Find the distance between X(-2,4) and Y(6,1)
Answers
Answer:
Exact Distance = \(\boldsymbol{\sqrt{73}}\) units
Approximate Distance = 8.544 units
====================================================
Explanation:
I'll relabel the points as A and B, and I'll be using the distance formula.
\(A = (x_1,y_1) = (-2,4) \text{ and } B = (x_2, y_2) = (6,1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-2-6)^2 + (4-1)^2}\\\\d = \sqrt{(-8)^2 + (3)^2}\\\\d = \sqrt{64 + 9}\\\\d = \sqrt{73}\\\\d \approx 8.544\\\\\)
The exact distance is \(\sqrt{73}\) units.
The approximate distance is roughly 8.544 units.
Round the approximate value however your teacher instructs.
Related Questions
Find the common difference of the sequence 4, 12, 20, ....
Answers
8
In this pattern, we have 4 12 then 20.
We can see that the difference 4 and 12 is 8.
Since the difference between 12 and 20 is also 8, the common difference of the sequence is 8.
The number line below shows information
about a variable, m.
Select all of the following values that m
could take:
-2, 4, -3.5, 0, -5, -7
-5 -4 -3 -2 -1 0 1 2 3 4 5
m
Answers
From the given number line, the variable "m" could take the values of -2, -3.5, 0, and -5
To determine which values the variable "m" could take from the given number line, we need to identify the points or intervals on the number line that correspond to the possible values of "m".
Looking at the number line, we can see the following values:
-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
From this list, the values that "m" could take are:
-2, -3.5, 0, -5
These values are present on the number line, indicating that they are possible values for "m".
Therefore, the variable "m" could take the values -2, -3.5, 0, and -5 from the given number line.
It's important to note that the values -7 and 4 are not present on the number line, so they are not possible values for "m" based on the information provided.
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need help asap please
Answers
Ali's strategy is essentially the same as Mary's strategy. Both strategies estimate the HST as 15% of the price. However, Mary's strategy involves taking half of 10% of the price.
How to explain the strategies usedMary suggests estimating the HST in Ontario as finding 10% of the price, taking half of this answer and adding the two. Ali proposes finding 10% of the price, then 5% of the price and adding the two answers.
Their strategies differ in the way they approach finding the estimate, but both methods can be used to arrive at the same result.
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The HST in Ontario is 13%, which can be estimated using 15%. Mary tells Ali that it can be estimated as: find 10% of the price, take a half of this answer and add the two. Ali tells Mary that he thinks they should find 10% of the price, then 5% of the price and add the two answers. Compare their strategies.
Mario constructs a scale model of a building with a rectangular base. His model is 4.2 inches in length and 2 inches in width. The scale of the model is 1 inch = 15 feet.
What is the actual area, in square feet, of the base of the building?
Answers
The actual base of the building is 1890 square feet.
What is a rectangle?A rectangle is a two-dimensional figure with length and width.
The area of a rectangle is Length x width.
We have,
1 inch = 15 feet
Rectangular base:
Length = 4.2 in
Width = 2 in
So,
4.2 in = 4.2 x 15 feet = 63 feet
2 in = 2 x 15 = 30 feet
Now,
The actual base of the building.
= 63 x 30
= 1890 square feet
Thus,
1890 square feet.
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What is the total number of digits required in numbering the pages of a book which has 1210 pages?
Answers
Answer:
3693 digits
Step-by-step explanation:
Answer:
3733
Step-by-step explanation:
9x1=9
90x2=180
900x3=2700
211x4=844
9+180+2700+844=3733
A train travels at 80 miles per hour. An equation can be written that compares the time (t) with the distance (d). What is the domain and range?
1. The domain is distance (d) and the range is time (t).
2. The domain is time (t) and the range is distance (d).
3. The domain is time (t) and the range is 80.
4. The domain is 80 and the range is time (t).
Answers
The required answer is the domain is time (t) and the range is a distance (d) i.e. Option 2.
What are domain and range?
The value range that can be plugged into a function is known as its domain. In a function like f, this set represents the x values f(x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
From the given question, and the above definition of domain and range,
the time (t) acts as an x-values or input value and the distance (d) acts as a y-value or output value
Hence, the domain is time (t) and the range is a distance (d) i.e. Option 2.
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A person on a moving sidewalk travels 12 feet in 4 seconds. The moving sidewalk has a length of 120 feet. How long will it take to move from one end to the other?
Answers
Answer:
40 seconds
Step-by-step explanation:
120/12 = 10
10*4 = 40
THEREFORE 40 seconds to walk 120 feet at that speed
How many coupons can be generated
Answers
The number of coupon codes that can be generated is given as follows:
247,808 coupon codes.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.
This can be extended to more than two events, where the number of ways to do all the events is the product of the number of ways to do each individual event, according to the equation presented as follows:
\(N = n_1 \times n_2 \times \cdots \times n_n\)
The codes are composed as follows:
Two letters -> each with 22 options, as letters can be repeated.Three digits -> each with 8 options, as digits can also be repeated.Thus the total number of codes is obtained as follows:
N = 22² x 8³
N = 247,808 coupon codes.
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Which of the following are factor pairs for 54?select all that apply.
Answers
Answer:
The Pair Factors of 54 are (1, 54), (2, 27), (3, 18), and (6, 9) and its Prime Factors are 1, 2, 3, 6, 9, 18, 27, 54.
Step-by-step explanation:
hope this helped:)
brainliest for the brains........................
The Pair Factors of 54 are (1, 54), (2, 27), (3, 18), and (6, 9) and its Prime Factors are 1, 2, 3, 6, 9, 18, 27, 54.
Here, we have,
The factors of 54 are the numbers, that can divide 54 completely or evenly. When a pair of factors are multiplied together to produce the 54, then they are said to be pair factors. The factors divide the number completely. Hence, these factors cannot be a fraction.
Factors of 54: 1,2,3,6,9,18,27 and 54
Factor pairs of the number 54 are the whole numbers which are not a fraction or decimal number.
To find the factors of a number, 54, we will use the factorization method.
To find factors of 54, we have to divide 54 by all natural numbers from 1 to 54.
54 ÷ 1 = 54
54 ÷ 2 = 27
54 ÷ 3 = 18
54 ÷ 6 = 9
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manager states that all 80 crates can be packed in a 2m x 2m area e store room. (Assume that the height of the store room is adequate stacked crates) y if this statement is correct. Show all your calculations.
Answers
Note that based on the volume calculations, the manager's statement is NOT correct. The given area of 2m × 2m is insufficient to store all 80 crates.
How is this so ?To verify if the manager's statement is correct, we need to derive the volume of each crate and the total volume required to store all 80 crates.
Volume = Length × Width × Height
Recall that
Length (L) = 690 mm
Width (W) = 445 mm
Height (H) = 180 mm
Thus, the Volume of one crate is
Volume = 690 mm × 445 mm × 180 mm
Converting mm to meters we have,
Volume = (690 / 1000) × (445 / 1000) × (180 / 1000)
= 0.690 × 0.445 × 0.180
= 0.055269 m³
Next , we calculate the total volume required for 80 crates as
Total Volume = Volume of one crate × Number of crates
= 0.055269 m³ × 80
= 4.42152 m³
Recall that the manager stated that all 80 crates can be packed in a 2m × 2m area in the store room.
Since area of store room is
Area = 2 m × 2 m
Area = 4 m²
Comparing the total volume required (4.380208 m³) with the available area (4 m²), we see that the volume exceeds the area. Tus, the manager's statement is incorrect.
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Full question:
Manager states that all 80 crates can be packed in a 2m x 2m area e store room. (Assume that the height of the store room is adequate stacked crates) y if this statement is correct. Show all your calculations.
See attached Image.
A circle is an assortment of focuses which are all on the periphery of the circle. Assuming that you use polynomial math and (x-h)^2 + (y-k)^2 = r^2 and the data contained in the directions (x,y) of every city, you can track down h, k and r. Then, at that point, r is the (equivalent) distance between every city and the focal point of the circle, where the new pinnacle will be assembled.
How would you make this construction to ensure that the location of the cities lie exactly on the circle?
Answers
Answer:
I don't understand the question
Answer: This is really hard I don't know
Step-by-step explanation:
Is 7,301,771 divisible by 6?
Answers
\(\huge\boxed{Hi\: there!}\)
\(\huge\mathfrak{Question:}\)
Is 7,301,771 divisible by 6?
\(\huge\mathfrak{Answer:}\)
No.
Remember, divisible by means the given number can be divided by a number without a remainder.
If we divide 7,301,771 by 6, we will get a remainder.
\(\huge\boxed{Therefore,\: 7,301,771 \: isn't \: divisible\: by 6.}\)
\(\huge\mathfrak{Good\: luck!}\\\huge\bold {~CheerfulTeen}\)
5. A map is drawn to a scale of 1: 20 000. (a) The perimeter of a lake is 2.5 km. Find, in cm, the perimeter of the lake on the map. (b) The area of the lake on the map is 12.5 cm². Find, in km², the actual area of the lake.
Answers
Step-by-step explanation:
2.5 km = 250000 cm
250000 cm /20000 = 12.5 cm on the map
12.5 cm ^2 x 20 0000 x 20 000 = 5 000 000 000 cm^2 = 500 000 m^2
Please see attached picture.
Need help answering.
Answers
In the given graph, the x-intercepts are (2,0) and (6,0).
The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.
The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).
The sign of the leading coefficient is positive, since it is 1/2.
To find the equation of the quadratic function, we start by using the vertex form:
\(y = a(x - h)^2 + k\)
where (h, k) is the vertex. Plugging in the given vertex (4,-2), we get:
\(y = a(x - 4)^2 - 2\)
Next, we use the other two points to find two additional equations:
\(6 = a(8 - 4)^2 - 2 (plugging in (8,6))\\0 = a(2 - 4)^2 - 2 (plugging in (2,0))\)
Simplifying these equations, we get:
\(6 = 16a - 2\\8a = 4 -- > a = 1/2 \\0 = 4a - 2 \\4a = 2 -- > a = 1/2 \\\)
So the equation of the quadratic function is:
\(y = (1/2)(x - 4)^2 - 2\)
Now, we can answer the questions:
The y-intercept is the point where the graph intersects the y-axis. To find it, we set x = 0 in the equation:
\(y = (1/2)(0 - 4)^2 - 2 = 6\)
So the y-intercept is (0,6).
To find the x-intercepts, we set y = 0 in the equation:
\(0 = (1/2)(x - 4)^2 - 2\)
Simplifying, we get:
\((x - 4)^2 = 4\\ - 4 = \pm 2 \\= 2, 6\)
So the x-intercepts are (2,0) and (6,0).
The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.
The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).
The sign of the leading coefficient is positive, since it is 1/2.
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The question above is what I need to know
Answers
Answer:
a
Step-by-step explanation:
Answer:
angles 1 and 3 are supplementary
Math homework help exponents
Answers
Answer + Step-by-step explanation:
\(\frac{5^{10}}{5^{5}} =5^{10-5} = 5^5\)
\(\text{used property :} \ \ \ \frac{a^{m}}{a^{n}} =a^{m-n}\)
_______________________
\((4^8)^3 = a^{8 \times 3}=a^{24}\)
\(\text{used property :} \ \ \ (a^n)^m = a^{n \times m}\)
_______________________
\(10^{-4}=\frac{1}{10^{4}} \ \text{not} \ \frac{1}{4^{10}}\)
_______________________
15⁶ × 15³ = 15⁶⁺³ = 15⁹
_______________________
Recall : If a ≠0 ⇒ a⁰ = 1
Then
Since 6⁸ ≠ 0 ⇒ (6⁸)⁰ = 1
The square root of the cube of 4 is equal to
3 or 4 or 16 or 8 or 2
Answers
Answer:
Step-by-step explanation: 1.587401052
Answer:
8
Step-by-step explanation:
this means
\( \sqrt{ {4}^{3} } \)
4³ = 4×4×4 = 64
the square root of 64 is 8.
If f(x) = 2x and g(x) = 5x + 2, what is (f + g)(x) when x = 3?
Answers
Answer:
f÷g=2x+5x+2=7x+2
x=3
7×3+2=21+2=23
The value of (f + g)(x) when x = 3, if f(x) = 2x and g(x) = 5x + 2, is 23.
What is function?The function is a relationship between a set of potential outputs and a set of possible inputs, where each input has a single relationship with each output. This means that if an object x is present in the set of inputs (also known as the domain), then a function f will map that object to exactly one object f(x) in the set of potential outputs (called the co-domain).
Given:
f(x) = 2x and g(x) = 5x + 2
Calculate (f + g)(x) as shown below,
f(x) + g(x) = 2x + 5x +2
f(x) + g(x) = 7x + 2
Put x = 3
f(3) + g(3) = 7 × 3 + 2
f(3) + g(3) = 23
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7.
The transformation described below adds 1 to the x-coordinate and doubles the y-coordinate of any given point.
(x,y) → (x + 1, 2y)
2
What is the effect of this transformation on distance and angle measure?
A. It preserves angle measure but does not preserve distance.
B. It preserves neither distance nor angle measure.
C. It preserves both distance and angle measure.
D
It preserves distance but does not preserve angle measure.
Answers
Answer: make me brainlist
Step-by-step explanation: CCCCCCC
A line passes through the points (-4,3) and (0,0). What is the slope of the line?
Answers
Answer:
slope = -0.75
Step-by-step explanation:
In order to calculate the slope of a line given the coordinates of two points, we can use the following formula:
\(\boxed{m = \frac{y_2 - y_1}{x_2 - x_1}}\),
where:
m ⇒ slope
\((x_1, y_1)\) , \((x_2, y_2)\) ⇒ known coordinates.
Substituting values into the formula:
\({m = \frac{0 - 3}{0 - (-4)}}\)
⇒ \(-\frac{3}{4}\)
⇒ \(\bf -0.75\)
∴ The slope of the line is -0.75.
Given f(x)=x^2+6x and g(x)=4 x^2, find fg. fg(x)=
Answers
The composite function f·g(x) is 4x⁴+24x³.
The given functions are f(x)=x²+6x and g(x)=4x².
We need to find f·g(x).
We know that, f·g(x)=f(x)×g(x)
Here, f·g(x)=(x²+6x)×4x²
= x²×4x²+6x×4x²
= 4x⁴+24x³
Therefore, the composite function f·g(x) is 4x⁴+24x³.
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PLEASE HELP ME ON QUESTION ASAP!!
IF YOU HAVE A TOPIC LIST IN YOUR EXAMS AND IT SAYS AVERAGES AND THE RANGE ARE YOU GOING TO BE HAVING MEAN AND RANGE IN YOUR TEST OR MEAN, RANGE MODE, MIDPOINT BASICALLY ALL OF IT ? IF ANSWERS CORRECT ILL RATE YOU FIVE STARS, GIVE YOU A THANKS AND MAYBE EVEN BRAINLIEST (sorry for caps)
Answers
Answer:
Step-by-step explanation:
Typically yes you need to know
Mean
Median
Mode
and Range
Mean = average, add all numbers then divide by how many
Median = midpoint, middle number. Be sure to list numbers from small to large if there are 2 middle numbers (this happens when there are an even amount), take the average of the 2 middle numbers
Mode = numbers that occurs the most in the list of numbers
Range = This is the largest number minus the smallest number.
HELP PLEASE I DONT KNOW WHAT TO DO I FORGOT PLEASE HELP
Answers
Answer:
B.
Step-by-step explanation:
The answer is B. If you go down from the y intercept 2 times, and then to the right 3 times, you get to the x intercept.
Answer: y = -2/3x + 2
Step-by-step explanation:
The graph shows a constant negative slope and also has a y-intercept.
The y-intercept is the point that intersects the y axis. We see that the point (0,2) intersects the y- axis, and we can use the positive value 2 at the end of equation of a line: y = mx + b
# = number
The slope is rise/run, or the # of y/# of x -> 2/3
since the slope is going downward, the slope would be negative -> -2/3
So the equation of the line is : y = -2/3x + 2
The instructor noted the following scores on the last quiz of the semester for 8 students. Find the range of this data set 59,61,83,67,81,80,81,100
Answers
answer: the range is 41.
to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.
then we subtract the minimum from the maximum.
59 - 100 = 41.
Helppppp pleaseeeeeeee
Answers
Answer:
74 cm squared
Step-by-step explanation:
because each triangle will be 7, and each rectangle will be 20. (7*2)+(3*20)=74
The explanation is:
Congruence - ASA criterion problemIll send a picture of the question
Answers
ASA-Congruence: If any two angles and the side included between the angles of one triangle are equivalnet to the corresponding two angles and side included between the angles of a second triangle, then the two triangles are congruent.
In the given diagram you have a side and a angle marked as equal, then to have a congruence by ASA the diagram needs to mark that the angle N and angle Q (angles that make the side marked as equal be the included side) are equal:
\(\angle N\cong\angle Q\)Answer: tick marks showing that angle N is congruent to angle Q (option D)Helppppppppp meeeeee
Answers
Answer:
A. x = 5 or 7
B. these are zeros of the quadratic
Step-by-step explanation:
A) To factor this equation, we look for factors of +35 that have a total of -12. We know that ...
35 = (-1)(-35) = (-5)(-7)
The latter factor pair has a total of -12, so we can use those in the binomial factors:
(x -5)(x -7) = 0
The solutions are the values of x that make these factors be zero:
x = 5 or x = 7
__
B) The graph of the quadratic on the left of the equal sign is shown in the attachment. The solution values are the values of x where that graph crosses the x-axis, where the quadratic is equal to 0. This should come as no surprise, since we're solving the equation x^2 -12x +35 = 0.
I need help with this differential equation.
Answers
(i) The partial fraction decomposition of\(100/(x^7 * (10 - x))\) is\(100/(x^7 * (10 - x)) = 10/x^7 + (1/10^5)/(10 - x).\) (ii) The expression for t in terms of x is t = 10 ± √(100 + 200/x).
(i) To express the rational function 100/(\(x^7\) * (10 - x)) in partial fractions, we need to decompose it into simpler fractions. The general form of partial fractions for a rational function with distinct linear factors in the denominator is:
A/(factor 1) + B/(factor 2) + C/(factor 3) + ...
In this case, we have two factors: \(x^7\) and (10 - x). Therefore, we can express the given rational function as:
100/(\(x^7\) * (10 - x)) = A/\(x^7\) + B/(10 - x)
To determine the values of A and B, we need to find a common denominator for the right-hand side and combine the fractions:
100/(x^7 * (10 - x)) = (A * (10 - x) + B * \(x^7\))/(\(x^7\) * (10 - x))
Now, we can equate the numerators:
100 = (A * (10 - x) + B * \(x^7\))
To solve for A and B, we can substitute appropriate values of x. Let's choose x = 0 and x = 10:
For x = 0:
100 = (A * (10 - 0) + B * \(0^7\))
100 = 10A
A = 10
For x = 10:
100 = (A * (10 - 10) + B *\(10^7\))
100 = B * 10^7
B = 100 / 10^7
B = 1/10^5
Therefore, the partial fraction decomposition of 100/(\(x^7\) * (10 - x)) is:
100/(\(x^7\) * (10 - x)) = 10/\(x^7\) + (1/10^5)/(10 - x)
(ii) Given the differential equation: dx/dt = (1/100) *\(x^2\) * (10 - x)
We are also given x = 1 when t = 0.
To solve this equation and obtain an expression for t in terms of x, we can separate the variables and integrate both sides:
∫(1/\(x^2\)) dx = ∫((1/100) * (10 - x)) dt
Integrating both sides:
-1/x = (1/100) * (10t - (1/2)\(t^2\)) + C
Where C is the constant of integration.
Now, we can substitute the initial condition x = 1 and t = 0 into the equation to find the value of C:
-1/1 = (1/100) * (10*0 - (1/2)*\(0^2\)) + C
-1 = 0 + C
C = -1
Plugging in the value of C, we have:
-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1
To solve for t in terms of x, we can rearrange the equation:
1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1
Multiplying both sides by -1, we get:
-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1
Simplifying further:
1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1
Now, we can isolate t on one side of the equation:
(1/100) * (10t - (1/2)t^2) = 1 - 1/x
10t - (1/2)t^2 = 100 - 100/x
Simplifying the equation:
(1/2)\(t^2\) - 10t + (100 - 100/x) = 0
At this point, we have a quadratic equation in terms of t. To solve for t, we can use the quadratic formula:
t = (-(-10) ± √((-10)^2 - 4*(1/2)(100 - 100/x))) / (2(1/2))
Simplifying further:
t = (10 ± √(100 + 200/x)) / 1
t = 10 ± √(100 + 200/x)
Therefore, the expression for t in terms of x is t = 10 ± √(100 + 200/x).
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A) Solve the Gompertz equation
dy dt = ryln(K/y)
subject to the initial condition y(0) = y0.
B) For the given data r = 0.73 per year, K = 80,300 kg, and y0 K = 0.25. Use the Gompertz model to find the predicted value of y(4).
C) For the same data as in part (b), use the Gompertz model to find the time τ at which y(τ) = 0.77K.
Answers
Answer:
a) \(y = Ke^{ln(\frac{y_0}{K})e^{-rt} }\)
b) \(y(4) = 1,082.043 kg\)
c) \(t = 2.286 years\)
Step-by-step explanation:
Find the step by step solution to the question in the attachment.
The stock of company a gained $0.76 throughout the day and ended at a value of $38.76. By what percentage did the stock rise
Answers
Answer:
Its either 1.98 percentage or 51.
Step-by-step explanation:
Divison?
Answer:2%
Step-by-step explanation: 38.76-0.76=38
38(1+r)=38.76
__________
38
1+r=1.02
R=0.02 (2%)