adj}[/tex][tex]\begin{gathered} tan50=\frac{5}{x} \\ x=\frac{5}{tan50} \\ x=\frac{5}{1.19175} \\ x=4.1955 \\ x=4.2\text{ \lparen nearest tenth\rparen} \end{gathered}[/tex]Therefore the correct value of x = 4.2
Which equation is set up for direct use of the zero-factor property? A. 3x2 - 19x - 14 = 0 C.X2 + x = 42 B. (7x + 9)2 = 3 D. (3x - 2)(- 2) = 0
Answers
Explanation:
The zero-factor property states that if ab=0, then either a = 0 or b = 0 (or both). A product of factors is zero if and only if one or more factors is zero.
From these options only B and D have factors, but B equals to 3. In D we have that (3x-2) = 0 or the other factor is zero (or both)
Answer:
The correct answer is option D
Find the x-intercept and y-intercept of the line.
5x-9y=-12
Answers
The x and y intercepts of the line is found as (12/5, 0) and (0, -4/3) respectively.
What is termed as the x and y intercepts?An intercept is a y-axis point that the slope of a line passes. It is the y-coordinate of the a point on the y-axis where a straight line or even a curve intersects. This is represented by the equation for a straight line, y = mx+c, where m is the slope and c seems to be the y-intercept. There are two types of intercepts: x-intercept and y-intercept.For the given question,
The equation of the line is 5x-9y=-12.
For the x intercept, Put y = 0.
5x-9×0=-12.
x = 12/5
x intercept = (12/5, 0)
For y intercept, put x = 0.
5×0-9y=-12
y = -12/9
y = -4/3
y intercept = (0, -4/3)
Thus, the x and y intercepts of the line is found as (12/5, 0) and (0, -4/3) respectively.
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3. State whether each sequence is arithmetic or geometric, and then find the explicit and recursive formulas for each sequence.Formulas:
Answers
A sequence is called arithmetic if the difference between two consecutives is a constant
In the first case we see a constant difference of 5
every two consecutives have difference of 5, for example 20-15, 30-25 and so on.
In the second case we see the division between two consecutives is a constant . That is called a GEOMETRIC sequence.
the constant in this case is 18/6 =3
lets return to the 1st case find the explicit
An = Ao +(n-1) d
An means the n term in the sucession
Ao means the first term
d means the constant
with that in mind we replace the values obtained
An= 5 + (n-1) •5
now for the recursive
a1= 5
An = An-1 + 5
Now lets go to the second part, the geometric sequence. Just is needed to replace the values in the ABOVE RIGHT formula
so then
An = A1 •(3)^(n-1)
An = 2• (3)^(n-1)