Answers
The pairs of points that on the linear equations are:
a) (1, 7) and (0, 10).
b) (1, 7/3) and (0, 2)
How to find the pair of coordinates on the lines?First, we need to find the slope of the equation of the line that passes through the points (-2, 6) and (1, -3).
Remember that if a line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
Here we know that the line passes through the points (-2, 6) and (1, -3), then the slope is:
a = (-3 - 6)/(1 + 2) = -9/3 = -3
a) A parallel equation will have the same slope, so it will be of the form:
y = -3*x + b
To find the value of b w euse the fact that this line should pass through the point (2, 4), so:
4 = -3*2 + b
4 = -6 + b
4 + 6 = b = 10
The linear equation is:
y = -3*x + 10
To find two points we can evaluate in x = 1 and x = 0, we will get:
y = -3*1 + 10 = 7
y = -3*0 + 10 = 10
So we have the pair of points (1, 7) and (0, 10).
b) A perpendicular equation will have a slope equal to the inverse of the opposite, so we will have a line like:
y = (1/3)*x + c
To find the value of c we use the fact that this line passes through (3, 3), them:
3 = (1/3)*3 + c
3 = 1 + c
3 - 1 = c
2 = c
This line is:
y = (1/3)*x + 2
Again we evaluate in 0 and 1 to get the two points:
y = (1/3)*1 + 2 = 1/3 + 6/3 = 7/3
y = (1/3)*0 + 2 = 2
So we have the pair of points (1, 7/3) and (0, 2)
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Related Questions
Find the midpoint of the segment with the following endpoints. (10, 10) and (2, 6)
Answers
Answer:
(6, 8 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = (10, 10 ) and (x₂, y₂ ) = (2, 6 ) , then
midpoint = ( [tex]\frac{10+2}{2}[/tex] , [tex]\frac{10+6}{2}[/tex] ) = ( [tex]\frac{12}{2}[/tex] , [tex]\frac{16}{2}[/tex] ) = (6, 8 )
The manager of a toy store bought 10 toy cars. The cars came in p packages. Write an expression that shows how many toy cars were in each package.
Answers
we can write x = 10/p to represent the number of toy cars x, in each package.
What is an Expression?Expression: An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.) Expressions can be thought of as similar to phrases. In language, a phrase on its own may include an action, but it doesn't make a complete sentence
The management purchased n cars, which equals 10.
There were p packages altogether, and each box contained one car. Per bundle, there should be x cars
Since there are x cars in each box, p packages would contain x*p cars
The equation can be written as 10 = x*p because we know there were p packages with 10 cars in them.
The multiplication of x and p is indicated by an asterisk (*).
You can write x = 10/p to represent the number of cars x, in each package.
The division symbol is denoted by a slash (/).
Because the number of cars and parcels can only be whole numbers, the values of x and p must also be whole numbers. Since the result of x and p is 10, both x and p must be factors of 10.
The factors of 10 are: 1,2,5 and 10
So, we get the following scenarios:
1 package with 10 cars inside it
2 packages each with 5 cars
5 packages each with 2 cars
10 packages each with 1 car
If the number of cars/packages must be greater than 1, then we have the following two cases:
2 packages each with 5 cars
5 packages each with 2 cars
we can write x = 10/p to represent the number of toy cars x, in each package.
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A 5 foot tall person standing near a tree casts a shadow 8 feet long. At the same time, the tree casts a shadow that is 24 feet long. The triangles shown in the diagram are similar.
What is the value of x, the height of the tree?
30 ft.
12 ft.
15 ft.
2.5 ft.
Answers
The height of the tree is 15 feet. Option C
What is proportion?Proportion can simply be defined as an arithmetic comparison between two quantities, numbers or elements.
It is also described as an equation where two given ratios are made equal or equivalent to each other.
From the information given, we have that;
5 foot tall person casts a shadow 8 feet longThe tree casts a shadow that is 24 feet long.To determine the height of the tree 'x', we have;
If 5 feet = 8 feet long shadow
Then x feet = 24 feet long
cross multiply
8 × x = 24 × 5
Multiply through
8x = 120
Divide both sides by 8, we have;
x = 120/8
x = 15 feet
Hence, the height is 15 feet
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i need help answering this question
Answers
The ordered pairs that are on the graph of the equation 4y - 6x = 12 include the following:
A. (-4, −3)
C. (0, -2)
What is an ordered pair?An ordered pair can be defined as a pair of two elements that are typically written in a fixed order within parentheses as (x, y), which represents the x-axis (abscissa) and the y-axis (ordinate) on a coordinate plane of a graph.
Next, we would test the ordered pairs to determine which are on the graph of the given equation as follows;
For ordered pair (-4, −3), we have:
4y - 6x = 12
4(-3) - 6(-4) = 12
-12 + 24 = 12
12 = 12 (True).
For ordered pair (-1, 1.5), we have:
4y - 6x = 12
4(-1) - 6(1.5) = 12
-4 - 9 = 12
-13 = 12 (False).
For ordered pair (0, -2), we have:
4y - 6x = 12
4(0) - 6(-2) = 12
0 + 12 = 12
12 = 12 (True).
For ordered pair (3, -4), we have:
4y - 6x = 12
4(3) - 6(-4) = 12
12 + 24 = 12
36 = 12 (False).
For ordered pair (0, 3), we have:
4y - 6x = 12
4(0) - 6(3) = 12
0 + 18 = 12
18 = 12 (False).
For ordered pair (6, 4), we have:
4y - 6x = 12
4(6) - 6(4) = 12
24 - 24 = 12
0 = 12 (False).
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Complete Question:
Select all the points that are on the graph of the equation 4y - 6x = 12. Show your work.
A. (-4, −3)
B. (-1, 1.5)
C. (0, -2)
D. (3, -4)
E. (0, 3)
F. (6, 4)
Subtract
f(x) = -5x²+x-2
g(x)=-3x² + 3x +9
Answers
a bald eagle sits in his nest in a tree at the top of the mountain. the nest is 1284 feet above the ground the eagle can dive at a rate of 88 feet/second what is the eagles height h after 7 seconds? the function rule for the height of the eagle after s seconds is? after 7 seconds the eagles height is?
Answers
The function rule for the height of the eagle after s seconds is h(s) = 1284 - 88s.
The height of eagle after 7 seconds is 668 feet.
Given that:-
Height of nest = 1284 feet
Speed of the bald eagle = 88 feet/second
Hence, we can write, after s seconds,
Height of eagle after s seconds = height of the nest - Time (in seconds) * Speed of the eagle
Hence,
h(s) = 1284 - s*88
h(s) = 1284 - 88s.
From the above equation, we can find the height of the eagle after 7 seconds.
h(7) = 1284 - 88*7 = 1284 - 616 = 668 feet.
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emma buys a camping van for £23500 plus VAT at 20%.
she pays a deposit for the camping van. she then pays the rest of the cost in 18 equal payments of £940 each month. Find the ratio of the deposit emma pays to the total of the 18 equal payments. give your answer in its simplest form
Answers
The ratio of the deposit Emma paid to the total of the 18 equal payments in its simplest form is 2/3
What is total cost of the van?
The total cost of the van is the its cost plus the VAT of 20%, which is determined as the 20% of the cost, as computed below:
VAT on the cost of van=20%*cost of van
cost of van=£23500
VAT on the cost of van=20%*£23500
VAT on the cost of van=£4,700
total cost=£23500+£4,700
total cost=£28,200
sum of 18 monthly payments=18*£940
sum of 18 monthly payments=£16,920
deposit=total cost-sum of 18 monthly payments
deposit=£28,200-£16,920
deposit=£11,280
deposit as a ratio of monthly payment=11280/16,920
divide both by 5640
deposit as a ratio of monthly payment=2/3
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pls help need to answer asap will mark brainliest
Answers
Depreciation expense is $20,121 in equation .
What is Depreciation expense?
When an asset is depreciated for a single period, the cost of the asset reflects how much of its value was used up during that year. This is known as depreciation expense. A piece of property's accumulated depreciation is the total amount of depreciation expense that has been incurred since the property first came into use.Additional to retained earnings = 5,900
Add : dividends paid = 2,040
Net income = $7940
Tax = 22%
Before tax income 97940 -/( 1 - 0.22) = $10179.48
Add : Interest expense = $4600
operating income = $14,779.48
Sales = $66,000
Less : costs = $31,100
Gross profit = $34,900
Depreciation expense = $20,121
(34,900 - 14,779.48)
Depreciation expense is $20,121 .
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what would be this answer and how to solve it?
-2/3 x 1/2 x -6/7
Answers
Answer:
2/7
Step-by-step explanation:
First off you would want to get rid of the negative because a negative times a negative equal a positive making the -2/3 and -6/7 a positive then you would want to cancel out the greatest common factor of 2 making the equation now 1/3 x 6/7 then you'll want to cancel out the greatest common factor of 3 by dividing 3 by 3 and 6 by 3 making it 1/1 x 2/7 and then after you multiply you get your answer of 2/7
17−{2+2[−1(7−10)]2}
help
Answers
Answer: 3
Step-by-step explanation: First, solve with the parenthesis. Next, solve the square brackets. Then, solve the quote brackets. And finally, solve the them after solving the brackets.
Answer:
Step-by-step explanation:
17-[4[-1(-3)2]
17-[4+3(2)]
17-[4+6]
17-10
7
What’s the answer and how do I find it?
Answers
Answer:
[tex] \dfrac{3a^2 + 3b}{a^2 - b^2} [/tex]
Step-by-step explanation:
You can try factoring the numerator and denominator.
[tex] \dfrac{3a^2 + 3b}{a^2 - b^2} = \dfrac{3(a^2 + b)}{(a + b)(a - b)} [/tex]
Nothing cancels out, so the expression is simplified as given.
Answer: [tex] \dfrac{3a^2 + 3b}{a^2 - b^2} [/tex]
please help ME !!!!!I need help !!!!!!!
Answers
BH and DF
AG and DF
Solve the inequality
2>8−43h
Answers
The solution to the inequality expression given as 2 > 8 - 43h is h > 6/43
How to determine the solution to the inequality?The inequality expression is given as
2 > 8 - 43h
Subtract 8 from both sides of the inequality expression
So, we have the following expression
2 - 8 > 8 - 8 - 43h
Evaluate the difference in the above expression
So, we have the following expression
-6 > - 43h
Divide both sides of the inequality by -43
So, we have
-6/-43 > - 43h/-43
Evaluate the quotient
6/43 < h
Rewrite as
h > 6/43
Hence, the value of the inequality is h > 6/43
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help help help help help help help help help
Answers
Answer:
72 jars per minute
Hope this helps!
Step-by-step explanation:
432/6 is 72.
If h(x) is the inverse of f(x), what is the value of h(f(x))?
A.) 0
B.) 1
C.) X
D.) f(x)
Answers
The value of h(f(x)) is x which is the C option in the question.
It is given in the question that h(x) is the inverse of f(x).
We have to find the value of h(f(x)).
If h(x) is the inverse of f(x), we can write is as:-
[tex]f^{-1}(x)=h(x)[/tex]
Hence,
h(f(x)) = [tex]f^{-1}(f(x))=(f^{-1}f)(x) = x[/tex]
Hence, the value of h(f(x)) is x.
Inverse function
An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1.
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i can provide additional photos if more info is needed
Answers
QUESTION A
To find the cost of making 300 minutes of calls, we can trace the graph from where the x-axis is 300 to the graph and then get the value on the y-axis. This is shown below:
Therefore, the cost of the plans are:
[tex]\begin{gathered} Plan\text{ }A=24 \\ Plan\text{ }B=20 \end{gathered}[/tex]Therefore, PLAN B costs less.
The difference between the two plans will be:
[tex]\Rightarrow24-20=4[/tex]Therefore, Plan B costs $4 less than Plan A.
QUESTION B
Both plans cost the same at the point where the two graphs intercept. Checking the graph, this occurs when:
[tex]x=250[/tex]Therefore, the number of minutes that both plans cost the same is 250 MINUTES.
Plan B has a constant price of $20, regardless of the number of minutes used. However, Plan A is variable. The cost of Plan A only exceeds $20 after 250 minutes.
Therefore, before this time, PLAN B costs more.
Geometry. Use the photo to help me find Length of T V
Answers
30 units
Since from point 0 to V, there are 25 units of distance
and from 0 to T, there are 5 units of distance
From T to V, 25 + 5 = 30 units
NB: Since we are only considering the length the - is not taken into account
Nathan earns $6.50 an hour, plus tips, as a waiter in a restaurant. Suppose he works 26 hours in a week. How much money in tips must he receive to earn at least $229?
Answers
If Nathan earns $6.50 an hour, plus tips, as a waiter in a restaurant, and he worked for 26 hours, then he must receive $60 in tips, to earn a total of $229 in that time period.
As per the question statement, Nathan earns $6.50 an hour, plus tips, as a waiter in a restaurant, and he worked for 26 hours.
We are required to calculate the amount of tips Nathan must receive to earn a total of $229, working for 26 hours.
To solve this question, we will first calculate the amount Nathan can earn from his regular salary rate, working for 26 hours, and then subtract that amount from $229 which he earned as his salary from the restaurant plus his tips while working for those 26 hours.
Therefore, Nathan will earn $(26 * 6.50) = $169 in his regular salary from the restaurant working for 26 hours.
But since Nathan earned a total of $229 working at the restaurant for the same 26 hours, the extra money over his salary must be the amount he earned in tips.
Therefore, Nathan received $(229 - 169) = $60 in tips, to earn a total of $229 working for 26 hours at the restaurant.
Hour: An hour is an unit of time, measured as twenty-fourth part of a full day (day and night), which is further divided into 60 sub units, known as minutes.Time-Period: In general Science, particularly in Physics, and also in our day-to-day life, the length of time during which an activity occurs or a condition remains is known as the Time-Period.
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True or False:
The Commutative Property of Addition states that for all expressions a and b, ab = ba
Answers
The answer to the given statement is FALSE. This is the commutative property of multiplication and not of addition.
What is the commutative property of addition?To "commute" is to move about or travel. According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added.
The formula for the commutative property of numbers is A + B = B + A if two numbers A and B are supplied.
A + B = B + A
A × B = B × A
A - B ≠ B - A
A ÷ B ≠ B ÷ A
According to the commutative property formula, the result is unaffected by the sequence in which two numbers are added or multiplied. However, the order of the integers matters for subtracting and dividing any two real numbers, so it cannot be changed.
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Complete the following conversion.
3,500 s = ________min
(60 s = 1 min)
Show work.
Answers
58 minutes and 20 seconds
Step by step explanation:
So I done 6x5 as if it was 600x5, then I would do 60x8
600x5=3000
60x8=480
3000+
480=
————
3480
You are doing a walkathon/runathon to raise money for your school. You can walk at a rate of 4 miles per hour and run at a rate of 6 miles per hour. You need to cover more than 8 miles in order to raise your part of the money. Which of the following linear inequalities can be used to determine how long you must walk (w) and run (r) in order to cover more than 8 miles? O 4w + 6r > 8 4w + 65 = 8 O 4w + 6r > 8 O 4w + 6r
Answers
We need to determine which of the given inequalities can be used to determine how long you must walk (w) and run (r) in order to cover more than 8 miles.
We know that you can walk at a rate of 4 mi/h, and run at a rate of 6mi/h.
Thus, if you walk for w hours, you will walk a distance d₁, in miles, given by:
[tex]d_1=4w[/tex]Also, if you run r hours, you will run a distance d₂, in miles, given by:
[tex]d_2=6r[/tex]Now, notice that the total distance is the sum of d₁ and d₂. And the total distance, in miles, must be greater than 8.
We represent 'greater than' using the symbol '>':
[tex]\begin{gathered} d_1+d_2>8 \\ \\ 4w+6r>8 \end{gathered}[/tex]Therefore, the correct option is:
[tex]4w+6r>8[/tex]
A biologist has an 8892-gram sample of a radioactive substance. Find the mass of the sample after three hours if it decreases according to a continuous
exponential decay model, at a relative rate of 18% per hour.
Do not round any intermediate computations, and round your answer to the nearest tenth.
Answers
Answer: 4902.8
Step-by-step explanation: take 8892 subtract 18% from it then do that again with the number you got from subtracting 18% from 8892 and so on and so fourth just do it one more time and you get 4902.76 which now you round it to the nearest tenth and that equals 4902.8.
Help please the image is attached!
Answers
Answer:
5+ ( n+10) 8(7) - n n/3 + 110 - 6(8) - n(1-n) - (2n) n(-n) +7The cost of 5 kg of oranges is sane as the cost of 3 kg of apples. How many kilograms of oranges are required to exchange 9 kg of apples ?
Answers
Answer:
15kg of oranges.
Step-by-step explanation:
cost of 3kg of apples = cost of 5kg of oranges
cost of 9kg of apples which is (3 x 3) = cost of (5 x 3) kg of oranges
= cost of 15kg of oranges.
Find the length of the sides of the special triangles
Answers
We will have the following:
Firs, we can see that once we find one side we will have both, since they are equal.
Now, using the law of sines:
[tex]\frac{4}{\sin(90)}=\frac{Z}{\sin(45)}\Rightarrow Z=\frac{4\sin (45)}{\sin (90)}[/tex][tex]\Rightarrow Z=2\sqrt[]{2}[/tex]So, the length of side Z is 2sqrt(2).
Two angles are congruent. One has a measure of 2x + 5. The other has a measure of 4x - 9. Find the value of x.
Answers
you get that by setting them equal to each other
Please Help! Im Giving 25 Points!
Answers
Answer:
33
Step-by-step explanation:
because 18 divided by 6 is 3
and 11 times 3 is 33
Answer: 1. 33
Step-by-step explanation:
I say 33 because the short side on the one is 6 and is 18 on the other so they multiply by 3. That being said 11 times 3 is 33. I hope this helps! :)
Find the value of the missing angles, marked a, b and c. Give a reason for each stage of your working.
Answers
The unknown angles of the diagram is as follows;
a = 32°b = 20°c = 128°How to find angles?The missing angles of the diagram can be found as follows:
The sum of angles in a triangle is 180 degrees.
Therefore,
32 + 128 + b = 180
160 + b = 180
b = 180 - 160
b = 20°
Therefore,
a = 32°(alternate angles)
Alternate angles are congruent.
180 - a - b = c (sum of angles on a straight line)
180 - 32 - 20 = c
c = 180 - 32 - 20
c = 128°
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Solve for x.
2x-6
4x + 18
x = [?]
X help please
Answers
hope this helps
The number of bacteria in a culture is given by the function
n(t) = 990e0.15t
where t is measured in hours.
(a) What is the relative rate of growth of this bacterium population?
Your answer is
percent
(b) What is the initial population of the culture (at t=0)?
Your answer is
(c) How many bacteria will the culture contain at time t=5?
Answers
It is discovered that:
a) 45 percent using the exponential function.
b) 950.
c)9013 bacterium
n(t)= n(0) e square( kt )
n(5) = 950 e square 0.45(5)
9013 microbes then.
The number of bacteria in a culture is increasing according to the law of exponential growth. There are 125 bacteria in the culture after 2 hours and 350 bacteria in the culture after 4 hours
A model for an exponential function is?
n(t)= n(0) e square( kt )
In which
n(0) represents the starting point.The constant rate of growth is k.The model in this quandary is:
So,
n(t)=950 e square( 0.45t)
also
k=0.45 n(0) = 950 ,and:
(A) 45 percent.
b) 950.
Item c:
We have that at t = 5:
n(5) = 950 e square 0.45(5)
9013 microbes then.
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