Line c passes through points (9, 10) and (1, 3). Line d is perpendicular to c. What is the slope
of line d?
Answers
Answer:
-8/7
Step-by-step explanation:
First, find the slope of line c.
(x1, y1) = (9, 10)
(x2, y2) = (1, 3)
The slope formula is:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Solve for the slope using the given values:
[tex]m=\frac{3-10}{1-9}\\\\m=\frac{-7}{-8}\\\\m=\frac{7}{8}[/tex]
The slope of line c is 7/8. To find the slope perpendicular to it, you need to find the negative reciprocal of that number. An example of that would be 2 and -1/2. Basically, flip the fraction and the +/-.
In this case, the negative reciprocal of 7/8 is -8/7. The image below doesn't account for the y-intercept, but it does show that the slopes are perpendicular.
Answer:
slope = - [tex]\frac{8}{7}[/tex]
Step-by-step explanation:
Calculate the slope m of line c using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (9, 10 ) and (x₂, y₂ ) = (1, 3 )
m = [tex]\frac{3-10}{1-9}[/tex] = [tex]\frac{-7}{-8}[/tex] = [tex]\frac{7}{8}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{7}{8} }[/tex] = - [tex]\frac{8}{7}[/tex] ← slope of line d
Related Questions
In an input/output table, all outputs are 0, regardless of the input. What could the function equation be? Select all that apply.
y = 0 x
y = x
y = x/0
y = 0/x
Answers
Answers:
choice A) y = 0x
choice D) y = 0/x
========================================================
Explanation:
Choice A is the same as y = 0 because 0x turns into 0. Multiplying 0 with any number always leads to 0.
Similarly, choice D is the same as y = 0 as well. Dividing 0 over any nonzero value leads to 0. Note the key term "nonzero" here. We cannot have 0 in the denominator. So x = 0 is not allowed for choice D.
So for any nonzero x, we have 0x and 0/x result in the same thing.
-----------
Extra info:
Choice B can be ruled out because something like x = 2 leads to y = 2.
Choice C is ruled out because we can never have 0 in the denominator.
1. Paulina wants to find the width, AB, of a river. She walks along the edge of the river 200 ft and marks point C. Then she walks 60 ft further and marks point D. She turns 90° and walks until her location, point A, and point C are collinear. She marks point E at this location, as shown. (a) Can Paulina conclude that ΔABC and ΔEDC are similar? Why or why not? (b) Suppose DE = 40 ft. Calculate the width of the river, AB. Show all your work and round answer to the nearest tenth. Answer
Answers
Answer:
Step-by-step explanation:
a). In ΔABC and ΔEDC,
Since, AB and DE are parallel and AE is a transversal,
Therefore, ∠CAB ≅ ∠CED [Alternate interior angles]
m∠D = m∠B = 90°
ΔABC ~ ΔEDC [By AA property of similarity of two triangles]
b). Therefore, by the property of similar triangles,
"Corresponding sides of two similar triangles are proportional"
[tex]\frac{DC}{BC}= \frac{DE}{AB}[/tex]
[tex]\frac{60}{200}=\frac{40}{AB}[/tex]
AB = [tex]\frac{40\times 200}{60}[/tex]
= 133.33
≈ 133.3 ft
Please help!![tex]2^x=\sqrt{2}[/tex]
Answers
The root can be change to 1/2
how many cups are in one liter?
Which conversions show a path to the solution? Check all that apply.
A. cups -> liters -> quarts
B. liters -> quarts -> cups
C. cups -> gallons -> liters
D. liters -> gallons -> cups
Answers
Answer:
b,d
Step-by-step explanation:
Thank you so much thank y’all
Answers
x < 12
Step-by-step explanation:
150 - 20 = 130
x < 130 / 10 - 1
x < 13 - 1
x < 12
what is the perimeter
A) 20.3
B)18.3
C)24.3
D)22.3
Answers
Answer:
b
Step-by-step explanation:
cuz u add them all
Complete the steps to solve the equation. 9 – 4x = 2x 1. Addition property of equality: 9 = 6x 2. Division property of equality: = x
Answers
Answer:
x = 3/2
Step-by-step explanation:
Given:
9 - 4x = 2x
Step 1: Addition property of equality
9 - 4x + 4x = 2x + 4x
9 = 6x
Step 2: Division property of equality:
9 = 6x
9/6 = 6x/6
9/6 = x
x = 9/6
= 3/2
x = 3/2
Check:
9 - 4x = 2x
9 - 4(3/2) = 2(3/2)
9 - 12/2 = 6/2
9 - 6 = 3
3 = 3
(4y¹²) (3y)
Please help me
Answers
Answer with explanation
Answers
Answer: a and d
Step-by-step explanation:
(to find all points of discontinuity, set denominator equal to zero and solve)
[tex]x^2-7x+10=0\\\\[/tex]
(to factor, find two numbers when added together equal -7 and when multiplied together equal 10)
-2 + -5 = -7
-2(-5) = 10
-2 and -5 are the two numbers
[tex](x-2)(x-5)=0\\\\x-2=0\\x=2\\\\x-5=0\\x=5\\\\x=2,5[/tex]
SOMEBODY HELP ME GET IT RIGHT IM ALREADY FAILING :( pls its Pythagorean theorem
Answers
Answer:
a = 8.7
Step-by-step explanation:
The Pythagorean theorem is
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
a^2+5^2 = 10^2
a^2 +25 = 100
a^2 = 100-25
a^2 = 75
Taking the square root of each side
sqrt(a^2) =sqrt(75)
a =8.660254038
Rounding to the nearest tenth
a = 8.7
8.7
Step-by-step explanation:
a^2 + b^2 = c^2
a^2 + 5^2 = 10^2
a^2 + 25 = 100
100 - 25 = a^2
a^2 = 75
sqrt rt 75 = 8.7
A man walks at the rate of 88 paces to the minute if the average length of his paces is 0.875m, find the time take to walk 2.31km.
Answers
Answer:
30 minutes
Step-by-step explanation:
Walk rate = 88 paces/ minute
Average length of pace = 0.875 m
Time taken to walk 2.31 km ;
The distance in metres :
1000 m = 1 km
2.31 km = (1000 * 2.31) = 2310 m
Recall :
Time taken = distance / speed
Distance walked in a minute = 88 * 0.875 = 77 m
Time taken = 2310 / 77
Time taken = 30 minutes
Five years from now peters age will be 2+3 times his current age Identify the equation represent the situation
Answers
Answer:
1.5 yrs
Step-by-step explanation:
let the present age=x
x+5=2+3x
3x-x=5-2
2x=3
x=3/2=1.5 years
Answer:
3x + 2 = x + 5.
Step-by-step explanation:
Peter is currently x years old. In 5 years, his age will be x + 5. According to the prompt, Peter's age will be 2 + 3 times his current age, x, which can be represented as 2 + 3x. 2 + 3x is the same age as x + 5, so we can represent it as...
2 + 3x = x + 5
3x - x = 5 - 2
2x = 3
x = 1.5
This means that Peter is 1.5 years old.
Hope this helps!
enter the following in the cash book applying cgst and sgst at 6% each for all transactions relating to the sales and purchase of the products
pls pls pls pls pls help me
Answers
Answer:
10,000
Step-by-step explanation:
cuhcuhcuhcuhcuhcuhc
evaluate without multiplying directly 998³ x 103³
Answer correctly I will mark them as brainlist
Answers
Answer:
1,086,183,741,982,184
Step-by-step explanation:
998^3
= (1,000)^3 - (2)^3 - 3 · 1,000 · 2 (1000 - 2)
= 1,000,000,000 - 8 - 6,000 (998)
= 999,999,992 - 5,988,000
= 994,011,992
103^3
= (100 + 3)^3
= (100)^3 + (3)^3 + 3(100) (3) + (100+3)
= 1,000,000 + 27 + 900(103)
= 1,000,027 + 92,700
= 1,092,727
994,011,992 · 1,092,727
= 994,011,992 · (1,000,000 + 90,000 + 2,000 + 700 + 20 + 7)
= (994,011,992 · 1,000,000) + (994,011,992 · 90,000) + (994,011,992 · 2,000) + (994,011,992 · 700) + (994,011,992 · 20) + (994,011,992 · 7)
= 994,011,992,000,000 + 89,461,079,280,000 + 1,988,023,984,000 + 695,808,394,400 + 19,880,239,840 + 6,958,083,944
= 1,086,183,741,982,184
What’s the sum in the diagram, a + b + c =
Answers
Answer:
Answer is 360 degrees
Step-by-step explanation:
The sum of the exterior angles of a triangle is 360°.
Answer: 360 degrees
Step-by-step explanation:
You know that in a triangle is 180 degrees. In the diagram, the figure shows a, b, and c, outside of the triangle. Also, the a, b, and c makes a circle. The circle is 360 degrees, so when you add a, b, and c that will equal 360.
if 2x +y=-7 and 3x=6+4y are simultaneous equation, what is the value of x-y
Answers
Step by step solution please
Answers
Answer:
I solved the question step by step in the pic, and I hope it helps
Given that 3=a+r/a-r,make r the subject of the formula?
Answers
i- dont know...sorry
A brick is in the shape of a rectangular prism with a length of 6 inches, a width of 3 inches, and a height of 5.5 inches. The brick has a density of 2.7 grams per cubic centimeter. Find the mass of the brick to the nearest gram.
pls pls pls help
Answers
y............. xnxnxnxnxnccncncncnnncncjcjnf
can you help me with this please.
Answers
Answer:
98 is the answer
Step-by-step explanation:
you add 8 each time
Answer:
a₁₃ = 98
Step-by-step explanation:
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 2 and d = a₂ - a₁ = 10 - 2 = 8 , then
a₁₃ = 2 + (12 × 8) = 2 + 96 = 98
Question 3 of 10
Which of the following is(are) the solution(s) to |15x+2| = 8?
Answers
Answer:
x = 6/5 x = -2
Step-by-step explanation:
|5x+2| = 8
There are 2 solutions
5x+2 = 8 and 5x+2 = -8
Subtract 2 from each side
5x+2 -2 = 8-2 and 5x+2-2 = -8-2
5x= 6 5x = -10
Divide by 5
5x/5 = 6/5 5x/5 = -10/5
x = 6/5 x = -2
Answer:
b
Step-by-step explanation:
|5x+2|=8
1) |5×(-2)+2|=8
|-10+2|=8
|-8|=8
8=8
2) |5×6/5+2|=8
|6+2|=8
|8|=8
8=8
The amount of money Aria has in the bank after T years is determined by the equation A = 1,000 · 1.0512^T. After how many years will Aria have $2,000 in the bank?
(1) 12.9 (2) 13.9
(3) 14.9
(4) 15.9
Answers
Answer:
Step-by-step explanation:
You are given most of the equation that you need to solve. To find the number of years it will take to have 2000, sub in 2000 for A and solve:
[tex]2000=1000(1.0512)^t[/tex] and begin by dividing away the 1000 on both sides to get
[tex]2=(1.0512)^t[/tex] now we have to take the natural log of both sides:
[tex]ln(2)=ln(1.0512)^t[/tex]. Taking the natural log allows us to bring the t down out front:
ln(2) = t ln(1.0512) and now divide both sides by ln(1.0512):
[tex]\frac{ln(2)}{ln(1.0512)}=t[/tex] and do this on your calculator to get
t = 13.9 years
Answer:
T = 13.9
Step-by-step explanation:
A = 1,000 · 1.0512^T
Let A = 2000
2000 = 1,000 · 1.0512^T
Divide each side by 1000
2000/1000 = 1,000/1000 · 1.0512^T
2 = 1.0512^T
Take the log of each side
log 2 = log 1.0512^T
We know log a^b = b log a
log 2 = T log 1.0512
Divide each side by log 1.0512
log 2 / log 1.0512 = T
T=13.88172
Rounding to the nearest tenth
T = 13.9
PLZZZ HELPPP, IF NOT 100% SURE PLZ DONT ANSWER…BRAINLIEST TO FIRST AND CORRECT ANSWER, THX TO SECOND AND CORRECT ANSWER
Answers
=============================================================
Explanation:
1/2 = 4/8 after multiplying top and bottom by 8
So the mixed number 7 1/2 is the same as 7 4/8
We can convert to an improper fraction like so
7 4/8
7 + 4/8
7*(8/8) + 4/8
56/8 + 4/8
(56+4)/8
60/8
Notice how dividing 60 over 8 leads to 7 remainder 4. Think of it like having 60 cookies and you want to share them amongst 8 friends. Each friend gets 7 whole cookies (7*8 = 56 taken so far) and then we have 60-56 = 4 left over as the remainder.
Through similar steps, you should find that the mixed number 1 7/8 converts to the improper fraction 15/8.
-----------------------------
To rephrase the problem with improper fractions would be to say:
"The electrician needs to buy 60/8 feet of wire. There are 15/8 feet of wire in each spool. How many spools should the electrician buy?"
Let x be the answer to that question.
We multiply the number of spools (x) by the amount of feet of wire per spool (15/8) to get the expression (15/8)x
Set this equal to the target 60/8 and solve for x
(15/8)x = 60/8
15x = 60 .... multiply both sides by 8 to clear out the fractions
x = 60/15
x = 4
The electrician needs to buy exactly 4 spools
-----------------------------
A different approach could have us convert each mixed number into decimal form
7 1/2 = 7 + 1/2 = 7 + 0.5 = 7.5
1 7/8 = 1 + 7/8 = 1 + 0.875 = 1.875
So the electrician needs to buy 7.5 ft total and each spool has 1.875 ft of wire.
Using the same idea as before, we would then have,
1.875x = 7.5
x = (7.5)/(1.875)
x = 4
Answer the question
Answers
Answer:
1,041,958.5, or 104,195 1/2
Step-by-step explanation:
All you have to do is 15787.25 times 66, because 15787.25 is the price for on acre, so 66 acres will be 15787.25 times 66. If you want to put it in fraction form, you can do 15787 1/4 times 66. I hoped you liked this answer!
please answer fast urgently
Answers
Answer:
{1,2,3,4,5,6}
.
.
.
.
1/3
correct answer
Answer:
1,2,3,4,5,6
1/3
the correct ans
Which figures are polygons?
Answers
Answer: A,C,D
Step-by-step explanation:
Answer:
pretty sure it's a, c, and d
Step-by-step explanation:
polygons have straight sides, not curved. it's a 2d figure, and it is enclosed. b doesn't fit the criteria of that because of the fact that the shape is a bit curved, as the other options do fit that criteria.
Proof that :
[tex] {sin}^{2} \theta + {cos}^{2} \:\theta= 1[/tex]
Thx.
Answers
Answer:
Solution given:
Right angled triangle ABC is drawn where <C=[tex]\theta[/tex]
we know that
[tex]\displaystyle Sin\theta=\frac{opposite}{hypotenuse} =\frac{AB}{AC}[/tex]
[tex]\displaystyle Cos\theta=\frac{adjacent}{hypotenuse}=\frac{BC}{AC} [/tex]
Now
left hand side
[tex] \displaystyle {sin}^{2} \theta + {cos}^{2} \:\theta[/tex]
Substituting value
[tex](\frac{AB}{AC})²+(\frac{BC}{AC})²[/tex]
distributing power
[tex]\frac{AB²}{AC²}+\frac{BC²}{AC²}[/tex]
Taking L.C.M
[tex]\displaystyle \frac{AB²+BC²}{AC²}[/tex]....[I]
In ∆ABC By using Pythagoras law we get
[tex]\boxed{\green{\bold{Opposite²+adjacent²=hypotenuse²}}}[/tex]
AB²+BC²=AC²
Substituting value of AB²+BC² in equation [I]
we get
[tex]\displaystyle \frac{AC²}{AC²}[/tex]
=1
Right hand side
provedplease answer this!!!
Answers
Answer:
A
Step-by-step explanation:
As the angles are equal, AB=BC, 16x-7=12x+1, 4x=8, x=2.
Find the accumulated value of an investment of $10,000 for 7 years at an interest rate of 5.5% if the money is a. Compounded semiannually;b. Compounded quarterly; c. Compounded monthly; d. Compounded continuously
Answers
Answer:
Results are below.
Step-by-step explanation:
Giving the following information:
Annual interest rate (i)= 0.055
Initial investment (PV)= $10,000
Number of years (n)= 7
To calculate the future value (FV), we need to use the following formula (except in d):
FV= PV*(1+i)^n
a.
Semiannual interest rate= 0.055/2= 0.0275
Number of semesters= 7*2= 14
FV= 10,000*(1.0275^14)
FV= $14,619.94
b.
Quarterly rate= 0.055/4= 0.01375
Number of quarters= 7*4= 28
FV= 10,000*(1.01375^28)
FV= $14,657.65
c.
Monthly interest rate= 0.055/12= 0.0045833
Number of months= 7*12= 84
FV= 10,000*(1.0045833^84)
FV= $14,683.18
d.
To calculate the future value using continuous compounding, we need to use the following formula:
FV= PV*e^(n*i)
FV= 10,000*e^(7*0.055)
FV= $14,696.14
8. Colleen times her morning commute such that there is an equal likelihood that she will arrive early or late to work on any given day. If she always arrives either early or late, what is the probability that Colleen will arrive late to work no more than twice during a five-day workweek
Answers
Solution :
Case I :
If Collen is late on [tex]0[/tex] out of [tex]5[/tex] days.
[tex]$= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} $[/tex]
[tex]$=\frac{1}{32}[/tex]
Case II :
When Collen is late on [tex]1[/tex] out of [tex]5[/tex] days.
[tex]$= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times ^5C_1$[/tex]
[tex]$=\frac{1}{32} \times 5$[/tex]
[tex]$=\frac{5}{32}[/tex]
Case III :
When Collen was late on [tex]2[/tex] out of [tex]5[/tex] days.
[tex]$= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times ^5C_2$[/tex]
[tex]$=\frac{1}{32} \times 10$[/tex]
[tex]$=\frac{5}{16}[/tex]
Therefore, the [tex]\text{probability}[/tex] that Collen will arrive late to work no more than [tex]\text{twice}[/tex] during a [tex]\text{five day workweek}[/tex] is :
[tex]$=\frac{1}{32} + \frac{5}{32} + \frac{5}{16} $[/tex]
[tex]$=\frac{1}{2}$[/tex]
