Answer:
y=2x+1
Step-by-step explanation:
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
To start, you know what m is; it's just the slope, which you said was 2. So you can right away fill in the equation for a line somewhat to read:
y=2x+b.
Now, what about b, the y-intercept?
To find b, think about what your (x,y) point means:
(1,3). When x of the line is 1, y of the line must be 3.
Because you said the line passes through this point, right?
Now, look at our line's equation so far: b is what we want, the 2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (1,3).
So, why not plug in for x the number 1 and for y the number 3? This will allow us to solve for b for the particular line that passes through the point you gave!.
(1,3). y=mx+b or 3=2 × 1+b, or solving for b: b=3-(2)(1). b=1.
The equation of the line that passes through the point (1,3) with a slope of 2
is
y=2x+1
A 20-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 6 feet from the base of the building. How high up the wall does the ladder reach?
Answer:
19.1 feet
Step-by-step explanation:
This forms a right triangle
use the pythagorean theorem
a^2 + b^2 = c^2
a^2 + 6^2 = 20^2
a^2 + 36 = 400
a^2 = 364
a = 19.0787840283
Rounded
19.1 feet
n is an integer greater than 1
Prove algebraically that 10+ n^2 - (n - 2)^2 is always an even number.
Your final line must have, 'always even' as part of the line.
Answer:
Proof below.
Step-by-step explanation:
Let f(n)=10+ n^2 - (n - 2)^2.
We want to prove f is even for integer n > or = 1.
Let's show f is even for the base case, n=1.
f(1)=10+1^2-(1-2)^2
f(1)=10+1-(-1)^2
f(1)=11-(1)
f(1)=10
f(1) is even.
Let's assume the for some integer k > or = 1 , we have f(k) is even. This means there is some integer m so that f(k)=2m.
Note: f(k)=10+ k^2 - (k - 2)^2.
We want to show f(k+1) is even.
f(k+1)=10+ (k+1)^2 - ([k+1] - 2)^2
f(k+1)=10+ (k+1)^2 - (k-1)^2
f(k+1)=10+ ((k+1)^2 - (k-1)^2)
That difference is a difference of squares. Let's try factoring it.
f(k+1)=10+ (k+1-[k-1])(k+1+[k-1])
f(k+1)=10+ (2)(2k)
Multiply:
f(k+1)=10+4k
Turns out we didn't even need to use our induction hypothesis since 10+4k is 2(5+2k) which makes f(k+1) even given the factor of 2 present.
This proves for all integers n>=1 that f(n) is even.
We could have this without induction then. Let's do that here below this line.
-------------------
10+ n^2 - (n - 2)^2
10+[n^2 - (n - 2)^2]
Factor difference of squares:
10+(n-(n-2))(n+(n-2))
Simplify:
10+(2)(2n-2)
Factor:
2[5+(2n-2)]
Because of the factor of 2, the given expression is always even for integer n.
Two consecutive numbers exist such that the sum of three times the first number and two less than the second number is equal to 144. What are third numbers
Step-by-step explanation:
two consecutive numbers means that one is larger by 1 than the other number.
so, we have to choices depending on whether the first number (multiplied by 3) is the larger one, or the second number.
to show what I mean, let's start with the second number being the larger one.
we are dealing therefore with x and (x+1).
3x + (x+1) - 2 = 144
4x - 1 = 144
4x = 145
x = 145/4
this is not an integer (but this is necessary to have 2 dedicated consecutive numbers).
so, it is actually not a valid solution.
therefore we are checking the other approach :
we are dealing therefore still with x and (x+1). but now we multiply the other number by 3.
3(x+1) + x - 2 = 144
4x + 1 = 144
4x = 143
x = 143/4
this is still not an integer (but this is necessary to have 2 dedicated consecutive numbers).
so, it is actually not a valid solution either.
and now I am beginning to think you left out some important information in the question.
could it be these 2 numbers are consecutive even or consecutive uneven numbers ?
because then the difference between the both of them is 2 and not 1.
we are dealing therefore with x and (x+2). first attempt to make the smaller number the "first" number :
3x + (x+2) - 2 = 144
4x = 144
x = 144/4 = 36
ah ! now that looks different !
36 and 38 are valid solutions under the changed assumptions. and we are dealing with consecutive even numbers.
let's check :
36×3 + 38 - 2 = 36×3 + 36 = 36×4 = 144
correct.
and fun fact, if we turn this around and make the larger number the "first" number, we are still dealing with x and (x+2), but now we multiply the larger number by 3 :
3(x+2) + x - 2 = 144
4x + 6 - 2 = 144
4x + 4 = 144
4x = 140
x = 140/4 = 35
35 and 37 are also valid solutions under the new assumptions and two consecutive uneven numbers ...
so, please check what your original question (and maybe the headlines and description around it) says. and then pick the right solution.
Khan academy how to find the domain of a function equation.
Answer:
I cant even see anything can you reupload your answer, please?
Step-by-step explanation:
Express the following ratio as a fraction then reduce the fraction to the lowest terms
4:6
Step-by-step explanation:
4:6 as a fraction is 4/6
4/6 in its lowest terms is 2/3
hope this helps
Haley has 48 colored pencils and 3 cups (A, B, C). Cup A holds one more colored pencil than cup C. Cup B holds 2 more colored pencils than cup C. How many pencils does cup B contain?
Answer:
17 pencils
Step-by-step explanation:
Assume that cup C holds x pencils. In this case, cup A holds x + 1 pencils, and cup B holds x + 2 pencils. We know that all of the cups together hold 48 pencils. If we add what we got together, we would get x + x + 1 + x + 2 = 48. 2x + 1 + x + 2 = 48. 2x + x + 1 + 2 = 48. 3x + 1 + 2 = 48. 3x + 3 = 48. 3x = 48 - 3. 3x = 45. x = 45 / 3. x = 15. Now, we know that cup C holds 15 pencils, and from here, we can find the number of pencils in cup B by adding 2 to 15 and getting 17, and that would be your answer.
Tell me if I'm wrong :)
Answer:
12
Step-by-step explanation:
0.0346 written in standard form
Answer:
3.46x10-2
×
10
−
2
3.46
×
10
−
2
Explanation:
a number expressed in
standard form
is.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣
∣
2
2
a
×
10
n
2
2
∣
∣
∣
−−−−−−−−−−−−
where
1
≤
a
<
10
and n is an integer
express
0.0346
as a number between 1 and 10
3
∙
46
we now have to move the decimal point 2 places to
the left to retain equality
move to the right
→
then n is positive
move to the left ←
then n is negative
⇒
0.0346
=
3.46
×
10
−
2
help please???!!!!?!!!!??!!?!!!!!!!!
Answer:
b，c，f
Step-by-step explanation:
a is -8
b 8
c 8
d -8
e 1-
f 8
g -8
h -8
PLS HELP WILL MARK YOU BRAINLIEST!
Answer:
Option C
Step-by-step explanation:
[tex]\frac{(2x^3y^2z)^2(-3xyz^2)^2}{18x^6y^7z^3} =[/tex]
[tex]\frac{(4x^6y^4z^2)(9x^2y^2z^4)}{18x^6y^7z^3} =[/tex]
[tex]\frac{36x^8y^6z^6}{18x^6y^7z^3} =[/tex]
[tex]\frac{2x^2z^3}{y}[/tex]
which ordered pair represents the coordinate of point h?
(0.6, - 1.4) (-1.4, 0.6) (-1.2 , 0.3) (0.3, - 1.2)
Answer:
-1.2 is the answer i think
Find the value of x and thank for answer
If you want to save $4500 to go to the Super Bowl, how much will you need to invest in an account now with 6.25% APR, compounding continuously, in order to reach your goal in 4 years? (Round to the nearest dollar)
Gabriella drove to her friend's house and
back. The trip there took six hours and the
trip back took five hours. She averaged
60 km/h on the return trip. Find the
average speed of the trip there.
She drove 5 hours back at a rate of 60 km/h. Total distance on the way back was 5 x 60 = 300 km
The trip there would be 300 km and she drove for 6 hours
Average speed = 300 km / 6 hours = 50 km/h
Answer: 50 km/h
I need #8 done (Show work) will mark brainliest
Answer:
see explanation
Step-by-step explanation:
Since BD bisects ∠ ABC , then
∠ ABD = ∠ DBC , substitute values
3x + 4 = 55 ( subtract 4 from both sides )
3x = 51 ( divide both sides by 3 )
x = 17
Step-by-step explanation:
Statement Reason
BD bisects ∠ABC Given
m∠ABD = (3x + 4)°, m∠DBC = 55° Given
∠ABD ≅ ∠DBC Definition of angle bisector
3x + 4 = 55 Definition of congruence
3x = 51 Subtraction property
x = 51/3 Division property
x = 17 Proved
10. El siguiente circulo está dividido en 8 rebanadas iguales. ¿Qué fracción del circulo está sombreada?
Answer:
2/8
Step-by-step explanation:
2/8 porque ahy 8 y 2 estan coloridas.Si gustarias simplifar seria .25
Select the correct answer.
Which graph best represents a function with zeros of -3, 0, and 2?
Answer: C
Step-by-step explanation:
The answer is C
The graph C. represents the polynomial with zeros of -3, 0 and 2.
What are zeros of a polynomial?The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero. They are interesting to us for many reasons, one of which is that they tell us about the x-intercepts of the polynomial's graph.
Or we can say that the x- intercept of the graph of the polynomial are the zeros of that polynomial. Thus, the graph with x - intercept -3, 0, 2 represent the required function.
Learn more about zeros of a polynomial here
https://brainly.com/question/10702726
#SPJ2
A school of salmon was swimming in the river 5 feet below the surface. To escape a hungry bear, they went down another 3 feet.
What is the position of the salmon now relative to the surface?
Answer:
-8 feet
Step-by-step explanation:
5 + 3 = 8
Answer:
its 8 feet down...
Step-by-step explanation:
just add 5 plus 3 ? well maybe your doing the math different if it's wrong I'll edit it to make it right.
CAN SOMEONE HELP ME PLEASE ASAP!
Answer:
1 and 3
Step-by-step explanation:
The reason 1 and 3 are similar due to the fact 3x2 is 6 (one side of 3) and 5x2 is 10 (another side of 3) therefore they are similar because one is sized up slightly.
Type the expression that results from the following series of steps
Start with y subtract d, multiply by a, then add c.
Answer:
(y-d) × a + c
Step-by-step explanation:
You start with y:
y
subtract d:
y-d
multiply by a:
(y-d) × a
then add c:
(y-d) × a + c
Hope that helps! :)
 Find the perimeter. Simplify the answer
Answer:
20v + 6
Step-by-step explanation:
Perimeter = v + 10 + v + 10 + 9v - 7 + 9v - 7
Perimeter = 2v + 18v + 20 - 14
Perimeter = 20v + 6
-Chetan K
Answer:
Perimeter = 9v - 7 + 9v - 7 + v + 10 + v + 10
= 20v + 6...ans
Step-by-step explanation:
Hope i lt Helps you!!Please help. I'm not really good at these kind of problems. Working alone, Dan can do a certain job in three hours and Stan can do the same job in two hours. At these rates, how long would it take Dan and Stan to do this job working together?
Answer: The answer is it would take Dan and Stan 1 hour if they work together, because 3-2=1, so make those hours and you have 1 hour.
Hope I helped:)
Which set of ordered pairs (x,y)(x,y) could represent a linear function?
Shama types at a constant rate she types 12 letters in 4 seconds what is the constant of proportionality for the relationship of letters to minutes
Answer choices
3
48
180
2,880
Help I need this answer fast I’m taking a test and I can’t fail 7th grade
Answer:
Shama types at a constant rate she types 12 letters in 4 seconds what is the constant of proportionality for the relationship of letters to minutes
Answer choices
3
48
180
2,880
Help I need this answer fast I’m taking a test and I can’t fail 7th grade
Step-by-step explanation:
Shama types at a constant rate she types 12 letters in 4 seconds what is the constant of proportionality for the relationship of letters to minutes
Answer choices
3
48
180
2,880
Help I need this answer fast I’m taking a test and I can’t fail 7th grade
The constant of proportionality for the relationship of letters to minutes is 180.
What is Proportionality?Two set of quantities are said to be directly proportional or just simply proportional if the corresponding elements of these two sets has a constant ratio. This constant is called the proportionality constant or coefficient of proportionality.
We have the proportional relationship between letters typing and the time in minutes taken to type the letters.
Time taken by Shama to type 12 letters = 4 seconds
= 4 / 60 minutes
= 1/15 minutes
Proportionality constant can be found by taking the ratio of these quantities.
That is, proportionality constant = 12 / (1/15)
The fraction in the denominator will be taken to the numerator as the reciprocal and the operation changes into multiplication.
Proportionality constant = 12 × (15/1) = 180
Hence the proportionality constant for the relationship of the quantities letters and minutes is 180.
To learn more about Proportionality, click :
https://brainly.com/question/29126727
#SPJ5
Please answer! I’ll give you Brainliest
A)
The four small squares are all 3x3, so the perimeter is 3+3+3+3 = 12.
12 * 4 = 48
We can find the perimeter of the large diamond shape using the Pythagorean theorem, a^2 + b^2 = c^2
a = 4
b = 4
4^2 + 4^2 = c^2
16 + 16 = c^2
32 = c^2
c = 5.65685425
So the perimeter of the large diamond shape is
5.65685425+5.65685425+5.65685425+5.65685425 = 22.627417
48+22.6 = 70.6
B)
The areas of the small squares are 3x3 = 9
9 * 4 = 36
The area of the large diamond shape is
5.65685425 * 5.65685425 = 32
36 + 32 = 68
write an equation of a line that passes through the point (5,-1) and is parallel to the line y = (-3/5)x -3
Answer:
y = -3/5x + 2
Step-by-step explanation:
-1 = -3/5(5) + b
-1 = -3 + b
2 = b
y = -3/5x + 2
what is the answer??????
Step-by-step explanation:
Take lcm of 6,8,10 = 120
40 + 60 + 60/ 120
= > 160/ 120
= > 4/3 = 4 (1/3)
Please help me, If you do not know do not answer
Rule for function
If Domains of relation have unique Range then it's function otherwise not a function.
Now
FunctionFunctionRelation/Not a functionNot a function/RelationA polynomial that has two terms is a(n) ?.
Answer: Binomial
Monomial= 1 term
Binomial= 2 terms
Trinomial=3 terms
Polynomial= 4 terms or more
help im not good in math
Answer:
4
Step-by-step explanation:
yeah 4/8 is the answer. yeah-ya
What is a scalar quantity ?
Answer:
A scalar quantity is defined as the physical quantity with only magnitude and no direction.