In point-slope form, the equation of the parallel line to y − 5 = 3/4(x − 2) is: y - 4 = 3/4(x + 1).
What is the Equation of Parallel Lines?If two lines are parallel their equation, written in point-slope form y - b = m(x - a), will have the same value of m, which is the same slope.
The slope of the line with the equation y - 5 = 3/4(x - 2), is 3/4. This means that the line that passes through the point (−1, 4), and that is parallel to the line with the equation y − 5 = 3/4(x − 2), will have the same slope, m = 3/4.
To write the equation of the line that is parallel to y - 5 = 3/4(x - 2), in point-slope form, substitute m = 3/4 and (a, b) = (-1, 4) into y - b = m(x - a):
y - 4 = 3/4(x - (-1))
y - 4 = 3/4(x + 1)
The equation of the line that is parallel to y − 5 = 3/4(x − 2) is therefore expressed in point-slope form as: y - 4 = 3/4(x + 1).
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40! points Which expression is equivalent to 2x + 7y + 4x - 3y * 1 point
6x + 10y
6x - 10y
6x + 4y
6x - 4y
find the inverse of
f(x) = 4x + 2 over 3
Answer: f^-1(x)=(3x-2)/4
Step-by-step explanation:
1. Change the x and y
y=(4x+2)/3 → x=(4y+2)/3
2. Swap sides (optional)
x=(4y+2)/3 → (4y+2)/3=x
3. Multiply the equation by 3 on both sides
(4y+2)/3=x → (3)*(4y+2)/3=x*(3)
4. Subtract 2 from both sides
(3)*(4y+2)/3=x*(3) → 4y=3x-2
5. Divide 4 from both sides
4y=3x-2 → y=(3x-2)/4
6 Substitute f^-1(x) for y
y=(3x-2)/4 → f^-1(3x-2)/4
A number is between 41 and 46. It has prime factors of 2 and 11. What is the number?
The answer you are looking for would be 44.
Step-by-step explanation:Here,
The number lies between 41 and 46 are 42, 43, 44, and 45
From the straightforward observation and according to the condition that must be divisible by 2 and 11 there is only one number that is divisible by both 2 and 11 is 44.
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I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
|6y-7|=-1 solve please
Answer:
no solution
Step-by-step explanation:
You want the solution to the absolute value equation |6y -7| = -1.
AnalysisThe expression on the left side of the equal sign is the output of the absolute value function. That output can never be negative: all negative input values are transformed to positive output values by the absolute value function.
The expression on the right side is negative. There is no value of the variable that will make the absolute value function give a negative output. There can be no solution.
helppppp plsssssss
what is the average rate of change of the function on the interval from x = 3 to x = 5? f(x)=10(2)x Enter your answer in the box.
The average rate of change of the function on the interval from x = 3 to x = 5 is 40.
What is meant by average rate of change?In mathematics, the average rate of change is a measure of how much a dependent variable (such as y) changes in proportion to a change in the independent variable (such as x). It is calculated by dividing the change in the dependent variable by the change in the independent variable during a certain time period. If the value of y rises by 5 units when the value of x rises by 2 units, the average rate of change is 5/2 Equals 2.5 per unit change in x. Calculus students frequently use this idea to compute the slope of a line on a graph or to calculate the rate at which a function changes. It is a crucial idea in several domains.
How to solve?
f(x) = 10(2)x,the interval is from x = 3 to x = 5
At x = 3, 10(2)3 = 80
at x = 5, 10(2)5 = 160
total change over the interval from x = 3 to x = 5 is 160 - 80 = 80.
the length of the interval is 5 - 3 = 2,
average rate of change is 80 / 2 = 40.
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NEED HELP!! Consider the following quadratic function.
f(x)= -3x^2 - 30x - 74
Write the equation in form f(x) = a (x - h)^2 +k. Then give the vertex of its graph.
As per the question, the solution to the equation f(x) = a(x-h)2+k is y = 3(x+5)2 -1.
What is an equation?Equations are mathematical expressions with two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be similar to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a simple fundamental equation.
As per the given values mentioned in the question,
a=3, b=30, c=74.
To fix this issue, employ the Vertex Formula,
(-b/(2a)) , f(-b/(2a))
-b/(2a)
= -(30)/(2 × 3)
h = -5.
f(-b/(2a))
= 3(-5)² + 30(-5) + 74
k = 75 +-150 +74
k = -1.
Vertex, V = (h,k)
V = (-5,-1).
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SOLVE FOR P
-2p = -3p + 8
P=
Answer:
P= 8
Step-by-step explanation:
-1 (-2p = -3p + 8)
2p = 3p - 8
-p = -8
p = 8
to check this...
-2(8) = -3(8) + 8
-16 = -24 + 8
-16 = -16
The sum of 10 and b, multiplied by 8
How many lines of symmetry does a peace sign have
Answer:
A peace sign has one line of symmetry.
The one line is up and down in the center.
Hope this helps! :D
Step-by-step explanation:
Suppose you go to work for a company that pays one penny on the first day, 2 cents on the second day, 4 cents on the third day and so on.
Hint: use an= a1 (r)^n-1 and Sn= a1 (1-r^n) / 1 - r
A. If the daily wage keeps doubling, what would your income be on day 31? Give your answer in dollars NOT pennies.
Income on day 31 = $ __________
B. If the daily wage keeps doubling, what will your total income be for working 31 days? Give your answer in dollars NOT pennies.
Total Income for working 31 days = $ _________
Using the given function, the income for day 31 is
$10,737,418.24the total Income for working 31 days is
$21 474 836.47 How to find the income on day 31Using the given function an = a1 (r)^n-1
where
a1 = first day = 1
r = common ratio = 2
The income on day 31, n = 31
= 1 * 2^(31 - 1)
= 2^30
= 1,073,741,824 cents
= $10,737,418.24
Total Income for working 31 days n = 31
Using Sn= a1 (1-r^n) / 1 - r
Sn = (1 * (1 - 2^31)) / (1 - 2)
Sn = (1 - 2^31)) / - 1
Sn = (1 - 2147483648) /-1
Sn = 2147483647
Sn = 2,147,483,647 cents
Sn = $21 474 836.47
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4.40x2.50
i really need this please
Answer:
11
Step-by-step explanation:
If it is correct, could you please give me brainliest? I would really appreciate it! Thank you!
A farmer purchased 480 meters of fencing, and will build a rectangular pen with it. To enclose the largest possible area, what should the
pen's length and width be? Model the pen's area with a function, and then find its maximum value.
To enclose the largest possible area, the pen's length should be__and width should be__.
The largest possible area will be 14400 meters², the pen's length should be 120 meters, and the width should be 120 meters.
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.
Let's assume that the length of the pen would be x.
We have been given the perimeter as 480 meters.
Let w be the width of the rectangle and l be the length of the rectangle
The perimeter of a rectangle = 2(l+w)
So, 480= 2(x + w)
240 = x + w
w = 240 - x
Length = x and width = (240 – x)
Area = x(240 - x) = 240x - x²
To get the maximum area, we equate the first derivative of the area to zero.
A = 240x - x²dA/dx = 240 - 2x = 0
2x = 240
x = 120
So, width = 240 – x = 240 – 120 = 120.
Maximum area = length × width
Maximum area = 120 × 120 = 14400 meters²
Thus, the pen should be 120 meters long and 120 meters wide, with a maximum possible area of 14400 meters².
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The functions f(x) and g(x) are shown in the graph. What is g(x)?
Connor borrows $8,000 at a rate of 19% interest per year. What is the amount due at the end of 7 years if the interest is compounded continuously?
$14,576.95
$30,248.35
$43,791.58
$29,215.37
Answer:
Step-by-step explanation:
30,248.35
please help please I need i real bad
Answer:
C
Step-by-step explanation:
Answer:
I think the Answer choice = C
Step-by-step explanation:
Supposed you invest 1000 at 9% interest, compound monthly . Find the amount you have after 18 months
The amount you have after 18 months is $ 1143.96 .
what is compound interest?
Interest that is added to a loan or deposit sum is known as compound interest. In our daily lives, it is the notion that is employed the most frequently. Compound interest is calculated for a sum using the principal and interest accrued over time. Compound interest and simple interest differ primarily in this way.
[tex]A=P {(1 +\frac{r}{n})^{nt} }[/tex]
Given:
P = 1000 , r in decimal = 0.09 ,
n = 12 , t = 1.5 ( 18 months = one and a half years).
Substituting the values into the formula:
A = 1000 ( 1 + 0.09/ 12 ) ^[12 ( 1.5 )]
≈ 1000 ( 1.143960 )
= 1143.960
Rounding to the nearest cent, we get $ 1143.96 .
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t/4+5=20 how would you solve this problem
Answer:
t = 60
t/4+5=20
Step 1:
multiply both sides of equation by 4 to separate t from the fraction t/4.
t + 20 = 80
Step 2:
Subtract 20 from both sides of the equation ( you have to put constant values on the same side)
t= 80 - 20
Step 3:
Do the math
80-20=60 so t=60
Step-by-step explanation:
hope this helps! please give brainiest ^^^
27. A boy and his sister together weighs 60kg. if the boy is 6.8kg heavier than his sister, calculate his sister's weight. A. 26.6kg 8.23.2kg C. 33.4kg D. 36kg
help uhh don't worry i won't be asking all the time it's just the ones i don't understand
PLS ASAP
An online bookstore sells hardcover books for a regular price of $17.95 and paperback books for a regular price of $9.95. The paperback books
are on sale for 25% off. The bookstore offers two shipping options:
• free shipping on orders of $59 or more
.
shipping charge of $5.95 on orders less than $59
Isa had planned to buy 2 hardcover and 3 paperback books.
How much more will Isa pay if she buys 2 hardcover and 4 paperback books instead of her original plan? Enter the answer in the box.
The extra amount that the store would have to pay for buying 2 hardcover and 4 paperback books instead of her original plan is $1.51
How to solve for the amount of books boughtThe paper back books have a discount of 25%
hence we what would be paid for in such category would be 1 - 25% charge = 75 %
price of hardcover = 17.95
price of paperback = 9.95 dollars
Isa bought 2 hardcover and 4 paper back
we are to find the cost of these items
2 x 17.95 + (4 x 9.95 x 75%)
= 35.9 + 29.85
= 65.75
We have to find the cost of the initial plan of 2 hardcover and 3 paperback books.
2 x 17.95 + 3 x 9.95 x 0.75
35.9 + 22.3875
= 58.29
This is less than 59 dollars, she would have to pay the shipping fee.
58.29 + $5.95
= 64.23
The extra amount that she has had to pay for going with 2 hardcover and 4 paperback books is:
65.75 - 64.23
= 1.51 dollars
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Question 6 of 10
Using the graphing function on your calculator, find the solution to the system
of equations shown below.
A. More than 1 solution
B. x = 4, y = 3
C. No solution
D. x = 3, y = 4
y-2x = -2
y-x = 1
Answer:
D x = 3 y = 4
(3.4)
Step-by-step explanation:
See below
Liam is setting up folding chairs for a meeting. If he arranges the chairs in 7 rows of the same length, he has 5 chairs left over. If he arranges the chairs in 5 rows of that same length, he has 17 left over. How many chairs does Liam have?
Answer: 47
Step-by-step explanation: Let's call the number of chairs Liam has x. We can set up the following equations to represent the problem:
7r = x - 5
5r = x - 17
Where r is the length of each row.
To solve for x, we can set the two equations equal to each other:
7r = x - 5
5r = x - 17
Then we can solve for x by combining like terms and solving for the value of x:
7r - 5r = x - 5 - x + 17
2r = 12
r = 6
We can substitute the value of r back into either of the original equations to solve for x:
7r = x - 5
7 * 6 = x - 5
x = 47
Therefore, Liam has 47 chairs.
Which statement is true about the algebraic expression 450 −15t?
A student has 450 marbles. Each of their t friends gives them 15 marbles. The expression represents the total marbles the student has.
A student has 450 marbles. They give t marbles to each of their 15 friends. The expression represents the total marbles the student is left with.
A student has 450 marbles. They give t marbles to one of their friend and 15 marbles to another. The expression represents the total marbles the student is left with.
A student has 450 marbles. One of their friends gives them t marbles and another friend gives them 15 marbles. The expression represents the total marbles the student has.
PLEASE HELP I'M SOOO CONFUSED
The statement that is true about the algebraic expression 450 −15t is B. A student has 450 marbles. They give t marbles to each of their 15 friends. The expression represents the total marbles the student is left with.
What is the definition of an algebraic expression?In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.
In this case, when a student has 450 marbles. They give t marbles to each of their 15 friends.
The expression represents the total marbles the student is left with will be:
= 450 - (15 × t)
= 450 - 15t
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A store manager created this table representing the relationship between the reported number of rainy days during a given month, x, and the sales revenue of raincoats, y, rounded to the nearest dollar.
The predicted number of coffee sales, in hundreds of dollars, for an average daily temperature of 32 degrees is of:
63.34.
What is defined by the line of best fit?The definition of the line of best fit in this problem is given as follows:
y = -0.68x + 85.1.
The variables in the context of this problem are defined as follows:
Variable x: average daily temperature.Variable y: predicted number of coffee sales, in hundreds of dollars.Hence, for an average daily temperature of 32 degrees, the estimate of the number of coffee sales is given as follows:
y = -0.68(32) + 85.1 = 63.34 thousand dollars.
Missing InformationThe problem is incomplete and is given by the image at the end of the answer.
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10 = 2(x - 2)
How would I solve for X?
Answer:
x = 7Step-by-step explanation:
10 = 2(x - 2)
How would I solve for X?
10 = 2(x - 2)
10 = 2x - 4
14 = 2x
x = 7
--------------------
check
10 = 2(7 - 2)
10 = 2 x 5
10 = 10
the answer is good
Answer:
x=7
Step-by-step explanation:
Given:
A linear equation is given as:
[tex]10=2(x-2)[/tex]
To Find:
The objective is to solve the equation and find the value of x.
Explanation:
[tex]10=2(x-2)\\[/tex]
⇒ [tex]\frac{10}{2}=x-2[/tex]
⇒[tex]5=x-2[/tex]
⇒ [tex]x=7[/tex]
Final Answer :
The value of x is 7.
HELP PLSPLSPSL QUICK
Answer:
B. y > 4x + 2
Step-by-step explanation:
The area of the graph above the dotted line is shaded; therefore, this inequality is greater than. The dotted line's slope is 4, hence x is multiplied by 4, and its y-intercept is at 2, hence + 2 on the right side.
Hector saved $726 in 6 months. he saved the same amount each month. How much did hector save each month? I don’t have the answer and I don’t get it !
Answer:
He saved $121
Step-by-step explanation:
All you have to do is divide $726/6 which gives you $121.
Given f(x)=ln x, evaluate
a) f (e⁴)
b) f (e ㏑ 5)
c) f (e³ ㏑ 5)
The natural logarithms of the given questions are f(e⁴) = 4, f(e ㏑ 5) = 5, and f(e³ ㏑ 5) = -0.5108.
What is the natural logarithm?
A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
Given,
f(x) = ln x,
a) f(e⁴)
f(e⁴) = In(e⁴)
= 4In(e)
= 4 * 1
f(e⁴) = 4
b) f(e ㏑ 5)
= f(e⁻⁵)
= [tex]f(e^{\frac{1}{5} })[/tex]
= In(1) - In(e⁵)
= 0 - 5In(e)
= 5*1
f(e ㏑ 5) = 5
c) f(e³ ㏑ 5)
[tex]= f(e^{\frac{3}{5} })[/tex]
= In(3) - In(e⁵)
= ln(3) - ln(5)
f(e³ ㏑ 5) = -0.5108
Hence, The natural logarithms of the given questions are f(e⁴) = 4, f(e ㏑ 5) = 5, and f(e³ ㏑ 5) = -0.5108.
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Find the Maclaurin series of the following functions.
(b) g(x) = sin(3x^2)
The Maclaurin series of sin(3x²) up to n = 3 is
[tex]=3x^2-\dfrac{9}{2}x^6+\frac{81}{40}x^{10}+\ldots[/tex]
The function is given in the question as
g(x) = sin(3x²)
Taylor (Maclaurin) series of sin(3x²) up to n = 3
A Maclaurin series is given by f(x),
[tex]f\left(x\right)=f\left(a\right)+\frac{f^'\left(a\right)}{1!}\left(x-a\right)+\frac{f^{''}\left(a\right)}{2!}\left(x-a\right)^2+\frac{f^{'''}\left(a\right)}{3!}\left(x-a\right)^3+\ldots[/tex]
[tex]f\left(x\right)=f\left(0\right)+\frac{f^'\left(0\right)}{1!}\left(x\right)+\frac{f^{''}\left(0\right)}{2!}\left(x\right)^2+\frac{f^{'''}\left(0\right)}{3!}\left(x\right)^3+\ldots[/tex]
We need to do to get the desired polynomial is to calculate the derivatives, evaluate them at the given point, and plug the results into the given formula.
f⁽⁰⁾(x) = f(x) =sin(3x²)
Evaluate the function at the point: f(0)=0
1st derivative: f(1)(x)=(sin(3x²))′ = 6xcos(3x²)
1st derivative at the given point: (f(0))′=1
2nd derivative: f(2)(x)=(f(1)(x))′=(6xcos(3x²))′=−36x2sin(3x2)+6cos(3x²)
Evaluate the 2nd derivative at the given point: (f(0))′′=6
3rd derivative: f(3)(x)=(f(2)(x))′=(6xcos(3x²))′=−36x2sin(3x²)+6cos(3x²)
Evaluate the 3rd derivative at the given point: (f(0))′′′=0
Now, use the calculated values to get a polynomial:
[tex]g(x)=0+\frac{0}{1!}x+\frac{6}{2!}x^2+\frac{0}{3!}x^3+\frac{0}{4!}x^4+\frac{0}{5!}x^5[/tex]
Thus, the Maclaurin series of sin(3x²) up to n = 3 is
[tex]=3x^2-\dfrac{9}{2}x^6+\frac{81}{40}x^{10}+\ldots[/tex]
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How do I solve this?
11) (Level 2):
I believe if you just multiply the shaded area (10x6), then maybe subtract the non-shaded area (20cm and 10 cm). After doing this process, I believe you will get: 200-60 = 140! (But then again I could be wrong, I’ll admit it I’m not a pro but at least I gave effort!)
Fraction: 14/10
Decimal: 1.4
Percent: 140%
12) (Level 3):
I have absolutely no idea about this question and I don’t want to guess! Sorry!
Clara and toby are telemarketers. yesterday, Clara reached 6 people in 12 calls, while Toby reached 7 people in 13 phone calls. If they continue at those rates, who will reach more peoples in 40 phone calls? How many more?
Step-by-step explanation:
Firstly we determine how many people clara will reach in 40 phone calls.
6 people=12 calls
X people=40 calls.
make X the subject of the formula.
X=(6×40)÷12=20
So clara will reach 20 people in 40 phone calls.
Now lets determine how many people Toby will reach in 40 phone calls.
7 people=13 calls
Y people=40 calls.
Therefore making Y the subject of the formula we have,
Y=(7×40)÷13=21 people.
So toby will reach more people in 40 calls