[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ \cfrac{1}{4}}(x-\stackrel{x_1}{8}) \\\\\\ y-6=\cfrac{1}{4}x-2\implies y=\cfrac{1}{4}x+4[/tex]
True or False? If a grapefruit cost
$0.32 in 1984 and $0.64 in 2006,
then it must have cost $0.48 in
1995.
Answer:
False
Step-by-step explanation:
Without a graph, figure, or any other context the cost of grapefruit in 1995 in not related to the other years by any other facts or figures.
two cruise ships leave port at the same time. ship a sails north at a speed of 60 mph while ship b sails east at a speed of 50 mph.
Answer: y= 60x, y=50x
Step-by-step explanation:
Please Provide the whole question
Simplify
(2m^3n^2)^5
[tex] \large \bf \implies{32 {m}^{15} {n}^{10} }[/tex]
Step-by-step explanation:[tex]\bf \longrightarrow{(2m^{3}n^{2})^{5} } \\ \\ \bf \longrightarrow {2}^{5} \times ( {m}^{3})^{5} \times ( {n}^{2})^{5} \\ \\ \bf \longrightarrow32( {m}^{3})^{5}( {n}^{2})^{5} \\ \\ \bf \longrightarrow32 {m}^{15} {n}^{10} [/tex]
Note : We have used the two exponent rules:
[tex](1) \: \: \large \bf \boxed{ \bf \green{(ab)^{n} = {a}^{n} \times {b}^{n} }}[/tex]
[tex](2) \: \: \large \bf \boxed{ \bf \green{(a^{n})^{m} = {a}^{nm} }}[/tex]
cly cloudy
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Solve for x, rounding to the nearest hundredth.
110 • 10^4x = 55
[tex]110\cdot 10^{4x}=55\implies 10^{4x}=\cfrac{55}{110}\implies 10^{4x}=\cfrac{1}{2}\implies 10^{4x}=2^{-1} \\\\\\ \log\left( 10^{4x} \right)=\log\left( 2^{-1} \right)\implies 4x\log_{10}\left( 10 \right)=-1\log_{10}(2)\implies 4x(1)=-\log(2) \\\\\\ 4x=-\log(2)\implies x=-\cfrac{\log(2)}{4}\implies {\LARGE \begin{array}{llll} x\approx -0.08 \end{array}}[/tex]
Determine the x- and y-coordinates of a point through which the resultant of the parallel forces passes.
The resultant of the parallel force passes, x=2.8888 in and y=-5.4444 in
Taking moment about 'y'
∈Mx=RXx
x=260/90
x=2.8888 in
Taking moment about 'x'
∈My=RXy
y= -490/90
y= -5.4444 in
What is the example of parallel forces?When two forces of equal strength act in the same direction within the same plane, with the counterforce in the centre, this is known as a parallel force system.
A see-saw is an illustration of this. The fulcrum in the middle provides the counterforce to keep the seesaw in a neutral position while the children apply the two forces at the ends. The significant vertical forces on an aeroplane while it is in flight is another illustration (see image at right).
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charlotte denning earns both $13/hour and $26 for every sale she completes. during the most recent week, she worked 47 hours and made a total of 71 sales.
Answer: nice for her
Step-by-step explanation:
what does the remainder theorem conclude given that f(x)x 5 has a remainder of 17?enter your answer by filling in the boxes.
The remainder theorem conclude given that F(-5)=17
When, x= -5
x+5=0
So, F(-5) = 17
What is Remainder Theorem explain?According to the remainder theorem, the result of dividing p(x) by (x - a) is p. (a). According to the factor theorem, (x - a) can only be a factor of p(x) if f(a) = 0. It is used to locate the rest. A linear polynomial's status as a factor of the input polynomial is determined using this method.
The remainder theorem is used to calculate the remainder when a polynomial is split by a linear polynomial. We are aware that long division of polynomials can be used to find the remainder after dividing one polynomial by another. The remainder can instead be discovered using the remainder theorem.
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scores on the act college entrance exam follow a bell-shaped distribution with mean 21 and standard deviation 5. wayne’s standardized score on the act was −0.6. what was wayne’s actual act score?
Wayne's actual act score is 18
A z-score tells you where the score lies on a normal distribution curve.
A standard deviation is a measure of how dispersed the data is in relation to the mean.
Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Given,
The mean = 21
Standard deviation =5
z-score = -0.6
We know z-score = (x-mean)/ Standard deviation
Substitute the values
-0.6 = [tex]\frac{x-21}{5}[/tex]
x-21 = -0.6 ×5
x-21 = -3
x=-3+21
x=18
Hence, the Wayne's actual act score is 18
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Question 5 pls help Pre algebra explain your answer
Answer: -6.62 x 10^-8
Step-by-step explanation:
a light is suspended at a height h above the floor. the illumination, i, at a point p is inversely proportional to the square of the distance, r, from the point p to the light and directly proportional to the cosine of the angle theta. assume k is the constant of proportionality. which of the following can be used to represent the illumination at point p? i
a light is suspended at a height h above the floor. the illumination, i, at a point p is inversely proportional to the square of the distance, r, from the point p to the light and directly proportional to the cosine of the angle theta , I = k cos x / r² can be used to find the illumination at point p.
Light must be at the height of 7.07 for maximum illumination.
I = k cos x / r²
r² = h² + 10²
cos θ = h / [tex]\sqrt{h^{2} +10^{2} }[/tex]
then
I = [tex]k \frac{h}{(h^{2} + 100)^{2/3}}[/tex]
on differentiating, we get,
[tex]\frac{dI}{dh} = k\frac{h^{2} + 100^{3/2 - 3h^{2}(h^{2} + 100 )^{1/2} } }{(h^{2} +100)^{3} }[/tex]
[tex]= k\frac{100 - 2h^{2} }{(h^{2} + 100)^{5/2} } \\\frac{dI}{dh} = 0\\ It gives that \\h = \sqrt{50} = 7.07\\on differentiating again,\\\frac{d^{2} I}{dh^{2} } = k \frac{(6h^{3} - 900h )}{(h^{2} + 100)^{7/2} }[/tex]
for h = 7.07,
[tex]\frac{dI^{2} }{dh^{2} } = -10267.6[/tex]
So , we can conclude that the light must be at the height of 7.07 for maximum illumination.
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can you solve for x −68<8x−4<−36
Answer:
- 8 < x < - 4
Step-by-step explanation:
- 68 < 8x - 4 < - 36 ( add 4 to each interval )
- 64 < 8x < - 32 ( divide each interval by 8 )
- 8 < x < - 4
I dont get it pls helpppp ihave ten min left it a test HELP
Answer:
d. p+1
a negative 1 point something decimal plus one negative decimal.
gl sh awty
Which expression is equivalent to this
expression?
√2³
1
2 12
Answer:
calculators are available
Step-by-step explanation:
What are the zeros of the polynomial function?
Select all correct zeros of each function.
The zeroes of the polynomial functions are listed below:
Roots: 2, 3, - 1. Roots: 3, - 2 (multiplicity 2), 1 Roots: 0 (multiplicity 3), 2, - 3.How to determine the zeros of a polynomial
Polynomials are algebraic constructions whose form is summarized by the following sum:
p(x) = ∑ cₙ · xⁿ, for n ∈ {0, 1, ..., m}
An alternative form to describe polynomials is using products of binomials of the form (x - r), where r is a root (zero) of the polynomial. The root of the polynomial is a value such that the result of the expression is equal to zero.
Then, we proceed to find the zeros of each polynomial function:
1) f(x) = 2 · x · (3 - x) · (x + 1). Roots: 2, 3, - 1.
2) f(x) = 2 · (x - 3) · (x + 2)² · (x - 1). Roots: 3, - 2 (multiplicity 2), 1
3) f(x) = x³ · (x - 2) · (x + 3). Roots: 0 (multiplicity 3), 2, - 3.
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identify the meanings of the varibles in the point-slope form of a line
The variables in the point-slope form of a line (x₁,y₁) is a given point on the line, m the slope of the line and (x,y) is any point on the line.
Given that the variables in the point-slope form of a line.
The general form of the equation of a line is y - y₁ = m (x-x₁) where m is the slope of line, y₁ and x₁ is any point on the line
It is an equation of degree one x and y represent the coordinate of the point on the line represented in the coordinate plane
m = slope of the line
The general equation of a line is y = mx + c where
m = slope of line
(x₁ , y₁) = it is the given point on the line as data points are represented as (x₁,y₁) , (x₂,y₂) , (x₃,y₃) and so on
(x ,y) = it is any point line where x is any point on the x-axis and y is any point on y-axis
Hence, the variables in the point-slope form of a line where (x₁,y₁) is a given point on the line, m the slope of the line and (x,y) is any point on the line.
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HELPPP 25 pointssss MATH
Answer: [tex]\frac{3}{4s}[/tex]
Step-by-step explanation:
3s^2 / 4(s)^3=
3s^2 / 4s^3=
3/4 * s^2/s^3=
3/4 * s^(2-3)=
3/4 * s^(-1)=
3/4 * 1/s=
3*1 / 4s=3/(4s)
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15. The dimensions of a cylindrical can are shown below.
1
10 in.
3 in.
What is the volume of the can, in terms of ?
A. 60 π cubic inches
TL
B. 90 cubic inches
C. 30 π cubic inches
D. 18 π cubic inches
Answer:
volume of cylinder is πr²h so whatever your radius is then square it multiply by height. don't multiply by pi as it gives it to you in the answer
What is the break-even quantity for the following situation? fc = $1,400 per week vc = $2 per unit rev = $6 per unit group of answer choices 100 600 1,400 350 250
According to the question, to calculate break-even quantity with the given data. And the data is in dollars which is as follows:
Fixed cost (f(c)) = [tex]$1400[/tex] per week;
Variable cost (v(c)) = [tex]$2[/tex] per unit
Revenue = [tex]$6[/tex] per unit
Let us consider the break-even quantity to be ‘a’.
As per break-even point formula: Total costs = Total Revenue
And Total costs = Fixed cost + variable cost ;
Total Revenue = (price per unit)(quantity sold)
Using above formulas, the above expression can be re-written as:
Fixed cost + variable cost = (price per unit)(quantity sold)
[tex]($1400)+($2a) = ($6a)[/tex]
[tex]4a = 1400[/tex]
[tex]a = 350[/tex]
Therefore, the break-even quantity is [tex]350[/tex] units.
What is the break-even quantity?
Break-even quantity in the firm is the incremental value which is used to sell in order to cover the cost of the marketing program or other companies investments. And in this, the total cost is equal to the total revenue.
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Help anyone with both
The word phrases given can be written in algebraic expressions as:
1. B. 4g
2. B. 6/(x + y).
How to Write an Algebraic Expression?"Product" means multiplication.
"The product of g and 4" can be written as an algebraic expression as: 4 × g = 4g.
"Quotient" means the result you get by dividing a number by another number.
"Sum" means addition, or what you get by adding two quantities together.
Therefore, "the sum of x and y" is written in algebraic expression as: x + y.
Thus, the quotient of 6 and (x + y) would be written in algebraic expression as: 6/(x + y).
Therefore, the word phrases given can be written in algebraic expressions as:
1. B. 4g
2. B. 6/(x + y).
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Can you help me solve for x in these 3
You start at (1, 3). You move up 2 units and left 6 units. Where do you end?
Answer:
(-5,5)
Step-by-step explanation:
A line passes through point (6, -6) and has a slope of -4/3
Write an equation in Ax+By=C form for this line.
Use integers for A, B, and C.
-
Answer:
4x + 3y = 6
A = 4
B = 3
C = 6
Step-by-step explanation:
A line have a function:
y = ax + b
Because the line has a slope of - 4/3
=> a = - 4/3
=> y = - 4/3 x + b
Because the line go through point (6; - 6)
=> - 6 = - 4/3 .6 + b
=> b - 8 = - 6
=> b = 2
=> The function of the line
y = - 4/3 x + 6
=> 3y = - 4x + 6
=> 4x + 3y = 6
When sampling from the population of interest, it is a good idea to have a representative sample. True or false?.
Answer: True, common sense dictates this.
Answer: true
Step-by-step explanation:
A car salesman earns 1/36 in commission. If he sold a car for $43,000, how much did he earn in commission?
Answer:
1194 ....................... is the answer
Aileen is a salesperson at Lopez Sporting Goods. She is paid a monthly commission on all Little League uniforms she sells. She receives 10% of her first $2,000 in sales and 12% of the balance of her sales. Last week she earned $231.20. What was the total value of the uniforms she sold?
The total value of the uniform Aileen sold is x= 2260 on monthly Commission sells.
Given,
Let us assume the all little League uniform = x
Aileen first commission 10% of 2000$ in sales.
Aileen Second Commission 12% of (x-2000)$
Total Commission Aileen Earner = 10% ×2000 + 12% × (x-2000)
231.2 = 0.1× 2000 + 0.12× (x-2000)
231.2 = 200 + (0.12x - 240 )
231.2 = 200 + 0.12x - 240
After Transformation, we get
0.12x = 231.2 - 200 +240
0.12x = 271.2
x = 271.2/.12
x = 2260
Aileen Sell the total value of Lopez Sporting Goods Uniform is 2260.
So the final Answer is x = 2260$.
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To maintain a healthy weight a dog requires 30 calories of food per pound of body weight. if a certain dog weighs 38.45 ibs how many calories would they require
Step-by-step explanation:
30 cal for 1 lb
x cal for 38.45 lbs
x = 38.45lbs × 30 cals
x = 1153.5 cals
Please help I need to get this one question right so I can pass my lesson
Answer:
I think the answer is
Statement A
Step-by-step explanation:
Write an algebraic expression that models the situation.
Jenny had $105, but she is spending $13 per week.
The algebraic expression that models the situation when Jenny had $105, but she is spending $13 per week is 105 - 13w.
How to calculate the value?Let the number of weeks be represented by x
Therefore, since Jenny had $105, but she is spending $13 per week, the appropriate expression will be:
= 105 - (13 × w)
= 105 - 13w
The expression is 105 - 13w.
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Show full work please
The temperature in degrees celcius in which bacteria cannot survive is greater than 3.66
Subject of formulaThis is a way of representing a variable with another
Given the inequality below;
q/5 C + 32 ≥ 120
Substitute C = 120oF
q/5(120) + 32 ≥ 120
24q + 32 ≥ 120
24q ≥ 120 - 32
24q ≥ 88
q ≥ 88/24
q ≥ 3.66
Hence the temperature in degrees celcius in which bacteria cannot survive is greater than 3.66
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What is the five number summary for this data set 9,14,15,18,20,22,29,36,36,42,45,51
Answer:
Min = 0
Max = 51
M = 25.5
Q1 = 16.5
Q3 = 39
Hope this helps! <3