Katie has to drive 15 miles east and 36 miles north to get to her aunt's house. Which of the following equations could be used to find the direct distance to her aunt's house?
1. 36 2 + b2 = 15 2
2. 15 2 + 36 2 = c2
3. a2 + 15 2 = 36 2
Answers
Related Questions
if x =5 and y=12 whats the volume of the square
Answers
hopefully this helps a bit
Find the center and radius of the circle represented by the equation below.
Answers
Answer:
centre = (5, - 6 ) , radius = 7
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
given
x² + y² - 10x + 12y + 12 = 0 ( subtract 12 from both sides )
x² + y² - 10x + 12y = - 12 ( collect terms in x/ y )
x² - 10x + y² + 12y = - 12
using the method of completing the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(- 5)x + 25 + y² + 2(6)y + 36 = - 12 + 25 + 36
(x - 5)² + (y + 6)² = 49 = 7² ← in standard form
with centre (5, - 6 ) and radius = 7
Answer:
Center = (5, -6)
Radius = 7
Step-by-step explanation:
To find the center and the radius of the circle represented by the given equation, rewrite the equation in standard form by completing the square.
To complete the square, begin by moving the constant to the right side of the equation and collecting like terms on the left side of the equation:
\(x^2-10x+y^2+12y=-12\)
Add the square of half the coefficient of the term in x and the term in y to both sides of the equation:
\(x^2-10x+\left(\dfrac{-10}{2}\right)^2+y^2+12y+\left(\dfrac{12}{2}\right)^2=-12+\left(\dfrac{-10}{2}\right)^2+\left(\dfrac{12}{2}\right)^2\)
Simplify:
\(x^2-10x+(-5)^2+y^2+12y+(6)^2=-12+(-5)^2+(6)^2\)
\(x^2-10x+25+y^2+12y+36=-12+25+36\)
\(x^2-10x+25+y^2+12y+36=49\)
Factor the perfect square trinomials on the left side:
\((x-5)^2+(y+6)^2=49\)
The standard equation of a circle is:
\(\boxed{(x-h)^2+(y-k)^2=r^2}\)
where:
(h, k) is the center.r is the radius.Comparing this with the rewritten given equation, we get
\(h = 5\)\(k = -6\)\(r^2 = 49 \implies r=7\)Therefore, the center of the circle is (5, -6) and its radius is r = 7.
How can I get number 2 with only the number 7 and 10 and 3
Answers
Answer:
One way to get the number 2 using the numbers 7, 10, and 3 is:
(10 - 7) x 3 = 9
9 / 10 = 0.9
0.9 + 2.1 = 3
So, 3 - 0.9 - 2.1 = 2.
Step-by-step explanation:
there is another way.
7 + 3 = 10, and 10 ÷ 5 = 2.
Therefore, you can get 2 with the numbers 7, 10, and 3 by adding 7 and 3 to get 10, and then dividing 10 by 5 to get 2.
which point is on the line 4y-2x=0
Answers
Answer:
(2,1)
Step-by-step explanation:
The line 4y - 2x = 0 can be written in slope-intercept form as y = 1/2x.
So any point that satisfies this equation will lie on the line. For example, the point (2,1) satisfies the equation:
4(1) - 2(2) = 0
So the point (2,1) is on the line.
The increasing annual cost (including tuition, room, board, books and fees) to attend college ) to attend college has been widely discussed in many publications including Money magazine. The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars.
Private Colleges
53.8 42.2 44.0 34.3 44.0
31.6 45.8 38.8 50.5 42.0
Public Colleges
20.3 22.0 28.2 15.6 24.1 28.5
22.8 25.8 18.5 25.6 14.4 21.8
Required:
a. Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for private colleges.
b. What is the point estimate (in thousand dollars) of the difference between the two population means?
Answers
Answer:
a) The sample mean is of 42.7 thousand dollars.
The standard deviation is of 6.38 thousand dollars.
b) The point estimate of the difference between the two population means is of 20.4 thousand dollars.
Step-by-step explanation:
a. Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for private colleges.
Sample mean is the sum of all values divided by the number of values. So
\(M = \frac{53.8 + 42.2 + 44.0 + 34.3 + 44.0 + 31.6 + 45.8 + 38.8 + 50.5 + 42.0}{10} = 42.7\)
The sample mean is of 42.7 thousand dollars.
Sample standard deviation is the square root of the sum of the difference squared between each number and the mean, divided by the number of values. So
\(S = \sqrt{\frac{(53.8-42.7)^2 + (42.2-42.7)^2 + (44.0-42.7)^2 + (34.3-42.7)^2 + (44.0-42.7)^2 + (31.6-42.7)^2 + (45.8-42.7)^2 + (38.8-42.7)^2 + (50.5-42.7)^2 + (42.0-42.7)^2}{10}} = 6.38\)
The standard deviation is of 6.38 thousand dollars.
b. What is the point estimate (in thousand dollars) of the difference between the two population means?
First, we have to find the sample mean for public colleges, and then subtract the sample mean of private colleges by the sample mean of public colleges. So, for public colleges:
\(M = \frac{20.3 + 22.0 + 28.2 + 15.6 + 24.1 + 28.5 + 22.8 + 25.8 + 18.5 + 25.6 + 14.4 + 21.8}{12} = 22.3\)
Point estimate of the difference:
42.7 - 22.3 = 20.4
The point estimate of the difference between the two population means is of 20.4 thousand dollars.
let x be a random variable taking values [0, 1, 2, 3] with respective probabilities [0.2, 0.5, 0.2, 0.1] (a) determine the expectation of x. (show work)
Answers
A total of 23800 cubes can fit inside the box of the given dimensions.
What is the volume of cube?The volume of a cube is given by -
Volume = a x a x a = a³
Given is that a box has a length of 10 inches, a width of 8\(\frac{3}{4}\) inches, and a height of 4\(\frac{1}{4}\) inches.
The volume of the box would be -
V = 10 x 8\(\frac{3}{4}\) x 4\(\frac{1}{4}\)
V = 10 x 35/4 x 17/4
V = 371.875 inches³
The volume of cube -
v = 1/4 x 1/4 x 1/4
v = 0.015625 inches³
Number of cubes that will fill the box would be -
n = V/v
n = 371.875/0.015625
n = 23800
Therefore, a total of 23800 cubes can fit inside the box of the given dimensions.
To solve more questions on volumes, visit the link below -
https://brainly.com/question/10498558
#SPJ1
Which rhetorical appeal or device does Susan B. Anthony use in the opening of her speech?
Ethos, because she creates trust by calling her audience her friends and fellow citizens to show she's just like them
Irony, because she is saying something that is the opposite of what she means about women's right to vote
Logos, because she presents facts and statistics about women's right to vote
Rhetorical question, because she wants the reader to think about an issue through a question
Answers
The rhetorical appeal used by Susan B. Anthony in the speech is Ethos because she creates trust by calling her audience her friends and fellow citizens to show she's just like them.
What is a rhetorical appeal?These are techniques speakers use to prove they are reliable and their words can be tursted as they should be considered to be truth. Some rethorical appeals include:
Ethos: The speaker shows he/she is reliable and due to this the information provided is true.Pathos: The speaker appeals to the emotions of the audience.Logos: The speaker uses logic to prove the main point.What is the rethorical appeal used by the speaker?The appeal used by Susan B. Anthony is the ethos appeal as she starts her speech by saying "Friends and Fellow-citizens: I stand before you to-night, under indictment for the alleged crime of having voted" and the first sentence show she is equal to the men she is talking to which validates her words.
Note: This question is incomplete; here is the missing excerpt:
Friends and Fellow-citizens: I stand before you to-night, under indictment for the alleged crime of having voted at the last Presidential election, without having a lawful right to vote. It shall be my work this evening to prove to you that in thus voting, I not only committed no crime, but, instead, simply exercised my citizen’s right, guaranteed to me and all United States citizens by the National Constitution, beyond the power of any State to deny.
Learn more about rhetorical appeal in: https://brainly.com/question/19264317
#SPJ1
8. The percentage of the moon's surface that is visible to someone on the Earth varies due to
the time since the previous full moon. The moon passes through a full cycle in 28 days. The
maximum percentage of the moon's surface that is visible from Earth is 50%. Find a function
for the percentage, P, of the surface that is visible as a function of the number of days, t,
since the previous full moon.
Answers
A functiοn fοr the percentage is P = 25cοs(π/14t) + 25.
What is a functiοn?In the case οf a functiοn frοm οne set tο the οther, each element οf X receives exactly οne element οf Y. The functiοn's dοmain and cοdοmain are respectively referred tο as the sets X and Y as a whοle. Functiοns were first used tο describe the idealized relatiοnship between twο varying quantities.
Here, we have
Given:
Tο find the percentage οf the full mοοn, we can write an equatiοn in the fοrm P = Acοs(Bt) + C
After 14 days, the percentage οf the mοοn is zerο
A = (max-min)/2 = 50/2 = 25
The periοd = 28 days
P = Acοs(BT = t) + c
B = 2π/periοd = 2π/28 = π/14
c = min + A = 0 + 25 = 25
We get,
P = 25cοs(π/14t) + 25,
Here, p is the percentage οf the mοοn visible cοmpared tο the previοus full mοοn.
Hence, a functiοn fοr the percentage is P = 25cοs(π/14t) + 25.
To learn more about the function from the given link
https://brainly.com/question/10439235
#SPJ1
Please help will give brainliest
The point C (-3,-1) is rotated 180 clockwise around the origin.
What are the coordinates of the resulting point, C'?
Answers
Answer: \((3,1)\)
Step-by-step explanation:
Given
The point C \((-3,-1)\) is rotated \(180^{\circ}\) clockwise about the origin
If a point is rotated \(180^{\circ}\) about the origin, then the sign of the co-ordinates changes without changing the order of coordinates.
So,C \((-3,-1)\) becomes C' \((3,1)\) after the rotation.
12a^4+ (-29a^4) simplify
Answers
Answer: -17a^4
Step-by-step explanation:
Combine like terms
12a^4 +(-29a^4)
(12a^4-12a^4) - (29a^4-12a^4) =
-17a^4
Hope this helps
Please answer the question in the picture. And give a good explanation for brain
Answers
Answer:
B
Step-by-step explanation:
4 gallons of juice is being divided by 1/6
This month my metro water services bill was $36.34 and my Madison Suburban Utilty District bill was $26.03. My total water bill was $
Answers
Total water bill for the month is $62.37.
It seems that you may have accidentally left out the total amount of your water bill.
The total amount by simply adding the amounts of the individual bills together:
Total water bill =\($36.34 + $26.03\)
= \($62.37\)
You have not provided enough information to determine your total water bill.
You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.
To find your total water bill, you simply need to add the two bills together.
So, the total amount you owe for water this month would be:
Total water bill = \($36.34 + $26.03\)
= \($62.37\)
It appears that you may have forgotten to include the full amount of your water bill by accident.
Simple addition of the separate bill amounts yields the following sum:
Water bill total = \($36.34 + $26.03\)
= \($62.37\)
Your total water bill cannot be calculated because not enough information has been given.
Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.
You just need to combine the two invoices together to get your total water bill.
As a result, this month's total water bill for you would be:
Water bill total = \($36.34 + $26.03\)
= \($62.37\)
For similar questions on water bill
https://brainly.com/question/31119915
#SPJ11
Consider the graph of some function y equals f left parenthesis x right parenthesis.
Answers
The limits of the function for this problem are given as follows:
lim x -> -2 f(x) = 3.lim x -> 1 f(x) does not exist.lim x -> 4 f(x) = -3.How to obtain the limits of the function?In this problem, we are given the graph of the function, hence the limit is given by the value of the function as the function approaches x = a, not the actual numeric value of the function at x = a.
At x = -2, we have that:
To the left of x = -2, the function approaches x = -2 at y = 3.To the right of x = -2, the function approaches x = -2 at y = 3.As the lateral limits are equal, lim x -> -2 f(x) = 3.
At x = 1, we have that:
To the left of x = 1, the function approaches x = 1 at y = 0.To the right of x = 1, the function approaches x = 1 at y = -4.As the lateral limits are different, the lim x -> 1 f(x) does not exist.
At x = 4, we have that:
To the left of x = 4, the function approaches x = 4 at y = -3.To the right of x = 4, the function approaches x = 4 at y = -3.As the lateral limits are equal, lim x -> 4 f(x) = -3.
More can be learned about lateral limits at https://brainly.com/question/26103899
#SPJ1
A pound of blueberries costs $3.98 and a pound of clementines costs
$2.49. What is the combined cost of 0.6 pound of blueberries and 1.8
pounds of clementines? Round your answer to the nearest cent. $
Answers
Answer:
Step-by-step explanation:
0.6 of blueberries
0.6*3.98=2.388=2.39 dollars
1.8 clementines
1.8*2.49=4
4+2.39=6.39
HELPP!!!
The area of the figure is ____ square units.
Answers
Answer:
The answer is 132 square units
Step-by-step explanation:
Cutting the shape
we have two trapeziums
A=(area of small +Area of big)Trapezium
A=1/2(3+9)8 + 1/2(9+12)8
A=1/2×12×8 + 1/2×21×8
A=12×4 + 4×21
A=48+84
A=132 square units
HELP PLEASEEEEEEE!!!!!
Answers
The similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12
What are similar shapesSimilar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other. When two shapes are similar, one can be obtained from the other by uniformly scaling (enlarging or reducing) the shape.
Given that the shape EFGH is a smaller shape of JKLM, and they are similar, then:
the measure of angle Z is equal to 65°
the side EF corresponds to JK and side FG corresponds to KL, so:
8/20 = 11/x
x = (11 × 20)/8 {cross multiplication}
x = 27.5
the side EF corresponds to JK and EH corresponds to JM, so:
8/20 = y/30
y = (30 × 8)/20 {cross multiplication}
y = 12
Therefore, the similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12
Read more about similar shapes here: https://brainly.com/question/21823811
#SPJ1
1. Find the value of X (In the picture) (giving points to best answer/brainlest)
Answers
Answer:
x = 33
Step-by-step explanation:
The sum of the angles of a triangle add to 180
x+ 32 + 115 = 180
Combine like terms
x + 147 =180
Subtract 147 from each side
x+147-147 =180-147
x = 33
Answer:
x = 33 °
Step-by-step explanation:
we know that sum of inner angle of a triangle is 180 °.
According to the question
115 ° + 32 ° + x = 180 °
Combine like terms
147 ° + x = 180 °
Subtracting each side by 147 °
147 ° - 147 ° + x = 180 ° - 147 °
x = 33°
In how many ways can a store select 2 assistant managers out of 6 assistant managers to open and close the store?
Answers
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
6/2=3
Maggie goes to a clothing store to shop for t-shirts. The store is having a sale on t-shirts for 25% off each shirt. She purchases 5 t-shirts that were regularly priced at $22. What was the total the store charged her with the discount, but before tax?
Answers
Because 22-5% x 5 is 109.75
Answer:
A
Step-by-step explanation:
6 * 10x^{-3}/8*10x^{-6}
Answers
The simplified form of the given expression, 6 × 10⁻³ / 8 × 10⁻⁶, is 3/4 × 10³
Simplifying an expressionFrom the question, we are to simplify the given expression
The given expression is
6 × 10⁻³ / 8 × 10⁻⁶
Simplifying the expression
6 × 10⁻³ / 8 × 10⁻⁶
This can be written as
6/8 × 10⁻³/10⁻⁶
Reduce the fraction
3/4 × 10⁻³/10⁻⁶
Apply the division law of indices
3/4 × 10⁻³ ⁻ ⁽⁻⁶⁾
3/4 × 10⁻³ ⁺ ⁶
3/4 × 10³
Hence, the value is 3/4 × 10³
Learn more on Simplifying an expression here: https://brainly.com/question/723406
#SPJ1
Captain Ashley has a ship, the H.M.S Crimson
Lynx. The ship is two furlongs from the dread
pirate Umaima and her merciless band of
thieves.
If her ship hasn't already been hit, Captain
1
Ashley has probability of hitting the pirate
2
ship. If her ship has been hit, Captain Ashley will
always miss.
If her ship hasn't already been hit, dread pirate
1
Umaima has probability of hitting the
3
Captain's ship. If her ship has been hit, dread
pirate Umaima will always miss.
If the Captain and the pirate each shoot once,
and the pirate shoots first, what is the probability
that both the pirate and the Captain hit each
other's ships?
Answers
HELP I WILL RATE !!!!!!!
Answers
No picture, nothing to rate here.
Based on the information in the table, what
was the approximate value of this item in
1980?
Answers
Answer:
B) 4,700
Step-by-step explanation:
6000 - 4000 = 2000
2000 in 15 year, find how much for each year
2000/ 15 = 133.3333333
133.3333333 estimated = 133
133 approximately for each year
1975 to 1980 is five years
133 x 5 = 665
4000 + 665 = 4665
4665 rounded the the nearest hundred
4700
30m3n4-5m4complete factored form of the polynomial
Answers
Factor of polynomial m are 0, 6n⁴.
What is polynomial in maths?
A polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients, and it only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of the variables. The polynomial x2 4x + 7 is an illustration of one with a single indeterminate x.
= 30m³n⁴ - 5m⁴
= 5m³(6n⁴ - m )
let 5m³(6n⁴ - m ) = 0
5m³ = 0
m = 0
6n⁴ - m = 0
m = 6n⁴
Learn more about polynomial
brainly.com/question/11536910
#SPJ1
What is 43% of 166? (Round to the nearest whole number)
Answers
Name each type of special quadrilateral that can meet the given condition.
exactly one pair of congruent sides.
Choose the correct answer below.
Trapezoid
parallelogram and kite
trapezoid and isosceles trapezoid
isosceles trapezoid
kite and isosceles trapezoid
Answers
Change 60% to fraction in its simplest form
Answers
Answer: 3/5
Step-by-step explanation:
60% as a fraction is 60/100.
You can simplify 60/100 to 30/50 then simplify that further to 15/25 then using the 5 times tables you can simplify that to 3/5.
Place the steps for finding f'(X) in the correct order.
Plz help
Thank you!
Answers
Answer:
See below
Step-by-step explanation:
Given function is ,
=> f(x) = 4x + 7.
Replace f(x) with y ,
=> y = 4x + 7
For finding the inverse , interchange x and y ,
=> x = 4y + 7
Now solve for y ,
=> 4y = x - 7
=> y = x-7/4
Replace y with f-¹(x) ,
=> f-¹(x) = (x-7)/4
These are the required steps .
4a) What is the unit rate of the equation? (Tell how you came up with this answer.)
Y=-4X
4b) What is the unit rate of the table? (Tell how you came up with this answer.)
X
2
3
4
5
6
4
6
8
10
12
I
4c) which proportional relationship has the greatest unit rate: the table or the equation? Tell how you arrived
at your answer, showing all work.
Answers
Answer:
Unit rate is 2
Step-by-step explanation:
Pick two columns of the ordered pairs. Lets use (2,4) and (3,6)
The x values are 2 and 3 and the y values are 4 and 6
Now you’re going to divide y by x so
4/2 = 2
6/3 = 2
(Always choose two ordered pairs so you know that your answer is right)
Unit rate of the table is 2.
Define unit rate.The units of concentration and rate are always going to be molars per second. We now understand that molar per second is equal to k times molar in units. An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.
Given,
Choose two columns from the paired ordered columns. Using (2, 4) and (3,6)
The x and y values are 2 and 3, respectively, and the
You will now divide y by x, so
4/2 = 2
6/3 = 2
Unit rate of the table is 2.
To learn more about unit rate, visit:
https://brainly.com/question/11258929
#SPJ13
please help with the following
Answers
Step-by-step explanation:
a^2 b^2 5^3
that's the answer
Step-by-step explanation:
\( {a}^{3} . {b}^{2} . {5}^{3} \)