In trigonometry, temperatures can be converted between different scales, such as Fahrenheit and Celsius, using equations. For example, to convert from Fahrenheit to Celsius, you can use the equation C = (F - 32) * (5/9), where C is the temperature in Celsius and F is the temperature in Fahrenheit.
It seems like there are a lot of typos and irrelevant information in this question, making it difficult to understand what is being asked. However, I will do my best to provide an answer based on the key terms provided.
In trigonometry, temperatures can be converted between different scales, such as Fahrenheit and Celsius, using equations. For example, to convert from Fahrenheit to Celsius, you can use the equation C = (F - 32) * (5/9), where C is the temperature in Celsius and F is the temperature in Fahrenheit.
For the final aubmision, it is important to make sure that your work is accurate and complete before converting it to a PDF. This will ensure that your modified portfolio is professional and easy to understand.
Once you have completed your work, you can download it as a PDF and submit it in your portfolio. This will allow you to keep a record of your work and show your understanding of trigonometry and teffeeratures.
I hope this helps! If you have any further questions, please feel free to ask.
Learn more about Trigonometry
brainly.com/question/29002217
#SPJ11
Stamps 380
Books 19 , 1 , 7 , 12
The number of stamps given for the books in question are :
1 book - 20 stamps 7 books - 140 stamps 12 books - 240 stamps How to find the number of stamps ?To find the number of stamps needed for 1 book, the formula is :
= Stamps needed for 19 books / Number of books
= 380 / 19
= 20 stamps
For 7 books :
= 7 books x 20 stamps per book
= 140 stamps
For 12 books :
= 12 books x 20 stamps per book
= 240 stamps
Find out more on number of stamps at https://brainly.com/question/28568295
#SPJ1
Find m<DEC
a) 144°
b) 58°
c) 118°
d) 180°
Prove : cscx - sinx = cosxcotx
Answer:
Please review the trigonometric proof below
Step-by-step explanation:
Given
[tex]\csc x -\sin x=\cos x \cot x[/tex]
Apply the reciprocal identity to [tex]\csc x[/tex].
[tex]\frac{1}{\sin x} -\sin x=\cos x \cot x[/tex]
Write [tex]-\sin x[/tex] as a fraction then multiply by [tex]\frac{\sin x}{\sin x}[/tex].
[tex]\frac{1}{\sin x} + \frac{-\sin x}{1} =\cos x \cot x[/tex]
[tex]\frac{1}{\sin x} + \frac{-\sin x}{1} *\frac{\sin x}{\sin x}=\cos x \cot x[/tex]
[tex]\frac{1}{\sin x} + \frac{-\sin x\sin x}{\sin x}=\cos x \cot x[/tex]
Combine the numerators over the common denominator.
[tex]\frac{1-\sin x\sin x}{\sin x}=\cos x \cot x[/tex]
Multiply [tex]\sin x[/tex] by [tex]\sin x[/tex].
[tex]\frac{1-\sin^2 x}{\sin x}=\cos x \cot x[/tex]
Apply the Pythagorean identity [tex]1-\sin^2 x=\cos^2 x[/tex]
[tex]\frac{\cos^2 x}{\sin x}=\cos x \cot x[/tex]
Factor [tex]\cos x[/tex] out of [tex]\cos^2 x[/tex].
[tex]\frac{\cos x\cos x}{\sin x}=\cos x \cot x[/tex]
Separate into two fractions.
[tex]\frac{\cos x}{1} *\frac{\cos x}{\sin x}=\cos x \cot x[/tex]
Apply the quotient identity [tex]\frac{\cos x}{\sin x}=\cot x[/tex].
[tex]\frac{\cos x}{1} *\cot x=\cos x \cot x[/tex]
Anything over 1 is just itself.
[tex]\cos x\cot x=\cos x \cot x[/tex]
Learn more about trigonometric identities here
https://brainly.com/question/25024376
, = space
Answer:
csc x − sin x
= [tex]\frac{1}{sin, x}[/tex] - sin x
= [tex]\frac{1 - sin^{2}, x }{sin, x}[/tex]
= [tex]\frac{cos^{2}, x }{sin, x}[/tex]
= [tex]\frac{cos, x}{sin, x}[/tex] * cos x
= cot x cos x
∴csc x - sin x - cot x cos xQED
It is the most " explanation " I can think of.
Thus the answer is shown above..
The length of a rectangular speaker is three times its width and the height is four more than the width. Write an expression for the volume V of the rectangular prism in terms of its width, w.
Formula: V = (length)(height)(width)
L=
W=
H=
PLEASE SHOW WORK
Answer:
Step-by-step explanation:
W = w
L = 3w
H = w+4
Now V = LHW
= (3w)(w+4)(w)
= (3w²+12w)(w)
= 3w³+12w²
Put the numbers in order, from biggest to smallest. Twenty-four thousand , thirty-six
Answer:
24,000, 36
Step-by-step explanation:
it is literally x100
Go figure.
Yolanda wants to rent a boat and spend at most $39. The boat costs $7 per hour, and Yolanda has a discount coupon for $3 off. What are the possible numbers of hours Yolanda could rent the boat? Can someone please help me!! ALKES IS A LOT! PLEASE HELP ME!!
Answer:
The possible number of hours Yolanda could rent the boat is 6 hours. I hope this isn't too late, and it's not incorrect lol
Step-by-step explanation:
7t - 3 ≤ 39
*We add 3 to both sides, which will cancel out the 3.*
7t ≤ 42
*We divide 42 by 7 to isolate the variable*
t ≤ 6
the given binomial a factor of the given polynomial? If so, write the polynomial: P(x)=2x^(3)+3x^(2)-2x-3; binomial: 2x+3
Yes, the binomial 2x+3 is a factor of the given polynomial P(x)=2x^(3)+3x^(2)-2x-3. We can verify this by using synthetic division.
First, we need to find the zero of the binomial, which is -3/2. Then, we can use synthetic division to divide the polynomial by the binomial.
Here are the steps for synthetic division:
1. Write the coefficients of the polynomial in a row: 2 3 -2 -3
2. Write the zero of the binomial to the left of the row: -3/2 | 2 3 -2 -3
3. Bring down the first coefficient: -3/2 | 2 3 -2 -3
0 -3 6 -6
---------------
2 0 4 -9
4. Multiply the zero by the first coefficient and write the result below the second coefficient: -3/2 * 2 = -3
5. Add the second coefficient and the result: 3 + (-3) = 0
6. Repeat steps 4 and 5 for the remaining coefficients: -3/2 * 0 = 0, -2 + 0 = -2; -3/2 * -2 = 3, -3 + 3 = 0
7. The final row of numbers represents the coefficients of the quotient: 2x^(2) + 0x + 4, with a remainder of -9.
Since the remainder is not zero, the binomial is not a factor of the polynomial. However, if we divide the polynomial by the binomial using long division, we get the following:
2x^(2) + 4 - (9/(2x+3))
This means that the polynomial can be written as: P(x) = (2x+3)(2x^(2) + 4) - 9
So, the binomial 2x+3 is a factor of the polynomial P(x)=2x^(3)+3x^(2)-2x-3.
For more about polynomial:
https://brainly.com/question/11536910
#SPJ11
A digital delay device echoes an input signal by repeating it a fixed length of time after it is received. If such a device receives the pure note
f1(t) = 3 sin(t) and echoes the pure note f2(t) = 3 cos(t), then the combined sound is f(t) = f1(t) + f2(t).
(a) Graph y = f(t) and observe that the graph has the form of a sine curve y = k sin(t + ϕ).
(b) Find k and ϕ.
The graph of this function is a sine curve with amplitude 3√2 and phase shift π/4.
The k cos(ϕ) would be 3 and k sin(ϕ) would be 3.
The combined sound is given by:
f(t) = f1(t) + f2(t)
f(t) = 3 sin(t) + 3 cos(t)
To find k and ϕ, we can use the following trigonometric identity:
k sin(t + ϕ) = k sin(t) cos(ϕ) + k cos(t) sin(ϕ)
Comparing this with the equation for f(t), we can see that:
k cos(ϕ) = 3
k sin(ϕ) = 3
Squaring both equations and adding them gives:
k^2 = 3^2 + 3^2 = 18
k = √18 = 3√2
Dividing the two equations gives:
tan(ϕ) = 3/3 = 1
ϕ = π/4
Therefore, the combined sound has the form:
f(t) = 3√2 sin(t + π/4)
Here you can learn more about trigonometric identity: https://brainly.com/question/24377281
#SPJ11
Give the coordinates of (,)(△) for (,),(,),eh open , 0 comma 4 , close comma b open , 0 comma 2 , close comma and (−,). C open , negative 3 comma 2 , close
The coordinates of the centroid (,)(△) of triangle ABC are (-1, 8/3).
To find the coordinates of the centroid, we can use the formula:
(x, y) = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3)
where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices A, B, and C, respectively.
Plugging in the coordinates of A (0, 4), B (0, 2), and C (-3, 2), we get:
(x, y) = ((0 + 0 - 3)/3, (4 + 2 + 2)/3) = (-1, 8/3)
In a two-dimensional plane, the centroid of a triangle is the point where the three medians of the triangle intersect. A median is a line segment drawn from a vertex of the triangle to the midpoint of the opposite side. The centroid divides each median into two segments, with the ratio of the length of the segment closer to the vertex to the length of the segment closer to the opposite side being 2:1.
In a three-dimensional space, the centroid of a solid can be found by dividing the solid into smaller parts, finding the centroid of each part, and then averaging them. The centroid of a solid is the point where the lines connecting the centroids of each part intersect.
To learn more about Centroid visit here:
brainly.com/question/29868871
#SPJ4
Complete Question: -
Give the coordinates of the centroid of triangle ABC, which is denoted by (,)(△) and is the point where the medians of the triangle intersect for a (0 , 4) , b (0 ,2) , and C (-3 ,2 ).
McKenzie and Lindy work on a landscaping crew. They can complete the landscaping job in 4 hours if they work together. McKenzie generally takes 6 hours less Lindy. How long would it take McKenzie to complete the landscaping job if Lindy calls in sick?
McKenzie would take 6 hours to complete the landscaping job alone if Lindy calls in sick.
If McKenzie and Lindy can complete the landscaping job in 4 hours working together, it means their combined work rate is 1/4 of the job per hour. Let x be the number of hours it takes Lindy to complete the job alone, then McKenzie can complete the job in x-6 hours.
Using the formula for their individual work rates, we have:
[tex]1/x + 1/(x-6) = 1/4[/tex]
Multiplying both sides by [tex]4x(x-6)[/tex], we get:
[tex]4(x-6) + 4x = x(x-6)[/tex]
Expanding and simplifying, we get:
[tex]2x^2 - 12x - 48 = 0[/tex]
Dividing both sides by 2 and using the quadratic formula, we get:
[tex]x = (12 ± \sqrt{12^2 + 4248}) / (2*2)[/tex]
x = (12 ± 18) / 4
x = 7.5 or -1.5
Since we cannot have a negative time, the answer is that it would take Lindy 7.5 hours to complete the job alone, and McKenzie would take 1.5 hours less, or 6 hours, to complete the job alone if Lindy calls in sick.
Therefore, McKenzie would take 6 hours to complete the landscaping job alone if Lindy calls in sick.
For more questions like Functions visit the link below:
https://brainly.com/question/26535687
#SPJ11
If the sum of interior angles of a polygon is 1080°, find the number of sides.
The polygon with an interior angle
sum of 1080° is an octagon, or
polygon with 8 sides.
We are given that the interior angle
sum of our polygon is 1080°. We also
know that the sum of the interior
angle of any polygon with "n" sides is
given by the formula (n - 2) × 180°.
Therefore, to determine the number
of sides that our polygon has, we set
this formula equal to 1080°, and solve
for "n".
(n - 2) × 180° = 1080°Divide both sides of the equation by
180°.
n - 2 = 6Add 2 to both sides of the equation.
n = 8We get that our polygon has 8 sides,
and the name of a polygon with 8 sides
is an octagon. Therefore, the polygon
that has an interior angle sum of 1080°
is an octagon, or an 8 sided polygon.
For the points ( 9.6,-19.7) and (6.6,-23.7) (a) Find the exact distance between the points. (b) Find the midpoint of the line segment whose endpoints are the given points. Part 1 of 2 (a)
The midpoint of the line segment whose endpoints are the given points is (8.1 , -21.7).
To find the exact distance between the points (9.6,-19.7) and (6.6,-23.7), we can use the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the given values:
distance = sqrt((6.6 - 9.6)^2 + (-23.7 - (-19.7))^2)
Simplifying:
distance = sqrt((-3)^2 + (-4)^2)
distance = sqrt(9 + 16)
distance = sqrt(25)
distance = 5
Therefore, the exact distance between the points is 5.
To find the midpoint of the line segment whose endpoints are the given points, we can use the midpoint formula:
midpoint = ((x1 + x2)/2 , (y1 + y2)/2)
Substituting the given values:
midpoint = ((9.6 + 6.6)/2 , (-19.7 + (-23.7))/2)
Simplifying:
midpoint = (16.2/2 , -43.4/2)
midpoint = (8.1 , -21.7)
Therefore, the midpoint of the line segment whose endpoints are the given points is (8.1 , -21.7).
Learn more about Exact distance
brainly.com/question/28676628
#SPJ11
Multiply 0. 035 times a power of ten so that the product is greater than 1, but less than 100. Write the expression. It's an Essay
Answer:
3.5 * 10²
Step-by-step explanation:
In standard form, the number before the point has to be less than ten so
0.035 = 3.5 *10²
A
man will go on a trip for 3 days, so he will take with him 3
shirts, if he has 7 shirts, how many combination of shirts can he
take, without repetition.
The man has 7 shirts in total, so he can take 3 of those shirts on his 3-day trip without repetition. This means that he can make 7 different combinations of shirts, since each shirt has only one choice. For example, he could take shirts A, B, and C; or he could take shirts D, E, and F; or he could take shirts G, A, and B. In total, he has 7 different combinations of shirts to choose from.
The number of combinations of shirts that the man can take without repetition can be found using the formula for combinations, which is:
C(n, r) = n! / (r! * (n-r)!)
In this case, n = 7 (the total number of shirts) and r = 3 (the number of shirts he will take with him).
Plugging in these values into the formula, we get:
C(7, 3) = 7! / (3! * (7-3)!)
C(7, 3) = 7! / (3! * 4!)
C(7, 3) = 5040 / (6 * 24)
C(7, 3) = 5040 / 144
C(7, 3) = 35
Therefore, the man can take 35 different combinations of shirts without repetition.
To learn more about combinations here:
https://brainly.com/question/28065038#
#SPJ11
PLEASE HELP ME!!!!!!!! I WILL GIVE POINTS
The most accurate comparison is that a gamma ray has more energy than a radio wave because it has a shorter wavelength and higher frequency.
How do radio waves and gamma rays compare?The most energetic and high frequency particles are gamma rays. On the other side, radio waves are the EM radiation types with the lowest energies, longest wavelengths, and lowest frequencies.
All electromagnetic radiation travels in a vacuum at the speed of light (c), which is the same for all electromagnetic radiation types, including microwaves, visible light, and gamma rays.
Learn know more about gamma here:
brainly.com/question/2196042
#SPJ1
Colin is making soap for gifts. The table shows the cost of the scented oils needed to make each kind of soap. He needs 1. 5 ounces of Scented oil to make a batch of soap. If he wants to make 2 batches of lavender soap and 2 batches of vanilla soap, how much money will he need for the oils? Almond oil - $1. 23 per ounce
Lavender -$1. 54
Vanilla -$1. 65
Melon -$1. 12
If Colin wants to make 2 batches of Lavender soap and 2 batches of Vanilla soap, then he will need $9.57 for the oils
Here, Colin needs 1.5 ounces of Scented oil to make a batch of soap.
He wants to make 2 batches of Lavender soap and 2 batches of vanilla soap.
So, the amount of scented oil for 2 batches would be:
1.5 × 2 = 3 ounces
The cost of an ounce of Lavender oil is $1.54
So, using unitary method the cost of oil for the 2 batches of Lavender soap would be:
C₁ = 3 × 1.54
C₁ = 4.62 dollars
The cost of an ounce of Vanilla oil is $1.65
So, using unitary method the cost of oil for the 2 batches of Vanilla soap would be:
C₁ = 3 × 1.65
C₁ = 4.95 dollars
Thus, the total cost would be,
C = C + C
C = 4.62 + 4.95
C = 9.57 dollars
Learn more about the unitary method here:
https://brainly.com/question/22056199
#SPJ4
A store pays $60 for an item your friend finds the selling price when the markup is20%
Answer:$72 Total
Step-by-step explanation:
20%=1/5
1/5 + 5/5(total) = 6/5
60 * 6/5 = $72
The delgados obtained an instrument loan of $12,000 from the credit union to pay for their son's tuitions. They obtained the loan at an apr of 10 percent and agreed to repay the loan in 12 mounths what is the finance charge the
The Finance Charge for the Delgados obtained for an instrument is $1200 to repay the loan in 12 months.
The given data is as follows:
Instrument loan = $12,000
Loan at APR = 10%
Number of months = 12 Months
The finance charge is calculated by using the formula,
Finance charge = Loan amount x APR x No' of months to repayment / No' of months in a year
Finance charge = ($12,000 x 10% x 12) / 12
Finance charge = 14400 / 12
Finance charge = $ 1200
Therefore we can conclude that the Finance charge for the Delgados obtained for an instrument is $1200.
To learn more about finance charge
brainly.com/question/3436429
#SPJ4
Practice and Problem S Subtract using the vertical form. 1. (5g^(2)+6g-10)-(2g^(2)+2g+9)
(5g^(2)+6g-10)-(2g^(2)+2g+9) = 3g^(2) + 4g - 19
To subtract the two polynomials, we will use the vertical form. This means that we will line up the like terms and subtract them.
Step 1: Line up the like terms in the vertical form.
5g^(2) + 6g - 10
- (2g^(2) + 2g + 9)
Step 2: Distribute the negative sign to each term in the second polynomial.
5g^(2) + 6g - 10
- 2g^(2) - 2g - 9
Step 3: Subtract the like terms.
5g^(2) - 2g^(2) = 3g^(2)
6g - 2g = 4g
-10 - 9 = -19
Step 4: Write the final answer.
3g^(2) + 4g - 19
Therefore, the answer is 3g^(2) + 4g - 19.
Learn more about polynomials here:
https://brainly.com/question/29961542#
#SPJ11
Which graph is correct?
The system of inequalities is correctly graphed on Shannon's graph.
Which graph shows the system of inequalities?Here we have the following system of inequalities:
y ≥ (1/2)*x - 1
x - y > 1
We can rewrite the second inequality as:
y < x - 1
Then the system becoimes:
y ≥ (1/2)*x - 1
y < x - 1
The first line will be one with positive slope, it is solid (due to the symbol ≥) and the shaded area is above the line.
For the second we will have a dashed line, and now the shaded area is below the dashed line.
From that, we caonclude that Shannon's graph is the correct one.
Learn more about systems of inequalities:
https://brainly.com/question/9774970
#SPJ1
Debra has two different square baking dishes.one has a side length of 8 inches, and the other has a side length of 9 inches. what is the difference in the area of Debra's two square baking dishes?
Debra's two area baking plates are 17 square inches different in size.
What distinguishes an area from a perimeter?The area surrounding a shape forms its perimeter. Area is a unit of measurement for interior space. Surface area is a measurement of a solid shape's exposed surface, whereas area is a two-dimensional measurement of the size of a flat surface (three-dimensional).
The square baking dish has the following surface area with an 8-inch side length:
Area of first square = (side length)² = 8² = 64 square inches
Similarly, the surface area of a square baking dish with 9-inch sides is:
Area of second square = (side length)² = 9² = 81 square inches
Difference in area = |Area of second square - Area of first square|
Difference in area = |81 - 64|
Difference in area = 17 square inches
To know more about area visit:-
https://brainly.com/question/27683633
#SPJ1
A chemist has 42 grams of aluminum. There are 2.70 grams/milliliter for aluminum. How many milliliters of aluminum does the chemist have? Set this up either as a proportion or unit analysis.
a. the chemist has 133 milliliters
b. the chemist has 155 milliliters
c. the chemist has 58 milliliters
d. the chemist has 16 milliliters
The 42 grams of aluminum implies that the chemist has 0.06429ml of aluminum
What is density ?The density of material shows the denseness of that material in a specific given area. A material’s density is defined as its mass per unit volume. Density is essentially a measurement of how tightly matter is packed together. It is a unique physical property of a particular object. The principle of density was discovered by the Greek scientist Archimedes. It is easy to calculate density if you know the formula and understand the related units The symbol ρ represents density or it can also be represented by the letter D.
How to determine the amount of aluminum?
The mass is given as: Mass = 42 grams
The density of aluminum is: Density = 2.7 g/cm³
So, we have: Volume = Density/Mass
This gives, Volume = 2.7/42
Evaluate : Volume = 0.06429cm³
Convert to ml
Volume = 0.06429ml
Hence, the chemist has 0.06429ml of aluminum
To learn more about the density here:
https://brainly.com/question/15382158
#SPJ9
Lesson 8 Practice Problems
1. A number line
can represent positions that are north and south of a truck stop on a
highway. Decide whether you want positive positions to be north or south of the
truck stop. Then plot the following positions on a number line.
a. The truck
stop
b. 5 miles north of the truck
stop
C. 3.5 miles south of the truck stop
We want to graph a number line and graph some locations on it, the graph can be seen at the end of the answer.
What is a number line?A number line is just a line with equidistant marks on it, that can be used to find the distance between numbers, so to graph the number line we just graph a line and do marks on it.
The north will be referred to as the right side of a number line that is positive, and the south will be the opposite.
Now let's complete the graph:
a) We want to graph the truck stop; we can do this at the zero of the number line.
b) 5 miles up north of the truck stop.
Here, if each mark represents a mile, we just mark a point that is 5 marks at the right of the truck stop.
c) 3.5 miles south of a truck stop, at this location.
Here we mark a point that is at 3 and a half marks at the left of the truck stop.
The graph can be seen below.
To know more about number lines, visit:
brainly.com/question/10851163
#SPJ9
whats smaller than 1/2
Answer:
1/4
Step-by-step explanation:
Fractions have two parts, the numerator and the denominator. The denominator is the bottom number and it tells us what unit of fraction we are working with (ie: it denotes fourths, halves, etc.)
Hope it helps! :D
The equation a = 6 000(1 + 0. 028t) represents the amount of money earned on a savings account with 2. 9% annual simple interest
Answer:
See below.
Step-by-step explanation:
This is the correct formula for simple interest, but be careful with the numbers.
a = 6 000(1 + 0. 028t)
0.028 means 2.8% interest rate.
For 2.9% interest rate it should be
a = 6 000(1 + 0. 029t)
If f(x)=2x+1 and g(x)=x^2 +5, what is g(f(2))?
If f(x)=2x+1 and g(x)=x^2 +5, the value of g(f(2)) = 30.
The question is asking to evaluate the composition of the two functions, g(f(2)). This means that first the innermost function, f(2), needs to be evaluated, and the result substituted in place of f(2) in the expression for g(f(2)).
First, evaluating f(2) yields f(2) = 2*2 + 1 = 5. Then, substituting 5 in place of f(2) in the expression for g(f(2)) yields g(f(2)) = g(5) = 5^2 + 5 = 30.
Therefore, the answer to the question is g(f(2)) = 30.
What is a composite function?A composite function is a function evaluated on another function.
For more information about composite function, visit:
https://brainly.com/question/10687170
#SPJ11
Find 3 ratios that are equivalent to the given ratio 7:11
hi, attached is the answer
Hope this helps:)
Find the equation of the line perpendicular to y = 35 x − 4 and
passing through the point (1, 2). Write your answer in
slope-intercept form (i.e., y = mx + b)
Answer:
y = -1/35x + 71/35
Step-by-step explanation:
slope of the perpendicular line = -1/35 (the negative reciprocal of 35)
use the point (1,2) and the point-slope form:
y - 2 = -1/35(x - 1) now put it in slope-intercept form
y = -1/35x + 1/35 + 2
y = -1/35x + 71/35
0r, y = -1/35(x - 71)
The equation of the line perpendicular to y = 35x − 4 and passing through the point (1, 2) is y = (-1/35)x + 71/35.
To find the equation of the line perpendicular to y = 35x − 4 and passing through the point (1, 2), we need to follow these steps:
1. Find the slope of the given line: The slope of the line y = 35x − 4 is 35.2. Find the slope of the perpendicular line: The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. So, the slope of the perpendicular line is -1/35.3. Use the point-slope form of a line equation to find the equation of the perpendicular line: The point-slope form of a line equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the values we have, we get:y - 2 = (-1/35)(x - 1)
4. Solve for y to get the equation in slope-intercept form: Distribute the -1/35 and then add 2 to both sides of the equation to get y on one side:y - 2 = (-1/35)x + 1/35
y = (-1/35)x + 1/35 + 2
y = (-1/35)x + 71/35
So, the equation of the line perpendicular to y = 35x − 4 and passing through the point (1, 2) is y = (-1/35)x + 71/35.
For more information about line perpendicular, visit:
https://brainly.com/question/1202004
#SPJ11
PLEASE HELPPP!!
and thank you in advance!!!
The requried value of the expression [tex]\sum_{n=11}^{30}n-\sum_{n=1}^{10}n[/tex] is 355.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.
Here,
To evaluate the expression:
[tex]\sum_{n=11}^{30}n-\sum_{n=1}^{10}n[/tex]
we can first simplify each summation separately and then subtract the second summation from the first.
[tex]\sum_{n=11}^{30}n[/tex]= 11 + 12 + 13 + ... + 29 + 30
We can use the formula for the sum of an arithmetic series to simplify this expression:
S = (n/2)(a + l)
In this case, a = 11, l = 30, and n = 20 (since we're summing 20 terms).
So, we have:
S = (20/2)(11 + 30)
S= 410
Similarly,
[tex]\sum_{n=1}^{10}n[/tex] = 1 + 2 + 3 + ... + 9 + 10
S = 55
Finally, we can subtract the second summation from the first:
= 410 - 55 = 355
Therefore, the value of the expression is 355.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ1
In 8 years, Claire will be three times her current age. In how many years will she be 20 years old?
Claire will be 20 years old in 16 years. To solve this problem, we use algebra.
Let's represent Claire's current age with the variable x. According to the problem, in 8 years, Claire will be three times her current age. We can write this as an equation:
x + 8 = 3x
Next, we can rearrange the equation to solve for x:
8 = 2x
x = 4
This means that Claire is currently 4 years old. To find out when she will be 20 years old, we can subtract her current age from 20:
20 - 4 = 16
To learn more about algebra here:
https://brainly.com/question/22399890#
#SPJ11
