PLEASE HELP!!! Find the equation , in the standard form of the line passing through the points (3,-4) and (5,1)
Answers
[tex]\bf y=\cfrac{5}{2}x-\cfrac{15}{2}-4\implies y=\cfrac{5}{2}x-\cfrac{23}{2}\impliedby \begin{array}{llll} \textit{now let's multiply both}\\ \textit{sides by }\stackrel{LCD}{2} \end{array} \\\\\\ 2(y)=2\left( \cfrac{5}{2}x-\cfrac{23}{2} \right)\implies 2y=5x-23\implies \stackrel{standard~form}{-5x+2y=-23} \\\\\\ \textit{and if we multiply both sides by -1}\qquad 5x-2y=23[/tex]
side note: multiplying by the LCD of both sides is just to get rid of the denominators
Related Questions
If there are 4 math courses, 3 psychology courses, and 5 english courses offered in non-overlapping times so that you could select one of each for your schedule, how many different schedules would be possible?
Answers
[tex]4 \times 3 \times 5 = 60[/tex]
Answer:
there are many different answers that is because there are four different ways to answer this one question.
Step-by-step explanation:
4*3*5=60
4-+5+3=12
1) 435 2) 435 3) 435
a hiker walks 12 miles north. then she walks 9 miles west. What is the shortest distance the hiker can travel to return tonher starting point
Answers
hypotenuse^2 = 12^2 + 9^2 = 225 return distance = 15 miles.
What is the quotient when 0.75 is divided by 5?
Answers
(its just 0.75 ÷ 5)
two cylindrical candles have a scale factor of 3:5. The larger candle has a volume of 40(3.14) cubic inches. Fund the volume of thel the smaller candle. Write your answer in term of (3.14)
Answers
[tex]5 = 40\pi \\ 3 =( (40 \div 5) \times 3)\pi \\ = 24\pi[/tex]
The volume of the smaller candle is 8.64π cubic inches.
How to find the volume
The volume of a cylinder is given by the formula
V = π r² h,
where
r is the radius and
h is the height.
The scale factor is given as 3:5, which means the ratio of the volumes is (3³ : 5³)
Using the ratio, let volume of the the smaller candle. be x
3³ : 5³
x : 40π
cross multiply
x = 40π * 3³ / 5³
x = 40π * 27 / 125
x = 8.64π cubic inches.
James bought $175 in accessories for his video game console. He spent $15 on a new power cord and the rest of his money on 5 new video games. Each video game cost the same amount. Write two equations you could use to find the cost of each video game.
Answers
I believe two equations you can make to represent the question are...
(175-15)/5
and
5x+15=175
The first equation, (175-15)/5, makes you subtract 15 from 175 to get 160. You'll then divide 160 by 5 to get 32.
The second equation, 5x+15=175, makes you subtract 15 from 15 and 175, so you'll equation will look like this...
5x=160
You'll then divide 5x and 160 by 5 to get x=32.
So for both equations, you'll get an answer of 32.
I hope this helps!
The solution is, two equations are: (175-15)/5 and, 5x+15=175
the cost of each video game is 32.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here, we have,
two equations we can make to represent the question are...
(175-15)/5
and
5x+15=175
The first equation, (175-15)/5, makes you subtract 15 from 175 to get 160. You'll then divide 160 by 5 to get 32.
The second equation, 5x+15=175, makes you subtract 15 from 15 and 175, so you'll equation will look like this...
5x=160
You'll then divide 5x and 160 by 5 to get x=32.
So for both equations, we'll get an answer of 32.
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A bag of rice weights 3.18 lbs find its mass in kilograms
Answers
Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. –2y2 + 6y = –2
–0.61, 6.61
–0.3, 3.3
–3.3, 0.3
–11.5, 14.5
Answers
-2y2 + 6y = -2
Rewriting we have:
-2y2 + 6y + 2 = 0
Using the quadratic formula we have:
x = (- b +/- root (b ^ 2 - 4 * a * c)) / (2 * a)
Substituting values:
x = (- (6) +/- root ((6) ^ 2 - 4 * (- 2) * (2))) / (2 * (- 2))
Rewriting:
x = (- 6 +/- root (36 + 16)) / (- 4)
x = (- 6 +/- root (52)) / (- 4)
x = (- 6 +/- root (4 * 13)) / (- 4)
x = (- 6 +/- 2 * root (13)) / (- 4)
x = (- 3 +/- root (13)) / (- 2)
The roots are:
x1 = (- 3 - root (13)) / (- 2)
x2 = (- 3 + root (13)) / (- 2)
Rewriting:
x1 = -0.3
x2 = 3.3
Answer:
–0.3, 3.3
if you change the sign of a point’s x -coordinate from positive to negative, how will the location of the point change?
Answers
we know that
If you add a negative to the x-coordinate of a point, then the point will move to another quadrant
example
if the point is on the first quadrant
then
the point will move to the second quadrant
if the point is on the fourth quadrant
then
the point will move to the third quadrant
in both cases the y-coordinate remains the same
hence
the answer is
The point will cross over the y-axis
Answer:
The point will cross over the y-axis
Step-by-step explanation:
Hope it help because i Just Answer the same question and got it before i come on Brainly
What is the value of x, if 105% of 90 is equal to 200% of x?
Answers
From the given equation
105% * 90 = 200% * x
105/100 * 90 = 200/100 * x
105*90 = 200*x
x = 105*90/200
X = 21*9/4
X = 189/4
x = 47.25
Value of x = 47.25 or 47 1/4
Aisha wants to make two quilts, each with the same area. The first quilt will be square with sides s feet long. The second quilt will be a rectangle with a width that is half the length of a side of the square quilt and a length that is 6 feet longer than a side length of the square quilt. Which quadratic equation can be used to find s, the side length of the square quilt?
s^2 =(1/2s) (s + 6)
s^2 = (s)(s + 6)
s^2 =(1/2s) (6s)
s^2 = (s)(6s)
Answers
Then, Area (A) = S^2
Width of rectangular shape = S/2
Length of rectangular shape = S+6
Then, Area (A) = (1/2S)(S+6)
The two area are equal. Therefore,
S^2 = (1/2S)(S+6)
The first option is the correct quadratic equation to solve for S.
Answer:
Option 1 - [tex]s^2=(\frac{1}{2}s)(s+6)[/tex]
Step-by-step explanation:
Given : Aisha wants to make two quilts, each with the same area. The first quilt will be square with sides s feet long. The second quilt will be a rectangle with a width that is half the length of a side of the square quilt and a length that is 6 feet longer than a side length of the square quilt.
To find : Which quadratic equation can be used to find s, the side length of the square quilt?
Solution :
The first quilt will be square,
Let the side of square be s
The area of the square is [tex]A=s\times s[/tex]
The second quilt will be a rectangle,
A width that is half the length of a side of the square quilt and a length that is 6 feet longer than a side length of the square quilt.
Width of the rectangle = [tex]\frac{1}{2}s[/tex]
Length of the rectangle = s+6
Area of the rectangle is [tex]A=(\frac{1}{2}s) \times (s+6)[/tex]
According to question,
Area of square and rectangle are equal,
So, [tex]s\times s=(\frac{1}{2}s) \times (s+6)[/tex]
[tex]s^2=(\frac{1}{2}s)(s+6)[/tex]
Therefore, Option 1 is correct.
The required equation is [tex]s^2=(\frac{1}{2}s)(s+6)[/tex]
Farmer Ed has 8500 meters of fencing and wants to enclose a rectangular plot that borders on a river. If farmer Ed does not fence the side along the river, what is the largest are that can be enclosed?
Width = 2x
Length = 8,500-2x
Answers
Area (A) = xy m^2
If the side bordering the river is x, then
Circumference (C) = 8500 = x+2y => x = 8500-2y
Substituting for w in the equation for A;
A = (8500-2y)y = 8500y -2y^2
For maximum area, derivative of A with respect to y is 0. That is;
dA/dy = 0 = 8500 -4y => 4y = 8500 => y = 8500/4 = 2125 m
And, x = 8500-2y = 8500 -2*2125 = 4250 m
Therefore,
One side = 4,250 m and second side = 2,125 m.
Largest area, A = 4250*2125 = 9,031,250 m^2
A survey was conducted at Springdale High to find the number of hours students sleep at night. The histogram shows the data collected in this survey. Which statement about the number of hours students sleep is true? Seventeen students sleep between 6 and 8 hours at night. Seventeen students sleep for 6 hours at night. Ten students sleep for 4 hours at night. Six students sleep between 2 and 4 hours at night. Four students sleep for 10 hours at night.
Answers
Han has 410,000 in a retirement accounts that earns 15,785 each year find the simple interest rate for this investment
Answers
Interest = principle * rate * time
I=prt
r=I/(pt)=15785/(410,000*1)= .0385
The simple interest rate on this investment is.0385 or 3.85%:
What is Simple Interest?Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.
Given:
Han has 410,000 in a retirement accounts that earns 15,785 each year.
Using Simple Interest
Interest = principle x rate x time / 100
Rate = Interest / ( principle x time )
Rate = 15785/(410,000x1)
Rate = 0.0385
Rate= 3.85 %
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The area of an artist's square canvas can hold 113 square inches of paint. What is the approximate length of one side of the canvas? (Approximate to the nearest hundredth inch.)
10.62 inches
10.63 inches
10.64 inches
10.65 inches
Answers
You'll need a calculator to find this exactly.
Answer:
The approximate length of one side of the canvas is 10.63 inches
Step-by-step explanation:
Given :The area of an artist's square canvas can hold 113 square inches of paint.
To Find :What is the approximate length of one side of the canvas?
Solution:
Canvas is in the shape of square
Area of square = [tex]Side^2[/tex]
Let the side of the canvas be x
Area of canvas = [tex]x^2[/tex]
Since we are given that The area of an artist's square canvas can hold 113 square inches
So, [tex]113=x^2[/tex]
[tex]\sqrt{113}=x[/tex]
[tex]10.630=x[/tex]
So, the approximate length of one side of the canvas is 10.63 inches
Hence Option B is correct.
ABC Bookstore sells new books according to the demand function P = -Q + 25, where P is the price and Q is the quantity. If the bookstore charges $18 for a new book, how many new books can the store expect to sell?
Answers
Therefore, the store can expect to sell 7 new books if they will charge $18 for the new books.
Answer:
P = -Q + 2518 = -Q + 2518-25 = -Q-7 = -Q-7/-1 = -Q/-1Q = 7
Therefore, the store can expect to sell 7 new books if they will charge $18 for the new books.
The radius of a cone can be found using the formula r=3Vπh , where V stands for the volume of the cone and h stands for the height. If r=3 , h=8 , and π is 3.14, find the volume (V). Round the answer to the nearest hundredths place.
Answers
r = Sqrt [(3V)/(πh)]
Making the V the subject of the formula
r^2 = (3V)/(πh)
V = πr^2h/3
Substituting,
V= 3.14*3^2*8/3 = 75.36 sq. units
Using the formula for the radius of a cone and the given values of r = 3, h = 8, and [tex]\pi[/tex] = 3.14, the volume of the cone is calculated to be approximately 25.12 [tex]cm^3[/tex].
To find the volume V of a cone, we need to solve for V in the given formula [tex]\( r = \frac{3V}{\pi h} \). With \( r = 3 \),[/tex] h = 8, and [tex]\pi = 3.14[/tex], let's proceed as follows:
Rearrange the Formula
1. Given that [tex]\( r = \frac{3V}{\pi h} \)[/tex], isolate V to get:
[tex]\[ V = \frac{r \cdot \pi \cdot h}{3} \][/tex]
2. Using r=3, h=8, and [tex]\( \pi = 3.14 \)[/tex]:
[tex]\[ V = \frac{3 \cdot 3.14 \cdot 8}{3} \][/tex]
3. Simplify and solve:
[tex]\[ V = 3.14 \cdot 8 \approx 25.12 \][/tex]
Rounding to the nearest hundredths place, the value for the volume V is approximately 25.12 cubic units.
In general, the y-intercept of the function F(x)=a•b^x is the point what????
Answers
The y-intercept is the point (0, a).
which expression defines the given series for seven terms? -13 + (-16) + (-19) +...
Answers
[tex] - 13 + ( - 3) = - 16 \\ - 16 + ( - 3) = - 19 \\ - 19 + ( - 3) = - 22 \\ - 22 + ( - 3) = - 25[/tex]
you have to plus (-3) for each numbers
Answer:
[tex]a_n =-3n-10[/tex]
Step-by-step explanation:
-13 + (-16) + (-19) +...
Difference between two terms = -3
-16 -(-13)= -3
-19 -(-16)= -3
Common difference is a constant so it is arithmatic
[tex]a_n = a_1+(n-1)d[/tex]
where 'd' is the difference = -3
a1 is the first term that is -13
[tex]a_n = -13+(n-1)(-3)[/tex]
[tex]a_n = -13-3n+3[/tex]
Combine like terms
[tex]a_n =-3n-10[/tex]
The scale factor of the dilation of figure ABCD is
Answers
The scale factor is 2.
Hey can you please help me posted picture of question
Answers
Reflection along x-axis can be obtained by multiplying the function by -1.
So, G(x) reflected along x-axis will be: - x²
Next the function is shifted down by 3 units. So this can be obtained by subtracting 3 from the function.
So, we can write
F(x) = -x² - 3
Thus, option C is the correct answer
what is the positive solution to the equation 0=⅓x²-3
Answers
3 = (1/3)x²
9 = x²
√9 = 3 = x
The positive solution to the equation is x = 3.
In a string of 100 christmas lights, there is
a.015 chance that a given bulb will fail within the first year of use (if one bulb fails, it does not affect the others). find the approximate probability that six or more bulbs will fail within the first year. (round your answer to 4 decimal places.) probability
Answers
[tex]\mathbb P(X\ge6)=1-\mathbb P(X<6)=1-\displaystyle\sum_{x=0}^5\binom{100}x0.015^x(1-0.015)^{100-x}\approx0.0041[/tex]
The approximate probability that six or more bulbs will fail within the first year is approximately 0.1461, rounded to four decimal places.
To find the approximate probability that six or more bulbs will fail within the first year, we can use the binomial probability formula:
P(X ≥ k) = 1 - P(X < k)
where:
P(X ≥ k) is the probability of getting "k" or more successes (bulbs failing).
P(X < k) is the probability of getting less than "k" successes (bulbs failing).
In this case, "k" is 6 (six or more bulbs failing), and the probability of a bulb failing in the first year is 0.015.
Now, let's calculate the probability of getting less than six failures (k < 6):
P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
Using the binomial probability formula:
P(X = k) = C(n, k) *[tex]p^k * (1 - p)^{n - k}[/tex]
where:
C(n, k) is the binomial coefficient (n choose k).
n is the number of trials (total bulbs, which is 100 in this case).
p is the probability of success (a bulb failing, which is 0.015).
k is the number of successes (bulbs failing).
Now, calculate P(X < 6):
P(X = 0) = C(100, 0) * 0.015⁰ * (1 - 0.015)^(100 - 0)
P(X = 1) = C(100, 1) * 0.015¹ * (1 - 0.015)^(100 - 1)
P(X = 2) = C(100, 2) * 0.015² * (1 - 0.015)^(100 - 2)
P(X = 3) = C(100, 3) * 0.015³ * (1 - 0.015)^(100 - 3)
P(X = 4) = C(100, 4) * 0.015⁴ * (1 - 0.015)^(100 - 4)
P(X = 5) = C(100, 5) * 0.015⁵ * (1 - 0.015)^(100 - 5)
After calculating each term, add them up:
P(X < 6) ≈ 0.8539
Now, find the probability of getting six or more failures:
P(X ≥ 6) = 1 - P(X < 6)
P(X ≥ 6) ≈ 1 - 0.8539 ≈ 0.1461
So, the approximate probability that six or more bulbs will fail within the first year is approximately 0.1461, rounded to four decimal places.
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What is the value of n for the equation 1n+4n+16n2−6n=4n−6?
Answers
To find the value of 'n' for the given equation, we first combine like terms to get 16n^2 - n = 4n - 6. Then, set the equation to zero to solve for 'n'. The resulting quadratic equation, 16n^2 - 5n + 6 = 0, can be solved by factoring, completing the square, or applying the quadratic formula.
Explanation:The student's equation is 1n + 4n + 16n2 − 6n = 4n − 6. To simplify and solve for n, we need to consolidate like terms and find the value of n that satisfies the equation.
First, we start by adding the like n terms. This gives us:
5n + 16n2 − 6n
Next, we combine the like terms:
16n2 − n (since 5n - 6n gives us -n)
Now, we set the equation equal to the right side of the original equation:
16n2 − n = 4n − 6
To find the value of n, we have to set the equation to zero and solve for n:
16n2 − 5n + 6 = 0
The student must now use techniques such as factoring, completing the square, or the quadratic formula to find the value(s) of n that satisfy the quadratic equation.
Final answer:
The value of n varies in different Chemistry contexts, such as in sequence manipulations, when converting to scientific notation, in electron configurations indicating n = 3 for a 3p electron, and when determining the total number of orbitals for n = 4.
Explanation:
The student question involves determining the value of n (the principal quantum number) in different scenarios within the field of Chemistry. Here are examples covering various cases:
For the expression of n terms leading to 2n², it's concluded by manipulating terms within a sequence.When converting numbers like 60.474 × 10-4 to scientific notation, n becomes more positive by 1 if the value of N decreases.The electron configuration of an atom indicates the last electron added is a 3p electron, which implies n = 3.For n = 4, an atom has s, p, d, and f subshells, leading to a total of 16 orbitals.During the first stages of an epidemic, the number of sick people increases exponentially with time. Suppose that at = 0 days there are 2 people sick. By the time = 3, 40 people are sick. a) Let be the number of sick people at time . Find an exponential equation = expressing in terms of .
b) How many people will be sick by the time = 6?
Answers
r = rate of growth
by 0 day, or t = 0, there are 2 folks sick,
[tex]\bf \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\to &2\\ P=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\to &0\\ \end{cases} \\\\\\ 2=P(1+r)^0\implies 2=P\cdot 1\implies 2=P\qquad \boxed{A=2(1+r)^t}[/tex]
by the third day, t = 3, there are 40 folks sick,
[tex]\bf \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\to &40\\ P=\textit{initial amount}\to &2\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\to &3\\ \end{cases} \\\\\\ 40=2(1+r)^3\implies 20=(1+r)^3\implies \sqrt[3]{20}=1+r \\\\\\ \sqrt[3]{20}-1=r\implies 1.7\approx r\qquad \boxed{A=2(2.7)^t}[/tex]
how many folks are there sick by t = 6? [tex]\bf \stackrel{that~many}{A=2(2.7)^6}[/tex]
The median number of business trips for 6 employees in a certain quarter is 10. The range of number of business trips for those employees that quarter is 9. The fewest business trips could be 0. True, false, or not enough information?
Answers
Answer:
False
Step-by-step explanation:
You want to know if it is true that the fewest number of business trips could be zero if the median of 6 values is 10 and their range is 9.
MedianThe median of 6 numbers is the average of the middle two when they are sorted into increasing order. That means the smallest number that can be the upper end of the range is 10. (In that case, 4 of the 6 values would be 10.)
Since the lower end of the range is 9 less than the upper end, the fewest number of business trips cannot be less than 10-9 = 1.
It is False that the fewest number could be 0.
__
Additional comment
The numbers of trips could be ...
1, 1, 10, 10, 10, 10
This 6-element data set has a median of 10 and a range of 9.
Complete the equation of the line whose slope is − 2 and y-intercept is ( 0 , 3 )
Answers
This is the equation in slope point form.
Get Brainliest if you answer What was Hammurabi's most important achievement as the ruler of Babylon? A. He built extensive canals, which carried water to many parts of his kingdom. B. He established permanent armies, which he used to control his empire. C. He appointed governors to rule over conquered cities. D. He was responsible for a codification of laws that influenced later societies.
Answers
Answer:
Its D
Step-by-step explanation:
I did the quiz
If a body moves in a straight line according to the law s = 24t + 3t2 - t3 , where s is the distance measured in meters from the origin and t is the time in seconds after it starts to move, calculate the body's velocity as a function of time. A. V = 30t - t2 B. V = 24 + 6t - 3t2 C. V = 24 + 3t - t2 D. V = 30t - 3t2
Answers
To solve this we are going to take the derivative of our position function [tex]s=24t+3t^2-t^3[/tex]. To do that er are going to apply the power rule of calculus: [tex] \frac{dy}{dx} x^n=nx^{n-1}[/tex]
[tex] \frac{dy}{dx} 24t+\frac{dy}{dx}3t^2-\frac{dy}{dx}t^3[/tex]
[tex]24+2(3)t-3t^2[/tex]
[tex]v=24+6t-3t^2[/tex]
We can conclude that the correct answer is: B. V = 24 + 6t - 3t2
9.
Leola Hain purchases 220 shares of Circuit City stock at $42.75 per share.
Find the annual dividend if the dividend per share is $0.0625.
$43
$55
$9,460
$9,405
Answers
$55 is the answer
Adair had 6 1/2 cups of tomato juice. He used 4/5 of the juice to make soup. How many cups of tomato juice did Adair use to make soup?
Answers
However, first we must convert 6 1/2 from a mixed number to an improper fraction to simplify the multiplication process. To do this, we have to multiply the whole number (6) by the denominator (2) and then add the numerator (1).
6*2=12, 12+1=13. Therefore, 6 1/2 = 13/2.
Now, we must multiply 4/5 by 13/2 to figure out how much tomato juice Adair used. To do this, we must multiply the two numerators and the two denominators together and simplify the resulting fraction.
4/5 * 13/2 = 4*13/5*2=52/10
To simplify 52/10, we must find the GCF, or greatest common factor of 52 and 10, which is 2.
52/2 = 26, 10/2 = 5, 52/10 = 26/5.
Therefore, Adair used 26/5, or 5 1/5 cups of tomato juice in his soup.
Hope this helps!
To find how many cups of tomato juice Adair used to make soup, we multiply the fraction representing the portion of tomato juice used (4/5) by the total amount of tomato juice Adair had (6 1/2 cups). The answer is 5 1/5 cups.
Explanation:To find how many cups of tomato juice Adair used to make soup, we need to multiply the fraction representing the portion of tomato juice used (4/5) by the total amount of tomato juice Adair had (6 1/2 cups). First, we can convert 6 1/2 cups to an improper fraction: 6 1/2 = 13/2 cups. Next, we multiply the fractions: 4/5 * 13/2 = 52/10 = 5 2/10 = 5 1/5 cups.
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