Step-by-step explanation:
The two adjacent vertices of the triangle are A(5; 3) and B(7; 7), and one point on the opposite side is P(-2; 9). To find the coordinates of the third vertex, we need to find the midpoint of AB and extend it to P.
The midpoint of AB can be calculated by finding the average of their x-coordinates and y-coordinates:
C = ((A_x + B_x)/2, (A_y + B_y)/2) = ((5 + 7)/2, (3 + 7)/2) = (6, 5)
Next, we can use the midpoint C and point P to find the slope of the line connecting them:
m = (P_y - C_y) / (P_x - C_x) = (9 - 5) / (-2 - 6) = 4 / -8 = -0.5
Since the slope of a line perpendicular to this one is -2, we can use the midpoint C and the slope to find the equation of the line connecting C and the third vertex D:
y - C_y = -2 (x - C_x)
y - 5 = -2 (x - 6)
Expanding and solving for x, we get:
y = -2x + 17
Substituting the y-coordinate of P (-2) into this equation:
-2 = -2x + 17
Solving for x:
x = 7.5
Finally, we can use the x-coordinate to find the y-coordinate:
y = -2x + 17 = -2 * 7.5 + 17 = 5.5
So the third vertex is D (7.5, 5.5).
The vertices of the triangle are A (5, 3), B (7, 7), and D (7.5, 5.5).
A diff diver plunges from a height of 25 ft above the water surface. The distance the diver falls in t seconds is given by the function (t) - 16eft. Which equation can be solved fort to find the time (in seconds) when the diver hits the water?
Answer: The equation that can be solved for t to find the time (in seconds) when the diver hits the water is:
h(t) = 25 - 16e^(-ft) = 0
Where h(t) is the height of the diver in feet at time t, and f is a positive constant related to the speed of the fall.
To find the time when the diver hits the water, we set h(t) equal to zero and solve for t. This gives us the time when the height of the diver is equal to the water surface.
25 - 16e^(-ft) = 0
25 = 16e^(-ft)
e^(-ft) = 25/16
-ft = ln(25/16)
t = -ln(25/16)/f
Note that the negative sign in the equation for t indicates that the time is counted from the moment the diver starts falling. The constant f can be determined from the physical characteristics of the diver and the conditions of the fall, but it is not necessary to know the exact value of f to find the time when the diver hits the water.
Step-by-step explanation:
What is the value of t in the following equation? t + 1/4 = 27/12
Answer:
t=2
Step-by-step explanation:
We have the equation:
[tex]t+\frac{1}{4} = \frac{27}{12}[/tex]
And the main thing here is if we do one thing to an equation we do it to both sides. So if we subtract 1/4 from one side, we do it to both sides. If we subtract 1/4 from the left side it cancels out with the 1/4 leaving us just with the "t" unknown, giving us a solution:
[tex]t=\frac{27}{12} - \frac{1}{4}[/tex]
Now from here we can just multiply the 1/4 by 3/3 so we get the same denominator and combine them into one fraction:
[tex]t=\frac{27}{12} - \frac{3}{12}[/tex]
Now subtract the numerators:
[tex]t=\frac{24}{12}[/tex]
Simplify:
t=2
How do I find the largest five-digit number which, when divided by 9, 12, 24 and 45, leaves remainders of 3, 6, 18, and 39, respectivly?
The average largest five-digit number which leaves remainders of 3, 6, 18 and 39 when divided by 9, 12, 24 and 45 respectively is 99741. This can be found by starting at the highest possible number (99999) and subtracting until the remainders of each division are obtained.
To find the largest five-digit number which leaves remainders of 3, 6, 18 and 39 when divided by 9, 12, 24 and 45 respectively, begin by setting the highest possible number (99999). Then, subtract until the remainders of each division become 3, 6, 18 and 39 respectively. This can be done by subtracting 3 from the initial number and then 6, 18, and 39 in order to get the correct remainders. This process can be repeated until the number reaches 99741, which is the largest five-digit number that leaves the given remainders. This number can also be found by using the formula (9x + 3)(12x + 6)(24x + 18)(45x + 39). By plugging in x = 999, the answer of 99741 is obtained.
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Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be
28.15 meters. She stands 23.1 meters away from the tree, so that the tip of her
shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest
hundredth of a meter.
A garden table and a bench cost S1000 combined. The cost of the garden table is three times the cost of the bench. What is the cost of the bench?
Answer:
Step-by-step explanation:
Let x be the cost of the bench. Then the cost of the garden table is 3x.
The combined cost of the bench and the table is 1000, so x + 3x = 1000.
Combining like terms, we get 4x = 1000.
Dividing both sides by 4, we get x = 250.
The cost of the bench is 250.
Answer:
250.
Step-by-step explanation:
Let's call the cost of the bench "x".
The cost of the garden table is then 3x.
So the combined cost of both is x + 3x = 4x = 1000
So x = 250, and the cost of the bench is 250.
find the value of x in the solution to the system of equations shown
y = 12x + 7
y = -6 + 25
Answer:
Substitute y = 12x + 7
12x+7=-6+25
Simplify
12x+7=19
Solve
19-7=12
12x=12
x=1
Help me for this question. I just want to know if it’s right or not!
How many starting points does a ray have?
0
1
2
infinite
The number of starting points a ray has is one.
Option B is the correct answer.
What is a ray?A ray is a line that has a starting point and no end.
We have,
A ray is a line that has one fixed point and the other point is endless.
So,
A ray has one starting point.
Thus,
A ray has one starting point.
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Zak has 18 tennis balls. This is 3 times as many as Joe has.
Matt has 9 more tennis balls than Zak and Joe combined.
How many tennis balls does Matt have?
The number of tennis ball mat have is 33.
What is an equation?
a formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.
We are given that zak has 18 tennis ball and this is 3 times as many as joe have
That means joe has 18/3 = 6 tennis balls
Matt has 9 more tennis ball that matt and joe combined
The combined tennis ball of matt and joe is 18 + 6 =24
Now we add 9 to it so that we have the number of tennis ball matt has
Which is 24+ 9 = 33
Hence matt has 33 balls
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Richard gambled and doubled his money. He gave one euro to his friend and gambled again. This time he tripled his money. After this he bought a hamburger for two euro. Now he had four times the euros in his wallet that he gambled the first time. How many euros did Richard have in the beginning?
The number of euros with Richard in the beginning is 2.5 euros.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the money with Richard at the beginning be $x.
Richard gambled and doubled his money.
Now, the money is 2x.
He gave one euro to his friend and gambled again.
Here, 2x-1
This time he tripled his money.
So, the money is 3(2x-1)
After this he bought a hamburger for two euro.
Now, 6x-3-2
6x-5
Now he had four times the euros in his wallet that he gambled the first time.
Here, 6x-5=4x
6x-4x=5
2x=5
x=2.5
Therefore, the number of euros with Richard in the beginning is 2.5 euros.
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(3x−1)(2x 3 +4x 2 −5) in standard form
The standard form is 6[tex]x^4[/tex] + 10x³ - 4x² - 15x + 5.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
(3x−1) (2x³ +4x² −5)
Simplifying
3x (2x³ +4x² −5) - 1 (2x³ +4x² −5)
6[tex]x^4[/tex] + 12x³ - 15x - 2x³ - 4x² + 5
Adding the like terms.
6[tex]x^4[/tex] + 10x³ - 4x² - 15x + 5
Thus,
6[tex]x^4[/tex] + 10x³ - 4x² - 15x + 5
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mackenzie collects bookmarks. She has 20 bookmarks with quotes. The bookmarks with quotes make up 20% of her whole collection.how many bookmarks does she have total?
1. How does an annual percentage rate (APR) for mortgages differ from a
more traditional interest rate?
Annual percentage rate (APR) for mortgages differs from a
more traditional interest rate as APR includes other charges and fees while interest rates do not include it.
How is this determined?The annual cost of a loan to a borrower is referred to as interest rate, and it is indicated as a percentage.
APR represents the total yearly cost of a loan to the borrower, including all fees. The APR is stated as a percentage, just like an interest rate. It does, however, contain other costs or fees such mortgage insurance, the majority of closing costs, discount points, and loan origination fees, unlike an interest rate.
Hence, Annual percentage rate (APR) for mortgages differs from a
more traditional interest rate as APR includes other charges and fees while interest rates do not include it.
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Daniel wants to predict how far he can hike based on the time he spends on the hike. He collected some data on the time (in hours) and distance (in kilometers) of some of his previous hikes. Which of linear equations best describes the given model?
When Daniel creates the linear equation, he will notice that the relationship between time spent and distance travelled is proportional.
What exactly is a linear equation?The equation is referred to as linear when a variable's maximum power is 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. This equation has three variables: x, A, and B. A is a coefficient. A linear equation in which there are only two variables typically takes the form Ax + By = C. In addition to the constant C, there are three other constants: the variables x and y, the coefficients A and B, and the variables.
Now,
When we create a linear equation for the distance of the hike, we will get a graph with a straight line.
A straight line's general equation is
y = mx + c
where m = is the slope of the line and
c = is the y-intercept
y = the distance covered
x = the time taken
Because distance is directly proportional to time,
more distance is covered in less time
Distance ∝ time
Hence,
Daniel will notice that the relationship between the time spent and distance covered are proportional.
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An album is downloaded 12000 times per week when its price is $12. It is downloaded 22000 times per week when the price drops to $9. Find the demand equation, assuming it is linear. The equation should express price p
in terms of quantity q
p=
The demand equation, by assuming it is linear. The equation expresses price p in terms of quantity q, q = -10000/3p + 52000
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
An album is downloaded 12000 times per week when its price is $12
It is downloaded 22000 times per week when the price drops to $9
The demand equation = ?
Suppose, price is expressed as p and quantity as q
Formula of linear relationship,
y = mx + c
So,
q = mp + c
when, p = 12 then q = 12000
12000 = 12m + c _________(i)
when, p = 9 then q = 22000
22000 = 9m + c _________ (ii)
Now by using elimination method solve equation i & ii
12m + c = 12000
- 9m + (-c) = -22000
3m = -10000
m = -10000/3
12m + c = 12000
c = 12000 - 12 x (-10000/3)
c = 12000 + 40000
c = 52000
q = -10000/3p + 52000
The equation is q = -10000/3p + 52000
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let x equal an integer selected at random from the first m positive integers, {1,2,...,m}. find the value of m for which e[x]
The expected value of x is (m+1)/2, and m must be a positive integer.
The expected value of x is the average value of x that we would expect to get if we selected an integer from the set {1, 2, ..., m} many times. To find the expected value of x, we multiply each possible value of x by its probability of being selected and then sum these products. In this case, each integer in the set {1, 2, ..., m} has an equal probability of being selected, so the expected value is (1 + 2 + ... + m) / m = (m(m+1)) / 2m = (m+1) / 2. So the expected value of x is (m+1)/2, and m must be a positive integer.
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Kunle and Peter shared 180 marbles in the ratio 5:7, how many will Peter receive
Answer: 108
Step-by-step explanation:
5+7 = 12
They split it into 12 parts.
Kunle gets 5/12, Peter gets 7/12
7/12 of 180
Divide by the bottom, multiply by the top
180/12 = 15
15x7 = 105
Therefore, Peter gets 108 marbles.
Please make me brainliest!
Answer:
k:p 5+7=7/12×180=15×7=105
Valentino is buying a movie at an online store. He can choose to use one of the three deals that are shown below or to just buy the movie without a deal. The online store charges a flat rate of $2.99 for shipping. Valentino is buying a movie for $12.99. He could buy the same movie with a digital download for $2.50 more.
The cheapest alternative that Valentino can select is to make the computation and discover which is less expensive when compared to others.
What is Algebra?The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions.
Given that the info is incomplete, Valentino needs to analyze the three options and make additions for extra charges or deductions for discount and make a purchase of the cheapest alternative.
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Microeconomics
The total cost function of a monopolist is (Q) = 3Q. The inverse demandfunction for
the monopolist’s products is P (Q) = 12 − Q.
A. find the profit-maximizing level of price and output
B. Find the maximum profit of the firm at an equilibrium price level
Step-by-step explanation:
A. To find the profit-maximizing level of price and output, we need to find the equilibrium point where the marginal revenue equals marginal cost.
The marginal cost of production is the derivative of the total cost function: MC = dC/dQ = 3.
The marginal revenue is the derivative of the inverse demand function: MR = dP/dQ = -1.
So at the profit-maximizing level of output, MC = MR.
3 = -1
Q = 6
Then we can substitute Q = 6 back into the inverse demand function to find the price:
P (Q) = 12 - Q
P (6) = 12 - 6
P = 6
So the profit-maximizing level of output is 6 units at a price of $6.
B. To find the maximum profit of the firm, we need to calculate the total revenue and the total cost at the profit-maximizing level of output.
The total revenue is the product of the price and the quantity:
TR = P * Q
TR = 6 * 6
TR = 36
The total cost is given by the total cost function:
TC = C (Q)
TC = 3 * Q
TC = 3 * 6
TC = 18
So the maximum profit is the difference between the total revenue and the total cost:
Profit = TR - TC
Profit = 36 - 18
Profit = 18
The maximum profit of the firm is $18 at an equilibrium price level of $6 and an output level of 6 units.
In a math class of 30 students, 17 are boys and 13 are girls. On a unit test, 4 boys and
5 girls made an A grade. If a student is chosen at random from the class, what is the
probability of choosing a girl or an A student?
i know that the answer is 5/36 its just that i dont know how to get there.
Answer:
17/30
Step-by-step explanation:
Number of students = 30
Number of girls and A students = 13+4 = 17
Probability of a student being chosen at random being either a girl or an A student = Total Number of girls and A students/Total No of students = 17/30
Probably of a student chosen at random being either a girl or an A student would be 17/30
The probability of choosing a girl or an A student is 17/30 or 0.567.
There are a couple of ways to approach this problem, but one common method is to use the formula:
P(girl or A) = P(girl) + P(A) - P(girl and A)
where P(girl) is the probability of choosing a girl, P(A) is the probability of choosing an A student, and P(girl and A) is the probability of choosing a student who is both a girl and an A student.
To calculate each of these probabilities, we first need to find the total number of girls and A students in the class:
Total number of girls: 13
Total number of A students: 4 boys + 5 girls = 9
Now we can calculate each probability:
P(girl) = number of girls / total number of students = 13 / 30
P(A) = number of A students / total number of students = 9 / 30
P(girl and A) = number of girls who made an A / total number of students = 5 / 30
Plugging in the values, we get:
P(girl or A) = P(girl) + P(A) - P(girl and A)
= 13/30 + 9/30 - 5/30
= 17/30
Therefore, the probability of choosing a girl or an A student at random from the class is 17/30, or about 0.567.
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The table below shows the favorite soft drink of each student in a statistics class. Find the frequency of each drink
Drinks
Sprite Sprite Dr Pepper
Dr Pepper Coke Coke
Coke Pepsi Mtn Dew
Pepsi Sprite Pepsi
Sprite Sprite Sprite
Pepsi Coke Pepsi
Dr Pepper Coke Coke
Coke Coke Pepsi
Dr Pepper Coke Dr Pepper
Coke Coke Pepsi
The frequency of each drink in the statistics class can be found to be :
Sprite - 6 Dr Pepper - 5Coke - 11Mtn Dew - 1 Pepsi - 7 How to find the frequency ?The frequency of something refers to the number of times that thing happens. In this case, it therefore means the number of students who prefer a certain drink over the other ones.
From the table, the number of students who chose Sprite was 6 students. 5 students chose Dr Pepper and 11 students chose Coke. Then only a single student chose Mtn Dew while 7 students chose Pepsi.
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Victoria can make 8 necklaces in 4 days. How long does it take her to make one bracelet. By the way I'm in 6th grade.
Answer: To find the time it takes Victoria to make one necklace, we can divide the total time by the number of necklaces she can make in that time. If it takes her 4 days to make 8 necklaces, it takes her 4/8 = 0.5 days to make one necklace.
Next, we can convert 0.5 days into hours to find the time it takes her to make one necklace. Since there are 24 hours in a day, it takes her 0.5 * 24 = 12 hours to make one necklace.
So, it takes Victoria 12 hours to make one necklace.
Step-by-step explanation:
In each of the following problems, type the price per unit per oz in blanks a. and b, then pick the best buy. a. Bread, 1 lb. loaf for 80¢ would = b. Bread, 2 lb. loaf for $1.95 would = c. The best buy would be
Answer:
a) $0.05 per ounce
b) $0.06 per ounce
c)The best buy would be 1lb for .80
Step-by-step explanation:
.80/16 = .05 16 ounces in a pound
1.95/32 = .06 32 ounces in 2 pounds
How many ways can 3 of 10 students come first, second and third place is a spelling contest, if there are no ties?
Answer:
Step-by-step explanation:
The number of ways to choose 3 students out of 10 to come in first, second, and third place in a spelling contest, with no ties, is calculated using the combination formula. The combination formula is:
C(n, r) = n! / (r! (n-r)!)
Where n is the total number of items, and r is the number of items to choose. In this case, n = 10 and r = 3.
So, the number of ways to choose 3 students out of 10 is:
C(10, 3) = 10! / (3! (10-3)!) = 10! / (3! 7!) = 10 x 9 x 8 / (3 x 2 x 1) = 120.
Therefore, there are 120 different ways to choose 3 students out of 10 to come in first, second, and third place in a spelling contest, with no ties.
What is an angle that is adjacent to ∠HBF?
Answer:
JCI is the angle :p
Step-by-step explanation:
Given that f(x)= 2x-1 g(x)=3x and h(x)=x^2+1
Compute the following
1. g(f(0))
2.f(f(2))
3.f(g(x))
4.g(h(x))
5.g(f(x))
6.f(f(x))
7.g(g(x))
We compute the functions as follows
1. g(f(0)) = -3
2. f(f(2)) = 5
3. f(g(x)) = 6x - 1
4. g(h(x)) = 3x² + 3
5. g(f(x)) = 6x - 3
6. f(f(x)) = 4x - 3
7. g(g(x)) = 9x
What is a function?A function is a mathematical equation that shows the relationship between two variables.
How to compute the given functions?Given that
f(x) = 2x - 1, g(x) = 3x and h(x) = x² + 1.Let's compute the given functions.
1. How to compute g(f(0))?To compute the function g(f(0)), we first compute g(f(x)).
So, g(f(x)) = 3f(x)
= 3(2x - 1)
= 6x - 3
So, g(f(0)) = 6(0) - 3
= 0 - 3
= -3
So, g(f(0)) = -3
2. How to compute f(f(2))?To compute the function f(f(2)), we first compute f(f(x)).
So, f(f(x)) = 2(f(x)) - 1
= 2(2x - 1) - 1
= 4x - 2 - 1
= 4x - 3
So, f(f(2)) = 4(2) - 3
= 8 - 3
= 5
So, f(f(2)) = 5
3. How to compute f(g(x))?To compute the function f(g(x)), since we have
f(x) = 2x - 1 and g(x) = 3x.So, f(g(x)) = 2(g(x)) - 1
= 2(3x) - 1
= 6x - 1
So, f(g(x)) = 6x - 1
4. How to compute g(h(x))?To compute the function g(h(x)), Since
g(x) = 3x and h(x) = x² + 1,So, g(h(x)) = 3(h(x))
= 3(x² + 1)
= 3x² + 3
So, g(h(x)) = 3x² + 3
5. How to compute g(h(x))?To compute the function g(f(x)), Since
g(x) = 3x and f(x) = 2x - 1,So, g(f(x)) = 3(f(x))
= 3(2x - 1)
= 6x - 3
So, g(f(x)) = 6x - 3
6. How to compute g(h(x))?To compute the function f(f(x)), Since f(x) = 2x - 1,
So, f(f(x)) = 2(f(x)) - 1
= 2(2x - 1) - 1
= 4x - 2 - 1
= 4x - 3
So, f(f(x)) = 4x - 3
7. How to compute g(g(x))?To compute the function g(g(x)), Since g(x) = 3x
So, g(g(x)) = 3(g(x))
= 3(3x)
= 9x
So, g(g(x)) = 9x
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From the age of a person if two-fifth of his age is subtracted, the result becomes 24 years Find the age of the person.
Answer:
60 years old
Step-by-step explanation:
-First multiply 24 and 5. → 24×5=120
-Then divide it by 2. →. 120÷2=60
what is the estimate square root of 63
State the sign (+ or -) of (a) sin t, (b) cos t and (c) tan t for values of t in the interval below.
Answer:
(a) Choice A + everywhere in (π/2, 3π/4)
(b) Choice A - everywhere in (π/2, 3π/4)
(c) Choice A - everywhere in (π/2, 3π/4)
Step-by-step explanation:
This can be answered by knowing that the interval (π/2, 3π/4) lies in the second quadrant which lies between π/2 and π
π/2 = 90° and 3π/4 = 135° which lies in the second quadrant
If an angle θ lies in the first quadrant, we have the following facts:
sin(θ) is positive
cos(θ) is negative
tan(θ) = sin(θ)/cos(θ) is also negative (+ve divided by -ve is negative)
Therefore sin(t) is positive in the interval (π/2, 3π/4).
Correct choice is A
(b)
cos(t) is negative in the interval (π/2, 3π/4).
Choice A
(c) tan(t) is negative in the interval (π/2, 3π/4).
Choice A
At t = π/2 tan(t) is undefined
need help with 1 and 2
The conversion of the units gives:
NUMBER 1: 75 mi/hr = 36.957 m/s
NUMBER 2: 5d = 432000 seconds
How to convert miles per hour to meters per second?Unit conversion is the process of converting a quantity expressed in one unit of measurement to another unit of measurement. For example, converting a distance measured in meters to feet, or converting a weight measured in kilograms to pounds.
NUMBER 1
1 mile = 5820 feet, 1 feet = 0.3048 meter.
1 hour = 60 minutes = 60 * 60 seconds = 3600 seconds
To convert 75 mi/hr to m/s, we have:
75 mi/hr = (75 * 5820 * 0.3048)m / (60 * 60)s = 36.957 m/s
NUMBER 2
Since we have 24 hours in a day, 60 minutes in 1 hour and 60 seconds in a minute. Thus, 5 days can be written as:
5d = 5 * 24 * 60 * 60 = 432000 seconds
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