if a line passed through (0,0),(1,8),(3,24) and (x,44) what is x?
Answers
Answer: x=5.5
Step-by-step explanation:
First you need to find the slope using the formula \(\frac{y2-y1}{x2-x1}\). Thankfully, we have (0, 0) and (1, 8) as points, which makes it easy to find that the slope is 8.
Once we have the slope, we divide 44 by 8 to get 5.5
Related Questions
a 17 feet ladder is placed against a building. the bottom of the ladder is sliding away from the building at a rate of 5 feet per second. find the rate at which the top of the ladder is slipping down at the instant when the bottom of the ladder is 15 feet from the base of the building.
Answers
The rate at which the top of the ladder is slipping down at the instant when the bottom of the ladder is 15 feet from the base of the building is -75/8 feet per second
The length of the ladder = 17
Consider the length of the base as x and the height is h
The rate at which the ladder is sliding = 5 feet per second
dx/dt = 5
Apply the Pythagorean theorem
x^2 + h^2 = 17^2
h^2 = 289 - x^2
h = \(\sqrt{289-x^2}\)
The rate of change of height with respect to x is
dh/dx = - x / (289 - x^2)^(1/2)
dh/dt = dh/dx × dx/dt
Substitute the values in the equation
= - 15 / (289 - 15^2)^(1/2) × 5
= -15/8 × 5
= -75/8 feet per second
Therefore, the rate of change of height when x = 15 is -75/8 feet per second
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notation: in this course, we will use regular letters as symbols for numbers, vectors, matrices, planes, hyperplanes, etc. you will need to distinguish what a letter represents from the context. recall the dot product of a pair of vectors and : when thinking about and as vectors in -dimensional space, we can also express the dot product as where is the angle formed between the vectors and in -dimensional euclidean space. here, refers to the length, also known as norm, of : what is the length of the vector ?
Answers
The length of a vector 'v' in an n-dimensional Euclidean space is calculated as the square root of the dot product of the vector with itself, or ‖v‖ = \(\sqrt{(v.v)}\) = \(\sqrt{(v1^{2}+v2^{2} +.... + vn^{2} )}\).
The length of a vector 'v' in an n-dimensional Euclidean space is denoted as ‖v‖ and can be calculated asthe vector's dot product with itself, square root:
‖v‖ = \(\sqrt{(v.v)}\) = \(\sqrt{(v1^{2}+v2^{2} +.... + vn^{2} )}\)
So, to find the length of the vector 'v', we simply substitute its components in the above equation.
The length of a vector, also known as its magnitude or norm, is a scalar value that represents the magnitude of the vector in a given space. In the context of an n-dimensional Euclidean space, the length of a vector can be calculated as the square root of the dot product of the vector with itself. This calculation is based on the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares formed by the other two sides' lengths.
In mathematical terms, the length of a vector 'v' in an n-dimensional Euclidean space is calculated as follows:
‖v‖ = \(\sqrt{(v.v)}\) = \(\sqrt{(v1^{2}+v2^{2} +.... + vn^{2} )}\)
where 'v' is the vector, and 'v1', 'v2', ..., 'vn' are its components in the n-dimensional space. The dot product of the vector with itself (v · v) is equivalent to the sum of the squares of its components. The square root of this sum is the final length of the vector.
The length of a vector is an important concept in linear algebra and geometry. It is used to measure the distance between two points in a space, to calculate angles between vectors, to normalize vectors, and for various other mathematical and practical applications.
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The image of point (-1, 7) under a reflection across the y-axis is (-1, -7). *
True
False
Answers
Answer:
False
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
(- 1, 7 ) → (1, 7 )
Answer: True
Step-by-step explanation:
Because since it's getting reflected over the Y-axis it's gonna be all negatives.
Pythagorean Question
A carpenter was asked to build a ramp that is 175 cm long. The height of the ramp is
35 cm. What is the horizontal length of the ramp (side b]? [APP]
175 cm
35 cm
b
Answers
35^2 (1225) + b squared = 175^2 (30,625)
30,625 - 1225 = 29400
square root 29400 = 171.5 cm
select all equations that have infinitely many solution
Answers
Answer:
1, 2
Step-by-step explanation:
1 and two end up being 0=0 solutions (infinite)
3 is 1 solution.
4 is no solutions.
The point of concurrency of the angle bisectors of a triangle is known as_____. a) Incentre. b) Centroid. c) Orthocentre. d) None
Answers
The required final answer is option a) Incentre
What is concurrency of the angle?The point of concurrency of the angle bisectors of a triangle is known as the "Incentre".
It is the center of the circle inscribed within the triangle, which is equidistant from all three sides of the triangle.
The incentre is the point where the angle bisectors of a triangle intersect, forming the incircle, which is the largest circle that can be inscribed inside the triangle.
The incentre is always within the triangle and is equidistant from all three sides of the triangle, making
it a useful tool in construction and design applications. In summary, the incentre is the center of the incircle of a triangle, and it is the point where the angle bisectors of the triangle intersect.
Thus, required answer is "Incentre".
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PLEASE HELP!!!!!!!!! WILL MARK BRAINLIEST IF CORRECT
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
A baseball coach takes her team out for pizza every time they win a game. Not everyone can come each time, so she orders the pizzas based on how many players are coming. After last week's victory, she bought 3 small pizzas and 4 large pizzas, the perfect amount for the 19 players going out for pizza. This week, there were 25 players going, so she ordered 5 small pizzas and 5 large pizzas, which was also just the right amount. How many people does each size of pizza feed?
Each small pizza feeds
people, and each large pizza feeds
people.
Answers
1 small pizza and 4 large pizza feeds people according to the system of equations.
Let the number of small pizza be x and the number of large pizza be y.
So, we get the two equations as:
3 x + 4 y = 19 ...(1)
5 x + 5 y = 25 ...(2)
Taking 5 common from equation 2, we get that:
x + y = 5
x = 5 - y
Put it in equation 1, we get that:
15 - 3 y + 4 y = 19
15 + y = 19
y = 4
x = 5 - 4 = 1
Therefore, we get that, 1 small pizza and 4 large pizza feeds people according to the system of equations.
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i always get it wrong.
Answers
The situations represented by 25/9 are "Melanie equally shares 25 meters of paper to create 9 banners" and "Joe makes 9 equal servings from a 25 ounce bag of peanuts".
What is an expression?Expression in mathematics is combination of variables with the use of operations and given rules. It can be in the form of equation, numbers etc.
We have the expression 25/9.
That means 25 divided in 9 equal parts.
Now the expression 1,
Melanie equally shares 25 meters of paper to create 9 banners.
We have to divide 25 meters of paper into 9 equal banners.
The above expression can be written as a mathematical term,
and that is 25/9.
Now the expression 2,
Quill gives away 9 baseball cards from a pack of 25.
In mathematical terms; 25 - 9.
Now the expression 3,
George invites 25 kids and 9 adults to his birthday party.
That means, the total 25 + 9 = 34 people
In mathematical terms : 25 + 9
Now the expression 4,
Becca creates 9 rows with 25 buttons each.
That means, each row has 25 buttons.
So the total 9 rows have 9 x 25 buttons.
In mathematical terms : 9 x 25
Now the expression 5,
Joe makes 9 equal servings from a 25 ounce bag of peanuts.
That means 25 ounce bag of peanuts equally divided into 9 parts.
In mathematical terms : 25/9
Therefore, expression 1 : Melanie equally shares 25 meters of paper to create 9 banners and expression 5: Joe makes 9 equal servings from a 25 ounce bag of peanuts, represented by 25/9.
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Sue and Gwen each have large collections of CDs. Sue has twice as many CDs as Gwen. Together the girls have 96 CDs. Which equation could be used to find the number of CDs, x, that Gwen has?
Answers
Answer:
3x=96
Step-by-step explanation:
From the information given, you can write the following:
a+x=96 (1)
a=2x (2)
where a is the number of CDs that Sue has and x is the number of CDs that Gwen has.
You can replace 2 in 1 and you would have the following:
2x+x=96
3x=96
From this, you can isolate x to find its value:
x=96/3
x=32
According to this, the equation that could be used to find the number of CDs, x, that Gwen has is: 3x=96.
Use the Venn diagram to calculate probabilities.
Circles A, B, and C overlap. Circle A contains 12, circle B contains 11, and circle C contains 4. The overlap of A and B contains 5, the overlap of B and C contains 3, and the overlap of C and A contains 6. The overlap of the 3 circles contains 8.
Which probabilities are correct? Select two options.
Answers
In probability theory, a Venn diagram is a diagrammatic representation of sets that shows all possible logical relations between them. Venn diagrams are widely used in probability and statistics to visualize the relationship between different sets of data.
The given Venn diagram shows the relationship between three sets, A, B, and C. In order to calculate probabilities using a Venn diagram, we need to know the number of elements or members in each set, as well as any overlapping regions.
We can then use these numbers to calculate the probability of different outcomes.Let's consider two possible probabilities from the given Venn diagram:1.
The probability that an element is in set A and set B but not in set C is 0.1/0.5 = 0.22. The probability that an element is in set B or set C but not in set A is 0.2/0.6 = 1/3The first probability can be calculated by dividing the number of elements in the overlapping region of sets A and B (which is 0.1) by the total number of elements in set B (which is 0.5).
This gives us a probability of 0.22 or 22%.The second probability can be calculated by dividing the number of elements in the union of sets B and C (which is 0.2) by the total number of elements in either set B or set C (which is 0.6). This gives us a probability of 1/3 or approximately 33%.
Therefore, the correct probabilities are:1.
The probability that an element is in set A and set B but not in set C is 0.1/0.5 = 0.22.
The probability that an element is in set B or set C but not in set A is 0.2/0.6 = 1/3
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what is $7.00-19 cent?
Answers
Answer:
$6.81 or 681 US Cents
Step-by-step explanation:
100 - 19 = 81
7 - 1 = 6
$7.00 - .19 = $6.81
or 681 US Cents.
In the given diagram , TY is a tangent to the circle TVS . If <SVT = 48° and |VS| = |ST| . What is < VTY.
Answers
Answer:
84°Step-by-step explanation:
∠VTY is the tangent chord angle
Tangent chord angle is the half of the intercepted arc∠TSV is the inscribed angle.
Inscribed angle is the half of the intercepted arcSince both of the mentioned angles refer to same arc, they are of same value.
∠VTY = ∠TSVΔTVS is isosceles as VS = ST, therefore the opposite angles are same.
m∠T = m∠V = 48°The measure of angle S
m∠S = 180° - 2*48° = 84°The required angle
m∠VTY = 84°Answer:
∠VTY = 84°
Step-by-step explanation:
because ΔTSV is isosceles (ST = SV) then ∠VTS = ∠SVT = 48°
Then ∠VST = 84° (180 - 48 - 48 = 84)
Well, I'm going back to the picture is worth a thousand words again.
Sketch attached:
A line from S to the center bisects ∠VST into two 42° angles.
A line from T to the center forms a 42° angle with line ST.
48°-42° = 6° = angle from perpendicular line CTR to line VT.
90° - 6° = 84° for ∠VTY
Suppose Lakeside Marina charges a $35 rental fee for a boat in addition to charging $15 per hour. The linear function is modeled by f(x)=15x + 35, where f(x) represents the total cost of renting the boat, and x represents the number of hours the boat was rented. What is the cost of renting the boat for 3 hours?
A.
$80
B.
$10
C.
$10
D.
$50
Answers
Answer:
A. $80
Step-by-step explanation:
Since f(x)=15x + 35, we know that x represents number or hours. By substituting x as 3 we get 15(3) + 35 = 80.
lacy draws a '10' from a standard deck of 52 cards. without replacing the first card, she then proceeds to draw a second card and gets a '4'. are these events independent? input yes or no
Determine the probability of drawing a spade and then a club without replacement.
Write your answer in decimal form, rounded to four decimal places as needed.
Answer =
Answers
The first two events are not independent, with a probability P = 0.00603
The second pair of events is independent, and the probability is P = 0.0625
First, all the cards on the deck have the same probability of being randomly drawn, which will be p = 1/52.
A) Now, if Lacy first draws a spade card, now the number of cards in the deck are less (now there are 51 cards on the deck). So the probability of drawing now a spade is larger than before. Then the first two events are not independent.
The probability of drawing a 10 card at first is:
P = 4/52 (because there are 4 10's and a total of 52 cards).
The probability of drawing a 4's after is:
Q = (4/51)
The joint probability is the product of the individual probabilities, this will give: p = P*Q = (4/52)*(4/51) = 0.00603
B) Now we replace the first card, then the events are now independent, as the probability of drawing a spade after the first draw is not changed (because the total number of cards will be 52).
The probability of drawing a spade is:
P = 13/52
Now we replace the spade card drawn.
The probability of drawing a club will be:
Q = 13/52
The joint probability is:
p = P×Q = (13/52)² = 0.0625
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Lyle and Shaun open savings accounts at the same time. Lyle deposits $100 initially and adds $20 per week. Shaun deposits $500 initially and adds $10 per week. Lyle wants to know when he will have the same amount in his savings account as Shaun.
Part A: Write two equations to represent the amounts of money Lyle and Shaun have in their accounts
f(x=
g(x)=
Part B: to solve the system you will make f(x)=g(x)
Answers
A. The equations for the amounts of money Lyle and Shaun have in their accounts are represented as:
f(x) = 20x + 100
g(x) = 10x + 500
B. When f(x) = g(x), x = 40.
How to Write the Equation of a System?A linear equation can be written in slope-intercept form y = mx + b. Here, the value of m is the unit rate or slope, while the value of b is its y-intercept or initial value.
Part A:
Equation for Lyle:
y-intercept / initial value (b) = $100
Slope / unit rate (m) = $20
To write the equation, substitute m = 20 and b = 100 into f(x) = mx + b:
f(x) = 20x + 100.
Equation for Lyle:
y-intercept / initial value (b) = $500
Slope / unit rate (m) = $10
To write the equation, substitute m = 10 and b = 500 into g(x) = mx + b:
g(x) = 10x + 500.
Part B: To solve the system, we would do the following:
20x + 100 = 10x + 500
20x - 10x = -100 + 500
10x = 400
x = 400/10
x = 40
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I need help for 5 questions and need a answer for them appreciate them
Answers
Answer:
Step-by-step explanation:
The two prism below are similar. What is the value of x?
Answers
Answer:
\(x = 4\)
Step-by-step explanation:
Since the two prisms are similar, the ratios of each of the sides of the larger prism to the corresponding sides of the smaller prism must be the same
\(\dfrac{16}{4} = \dfrac{24}{6} = \dfrac{x}{1} = 4\)
So each side of the larger prism is 4 times the corresponding side of the smaller prism
\(\dfrac{x}{1} = 4\\\\x = 4\)
I really need help please
Fill in this outcome (sample space) for this table showing the roll of a 6 sided dice and then the toss of a coin Coin Toss heads Tails Dice Roll What is P(4, T) What is P(odd, H)
Answers
Answer:
Benidorm quiz
1. Where is Benidorm holiday resort located?
JORDAN
2. What is the average temperature of Benidorm in summer?
26 C
3. Before 1950s Benidorm was a small ___FISHING______ village.
4. Why did the town council encourage tourism in Benidorm?
TO VISIT BENIDORM
5. How many hotels were found in Benidorm in 1959?
6. Explain package holidays as they were used in Benidorm
7. Give three reasons why Benidorm is an excellent tourist resort
(a)
(b)
©
8. State four tourist attractions at Benidorm
Step-by-step explanation:
Benidorm quiz
1. Where is Benidorm holiday resort located?
JORDAN
2. What is the average temperature of Benidorm in summer?
26 C
3. Before 1950s Benidorm was a small ___FISHING______ village.
4. Why did the town council encourage tourism in Benidorm?
TO VISIT BENIDORM
5. How many hotels were found in Benidorm in 1959?
6. Explain package holidays as they were used in Benidorm
7. Give three reasons why Benidorm is an excellent tourist resort
(a)
(b)
©
8. State four tourist attractions at Benidorm
Olivia has a beaded necklace business. She can make 12 necklaces in 2 hours. How long will it take her to make 9 necklaces?
Answers
Answer:
1.5hours
Step-by-step explanation:
PLEASEEE HELP WILLL GIVE BRAINLEAST!!!!!!
Which equation models the trend line?
A. y = –1.3x + 2
B. y = 1.3x + 2
C. y = –1.3x – 2
D.y = 1.3x – 2
Answers
Answer:
B. y = 1.3 + 2
Step-by-step explanation:
The slope is positive, and the y intercept is at positive 2.
Create and use a model, to find the distance from point Q to the ground when the angle created by the left side of the seating board and the central support is 80°. Show your work or explain your answer. Round your final answer to the nearest tenth of a foot. RT=1.7 ft
Answers
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The distance between the point Q and the ground is, h-[L cos(80°)].
Since, The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
tan θ = perpendicular / base
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The Base is the adjacent smaller side of the angle θ.
Let the height of the support be h and the height between the point q and the ground is x. Also, the distance between point Q and the support of the seesaw is L.
Now if we look at the ΔQAR, the measure of the ∠QRA is 80°, therefore, the sine of ∠QRA can be written as,
cos θ = base / perpendicular
cos ∠QRA = AR/QR
cos ∠QRA = (h - x) / L
L × cos ∠QRA = (h - x)
x = h - L cos ∠QRA
Hence, the distance between the point Q and the ground is,
⇒ h-[L cos(80°)].
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Maddy and her cousin work during the summer for a landscaping company. Maddy's cousin has been working for the company longer, so her pay is 30% more than Maddy's. Last week, Maddy's cousin worked 27 hours, and Maddy worked 23 hours. Together, they earned $493.85. What is Maddy's hourly pay?
Answers
Find the area of the shaded figure. To do so, subtract the area of the smaller
square from the area of the larger square,
Square
(x²-3)
x meters
meters
The area of the shaded region is
(Simplify your answer. Do not factor)
Answers
Answer:
x⁴ - 8x² + 9
Step-by-step explanation:
The Area of the smallest square is A1 = x . x = x²
The Area of the second square is A2 = ( x² - 3 )(x² - 3)
A2 = x⁴ - 3x² - 3x² + 9
A2 = x⁴ - 6x² + 9
The Area of the Shaded shape is A2 - A1
x⁴ - 6x² + 9 - x²
x⁴ - 8x² + 9
The value of the expression 2^3+3^2-3times4-5^2/5+(7times4) is
Answers
The value of expression will be 28, using BODMAS rule in mathematics.
What is BODMAS rule ?
BODMAS stands for :
B: Brackets
O: Of
D: Division
M: Multiplication
A: Addition
S: Subtraction
BODMAS is an acronym to help children remember the order of mathematical operations.
The BODMAS rule states that mathematical expressions with multiple operators need to be solved from left to right in the order of BODMAS.
If exponential function is given then solve before division .
The given expression :
2^ 3+3^ 2-3*4-5^2/5+(7*4)
Using BODMAS :
solving braces : 2^3+3^2-3*4-5^2/5+28
solving exponential function : 8+9-3*4-25/5+28
solving division and multiplication: 8+9-12-5+28
Solving addition and subtraction: 28.
So, the solution is 28.
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Which of the following expression(s) are equivalent to 9? Select all that apply.
A. 3²
B. 4-(-5)
C. √-81
D. √81
Answers
9 is represented by the term, which is 3². A mathematical expression is composed of numbers, variables, and functions .
what is expression ?You can multiply, halve, add, or take something away in mathematics. An expression is put together as follows: Expression, numeric value, and math operator A mathematical expression is composed of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Contrasting phrases and expressions is possible. An algebraic expression is any mathematical statement that has variables, quantities, and an arithmetic operation. As an illustration, the phrase 4m + 5 consists of the phrases 4m and 5, as well as the given equation's variable m, each of which are split by the algebraic sign +.
given
As 3 * 3 equals 9,
As 3 * 3 equals 9, the formula 3²
equals 9 and 3² is a perfect square of 9.
9 is represented by the term, which is 3². A mathematical expression is composed of numbers, variables, and functions.
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Amy is baking muffins each baking tray can hold 6 muffins a. If Amy bakes 4 tray of muffins how many muffins will she have in all? b. the corner bakery produced 10 time as many muffins, how many muffins did the bakery produce ? c. If the Corner Bakery bakes the muffin in box of hundreds how many box of hundred could they make
Answers
Answer:
Explanation:
Each baking tray can hold 6 muffins.
(a) If Amy bakes 4 tray of muffins, the number of muffins she will have in all will be:
\(\begin{gathered} =4\times6 \\ =24\text{ muffins} \end{gathered}\)(b)The corner bakery produced 10 times as many muffins
The number of muffins produced by the bakery will therefore be:
\(\begin{gathered} =10\times24 \\ =240\text{ muffins} \end{gathered}\)month? rRound vour answer to the nearest cent?) 5
Answers
The monthly payment required to amortize a loan of $40,000 over 15 years, with an interest rate of 6% per year, and monthly compounding, is approximately $331.13.
To calculate the monthly payment, we can use the formula for the amortization of a loan, which is:
Monthly Payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1),
where P is the principal amount (loan amount), r is the monthly interest rate, and n is the total number of payments.
Given:
Principal amount (P) = $40,000,
Annual interest rate = 6%,
Number of years (n) = 15.
First, we need to convert the annual interest rate to a monthly interest rate. Since interest is compounded monthly, the monthly interest rate (r) is calculated by dividing the annual interest rate by 12 and converting it to a decimal:
Monthly interest rate (r) = 6% / 12 / 100 = 0.005.
Next, we calculate the total number of payments (n) by multiplying the number of years by 12 (since there are 12 months in a year):
Total number of payments (n) = 15 years * 12 months/year = 180.
Now we can plug these values into the formula to calculate the monthly payment:
Monthly Payment = $40,000 * (0.005 * (1 + 0.005)^180) / ((1 + 0.005)^180 - 1).
Using a calculator or spreadsheet, we find that the monthly payment is approximately $331.13.
Therefore, the monthly payment required to amortize the loan of $40,000 over 15 years, with a 6% annual interest rate and monthly compounding, is approximately $331.13.
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What monthly payment is required to amortize a loan of $40,000 over 15 years if interest at the rate of 6%/year is charged on the unpaid balance and interest calculations are made at the end of each month?
I need help and I will give five stars and a big thank you comrades
Answers
Answer:
A.
Step-by-step explanation:
A way to find the equation of the graph is to find the solutions.
On the graph, the solutions are where the function intersects the x-axis. That would be where x = -2, x = 1, and x = 3.
In the equations, you will need to find factors when the x is inputted, the factor equals 0. For example, one of the factors is (x + 2). This is because x + 2 = 0, so x = 0 - 2, so x = -2. So, the three factors are (x + 2), (x - 1), and (x - 3).
The correct equation is A.
Hope this helps!
in the analysis of variance procedure (anova), factor refers to:____.
Answers
Answer:
The independent variable.
i need help on this, thanks
Answers
Answer:
x=15, y=7
Step-by-step explanation:
Angles that form a linear pair are supplementary, so:
\(2(5x-5)+3x-5=180 \\ \\ 10x-10+3x-5=180 \\ \\ 13x-15=180 \\ \\ 13x=195 \\ \\ x=15 \\ \\ \\ \\ 5y+5+20y=180 \\ \\ 25y+5=180 \\ \\ 25y=175 \\ \\ y=7\)