(a). The equation of the line L in the form of y = mx + b is y + 2x = 0.
(b). The equation of the line K that passes through the point (0, -1) and is perpendicular to the line L is y = 2x - 1.
(c). The intersection of the lines and K is located at a location with the coordinates (0,-1).
Define equation of line.The equation of a line has the usual form axe + by + c = 0. Here, x and y are the variables, a and b are the coefficients, and c is the constant term. You may also find and see the equation of a line in the slope-intercept form, point-slope form, two-point form, intercept form, and normal form.
The formula of slope is given by m = (y₂-y₁)/(x₂-x₁).
Here, m is the slope of the line.
(x₁, y₁) and (x₂, y₂) are the two points of the line.
Now put the value of x₁, y₁, x₂, y₂ in
m = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
m = [tex]\frac{3-1}{-1-1}[/tex]
m = 2/-1
m = -2
The slope of the line perpendicular is:
mₐ = - 1/m
mₐ = -1/-2
mₐ = 2
(a) The equation (in the form y = mx + b) of the line L.
(y-y₁) = m(x-x₁)
(y-1) = -2(x-1)
y-1 = -2x-1
y = -2x
y + 2x = 0
(b) The equation of the line K that passes through the (0, -1) and is perpendicular to the line L.
x = 0 and y = -1
y = mx + b
y = 2x + b
-1 = 2×0 + b
-1 = b
b = -1
Substituting the above in y = mx + b to get:
y = mx + b
y =2x + (-1)
y = 2x - 1
(c) The coordinates of the point at which the lines and K intersect.
y = 2x - 1
y+2x+1=0
(2x-1)+2x+1=0
4x =0
x = 0, y = -1
The intersection of the lines and K is located at a location with the coordinates (0,-1).
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Precipitation for the month of March was 4 3/4 inches less than average. I’m April, the precipitation was 1 1/2 inches less than average. How many inches below average was the precipitation for both March and April?
The inches below average was the precipitation for both March and April is 6 1/4 inches
How to compute the value?From the information given, the precipitation for the month of March was 4 3/4 inches less than average. In April, the precipitation was 1 1/2 inches less than average.
Therefore, the inches below average will be:
= 4 3/4 + 1 1/2
= 4 3/4 + 1 2/4
= 6 1/4
The inches is 6 1/4 inches.
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how many times does the digit 9 appear in the counting numbers from 1 to 99?
In the counting of numbers from 2 to 99, the digit 9 appears 20 times.
Listing the Numbers
To identify how many times the digit 9 appears, we can first list the numbers we know have a 9 in them:
9, 19, 29, 39, 49, 59, 69, 79, 89, 99
Although we've identified these numbers, we are not finished. Numbers in the 90s also qualify as digits of 9. Therefore, these numbers also are included:
91, 92, 93, 94, 95, 96, 97, 98
Answer RecapNow that we have all the numbers from 1 to 99 with the digit 9 in them, we can count up how many numbers there are with consideration that the number 99 also has two digits of 9 in it:
[(10 + 8) + 2] = 20
Hence, the digit 9 appears 20 times in the counting numbers from 1 to 99.
Answer:
There are 20 times the digit 9 appears in counting numbers from 1 to 99.
Step-by-step explanation:
To see why this is the case, we can break the counting numbers down into two categories: numbers with a 9 in the units place and numbers without a 9 in the units place.
For the first category, we can count the number of times a 9 appears in the units place by counting from 9 to 99 in increments of 10. There are 10 numbers in this category.
For the second category, we can count the number of times a 9 appears in the tens place by counting from 19 to 99 in increments of 100. There are 10 numbers in this category as well.
Therefore, the total number of times the digit 9 appears in counting numbers from 1 to 99 is 20 times.
An airplane descended 225 m in 10 s. What was the airplanes rate of change in elevation
The rate of change in elevation will be:
R = -225m/10s = -22.5 m/s
The airplaen descends at a rate of 22.5 meters per second.
What was the airplane's rate of change in elevation?The rate in change of the elevation will be given by the quotient between the change in elevation and the time in which that change happens.
Here we know that the airplane descended 225 meters, so the change in elevation is:
C = -225m
And that change happens in 10 seconds, so the rate of change in elevation will be:
R = -225m/10s = -22.5 m/s
The airplane descends at a rate of 22.5 meters per second.
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3. Rhombus KLMN with vertices K(-3, 2), L(1, 4),
and N(-5, -2): (x,y) → (x+2, y-5)
The translated vertices of the rhombus are: K(-1,-3), L(3,-1), M(1,-5) and N(-3,-7)
The rhombus is a parallelogram which has all sides equal. the diagonals of a rhombus bisect at right angles. the difference between a rhombus and a square is that none of the angles of a rhombus are 90°.
To translate a figure with given co-ordinates into another figure with a particular translation we simply add or subtract the given values from the coordinates of the available points.
Given co-ordinates of Rhombus are K(-3, 2),L(1, 4),M(-1 ,0)and N(-5, -2).
The translation is given as (x,y) → (x+2, y-5)
So we calculate the coordinates as:
The translated co-ordinate K(-3, 2)→ K'(-1,-3)
The translated co-ordinate L(1, 4)→ L'(3,-1)
The translated co-ordinate M(-1 ,0)→ M'(1,-5)
The translated co-ordinate N(-5, -2)→ N'(-3,-7)
Hence the co-ordinates of rhombus translated by (x,y) → (x+2, y-5) are K(-1,-3), L(3,-1), M(1,-5) and N(-3,-7).
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Davis is trying to decide between two part time jobs on Saturdays. He could make $16.25 per hour working
at the city's ice arena, but getting to work and back would cost him $7.50 round trip for travel. His other
option is to work as a dog walker in his neighborhood for $12.50 per hour but he can ride his bike or walk
there for free. He estimates he could work up to 7 hours at the arena but up to 10 hours walking dogs. He
always works at least 1 hour if he goes to the arena.
1. Write two different functions that represent Davis's gross wages, where h is the number of
hours Davis works per week, a(h) is his gross wages at the ice arena minus travel expenses, and
d(h) is his gross wages from walking dogs.
1. State the domain and range for each function.
2. If Davis works 1 hour, what would be his gross pay at each job? What if he worked 6 hours?
3. Davis wants to know what his net pay, also called take-home pay, is going to be. Assume that
10.5% of just his paycheck, not his travel expenses, is withheld for taxes at the arena. Because
dog walking is a self-employed activity, Davis estimates he needs to set aside 18% of his income
for taxes. Modify your functions from question 1 to model net pay including these tax
withholdings.
4. State the domain and range for each of these new functions.
1) Two different functions that could represent Davis' gross wages, where h is the number of hours Davis works per week, a(h) is his gross wages at the ice arena minus travel expenses, and d(h) is his gross wages from walking dogs are:
Function A: a(h) = 16.25h - 7.50
Function B: d(h) = 12.50h
2) If Davis works 1 hour, his gross pay at each job is:
1 Hour 6 Hours
a) $16.25 $97.50
b) $12.50 $75
3) To find Davis' net pay after tax, the modified functions in question 1 are as follows:
Function A: a(h) = (16.25h - 7.50)(1 - 0.105)
Function B: d(h) = 12.50h(1 - 0.18)
4) The domain and range for each of these new functions are:
Domain Range
a) Function A [1, 2, ... 7] [7.83, 15.66, ... 54.81]
b) Function B [1, 2, ... 12] [10.25, 20.5, ... 123]
What are the domain and range of a function?The domain refers to all the possible values of the independent (input) variables.
The range refers to the possible values of the dependent (output) values.
Data and Calculations:Arena Dog Walking
Pay rate per hour $16.25 $12.50
Travel expense $7.50 $0
Maximum hours worked 7 hours 10 hours
Gross pay for one hour $16.25 $12.50
Gross pay for 6 hours $97.50 $75
After
Tax 10.5% 18%
After-tax factor (1 - 0.105) (1 - 0.18)
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2) a) If the function f(x) = |x| is changed to g(x) = 3|x-1| +3,
how is the graph transformed? (left, right, up, down? By how much?)
b) On the blank graph, graph the function g(x) = 3 |x-1| +6
8
6
21
-10 -8 6-4-2 2468
-24
7
f
8
Step-by-step explanation:
a) right - 1 unit; up - 3 units; angle between branches is decreased. All the details are in the attachment;
b) the required graph is in the attachment.
Regan swims for the Sharks swim team. Last season, the Sharks won 5 swim meets for every 3 they lost.
Pick the diagram that models the ratio in the story.
If the Sharks had 16 swim meets in all, how many did they win?
If the Sharks had 16 swim meets in all, they won 10 swims.
Given,
Regan swims for the Sharks swim team. Last season, the Sharks won 5 swim meets for every 3 they lost.
We need to find out if the Sharks had 16 swim meets in all, and how many did they win.
How to compare two units?Example:
2 cups = 4 eggs
To find for 4 cups.
We need to multiply 2 so that 2 cups becomes 4 cups.
4 cups = 2 x 4 eggs = 8 eggs
We have,
5 sims own for every 3 swims lost.
We can write it as:
5 own = 3 lost
Multiply 2 on both sides
2 x 5 own = 2 x 3 lost
10 own = 6 lost
We have,
16 swims in total.
It can be written as,
10 own = 6 lost
And we see that,
10 + 6 = 16 swims
Thus,
If the Sharks had 16 swim meets in all, they won 10 swims.
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How do you find the surface area of the pyramid
The pyramid's surface area is = 409.6 cm2.
The provided pyramid's surface area is equal to its square base plus its lateral sides.
The square base's area is given by (Side)2
= (8)2
= 64 cm2.
Area of the lateral side = 1/2 (Lateral height)(Base)
= √4² + (9.2)
2 [By applying Pythagoras theorem]
82.81+36
= √100.64
= 10.8 cm
Area of the lateral side = (8)(10.8)
= 86.4 cm²
The provided pyramid's surface area is calculated as follows:
Area of the base + 4(Area of one lateral side)
= 64 + 4(86.4)
= 409.6 cm2.
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If two angles
complementary, then their measures sum to 90
It is necessary that the for complementary angles then their measures sum to 90 degree.
According to the statement
We have to explain all about the complementary angles.
So, For this purpose, we know that the
Complementary angles are pair angles with the sum of 90 degrees.
From the given information:
We have to prove that the If two angles complementary, then their measures sum to 90.
Then
Contrapositive of p → q is ~q → ~p where p is that the hypothesis and q is that the conclusion.
Hypothesis (p) = Two angles are complementary
~p = Two angles aren't complementary
Conclusion (q) = The sum of their measures is 90°
~q = The sum of their measures isn't 90°
~ p → ~q = If the sum of the measures of two angles isn't 90°,
then they're not complementary angle.
So, It is necessary that the for complementary angles then their measures sum to 90 degree.
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Using the following information about the family’s assets and liabilities, calculate the total assets: Checking account: $3,000 Savings account: $13,000 Credit card balance: $5,500 Utility bill: $500 Home: $320,000 Mortgage (30 years): $210,000 Car: $25,000 Car loan (60 months): $18,000 Student loan (7 years): $25,000 Household items: $15,000 Retirement account: $64,000 Other assets: $39,000
The net worth of a given family is $227500.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
Assets are simply subtracted from liabilities to determine net value. Your money and investments, your home and other properties you own, your automobiles, and any other valuable possessions you own are all considered assets.
Assets = 3,000 + 13,000 + 5,500 + 15,000 + 64,000 + 320,000 + 25,000 + 39,000 = 484500
Liabilities = 500 + 210,000 + 18,000 + 25,000 = 257000
Net worth = Assets - Liabilities
Net worth = $484500- $257000 = $227500
Thus, the net worth of a given family is $227500.
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Points A, B, C and D are collinear. Point B is between A and C. Point C is between B and D. Suppose BC = 14 + x, AD = 42 + x, and AC = x + 32. Find x =, AB =, BC =, CD =, AC =, AD=
A possible solution for this case of collinear points is (x, AB, BC, CD, AC, AD) = (0, 18, 14, 10, 32, 42).
What are the lengths of collinear line segments?
In this question we have four points that are collinear, that is, that lie on the same line. Mathematically, speaking we have the following equations representing the geometric system:
BC = 14 + x (1)
AD = 42 + x (2)
AC = x + 32 (3)
By (1) and (3):
AB = (x + 32) - (14 + x)
AB = 18
By (2) and (3):
CD = (42 + x) - (x + 32)
CD = 10
If x = 0, then BC, AD and AC are, respectively:
BC = 14, AD = 42, AC = 32
Then, a possible solution for this case of collinear points is (x, AB, BC, CD, AC, AD) = (0, 18, 14, 10, 32, 42).
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74% of 315 but also please round if you can
?
Answer:
233.1 or if you round just 233
Step-by-step explanation:
brianlist?
Answer:
233.1 but it would be 233 or 230 rounded
Natasha treats herself to some choco-vanilla ice cream. She prepares the treat with
1
8 scoops of chocolate ice cream and 2- times as much vanilla ice cream as chocolate.
2
How much vanilla ice cream does she use?
Answer:
Step-by-step explanation:
Given the function, complete the table of values then graph the ordered pairs.
Answer: a
Step-by-step explanation:
Given the graph below, determine the correct translation rule.
a. (x, y) → (x - 5 , y + 1)
b. (x, y) → (x + 1, y - 5)
c. (x, y) → (x - 1, y + 5)
d.(x, y) → (x + 5, y - 1)
Convert -56 degree c to Kelvin
Teacher Guided 1. In a book club, the ratio of male to the number of female members was 2:7. After 12 male members left the club, the ratio became 1:4. How many member were there in the book club at first?
Answer:
16
Step-by-step explanation:
Answer:
teacher guided 1 in a book
Step-by-step explanation:
At a toy company every fourth stuffed animal has its eyes inspected, and every tenth stuffed animal has its tag inspected. Which animal will be the first to have both its eyes and tag inspected?
Answer:
the 20th animal
Step-by-step explanation:
we need to find the least number dividable by 4 and 10
20 is the lowest number divided by both
20 divided by 4 = 5
20 divided by 10 = 2
Simplify this question
Answer:
10.5
Step-by-step explanation:
1 + 5 = 6
6 * 7 = 42
3 - 1 = 2
2^2 = 4
42 / 4 = 10.5
Answer:
[tex] = { \rm{ \frac{1 + 5.7}{ {(3 - 1)}^{2} } }} \\ \\ = { \rm{ \frac{1 + 5.7}{4} }} \\ \\ = { \rm{ \frac{6.7}{4} }} \\ \\ = { \rm{1 \frac{27}{40} }}[/tex]
At a coffee shop, the first 100 customers' orders were as follows. Small Medium Large Hot un 48 22 Cold 8 12 5 What is the probability that a customer ordered a small given that he or she ordered a larg drink? Rounded to the nearest percent, [? ]% Enter
The probability that a customer ordered a large given that he or she ordered a hot drink is 88 % .
What is Probability ?
The probability is equal to the variety of possible outcomes. the total number of outcomes that could occur. For instance, there is only one way to receive a head and there are a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail).The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.
Probability Formula = f/n
where,
f is the number of times an event occurs
n is the total number of trial
The probability is represented as:
P(Large | Hot)
This is calculated using:
P(Large | Hot) = n(Large and hot)/n(hot)
Using the data on the given table, we have:
P(Large | Hot) = 22/(8 + 12 + 5)
P(Large | Hot) = 0.88
In percentage
P(Large | Hot) = 88%
Hence, the probability that a customer ordered a large given that he or she ordered a hot drink is 88 % .
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8/5 minus 1/6 please help me lol
1. A honeybee leaves the hive and travels 2 KM before returning. What distance did the
honeybee travel and what was the honeybee's displacement
Total distance travelled by the honey bee is 4km and honeybee’s displacement is 0
Displacement is defined as the shortest distance travelled by the object.
According to the question we have been given that the honeybee travelled 2km before returning to the hive.
Thus the total distance travelled by the honeybee is = 2 + 2 km
= 4 km
And the honeybee’s displacement = 0
Because the bee has returned to the same from where she had left and displacement is a vector quantity that has magnitude and direction and depends upon the initial and final position. So as the initial and final destination is same for the honeybee. Thus the displacement will be zero.
Hence total distance = 4km
And displacement = 0
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Simplify to lowest terms if possible: 14c/12c
Hello!
[tex]\frac{14c}{12c}[/tex] simplified to lowest terms is [tex]\frac{7c}{6c}[/tex]
Step-by-step explanation:
Other simplified versions of the expression is [tex]\frac{7}{6}[/tex], [tex]1.16[/tex], 1 [tex]\frac{1}{6}[/tex]
Hope this helps!
7. If U= {2, 4, 6, 8, 10, 12, 14, 16} and
A = {6, 10, 14}, what is A'?
The compliment of set A that is A' is equal to {2, 4, 8, 12, 16}.
We are given the universal set as:
U = {2, 4, 6, 8, 10, 12, 14, 16}
We are also given that set A is:
A = {6, 10, 14}
We need to find A'
For this, we will subtract set A from the universal set, U.
So, we get that:
A' = U - A
A' = {2, 4, 6, 8, 10, 12, 14, 16} - {6, 10, 14}
Solving the expression, we get that:
A' = {2, 4, 8, 12, 16}
Therefore, we get that, the compliment of set A that is A' is equal to {2, 4, 8, 12, 16}.
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Find the domain of the function g(x)= 4/x^2 +3x +2. Write your answer in set builder notation
Answer:
[tex] \{x|x \neq -2, -1 \}[/tex]
Step-by-step explanation:
The denominator cannot equal 0 because division by zero is undefined.
[tex]x^2 + 3x+2 \neq 0 \implies (x+1)(x+2) \neq 0 \implies x \neq -1, -2[/tex]
[tex]\therefore \{x|x \neq -2, -1 \}[/tex]
Answer:
[tex] \{x|x \neq -2, -1 \}[/tex]
Step-by-step explanation:
The denominator cannot equal 0 because division by zero is undefined.
[tex]x^2 + 3x+2 \neq 0 \implies (x+1)(x+2) \neq 0 \implies x \neq -1, -2[/tex]
[tex]\therefore \{x|x \neq -2, -1 \}[/tex]
If p=7 and q=1, what is 4pq squared + (-7)pq squared +5p?
14
Step-by-step explanation:
4pq² + (-7)pq² +5p
Evaluate for p=7,q=1
(4)(7)(1²)+((−7)(7))(1²)+(5)(7)
(4)(7)(1²)+((−7)(7))(1²)+(5)(7)
=14
I really don’t understand Exponents Much. Could someone explain the subject to me? I learn best with examples!
Tysm <3
Exponentiation is a mathematical operation denoted by the symbol bn that consists of two numbers, the base b, and the exponent or power n, and is pronounced as "b (raised) to the (power of) n."
What are exponents?Exponentiation is a mathematical operation denoted by bⁿ the symbol bn that involves two numbers, the base b, and the exponent or power n, and is pronounced as "b (raised) to the (power of) n." Exponentiation corresponds to repeated multiplication of the base when n is a positive integer: bⁿ is the product of multiplying n bases:[tex]b^n=\underbrace{b \times b \times \cdots \times b \times b}_{n \text { times }}[/tex]
Typically, the exponent is shown as a superscript to the right of the base. In that case, bⁿ is referred to as "b raised to the nth power," "b (raised) to the power of n," "the nth power of b," "b to the nth power," or simply "b to the nth."Several other properties of exponentiation follow directly from the basic fact stated above that, for any positive integer display style n, display style bⁿ is displayed style n occurrences of display style bb all multiplied by each other. More specifically:[tex]\begin{aligned}b^{n+m} &=\underbrace{b \times \cdots \times b}_{n+m \text { times }} \\&=\underbrace{b \times \cdots \times b}_{n \text { times }} \times \underbrace{b \times \cdots \times b}_{m \text { times }} \\&=b^n \times b^m\end{aligned}[/tex]
For example, the number of times a number is multiplied by itself is referred to as its exponent. For instance, 2 to the third (written as 2³) means: 2 x 2 x 2 = 8.Therefore, exponentiation is a mathematical operation denoted by the symbol bn that consists of two numbers, the base b, and the exponent or power n, and is pronounced as "b (raised) to the (power of) n."
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please help
please hurry
Step-by-step explanation:
we have no continuous curve here, the supposed function only consists of a few data pair points. and that is absolutely ok.
any function just maps a set of x (input) values to a set of y (function result) values.
A.
yes, it is a function, because every "used" x value has exactly 1 assigned y value.
when we draw a vertical line and move it across the grid, there are never 2 or more of the points in the line. always only one.
the opposite (every y value has exactly 1 x value as origin) is NOT necessary to be a function. but it would have to be true for the inverse function to be a function too.
B.
the domain is the interval or set of all valid x values.
since we have only single points, it is a set here :
{-4, -3, -2, 0, 2, 3}
C.
the range is the interval or set of all valid y values :
{-3, -1, 0, 2, 3}
D.
as we can see on the chart, the only point with x value = 2 has the y value = -3.
so,
y = -3 when x = 2
or formally
f(2) = -3
Emergency helppppp mee one questionn plsss yikessss!!!
Answer:
It is the last answer shown where the absolute value of -4 is the greatest
-2.47, -2, -1 3/4, -3/8, | -4 |
Step-by-step explanation:
Absolute value indicates how far away a value is from zero. The sign is not relevant in that context.
Find the degree of the polynomial and determine whether it is a monomial, binomial, trinomial, or none of these.
13x²-x³-13x4
What is the degree of the polynomial?
