Part (a)
Answer: y1 and y3 are perpendicularThis is because the two slopes 2 and -1/2 multiply to -1. Perpendicular slopes multiply to -1 assuming neither line is vertical or horizontal.
=====================================================
Part (b)
Graph each line to see where they cross. The three points of intersection are
(0,4)
(2,-2)
(4,2)
The order of the points doesn't matter.
You could also form three systems of equations pairing up the equations, and solving each system. That way you can find the points of intersection. Graphing may be a better and faster route in my opinion. See the diagram below.
Answer: c) y₁ and y₃ are perpendicular
Step-by-step explanation:
Perpendicular (⊥) means the lines have opposite (change the sign) and reciprocal (flip the fraction) slopes.
y₁ = 2x - 6
↓
m= 2
m⊥= -(1/2)
y₂ = -3x + 4
↓
m= -3
m⊥= +(1/3)
y₃ = -(1/2)x + 4
↓
m= -(1/2)
m⊥= +2
y₁ and y₃ have opposite reciprocal slopes so they are perpendicular to each other.
Gavin drew a circle with a circumference of 10π centimeters. Which best represents the area of Gavin's circle in square centimeters?
Answer:
78.5cm^2
Step-by-step explanation:
Circumference equation = 2πr with radius r
10π = 2πr so r = 10π/2π = 5
Area of circle = πr^2
π * 5^2 = π * 25 = 25π = 78.53981... = 78.5 cm^2
you are helping your sister plan her sweet 16. the venue you want to host it at charges $75 for every 3 guest as well as a rental deposit of $200 write an equation to determine the total party cost
Answer:
y = 25x + 200
Step-by-step explanation:
y = the total cost of the party
x = the number of guests
75/3 = 25
25 is the cost per guest.
Helping in the name of Jesus.
c or b???????????????
Answer:
i think it's b4
Step-by-step explanation:
Look at this table what value is missing from the table ?
Ok, it seems that the table gives the values of a function that reltes time and speed, to complete it we are gonna need to find that function.
if you saved your 76$ monthly allowance for 3 years, how much money would you have?
What base could be written in the blank to make the exponential function model 15% decay? y=(_)t1/2
The exponential function that models a 15% decay is: y = (0.85)^t^(1/2)
To find the base that could be written in the blank to make the exponential function model a 15% decay, we can start by understanding the nature of exponential decay.
The general formula for exponential decay is given by:
y = A(1 - r)^t
Where:
y represents the final amount or value after time t.
A is the initial amount or value.
r is the decay rate (expressed as a decimal).
t is the time.
In this case, we want to find the decay rate (r) that corresponds to a 15% decay. A 15% decay means that the final amount is 85% of the initial amount. So, we can write the equation as:
y = A(1 - 0.15)^t
Simplifying further:
y = A(0.85)^t
Comparing this equation to the given form y = (_)t^(1/2), we see that the base in the blank must be 0.85.
Therefore, the exponential function that models a 15% decay is:
y = (0.85)^t^(1/2)
This equation represents a scenario where the initial value or amount (A) is being reduced by 15% over time (t), with the exponent of 1/2 indicating that the decay occurs at a square root rate.
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Pat's income is 20 % more than Adam. How much percent is Adam's income less than Pat's?
Adam's income is 16.67% less than Pat's income.
Let's assume Adam's income is $100
Then Pat's income is 20% more than Adam's income, which means Pat's income is:
$100 + $20 = $120
Now, we need to find out how much percent Adam's income is less than Pat's income. We can use the following formula to calculate the percentage decrease:
Percentage decrease = (Decrease in value / Original value) x 100
Decrease in value is the difference between Pat's income and Adam's income, which is:
$120 - $100 = $20
The original value is Pat's income, which is $120
So, the percentage decrease in Adam's income compared to Pat's is:
(20 ÷ 120) × 100
= 0.16666 × 100
= 16.666%
= 16.67% (approx)
Therefore, Adam's income is 16.67% less than Pat's income.
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a certain number plus two is five find the number
x=3
Step-by-step explanation:
x+2=5
x=5-2
x=3
PLEASE WILL NAME BRAINLIST
The table shows the length y (in inches) of a person’s hair after x months.
months x: 0 3 6
hair Length y:11.0 12.5 14.0
a. Write and graph a linear function that relates y to x .
y=
b. Interpret the slope and the y-intercept
The slope indicates that the hair length increases by what
inch per month. The y-intercept indicates that the initial hair length is what
inches.
Which of the following is most likely the next step in the series?
B
Answer:
C
Step-by-step explanation:
The pattern seems to go as follows:
1. Top left portion is in blue
2. Top left portion is in blue as well as the rest of the upper half filled with red.
3. Another portion of blue is added directly underneath the red.
This leads me to believe that the colors are alternating from blue to red to blue to finally, red. This makes your answer C. Please let me know if you still need help!
True or false? ( 1x77x36x89x868x757x=68x88x88x765x7)
Answer:
false
Step-by-step explanation:
Answer:
TRUE
Step-by-step explanation:
Im sorry if im wrong
math math math math math math math
The angle m∠JIX is 90 degrees.
How to find angles in line intersection?IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.
IG bisect CIJ. Hence,
m∠CIG ≅ m∠GIJ
Therefore,
m∠CIX = 150 degrees
Hence, let's find m∠JIX.
Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.
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The measure of angle m∠JIX is estimated to be 90⁰.
How to find the angles?You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.
IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.
Frim the given parameters,
IG⊥CIJ.
But; m∠CIG ≅ m∠GIJ
⇒ m∠CIX = 150⁰
Hence, let's find m∠JIX.
Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.
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If 16= seven
nine = IV,
XLV =9
105= fourteen
and two = III
Then what is LXXXVIII?
Answer:
88
Step-by-step explanation:
L = 50, X = 10, V = 5, I = 1
LXXXVIII is: \((50*1)+(10*3)+(5*1)+3\)
This is going off of pure roman numerals, I don't know if there's a special system behind this.
edit: nvm there is
The value of LXXXVIII will be equal to 88
What will be the value of LXXXVIII?We know that
L=50
X=10
V=5
I=1
So from the above values
\(\rm LXXXVIII=(50\times1)+(10\times3)+(5\times1) +(3\times1)=88\)
Thus the value of LXXXVIII will be equal to 88
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Triangle FGH, with vertices F(-5,-7), G(-2,-5), and H(-6,-2), is drawn inside a rectangle, as shown below.
The area of the triangle FGH is equal to 13√10 unit²
Given that the vertices;
F(-5,-7), G(-2,-5), and H(-6,-2)
We have to find the area of the triangle as;
Area of triangle = 1/2bh²
Here,
Area of triangle FGH = 1/2 (GH) (FG)²
Now,
Length of FG = √26
Length of GH = √10
Then,
Area of triangle FGH = 1/2 (GH) (FG)²
Area of triangle = 1/2 × √10 × √26²
Area of triangle = 1/2 × √10 × 26
Area of triangle FGH = 13√10
Therefore,
The area of the triangle FGH = 13√10 unit²
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Find the x-intercept of the line graphed by the equation x - 7y = 7. (0, 14) (7, 0) (14, 0) (0, 7)
Dawn was driving at a steady speed of 67 mph for 10 minutes. How far did she travel in that time?
Answer:
11 1/6 miles
Step-by-step explanation:
10 min = 1/6hr
67 * 1/6 = 11 1/6 miles
In western music, an octave is divided into 12 pitches. For the film Close Encounters of the Third Kind, director Steven Spielberg asked composer John Williams to write a five-note theme, which aliens would use to communicate with people on Earth. Disregarding rhythm and octave changes, how many five-note themes are possible if no note is repeated?
Answer:
This should be a permutation
Step-by-step explanation:
P (n, r) = n!/(n-r)!
P (12,5) = 12!/(12-5)!
P (12,5) = 12!/7!
P(12,5) = 95040
I WILL GIVE THE BRAINIEST
A high school class is planning a field trip to an art museum in their city. The class collected a total of $1259 from all of the students, which will go towards renting a bus, museum admission, and lunch
However, a week before the trip 9 students had to drop out and their portion of the collected money had to be given back to them. Due to this, the students that are all still going must contribute an
Now let a be the number of students who went on the trip and s9 be the original number of students who had planned to go on the trip
What equation can be written to determine the number of students that went on this trip?
An equation can be written to determine the number of students that went on this trip is: C. \(\frac{1259}{s} + 12=\frac{1259}{s+9}\)
How to write an equation to determine the number of students that went on this trip?In order to write an equation to determine the number of students that went on this trip, we would have to assign a variable and an expression to the number of students who went on the trip and the original number of students who had planned to go on the trip as follows;
Let the variable s represent the number of students who went on the trip.Let the expression s + 9 represent the original number of students who had planned to go on the trip.Since a total of $1259 was collected from all of the students with 9 students dropping out and their portion of the money collected given back to them while the students that are all still going must contribute an additional $12, an equation to determine the number of students that went on this trip is given by;
\(\frac{1259}{s} + 12=\frac{1259}{s+9}\)
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Complete Question:
A high school class is planning a field trip to an art museum in their city. The class collected a total of $1259 from all of the students, which will go towards renting a bus, museum admission, and lunch.
However, a week before the trip 9 students had to drop out and their portion of the collected money had to be given back to them. Due to this, the students that are all still going must contribute an additional $12 each to cover all of the cost.
Now let s be the number of students who went on the trip and s + 9 be the original number of students who had planned to go on the trip
What equation can be written to determine the number of students that went on this trip?
what is the equivalent ratio of 2 over 9?
On the coordinate plane, plot the following points. Then, connect the points in order from A to E then back to A to form a figure. what is the area of the figure?
A (1, 2) B (1, 7) C (9, 7)
D (9, 3) E (6, 5)
The calculated area of the figure is 59/2 square units
Calculating the area of the figureFrom the question, we have the following coordinates that can be used in our computation:
A (1, 2) B (1, 7) C (9, 7) D (9, 3) E (6, 5)
The area is then calculated as
Area = 1/2 * | (x1y2 + x2y3 + ... + xny1) - (y1x2 + y2x3 + ... + ynx1) |
So, we have
Area = 1/2 * | (1 * 7 + 1 * 7 + 9 * 3 + 9 * 5 + 6 * 1) - (2 * 1 + 7 * 9 + 7 * 9 + 3 * 6 + 5 * 1) |
Evaluate
Area = 1/2 * 59
So, we have
Area = 59/2
Hence, the area is 59/2 square units
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A total if 713 tickets were sold. They were either adult or student tickets. There were 63 more student tickets sold than adult tickets. How many adult tickets were sold
There were 325 adult tickets sold that day student had 388 tickets
So, total no. of tickets = 713
Let the no. of tickets sold to adults be x
Then the no. of tickets sold to student = x + 63
Now, we have the equation as
⇒ x + x + 63 = 713
⇒ 2x = 713 - 63
⇒ 2x = 650
⇒ x = 650/2
⇒ x = 325 tickets
What is an equation?An equals symbol (=) is fundamental in equations. You can think of an equation as having a left-hand side and a right-hand side as there will be a mathematical expression on either side.
Imagine a set of scales to represent an equation. To solve it, each side must be balanced, even if you place different amounts on the left or right.
There is always an unknown in an algebraic equation. A symbol, such as x, y, or z, is used to symbolize this.
Here's an illustration of an equation:
y + 5 = 10
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Point A is located in which quadrant? On a coordinate plane, point A is at (negative 3, 5). Quadrant I Quadrant II Quadrant III Quadrant IV
Answer:
quadrant 2
Step-by-step explanation:
A survey asked people whether their pets are picky eaters. For theseresults, are being a picky eater and being a dog independent ordependent events? Justify your answer.PickyNot picky TotalCats111425Dogs61925Total173350A. Independent;P(picky) = 34%P(doglpicky) = 35%Since these probabilities are nearly equal, the events areindependent.B. Dependent;P(picky) = 34%P(pickyldog) = 24%Since these probabilities are not equal, the events aredependent.c. Dependent;P(picky) = 34%P(doglpicky) = 35%Since these probabilities are not equal, the events aredependent
Given:
The data table of the survey of pets is given.
Required:
Find results, are being a picky eater and being a dog with independent or dependent events.
Explanation:
The total number of pets = 50
The number of picky eater pets = 17
The probability of an event is given by the formula:
\(P=\frac{number\text{ of possible outcomes}}{Total\text{ number of outcomes}}\)The probability of randomly choosing a picky eater is:
\(\begin{gathered} P(picky)=\frac{17}{50} \\ P(picky)=0.34 \\ P(picky)=34\% \end{gathered}\)The total number of dogs = 25
The number of picky eater cats = 6
The probability of a picky eater dog
\(\begin{gathered} P(picky\text{ \mid cat \rparen=}\frac{6}{25} \\ P(picky\text{ \mid cat \rparen=0.24} \\ P(picky\text{ \mid cat \rparen=24}\% \end{gathered}\)We notice that both results are different. The fact that the pet selected is a dog changes the probability of P(picky).
This means the events are dependent.
Final Answer:
Option B is the correct answer.
Which of the following is true about the linear function 4x+2y=12
1.it has a slope of -2 and a y intercept of 6
2. It has a slope of -2 and a y intercept of 12
3 it has a slope of -1/2 and a y intercept of 6
4 it has a slope of -4 and a y intercept of 12
Answer:
i believe is 4
Step-by-step explanation:
If you 2y=-4x+12
need to get the Y by it self
40% of the plants in Marcy's garden are root vegetables. If 20 plants are root vegetables, how many plants are in Marcy's garden in all?
Answer:
dont do anything if im wrong but i thinks its 50 plants
Step-by-step explanation:
EPlease help me i don't know
this is 7 grade math :(
Answer: D, 1728
Step-by-step explanation: multiply the base, width and height
However, we must leave one inch at the top so 10 becomes 9
Working out- 24x8x9=1728
Which of the following is the fourth vertex needed to create a rectangle with vertices located at (−15, 3), (−15, −6), and (25, −6)?
(−6, 25)
(−25, −3)
(6, −25)
(25, 3)
The missing fourth vertex needed to create a rectangle is (25, 3) option D.
Define the term vertices?Vertices (singular: vertex) are the corners or points where two or more lines, edges, or curves intersect and form an angle.
Here, the width of one side of the rectangle;
⇒ +3 - (-6) = 9 unit (left side y-coordinates)
Similarly the length of the rectangle;
⇒ 25 - (-15) = 40 unit (up-side x-coordinates)
Since a rectangular shape has two sets of equal sides of equivalent width (y-coordinates) and length (x-coordinates), we realize that the missing fourth vertex should be 9 units and 40 units over the point (25, -6). and (-15, 3)
So, we add 9 to the y-coordinate of (25, -6) and add 40 to the x-coordinate of (-15, 3) to get the missing vertex:
⇒ (25, -6+9) = (25, 3)
⇒ (-15+40, 3) = (25, 3)
Therefore, the missing fourth vertex is (25, 3)
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1.
Anthony has a sink that is shaped like a half-sphere. The sink has a volume of 3000/3 π, in^3?. One day, his sink
clogged. He has to use one of two cylindrical cups to scoop the water out of the sink. The sink is completely
full when Anthony begins scooping.
(a) One cup has a diameter of 5 in, and a height of 6 in. How many cups of water must Anthony scoop
out of the sink with this cup to empty it? Round the number of scoops to the nearest whole
number. Show all your work.
(b) One cup has a diameter of 6 in, and a height of 6 in. How many cups of water must he scoop out of
the sink with this cup to empty it? Round the number of scoops to the nearest whole number.Show all your work
Answer:
a) 27
b) 19
Step-by-step explanation:
a) Calculate the volume of the the cup using volume of cylinder equation: \(V = \pi r^{2} h\)
Where V = Volume, r=radius, and h=height. Your answer should be in cubic inches (\(in^3\)).
You're given diameter, so use equation \(d/2 = r\) to find radius.
Substituting these equations will give you: \(V = \pi (d/2)^2 h\)
However, the given volume of the sink is 3000/3\(\pi\) or 1000\(\pi\), meaning that you should modify your results to match this value. Do not substitute \(\pi\) for 3.14..., leave it as a symbolic value. Your final V of the cup should = 37.5 \(\pi\)
Divide the volume of the sink by the volume of the cup. This number will be the amount of cups needed to empty it. In equation form:
\(Vsink / V cup =\) # of cups.
Note the the \(\pi\) will cancel each other out, so there's not need to factor that in.
b) Repeat the steps above with the new d (diameter) value.
Solve for x −ax + 2b > 8
Answer:
x < -( 8-2b) /a a > 0
Step-by-step explanation:
−ax + 2b > 8
Subtract 2b from each side
−ax + 2b-2b > 8-2b
-ax > 8 -2b
Divide each side by -a, remembering to flip the inequality ( assuming a>0)
-ax/-a < ( 8-2b) /-a
x < -( 8-2b) /a a > 0
Answer: \(x<\frac{-8+2b}{a}\)
\(a>0\)
Step-by-step explanation:
\(-ax+2b>8\)
\(\mathrm{Subtract\:}2b\mathrm{\:from\:both\:sides}\)
\(-ax>8-2b\)
\(\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\)
\(\left(-ax\right)\left(-1\right)<8\left(-1\right)-2b\left(-1\right)\)
\(ax<-8+2b\)
\(\mathrm{Divide\:both\:sides\:by\:}a\)
\(\frac{ax}{a}<-\frac{8}{a}+\frac{2b}{a};\quad \:a>0\)
\(x<\frac{-8+2b}{a};\quad \:a>0\)
243, 81, 27, 9, 3, 1
Which of the following is the next term in the geometric sequence show above?
A. \\\ -3
B. \\\\ -1
C. \ -1/3
D. \\\\\\\ 0
E. \\\\\\ 1/3
Answer:
E. 1/3
Step-by-step explanation:
In this sequence, the numbers are descending and are 1/3 of the previous number.
243 / 3 = 81
81 / 3 = 27
9 / 3 = 3
3 / 3 = 1
1 / 3 = 1 / 3 (the next term)