Find the distance from point A(2,-1) to the line y=-x+4
Answers
9514 1404 393
Answer:
(3/2)√2 ≈ 2.1213 units
Step-by-step explanation:
The distance d from point (x, y) to line ax+by+c = 0 is given by ...
d = |ax +by +c|/√(a^2 +b^2)
We can write the equation of the line as ...
x + y -4 = 0
so the distance is ...
d = |x + y - 4|/√(1^2 +1^2)
For point (x, y) = (2, -1), the distance is ...
d = |2 +(-1) -4|/√2 = 3/√2 = (3√2)/2
The distance from A(2, -1) to the line y = -x +4 is (3√2)/2 units.
Related Questions
5 cm
What is the surface area of the cube?
A. 25 cm?
B. 70 cm
C.125 cm?
D. 150 cm?
E. 200 cm
Answers
Answer:
Step-by-step explanation:
Answer:
D. 150 cm²
[tex]area = 5 \times 5 \\ = 25 \: {cm}^{2} [/tex]
= 25 × 6 sides
= 150 cm²
In the diagram, three currents x, y and z are flowing in a circuit. The current y is 1 amp less than twice the current x. The current z is 2 ampere more than the current y. The total current x, y and z is 15 amperes. How many amperes is current x?
Answers
Answer:
3 A
Step-by-step explanation:
Current X = x
current Y = 2x -1
current Z = y + 2 = 2x - 1 + 2 = 2x + 1
Here, x + y + z = 15
x + 2 x - 1 + 2 x + 1 = 15
5 x = 15
x = 3 A
So, the current in x is 3 A.
Match each verbal description to its equivalent function rule as applied to the given function below. 3a – 7 = 6 - 9 = -3.1 14 (1) و = 3x - 7 = 121 – 19 = 60 - 2 = -31 28 The function fstretched vertically by a factor of 4 and translated up by 9 units The function ftranslated 6 units up and 2 units right The function freflected about the y-axis and translated 7 units left The function f stretched vertically by a factor of 2 and translated up by 5 units
Answers
Answer:f(x) = 3x - 7
6 up; 2 right = 3(x-2) - 7 + 6
= 3x - 6 - 7 + 6
= 3x - 7
reflected about y-axis; 7 left = -3(x+7) -7
= -3x - 21 - 7
= -3x - 28
up 5 ; 2 vert stretch = (2)(3x - 7) + 5
= 6x - 14 + 5
= 6x - 9
up 9 ; 4 vert stretch = (4)(3x - 7) + 9
= 12x - 28 + 9
= 12x - 19
Step-by-step explanation:
The transformation of a function may involve any change. The function f(x) stretched vertically by a factor of 2 and translated up by 5 units is (6x - 9).
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift:
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k × f(x)Horizontal stretch by a factor k: y = f(x/k)Given the function f(x)=3x-7, which can be transformed as shown below.
1. The function f(x) stretched vertically by a factor of 4 and translated up by 9 units.
Vertical stretch → 4(3x - 7) = 12x - 28
Up by 9 Units → (12x - 28) + 9
g(x) = 12x - 19
2. The function f(x) translated 6 units up and 2 units right
Up by 6 units → (3x - 7) +6 = 3x - 1
2 units Right → 3(x-2) - 1 = 3x - 6 - 1 = 3x - 7
g(x) = 3x - 7
3. The function f(x) reflected about the y-axis and translated 7 units left
Reflected about the y-axis → -3x - 7
7 units left → -3(x+7) - 7 = -3x - 21 -7 = -3x-28
g(x) = -3x-28
4. The function f(x) stretched vertically by a factor of 2 and translated up by 5 units
Stretched vertically by a factor of 2 → 2(3x - 7) = 6x - 14
Translated up by 5 units → 6x - 14 + 5 = 6x - 9
g(x) = 6x - 9
Learn more about Transforming functions here:
https://brainly.com/question/17006186
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62n−1=36 help quick thank you soosoo much!!
Answers
Answer:
n = 37/62
Step-by-step explanation:
62n - 1 = 36
(Add 1 on both sides)
62n - 1 + 1 = 36 + 1
62n = 37
(Divide 62 on both sides)
62/62n = 37/62
n = 37/62
Answer:
n equals 0.596!
Step-by-step explanation:
62n − 1 = 36
62n = 36 + 1
62n = 37
n = [tex]\frac{37}{62}[/tex]
n = 0.596 (the number is huge but it can be written in short like this)
Stewart has 18 birds remaining in avery. However he did have 29 until Tim left the door open. There are 8 blue birds and 4 Galahs. What percentage flew away?
Answers
Answer:
37.9%
Step-by-step explanation:
percentage that flew away = number that flew away /total number of birds x 100
number that flew away = 29 - 18 = 11
9/29 x 100 = 37.9%
Use a net of the square pyramid necessary to fnd the surface area of the pyramid
Answers
5/(x+2) + 2/(x+7) please solve for me
Answers
Step-by-step explanation:
this is the answer i guess
the pattern continues, what would be the eighth number in the pattern?4. 25, 28, 32, 37, 43 ______ PLS HELP ME
Answers
[tex]25,28,32,37,43,50,58,67.[/tex]
[tex]\boxed{The\:eighth\:number\:in\:the\:pattern\:is\:67.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]25, 28, 32, 37, 43,50,58,67\\ ✒ \: 25 + 3 = 28 \\ ✒ \: 28 + 4 = 32 \\ ✒ \: 32 + 5 = 37 \\ ✒ \: 37 + 6 = 43 \\ ✒ \: 43 + 7 = 50 \\ ✒ \: 50 + 8 = 58 \\ ✒ \: 58 + 9 = 67[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]
A ship is sighted from the top of a lighthouse. The angle of depression from the lighthouse to the ship is 45degrees. The distance from the top of the lighthouse directly to the ship is 4miles.Calculate the horizontal distance of the ship from the bottom of the lighthouse
Answers
Answer:
[tex]2\sqrt{2} \text{ mi}[/tex]
Step-by-step explanation:
See the attached image for a picture of the situation. The angle of depression lets you find the angle next to it but inside the triangle. It, too, must measure 45 degrees.
That means the triangle is an isosceles triangle (two legs of equal length).
Apply the Pythagorean Theorem.
[tex]x^2+x^2=4^2\\2x^2=16\\x^2=18\\x=\sqrt{8}=2\sqrt{2}\approx 2.83\text{ mi}[/tex]
17
Drag each tile to the correct box.
Match each savings plan to its description
401(k)
Roth IRA
403(b)
529 plan
health FSA
a tax-deferred retirement savings plan available to employees of some nonprofit
organizations and educational Institutions
a tax-advantaged college savings plan
an employer-offered retirement account that accepts contributions from
employees and employers
a tax-advantaged savings account available through employers to pay for
qualified medical expenses
Answers
Answer:
●an employer-offered retirement account that accepts contributions from employees and employers - 401(k)
●a tax-deferred retirement savings plan available to employees of some nonprofit - 403(b)
●a tax-advantaged college savings plan- 529 plan
●a tax-advantaged savings account available through employers to pay for qualified medical expenses- health FSA
Step-by-step explanation:
●401(k): Retirement
A 401(k) is one of the most well-known tools for retirement savings. A 401(k) is an employer-sponsored retirement plan that allows employees to contribute money on a pre-tax basis. Your contributions and earnings are not taxed until you start making withdrawals.
●403(b): Retirement
Like 401(k) accounts, a 403(b) is a form of an employer-sponsored retirement account. If you work for a public school, university, or non-profit organization, you may be eligible for a 403(b) account.
With a 403(b), you make contributions before taxes are taken out of your paycheck. You don’t pay taxes on the contributions .
● ROTH IRA: Retirement
A Roth IRA works differently than a Traditional IRA. Your contributions are not tax-deductible, and you make contributions with after-tax dollars. However, Roth IRAs offer a unique advantage: your earnings and withdrawals are tax-free. Roth IRAs have the same contribution limits as Traditional IRAs.
● 529 Plan: Education
A 529 education savings plan is a tool you can use to save for your child’s college tuition and fees. The money you invest can grow over time, and if the money is withdrawn to pay for qualified educational expenses, earnings are not subject to federal income tax. Depending on your state, your contributions may also be tax-deductible.
While 529 plans do not have contribution limits, contributions toward a 529 plan count as gifts and are subject to gift-tax laws.
● Flexible Spending Accounts: Health
Some employer-offered health insurance plans include flexible spending accounts (FSAs). With an FSA, you make pre-tax contributions into a separate account to use for health expenses. You can use your FSA dollars to purchase prescription and over-the-counter medications, pay your deductibles or coinsurance, and purchase medical supplies.
What geometric figure is the union of two non-collinear rays AB and AC?
ZBAC
ΔΑΒC.
BC
AB
Answers
suppose △BUG is an isosceles triangle. Find the measure of <B.
Answers
Answer:
B=44°
Step-by-step explanation:
x+10+3x+x=180
5x= 180-10
x=34
B= 34+10
B=44°
PLEASE!!! I JUST REALLY NEED HELP RIGHT NOW! T∆T
Using the 45o -45o -90o triangle theorem, solve this triangle.
Answers
Answer:
[tex] k = 24 \sqrt{2} [/tex]
Step-by-step explanation:
Given is a 45° - 45° - 90° triangle.
According to the 45° - 45° - 90° triangle theorem, measure of the side opposite to 45° angle is equal to [tex] \frac{1}{\sqrt 2} [/tex] times of the hypotenuse.
[tex]\therefore 24 = \frac{1}{ \sqrt{2} } k \\ \\ \therefore \: 24 \sqrt{2} = k \\ \\ \therefore \:k = 24 \sqrt{2} [/tex]
Answer:
Step-by-step explanation:
take 45 degree as reference angle
using cos rule
cos 45=adjacent/hypotenuse
1/[tex]\sqrt{2}[/tex]=24/k(do cross multiplication)
24*[tex]\sqrt{2}[/tex] =k*1
24[tex]\sqrt{2}[/tex] =k
Please help
LOLZ PLEADE BE WUICCKK
Answers
Answer:
answer is 30π cm
Step-by-step explanation:
use formula=2πr
=2*π*r
=2*π*15
=30π
Answer:
30[tex]\pi[/tex]
Step-by-step explanation:
So there is one thing we need to remember to solve thi:
circumfernce = 2[tex]\pi[/tex]r.
We know r(radius) is 15.
Lets plug that in:
2[tex]\pi[/tex]15
Multiply the 2 and 15 together:
30[tex]\pi[/tex]
So, depending on your math teacher, or math question, you might be required to write this in a different form.
So in your case, it seems the answers are written in terms of [tex]\pi[/tex], however sometimes you need to multiply your number by
30[tex]\pi[/tex]
Or
94.248
Looking at your answers, it seems 30[tex]\pi[/tex] is the third answer down.
Hope this helps! :D
Write an equation in slope intercept form of the line with the given characteristics. = through: (-3,1), slope · 2
Answers
Answer:
y=2x+7
Step-by-step explanation:
Hi there!
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
we are given the slope (2), and a point (-3,1)
we can subsitute 2 as m into the equation
y=2x+b
we need to find b
Since the equation will pass through the point (-3,1), you can use it to solve for b.
substitute -3 as x and 1 as y
1=2(-3)+b
multiply
1=-6+b
7=b
therefore the equation of the line is y=2x+7
Hope this helps!
Find the volume of the triangular prism.
Answers
Answer:
theres no picture
Step-by-step explanation:
In circle S with \text{m} \angle RUT= 30m∠RUT=30, find the \text{m} \angle RSTm∠RST.
Answers
Answer:
m∠RST= m RT= 60°
⭒⭒⭒⭒⭒⭒⭒⭒⭒⭒⭒⭒
m RT=2 m∠ROT= 2 (30)=60°✎--------------
hope it helps...
have a great day!!
In the diagram of
△△NRQ below, SP∥∥RQ, NS=10, SR=50, and PQ=40. What is the length of NQ?
Answers
Answer:
Step-by-step explanation:
Does the table show growth or decay?
Answers
Answer:
growth because the numbers are clearly getting higher.
GROWTH
because each x theres more and more y
An architect makes a model of a new house. The model shows a tile patio in the backyard. In the model, each tile has length 1/4 in. and width 1/6 in. The actual tiles have length 1/6 ft and width 1/9 ft.
What is the ratio of the length of a tile in the model to the length of an actual tile? What is the ratio of the area of a tile in the model to the area of an actual tile
Answers
Answer:
The answer is below
Step-by-step explanation:
The model is a tile with length 1/4 in. and width 1/6 in while the actual tile has length 1/6 ft. and width 1/9 ft.
Firstly we have to convert the model length and width from inches to feet.
1 feet = 12 inches
model length = 1/4 in. = 1/4 in * (1/12) ft./in = 1/48 ft.
model width = 1/6 in. = 1/6 in * (1/12) ft./in = 1/72 ft.
Therefore:
Ratio of model length to actual length of tile = (1/48 ft.) / (1/6 ft.) = 1 / 8
Ratio of model length to actual length of tile = (1/72 ft.) / (1/9 ft.) = 1 / 8
Area of model tile = length * width = 1/48 ft. * 1/72 ft. = 1/3456 ft²
Area of actual tile = length * width = 1/6 ft. * 1/9 ft. = 1/54 ft²
Ratio of model area to actual area of tile = (1/3456 ft²) / (1/54 ft²) = 1 / 64
(( THIS GIVES 50 POINTS )) PLEASE HELP ASAP
A car company’s profit can be modeled by the equation P = –2x^2 + 44x – 42, where P is the profit in millions of dollars and x is the number of cars sold in thousands.
(a.) How many cars are sold when the company breaks even?
(b.) What is the company’s maximum profit? How many cars sold gives the maximum profit?
Answers
Answer:
a) 1000,21000 are the break even number of cars
b) the maximum profit is 200 at 11000 cars
Step-by-step explanation:
P = –2x^2 + 44x – 42
To break even, P =0
0 = –2x^2 + 44x – 42
Factor
0 = -2( x^2 -22x+21)
0 = -2 ( x-21)(x-1)
Using the zero product property
0 = x-21 0 = x-1
x=21 x=1
Remember that x is the number of cars in thousands
When the profit is maximum is at the vertex
The vertex is 1/2 way between the two zeros
(1+21)/2 = 22/2 = 11
11 cars sold
The maximum profit is
P(11) = –2(11)^2 + 44(11) – 42=--242+484-42=200
The maximum profit is 200
Determine the volume of a cube with a side length of 3 2/3 cm.
Answers
Answer:
The volume would be 27
Hope this helps!
Brainliest??
if you multiply a certain number by 4 and then by 25 what is the number? (i know the answer but how do i write it in an algebraic equation?)
Answers
Answer:
the algebraic equation would be
4n x 25
At the beginning of the week, a puppy weighed 514 pounds. During the week, the puppy gains 8 ounces.
How much does the puppy weigh, in pounds, at the end of the week?
Enter your answer as a mixed number in simplest form by filling in the boxes
Answers
♣ explanation ♣
---------------------------------------------------------------------------------------------------------------
Add 8 ounces onto 5 to get 13, and then, add the unit fraction 1/4 onto it and you get 13 1/4 as your non-simplified mixed number answer.
---------------------------------------------------------------------------------------------------------------
But wait! The answer must be simplified into the mixed number, "5 3/4" by dividing the current answer by 8 1/2, or any other number that involves similarities to the fractions' characteristics.
simplify 5^-2
please help me! i don't know how to do it and its due today
Answers
0.04
jndjnwjnc jwnfjnjwfjn jn jnwjnj njnfjbfwhijfkwb jnj nwjnjfjwkf n
A gardener has a rectangle garden with an area of 374 yd.²The length of the garden is 17 yards the gardener wants to enlarge the garden by doubling only the width of the current garden how much fencing will the gardener need to enclose a new garden?
Answers
Answer:
105 yards
Step-by-step explanation:
The other side is Width = 374/17 = 22.
So, the new width is 44 ( and the length is 17/2).
Perimeter = 2(17/2) + 2(44) = 17+88=105 yds.
So, 105 yards.
Mark me as Brainliest if this is correct! I really appreciate it! :D
The perimeter of the new garden is 105 yards
The area of a rectangle is expressed as:
A = lww = A/l
w = 374/17
w = 22 yards
The perimeter of the new garden if the width is doubled is expressed as:
P = 2(l + w)
P = 2(17/2 + 2(22))
P = 17 + 88
P = 105 yards
Hence the perimeter of the new garden is 105 yards
Learn more on perimeter of rectangle here: https://brainly.com/question/19819849
The figure below is a square inside a rectangle
Answers
Answer:
ummmm their isn't no picture showing
have a good day :)
Step-by-step explanation:
Changing a single verb can change the story the sentence creates.
a.true
b.false
Answers
Answer:
yeah its totally true, it happened from me to
answer
the answer is true
Help I don’t get it
Answers
Answer:
143
Step-by-step explanation:
Your equation to find x is:
140+146/2 = 143
A cylinder has a diameter of 10cm. The height of the cylinder is 2 5 the length of the diameter. Calculate the volume of the cylinder in terms of π.
Answers
Answer:
625 π cm^3
Step-by-step explanation:
volume of a cylinder = πr^2h
π = 22/7
r = radius = 10/2 = 5cm
the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.
A radius is half of the diameter
π x (5^2) x 25 = 625 π