S is a subset within a universal set, U
If S = {x, y, 4, 9, ?}, which could
describe U?
U = {keys on a keyboard}
U = {letters}
U = {numbers}
U = {punctuation marks}
The solution is, U={ keys on a keyboard}, could describe U .
What is set?A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
Here, we have,
S is a subset of U,
so all of the elements of S must be also elements of U
If U was {letters}, 4, 9, ? would not belong there
If U was {numbers }, x, y, ? would not belong to U
If U was {punctuation marks }, 4, 9, x, y would not be in U
all the elements of S are in U={ keys on a keyboard}
Answer: U={ keys on a keyboard}, could describe U.
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Which expression is equal to
CSC X
- cOs x cot x
using identities?
Step-by-step explanation:
Because the two sides have been shown to be equivalent, the equation is an identity.
what is the measure of an angle if it is 660 less than 6 times its own supplement
Answer:
60
Step-by-step explanation:
Since this angle is unknown, let's just represent it with the variable "x". So the supplement angle of "x" is essentially, the value of the angle that we need to add to "x" to get 180. In other words let's just say that the supplement angle is "y". This means that: [tex]x+y=180[/tex]. If we subtract x from both sides we can represent "y" or the supplement angle as: [tex](180-x)[/tex].
Since it's 660 less than 6 times it's own supplement let's first multiply the supplement by 6
[tex]6(180-x) = 1,080-6x[/tex]
Now let's subtract 660 from it, since it's 660 less
[tex](1,080 - 6x) - (660) = 420 - 6x[/tex]
This value should be equal to the angle, which is represented as "x". So let's set it equal to x
[tex]420-6x=x[/tex]
Add 6x to both sides
[tex]420=7x[/tex]
Divide both sides by 7
[tex]60 = x[/tex]
The total surface area if a cylindrical can, whose height is equal to the radius of the base is 2464 cm^2, find its volume.
Step-by-step explanation:
TSA of cylinder = 2πr (h + r)
according to the question
height = radius
then,
TSA = 2πr (r + r)
2464=2 × 3.1415×r ×2r
2464/4 ×3.1415 = r×r
196.08 = r^2
r = 14.00
r = 1 4 cm
We know,
volume = 2πr ^2 ×h
=2×3.1415×14×14×14 (h=r)
=17240.552 cm^3
Answer:
8620.5 cm³
Step-by-step explanation:
h = r
SA = 2πrh + 2πr²
Since h = r, we can substitute h with r.
SA = 2πr² + 2πr² = 4πr²
4πr² = 2464 cm²
r = 14 cm
V = πr²h
r = h = 14 cm
V = π(14 cm)²(14 cm)
V = 8620.5 cm³
Find the area of a circle that has a radius of 9 mm. Use 3.14 for π.
254.34 mm²
56.52 mm²
63.59 mm²
28.26 mm²
Answer: 254,34 mm².
Step-by-step explanation:
[tex]S{circle}=\pi R^2\\S{circle}=3,14*9^2\\S{circle}=3,14*81\\S{circle}=254,34\ mm^2.[/tex]
Hi :)
Let's first find the area of this circle
—————————For finding the area of a circle we use
[tex]\longrightarrow\sf{A_{\circ}=\pi r^2}[/tex], where only r (radius) is squared
[tex]\textit{We know that :}\begin{cases} \sf{Radius = 9 mm} \\ \sf{\pi =3.14} \end{cases}}[/tex]
Thus
[tex]\longrightarrow\sf{A_{\circ}=3.14\cdot9^2}[/tex]
[tex]\longrightarrow\sf{A_{\circ}=3.14\times81}[/tex]
[tex]\longrightarrow\sf{\underline{A_{\circ}=254.34\: mm}}[/tex]
[tex]\tt{Learn\:More;Work\;Harder}[/tex]
:)
The graph of function f is shown. The graph of an exponential function passes through (minus 10, minus 1), (2, 8) also intercepts the x-axis at minus 2 units and y-axis at 2 units Function g is represented by the table. x -2 -1 0 1 2 g(x) 0 2 8 26 Which statement correctly compares the two functions? A. They have the same x-intercept and the same end behavior as x approaches ∞. B. They have the same x- and y-intercepts. C. They have the same y-intercept and the same end behavior as x approaches ∞. D. They have different x- and y-intercepts but the same end behavior as x approaches ∞.
The correct description that cab made of these graphs is that They have the same x- and y-intercepts.
What is the end behavior of a function?This is the term that is used to describe the behaviors of these functions as they approach infinity.
the y-intercept of a function
This is what is used to tell us the y value when we put x to be = 0
The y-intercept of f(x) is y = -2
The y-intercept of g(x) is y = -2
the x-intercept of a function
It is the value of x when y = 0.
The x-intercept = 2
The x-intercept = 2
Hence statement B is correct. They have the same x- and y-intercepts.
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Factor the GCF:-12x4y - 9x³y² + 3x²y³ (5 points)
O-3x²y(4x2 + 3xy - y²)
O 3x²y(-4x² + 3xy - y²)
O-3(4x²y + 3x³y² - x²y³)
O-3x²y(-4x2-3xy + y²)
Answer:
A. 3x^2y(4x2 + 3xy - y^2)
Step-by-step explanation:
-12(x^4)y - 9x³y² + 3x²y³
-3x²y(4x² + 3xy - y²)
Consider the first four terms of the sequence below. -3, -12, -48, -192, . . . what is the 8th term of this sequence?
Answer: -49152
Step-by-step explanation: the pattern here is that each term is subtracting 3 times its absolute value. Going from -3 to -12 there is a difference of 9 which is 3 times to absolute value of -3. So, the sequence will continue like this : -192, - 768, -3072, - 12288, -49152.
A pizza has a radius of 10 inches. A slice is removed. The length of the crust of the missing slice is 3 inches. What is the area of the missing slice?
The area of the missing slice is 15 inches ²
How to determine the area
From the information given, we can see that the pizza takes the form of a circle;
Area of the missing slice takes the shape of a triangle
Area of a triangle = 1/ 2 base × height
base = 10 inches
height = 3 inches
Area of missing slice = 1/ 2 × 10 × 3
Area = 1/ 2 × 30
Area = 15 inches ²
Thus, the area of the missing slice is 15 inches ²
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A gardener uses 1/3 of a liter of water to water 2/7 of a garden.
1 1 / 6 litres of water is needed to watering the entire garden at the given rate.
How to find the amount of water using rate?We need to find how many litres of water is needed to watering the entire garden at this rate.
Let the total garden be x parts then,
Therefore,
2 / 7 x = 1 / 3
cross multiply
2x × 3 = 7
6x = 7
divide both sides by 6
6x / 6 = 7 / 6
x = 1 1 / 6
Therefore, Thus, 1 1 / 6 litres of water is needed to watering the entire garden at the given rate.
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What is [tex]\frac{a+3}{8}[/tex] x [tex]\frac{2}{a}[/tex]
Answer: [tex]\frac{2a+6}{8a}[/tex]
Step-by-step explanation:
[tex]\frac{2(a+3)}{8a}=\frac{2a+6}{8a}[/tex]
ind the present value that will grow to $4000 if the annual interest rate is 8.5% compounded quarterly for 9 yr.
Answer:
$1876.31
Step-by-step explanation:
The present value can be found using the compound interest formula.
Present valueThe formula for the future value of an investment of P earning annual interest rate r compounded n times per year for t years is ...
FV = P(1 +r/n)^(nt)
Filling in the known values gives ...
4000 = P(1 +0.085/4)^(4·9) = P(1.02125^36)
Then the amount to be invested is ...
P = 4000/1.02125^36 ≈ 1876.31
The present value is $1876.31.
please help I'm so tired and I need to turn this in tomorrow
Considering the given box plots, it is found that:
a) They had the same IQR.
b) Athlete A went on the shortest training ride.
c) Athlete B went on more rides longer than 35 miles.
d) Athlete B had a greater median distance.
What is a box plot?It is a plot that focuses the interquartile range of the population, which is the difference between the third and the first quartile, but gives a five number summary of the population, composed by these following measures.
The smallest value.The first quartile.The median.The third quartile.The highest value.Hence, for Athlete A, we have that:
The smallest value is 12.The first quartile is 27.The median is of 29.The third quartile is 34.The highest value is of 45.IQR: 34 - 27 = 7.For Athlete B, we have that:
The smallest value is 18.The first quartile is 32.The median is of 37.The third quartile is 39.The highest value is of 41.IQR: 39 - 32 = 7.Hence:
a) They had the same IQR.
b) Athlete A went on the shortest training ride.
c) Athlete B went on more rides longer than 35 miles(as it is less than his median).
d) Athlete B had a greater median distance.
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DIVINE TOK A MATH TEST AND GOT 36 CORRCET AND 9 INCORRECT WHAT WAS THE PERCANTHGE OF CORRECT ANSWERS
Answer: 80% correct
Step-by-step explanation:
If Divine got 36 correct and 9 incorrect, then we can find the total number of questions.
36 + 9 = 45 questions
Now, we will divide the number of questions answered correctly by the total number of questions.
[tex]\displaystyle \frac{36}{45} =0.8[/tex]
Lastly, we will multiply it by 100 to find the percentage.
0.8 * 100 = 80%
Answer:
80% was correct.
Step-by-step explanation:
The total number of questions is 45 (36 + 9). The percentage is the part correct over the total.
36/45 = .8. The answer is given in the decimal form. To change a decimal to a percent, move the decimal two places to the right.
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
C (Third option)
Step-by-step explanation:
The prime factorization of 675 is 5*5*3*3*3 or 5^2*3^3. With the square root, we take out all square integers, leaving (5*3)(sqrt3). The answer is 15(sqrt3) or C.
Break
√225×3√225√3√15²√315√3Option C
A number, h, rounded to 1 d.p. is 47.2
Another number, k, rounded to 1 d.p. is 4.8
What are the lower and upper bounds of
h - k?
The lower and upper bounds of h - k are 42.31 and 42.49 respectively.
Upper and lower bounds are the maximum and minimum values that a number could have been before it was rounded. They can also be called limits of accuracy.
The upper and lower bounds can be written using error intervals
The lowest value of h is 47.15
The greatest value of h is 47.24
The greatest value of k is 4.84
The lowest value of k is 4.75
Thus upper bound of h -k = 47.24 - 4.75 = 42.49
Thus lower bound of h -k = 47.15 - 4.84 = 42.31
Thus the lower and upper bounds of h - k are 42.31 and 42.49 respectively.
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Stuck on this problem. Help is needed please!
Step-by-step explanation:
A.
the height, the 17cm leg and half of the baseline (16/2 = 8cm) create a right-angled triangle.
so, Pythagoras applies.
c² = a² + b²
c being the Hypotenuse (side opposite of the 90° angle).
so, we get
17² = height² + 8²
289 = height² + 64
225 = height²
height = sqrt(225) = 15cm
B.
the answer to this is the surface area of the whole box.
it has 5 sides :
bottom : 20×16 rectangle = 320 cm²
left and right : 20×17 rectangles = 340×2 = 680 cm²
front and back : 16×15/2 triangles = 120×2 = 240 cm²
in total that is
320 + 680 + 240 = 1,240 cm² of cardboard
HELP ASAP
Consider functions H and K
What is the value of (h o k)(2)?
and look at this graph and please tell me what the answers are
Answer:
-3
Step-by-step explanation:
(h o k)(2) means
h( k(2)).
Remember when you have a function like f(x) or g(x) or h(x) or k(x), whatever number (or expression) is inside of the parenthesis, they're telling you to use that in place of x.
What h( k(2) ) means is we're going to put k(2) into h.
Well, what's k(2)? We need to find that first. k(x) is given as the oval and arrows thing going on there. If we're looking for k(2) then 2 is being the x. Find 2 in the first oval, follow the arrow to the output which is k(2).
If x = 2, the k(2)= -2
So back to
(h o k)(2):
(h o k)(2)
= h( k(2) )
= h(-2)
Since h(x)= 3/x+1
and x is -2, we'll put -2 in place of x.
h(-2) = 3/-2+1
= 3/-1
= -3
Assuming that any increase occurs in whole dollar amounts, what is the maximum possible increase that maintains the desired minimum revenue? explain why this is true.
The desired minimum revenue is $130.
What is revenue?
Revenue, which is determined by multiplying the average sales price by the quantity of units sold, is the money made from regular business operations. The top line (or gross income) figure is what is used to calculate net income by deducting costs. Sales are another name for revenue in the income statement.
The money received from routine business activities is referred to as revenue, sales, or the top line.Revenue (from the sale of goods or services) less operational expenses equals operating income.Non-operating income is irregular or irregular money that comes from other sources (e.g., lawsuit proceeds).Governments, nonprofit organizations, and private persons are examples of non-business entities that also declare revenue, albeit their methods and resources vary.Let us assume,
charge = b
customer= c
revenue= r
We know that,
r= bc
⇒ [tex]r=16\times 10[/tex]
⇒ [tex]r=\ 160[/tex]
Also,
[tex]b+1[/tex] ⇒ [tex]c-2[/tex]
with a target of [tex]r \geq 130[/tex]
Therefore,
[tex]b=10+x[/tex] ⇒ [tex]c=16-2x[/tex]
[tex](10+x)(16-2x)\geq 130\\160-20x+16x-2x^2 \geq 130\\-2x^2 -4x+30\geq 0\\x^2+2x-15\leq 0\\(x+1)^2 \leq 4^2\\x+1 \leq 4[/tex]
as negative value is not considered.
[tex]x\leq 3[/tex]
We get the result that [tex]\[/tex]3 is the maximum increase amount.
Therefore, revenue will be:
[tex](10+3)(16-3\times2)=13\times 10\\[/tex]
revenue = [tex]\[/tex]130
Full Question: Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose the buffet as their meal every hour. After surveying several customers, Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour. Noah wants to model this situation with an inequality and use the model to help him make the best pricing decisions. Assuming that any increase occurs in whole dollar amounts, what is the maximum possible increase that maintains the desired minimum revenue? Explain why this is true.
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Answer:
The desired minimum revenue is $130.
What is revenue?
Revenue, which is determined by multiplying the average sales price by the quantity of units sold, is the money made from regular business operations. The top line (or gross income) figure is what is used to calculate net income by deducting costs. Sales are another name for revenue in the income statement.
Step-by-step explanation:
Worked out for me :)
How long does it take for millions of dollars worth of emerald transactions to occur in bogota? a year three months a day a week
Answer: It will be A Day
Step-by-step explanation:
2/5x + 7/8y - 4/15x - 1/4y=?
Answer:
Simplified: 2x/15 + 5y/8
Step-by-step explanation:
Simplify the expression.
Answer:
Answer: 2x/15 + 5y/8
Step-by-step explanation:
Just Simplify the expression dude.
It’s the start of a new football season and my favorite team, the WACO Hawks, is looking good! They won their first
game by beating Dublin Irish 28-27 on a last second play.
In the course of the game they piled up a lot of running yards, divided among four players:
• The bruising fullback, Vernon Variable, accounted for a chuck of those yards.
• The star halfback, Reggie Root, ran for 15 less than three times as many yards as Vernon did.
• The speedy wide-out, Larry Linear, only ran once but he picked up 11 more yards than Vernon’s total on that
play, a fancy reverse that went for a touchdown.
• The crafty quarterback, Quentin Quadratic, ran for a total of 18 yards on a variety of scrambles.
If the WACO Hawks ran for 229 yards, how many yards did each of the four players gain? Remember to define a
variable, write an equation, and explain your work (focusing on the why you did what you did)
Vernon Variable ran 43 yards, Reggie Root ran 114 yards, Larry Linear ran 54 yards, and Quentin ran 18 yards.
How to solve Linear Equations Word Problems?We are told that the total number of yards the WACO Hawks ran is 229. Thus, we can say that: W = 229
Now, we know that Vernon Variable gained many yards. Thus, the amount of yards will be indicated by "V"
Now, Reggie Root ran for 15 less than three times as many yards as Vernon did. Thus, distance Reggie root ran is represented by;
R = 3V-15
Larry Linear picked up 11 more yards than Vernon’s total. Thus, total yards by Larry Linear is: L = V + 11
Quentin Quadratic ran a total of 18 yards. Thus; Q=18.
Now, all of the player's totals add up make what the total team ran. Thus, the expression is;
V + 3V - 15 + V + 11 + 18 = 229
Simplifying this gives;
5V + 14 = 229
5V + 14 = 229
Subtract 14 from both sides to get;
5V = 215
Divide both sides by 5 to get;
V = 43
Thus, Vernon ran a total of 43 yards.
Total run by Reggie is:
R = 3(43) -15
R = 129 - 15
R = 114 yards.
Total run by Larry:
L = V + 11
L = 43 + 11
L = 54 yards.
Thus, we conclude that Vernon Variable ran 43 yards, Reggie Root ran 114 yards, Larry Linear ran 54 yards, and Quentin ran 18 yards.
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Which equation represents the relationship shown in the
graph?
pleasee mwa mwa mwa help me
Answer: About (-2.414, 0) and (0.414, 0)
Step-by-step explanation:
Let us graph the equation given and see what the x-intercepts are. These are points where the line intercepts the x-axis. See attached.
This means our x-intercepts are at about (-2.414, 0) and (0.414, 0).
These are also equal to [tex]-1-\sqrt{2}[/tex] and [tex]-1+\sqrt{2}[/tex]
Answer:
[tex]x = \bold{0.414} \textrm{ and } x= \bold{-2.414}[/tex]
Step-by-step explanation:
See attached graph for a visual
The x-intercepts of a graph are where the graph crosses the x-axis ie where the value of y = 0 The equation of the graph is y=-x^{2}-2x+1
Setting y = 0 and solving for the resultant equation will provide the x-intercepts
[tex]0=-x^{2}-2x+1or-x^{2}-2x+1=0[/tex]
Reversing the signs gives us
[tex]x^{2}+2x-1=0[/tex]
This is a quadratic equation of the form [tex]ax^{2}+bx+c=0[/tex] with a = 1, b = 2 and c=-1
For an equation of this form the roots of the equation ie the values of x which satisfy the equation are given by
[tex]\frac{-b\pm\sqrt{{b^{2}-4ac}}}{2a}[/tex]
Substituting we get the two roots as
[tex]x=\frac{-2\pm\sqrt{{2^{2}-4(1)(-1}}}{2}=\frac{-2\pm\sqrt{{4-(-4)}}}{2}x=\frac{-2\pm\sqrt{8}}{2}8 = 4(2)\sqrt{8}=\sqrt{4}\sqrt{2} = 2\sqrt{2}[/tex]
So the two roots are
[tex]x=\frac{-2\pm2\sqrt{2}}{2}[/tex]
Dividing by 2 we get the two roots(x-intercepts) as
[tex]x=-1\pm\sqrt{2}\\\\x_{1}=-1+\sqrt{2} =-1+1.414=\bold{0.414}[/tex]
[tex]x_{2}=-1-\sqrt{2}=-1-1.414=\boldsymbol{-2.414}[/tex]
On June 10, Bertha Wooten deposited $8,241.78 in a savings account that pays 5.5% interest compounded
daily. How much interest will the money earn in 31 days?
The amount of interest that Bertha Wooten's deposit will earn in 31 days is $38.59, which is the difference between the future value and the present value.
What is the future value?The future value represents the amount that will be in the account after the present value investment is compounded at an interest rate periodically.
The future value of an investment can be calculated using the future value formula, A = P (1 + i)^n.
Where:
A = future value
P = Present value of investment
i = interest rate
n = number of periods.
The future value of the investment can also be determined using an online finance calculator, as follows.
Then the interest is the difference between the future value and the present value.
Data and Calculations:Initial deposit = $8,241.78
Interest rate = 5.5% compounded daily
Investment period = 31 days
N (# of periods) = 31 days
I/Y (Interest per year) = 5.5%
PV (Present Value) = $8,241.78
PMT (Periodic Payment) = $0
Results:
FV = $8,280.37
Total Interest $38.59 ($8,280.37 - $8,241.78)
Thus, the amount of interest that Bertha Wooten's deposit will earn in 31 days is $38.59.
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The function p(x) = 2x +1 determines how many pizzas need to be purchased for an after school meeting, where x is the number of students at the meeting. The club leader uses r(p(x)) to find the amount of money to bring for the pizza purchase. The function r(x) = 4x − 3. Solve for how much money to bring when there are 9 students in the meeting. (6 points)
Answer:
The club leader needs $73 for pizzas for 9 students.
Step-by-step explanation:
p(x) = 2x +1
r(x) = 4x − 3
r(p(x)) = 4(2x +1) − 3
r(p(x)) = 8x +4 − 3
r(p(x)) = 8x +1
r(p(9)) = 8(9) +4 − 3
r(p(9)) = 72 +1
r(p(9)) = $73
A bank loans a family $90,000 at 4.5% annual interest rate to purchase a house. The family agrees to pay the loan off by making monthly payments over a 15 year period. How much should the monthly payment be in order to pay off the debt in 15 years? Show all your calculations
Using it's formula, it is found that the monthly payment should be of $688.49 in order to pay off the debt in 15 years.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.For this problem, the parameters are given as follows:
A = 90000, r = 0.045, n = 15 x 12 = 180.
Hence:
r/12 = 0.045/12 = 0.00375.
Then we solve for A to find the monthly payment, as follows.
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 90000(0.00375)\frac{(1.00375)^{180}}{(1.00375)^{180} - 1}[/tex]
A = $688.49
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Consider a single spin of the spinner. A spinner contains 4 equal sections: 1, 2, 4 and 3. Sections 1 and 4 are shaded. The spinner is pointed at number 2. Which events are mutually exclusive
Answer:
Events that mutually exclusive are 1. Landing on a shaded portion and landing on a 3.2. Landing on an unshaded portion and landing on a number less than 2.
Blue points, blue line segments, red points, and red line segments arranged on a Cartesian coordinate plane. Here are the blue points and their coordinates. Point A: (negative nine, 3). Point B: (negative 11, 3). Point C: (negative 10, 3). Point D: (negative 10, 5). Point F: (negative 10, 4). Point E: (negative 11, 4). Here are the red points and their coordinates. Point A-1: (negative 1, 6). Point A-2: (negative 3, 4). Point B-1: (negative 2, 4). Point B-2: (negative 5, 4). Point C-2: (negative 3, 3). Point D-1: (negative 5, 5). Point D-2: (negative 5, 3). Point E-1: (negative 6, 6). Point F-1: (negative 5, 6). A semicircle that lies below its line of symmetry AB. A semicircle that lies above its line of symmetry B-2 A-2. A triangle DEF. A triangle D-1 E-1 F-1. Line segments are drawn from C to D, from A-1 to B-1, from A-2 to B-2, and from C-2 to D-2. Triangle DEF, segment CD, and the semicircle with line of symmetry BA are arranged so that they look like a boat.
1. What transformations would you use on the blue segment CD to get it to match with the red segment C2D2? Explain your movement using the coordinates of the vertices.
2.
What transformations would you use on the blue triangle to get it to match with the red triangle? Explain your movement using the coordinates of the vertices.
3.
Which line segments on the boat are parallel? Explain your answer.
4.
Which line segments on the boat are perpendicular? Explain your answer.
5.
Which line segments on the boat have a slope of 0? Explain your answer.
6.
Which line segments on the boat have an undefined slope? Explain your answer.
7.
What is the slope of ED? Explain your answer using the change in coordinates given that E is at (−11,4) and D is at (−10,5).
The transformations that would be used on the blue segment CD to get it to match with the red segment C2D2 is to effect a 180° clockwise rotation, so that C remains at (3, -10) and D assumes (3, -11). Recall that original coordinates were: C (3, -10); D (5, -10).
What is transformation in math?A transformation is a broad phrase covering four distinct methods of changing the shape and/or location of a point, line, or geometric figure.
The pre-Image is the original shape of the item, and the Image during the transformation is the final shape and location of the object. The following are different types of transformation in math:
TranslationRotationReflection; and Dilation.What transformations would you use on the blue triangle to get it to match with the red triangle?The type of transformation that will be used here is called reflection.
D retains it's original coordinates of (5, -10); E goes to (6, -11) and F (6, -10).
Which line segments on the boat are parallel?The line with the coordinates [(4, -11) and (4, -10) that is EF is parallel to [(3,-11) and (3, -10).
Parallel lines are lines that are always the same width apart in a plane. Parallel lines never cross.
Which line segments on the boat are perpendicular?The lines that are perpendicular are: AB with coordinates A(3, -9) & B(3, -11) and CD with coordinates (3, -10) and (5, -10). Lines that intersect each other forming a right angle are called perpendicular lines.
The line segments on the boat that have a slope of zero are:
EF, AB AC, BC. A line with zero slope is one that has a constant value shown along the y-axis that does not vary over the line's points.
The line segments on the boat that are undefined are:
CD, CF, and DF. The gradient or slope of any vertical line that travels up or down is the undefined slope.
The slope (m) is calculated as:
(Y2-Y1)/(X2 - X1)
Given that:
Y1 = 5
Y2 = 4
X1 = -10
X2 = -11
Hence,
m = (5-4)/(-11 -10)
m = -0.048
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A horizontally thrown dart falls 5 cm before it travels 2. 5 m to hit the dart board. how fast was it thrown?
The dart player throws a dart horizontally at a speed of 24.75 m/s.
In this question,
The horizontal distance traveled by the dart, x = 2.5 m
The dart hits the board 5 cm below the height from which it was thrown.
⇒ 5 cm = 0.05 m
Let the time taken by the dart to hit the board is t.
The time taken can be calculated using the Newton's second law of motion,
[tex]y = ut+\frac{1}{2}at^{2}[/tex]
Put, u = 0, a = -g and g = 9.8
On substituting the above values, we get
⇒ [tex]-0.05 = 0-\frac{1}{2}(9.8)t^{2}[/tex]
⇒ [tex]0.05(\frac{2}{9.8}) = t^{2}[/tex]
⇒ [tex]t^{2} =0.0102[/tex]
⇒ [tex]t=\sqrt{0.0102}[/tex]
⇒ t = 0.1010 s
Now, the velocity (speed) can be calculated as
displacement = speed × time
⇒ 2.5 = speed × 0.1010
⇒ speed = [tex]\frac{2.5}{0.1010}[/tex]
⇒ speed = 24.7524 m/s
Hence we can conclude that the dart player throws a dart horizontally at a speed of 24.75 m/s.
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