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.
2z^8- 32z^8
Help plz
Answer:
-30z^8
Step-by-step explanation:
[tex]2 {z}^{8} - 32 {z }^{8} \\ = - 30 {z}^{8} [/tex]
Answer:
-30z^8
Step-by-step explanation:
2z^8- 32z^8
-30z^8
Can some one help me solve these 3 questions?
Q5. Evaluate this expression when a=6
Q6. Which option shows this expression simplified correctly?
Q7. Which option shows this expression simplified correctly?
Q8. Find the following:
Q9. Which option shows this expression expanded correctly?
The zeros of polynomial function g are -5, -1, and 7. Complete the factors to write an equation for function g. Assume that g has only three zeros and three factors.
Answer:
g(x) = (x + 5)(x + 1)(x - 7)
Step-by-step explanation:
i know for a fact im right
The complete equation of function whose zeros are given;
f(x) = (x+5)(x+1)(x-7)
What is Polynomial?
A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number.
Here, given zeros are;
-5, -1, 7
then we can write;
x = -5, x = -1; x = 7
x +5 = 0 ; x + 1 = 0 ; x - 7 = 0
On multiplying all the terms we get;
(x+5)(x+1)(x-7) = 0
Thus, The complete equation of function whose zeros are given;
f(x) = (x+5)(x+1)(x-7)
Learn more about Polynomial from:
https://brainly.com/question/17822016
#SPJ2
Suppose that a1, a2, a3, . . . is an arithmetic sequence, in which a3 = 19 and a14 = 96. Find a1.
If f(x) =3x^2 +1 and g(x) = 1 -x, what is the value of (f-g) (2)?
Answer:
(f-g)(2) = 14
Step-by-step explanation:
f(x) =3x^2 +1 and g(x) = 1 -x
f(2) = 3(2)^2 +1 = 3(4)+1 = 12+1 = 13
g(2) = 1-2 = -1
f(2) - g(2) = 13 - -1 = 13+1 =14
Answer:
14
Step-by-step explanation:
(f-g)(2) means f of x minus g of x when x equals 2.
To solve, first set up the equation
[tex](3x^2}+1)-(1-x)[/tex]
Change the signs in the second part. {because this is subtraction}
[tex]3x^2}+1-1+x[/tex]
Replace x with 2.
[tex]3(2^2})+1-1+2[/tex]
Solve.
[tex]3(4)+2[/tex]
[tex]12+2[/tex]
[tex]14[/tex]
In Australia, road distance is measured in kilometres.
In the USA, road distance is measured in miles.
5 miles is about the same distance as 8 kilometres.
About how many miles is 120 kilometres?
Answer:
75
Step-by-step explanation:
5 miles-8km
x miles-120 km
x=120×5÷8
x=75 (miles)
Answer:
s
Step-by-step explanation:
since 5 miles is the same as 8 kilometers,how many miles is 120 kilometers..use ratio and proportion
5miles:8kilometers
x. :120kilometers
8x/8=600/8
x=75miles
I hope this helps
Ross walked 3 m east and 6 m north. How far is he from the starting point
Answer:
3 sqrt(5) meters
Step-by-step explanation:
This is a right triangle so we can use the Pythagorean theorem.
a^2 +b^2 = c^2 where a and b are the legs and c is the hypotenuse
3^2+6^2 = c^2
9+36 = c^2
45 = c^2
Taking the square root
sqrt(45) = sqrt(c^2)
sqrt(9*5) = c
sqrt(9) sqrt(5) =c
3sqrt(5) = c
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
Given:-Ross walked 3 m east and 6 m north. Find:-How far is she from the starting point?solution:-Ross walked 3 m east and 6 m north.
so her path is a right angle triangle path.
we know that,
in a right angle triangle, According to the Pythagorean theorom,
[tex]\boxed{\sf{l^2+b^2=h^2 }}[/tex]
where
l= legs b=baseh=hypotenuse According to the question, [tex]\sf{3^2+6^2=f^2 }[/tex] [tex]\sf{9+36=f^2 }[/tex] [tex]\sf{ f^2=45 }[/tex] [tex]\sf{f=\sqrt{45} }[/tex] [tex]\sf{f=3\sqrt{5} }[/tex] Therefore:-he is [tex]\sf{3\sqrt{5} }[/tex] far from the starting point
Jernel has to figure out the area of her square garage. She knows that one side of the garage is equal to the length of her rabbit pen. The dimensions of the rectangular rabbit pen are 13 by 10.
Answer:169
Step-by-step explanation:13 x 13 = 169
You would take the larger side of the pen (13) or else it wouldn’t fit if you chose 10.
plzzz helpppp dont ignoreeee
Answer:
X= 40
Step-by-step explanation:
2(110 + 4x) = 220 + 8x = 540
8X = 320
X= 40
SECTION B
A matatu and Nissan left town A for town B 240km away at 8.00 a.m travelling at 90km/hr
and 120km/hr respectively. After 20 minutes the Nissan had a puncture which took 30
minutes to mend.
(5mks
a) How far from town A did the Nissan catch up with the matatu?
9514 1404 393
Answer:
180 km
Step-by-step explanation:
The Nissan had traveled (120 km/h)(1/3 h) = 40 km when it had the puncture. It started from that location when the puncture was repaired at t = (1/3+1/2) = 5/6, where t is in hours. Then the two vehicles met (again) when ...
Matatu distance = Nissan distance
90t = 40+120(t -5/6)
0 = 40 +30t -100 . . . . . . subtract 90t, eliminate parentheses
60 = 30t . . . . . . . . . . . add 60
2 = t . . . . . . . . . . . . . 2 hours after leaving, the cars meet again
That distance from town A is ...
y = 90t = 90(2) = 180 . . . . km
What are the coordinates of the image of L for a dilation with center (0, 0) and scale factor ?
Answer:
The vertices of ABCD:
A ( - 3, 1 )
B ( 4 , - 3 )
C ( 1, 3 )
D ( - 1 , 4 )
∴ ( 4 x, 4 y ):
A ` ( - 12, 4 )
B ` ( 16, - 12 )
C ` ( 4, 12 )
D ` ( - 4 , 16 )
Step-by-step explanation: I hope this helps! ™(*/ω＼*)
Evaluate (5.6 x 10^-4 ) - (9.3x10^-6)
Give your answer in standard form to 3SF
Answer:
I got 5.51x10^-4
Step-by-step explanation:
Answer:
.0005507
Step-by-step explanation:
5.6 x [tex]10^{-4}[/tex]
9.3 x [tex]10^{-6}[/tex]
560 x [tex]10^{-6}[/tex]
- 9.3 x [tex]10^{-6}[/tex]
550.7 x [tex]10^{-6}[/tex]
.0005507
3 of 9
Express the ratio below in its simplest form.
2:4:2
Answer:
1 : 2 : 1
Step-by-step explanation:
2:4:2
Divide each term by 2
2/2:4/2:2/2
1 : 2 : 1
Mr. Sun borrowed $15,600 for 54 months at simple interest to pay for a new swimming pool. If Mr. Sun paid the bank a total of $21,567.00, what was the simple interest rate of the loan?
Given:
Mr. Sun borrowed $15,600 for 54 months at simple interest.
Mr. Sun paid the bank a total of $21,567.00.
To find:
The rate of simple interest.
Solution:
We know that,
12 months = 1 year
1 month = [tex]\dfrac{1}{12}[/tex] year
54 months = [tex]\dfrac{54}{12}[/tex] year
54 months = 4.5 years
Simple interest is:
[tex]S.I.=Amount-Principal[/tex]
[tex]S.I.=21567-15600[/tex]
[tex]S.I.=5967[/tex]
Formula for simple interest is:
[tex]S.I.=\dfrac{P\times r\times t}{100}[/tex]
Where, P is principal, r is the rate of interest in percent and t is the number of years.
Putting [tex]S.I=5967,P=15600,t=4.5[/tex], we get
[tex]5967=\dfrac{15600\times r\times 4.5}{100}[/tex]
[tex]596700=70200r[/tex]
[tex]\dfrac{596700}{70200}=r[/tex]
[tex]8.5=r[/tex]
Therefore, the rate of simple interest is 8.5%.
solve for x−4 + x ≤ 9
Answer:
x ≤ 6.5
Step-by-step explanation:
x−4 + x ≤ 9
Combine like terms
2x-4≤ 9
Add 4 to each side
2x-4+4≤ 9+4
2x≤ 13
Divide by 2
2x/2 ≤ 13/2
x ≤ 6.5
help asap no wrong answers----------------------
Answer:
[tex]y=-2(sin(2x))-7[/tex]
Step-by-step explanation:
1. Approach
Given information:
The graph intersects the midline at (0, -7)The graph has a minimum point at ([tex]\frac{\pi}{4}[/tex], 9).What conclusions can be made about this function:
The graph is a sine function, as its y-intercept intersects the midlineThis graph has a negative coefficient, this is because after intersecting the midlines at the y-intercept, the function has a minimum.This graph does not appear to have undergone any horizontal shift, as it intercepts the midlines with its y-interceptTherefore, one has the following information figured out:
[tex]y=-n(sin(ax))+b[/tex]
Now one has to find the following information:
amplitudemidlineperiod2. Midline
The midlines can simply be defined as a line that goes through a sinusoidal function, cutting the function in half. This is represented by the constant (b). One is given that point (0, -7) is where the graph intersects the midline. The (y-coordinate) of this point is the midline. Therefore, the midline is the following:
y = -7
2. Amplitude
The amplitude is represented by the coefficient (n). It can simply be defined by the distance from the midline to point of maximum (the highest part of a sinusoidal function) or point of minimum (lowest point on the function). Since the function reaches a point of minimum after intercepting the (y-axis) at its midlines, the amplitude is a negative coefficient. One can find the absolute value of the amplitude by finding the difference of the (y-coordinate) of the point of minimum (or maximum) and the absolute value of the midline.
point of minimum: [tex](\frac{\pi}{4},9)[/tex]
midline: [tex]y=-7[/tex]
Amplitude: 9 - |-7| = 9 - 7 = 2
3. Period
The period of a sinusoidal function is the amount of time it takes to reach the same point on the wave. In essence, if one were to select any point on the sinusoidal function, and draw a line going to the right, how long would it take for that line to reach a point on the function that is identical to the point at which it started. This can be found by taking the difference of the (x- coordinate) of the intersection point of the midline, and the (x-coordinate) of the point of minimum, and multiplying it by (4).
point of minimum: [tex](\frac{\pi}{4},9)[/tex]
midline intersection: [tex](0, -7)[/tex]
Period: [tex]4(\frac{\pi}{4}-0)=4(\frac{\pi}{4})=\pi[/tex]
However, in order to input this into the function in place of the variable (a), one has to divide this number by ([tex]2\pi[/tex]).
[tex]a=\frac{2\pi}{\pi}=2[/tex]
4. Assemble the function
One now has the following solutions to the variables:
[tex]n =-16\\a=2\\b=-7\\[/tex]
Substitute these values into the function:
[tex]y=-2(sin(2x))-7[/tex]
Niko wants to put soil in his garden shown below. If soil comes in bags that fill 6 square yards each, how many bags of soil should Niko buy? Hint: you may have some leftover soil.
Answer:
444 pot soils
Step-by-step explanation:
If the outliers are not included what is the mean of the data set 76,79,80,82,50,78,79,81,82
Answer:
The answer is 80
Step-by-step explanation:
we know that
the outlier is 50, as it is not around the other numbers in the data set.
therefore
mean=[76+ 79 + 80 + 82+ 78 + 83 + 79 + 81 + 82]/9
mean=[720]/9
mean=80
Answer:
80
Step-by-step explanation:
mean=[76+ 79 + 80 + 82+ 78 + 83 + 79 + 81 + 82]/9
mean=[720]/9
mean=80
How would I answer this: How many minutes are in a 30-day month.... use vertical multiplication to get the right answer
Answer:
There are 43200 minutes in a 30-day month.
Step-by-step explanation:
We know that:
60 minutes = 1 hour
24 hours = 1 day
Thus to determine the minutes in a 30-day month, let us first determine the number of hours in the month.
30
x 24
_______
120
60
_______
720 hours
The 30-day month has a total of 720 hours.
So that the number of minutes that make up 720 hours can be determined by;
720
x 60
_______
000
4320
_______
43200
Therefore, there are 43200 minutes in a 30-day month.
Instructions: Find the measure of the indicated angle to the nearest
degree.
26
?
32
? =
Answer:
36
Step-by-step explanation:
Since this is a right triangle we can use trig functions
cos theta = adj side / hyp
cos ? = 26/32
Taking the inverse cos of each side
cos^-1(cos ?) = cos^-1( 26/32)
? = 35.65908
To the nearest degree
? = 36
Find the percentage of the following:
20/60
18/60
21/60
31/60
Answer:
20/60 = 33%
18/60 = 30%
21/60 = 35%
31/60 = 52%
Step-by-step explanation:
Just divide em'
Simple as that.
Answer:
20/60 = 33%18/60 = 30%21/60 = 35%31/60 = 51.67%I hope th is helps you I just divided the fractions by the way :)
look at photo! please help needed! 1.
Answer:
5/12
Step-by-step explanation:
it says in the question that 1/4 +1/3 is used so in order to make it simple we have to find the common denominator that is 12. so converting 1/4 is 3/12 and 1/3 is 4/12.so u add the numerator and u get 7 over 12 .so now the whole container of peanuts is 12/12 but 7/12 is used so 12-7= 5. so ur ans is 5/12
What number cube has faces numbered 1 to 6.
Answer:
I don`t see the attachment
Step-by-step explanation:
Strat with k add 2 multiply by 6 then subtract 8
Answer:
6(k+2) -8
Step-by-step explanation:
Start with k
k
Add 2
(k+2)
Multiply by 6
6(k+2)
Then subtract 8
6(k+2) -8
6(k+2)-8 is a required answer.
Answer:
Solution given:
Start with k.
Kadd 2
k+2multiply by six
(k+2)*6subtract by 8
6(k+2)-8solve: 5y +12 - 3y + 12 = 18
Answer:
5y-3y+12+12=18
2y = 18 - 24
y = -6/2
y = -3
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{5y + 12 - 3y + 12 = 18}\\\\\large\text{COMBINE the LIKE TERMS}\\\\\large\textsf{(5y - 3y) + (12 + 12) = 18}\\\\\large\text{NEW EQUATION: \textsf{2y + 24 = 18}}\\\\\large\text{SUBTRACT 24 to BOTH SIDES}\\\\\large\textsf{2y + 24 - 24 = 18 + 24}\\\\\large\text{Cancel out: \textsf{24 - 24} because it gives you 0}\\\\\large\text{Keep: \textsf{18 - 24} because it helps solve it helps solve for y}\\\\\large\textsf{18 - 24 = \bf -6}[/tex]
[tex]\large\text{NEW EQUATION: \textsf{2y = -6}}\\\\\large\text{DIVIDE 2 to BOTH SIDES}\\\\\mathsf{\dfrac{2y}{2y}=\dfrac{-6}{2}}\\\\\large\text{Cancel out: }\mathsf{\dfrac{2}{2}}\large\text{ because it gives you 1}\\\\\large\text{KEEP: }\mathsf{\dfrac{-6}{2}}\large\text{ because it gives you the y-value}\\\\\large\textsf{y = }\mathsf{\dfrac{-6}{2}}\\\\\mathsf{\dfrac{-6}{2}= \bf -3}\\\\\\\\\\\boxed{\boxed{\huge\textsf{Answer: y = \bf -3}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}\\\\\\\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]
Please helppppp!!!!!!!!
Answer:
128 cm^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 (b1+b2) h
where b1 and b2 are the lengths of the bases and h is the height
A =1/2( 10+22) * 8
A = 1/2 (32)8
= 128
Answer:
A=128 cm²
Step-by-step explanation:
Hi there!
We are given a trapezoid and we want to find the area of it
The area of a trapezoid is given as [tex]\frac{a+b}{2}h[/tex], where a and b are the bases and h is the height
The bases are the parallel sides
They are the sides marked as 10 cm and 22 cm in this case
The height is the distance between the bases
In this case, it is the side marked as 8 cm
We know everything needed for the area, let's just label everything to avoid any confusion
a=10
b=22
h=8
Now substitute into the formula
A=[tex]\frac{a+b}{2}h[/tex]
A=[tex]\frac{10+22}{2}*8[/tex]
add the numbers on the numerator together
A=[tex]\frac{32}{2}*8[/tex]
Divide 32 by 2
A=16*8
multiply
A=128 cm²
Hope this helps!
Find the measure of arc BC?
Answer:
129
Step-by-step explanation:
Since,
AD = BC
AD = 3x + 24
BC = 4x - 11
3x + 24 = 4x - 11
4x - 11 = 3x + 24
4x - 3x = 24 + 11
x = 35
BC = 4x - 11
= 4 ( 35 ) - 11
= 140 - 11
BC = 129
Answer:
[tex]AB=BC[/tex]
[tex]3x+24=4x-11[/tex]
[tex]3x-4x=-11-24[/tex]
[tex]x=35[/tex]
[tex]BC=4\times 35-1[/tex]
[tex]=140-11[/tex]
[tex]=129[/tex]
--------------------------
Hope it helps..
Have a great day!!
WORD PROBLEM -
Sohanlal is a gardener He is paid 160 daily find how much money will he get in the month of September
GIVE ME UR ANSWERS SOON PLS
Help fast please in a test and don’t know the answer I have tried Googling and everything please help
Answer:
Surface Area = 3,543.7 cm²
Step-by-step explanation:
Surface area of the cylinder = 2πr(h + r)
Where,
radius (r) = 12 cm
height (h) = 35 cm
Plug in the values into the surface area formula
S.A = 2*π*12(35 + 12)
S.A = 24π(47)
S.A = 3,543.71651 cm²
≈ 3,543.7 cm² (approximated to the nearest tenth)
