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
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Chloe can read 75 words in 45 seconds. At this rate, how many words can she read in 15
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Answer:
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Step-by-step explanation:
Calculate the HCF of 8a³-27, 4a²-9 and 4a²-12a+9
Answers
[tex] \: \: \: \: \: [/tex]
first add
(3a²-5a+5)+(a³-5a²+8)
=3a²-5a+5+a³-5a²+8
=a³-2a3a²-5a²+5+8
=a³-2a²+13
and now,
substract a³-2a²+13 from a²-4a²-9
=7a²-4a²-9-(a³+13)
=7a²-4a²-9-a³+2a²-13
= a³+7a²-4a²+2a²-9-13
=-a³+5a²-22
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50% of what number is 60?
Answers
Answer:
50% of 60 is 30
Step-by-step explanation:
Please help me with my Geometry.
Answers
Step-by-step explanation:
2 similar triangles (the angles are the same, and the lengths of the corresponding sides have the same multiplication factor from one triangle to the other) :
1. support post (14ft), post to back (b), the long roof line
2. front to post (f), support post (14ft), dotted line
so, because the multiplication factor is the same for the sides, the ratio
"support post" / f
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b / "support post"
14 / f = b / 14
b = 14²/f = 196/f
and then we know that
f + b = 53
by putting the first into the second equation we get
f + 196/f = 53
f² + 196 = 53f
f² - 53f + 196 = 0
the solution of such a quadratic equation in general is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = f
a = 1
b = -53
c = 196
f = (53 ± sqrt(53² - 4×1×196))/(2×1) =
= (53 ± sqrt(2809 - 784))/2 = (53 ± sqrt(2025))/2 =
= (53 ± 45)/2
f1 = (53 + 45)/2 = 98/2 = 49
f2 = (53 - 45)/2 = 8/2 = 4
as the distance "front to post" is shorter than "back to post", f2 = 4 must be or solution.
therefore, the support post is positioned 4ft from the front of the house.
Roger ran eight laps around a ¼ mile track during PE on Monday.How many feet did Roger run in completing eight laps
Answers
Answer:
10560 feet
Step-by-step explanation:
you're welcome :)
6. Michelle got a new job through the McCartney Employment Agency. The job pays $49,400 per year, and the agency fee is equal to 35% of one month's pay. How much must Michelle pay the agency?
Answers
Answer:
$4, 116.66 times 35%=1,440.83 is the answer.
Step by step equation:
The agency fee is 35% of one months payment ($4,116.66) or ($1,440.83)
all you had to do is 49,400 divided by 12 months and you get $4,116.66 and then you times that by 35% and you get $1,440.83
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Answers
Answer:
54m^2
Step-by-step explanation:
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12 x 9 = 108
108/2 = 54
PLZ HELP, I need it done in like 20 mins. PLZZZ
Answers
Answer:
16.8
Step-by-step explanation:
Plug the equation (700+(-196))/((30+(3.5-(1/2))))+(-3)) into a calculator
PLEASE HELP URGENTLY!!
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Answers
Answer:
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answer in the photo thank me later mate
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[tex]\huge\bold\green{ANSWER}[/tex]
The inverse trig ratios, you can find the angle measure, given two sides.
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0.708 > 0.737
0.737 = 0.708
0.737 < 0.708
0.737 > 0.708
Answers
Answer:
0.737>0.708
Step-by-step explanation:
it must me d because 0.737 is greater than 0.708 and it's the only true Statement
How to solve math equation 45+5
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Answer:
50 is the answer
Step-by-step explanation:
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Answers
Answer:
y=7
Step-by-step explanation:
42/6=7
Answer:
y =7 iits divided
Step-by-step explanation:
y =6/42
y= 7
a) Complete the table of values for x + y = 6
Х
-2
-1
0
1
2
3
y
Answers
Answer:
8 , 7 , 6 , 5 , 4 , 3
Step-by-step explanation:
Insert your x into the equation, then simplify for y.
Jaz is going to the florist to buy foxgloves and orchids. The foxgloves can only be purchased in groups of 11 and the orchids can only be purchased in groups of 5. If Jaz wants to buy the same amount of foxgloves and orchids, then what is the lowest quantity of foxgloves that Jaz can buy?
Answers
Answer:
5
Step-by-step explanation:
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If Ambrea deposits $4000 in the bank and there is a 3% interest rate, how long will it take her to save $7000
Answers
Answer:
I believe the answer is 25 years
Step-by-step explanation:
3% of 4000 is 120
3000 divided by 120 is 25
Answer:
25 years
Step-by-step explanation:
So you have $4000, with a rate of 3% interest.
You want to see how long it takes to save up to $7000.
Do,
3% of $4000 is $120.
It takes a year to get a interest.
And you need $3000 dollars.
Now do 3000 ÷ 120.
You get 25.
1 point
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took. If she scored 14 goals, how many shots did she take? *
20 shots
98 shots
10 shots
200 shots
Answers
7/100 * x = 14
x = 200 shots
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&
4y+2x+9
Answers
A commercial airplane is flying at an elevation of 15,000 feet and ascends to an elevation of 20000 feet at a rate of 1250 feet per minute. How many minutes does this ascent take?
Answers
Answer:
4 minutes
Step-by-step explanation:
Put it into an equation
20000 = 1250x + 15000
Subtract 15000 from both sides
5000 = 1250x
Divide both sides by 1250
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Java 1
Question 15
Another word for "looping" is:
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b. iteration
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d. generalization
e. inheritance
Answers
Answer:
the anwser is b
Step-by-step explanation:
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Calvin works at a facility which processes apples. It costs the facility $0. 68 to make either a jar of applesauce or a bottle of apple juice. Due to the nature of the process and contractual agreements, Calvin’s facility must make and sell three jars of applesauce for every two bottles of apple juice. A jar of applesauce sells for $2. 20, and a bottle of apple juice sells for $3. 15. If the facility has annual overhead costs of $368,500, not including production costs, how many bottles of apple juice will the facility have sold when it breaks even every year? Round to the nearest whole bottle, if necessary. A. 38,789 b. 77,579 c. 116,368 d. 167,500.
Answers
The number of bottles the facility requires to sell when it breaks is given by
a system of two simultaneous equations.
When the facility breaks even, it would have sold 77,579 bottles of apples juice.Reasons:
The cost to make a jar of applesauce or a bottle of apple juice = $0.68
Number of jars of applesauce to be sold foe every 2 bottles of apple juice = 3 jars
The selling price for a jar of applesauce = $2.20
Selling price for a bottle of apple juice = $3.15
Annual overhead cost excluding production cost = $368,500
Required: Number of bottles of apple juice sold by the facility when it breaks even annually.
Solution:
Let J represent the number of bottles of apple juice sold, and let S represent the number of jars of apple sauce, by excluding the production cost, we have;
(3.15 - 0.68)·J + (2.2 - 0.68)·S = 368,500
S : J = 3 : 2
Which gives;
[tex]\displaystyle \frac{S}{J} = \mathbf{ \frac{3}{2}}[/tex]
[tex]\displaystyle S= \frac{3}{2} \cdot J[/tex]
Therefore;
[tex]\displaystyle (3.15 - 0.68) \cdot J + (2.2 - 0.68) \cdot S = (3.15 - 0.68) \cdot J + (2.2 - 0.68) \cdot \frac{3}{2} \cdot J = \mathbf{368,500}[/tex]
Which gives;
[tex]\displaystyle (3.15 - 0.68) \cdot J + (2.2 - 0.68) \cdot \frac{3}{2} \cdot J = \mathbf{ \frac{19 \cdot J }{4} } = 368,500[/tex]
[tex]\displaystyle J = \frac{368,500 \times 4}{19} = \frac{1474000}{19}=77578\frac{18}{19} \approx 77,579[/tex]
The number of bottles of apple juice sold, J ≈ 77,579 bottles
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Select all relations that represent function
Answers
Answer:
The last three are all functions.
The first one is not because by defenition of function, an x value cannot have two y values.
The second one is because a function f(x) is the same thing as y
The third one is because x value does not repeat, and that is all that matters.
The fourth one is a function too since x values do not have two y values
Please help!
5^3 x 5^-7
Answers
Answer: 0.0016
Step-by-step explanation:
5^3 = 125
5^-7 = 0.0000128
125 * 0.0000128 = 0.0016
Help help help help math math
Answers
Answer:
5
Step-by-step explanation:
Shanice won 88 pieces of gum playing the bean bag toss at the county fair. At school she gave four to every student in her math class. She only has 8 remaining. How many students are in her class?
Equation:
Answer:
Steps to solve:
Answers
80/4=20
Answer: there are 20 students in her class
Steps: Subtract what was remaining. Use the difference(80) and divide by how much she gave the students(4). After dividing the quotient would be 20 which is the amount of students in her class.
Answer:
20
Step-by-step explanation:
88 divided by 4 = 22, She gave 4 gums to each student, 8 divided by 4 = 2.
22 - 2 = 20
help with this graph please and thanks
Answers
what is equivalent to the following expression:
2(- a + 5) – 3 (a + 5b-2)+b (6-a)
Answers
From the information given, it can be inferred that the expansion of the equation will be 5a - 9b + 16 - ab.
= 2(- a + 5) – 3 (a + 5b-2)+b (6-a)
We've to expand the functions and this will be:
= -2a + 10 - 3a - 15b + 6 + 6b - ab
Collect like terms
= - 2a - 3a - 15b + 6b + 10 + 6 - ab
= -5a - 9b + 16 - ab
Therefore, the expression is equivalent to 5a - 9b + 16 - ab.
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A shop has a sale that offers 40% off all prices. On the final day, they reduce all sale prices by 30%. Alex buys a hairdryer on the final day.
Work out the overall percentage reduction on the price of the hairdryer.
Answers
Answer:
82%
Step-by-step explanation:
They are doing 0.6x with the first sale, then 70% of 0.6x for the second. So, the first sale would be 0.6x, and the second sale would be 0.42x. You subtract them to get 0.18x. So, 0.18x/x=18%. You would pay 18%, and the shop reduced 82%