thank you, you too! :D
The town of Lakehorn is built on a grid system. Town hall is located downtown at point (0,0). A new school is located 3 miles north and 2 miles east of town hall. Only students who live outside a 5-mile radius from the school are eligible to ride the school bus. Which of the following students are eligible to ride the bus? Select all that apply.
The students eligible to ride the bus are: Marinna, Kaleb and Thomas
What is the distance between two points?The distance between two points [tex](x_1,y_1),(x_2,y_2)[/tex] is,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
What is an equation of circle with center at (h, k)?An equation of circle with center at (h, k) and radius 'r' is,
[tex](x-h)^2 + (y-k)^2=r^2[/tex]
For given example,
Town hall is located downtown at point (0,0). A new school is located 3 miles north and 2 miles east of town hall.
Considering positive x-axis = East
negative x-axis = West
positive y-axis = North
negative y-axis =South
Also, locate the position of each student on the graph.
Then the given situation would as shown in following diagram.
We have been given, only students who live outside a 5-mile radius from the school are eligible to ride the school bus.
Using the equation of the circle,
the equation for the area within a circle of 5-mile radius from the school would be,
[tex](x-2)^2+(y-3)^2=5^2[/tex]
From the graph we can observe that, Marinna, Kaleb and Thomas live outside a 5-mile radius from the school.
Therefore, the students eligible to ride the bus are: Marinna, Kaleb and Thomas
Learn more about the equation of circle here:
https://brainly.com/question/10618691
#SPJ2
What is the measure of x in the figure below?
Answer:
115 degree
Step-by-step explanation:
x + 65 = 180 (Sum of angles in a straight line = 180 [Also known as Linear pair])
x = 180 - 65
x = 115 degree
please help -------------------- ASAPPP
Hello,
[tex]f^{-1}(f(58))=(f^{-1}*f)(58)=1(58)=58\\f(f(5)=f(9)=11\\[/tex]
Which is the area between the x-axis and y=x from x=1 to x=5
Answer:
[tex]\displaystyle A = 12[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
FunctionsFunction NotationGraphingCalculus
Integrals
Definite IntegralsArea under the curveIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
y = x
Interval: x = 1 to x = 5
Step 2: Sort
Graph the function. See Attachment.
Bounds of Integration: [1, 5]
Step 3: Find Area
Substitute in variables [Area of a Region Formula]: [tex]\displaystyle A = \int\limits^5_1 {x} \, dx[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle A = \frac{x^2}{2} \bigg| \limits^5_1[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle A = 12[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
You want to buy juices while shopping at ShopRite but are stuck between buying a bottle of apple juice and orange juice. The apple juice is 2 Liters and costs $3.00 while the orange juice is 3 Liters and costs $3.99. Which juice bottle is the better deal?
Answer:
Orange juice
Step-by-step explanation:
The bottle of apple juice costs 3 dollars for 2 liters, and the bottle of orange juice costs 3.99 dollars for 3 liters. To see which bottle has the better deal, we need to make the liters the same so we can compare them.
We can divide the 2 liters for 3 dollars ratio by 2 to get that 1 liter of apple juice costs 1.5 dollars, and we can divide the orange juice ratio by 3 to get that 1 liter of orange juice costs 1.33 dollars. We see that for 1 liter, orange juice is cheaper, so it is the better deal.
Cosella is conducting an experiment where she assesses how quickly teenagers can run a 100-meter race after consuming specific amounts of caffeine. She divides her sample up into three groups. Group 1 receives a glass of water with no caffeine added. Group 2 receives a glass of water with an amount of caffeine equivalent to that in one cup of coffee. Group 3 receives a glass of water with an amount of caffeine equivalent to that in two cups of coffee. Each participant is then timed as they run the course. In this study, the dependent variable is
Answer:
The dependent variable is the time taken to run 100 metres
Step-by-step explanation:
A dependent variable is simply one that is being measured or sometimes tested in an experiment.
Now, in this case, what is being determined is the time each group of participants will take to run a 100-meter race.
Thus, the dependent variable is the time each group of participants will take to run a 100-meter race.
What is the slope of the line? What is the y-intercept of the line? y = 1
Answer:
m = 0
y intercept = 1
Step-by-step explanation:
The given equation of the line is ,
[tex]\implies y = 1[/tex]
We know that the Standard equation of Slope Intercept Form of the line is,
[tex]\implies y = mx + c[/tex]
Where ,
m is slope c is y interceptOn comparing to the Standard form of the line we get ,
[tex]\implies Slope = 0 [/tex]
[tex]\implies y - intercept= 1[/tex]
Slope of the line is 0, since y=mx+c, if m = 0, then y = c, where the constant (c)=1
y intercept of the line is y = 1.
Answered by GAUTHMATH
A farmer wants to fence in a rectangular plot in a large field, using a rock wall which is already there as the north boundary. The fencing for the east and west sides of the plot will cost $4 a yard, but the farmer needs to use special fencing which cost $5 a yard on the south side of a plot. If the area of the plot is to be 600 square yards, find the dimensions for the plot which will minimize the cost of the fencing.
Hello,
Let's assume x the length of the north's wall
and y the length of west side .
Area:x*y=600 ==> y=600/x
Cost: 2*y*4+5*x=8y+5x= 4800/x+5x
Minimize cost: (4800/x+5x)'=0
-4800/x²+5=0
x²=4800/5
x²=960
[tex]x=8\sqrt{15} \\\\y=5\sqrt{15} \\[/tex]
Annie invests $400 in a bank that offers 5.5% simple annual interest after 6 years her investment will increase by blank dollars
Answer:
Her investment will increase by 551.54 dollars
Step-by-step explanation:
So we know that the exponential function formula is f(x)=a(1+r)^x
So knowing that we can input values
So now we have f(x)=400(1+0.055)^6
Since it is annual we will only have the interest yearly so that changes are equation to look like this f(x)=400(1+0.055/1)^6
So next we have to add 1 and 0.055 which is 1.055
So we input that into the equation so now we have f(x)=400(1.055/1)^6
Now we have to do (1.055/1) to the power of six, so we get 1.37884280676
Now we have to 1.37884280676 times 400, which would be 551.537122705.
Assuming they want to the nearest 100th it would be 551.54
So the answer is 551.54 dollars
Hopefully, that helped. If I made any mistake or I am incorrect feel free to correct me. :)
Michael modeled from play dough a 15cm high pyramid with a rectangular base with dimensions of a = 12 cm and b = 8 cm. Jane remodeled Michael’s pyramid into a come with a base diameter of d = 10cm, what was the height of Jane’s cone?
Answer: 251.2 cm3
Step-by-step explanation:
10x3.14x 8 = 251.2
Please help me with this problem
Answer:
Step-by-step explanation:
a*b *c = abc
15c = 15 . c
2a * 10b = 2* 10 * a * b = 20ab
The above mentioned expressions are true
That are false
12ab = 12a * 12b ----> false because 12ab = 12 * a* b
7a *7b = 14ab is false because 7a * 7b = 7 * 7* a *b = 49ab
How many fives makes 6 tens
Answer:
12.
Step-by-step explanation:
6x10 = 60.
60 divided by 12 =5.
Answer:
12
Step-by-step explanation:
5x = 60
x = 12
A department store holds a year-end clearance sale that includes a 5.5% discount on cosmetics. Find the sale price of a bottle of perfume if its original price was $48.41.
Answer:
Sale price = $45.75
Step-by-step explanation:
Original price = $48.41
Percentage Discount = 5.5%
Amount of discount = Percentage Discount × Original price
= 5.5% × $48.41
= 5.5/100 × $48.41
= 0.055 × $48.41
= $2.66255
Sale price = Original price - Amount of discount
= $48.41 - $2.66255
= $45.74745
Approximately,
Sale price = $45.75
Solve x2 + 10x = 24 by completing the square. Which is the solution set of the equation?
(negative 5 minus StartRoot 34 EndRoot comma negative 5 + Startroot 34 EndRoot)
(negative 5 minus StartRoot 29 EndRoot comma negative 5 + StartRoot 29 EndRoot)
{–12, 2}
{–2, 12}
Answer:
(-12,2)
Step-by-step explanation:
x^2 + 10x = 24
x^2 + 10x + (10/2)^2 = 24 + (10/2)^2
10/2 = 5
5^2 = 25
x^2 + 10x + 25 = 24 + 25
x^2 + 10x + 25 = 49
(x + 5)^2 = 49 Take the square root of both sides
(x + 5) = sqrt(49)
x + 5 = +/- 7
x = +/- 7 - 5
x = +7 - 5 = 2
x = -7 - 5 = -12
Answer:
{ -12 , 2}
Step-by-step explanation:
x² + 10x = 24
In order to complete the square, the equation must first be in the form x² + bx =c.
x² + 10x = 24Divide 10, the coefficient of the x term, by 2 to get 5. Then add the square of 5 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x² + 10x + 5² = 24 + 5²expand exponents.
x² + 10x + 25 = 24 + 25Add 24 and 25
x² + 10x + 25 = 49Factor x² + 10x + 25. In general, when x² + bx + c is a perfect square, it can always be factored as ( x + b/2)².
( x + 5 )² =49Take the square root of both sides of the equation.
[tex] \small \sf \sqrt{(x + 5) {}^{2} } = \sqrt{49} [/tex]
simplify
x + 5 = 7x + 5 = +/- 7Subtract 5 from both sides.
x + 5 - 5 = 7 - 5
x = 2x + 5 - 5 = +/- 7 -5
x = -7 - 5 = -12The sales tax rate for the state of Washington was 7.6%.
What is the state sales tax on a $5,300 car in WashingtoN
What is the final cost of the car, including tax?
Answer:
Sales tax: 402.80 Final cost: 5,702.80
Step-by-step explanation:
Sales price x sales tax rate = sales tax
5300 x .076 (7.6%) = 402.80
Sales price + tax = final cost
5300 + 402.80 = 5702.80
Someone pls help me ill give out brainliest pls don’t answer if you don’t know
Answer:
i dont know
Step-by-step explanation:
figure it out yourself
simplify the ratio 4.5: 3 1/2 in its simplest form
Answer:
9 : 7
Step-by-step explanation:
Given
4.5 : 3 [tex]\frac{1}{2}[/tex] ( multiply both parts by 2 to clear the fractions )
= 9 : 7
What is the value of -97-7 when /= 2?
-25
-18
11
45
Step-by-step explanation:
there must be something wrong or missing in your problem description.
what I can read here :
-97 - 7 when divided by 2
-97 - 7 = -104
this divided by 2 is -52.
but there is no such answer.
so, the provided answers and the problem description do not fit to each other.
What 23.5 x 10 to the power of two in scientific notation explain please
Answer:
2.35 x 10^3
Step by Step:
Rewrite the number in scientific notation.2.35 x 10^3
.The endpoints of AB are A(1,4) and B(6,-1).
Answer:
5√2
Step-by-step explanation:
Finding distance :-
d = √{ ( 1 -6)² + (4+1)²}d = √{ -5² + 5² }d = √{ 25 + 25} d = √50 d = 5√2Graph the integer 3 and its opposite on a number line.
pls answer w explanation!
What is the product of the complex numbers 2 + 6i and 2 - 6i? (Note: i= √-1)
Answer:
10
Step-by-step explanation:
Apply difference of squares.
[tex](x + y)(x - y) = {x}^{2} - {y}^{2} [/tex]
[tex](2 + 6i)(2 - 6i) = {2}^{2} - {6i}^{2} [/tex]
[tex] = 4 + 6[/tex]
[tex] = 10[/tex]
Express each of the following negative angles as its equivalent positive angle between 0°and360°
+120°
Answer:
Dilated pupils
Long periods of wakefulness
Loss of appetite
Overconfidence
Over-excitement
Paranoia
Runny nose or frequent sniffles
White powder around nostrils
Legal issues
Missing or being late to work
Financial problems
Mood swings
Irritability
Depression
help asap ---- ---- ---- ---- ----v ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
Given:
The graph of h(x) is the greed dashed line segment.
To find:
The endpoints of the function [tex]h^{-1}(x)[/tex].
Solution:
If (a,b) is the point on the graph of the function f(x), then (b,a) must be the point on the inverse function [tex]f^{-1}(x)[/tex]
From the given graph, it is clear that the endpoint of the line segment h(x) are (-8,1) and (3,-4).
So, the endpoints of the inverse function [tex]h^{-1}(x)[/tex] are (1,-8) and (-4,3).
Therefore, the endpoints of [tex]y=h^{-1}(x)[/tex] are (1,-8) and (-4,3), and the graph is shown below.
Instructions: Find the measure of
Answer:
93
Step-by-step explanation:
Add the two angles 48 and 39 =87. 180-87=93
From the top of a 200 foot lighthouse, the angle of depression to a ship on the ocean is 23 degrees. How far is the ship from the base of the lighthouse?
Answer:
84.89 feets
Step-by-step explanation:
The solution triangle attached below :
The distance between base of lighthouse and ship, d, can be calculated using trigonometric relation :
Tan θ = opposite / Adjacent
Tan 23 = d / 200
d = 200 * tan23°
d = 84.89 feets
plisss help me in thiss
Answer:
x=80
Step-by-step explanation:
The angle of a line is 180*.
The equation would be (x+20)+x=180
Subtract 20 from both sides: 2x=160
Divide by 2: x=80
That's your answer!
I hope this helps!
Answer:
x=80
Step-by-step explanation:
I cant explain well but edge 2021 never lie's!
Sven determined that the x-coordinate is approximately 3.6 because the point is closer to 4 than 3 and seems to be a little more than halfway between them. What is the approximate value for the y-coordinate? y Almost-equals –1.1 y Almost-equals –1.4 y Almost-equals –1.8 y Almost-equals –1.9
Answer:
The answer is "[tex]y\approx 1.4[/tex]".
Step-by-step explanation:
In the given question the y-coordinates range between -1 to -2. Its distance between -1 and -2 is near, and less than halfway.
Answer:
b
Step-by-step explanation:
What is the order of rotational symmetry of a regular pentagon?
Answer:
yeet
Step-by-step explanation:
urmom
Instructions: Find AB. given that line AD is the perpendicular bisector of BC.
Answer:
19
Step-by-step explanation:
because line a d divided the triangle ABC into two equal halves therefore line a b is equal to line AC which is equal to 19
