Answers
[tex]\bf d=\sqrt{\left[ \frac{3}{8}-\frac{1}{8} \right]^2+\left[-\frac{4}{5}-\left( -\frac{9}{5} \right) \right]^2}\implies d=\sqrt{\left( \frac{3}{8}-\frac{1}{8} \right)^2+\left(-\frac{4}{5}+\frac{9}{5} \right)^2} \\\\\\ d=\sqrt{\left( \frac{2}{8}\right)^2+\left(\frac{5}{5} \right)^2}\implies d=\sqrt{\left( \frac{1}{4} \right)^2+\left( 1 \right)^2}\implies d=\sqrt{\frac{1^2}{4^2}+1}[/tex]
[tex]\bf d=\sqrt{\frac{1}{16}+1}\implies d=\sqrt{\cfrac{17}{16}}\implies d=\cfrac{\sqrt{17}}{\sqrt{16}}\implies d=\cfrac{\sqrt{17}}{4}[/tex]
AB = √[(x₂ - x₁)² + (y₂ - y₁)²]
A(1/8 , 9/5) and B(3/8 , - 4/5)
Plug in the related value:
AB = √[(3/8 - 1/8)² + ( - 4/5 - 9/5)²] = √(2729/400) (ALREADY SIMPLIFIED)
AB = distance = 2.61
Related Questions
Ivan was given two data sets, one without an outlier and one with an outlier.
Data without an outlier: 108, 113, 105, 118, 124, 121, 109
Data with an outlier: 108, 113, 105, 118, 124, 121, 109, 61
How is the median affected by the outlier?
Answers
Answer:
b
Step-by-step explanation:
The outlier affects the median of the data sets collected by Ivan by reducing the median.
What is an outlier?An outlier is a number that is way smaller or way larger than that of other numbers in a data set. The outlier in the data set is 62. Median is the number at the center of a data set.
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Classify the four angles of the quadrilateral.
A
B
C
D
90°
105°
75°
90°
Right , Acute, Obtuse
∠A
∠B
∠C
∠D
Answers
Any angle bigger than 90 is obtuse and any angle smaller than 90 is acute
All the angles of the quadrilateral are,
⇒ ∠A = Right angle
⇒ ∠B = Obtuse angle
⇒ ∠C = Acute angle
⇒ ∠D = Right angle
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
Now, We know that;
Any angle which is greater than 90° is called obtuse angle and less than 90° is called acute angle and 90° is called Right angle.
Here, The four angles of the quadrilateral are,
⇒ ∠A = 90°
⇒ ∠B = 105°
⇒ ∠C = 75°
⇒ ∠D = 90°
Hence, We get;
⇒ ∠A = Right angle
⇒ ∠B = Obtuse angle
⇒ ∠C = Acute angle
⇒ ∠D = Right angle
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If Kendra started working at 10:30 a.m.and left at 6:15, how many hours of work should she record for the day on her time card
Answers
6.25+12-10.5
7.75 hrs
A brace for a shelf has the shape of a right triangle. Its hypotenuse is 8 inches long and the two legs are equal in length. How long are the legs of the triangle?
Answers
[tex]\bf \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ -------\\ c=8\\ b=a \end{cases}\implies 8^2=a^2+a^2 \\\\\\ 64=2a^2\implies \cfrac{64}{2}=a^2\implies 32=a^2\implies \sqrt{32}=a \\\\\\ \sqrt{16\cdot 2}=a\implies \sqrt{4^2\cdot 2}=a\implies 4\sqrt{2}=a[/tex]
Suppose that it costs $25 to place a classified advertisement in the newspaper, plus $4 for each line. Then the cost to place an ad x lines long is given by y dollars, where y= 4x + 25.
express as an ordered pair the fact that a 14 line cost $81. _
Express as an ordered pair the fact that an ad costing $37 is 3 lines long. _
Answers
We have a function y = f(x), that associates for each value of x a value in y. We represent this in a ordered pair (x, y). In this exercise, we have the price in function of the number of lines, so, the first element of the pair is the number of lines and the following is the price.
Therefore, for 14 lines and $81, we have x = 14 and y = 81 and the pair is:
(14, 81)
b) The cost is the value in y, so, we have y = 37 and x = 3. The pair is:
(3, 37)
Find the zeros of the function. f(x)=-3x^2+75
Answers
3x^2=75
x^2=25
x=+-5
Final answer: x=-5, x=5
Question 1(Multiple Choice Worth 5 points) (04.03 MC) Because of the rainy season, the depth in a pond increases 3% each week. Before the rainy season started, the pond was 10 feet deep. What is the function that best represents the depth of the pond each week and how deep is the pond after 8 weeks? Round your answer to the nearest foot. Hint: Use the formula, f(x) = P(1 + r)x. f(x) = 10(0.03)x, 36 feet f(x) = 10(1.03)x, 14 feet f(x) = 10(1.3)x, 37 feet f(x) = 10(1.03)x, 13 feet
Answers
I think P is the principal amount of depth. This is the base depth before the experiment has even started. Hence, P=10 feet. Then, r is the rate of change. Since it was mentioned that the depth increases by 3% each week, r = 3% or 0.03. Lastly, you want to find the depth after 8 weeks, so x=8. Therefore, the formula becomes:
f(x) = 10(1+0.03)*8 = 82.4
However, this is not one of the choices. There must be some typographical error. The equation must be f(x) = P(1+r)^x. Using this equation instead,
f(x) = 10(1+0.03)^8 = 13 ft
What are two numbers whose sum is 11 and whose product is -60?
Answers
Enumerate pairs of numbers whose product is 60
(1,60)
(2,30)
(3,20)
(4,15)
(5,12)
(6,10)
(10,6)
...
2. identify the pair whose components have a difference of 11.
(4,15)
3. attach a negative sign to the smaller component so that the sum is +11.
(-4,15)
Answer: the numbers are -4 and 15.
Factor 2a^5b + 2a^4b^2 + 2a^3b^3.
A.)2a^2b(a^2+a
Answers
2a^3b (a^2 + ab + b^2) <==
Dots sells a total of 267 T-shirts ($2) and shorts ($3). In April, total sales were $633.
How many T-shirts and shorts did Dots sell?
Answers
s = # of shorts sell
and
t = # of shirts sell
s + t = 267 so s = 267 - t
3s + 2t = 633
substitute s = 267 - t into 3s + 2t = 633
3s + 2t = 633
3(267 - t) + 2t = 633
801 - 3t + 2t = 633
-t = -168
t = 168
s = 267 - t
s = 267 - 168
s = 99
answer
shirts = 168
shorts = 99
if I have 3 layers of 14 cases per layer of an item,how many total cases should I have
Answers
3×14=42 cases
The total number of cases I should have is 42.
How many cases should I have?
Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
Total number of cases = number of layers x cases per layer
14 x 3 = 42
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How do you subtract an integer from another integer without using a number line or counters? Give an example.
Answers
Stacy is walking his dog on a path and his dog wiggled out of his collar. If the dog is 30 feet lower than the owner and the angle of elevation from the dog to the owner is 10 degrees, find the distance from the dog to the owner.
Answers
sine 10 = 30 feet / hypotenuse
hypotenuse = 172.76 feet ( distance of the dog to its owner )
estimate the product 731+207
Answers
I know this because...
- 731 is rounded to 700
- 207 is rounded to 200
- 700 + 200 = 900
Hope this helps! :)
yesterday's low temperature was -2.5 degrees celsius. today's low temperature is 5 times as low as yesterday's low temperature. what was the low temperature today?
Answers
Answer:
The temperature is -12.5 degrees Celsius.
Step-by-step explanation:
The daily maximum temperature, or high, describes how warm you can expect the air to be, usually from 7 a.m. to 7 p.m. The daily minimum temperature, or low, tells how much the air is expected to cool, usually overnight from 7 p.m. to 7 a.m.
The length of a rectangle is 7 inches more than its width. The area of the rectangle is equal to 2 inches less than 5 times the perimeter . What is the length and width
Answers
The area of the rectangle is [tex]A=w(w+7)= w^{2}+7w [/tex].
The perimeter of the rectangle is:
P = 2(Width + Length)=2(w+w+7)=2(2w+7)=4w+14
"The area of the rectangle is equal to 2 inches less than 5 times the perimeter." means that:
A = 5P - 2
[tex]w^{2}+7w=5(4w+14)-2[/tex]
[tex]w^{2}+7w=20w+70-2[/tex]
[tex]w^{2}-13w-68=0[/tex]
to solve the quadratic equation, let's use the quadratic formula
let a=1, b=-13, c=-68
[tex]D= b^{2} -4ac=169-4(1)(-68)=169+272=441[/tex]
the root of the discriminant is 21
the roots are
w1=(13+21)/2=34/2=17
and
w2=(13-21)/2=-8/2=-4, which cannot be the width.
The width is 17 units, and the length is 17+7=24 units
Answer: w=17, l=24
Fill in the blanks to write the solutions to the quadratic equation. x2 + 2x + 10 = 0
Answers
Can also be written as 2x +2x + 10 =0
4x + 10 =0
4x = -10
x= -10/4
x= -5/2
A video game sets the points needed to reach the next level based on the function g(x) = 7(3)^x − 1, where x is the current level. The hardest setting promises to multiply the points needed in each level according to the function h(x) = 4x. How many points will a player need on the hardest setting of level 4?
Answers
however, if the player is using the hardest setting, the hardest setting promises to quadruple any points on the current level, so, he/she will only need a quarter of 7(3)⁴-1.
now, 7(3)⁴-1 is 566, however, you don't need all 566 in hardest setting, you can do with only 566/4, since the hardest setting will give you 4x or quadruple of the amount of points.
A player will need 2,264 points on the hardest setting of level 4 as calculated by evaluating g(4) using the function g(x) = 7(3)^x - 1 and then applying the function h(x) = 4x.
To calculate the number of points a player will need on the hardest setting of level 4, we need to consider the function h(x) = 4x provided in the context of the question. However, the question also mentions the function g(x) = 7(3)^x - 1, which indicates the points needed to reach the next level normally. Since we need to find the hardest setting value, we will use the function h(x) but before that, we need to evaluate g(4) to find out the base points at level 4.
To find g(4), we substitute x = 4 into g(x):
g(4) = 7(3)^4 - 1 = 7(81) - 1 = 567 - 1 = 566
Now we apply the function h(x) to this value to get the points on the hardest setting:
h(g(4)) = 4 × 566 = 2264
Therefore, a player will need 2,264 points on the hardest setting of level 4.
A basketball is thrown with an initial upward velocity of 25 feet per second from a height of 8 feet above the ground. The equation h=-16t^2+25t+8 models the height in feet t seconds after it is thrown. After the ball passes its maximum height, it comes down and then goes into the hoop at a height of 10 feet above the ground. About how long after it was thrown does it go into the hoop?
Answers
10=-16t^2+25t+8
16t^2-25t+2=0
Using the quadratic formula for expediency...
t=(25±√497)/32, we want the time when it was falling so
t=(25+√497)/32
t≈1.48 seconds (to nearest hundredth of a second)
Answer:
A quadratic equation is in the form of [tex]ax^2+bx+c =0[/tex]........[1], then the solution for this equation is given by:
[tex]x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
As per the statement:
The equation is given by:
[tex]h=-16t^2+25t+8[/tex]
where, h is the height in feet t seconds after it is thrown.
After the ball passes its maximum height, it comes down and then goes into the hoop at a height of 10 feet above the ground.
⇒h = 10 feet
then;
[tex]-16t^2+25t+8=10[/tex]
Subtract 10 from both sides we have;
[tex]16t^2-25t+2=0[/tex]
On comparing this equation with [1] we have;
a =16 , b =-25 and c =2
then;
[tex]t= \frac{25 \pm \sqrt{(-25)^2-4(16)(2)}}{2(16)}[/tex]
⇒[tex]t= \frac{25 \pm \sqrt{625-128}}{32}[/tex]
⇒[tex]t= \frac{25 \pm \sqrt{497}}{32}[/tex]
as we want the time when it was falling so ,
[tex]t= \frac{25 + \sqrt{497}}{32}[/tex]
Simplify:
[tex]t \approx 1.48[/tex] sec
Therefore, 1.48 sec long after it was thrown does it go into the hoop
Find f(-5), if f(x) = -x^2 - 2x+1
Answers
f(-5) = -(-5)² - 2(-5) + 1
= -25 + 10 + 1
= -14
f(-5) = -(-5)² - 2(-5) + 1
f(-5) = -25 + 10 + 1
f(-5) = -15 + 1
f(-5) = -14
-14 <----- answer
The units digit of a perfect square is 6. What are the possible values of the tens digit?
Answers
Final answer:
The tens digit of a perfect square with a units digit of 6 could be any digit from 0 to 9. This is because when numbers ending in either 4 or 6 are squared, the tens digit can take any value in the range of 0-9 due to the cyclic nature of the squares.
Explanation:
The units digit of a perfect square can be 6, and this occurs when a number ending in either 4 or 6 is squared since 42 is 16 and 62 is 36. Considering this, the possible values for the tens digit of a perfect square with a units digit of 6 could be derived from these squares. For the tens digit, we must look at the squares of numbers ending in 4 or 6 and check the ten's place of the resulting product.
For example, if we consider 142 (which is 196) and 162 (which is 256), the tens digit can be either 9 or 5. Continuing with this pattern for numbers ending in 4 or 6 all the way to 942 and 962, we find that the tens digit is cyclic and can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. Therefore, all ten digits are possible for the tens place of a number whose square ends in 6.
You are hiking on a trail that leads to the top of a mountain. At 12 P.M. you reach an elevation of 3700 feet. At 4 P.M. you reach an elevation of 4500 feet. What is your mean hourly change in elevation?
Answers
r=(4500-3700)/(4+12-12)
r=800/4
r=200 ft/hr
200 feet per hour.
Answer: 200 ft per hour
Step-by-step explanation:
Given : You are hiking on a trail that leads to the top of a mountain.
At 12 P.M. you reach an elevation of 3700 feet. At 4 P.M. you reach an elevation of 4500 feet.
The formula for the mean hourly change in elevation is :-
[tex]\dfrac{\text{Change in elevation}}{\text{Time in hours}}[/tex]
From the given information, the change in elevation=4500 ft-3700 ft= 800 ft
Time taken = 4 hours [From 12 pm to 4 pm]
Now, Mean hourly change in elevation=[tex]\dfrac{800}{4}=200[/tex]
Hence, the mean hourly change in elevation = 200 ft
What is the next number?
3,4,6,9,13,18,24=
Answers
3 + 1 = 4
4 + 2 = 6
6 + 3 = 9
9 + 4 = 13
13 + 5 = 18
18 + 6 = 24
24 + 7 = 31
In the sequence above, the next number would be 31.
Observe.
3 + 1 = 4
4 + 2 = 6
6 + 3 = 9
9 + 4 =13
13 + 5 =18
18 + 6 =24
24 + 7 = 31
As you can see the rule is: +1 x 2
Consider the function f(x) = (x − 3)2(x + 2)2(x − 1). The zero has a multiplicity of 1. The zero −2 has a multiplicity of?
Answers
The zero with a multiplicity of 1 is x = 1, and the zero x = -2 has a multiplicity of 2.
How to find the multiplicity of zeros in a polynomial?For a general polynomial like:
[tex]p(x) = (x - x_1)^n*(x - x_2)^m*...[/tex]
The zero x₁ has a multiplicity of n (same as the exponent in the term where the zero appears), while the zero x₂ has a multiplicity m.
Now let's go to our polynomial:
[tex]f(x) = (x - 3)^2(x + 2)^2(x - 1)[/tex]
Here we can see that the only zero with a multiplicity of 1, is x = 1, while the zero x = -2 has a multiplicity of 2.
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Answer:
first one is 1 and second is 2
Step-by-step explanation:
just got it right
If gasoline costs
2.50
2.50 euros per liter, it will cost $
how much
to drive
220 kilometers
Answers
220 x 2.50 = 550 euros or 220 x 2.91 =$ 640.20;
Below are grades in a course and how many students earned each grade:
5 students earned an A,
8 students earned a B,
10 students earned a C,
3 students earned a D
and 2 students earned a F.
What percent passed the course with a C or better? (Round your answer to one decimal place.)
Answers
The percentage of students who passed the class with a C or better is 82.1%. This is found by adding the number of students who earned A, B, or C grades, dividing by the total number of students, and multiplying by 100.
Explanation:The subject is Mathematics, specifically a problem in percentages. First, we need to find the total number of students in the class. We add the number of students that earned each grade: 5 (A) + 8 (B) + 10 (C) + 3 (D) + 2 (F) = 28 students in total.
Next, we need to identify the number of students who passed the class with a C or better. This includes the students who earned an A, B, or C. Adding these numbers together gets us 5 (A) + 8 (B) + 10 (C) = 23 students.
Then, to find the percentage of students who passed the class, we divide the number of students who passed (23) by the total number of students (28) and then multiply by 100 to convert the result to a percentage. So the calculation is as follows: (23/28)*100 = 82.14. Rounded to one decimal place, that is 82.1%. Therefore, 82.1% of students passed the class with a grade of C or better.
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The percent of students who passed the course with a C or better is: 82.14%
To find the percent of students who passed the course with a C or better, we need to divide the number of students who passed by the total number of students and multiply by 100%.
The number of students who passed is 5 + 8 + 10 = 23.
The total number of students is 5 + 8 + 10 + 3 + 2 = 28.
Therefore, the percent of students who passed the course with a C or better is:
(23 / 28) * 100% = 82.14%
Rounding to one decimal place, the answer is 82.1%.
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a plane takes 2hr to travel 1000mi with the wind. it can travel only 880mi against the wind in the same amount of time. find the speed of the wind and the speed of the plane in still air
Answers
so... let's say, the plane's speed in still air is "p", and the speed of the wind is "w".
when the plane is travelling with the wind over those 1000 miles, is really not going "p" fast, is going " p + w " fast, since it's going with the wind.
now, when the plane is travelling against the wind, is not going "p" fast either, is going " p - w " fast, since the wind is subtracting speed from it.
bearing in mind he cover the 1000 miles as well as the 880 miles in 2 hrs each way.
[tex]\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ \textit{with the wind}&1000&p+w&2\\ \textit{against the wind}&880&p-w&2 \end{array} \\\\\\ \begin{cases} 1000=2(p+w)\\ \qquad 500=p+w\\ \qquad 500-p=\boxed{w}\\ 880=2(p-w)\\ ----------\\ \frac{880}{2}=p-w\\ 440=p-\left( \boxed{ 500-p }\right) \end{cases} \\\\\\ 940=2p\implies \cfrac{940}{2}=p\implies 470=p[/tex]
what's the speed of the wind? well, 500 - p = w.
how do you solve this problem? I need help
Answers
notice the bottom part of the picture, just using the tangent of the angle, we can get the angle itself, and you'd know what "x" and "y" are from the above part.
how much farther would they have to walk up? well, the hypotenuse of the longer triangle is "h", the hypotenuse of the shorter triangle is 122, so, they'd have to walk " h - 122 " more.
If the constant c is chosen so that the curve given parametrically by ct, c 2 8 t 2 , 0 ≤ t ≤ 3 , is the arc of the parabola 8y = x 2 from (0, 0) to (4, 2), find the coordinates of the point p on this arc corresponding to t = 2.
Answers
[tex]4=3c\implies c=\dfrac43[/tex]
So when [tex]t=2[/tex], the [tex]x[/tex]-coordinate of the point [tex]p[/tex] would be
[tex]x=\dfrac43(2)=\dfrac83[/tex]
I'm not sure how [tex]y[/tex] is parameterized, but my best guess is that you mean to say
[tex]y(t)=\dfrac{c^2}8t^2[/tex]
which means when [tex]t=2[/tex] we would get a [tex]y[/tex]-coordinate of
[tex]y=\dfrac{\left(\frac43\right)^2}82^2=\dfrac89[/tex]
By solving the given equations using the provided information, and assuming the constant c = 4/3, we can find the coordinates of the point P on the curve corresponding to t = 2 are (8/3, 32/9). There is a probable discrepancy in the question which causes two different solutions for c, therefore making the canonical form of the parabola ambiguous.
Explanation:The given parametric curve has its equations as x = ct and y = c/8 * t^2. We're given that it's the arc of the parabola 8y = x^2 from (0, 0) to (4, 2), meaning that we can set x = ct = 4 and y = c/8 * t^2 = 2 when t=3 (the upper limit of t) to find the value of the constant c. Solving these equations gives c=4/3 and c=48. Since c must be the same in both equations, there seems to be a discrepancy here, which could possibly originate from a mistake in the question. However, if we only use c from the first equation (x = ct), we get c = 4/3.
The question asks for the coordinates of the point on the curve corresponding to t = 2. Substituting t = 2 into x = ct and y = c/8 * t^2 gives x = 8/3 and y = 32/9, assuming c = 4/3. So, the coordinates of the point would be (8/3, 32/9).
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Choose if the following function is even, odd or neither. f(x) = x^3