First we find the slope of the line 2x−3y+8=0 by placing it into slope intercept form:
2x−3y+8=0
⇒−3y=−2x−8
⇒3y=2x+8
⇒y=
3
2
x+
3
8
Therefore, the slope of the line is m=
3
2
.
Now since the equation of the line with slope m passing through a point (x
1
,y
1
) is
y−y
1
=m(x−x
1
)
Here the point is (2,3) and slope is m=
3
2
, therefore, the equation of the line is:
y−3=
3
2
(x−2)
⇒3(y−3)=2(x−2)
⇒3y−9=2x−4
⇒2x−3y=−9+4
⇒2x−3y=−5
Hence, the equation of the line is 2x−3y=−5.
Answer:
y=2/3x-11/3
Step-by-step explanation:
Hi there!
We are given the equation 2x-3y=9 and we want to write an equation that is parallel to it and that passes through (4,-1)
Parallel lines have the same slopes
So we need to first find the slope of 2x-3y=9
We can do this by converting the equation of the line from standard form (ax+by=c where a, b, and c are integers) to slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)
To do this, we need to isolate y on one side
2x-3y=9
subtract 2x from both sides
-3y=-2x+9
divide both sides by -3
y=2/3x-3
as 2/3 is in the place where m is, 2/3 is the slope of the line
It's also the slope of the line parallel to it that passes through (4,-1).
Here's the equation of that line so far:
y=2/3x+b
now we need to find b
as the line will pass through the point (4,-1), we can 4 as x and -1 as y in order to solve for b
-1=2/3(4)+b
multiply
-1=8/3+b
subtract 8/3 to both sides
-11/3=b
Substitute -11/3 as b into the equation
y=2/3x-11/3
There's the equation
Hope this helps!
Please solve 3^(x+3) + 3^(x+4)/3 = 162
Can someone explain this to me please
Answer:
c. 36·x
Step-by-step explanation:
Part A
The details of the circle are;
The area of the circle, A = 12·π cm²
The diameter of the circle, d = [tex]\overline {AB}[/tex]
Given that [tex]\overline {AB}[/tex] is the diameter of the circle, we have;
The length of the arc AB = Half the the length of the circumference of the circle
Therefore, we have;
A = 12·π = π·d²/4 = π·[tex]\overline {AB}[/tex]²/4
Therefore;
12 = [tex]\overline {AB}[/tex]²/4
4 × 12 = [tex]\overline {AB}[/tex]²
[tex]\overline {AB}[/tex]² = 48
[tex]\overline {AB}[/tex] = √48 = 4·√3
[tex]\overline {AB}[/tex] = 4·√3
The circumference of the circle, C = π·d = π·[tex]\overline {AB}[/tex]
Arc AB = Half the the length of the circumference of the circle = C/2
Arc AB = C/2 = π·[tex]\overline {AB}[/tex]/2
[tex]\overline {AB}[/tex] = 4·√3
∴ C/2 = π·4·√3/2 = 2·√3·π
The length of arc AB = 2·√3·π cm
Part B
The given parameters are;
The length of [tex]\overline {OF}[/tex] = The length of [tex]\overline {FB}[/tex]
Angle D = angle B
The radius of the circle = 6·x
The measure of arc EF = 60°
The required information = The perimeter of triangle DOB
We have;
Given that the base angles of the triangles DOB are equal, we have that ΔDOB is an isosceles triangle, therefore;
The length of [tex]\overline {OD}[/tex] = The length of [tex]\overline {OB}[/tex]
The length of [tex]\overline {OB}[/tex] = [tex]\overline {OF}[/tex] + [tex]\overline {FB}[/tex] = [tex]\overline {OF}[/tex] + [tex]\overline {OF}[/tex] = 2 × [tex]\overline {OF}[/tex]
∴ The length of [tex]\overline {OD}[/tex] = 2 × [tex]\overline {OF}[/tex] = The length of [tex]\overline {OB}[/tex]
Given that arc EF = 60°, and the point 'O' is the center of the circle, we have;
∠EOF = The measure of arc EF = 60° = ∠DOB
Therefore, in ΔDOB, we have;
∠D + ∠B = 180° - ∠DOB = 180° - 60° = 120°
∵ ∠D = ∠B, we have;
∠D + ∠B = ∠D + ∠D = 2 × ∠D = 120°
∠D = ∠B = 120°/2 = 60°
All three interior angles of ΔDOB = 60°
∴ ΔDOB is an equilateral triangle and all sides of ΔDOB are equal
Therefore;
The length of [tex]\overline {OD}[/tex] = The length of [tex]\overline {OB}[/tex] = The length of [tex]\overline {DB}[/tex] = 2 × [tex]\overline {OF}[/tex]
The perimeter of ΔDOB = The length of [tex]\overline {OD}[/tex] + The length of [tex]\overline {OB}[/tex] + The length of [tex]\overline {DB}[/tex] = 2 × [tex]\overline {OF}[/tex] + 2 × [tex]\overline {OF}[/tex] + 2 × [tex]\overline {OF}[/tex] = 6 × [tex]\overline {OF}[/tex]
∴ The perimeter of ΔDOB = 6 × [tex]\overline {OF}[/tex]
The radius of the circle = [tex]\overline {OF}[/tex] = 6·x
∴ The perimeter of ΔDOB = 6 × 6·x = 36·x
Mary has a rectangular driveway. She measures it and finds out it is 14 1/4 feet long by 17 1/2 feet wide. She wants to know how many square feet of paint she will need to completely cover the driveway.
Answer:
253.75 square feet
What is the common ratio between successive terms in the sequence?
27, 9, 3, 1,
,
1,
3
O-3
mp
Answer:
1/3
Step-by-step explanation:
If it was supposed to be a negative answer, there would be negative numbers in the sequence. So that narrows it do to 3 and 1/3. And now we know that 27*3 isn't 9 but 27*1/3=9 and so on.
Answer:
your answer will have to be 3
Step-by-step explanation:
from 27 to 9, we divided by 3
from 9 to 3, we divided by 3
from 1 to 1/3, we divided by 3
from 1/3 to 1/9, we divided by 3
from 1/9 to 1/27, we divided by 3
so basically the common ratio will have to be 3
Can someone help me please
Answer:
yes what would u like help with
Here is some information about a holiday.
7 night holiday
$340 per person
8% discount if you book before 31 March
On 15 February, Naseem books this holiday for 2 people.
Calculate the total cost of his holiday.
Answer:
$625.6
Step-by-step explanation:
Information about the holiday:
7 night holiday
$340 per person
8% discount if you book before 31 March
Number of people Naseem booked the holiday for = 2
Date of booking of the holiday = 15 February
Total cost of the holiday per person = cost per person - discount before March 31
= $340 - 8% of $340
= 340 - 8/100 * 340
= 340 - 0.08 * 340
= 340 - 27.2
= $312.8
Total cost of the holiday for 2 persons = 2 × Total cost of the holiday per person
= 2 * $312.8
= $625.6
Jada walks dogs to earn money. The points in this graph represent the total amount of money Jada earns based on the number of hours she walks dogs. Jada wants to purchase a new jacket that costs $32.
How many hours does Jada need to walk dogs to earn enough money to buy the jacket?
6 hours
7 hours
8 hours
9 hours
Answer:
8 hours
Step-by-step explanation:
In 4 hours she earns 16 dollars
Since this is proportional ( goes through zero), we can multiply by 2
8 hours = 32 dollars
Jada needs to walk the dog for, 8 hours.
4x8 = 32
3/4 part of a rope is 150m. find the length of 7/10 part of the rope
Please help ASAP with step by step explanation.
Answer:
140m
Step-by-step explanation:
3/4 = .75
x/.7 = 150/.75
multiply both sides by .7
x = 150/.75 * .7
x = 140m
The graph shown is a scatter plot:
Which point on the scatter plot is an outlier?
Answer:
D is the outlier
Step-by-step explanation:
An outlier is a point that is far from the other points
We can draw a line that roughly represents an equation for the points
A,B ,C are all near the line
D is not along the line
Carl is filling flowerpots with soil. Each flowerpot is a cylinder with a radius of 7cm and a height of 10 cm. If Carl has 24,000 cubic centimeters of soil, how many flowerpots can he fill?
Answer:
16 pots
Step-by-step explanation:
We first need to find out the amount of dirt that can be filled into a single flowerpot.
We use the formula to find the cylinder's volume.
π[tex]r^{2}[/tex][tex]* h[/tex]
Height is equal to ten, Radius is equal to 7.
49π [tex]* 10[/tex]
≈ 1539.38
25,000 divided by 1539.38
≈ 16.24
He can fill 16 pots fully.
how would 3 over 5
be Classified
Answer:
3/5 is expressed as 60% in terms of Percentage.
Let's convert the fraction 3/5 into percent. Now, 60/100 is expressed as 65% in terms of percentage.
f(x)=3(0.75)x exponential growth or exponential decay
QUICK I NEED HELP! I WILL MARK BRAINLIEST!
Answer:
go a head what can i help you with
Answer:
Step-by-step explanation:
[tex]y_A = 9x -3x - 4 \\y_A = 6x - 4\\\\y_B = 12x - 4\\\\y_C = 5x + x - 4\\y_C = 6x -4[/tex]
Standard equation of a line with slope, m and y - intercept b is y = mx + b.
Clearly. for the second equation has a different coefficient for x.
a ) The coefficient for x , is the slope of the line.
Though the y - intercept for each equation is same = - 4.
For example :
Expression A = 2 , when x = 1
Expression B = 8 , when x = 1
Expression C = 2 , when x = 1
b) From above :
[tex]y_A \ and \ y_C \ are \ the \ same \ expression.[/tex]
c) Expression A and C are equivalent because the coefficient of x
is the same for A and C.
The function f is defined by f(x) = (x − 2) 2 − 3 for x > −2. The function g is defined by g(x) = 2x+6 x−2 for x > 2. Find fg(7).
Answer:
[tex]fg(7)=143.95[/tex]
Step-by-step explanation:
We are given that
[tex]f(x) = (x -2)^2 -3[/tex] for x > −2
[tex]g(x) = 2x+6x^{-2}[/tex] for x > 2
We have to find fg(7)
[tex]fg(7)=f(g(7))[/tex]
[tex]=f(2(7)+6(7)^{-2})[/tex]
=[tex]f(14+\frac{6}{49})[/tex]
=[tex]f(\frac{692}{49})[/tex]
692/49>-2
fg(7)=[tex](\frac{692}{49}-2)^2-3[/tex]
=[tex]146.95-3[/tex]
Hence, [tex]fg(7)=143.95[/tex]
Question 54 of 98
Which expression uses the associative property to make it easier to evaluate
20(3-6)
O A. 20(6)
B. 20(-5)
c. - 6)20
D. (20 - )6
SUBMIT
submitdjememendixodme ejej
Find the width of the rectangular prism which has Surface area of 10 CM2, length of 2cm and height of 1 cm
Answer:
width is 1 cm
Step-by-step explanation:
The SA of a rectangular prism is SA = 2(lw + wh + hl)
We are given the length, the height, and the SA, and we need to find the width. So we plug in the known values into this equation:
10 = 2(2w + w + 1*2)
10 = 2(3w+2)
10 = 6w+4
6=6w
w=1
We can check the answer by plugging in all the values into the equation:
10 = 2(2*1+1*1+1*2)
10 = 2(5)
10 = 10
can someone please help for brainlest
Answer:125√3:6
Step-by-step explanation:
7- write the equation of the line that passes through points A(6,1) and B(9,4)
I
Answer:y=x-5
Step-by-step explanation: Use (y2-y1)/(x2-x1) fill those in and get (4-1)/(9-6) which is 3/3 and that is 1 for the slope. Now fill in y=1x with a given coordinate and try to find the y-intercept so we would do 1=1(6) and we need to make the right side equal to the left so we subtract 5. Ending us with y=x-5.
HELP ME!
Line segment EQ consists of the points ____________. ???
Answer:
{F, G, H, I, J, K, L, M, N, O, P}
are the points between segment EQ :)
Please help me out for the question is it
A.275 centimeters
B.94 centimeters
C.144 centimeters
D.85 centimeters
You’ll be marked as brainliest
I think c because from what remember taking this test
plzz help 100 points
Part B
What is the measurement of angle G? Part C
Let the variable c represent the measurement of angle C. Use the measurement of angle G to write an equation that you can use to solve for c. Part D
What is the measurement of angle C?
Finishing the angles of the smaller triangle if E is 90 and F is 30 then G needs to be 180-90-30 = 60 degrees.
Angles G and C are supplementary angles which need to equal 180 degrees
Angle c = 180-g = 180-60 = 120
Angle c = 120 degrees.
Answer:
see explanation
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180° , then Δ EGF
∠ G = 180° - (90 + 30)° = 180° - 120° = 60°
------------------------------------------------------------
c and g are adjacent angles and sum to 180° , then
c + g = 180° , that is
c + 60° = 180° ( subtract 60° from both sides )
c = 120
That is ∠ C = 120°
Find the quotient.the fraction
8 1/3 divided by 4 1/2
Answer:
[tex]8 \frac{1}{3} \div 4 \frac{1}{2} = \frac{50}{27} = 1.851 = 1 \frac{23}{27} [/tex]
If f (x) = 2 x + 5 and three-halves are inverse functions of each other and f (x) = 2x + 5, what is
Answer:
See explanation
Step-by-step explanation:
The question has conflicting details
[tex]f(x) = 2x + 5[/tex]
[tex]f(x) = 2x + 5[/tex] and three halves doesn't sound correct.
So, I will take f(x) as
[tex]f(x) = 2x + 5[/tex]
Next, solve for the inverse function
Replace f(x) with y
[tex]y = 2x + 5[/tex]
Swap x and y
[tex]x = 2y + 5[/tex]
Make 2y the subject
[tex]2y = x-5[/tex]
Make y the subject
[tex]y = \frac{x-5}{2}[/tex]
Replace y with the inverse sign
[tex]f^{-1}(x) = \frac{x-5}{2}[/tex]
So, now we can calculate any value from the original function and from the inverse function.
For instance:
[tex]f^{-1}(7) = \frac{7-5}{2} = \frac{2}{2} = 1[/tex]
[tex]f(1) = 2*1 + 5 = 2+5=7[/tex]
Put these numbers in order from least to greatest.
0.92,0.43, and 9/10
Answer:
0.43,9/10,0.92
Step-by-step explanation:
Answer:
0.43, 9/10, 0.92
Step-by-step explanation:
9/10=0.9=0.90
Find angle N and arc NQ. See the image below.
Answer:
Angle N=32
Arc NQ=106
Step-by-step explanation:
Angle N is a inscribed angle of Arc MP so that means Angle N measures 32.
Angle NPQ is a inscribed angle of Arc NQ so that means Arc NQ is twice the measures of NPQ so
Arc NQ=106
What is the vertex of the graph of the function below? y= x2 - 4x + 3
A. (2.-1)
B. (1,-1)
C. (1,0)
D. (2,0)
Please help. Thank you
Given:
[tex]PQRS\sim TUVW[/tex]
In the given figure, PS=x, RS=35, UV=20, VW=25 and TW=15
To find:
The scale factor from PQRS to TUVW.
Solution:
We have,
[tex]PQRS\sim TUVW[/tex]
We know that the corresponding sides of similar figures are proportional. The scale factor is the ratio of one side of image and corresponding side of preimage.
The scale factor is:
[tex]k=\dfrac{VW}{RS}[/tex]
[tex]k=\dfrac{25}{35}[/tex]
[tex]k=\dfrac{5}{7}[/tex]
Therefore, the scale factor from PQRS to TUVW is [tex]k=\dfrac{5}{7}[/tex].
Pls help me and thank you!
Answer:
Substitute your answer for Step 1 into the second equation to solve for Z.
Find the percentage decrease ???
Step-by-step explanation:
Price of a book costing sh.250
reduced to sh.200
percentage decrease on the price = (250-200)/250×100
= 20%
pls answer the underline questions
Answer:
What is the question?
Step-by-step explanation:
I will edit this and answer when you comment the question in this answer.