Answers
If the equation y = -x, then the equation of the line that is parallel to the given line and passes through the point (-8,2) is y = -x-6
The equation is
y = -x
The slope intercept form
y = mx+b
Where m is the slope of the line
Comparing the slope intercept form and the given equation
Slope of the line m = -1
The line is passing through the points (-8,2)
The point slope form of the line
[tex](y-y_1)=m(x-x_1)[/tex]
Substitute the values in the equation
y-2 = -1(x-(-8))
y-2 = -1(x+8)
y-2 = -x-8
y = -x-8+2
y = -x-6
Hence, if the equation y = -x, then the equation of the line that is parallel to the given line and passes through the point (-8,2) is y = -x-6
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Related Questions
y=600(0.75)^x
growth or decay by what precent?
Answers
The function f(x) = 600(0.75)^x. is a decay function by 25%
How to graph the function?The equation of the function is given as
f(x) = 600(0.75)^x.
The above function is an exponential function
An exponential function is represented as
y = ab^x
When f(x) = 600(0.75)^x. and y = ab^x are compared, we have
b = 0.75
The value of b in this case is the factor
Also if b is less than 1, then the function is a decay function
0.75 is less than 1
So, the function represents a decay function
The decal percentage is then calculated as
Decay = 1 - b
So, we have
Decay = 1 - 0.75
Evaluate
Decay = 25%
Hence, the function is a decay function
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Select the correct answer. Consider the graph of f(x) given below. The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)? A. g(x) = f(x - 5) B. g(x) = f(x) - 2 C. g(x) = f(x) - 5 D. g(x) = f(x + 2)
PLEASE OFFER ME YOUR ANSWER, I ASK OF YOU...PLS
Answers
The function that could represent g(x) is (c) g(x) = f(x) - 5
How to determine the function g(x)?The figure of the graph that completes the question is added as an attachment
From the attached graph, we have the equation of the function to be
y = f(x)
Also, the graph of the function f(x) has its intercept to be
y-intercept of f(x) = 3
From the question, we have
y-intercept of g(x) = -2
Subtract the intercepts
Difference = y-intercept of g(x) - y-intercept of f(x)
So, we have
Difference = -2 - 3
Evaluate
Difference = -5
The function g(x) is then represented as
g(x) = f(x) + Difference
So, we have
g(x) = f(x) - 5
Hence, the function g(x) is g(x) = f(x) - 5
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A circle has a radius of 5 units, 3 students tried to calculate the circumference of the circle, put their answers in order from most accurate to least accurate31.4π units 10π units 31.4 units
Answers
A circle has a radius of 5 units, 3 students tried to calculate the circumference of the circle, put their answers in order from most accurate to least accurate
31.4π units
10π units
31.4 units
we know that
the circumference of a circle is equal to
[tex]C=2\pi r[/tex]we have
pi=3.14
r=5 units
substitute
[tex]\begin{gathered} C=2\pi(5) \\ C=10\pi\text{ units} \end{gathered}[/tex]the exact value is 10pi units
the approximate value (assume pi=3.14)
C=31.4 units
so
order from most accurate to least accurate is
10π units
31.4 units
31.4π units
order from least accurate to most accurate is31.4π units31.4 units10π unitsIf segment BD is congruent to segment BC, BD=4x-18, BC=x+3, and AC=34, find AB
Answers
If segment BD is congruent to segment BC, and BD = 4x - 18, BC = x + 3, and AC = 34, then AB = 31/x.
What is meant by Congruent angles?Congruent angles are two or more angles that are exactly the same. As a result, the lengths of these angles are equal. Angle measurement is the same for congruent angles. A regular pentagon, for example, has five sides and five angles, each of which is 108 degrees. Angles in a regular polygon will always be congruent regardless of size or scale. Congruent angles are another name for equal angles. Angles that are congruent are those that are vertically opposite each other. Congruent angles are those formed by the intersection of two parallel lines and a transversal.Let the equation be AB + BC = AC
substitute the values in the above equation, we get
AB + x + 3 = 34
simplifying the value of x,
Subtract A B from both sides AB + x + 3 - AB = 34 - A B
x + 3 = 34 - AB
Subtract 3 from both sides,
x + 3 - 3 = 34 - AB - 3
x = -AB + 31
Plug in this value of x into the line segments to find BC and AC.
Where, BC = x + 3
substitute the value of x in the above equation, we get
BC = [-AB + 31 ] + 3
BC = -AB + 34
Then, AB + BC = AC
x = -AB + 31
AB = 31/x
Hence, If segment BD is congruent to segment BC, and BD = 4x - 18,
BC = x + 3, and AC = 34, then AB = 31/x.
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MTR
3 MAINTAIN ACCURACY In Exercises 27-30, determine
whether the statement uses the word function in a way
that is mathematically correct. Explain your reasoning.
27. The selling price of an item is a function of the cost of
making the item.
28. The sales tax on a purchased item in a given state is a
function of the selling price.
29. A function pairs each student in your school with a
homeroom teacher.
30. A function pairs each chaperone on a school trip
with 10 students.
Please just do 28 and 30
Answers
Answer:
28. Correctly used
30. Incorrectly used
Step-by-step explanation:
You want to know if the word "function" is correctly used in the following cases:
28. The sales tax on a purchased item in a given state is a function of the selling price.
30. A function pairs each chaperone on a school trip with 10 students.
28. Sales taxThere is exactly one value of sales tax associated with any given selling price. This means the ordered pair (selling price, sales tax) will be unique for any given selling price. Hence, the relation between selling price and sales tax is a function. The word function is used correctly in describing this relation.
29. ChaperonesThere are 10 different students associated with any given chaperone. This means there will be multiple (chaperone, student) ordered pairs for any given chaperone: (c1, s1), (c1, s2), ..., (c1, s10), (c2, s11), (c2, s12), ..., (c2, s20), .... The relation between chaperones and students is not a function. The word function is used incorrectly in describing this relation.
75% of the marbles in a bag are orange and the rest are blue. What fraction of the orange marbles must be removed from the bag so that 50% of the remaining marbles are orange?
Answers
Answer:
1/2
Step-by-step explanation:
75% of the marbles in a bag are orange and the rest are blue. The percentage for blue will be:
= 100% - 75%
= 25%
The fraction of the orange marbles that must be removed from the bag so that 50% of the remaining marbles are orange will be:
= 75% - 25%
= 50%
= 1/2
a bank of 10 movies is chosen from for a movie marathon in which 7 movies will be played in a specific order. in how many different ways can the movies for the movie marathon be chosen?
Answers
The movies for the movie marathon can be chosen in 120 different ways .
In the question ,
it is given that
total number of movies = 10 movies
number of movies that need to be played in specific order = 7 movies .
we have to find how many different ways can the movies be selected for the movie marathon .
we can solve this with Combination ,
where n = 10 and r = 7
So C(n,r) = C (10,7)
= 10! / (3! * 7! )
= (10*9*8*7!)/(3! * 7! )
= ( 10*9*8) / (3*2 )
= 10 * 3 * 4
= 120 ways .
Therefore , The movies for the movie marathon can be chosen in 120 different ways .
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A ride-all-day amusement park ticket last season was $35, and this season it is $27
.
What is the percent Markdown?
Answers
Answer:
Step-by-step explanation:
35-27=8
Answer:22.85%
Step-by-step explanation:
27 - 35
|35|
× 100% =
-8
35
× 100 = -22.8571428571% (decrease)
Joe, Keitaro, and Luis play tennis. To decide who will play against each other in the first match, they put their names in a hat and choose two names without looking.
What subset of the sample space, A, represents the complement of the event in which Joe plays in the first match?
A = {KL}
A = {KJ, KL}
A = {KL, LK}
A = {KJ, KL, LJ}
Answers
Answer:
A = {KL}
Step-by-step explanation:
The subset of the sample space that represents the complement of the event in which Joe plays in the first match is A = {JL, KL}
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
The sample space of this experiment consists of all possible ways of choosing two names from a group of three.
Since the order in which the names are chosen does not matter, the size of the sample space is given by the number of combinations of 3 things taken 2 at a time, which is 3.
The three possible outcomes are: {JK, JL, KL}.
If we want to find the complement of the event in which Joe plays in the first match, we need to find the outcomes in which Joe does not play in the first match.
There are two such outcomes: JL and KL.
Therefore, the subset of the sample space that represents the complement of the event in which Joe plays in the first match is A = {JL, KL}
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Kirby is buying a new grill that has been reduced for an end of summer sale by 25% to $496. what was the original price of the grill?
Answers
Given:
percentage decerease = 25%
current price of the grill = $496
Let the original price of the grill be x
We can calculate percentage decrease using the formula:
[tex]\text{Percent decrease = }\frac{Orig\text{ inal value - new value}}{Orig\text{ inal value}}\text{ }\times\text{ 100}[/tex]Substituting the given values we have:
[tex]\begin{gathered} 25\text{ = }\frac{x-496}{x}\times\text{ 100} \\ 25\text{ = }\frac{(x-496)\times100}{x} \end{gathered}[/tex]Cross-Multiply:
[tex]\begin{gathered} 25x\text{ = 100x - 49600} \\ \text{Collect like terms:} \\ -75x\text{ = -49600} \\ \text{Divide both sides by -75} \\ \frac{-75x}{-75}\text{ = }\frac{-49600}{-75} \\ x\text{ }\approx\text{661.33} \end{gathered}[/tex]Hence, we can conclude that the original price of the grill is approximately $661.33
Answer:
$661.33
I need help fast with my math homework.
Answers
Answer:15 twice
Step-by-step explanation:
Write the equation in slope intercept form: -6x+4y=20
Answers
Answer:
[tex]y=\frac{3}{2}x+5[/tex]
Step-by-step explanation:
[tex]-6x+4y=20 \\ \\ 4y=6x+20 \\ \\ y=\frac{3}{2}x+5[/tex]
what are the roots of the equation ?-3x = -10x^2-4
Answers
Given the following Quadratic equation:
[tex]-3x=-10x^2-4[/tex]You can use the Quadratic formula to solve it:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this case, you need to add "3x" to both sides of the equation:
[tex]\begin{gathered} -3x+(3x)=-10x^2-4+(3x) \\ 0=-10x^2+3x-4 \end{gathered}[/tex]You can identify that:
[tex]\begin{gathered} a=-10 \\ b=3 \\ c=-4 \end{gathered}[/tex]Substituting values into the formula and evaluating, you get:
[tex]\begin{gathered} x=\frac{-3\pm\sqrt[]{3^2^{}-4(-10)(-4)}}{2(-10)} \\ \\ x_1=\frac{3}{20}-\frac{i}{20}\sqrt[]{151} \\ \\ x_2=\frac{3}{20}+\frac{i}{20}\sqrt[]{151} \end{gathered}[/tex]Answer
Complex roots:
[tex]\begin{gathered} x_1=\frac{3}{20}-\frac{i}{20}\sqrt[]{151} \\ \\ x_2=\frac{3}{20}+\frac{i}{20}\sqrt[]{151} \end{gathered}[/tex]I need help with this practice problem solving the subject is trig I have an additional picture that is the answer options, I will send this to you
Answers
Given
[tex]f(x)=\tan x[/tex]To fill the blanks.
Now,
The grpah of f(x)=tanx is given as,
Therefore, from the graph,
[tex]\tan x=\tan (x+\pi)=\tan (x+2\pi)[/tex]Then,
[tex]\pi\text{ is the fundamental period of tanx.}[/tex]Also,
For x=0, tan(0)=0.
Therefore, the y-intercept is (0,0).
The points for the function f(x)=tanx is,
[tex]\begin{gathered} x=\frac{\pi}{3},\text{ y=tan(}\frac{\pi}{3})=\sqrt[]{3} \\ x=\frac{\pi}{4},y=\tan \frac{\pi}{4}=1 \end{gathered}[/tex]Since
[tex]\tan (-A)=-\tan A[/tex]Then, the points of the graph y=tanx is,
[tex](-\frac{\pi}{3},-\sqrt[]{3}),(-\frac{\pi}{4},-1),(0,0),(\frac{\pi}{3},\sqrt[]{3}),(\frac{\pi}{4},1)[/tex]Hence, the answer should be in the order,
i)
[tex]\pi[/tex]ii)
[tex](0,0)[/tex]iii)
[tex](-\frac{\pi}{3},-\sqrt[]{3}),(-\frac{\pi}{4},-1),(0,0),(\frac{\pi}{3},\sqrt[]{3}),(\frac{\pi}{4},1)[/tex]a top speed an object travels 3,200 millimeters in 4 seconds how many millimeters does the object travel each second
Answers
Write in words the meaning of P^2 - 7P.
Answers
Answer:
P squared minus 7 times P
Step-by-step explanation:
If Y Varies inversely as X. If Y=6 and X=10. FIND X when Y=18, correct to 3 significant figures.
Answers
Answer:
x ≈ 3.33
Step-by-step explanation:
given y varies inversely as x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
to find k use the condition y = 6 , x = 10
6 = [tex]\frac{k}{10}[/tex] ( multiply both sides by 10 )
60 = k
y = [tex]\frac{60}{x}[/tex] ← equation of variation
when y = 18 , then
18 = [tex]\frac{60}{k}[/tex] ( multiply both sides by k to clear the fraction )
18k = 60 ( divide both sides by 18 )
k = [tex]\frac{60}{18}[/tex] ≈ 3.33 ( to 3 significant figures )
If h = {(1,5), (-2,6), (4, -3), (6,9)} and
m = {(3,4), (2,-2), (-2,6), (5,8)}, what is (hm) (2)? (See image below)
Answers
Answer: [tex](h\circ m)(2) = 6[/tex]
=======================================================
Explanation:
The notation [tex](h \circ m)(2)[/tex] refers to function composition
It's the same as writing [tex]h(m(2))[/tex]
According to
m = {(3,4), (2,-2), (-2,6), (5,8)}
We have m(2) = -2 since x = 2 leads to m(x) = -2
Then the output -2 is treated as the input of the outer function h(x)
Looking through
h = {(1,5), (-2,6), (4, -3), (6,9)}
shows that h(-2) = 6
Therefore, [tex]h(m(2)) = h(-2) = 6, \ \text{ and } \ (h\circ m)(2) = 6[/tex]
Optionally we can write out a table like shown below.
The row highlighted shows the input x = 2 leading to m(x) = -2, which is then plugged into h(x) to get 6 as the final output. Think of it like a chain of dominoes.
Suppose that 12 inches of wire costs 60 cents.
At the same rate, how many inches of wire can be bought for 25 cents?
Answers
Answer:
5 inches of wire.
Step-by-step explanation:
60/12 = 5
So at .05 an inch, you can afford 5 inches at 25 cents
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Use the following stem and leaf plot to write out the individual numbers and calculate the mean, median and range for the data
Stem and leaf plot
4 1
5 2 7 8
6 5 6
7 0 5 8
8 0 1
9 5
Use the stem and leaf plot to the right to answer the questions below.
A. How many data values are in the set?
B. What is the greatest and least value from the set?
C. What is the median and range?
D. Is the value 85 in the data set? Explain.
Answers
Part A
Answer: 12Explanation: Count the number of leaves.
======================================================
Part B
Answers: Greatest = 95 , least = 41Reason:
Look at the largest stem (9) and the largest leaf of this largest stem (5).
This forms the largest value of 95.
The smallest value is 41 since it corresponds to the smallest stem and smallest leaf.
The term "min" and "max" are often used here.
======================================================
Part C
Answers: Median = 68, range = 54Explanation:
The data set is
41, 52, 57, 58, 65, 66, 70, 75, 78, 80, 81, 95
There are n = 12 items in this set.
Splitting in half gets us n/2 = 12/2 = 6.
The item in slot 6 is 66, and the next item over is 70.
The midpoint of these values is the median. (66+70)/2 = 68.
This midpoint rule only applies if n is even.
To find the range, we subtract the largest and smallest items.
range = max - min = 95 - 41 = 54
======================================================
Part D
Answer: No, 85 is not in the data setReason:
The stem 8 doesn't have a leaf of 5 attached to it.
It only has the leaves 0 and 1 to form the numbers 80 and 81.
Expand and simplify each polynomial (Answer both problems)
1. (a^2-3a)^2
2. (1/2x^3 +6x)^2
Answers
The simplified form of polynomials are:
1. (a² - 3a)² = 3a²
2. (1/2x³ + 6x)² = -12x²
Given,
We have to expand the given polynomials and simplify them.
1. The polynomial: (a² - 3a)²
Here,
The polynomial is in the form of (a - b)²
So,
(a - b)² = a² - 2ab + b²
Then,
(a² - 3a)² = (a²)² - (2 × a² × 3a) + (3a)²
(a² - 3a)² = a⁴ - 6a³ + 9a²
(a² - 3a)² = a²(a² - 6a + 9)
Here,
(a² - 6a + 9) is in quadratic form. Solve using quadratic formula.
a = 1, b = -6 and c = 9
[tex]\frac{-b(+-)\sqrt{b^{2} -4ac} }{2a}[/tex] = [tex]\frac{6(+-)\sqrt{(-6)^{2}-4(1)(9) } }{2(1)}[/tex] = [tex]\frac{6(+-)\sqrt{36 - 36} }{2}[/tex] = [tex]\frac{6(+-)\sqrt{0} }{2}[/tex] = (6±0) / 2
= 6/2 = 3
Then,
(a² - 3a)² = a²(a² - 6a + 9)
Here,
(a² - 6a + 9) = 3
So,
(a² - 3a)² = 3a²
2. The polynomial: (1/2x³ + 6x)²
Here, the polynomial is in the form (a + b)²
(a + b)² = a² + 2ab + b²
Here,
(1/2x³ + 6x)² = (1/2x³)² + (2 × 1/2x³ × 6x) + (6x)²
(1/2x³ + 6x)² = 1/4x⁶ + 6x⁴ + 36x²
(1/2x³ + 6x)² = x²(1/4x⁴ + 6x² + 36)
a = 1/4, b = 6 and c = 36
Quadratic formula: [tex]\frac{-b(+-)\sqrt{b^{2} -4ac} }{2a}[/tex]
= [tex]\frac{-6(+-)\sqrt{(-6)^{2} -4(1/4)(36)} }{2(1/4)}[/tex] = [tex]\frac{-6(+-)\sqrt{36-36} }{1/2}[/tex] = (-6±0) / (1/2) = -6 × 2 = -12
Therefore,
(1/2x³ + 6x)² = x²(1/4x⁴ + 6x² + 36)
Here,
(1/4x⁴ + 6x² + 36) = -12
Then,
(1/2x³ + 6x)² = -12x²
That is,
The simplified form of polynomials are:
1. (a² - 3a)² = 3a²
2. (1/2x³ + 6x)² = -12x²
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Which relation is a function?
Answers
a³ = 125
Each edge of the cube is
feet long.
Answers
Answer:
each cube is 5 feet long because 5*5*5 = 125
Step-by-step explanation:
Please help me with this (will give more credit for the best answer)
Answers
Answer:
1. 5ft
2. 2ft
3. 2ft
4. 1ft
Step-by-step explanation:
A store is having a sale in which all items
are discounted 20%. Including tax, Colin paid $21 for a picture. If the
sales tax rate is 5%, what was the original price of the picture?
Answers
In linear equation, that price of shorts before discount was $25
What in mathematics is a linear equation?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x).The dependent variable in this scenario is y since it depends on the independent variable, x.Assume that the price of shorts after the discount is x
Total payment = price of shorts + taxes
We know that:
total payment = $21
taxes = 5% = 0.05 of the price
This means that:
21 = x + 0.05x
21 = 1.05x
x = $20
Therefore, the price of the shorts is $20 after the discount
Now, we will get the price of the shorts before the discount:
Assume that the price of shorts before discount is y
We know that:
The discount was 20%
This means that Jennifer paid:
100% - 20% = 80% of the price of the shorts
Therefore:
80% of the price = $20
0.8y = 20
y = $25
This means that price of shorts before discount was $25.
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which fraction on the number line is equal to 3
Answers
Answer:
? can't answer if there's no number line
A cyclist leaves New York traveling at an average speed of 9 miles per hour. 4 hours later, a car leaves Bay Shore, on the same route, traveling at an average speed of 21 miles per hour. How many hours after the car leaves New York will the car catch up to the cyclist? *
Answers
The car will catch up with cyclist in 3 hours
What is time ?Time refers to the interval in seconds , minutes or hours it took for an event to take place
How to calculate How many hours it will take the car to catch up with cyclistInformation given for the question include
A cyclist has average speed of 9 miles per hour
A car leaves has average speed of 21 miles per hour
following same route when
The question is asking at what time will the distance be equal if the cyclists have advantage of 4 hours already
Calculation of distance covered by the cyclist
average speed = distance / time
distance = 9 mph * (x + 4)
Calculation of distance covered by the car
average speed = distance / time
distance = 21 mph * x
equating both gives
9 mph * (x + 4) = 21 mph * x
9x + 36 = 21x
36 = 21x - 9x
12x = 36
x = 3
hence the car will meet the cyclist in 3 hours
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50 points if this is correct i need this asap please
Which is the best definition of a two-step equation?
In a two-step equation, you must always start by using the division property of equality.
In a two-step equation, you need to use one inverse operation to solve.
A two-step equation is one that you need to use two properties of equality to solve.
A two-step equation is one that you need to use only a single property of equality to solve.
Answers
Answer:
c
Step-by-step explanation:
A two-step equation is one that you need to use two properties of equality to solve.
12. Six hundred people will buy tickets at $4 each
for a district championship game. For each 20¢
decrease in price, 50 more people will buy
tickets. Find the best ticket price, the maximum
income, and the corresponding number of
tickets.
Answers
Using concept of Quadratic Equation we got that best ticket price is $16, maximum income is $19,200 and the corresponding number of tickets are 1200.
What is Quadratic Equation?A Quadratic Equation is one of the following: f(x) = ax2 + bx + c, where a, b, and c are positive integers and an is not equal to zero. A parabola is basically a curve that represents the graph of a quadratic equation. Parabolas can open up or down, and their "width" or "steepness" can vary, but they all have the same basic "U" shape.
We know that,
No. of people who will buy tickets at $4 = 600
For each 20¢ decrease, additional no. of people buying tickets = 50
Revenue = (No. of tickets sold)(Pricing)
Revenue = (600+50x)(4+x)
= 50[tex]x^{2}[/tex] + 800x + 2400
Solving the quadratic equation we got,
x = -4 or -12
Since we're dealing with real-life entities such as money, we'll take the value of x as positive.
Taking x as 12 (higher value),
No. of tickets sold = 600 + 50x = 1200
Pricing = 4 + x = 16
Revenue = 1200×16 = $19,200
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Which of the following sentences properly uses semicolons in a serial list?
There is so much you can do to cut down on waste; such as composting, which uses food waste to help plants grow, recycling, which keeps plastic, metal, and glass out of landfills, and thrifting, which cuts down on clothing waste from fast fashion.
There is so much you can do to cut down on waste, such as composting, which uses food waste to help plants grow; recycling, which keeps plastic, metal, and glass out of landfills; and thrifting, which cuts down on clothing waste from fast fashion.
There is so much you can do to cut down on waste, such as composting; which uses food waste to help plants grow; recycling; which keeps plastic; metal; and glass out of landfills; and thrifting; which cuts down on clothing waste from fast fashion.
There is so much you can do to cut down on waste; such as composting; which uses food waste to help plants grow, recycling; which keeps plastic, metal, and glass, out of landfills, and thrifting; which cuts down on clothing waste from fast fashion.
Answers
The sentence that properly uses semicolons in a serial list is B. There is so much you can do to cut down on waste, such as composting, which uses food waste to help plants grow; recycling, which keeps plastic, metal, and glass out of landfills; and thrifting, which cuts down on clothing waste from fast fashion.
What are semicolons?A semicolon is a punctuation mark consisting of a period put on top of a comma.
Semicolons can be used for the following purposes:
To join two independent clauses without the coordinating conjunctions (and, but, or, nor, for, so, yet)As a serial listTo introduce evidence for a preceding statement.Thus, the proper use of semicolons in a serial list is Option B.
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Answer:
B. There is so much you can do to cut down on waste, such as composting, which uses food waste to help plants grow; recycling, which keeps plastic, metal, and glass out of landfills; and thrifting, which cuts down on clothing waste from fast fashion.
Step-by-step explanation: