Answer:
The first line:
y₁ = (2/3)*x + 6
Has the larger y-intercept, by 5 units.
Step-by-step explanation:
Here we need to find the equation for each line.
First, some theory.
A linear relationship can be written as:
y = a*x + b
where a is the slope and y is the y-intercept.
We know that if the line passes through the points (x₁, y₁) and (x₂, y₂), then we can write the slope as:
a = (y₂ - y₁)/(x₂ -x₁)
And, if a line is:
y = a*x + b
a perpendicular line to that one must have a slope equal to:
-(1/a).
Now we can answer this question.
We know that the first line, let's call it y₁, passes through the points (3, 8) and (-3, 4), then its slope will be:
a = (8 - 4)/(3 - (-3)) = 4/6 = 2/3
then the line is something like:
y₁ = (2/3)*x + b
to find the value of b, we can use the fact that we know that the line passes through the point (3, 8)
this means that when x = 3, we must have y₁ = 8
replacing these in the above equation, we get:
8 = (2/3)*3 + b
8 = 2 + b
8 - 2 = b = 6
then the equation for this line is:
y₁ = (2/3)*x + 6
Now let's find the equation for the other line, that we will call y₂.
We know that this line is perpendicular to:
y = (1/3)*x - 2
The slope of that line is:
a = (1/3)
then the slope of a line perpendicular to that one will be:
slope = -(1/a) = -(1/1/3) = -3
slope = -3
then we have:
y₂ = -3*x + b
to find the value of b, we can use the fact that our line passes through the point (2, -5)
This means that when x = 2, we must have y₂ = -5
then:
-5 = -3*2 + b
-5 = -6 + b
-5 + 6 = b = 1
b = 1
then this equation is:
y₂ = -3*x + 1
Now we know both equations:
y₁ = (2/3)*x + 6
y₂ = -3*x + 1
Which equation does have the larger y-intercept?
We can see that the first line has an y-intercept of 6, and the second line has an y-intercept of 1, then the first line has the larger y-intercept, and is larger by 5 units.
13. Which equation represents the line below?
A. y = -x +3
B. y = 2x - 6
c. y = -x + 4
D. y = 1/2x -3
Answer:
y = -2/3x + 3
Step-by-step explanation:
First, we need to calculate the slope of the line. We can do this by using the slope formula using two points:
(y₂ - y₁) / (x₂ - x₁)
If we take the points (-3,5) and (3,1), then: y₂ = 1; y₁ = 5; x₂ = 3; x₁ = -3
Next, we can substitute in values in the equation above to get (1 -5)/(3+3)
** We got 3+3 because it was 3 - (-3), where two negatives equal a positive**
Then, we get, -4/6, which simplifies to -2/3. Our slope is -2/3
After that, we need to find the y-intercept, which is where the line intercepts the y-axis. Here, that is at (0,3).
Therefore, if we put the above information into slope-intercept form:
y = mx + b --> m = -2/3; b = 3
y = -2/3x + 3
Though I don't think that answer choice is there...
given that (2*(x -3) ) / 8*( 2 y - 3) = 16*( x - y )
Answer:
2 ^ (x - 3) ÷ 2 ^ 3(2y - 3)=2 ^ 4(x - y)
The two are common so we give it out then
x - 3 ÷ 6y - 9 =4x - 4y
x - 3 -4x - 4y = 6y -9
-3x -2y = -6
6=3x+2y
Answer:
Step-by-step explanation:
[tex]\frac{2^{x-3}}{8^{2y-3}}=16^{x-y}\\\\\frac{2^{x-3}}{(2^{3})^{2y-3}}=(2^{4})^{x-y}\\\\\frac{2^{x-3}}{2^{3*(2y-3)}}=2^{4*(x-y)}\\\\\frac{2^{x-3}}{2^{6y-9}}=2^{4x-4y}\\\\2^{x-3 -(6y-9)}=2^{4x-4y}\\\\2^{x-3-6y+9}=2^{4x-4y}\\\\2^{x-6y+6}=2^{4x-4y}[/tex]
base is same, so equate the powers
x - 6y + 6 = 4x - 4y
Subtract 'x' from both sides
-6y + 6 = 4x -x - 4y
-6y + 6 = 3x - 4y
Add '6y' to both sides
6 = 3x - 4y + 6y
6 = 3x + 2y
Hence proved
(A) What is the domain of K
(B) What is the range of K
Which angles are congruent to each other?
Angle 4 and Angle 3
Angle 3 and Angle 7
Angle 8 and Angle 5
Angle 1 and Angle 3
Answer:
1 and 3 are congruent
Answer:
Angle 1 and angle 3 are congruent
Please do this ASAP!
No links, thank you!
Answer:
D
Step-by-step explanation:
Slope is (1/8) and y intercept can be found by setting x=0.
AHHHHHHHHHHHH I HATE THIS PLS HELP ME
Answer:
y = 2/3x - 13/3
Step-by-step explanation:
Implying the x and y coordinates, you get this.
How do radical expressions relate to everyday life , give atleast 3 examples !!!!!
If 55% people in a city like Cricket, 30% like Football and the remaining like nother games, then what per cent of the people like other games? If the total people is 60 lakh, find the exact number who like each type of games Answer it fast, no spam please
write in notebook
[tex]\large{\dag\:{\underline{\underline{\frak{\pmb{\red{Answer:-}}}}}}}[/tex]
Cricket = 55%Football = 30%Other games = Remaining (?)So, the percent of people who like other games equals:
= 100 – (55 + 30)
= 100 – 85
= 15%
If the total no. of. people is 60,00,000:
★ Cricket
= 60,00,000 × 55/100
= 33,00,000
★ Football
= 60,00,000 × 30/100
= 18,00,000
★ Other sports
= 60,00,000 × 15/100
= 9,00,000
How do I do this I need a little help
Answer:
B
Step-by-step explanation:
the decay will cause loss so it's the function B
Answer:
B
Step-by-step explanation:
trust
express 23/7 in decimal form
Answer:
3.285714286
Step-by-step explanation:
The points E, F, G and H all lie on the same line segment, in that order, such that the
ratio of EF: FG: GH is equal to 5 : 2:3. If EH = 60, find GH
Answer:
Hello,
Step-by-step explanation:
ratio of EF: FG: GH is equal to 5 : 2:3.
[tex]\Longrightarrow \dfrac{EF}{5} =\dfrac{FG}{2}=\dfrac{GH}{3}=k\\\\EF=5*k\\FG=2*k\\GH=3*k\\\\\\EH=EF+FG+GH=5k+2k+3k=10k\\\\EH=10k=60 \Longrightarrow k=6\\\Longrightarrow GH=3*k=3*6=18(cm)[/tex]
The length of GH is 18 units.
What is a Line Segment?A line segment is defined as a measured path between two places. Line segments can make up any polygon's sides because they have a set length.
The figure given below shows a line segment EH, where the length of line segment EH refers to the distance between its endpoints, E and H.
Given that the points E, F, G and H all lie on the same line segment
E______________F______________G_____________H
We have to determine GH
We have the ratio of EF: FG: GH is equal to 5 : 2 : 3.
Then EF/5 = FG/2 = GH/3 = c
So EF = 5c, FG = 2c, and GH = 3c
Given that EH = 60,
⇒ EH = EF + FG + GH
⇒ 60 = 5c+ 2c+ 3c
⇒ 10c = 60
⇒ c = 60/10
⇒ c = 6
So GH = 3(6) = 18
Hence, the length of GH is 18 units.
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how do i convert y = 6x into y = mx + b form?
Answer:
it already is in that form
y = 6x
technically Y = 6x + 0 could be the answer...
but in math we tend to not rite "obvious" information
to reduce clutter and confusion
+1[tex]x^{1}[/tex] is technically correct but we drop the + sign for positive numbers
and also drop the exponent if it is a 1 ... similarly
+1[tex]x^{1}[/tex] + 0 + 0 + 0 would also be silly and we don't write the zeros
+1[tex]x^{1}[/tex] + 0 + 0 + 0 = x
Step-by-step explanation:
The square pyramids are similar. Find the volume of the smaller pyramid. Round your answer to the nearest hundredth.
A. 3.70 yd
B. 3.90 yd
C. 4.21 yd
D. 4.68 yd
Answer:
A
Step-by-step explanation:
Since the pyramids are similar, the scale factor will be 3. So the height of the small pyramid is 6.3/3=2.1. The volume will be (1/3)*(2.1)*(2.3)^2=3.70
The volume of smaller square pyramid is 3.703 cubic yards. Therefore, option A is the correct answer.
What are similar figures?Similar figures mean when two figures are of the same shape but are of different sizes. In other words, two figures are called similar when they both have a lot of the same properties but still may not be identical.
Given that, the two square pyramids are similar.
Let the height of smaller square pyramid be h.
As we know, when two geometrical figures are similar, their sides will be in proportion.
Now, 6.9/2.3 = 6.3/h
3=6.3/h
h=2.1 yd
The volume of square based pyramid =a²h/3.
Thus, volume = (2.3²×2.1)/3
= 11.109/3
= 3.703 cubic yards
Therefore, option A is the correct answer.
Learn more about the similar figures here:
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A rectangular shape of dimension 95 m by 75 m is drawn to a scale of 1 cm to 10 m . Find the area of the drawing
Answer:
71.25
Step-by-step explanation:
That's the answer
A moving company uses plastic wrap to bundle groups of boxes together. If a portion of plastic wrap that measures 900 inches in length is used to bundle each group of boxes, how many groups of boxes can be bundled using 1500 feet of the same type of plastic wrap?
Answer: 20 boxes
Step-by-step explanation:
First and foremost, we need to know that 1 foot = 12 inches. Therefore, 1500 feet will be converted to inches and this will be:
1500 feet = 1500 × 12 = 18000 inches
Since each group of box requires 900 inches, then the number of group of boxes that can be used in this case will be:
= 18000/900.
= 20 groups of boxes
What statement describes the graph?
Answer:
D.
Step-by-step explanation:
The gragh crosses the y-axis at (0,-5), decreasing from x=-10 to x=-2 and remaining constant from x=-2 to x=10
( √8/3 - √24 + √50/3) . √6
Answer:
6(3√3-2)
Step-by-step explanation:
(√8/3 - √24 + √50/3) . √6
(√8/3 - 2√6 + 25√2/3) . √6
(2√2/3 - 2√6 + 25√2/3) . √6
(27√2/3 - 2√6) . √6
(27√12/3 - 12)
9√12-12
√12(9-√12)
2√3(9-2√3)
6(3√3-2)
Answer:
2Step-by-step explanation:
[tex]( \sqrt{8/3} - \sqrt{24} + \sqrt{50/3} )* \sqrt{6} =\\\sqrt{48/3} - \sqrt{144} + \sqrt{300/3} =\\\sqrt{16} - 12 + \sqrt{100} =\\4 - 12 + 10 =\\2[/tex]
Five consecutive multiples of 7 have a sum of 350. What is the smallest of these numbers?
A. 70
B. 56
C. 77
D. 84
Answer:
B. 56
Step-by-step explanation:
x + (x + 7 ) + ( x + 14 ) + ( x + 21 ) + ( x + 28 ) = 350
( x + x + x + x + x ) + ( 7 + 14 + 21 + 28 ) = 350
5x + 70 = 350
- 70 - 70
_____________
5x = 280
x = 56
Hope this helps!
The smallest number is 56, the correct option is B.
What is Sum?The sum is the output of the mathematical operation, Addition.
Let the first number is x, they are multiples of 7,
As they are multiples of 7, the consecutive numbers will be added by 7 for next term.
The 5 consecutive numbers can be written as x, (x+7), (x+14), (x+21), (x+28).
The equation can be formed for the numbers that are given as,
An equation is a mathematical statement that relates an algebraic expression with other expression by an equal sign.
The sum of the multiples is 350
x + (x + 7 ) + ( x + 14 ) + ( x + 21 ) + ( x + 28 ) = 350
Grouping the variables and the constants separately
( x + x + x + x + x ) + ( 7 + 14 + 21 + 28 ) = 350
5x + 70 = 350
Adding (-70) to both sides of the equation
5x = 280
Dividing both sides by 5
x = 56
The value of the first number of the series is obtained.
The first value is the smallest number of the series.
To know more about Sum
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The dot plot below represents this set of data:
30, 29, 30, 28, 28, 27, 22, 28, 28, 22, 27, 26, 25, 27
Answer:
True
Step-by-step explanation:
All of them match up
To join the tennis club, there is a $10.20
initial fee and a $3.90 yearly fee. What
would be the value of the slope in this
situation?
Use this space to write down notes or work through problems
Your teacher will see what you wrate.
Answer:
10.20
Step-by-step explanation:
Let
y = Total fee
Initial fee = $10.20
Yearly fee = $3.90
Number of years = x
The equation:
y = 3.90x + 10.20
Recall,
y = mx + c
Where,
x = slope
c = y - intercept
Therefore,
The y - intercept from y = 3.90x + 10.20 is 10.20
Thirty- five out of sixty students preferred to eat their lunch at school rather going home in lunch break. Express the numbers in decimal.
Answer:
0.583
Step-by-step explanation:
Use a caluclator
Can someone help me out plz
Answer:
Around 59.69026
Step-by-step explanation:
C = Circumference (What we are looking for)
R = 9.5yd (Radius)
C = 2(Pie [I can't find the symbol])rC = 2(Pie)9.5C ≈ 59.69026A rectangle has side lengths 2x + 3 and 5x - 2.
Write an expression without brackets for the area of the rectangle
Answer:
10x² + 11x - 6
Step-by-step explanation:
The area (A) is the product of the sides, that is
A = (2x + 3)(5x - 2) ← expand using FOIL
= 10x² - 4x + 15x - 6 ← collect like terms
= 10x² + 11x - 6
What are the zeros of f(x) = x2 - 8x+16?
O A. x= 4 only
B. x = -4 and x = 4
C. X=-2 and x = 8
D. x=-4 only
Answer:
x=4
Step-by-step explanation:
f(x) = x^2 - 8x+16
Set equal to zero
0 = x^2 -8x +16
Factor
what 2 numbers multiply to 16 and add to -8
-4*-4 = 16
-4+-4 = -8
0= (x-4)(x-4)
Using the zero product property
x-4 = 0 x-4 =0
x=4 x=4
The height and radius of a cone are each multiplied by 11. What effect does this have on the volume of the cone?
The volume of the cone is multiplied by (Blank 1).
The volume of the new cone would be 1331 times more than the volume of the original cone. Thus, The volume of the original cone is multiplied by 1331
The volume of the cone can be calculated by the given formula:
The volume of cone = [tex]\frac{1}{3} \pi r^{2} h[/tex]
where r = radius of the cone
h = height of the cone
Solution:
The volume of the original cone= .......1
It is given that the height and radius of a cone are multiplied by 11.
then volume
= [tex]\frac{1}{3} \pi (11r)^{2} (11h)[/tex]
= [tex]\frac{1}{3} \pi (121r^{2}) (11h)[/tex] .........2
The change in volume of the cone after multiplying 11 to r and h would be
dividing equation 2 by equation 1
= [tex]\frac{1}{3} \pi (121r^{2}) (11h)[/tex]/[tex]\frac{1}{3} \pi r^{2} h[/tex]
= 121*11
= 1331
Thus, The volume of the original cone is multiplied by 1331
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The 12th term of the arithmetic sequence is 10.5. The 18th term of this sequence is 13.5. Find the common difference and the first term.
let the n'th term be called x, and the value of the term y,
then there is a function y=a*x + b
that will give us all term we want.
this formula is also used for straight lines.
we just need a and b. we already got two data points. we can just plug the known x/y pairs into the formula
10.5 = a*12 + b
13.5 = a*18 + b
now lets manipulate these lines.
multiply the first line by 3 and the second line by 2
31.5 = a*36 + 3b
27 = a*36 + 2b
subtract the second line from the first line
4.5 = b
yey, we now know b, let's plus b into either line from above, I'll go with the first one, looks easier.
10.5 = a*12 + 4.5
6 = a*12
0.5 = a
now y=a*x + b can be filled with a and b
y = 0.5 * x + 4.5
for x=1 (the first term) it's f(1)=5
each step is 0.5, hence the common difference.
2and way:(13.5-10.5)/(18-12)
= 3 / 6
= 0.5
we got the comment difference by looking at the full difference over 6 steps and divined by these 6 steps.
from step 12 to step one it's 11 steps down
10.5 - 0.5*11
= 10.5 - 5.5
= 5
okay I admit... 2and way to do it might be faster and more intuitive... :DFind the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.
A. 11.7
B. 11.9
C. 11.4
D. 14.4
Answer:
Option A, 11.7
Step-by-step explanation:
To find height,
tan 68 = 26/h
h = 26/tan(68)
to find x
tan(42) = h/x
x = h/tan(42)
x = 11.7 (rounded to the nearest tenth)
Answered by GAUTHMATH
Triangle ABC is a right triangle.
Triangle A B C. Angle A is x degrees, B is 90 degrees, C is (x minus 10) degrees. The exterior angle to angle C is (2 x + 40) degrees.
Which equations can be used to find the value of x? Check all that apply.
x + 90 + (x minus 10) = 180
x + 90 + (2 x + 40) = 180
2 x + 80 = 180
x + 90 = 2 x + 40
(x minus 10) + 90 = 2 x + 40
Answer:
x + 90 + (x minus 10)= 180° can be used to find the value of x.
Answer:
A) X+90+ (x-10) - 180
C) 2x+80 = 180
D) x+90 = 2x+40
Step-by-step explanation:
Hey I’m having trouble finding out how to divide fractions
The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed.
Sally and Mia run a furniture making company. They work together to build and paint custom dressers.
Sally charges a $100 flat fee for each dresser she builds, plus $420 for each hour she spends building.
Mia charges a $150 flat fee for each dresser she paints, plus $390 for each hour she spends painting.
a) Represent what Sally charges for one dresser as a polynomial. Remember to define any variables!
b) Represent what Mia charges for one dresser as a polynomial. Remember to define any variables!
c) Write a new SIMPLIFIED polynomial that represents their total charges, together, for one dresser.
Answer:
y = 250 + 810x
Step-by-step explanation:
Let
y = total charges
x = cost per hour
Sally: building
y = 100 + 420x
Mia: painting
y = 150 + 390x
Find their total charges of building and painting
Add the total charges of both of them
y = 100 + 420x + 150 + 390x
y = 250 + 810x
