Answer:
The desired distance is √5
Step-by-step explanation:
Recall that the distance from a point to a line is measured along a path perpendicular to the line. Thus, given the line y = -2x + 5, the slope of any line perpendicular to it is the negative reciprocal of -2: +1/2.
The line perpendicular to y = -2x + 5 and passing through (4, 2) is
y - 2 = (1/2)(x - 4), or
2y - 4 = x - 4, or 2y = x, or y = (1/2)x.
Now our problem becomes "find the length of the line connecting (4, 2) and the intersection of y = -2x + 5 and y = (1/2)x."
Equating these, we get (1/2)x = -2x + 5, which, if multiplied through by 2, becomes x = -4x + 10, or 5x = 10, or x = 2. If x = 2, then y = (1/2)(2) = 1.
Finally, find the distance between (2, 1) and (4, 2):
Using the Pythagorean Theorem, d = √(2^2 + 1^2) = √5
The distance from (4, 2) to the line y = -2x + 5 is √5
Factor completely, then place the factors in the proper location on the grid. 25a2 +9b2 + 30ab
Answer:
(5a+3b)(5a+3b) or SQ(5a+3b)
Step-by-step explanation:
Now you can plot by referring to the above factors
Jill calls a plumber to her house to fix the leaking faucets . The plumber charges a one-time fee of $50 plus an additional $35 per hour of labor. What are the independent and dependent variables
Answer:
independent=$50
dependent=$35X
Step-by-step explanation:
50 is the independent variable because it doesn't change.
35X is the dependent variable because it does change.
In this scenario, the independent variable is the number of hours of labor and dependent variable is the total cost.
The independent variable is the number of hours. It is the variable that we can control or change.
The dependent variable is the total cost charged by the plumber.
It depends on the number of hours of labor and is determined by the plumber's fee structure, which includes a one-time fee of $50 plus $35 per hour of labor.
The total cost is calculated based on the number of hours of labor, making it the dependent variable in this situation.
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Eric wants to buy a new hat
which costs $17. He made
$5 by raking leaves and
$8 by washing cars.
How much more money does he need?
Answer:
the answer is 4
Step-by-step explanation:
you subtract 13 from 17 =4
1/6 of ______ equals 9
What is the blank?
Answer:
54
Step-by-step explanation:
1/6 × y = 9
y ÷ 6 = 9
y ÷ 6 × 6 = 9 × 6
y = 54
There are twelve empty rooms in the office of Acme Softwares, inc. Alif and Laila joins the company. How many ways can they be assigned a room each from these twelve
Answer:
132.
Step-by-step explanation:
That would be the number of permutations of 2 from 12.
12P2 = 12! / (12-2)!
= 132.
If f(x)=2x²-x find f(-3)
Answer:
21
Step-by-step explanation:
f(x) = 2x^2 - x
f(-3) = 2*(-3)^2 - (-3)
=2*9 +3
=18 +3
=21
Answer: 21
Step-by-step explanation: To find f(-3) or the value of the function when x = -3, we plug in a -3 for the x in our function and we have 2(-3)² - (-3).
Start by simplifying the exponent to get 9.
So we have 2(9) - (-3) or 18 + 3 which is 21.
Differentiate the function. y = (2x - 5)^2 (5 - x)?
Answer:
[tex]\displaystyle y' = -(2x - 5)(6x - 25)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsFactoringCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
y = (2x - 5)²(5 - x)
Step 2: Differentiate
Derivative Rule [Product Rule]: [tex]\displaystyle y' = \frac{d}{dx}[(2x - 5)^2](5 - x) + (2x - 5)^2\frac{d}{dx}[(5 - x)][/tex]Chain Rule [Basic Power Rule]: [tex]\displaystyle y' = [2(2x - 5)^{2 - 1} \cdot \frac{d}{dx}[2x]](5 - x) + (2x - 5)^2\frac{d}{dx}[(5 - x)][/tex]Simplify: [tex]\displaystyle y' = [2(2x - 5) \cdot \frac{d}{dx}[2x]](5 - x) + (2x - 5)^2\frac{d}{dx}[(5 - x)][/tex]Basic Power Rule: [tex]\displaystyle y' = [2(2x - 5) \cdot 1 \cdot 2x^{1 - 1}](5 - x) + (2x - 5)^2(1 \cdot -x^{1 - 1})][/tex]Simplify: [tex]\displaystyle y' = [2(2x - 5) \cdot 2](5 - x) + (2x - 5)^2(-1)[/tex]Multiply: [tex]\displaystyle y' = 4(2x - 5)(5 - x) - (2x - 5)^2[/tex]Factor: [tex]\displaystyle y' = (2x - 5)[4(5 - x) - (2x - 5)][/tex][Distributive Property] Distribute 4: [tex]\displaystyle y' = (2x - 5)[20 - 4x - (2x - 5)][/tex][Distributive Property] Distribute negative: [tex]\displaystyle y' = (2x - 5)[20 - 4x - 2x + 5][/tex][Subtraction] Combine like terms (x): [tex]\displaystyle y' = (2x - 5)[20 - 6x + 5][/tex][Addition] Combine like terms: [tex]\displaystyle y' = (2x - 5)(25 - 6x)[/tex]Factor: [tex]\displaystyle y' = -(2x - 5)(6x - 25)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
Look at the illustration.
What is WX?
Answer:
O 0.5 units
Step-by-step explanation:
so the first thing we have to do is to calculate for the dilation factor. Taking point G as the reference point, we can see that the distance of point G from rectangle W'X'Y'Z is 1.5 while the distance from rectangle WXYZ is (1.5 + 7.5) = 1.5 / 9 = 1/6
Since WX has an initial measure of 3 units, therefore the measure of W'X' is:
W'X' = 3 units *(1/6) = 0.5 units
emma can read 4 pages of a book in 8 minutes how many pages can she read per minute if she still had it 24 pages how many pages are there in the book
Answer:
Emma can read 30 pages per minute
Number of book pages 28
Step-by-step explanation:
Rewrite the equation by completing the square.
x^2 + 7x + 12 = 0
Answer:
x^2 + 7x + 12 = 0
x^2 + 7x = -12
(+3)(+4)=0
=−3
=−4
I also love r o blox
Hope This Helps!!!
Answer:
(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{1}{4}[/tex] = 0
Step-by-step explanation:
Given
x² + 7x + 12 = 0
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² + 7x
x² + 2([tex]\frac{7}{2}[/tex] )x + [tex]\frac{49}{4}[/tex] - [tex]\frac{49}{4}[/tex] + 12 = 0
(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{49}{4}[/tex] + [tex]\frac{48}{4}[/tex] = 0 , that is
(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{1}{4}[/tex] = 0
Simplify the expression
Answer:
6
Step-by-step explanation:
3 sqrt(20) / sqrt(5)
We know that sqrt(a) /sqrt(b) = sqrt(a/b)
3 sqrt(20/5)
3 sqrt(4)
3 *2
6
16. Using divisibility tests, check whether the number 240720 is divisible by
2, 3, 4, 5, 6, 8, 9, 10 and 11. (Give reason)
Evan wants to make an array of 32 miniature cars What are all the different ways Evan can place the cars?
Answer:
1 × 32, 2 × 16, 4 × 8, 8 × 4, 16 × 2, 32 × 1
Step-by-step explanation:
There are 6 different ways for Evan to create a array of 32 miniature cars.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
An array would constitute the shape of a parallelogram, in which you are essentially solving for s₁ and s₂.
Since there are 32 miniature cars in all, in which both sides, when multiplied, must result in said number:
32 x 1 = 32
2 x 16 = 32
4 x 8 = 32
8 x 4 = 32
16 x 2 = 32
1 x 32 = 32
Hence, There are 6 different ways for Evan to create a array of 32 miniature cars.
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What is the period of the graph of y = 5 sin (πx) + 4?
Answer:
I think it’s 2 hope my answer was good have a nice day as well
Step-by-step explanation:
The period of the given function y = 5 sin (πx) + 4 is π.
We have given that,
y = 5 sin (πx) + 4
We have to determine the period
What is the period?
The period of the sine curve is the length of one cycle of the curve. The natural period of the sine curve is 2π.
Therefore the period of the given function is π.
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A trinomial is a perfect square when two terms are
a. Positive
b.negative
c. Neither positve
d. Either negative
Answer:
a trinomial is a perfect square trinomial if it can be factorized into a binomial multiplies to itself. In a perfect square trinomial, two of your terms will be perfect squares.
PLEASE HELP ME WILL MARK YOU JF YOU HELP ME PLEASE!!!
Answer:
2, 3, 4, 7, 8, 10 I hope
Answers
Congruent by AAS (shown in the example)Congruent by SASCongruent by SSSCongruent by ASANot enough info (shown in the second example)Congruent by AASCongruent by SASCongruent by SSSCongruent by AASNot congruent=================================================
Explanations:
As the example shows, we have two pairs of congruent angles and a pair of congruent sides. The side are not between the angles in question. So AAS is slightly different from ASA.We have two pairs of congruent sides, and a pair of congruent angles. The angles are between the sides. So we use SAS which is a valid congruence theorem. Recall that SSA is not a valid theorem, so the order matters.We have three pairs of congruent sides, so we go with SSS. The order doesn't matter here.Similar to problem 1, but now the sides are between the angles. So we go with ASA this time instead of AAS.We unfortunately don't have enough info to determine if the triangles are congruent or not. We need to know something about the side lengths to determine congruency.As the hint suggests, marking the vertical angles will produce the other pair of congruent angles. So that's why we go for AAS (the side is not between the angles).This is similar to problem 2, as both use SAS. Note the unmarked vertical angles which are congruent.This is similar to problem 3. We use SSS here because we have 3 pairs of congruent sides as indicated by the tickmarks.The unmarked vertical angles can get double arcs to show they are congruent. We have a pair of congruent sides that are not between the two pairs of congruent angles, so we go for AAS (problems 1 and 6 also use AAS).For the triangle on the left, the arc is between the tickmarked sides. The triangle on the right has the arc not between the tickmarked sides. So there's no way the triangles are the same. The arc needs to be between the marked sides for each triangle, if we wanted them to be congruent (using SAS).---------------
Acronyms
SSS = side side side
SAS = side angle side
ASA = angle side angle
AAS = angle angle side
What is a demand schedule?
А.
a chart that shows the demand for a type of product at various prices
B.
a graph that shows the demand for a product at a single price point
C.
a chart that shows the demand for a product at various prices
Answer:
Answer is C
Step-by-step explanation:
In demand when the price goes up the quantity goes up and when the price goes down the quantity also goes down
In Supply when the price goes up the quantity goes down and when the price goes down the quantity goes up
Demand Schedule is a Chart
Demand Curve is a graph
Supply Schedule is a Chart
Supply Curve is a graph
Hope this helps
Step-by-step explanation:
[tex]hope \: it \: helps[/tex]
A stamp collection is purchased for $1,000. Twenty years later, the owner is told that the collection is worth quite a bit of money! If the rate of return on the stamp collection is 4% per year, what is the current value of the stamp collection? In your final answer, include all of your calculations.
Answer:
The current value of the stamp collection is of $2,191.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
A stamp collection is purchased for $1,000.
This means that [tex]P = 1000[/tex]
The rate of return on the stamp collection is 4% per year
This means that [tex]n = 1, r = 0.04[/tex]
So
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 1000(1 + 0.04)^{t}[/tex]
[tex]A(t) = 1000(1.04)^{t}[/tex]
What is the current value of the stamp collection?
This is A(20). So
[tex]A(20) = 1000(1.04)^{20} = 2191[/tex]
The current value of the stamp collection is of $2,191.
Answer:
Step-by-step explanation:
y = 1000(1+0.04)^20
y = 1000(1.04)^20
Rounded to the nearest hundredth
y = 1000(2.19)
y = $2190
The sum of three numbers is fourteen. The first number minus three times the third number is the second number. The second number is six more than the first number. Find the three numbers.
Answer:
1st number (x) = 5
2nd number (y) = 11
3rd number (z) = -2
Step-by-step explanation:
Let the generic solution for this problem be x + y + z = 14.
The first number minus three times the third number equals the second number, so x - 3z = y. The second number is 6 more than the first number, so y = 6 + x.
x - 3z = y, we know that y = 6 + x, so the equation becomes x - 3z = 6 + x.
After some arithmetic, we find that z = -2.
Plugging our knowns back into the generic solution becomes:
x + x - 3z + z = 14
2x - 3(-2) - 2 = 14
2x + 6 - 2 = 14
2x + 4 = 14
2x = 10
x = 5
So we know that z = -2, and x = 5, it's just simple substitution from there.
5 + y + (-2) = 14
5 + y = 16
y = 11
find the quotient of 8 divided by one-third, multiply 8 by
A:1/8
B:1/3
C:3
D:8
are the possible answers
Answer:
find the quotient of 8 divided by one-third, multiply 8 by
A:1/8
B:1/3( true
C:3
D:8
are the possible answers
what is 72 Times 27 equal
Answer:
1,944
Step-by-step explanation:
72x27=1,944
Have a wonderful day or night
Answer
1944
Step-by-step explanation:
72*27 = 1944
the image above should clarify how you're actually supposed to do it! couldn't submit this without 20 characters :,)
A right rectangular container is 10 cm wide and 24 cm long and contains water to a depth of 7cm. A stone is placed in the water and the water rises 2.7 cm. Find the volume of the stone.
Answer:
The volume of the rock is 648 cm^3
Step-by-step explanation:
Likely the only dimension that is free to move is the depth of 7 cm.
Volume of the Rock = L * W * h1
L = 24
W = 10
h1 = 2.7
V = 24 * 10 * 2.7
V = 648 cm^3
Answer fast please and thanks!
Answer:
tan 30 = x / 15
General Formulas and Concepts:
Trigonometry
[Right Triangles Only] SOHCAHTOA[Right Triangles Only] tanθ = opposite over adjacentStep-by-step explanation:
Step 1: Define
Identify variables
Angle θ = 30°
Opposite Leg = x
Adjacent Leg = 15
Step 2: Solve for x
Substitute in variables [tangent]: tan 30 = x / 15Answer:
3rd one
Step-by-step explanation:
Recall that
Sin = opposite over hypotenuse
Cos = adjacent over hypotenuse
Tan = opposite over adjacent
For the angle with a measure of 30 degrees we are given it's adjacent side length and need to find it's opposite side length
When dealing with opposite and adjacent we use tangent
If tan = opposite over adjacent
Then tan30 = x / 15 and the correct answer choice is the third one
what number must you add to complete the square? x^2+24x=50
Answer:
144
Step-by-step explanation:
Divide the b term which is 24 by 2
Gives you 12, then square it.
that's 144
formula for completing squares is [tex](b/2)^{2}[/tex]
100° - y А (x+2) units Match the values based on parallelogram ABCD, shown in the figure. length of BC value of y mZDAB value of I 56 4 44 2
Answer:
BC = 4 units
Value fo y = 44
∠DAB = 56°
Value of x = 2
Step-by-step explanation:
100 - y = 12 + y (opposite angles of parallelogram are equal)
2y = 88
y = 44
Similarly,
6-x = x+2 (opposite sides of parallelogram are equal)
2x = 4
x = 2
Write the word sentence as an equation.
The quotient of a number n and 5 is 18.
Answer:
n/5 = 18
Step-by-step explanation:
Quotient means division.
n/5 = 18
using the digits 0-9 at most one time each fill in the boxes so that the fraction equals the decimal
Step-by-step explanation:
Z 00m
336"083"2553
(wZE2XQ) are
The following data represent the maximum wind speed (in knots) and atmospheric pressure (in millibars) for a random sample of hurricanes that originated in the Atlantic Ocean.
Atmospheric Pressure (mb) Wind Speed (knots) Atmospheric Pressure (mb) Wind Speed (knots)
993 50 1006 40
995 60 942 120
994 60 1002 40
Required:
a. Find the y-intercept of the least-squares regression line, treating atmospheric pressure as the explanatory variable (round to four decimal places.)
b. Find the slope of the least-squares regression line, treating atmospheric pressure as the explanatory variable (round to four decimal places.)
c. Is it reasonable to interpret the y-intercept of the least-squares regression line, treating atmospheric pressure as the explanatory variable? Why or why not?
Answer:
Step-by-step explanation:
X Y X² Y² XY
993 50 986049 2500 49650
995 60 990025 3600 59700
994 60 988036 3600 59640
1006 40 1012036 1600 40240
942 120 887364 14400 113040
1002 40 1004004 1600 40080
[tex]\sum X: 5932[/tex] [tex]\sum Y : 370[/tex] [tex]\sum X^2 : 5867514[/tex] [tex]\sum Y^2 = 27300[/tex] [tex]\sum XY : 362350[/tex]
To determine the regression:
[tex]Mean \ (X) = \dfrac{\sum X }{n} \\ \\ = \dfrac{5932}{6} \\ \\ = 988.67[/tex]
[tex]Mean \ (Y) = \dfrac{\sum Y}{n} \\ \\ = \dfrac{370}{6} \\ \\ = 61.67[/tex]
Intercept [tex]b_o = \dfrac{\sum YX *\sum X^2 - \sum X \sum Y}{n(\sum X^2) - (\sum X)^2}[/tex]
[tex]=\dfrac{370(5867514) -(5932)(370)}{6(5867514) - (5932)^2}[/tex]
= 131760.9563
Slope [tex]b_1 = \dfrac{n(\sum XY) -(\sum X *\sum Y) }{n(\sum X^2)-(\sum X)^2}[/tex]
[tex]b_1 = \dfrac{6(362350) -(5932*370) }{6(5867514)-(5932)^2}[/tex]
[tex]b_1 = -1.2600[/tex]
The regression line equation [tex]Y = b_o +b_1X[/tex]
[tex]Y = 131760.96 -1.2600 X[/tex]
We then make a comparison of the slope of the equation to y = mx+c
slope of the equation = -1.2600
the y-intercept corresponds to when X = 0, thus:
y-intercept = 131760.9563
Yes, it is reasonable to interpret the y-intercept of the regression line, Using atmospheric pressure as an explanatory variable due to the fact that:
X is the independent variable and Y exists as the dependent variable.
Sketch the region enclosed by the given curves and calculate its area.
y=4-x^2 ,y=0
The answer is 32/3. But how do I get to that answer?
Answer:
Step-by-step explanation:
1.) we need to find the bounds of integration which is just the points of intersection
here is it (-2,0) and (2,0)
which means we will integrate from -2 to 2
next, we take the upper equation and subtract that from the lower one
kind of confusing but it would look like (sketch it out if you're not sure)
(4-x²)-0= 4-x²
then we can integrate
[tex]\int\limits^2_{-2} {4-x^2} \, dx =4x-\frac{x^3}{3}|_{-2}^{2}=(4*(2)-\frac{2^3}{3})-(4(-2)-\frac{-2^3}{3})=5.333333-(-5.3333333)= 10.666666667=\frac{32}{3}[/tex]
