Sharon and Jacob started at the same place. Jacob walked 3 m north and then 4 m west. Sharon walked 5 m south and 12 m east. How far apart are Jacob and Sharon now?
Answers
Drawing this on a coordinate plane gives us coordinates for Jacob (-4, 3) and coordinates for Sharon (12, -5).
The distance formula is:
[tex] \sqrt{( x_{2}-x_{1})^{2} +(y_{2}-y_{1})^2 } [/tex]
Substituting our values for Jacob and Sharon in we get:
[tex]\sqrt{(-4-12)^2+(3--5)^2} \\ \sqrt{(-16)^2 + (3+5)^2} \\ \sqrt{256+(8)^2} \\ \sqrt{256+64} \\ \sqrt{320}=17.89[/tex]
They are now 17.89 m apart.
Answer:
17.89
Step-by-step explanation:
Related Questions
Which rule describes the translation?
PLEASE ANSWER
(x, y) → (x – 8, y – 3)
(x, y) → (x – 3, y + 8)
(x, y) → (x + 8, y – 3)
(x, y) → (x + 3, y + 8)
Answers
Justification:
1) From the figure you can tell that the original trapezoid ABCD was translated 8 units to the right and 3 units down to yield the trapezoid A'B'C'D'.
2) Translating 8 units to the right means: x → x + 8
3) Translating 3 units down means y → y - 3
4) Therefore, the pair (x,y) is transformed into the pair (x + 8, y - 3); that is the rule (x,y) → (x + 8, y - 3)
Answer:
its C
Step-by-step explanation:
(x, y) → (x + 8, y – 3)
ryan invests a sum of money in a saving account with a fixed annual interest rate of 4.31% compounded monthly. After 10 years, the balance reaches $12,835.94. What was the amount of the initial investment?
Answers
We calculate P to be approximately $7,759.58, which is the amount Ryan invested initially.
To determine the initial investment that Ryan made, which grew to $12,835.94 after 10 years with an annual interest rate of 4.31% compounded monthly, we will use the formula for compound interest:
[tex]A = P(1 + r/n)^{nt}[/tex]
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
We know that:
A = $12,835.94
r = 4.31/100 = 0.0431
n = 12
t = 10
We need to solve for P:
P = A /[tex](1 + r/n)^{nt}[/tex]
Substituting the known values, we get:
P =[tex]$12,835.94 / (1 + 0.0431/12)^{12*10}[/tex]
P = $12,835.94 / [tex](1 + 0.0035925)^{120}[/tex]
P = $12,835.94 / ([tex]1.0035925)^{120}[/tex]
Calculating the value inside the parenthesis first:
[tex](1.0035925)^{120}[/tex] = 1.654297553
Now, we divide the final amount by this compound factor:
P = $12,835.94 / 1.654297553
P ≈ $7,759.58
Therefore, Ryan's initial investment was approximately $7,759.58.
The Wilsons drove 324 miles in 6 hours if they drilled the same number of miles each hour how many miles did they drive in 1 hour
Answers
324/6=54
Evaluate without the use of a calculator 10^-2
Answers
(8)
7/x 11/x cross multiply x^2 = 77, square root of both sides x = sqroot of 77
My answer: D
Answers
How far does a bus travel in 2.5 hours at 65mph?
Answers
162.5 miles
Kia has 10 coins in a bag. T here are three $1 coins and seven 50 pence coins. Kia takes at random 3 coins from the bag. workout the probability she takes out exactly $2.50
Answers
Answer:
7/40
Step-by-step explanation:
once again not bothered
The probability she takes out exactly $2.50 is 7/40.
What is probability?Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.
For the given situation,
Number of coins in Kia bag = 10 coins
Number of $1 coins = 3
Number of 50 pence coins = 7
Kia takes at random 3 coins from the bag and the number of ways are
[tex]10C_{3} =\frac{(10)(9)(8)}{(1)(2)(3)}[/tex]
⇒ [tex]10C_{3} =\frac{720}{6}[/tex]
⇒ 120
Kia takes out exactly $2.50
So the combination could be two $1 coins and one 50 pence coins,
⇒ [tex](3C_{2}) (7C_{1} )[/tex]
⇒ [tex](\frac{(3)(2)}{(1)(2)} )(7)[/tex]
⇒ 21
Thus the probability she takes out exactly $2.50 is P(E) = [tex]\frac{21}{120}[/tex]
⇒ 7/40
Hence we can conclude that the probability she takes out exactly $2.50 is 7/40.
Learn more about probability here
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Given the functions m(x) = 4x − 11 and n(x) = x − 10, solve m[n(x)] and select the correct answer below. (2 points)
Select one:
a. m[n(x)] = 4x − 51
b. m[n(x)] = 4x − 29
c. m[n(x)] = 4x^2 − 51
d. m[n(x)] = 4x^2 − 29
Answers
m (x) = 4x - 11
n (x) = x - 10
We have then:
m [n (x)] = 4 (x - 10) - 11
Rewriting the function:
m [n (x)] = 4x - 40 - 11
m [n (x)] = 4x - 51
Answer:
a. m [n (x)] = 4x - 51
Answer:
got it right and was option A thx
Step-by-step explanation:
What is the 30th term of the arithmetic series 4, 7, 10, …? 88 89?
Answers
d = a2 - a1 -> d = 7 - 4 = 3
an = a1 + (n-1) d -> an = 4 + (n-1) * 3 = 4 + 3n - 3n + 1
[an = 3n + 1]
a30 = 3 * 30 + 1 = 90 + 1 = 91
Answer: a30 = 91
"how many distinct ways can the letters in tallahassee be arranged"
Answers
[tex] \frac{n!}{ n_{1}! n_{2}! n_{3}! ... n_{k}! } [/tex]
where: n is the number of elements in the set
n1 is the number of identical element (object 1)
n2 is the number of identical element (object 2)
n3 is the number of identical element (object 3)
So first let's see how many identical objects there are and the number of each.
A = 3 L= 2 S = 2 E= 2
How many elements in the set? 11
Now input your given:
[tex] \frac{11!}{3! 2! 2! 2!} [/tex]
[tex] \frac{39,916,800}{48} [/tex]
= 831,600 arrangements
The number of distinct ways the letters in TALLAHASSEE can be arranged is calculated using permutations with repetitions. It involves taking the factorial of the total number of letters and dividing by the factorial of the number of times each letter repeats.
To determine the number of distinct ways the letters in TALLAHASSEE can be arranged, we must consider it as a permutation problem with repeating elements. We need to calculate the factorial of the total number of letters and then divide by the factorial of the number of times each individual letter repeats.
The word TALLAHASSEE contains 11 letters in total:
'T' occurs once.'A' occurs twice.'L' occurs twice.'H' occurs once.'S' occurs twice.'E' occurs twice.The permutation formula considering repetitions is:
Number of arrangements = Total letters factorial / (Product of each letter's factorial)
Therefore:
Number of arrangements = 11! / (2! * 2! * 2! * 2!)
This would give us the total number of distinct arrangements of the letters in TALLAHASSEE.
A carpenter's square is a tool that is used to draw right angles. suppose you are buildong a toy car and you have four small circles of wood that will serve as the wheels . you need to drill a hole in the center of each wheel for axle. explain how you can use the carpenter 's square to find the center of each wheel. answer
Answers
Final answer:
To find the center of a wooden wheel for a toy car, use a carpenter's square to draw two perpendicular diameters across the wheel; their intersection is the center where the axle hole should be drilled.
Explanation:
To find the center of a wooden wheel using a carpenter's square, which is used to draw right angles, follow these steps:
Place the wheel on a flat surface.Use the carpenter's square to draw two diameters across the wheel by aligning the square with the edge of the wheel and drawing a line from one side of the wheel to the opposite side.Turn the wheel or the square 90 degrees and draw another diameter that intersects the first one. The two lines should cross at the wheel's center, providing the exact location to drill a hole for the axle.This method effectively divides the wooden wheel into four equal quadrants, and the intersection point of the diameters marks the center, where the axle hole should be drilled.
There are 40 total students in the class and 12 of them are girls. what percentage of the class is boys?
Answers
28/40 X 100 = 70%
The graph of the function f(x) = (x + 2)(x + 6) is shown below. Which statement about the function is true?
a.The function is positive for all real values of x where x > –4.
b.The function is negative for all real values of x where –6 < x < –2.
c.The function is positive for all real values of x where x < –6 or x > –3.
d.The function is negative for all real values of x where x < –2.
Answers
So that's why the answer is choice B.
Kaylie had $1250 in her savings account. She withdrew $82 each month for 8 months in order to pay for a summer vacation. How much did Kaylie have in her account at the end of the 8 months?
Answers
In how many ways can you choose 3 kinds of ice cream and 2 kinds of toppings from a dessert buffet with 10 differnt kinds of ice cream and 6 kinds of toppings
Answers
To choose 3 kinds of ice cream and 2 kinds of toppings from the dessert buffet with 10 different kinds of ice cream and 6 kinds of toppings, you can use the concept of combinations. The total number of ways to choose is 1800.
Explanation:To determine the number of ways to choose 3 kinds of ice cream and 2 kinds of toppings from the dessert buffet, we can use the concept of combinations. We have 10 different kinds of ice cream to choose from, and we want to choose 3 of them. The number of combinations can be calculated using the formula:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of objects (10 ice cream flavors) and r is the number of objects to be chosen (3 ice cream flavors), and ! denotes factorial.
In this case, the number of combinations of ice cream flavors is:
C(10, 3) = 10! / (3!(10-3)!) = 120
Similarly, we have 6 different kinds of toppings to choose from, and we want to choose 2 of them. The number of combinations of toppings is:
C(6, 2) = 6! / (2!(6-2)!) = 15
Therefore, the total number of ways to choose 3 kinds of ice cream and 2 kinds of toppings is the product of the number of combinations of ice cream flavors and toppings:
Total number of ways = 120 * 15 = 1800
Use Distributive Property to write 4m + 4p
Answers
4(m + p) <==
Factor out the common numbers/variables from the terms given
4 is a common number
4m + 4p
4(m + p) is your answer
hope this helps
if 2 inches equals 25 miles. how many miles would 0.25in (1/4 inch) equal?
Answers
Hope this helps!
Find the product. (7 q - 5)(7 q + 5)
49q^2 - 10q - 25
49q^2 + 10q - 25
49q^2 - 25
Answers
[tex]Use\ (a-b)(a+b)=a^2-b^2.\\\\(7q-5)(7q+5)=(7q)^2-5^2=\boxed{49q^2-25}[/tex]
Final answer:
The product of the binomials (7q - 5) and (7q + 5) is found using the difference of squares formula, resulting in 49q² - 25.
Explanation:
To find the product of the given expressions (7q - 5)(7q + 5), we can use the difference of squares formula, which states that (a - b)(a + b) = a² - b².
Here, a is 7q and b is 5.
Applying the formula, we get:
(7q)² - (5)²49q² - 25This is because the mixed term +7q(-5) and the term -7q(+5) cancel each other out, leaving us with just the square terms.
A circle has a diameter with endpoints (7, -7) and (5, -3). What is the equation of the circle?
Answers
both can be found by using distance formula between 2 points:
[tex]d = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \\ = \sqrt{ {(5 - 7)}^{2} + {( - 3 - - 7)}^{2} } \\ = \sqrt{ {(2)}^{2} + {(4)}^{2} } = \sqrt{4 + 16} [/tex]
[tex]d = \sqrt{20} = \sqrt{4} \times \sqrt{5} = 2 \sqrt{5} [/tex]
So our diameter is 2sr5, therefore our radius is half that: r = d/2 = 2sr5/2 = sr5
Now to calculate the center, go halfway between the x's and between the y's:
((7-5)/2 + 5, (-7--3)/2 + -3)
= ((2)/2 + 5, (-7+3)/2 + -3) = (1 + 5, (-4)/2 + -3)
= (1 + 5, -2 + -3) = (6, -5)
So our center is at (6, -5), where (h, k) is center for the formula, so h = 6, k = -5
Equation of a circle:
[tex] {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} \\ {(x - 6)}^{2} + {(y + 5)}^{2} = {( \sqrt{5}) }^{2} \\ {(x - 6)}^{2} + {(y + 5)}^{2} = 5 [/tex]
Final answer:
To find the circle's equation from its diameter's endpoints, calculate the circle's center using the midpoint formula, then determine the radius with the distance formula. Finally, use these values in the circle's standard equation.
Explanation:
To find the equation of the circle, we first need to determine its center and radius. The midpoint of the diameter will give us the center of the circle, and the distance from one of the endpoints to the midpoint will give us the radius.
Step 1: Find the Center of the Circle
The midpoint formula ((x1 + x2)/2, (y1 + y2)/2) gives us the center of the circle. Applying this to our points (7, -7) and (5, -3):
Center = ((7 + 5) / 2, (-7 - 3) / 2) = (6, -5)
Step 2: Calculate the Radius
We use the distance formula, √((x2 - x1)² + (y2 - y1)²), between one of the endpoints and the center:
Radius = √((7 - 6)² + (-7 + 5)²) = √(1 + 4) = √5
Step 3: Write the Equation
Using the standard equation, (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius:
Equation: (x - 6)² + (y + 5)² = 5
This equation gives the precise location and size of the circle based on its diameter's endpoints.
which completely describes the polygon
Answers
Answer:
NONE OF THE ABOVE!!
Step-by-step explanation:
A regular polygon is equilateral and equiangular, and also, can be inscribed into a circle. The polygon shown doesn't meet any of these conditions.
Please help, picture included!
State the domain of the relation.
A) {-4, -3, -2, -1, 0, 2, 5, 8}
B) {-4, -3, -2, -1, 0}
C) {-4, -3, -2, -1}
D) {-4, -1, 2, 5, 8}
Answers
recall that the domain is the values for the x-coordinate, whilst the range is the values for the y-coordinate.
If F(x)=x-5 and G(x)=x^2, what is F(F(x))?
Answers
I really hope this helps
Given F(x)=x-5 and G(x)=x^2 you want to find F(F(x)).
In order to do this, you don't need to know what G(x) is. Just put F into F...
F(x)=x-5
F(x-5)=x-5-5
F(F(x))=x-10
This is the question that you asked, but the photo makes it look like they want you to do G(F(x)) so I will do that one too.
G(x)=x^2
G(x-5)=(x-5)^2
THEREFORE...
G(F(x))=(x-5)^2
A is the answer!
EXPLANATION:
Remember that a function is like a machine. F(x) is a machine and G(x) is also a machine. Plugging F into G is basically taking the output of the F machine and putting it into the G machine.
I really hope this helps! If you need a more detailed explanation, feel free to message me.
BEST WISHES:)
does y vary directly as x in this function? y= -3x+4
Answers
- y varies inversely as x in this function
For y varies directly as x
For y varies inversely as x
for example:
when x = 10, y will = -24
y = -3(10) + 4
y = -30 + 4
y = -24
when x = -10, y will = 34
y = -3(-10) + 4
y = 30 + 4
y = 34
hope this helps
look at the pictures below // please help // 50 points
Answers
How many solutions does the equation have?
7x+3−x=3(1+2x)7x+3−x=3(1+2x)
0
1
infinitely many
Answers
0 = 0
many solutions
answer
infinitely many
Answer:
0
if you were confused to the one on top
A new board game uses special dice. Each die has eight sides. The game uses three of these special dice. How many outcomes are possible?
Answers
Final answer:
To find the number of possible outcomes when rolling three eight-sided dice, you multiply the number of outcomes of each die together, resulting in 512 total outcomes.
Explanation:
To determine how many outcomes are possible when rolling three eight-sided dice, we need to calculate the total number of combinations that can occur. Since each die has eight possible outcomes and the dice are rolled simultaneously, the number of outcomes for each die can be multiplied together to find the total number of outcomes for all three dice.
So, the calculation for the total number of outcomes is as follows:
8 (outcomes for die 1) × 8 (outcomes for die 2) × 8 (outcomes for die 3) = 512 total outcomes.
Therefore, there are 512 different possible outcomes when rolling three eight-sided dice.
QRS~TUV. What is the measure of V?
What’s the answer?
Answers
Therefore, QS=TV
3v+2 = 7v-6
4v = 8
v = 2
Therefore; QS= 3(2)+2
= 8 units
TV = 7(2)-6
= 8 units
∠V is calculated to be 70°.
When two triangles are similar (QRS ~ TUV), their corresponding angles are equal. This means:
∠Q corresponds to ∠T∠R corresponds to ∠U∠S corresponds to ∠VGiven ∠R = 47° and ∠Q = 63°, we know that ∠T = 63° and ∠U = 47°.
Since the sum of the angles in any triangle is 180°:
∠Q + ∠R + ∠S = 180°
Substituting the known values:
63° + 47° + ∠S = 180°
Solving for ∠S:
∠S = 180° - 63° - 47° = 70°
Therefore, ∠V = 70° because ∠S corresponds to ∠V in the similar triangles.
Complete question: Triangle QRS is similar to triangle TUV. ∠R=47°, ∠Q=63°. What is the measure of angle V?
At summer camp, 150 kids had the opportunity to choose their activities. of those kids selected archery for their morning activity. Of that group, also chose to study drama in the afternoons. How many kids chose both archery in the morning and drama in the afternoons?
Answers
The correct answer is [tex]D = 23[/tex]
To solve this problem , let's define the given information:
Let [tex]T[/tex] be the total number of kids at the summer camp:
[tex]T = 150[/tex]
Let [tex]A[/tex] be the number of kids who chose archery for their morning activity:
[tex]\frac{A}{T} = \frac{3}{5}[/tex]
Let [tex]D[/tex] be the number of kids from the archery group who also chose drama in the afternoons:
[tex]\frac{D}{A} = \frac{1}{4}[/tex]
We want to find the value of [tex]D[/tex], which represents the number of kids who chose both archery in the morning and drama in the afternoons.
We can set up the following equations:
[tex]\frac{A}{T} &= \frac{3}{5}[/tex]
[tex]A &= \frac{3}{5}T[/tex]
[tex]A &= \frac{3}{5}(150)[/tex]
[tex]A &= 90[/tex]
[tex]\frac{D}{A} &= \frac{1}{4}[/tex]
[tex]D &= \frac{1}{4}A[/tex]
[tex]D &= \frac{1}{4}(90)[/tex]
[tex]D &= 22.5[/tex]
Therefore, the number of kids who chose both archery in the morning and drama in the afternoons is [tex]22.5 or 23[/tex] (since we cannot have a fractional number of kids).
[tex]D = 23[/tex]
Given a right circular cone, you put an upside-down cone inside it so that its vertex is at the center of the base of the larger cone, and its base is parallel to the base of the larger cone. if you choose the upside-down cone to have the largest possible volume, what fraction of the volume of the larger cone does it occupy?
Answers
then x/b=h/r, and
volumeof smaller is 1/3pi(h-x)b^2, or
1/3pi(h-x)(x^2r^2/h^2=
1/3pi((x^2r^2/h)-(x^3r^2/h^2).
Now differinate with respect to x,
and set to 0, so
((2xr^2/h)-(3x^2r^2/h^2)=0,
so you get x=2/3h.
So, fraction is ((1/3pi(h-2/3h)(4/9r^2)/(1/3pir^2h)= 4/27
When a smaller, upside-down cone is placed inside a larger cone, both cones being similar and the vertex of the smaller one being at the center of the base of the larger one, the smaller cone would occupy 1/8 or 12.5% of the volume of the larger cone.
Explanation:The relationship between the volume of the larger cone and the smaller, upside-down cone placed inside it is represented through the formula for the volume of a cone, which is 1/3 * π * r² * h, where 'r' is the radius of the base and 'h' is the height. If you manage to place the smaller cone such that it has the largest possible volume (which will happen when the smaller cone is similar to the larger cone), the smaller cone will have a height and radius proportionately smaller than the larger one.
Thus, the volumes are proportional to the cube of their corresponding proportions, so the smaller cone will occupy 1/n³ of the volume of the larger cone, where 'n' is the proportion between their linear dimensions. In this particular set-up, the 'n' will equal 2 because when the vertex of the smaller cone is at the center of the base of the larger cone, the smaller cone's height is half that of the larger cone. Hence, the smaller cone will occupy 1/2³ = 1/8 or 12.5% of the volume of the larger cone.
Learn more about Cone Volume Proportion here:https://brainly.com/question/32854147
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A) –72
B) 72
C) –36
D) 36
Answers
[tex] \frac{(-9)(-8)}{(-2)} [/tex]
[tex](-9)(-8) = 72 [/tex]
Problem becomes: [tex] \frac{72}{-2} = ? [/tex]
Answer: [tex]-36[/tex]
Remember
-,- = +
+, + = +
-,+ = -
+,- = -
Good luck on your assignment and enjoy your day!
~[tex]LoveYourselfFirst:)[/tex]