The equation of the ordered pairs (1, 4), (–1, 2), and (0, 3) is y = x + 3
How to determine the equation?The ordered pairs are given as:
(1, 4), (–1, 2), and (0, 3)
From the above ordered pairs, we can see that the difference between the x and y values is 3.
This means that:
y - x = 3
Add 3 to both sides
y = x + 3
Hence, the equation of the ordered pairs (1, 4), (–1, 2), and (0, 3) is y = x + 3
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Given lJK , which is an isosceles right triangle, IJ=4 and m
Answer:
[tex]IK = IJ\sqrt{2}[/tex]
Step-by-step explanation:
First, it's an isosceles right triangle, which means there is a 90 degree angle and the two other angles are equal.
To find what the two other angles are, you can set up a quick equation:
let x be angle
90 + 2x = 180, since the sum of the interior angles in a triangle is always 180.
then,
[tex]2x = 90\\x = 45[/tex]
Therefore, the triangle is a 45-45-90 triangle.
You have the measure of IJ, which is one of the legs of the triangle. The way you can find the length of the hypotenuse of a 45-45-90 triangle is by multiplying the length of one of the legs by [tex]\sqrt{2}[/tex].
This means the equation is [tex]IK = IJ\sqrt{2}[/tex]
Answer:
[tex]\sf IK=IJ\sqrt{2}[/tex]
Step-by-step explanation:
The interior angles of a triangle sum to 180°. Therefore, if ΔIJK is an isosceles right triangle where m∠J = 90°:
vertex is m∠J = 90°two base angles are m∠K and m∠ITo calculate the base angles:
⇒ m∠K + m∠I + m∠J = 180°
⇒ m∠K + m∠I + 90° = 180°
⇒ m∠K + m∠I = 90°
⇒ m∠K = m∠I = 45°
Therefore, IJ and JK are the legs of the right triangle and IK is the hypotenuse.
To find the length of the hypotenuse, use Pythagoras' Theorem.
Pythagoras’ Theorem: [tex]\sf a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Given:
a = IJ = 4b = JK = 4c = IKSubstitute the given values into the formula and solve for IK:
[tex]\sf \implies IJ^2+JK^2=IK^2[/tex]
[tex]\sf \implies 4^2+4^2=IK^2[/tex]
[tex]\sf \implies IK^2=32[/tex]
[tex]\implies \sf IK=\sqrt{32}[/tex]
[tex]\implies \sf IK=\sqrt{16 \cdot 2}[/tex]
[tex]\implies \sf IK=\sqrt{16}\sqrt{2}[/tex]
[tex]\implies \sf IK=4\sqrt{2}[/tex]
As IJ = 4 then:
[tex]\implies \sf IK=IJ\sqrt{2}[/tex]
What is the missing reason in the proof?
A.) Segment addition
B.) Congruent Segments Theorem
C.) Transitive Property of Equality
D.) Subtraction Property of Equality
Answer:
I think it's C. transitive property of equality
AB is a common external tangent to circles D and C. The points of tangency are at A and B. DC = 13, BC = 2 and AD = 7.
Find AB.
Based on the calculations, the length of side AB is equal to 13.93 units.
How to find the length of AB?Since the points of tangency are at A and B, we would determine the side length of the point lying between side A and D as follows:
AM = AD - BC
AM = 7 - 2
AM = 5 units.
Now, we can determine the length of side AB by applying Pythagorean's Theorem:
AB² = BM² + AM²
AB² = 13² + 5²
AB² = 169 + 25
AB = √194
AB = 13.93 units.
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A survey found that 50% of teenagers prefer to watch a movie at a theater over other viewing options. You want to know the estimated probability that three out of four randomly chosen teenagers do not prefer watching a movie at a theater. How could you design a simulation for this situation?
To design a simulation for this situation, one can generate a set of four numbers by using the number generator with numbers 0 to 5 representing those who prefer watching a movie at a theatre and 6 to 9 representing those who do not.
How to depict the information?From the information given about the probability, the goal here is to design a simulation for this situation.
In this case, to design a simulation for this situation, one can generate a set of four numbers by using the number generator.
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can someone please help me(20 points and I will give brainliest!!!)
Answer:
a)(0,k)
b)(0,-k)
Step-by-step explanation:
Finding the vertex: Using calculusGiven:
[tex] \begin{cases} y = a {x}^{2} + k \\ y = a {x}^{2} - k \end{cases}[/tex]
Taking the derivative of y's yields
[tex] \begin{cases} y '= \dfrac{d}{dx} a {x}^{2} + k \\ \\ y '= \dfrac{d}{dx} a {x}^{2} - k \end{cases} \\ \implies\begin{cases} y '= 2a x\\ \\ y '=2ax\end{cases} [/tex]
Now set y' to 0 and solve for x:
[tex] \implies\begin{cases} 2a x = 0\\ \\ 2ax = 0\end{cases} \\ \implies\begin{cases} x= 0\\ \\ x= 0\end{cases} [/tex]
plug in the value of x into the original equation thus
[tex] \begin{cases} y = a ({0}^{2}) + k \\ y = a ({0}^{2} )- k \end{cases}\\ \implies \begin{cases} y = k \\ y= - k \end{cases} [/tex]
Hence,
a. vertex (0,k)b. vertex (0,-k)find the domain of the function of the graph.
Answer:
[-3, 5)
Step-by-step explanation:
At x = -3, the circle is filled in, so -3 is part of the domain. At x = 5, the circle is not filled in, so 5 is not part of the domain. So the domain is [-3, 5).
if each element in the input is mapped to one element in the output, then the relation is called as a
Answer:
function
Step-by-step explanation:
Skf theatre bought a movie license for rs. 1,500 per week. the cost of keeping the stuff and the hall is rs. 20,000 per month. if they charge rs. 10 per seat, then how many people would have to see the movie in the first four weeks in order for them to recoup the costs?
Answer:
21500
Step-by-step explanation:
21500 people would have to see the movie to recuperate their losses.
The number of people would have to see the movie is given by the equation A = 2600 people
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of people to see the movie in first four weeks be A
Now , the equation will be
The cost of movie license per week = ₹ 1500
The cost of movie license per month = 4 x ₹ 1500
The cost of movie license per month = ₹ 6000
And ,
The cost of keeping the stuff and hall for a month = ₹ 20,000
So ,
The cost of movie license and the hall for a month = 20,000 + 6000
The cost of movie license and the hall for a month = ₹26,000
The cost of charge of each seat = ₹ 10
So , the number of people to see the movie in the first four weeks in order for them to recoup the costs A = cost of movie license and the hall for a month / cost of charge of each seat
Substituting the values in the equation , we get
Number of people to see the movie in first four weeks A = 26000/10
Number of people to see the movie in first four weeks A = 2600 people
Hence , the number of people is 2600 people
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Two sets of values are given below.
set 1: 29 , 31 , 27 , 33 , 30
set 2: 33 , 31 , 26 , 31 , 29
Which of the following conclusions can be drawn about the means of these two sets?
A. The mean for set 2 is equal to the mean for set 1.
B. The medians of both sets are equal to the means of both sets.
C. The mean for set 2 is lower than the mean for set 1.
D. The mean for set 2 is higher than the mean for set 1.
The correct option is the mean for set 2 is equal to the mean for set 1. (option A).
What is the true option?
Mean is a measure of central tendency that is used to determine the average of a set of numbers.
Mean = sum of the numbers / total number
Mean of set 1 = (29 + 31 + 27 + 33 + 30) / 5
= 150 / 5 = 30
Mean of set 1 = (33 + 31 + 26 + 31 + 29) / 5
= 150 / 5 = 30
Median is the measure of center of a dataset. It determines the value that is at the center of a dataset that is arranged in either ascending or descending order.
Set 1 arranged in ascending order : 27, 29, 30, 31, 33
Median of set 1 = 30
Set 2 arranged in ascending order : 26, 29, 31, 31, 33
Median of set 2 = 31
Differnce in the median = 31 - 30 = 1
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Question 11 of 25
What is an equation of the line that is perpendicular to y + 1 = -3(x-5) and
passes through the point (4, -6)?
Ay-6--(x+4)
OB. y-6=3(x+4)
C. y+6=(x-4)
D. y+6=-3(x-4)
SUBMIT
Answer: y+6 = 1/3(x-4
The equation of line perpendicular to the given line and passes through the point P ( 4 , -6 ) is y + 6 = ( 1/3 ) ( x - 4 )
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
y + 1 = -3 ( x - 5 )
So , the slope of the line is m = -3
Now , the lines are perpendicular , so the slope of the line m₂ is
m₂ = 1/3
Let the first point be P ( 4 , -6 )
And , the equation of line is y - y₁ = m ( x - x₁ )
On simplifying , we get
y - ( -6 ) = ( 1/3 ) ( x - 4 )
y + 6 = ( 1/3 ) ( x - 4 )
Hence , the equation of line is y + 6 = ( 1/3 ) ( x - 4 )
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find L.C.M. of:
a) 3 x (x + 1) (x-1) and 2x² (x-1) (x+3).
Answer:
f
Step-by-step explanation
Question 9 of 30 If f(x) = 3*-¹ + 4 and g(x) = 4x-7, what is (f - g) (x) ? O A. (f - g)(x) = 3*-1 - 4x-11 B. (f - g)(x) = 3*-1 - 4x +11 C. (f - g)(x) = 3*-1 - 4x+3 O D. (f-g)(x) = 3×-¹ - 4x - 3 NEED HELP ASAP
Answer:
I really don't know
Step-by-step explanation:
what is even that
someone help me asap pleaseee!!
Answer:
B is correct.
Find the range of the given function y = 5x + 2, where x > -2
The range of the function given the domain x > -2 is; Range; y < -8.
What is the range of the function?The range of a function is the set of all possible outcomes of the function. In this scenario, since the domain of the function is given as X > -2. It follows from the function that at all times, the range of the function is given by; y < -8 from; y < 5(-2) +2; y< -8.
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tch and his brother, Terry, went on a hiking expedition. Starting at sea level, the brothers climbed to a scenic cliff located 6.6 kilometers above them. From there, they descended 1.3 kilometers in one hour. Mitch discovered that he had left behind some essential supplies on the cliff. So, the brothers decide to head back up. They climbed 0.8 kilometer within the next hour. At this point, Mitch and Terry were
away from the scenic cliff.
Mitch and Terry were 0.5 km away from the scenic cliff
What is Sea Level ?Sea level is the base for calculating the depth and the elevation of Earth
It is given that
Total Height of the scenic Cliff = 6.6km
After 1 hour the brothers are at = 6.6 - 1.3 km = 5.3 km from the sea level.
They climb back 0.8 km in the next hour so they will be
5.3 +.8 = 6.1 km from the sea level
6.6 - 6.1 = 0.5 km
Therefore the brothers are 0.5 km away from the scenic cliff
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question 10 please
need help
Answer:
Denes Dynamos =
2012 attendance = 34500
2013 attendance = 30705
change = 30705 - 34500= -3795
change percentage = -3795 * 100 / 34500 = -11%
Edgefield Eagles =
2012 = 24100
2013 = 21208
change = -2892
change Percentage = -2892 * 100 / 24100 = -12%
can someone please help mee(10 points)
Answer:
(2,-3)
Step-by-step explanation:
Thats where the parabola is the lowest at
i need help asappppppppppppp
Answer: Choice [D] - "power of a power" ✅
Step-by-step explanation:
Hii, do you need to know which law you should use to simplify [tex]\sf\bigg(x^4\bigg)^9[/tex]?
No problem!
The law we will use here is "power of a power".
What "power of powers" means is we raise a power to a power, which is exactly what we do here: We raise x^4 to the power of 9. To simplify our expression, we multiply the powers. ([tex]\boldsymbol{4\cdot9}[/tex])
So the right answer is: Choice [D] - "Power of a power"
The simplified answer is [tex]\LARGE\boldsymbol{x^{4\cdot9}=x^{36}}[/tex]
Voila! There's our answer, cheers!
--
Hope that this helped! Best wishes.
[tex]\it Reach\;far.\;Aim\;high.\;Dream\;big.}[/tex]
--
hii can someone help thank you
A train travels at 100 milers per hour. An equation can be written that compares the time (t) with the distance (d). Define the domain and range
Answer:
The domain is t ≥ 0
The range is D ≥ 0
Step-by-step explanation:
[tex]rate = \frac{distance}{time}[/tex]
D(t) = 100t + d₀
t is the time measured in hours.
d₀ is the initial position of the train.
We can assume the distance they go is not negative so...
The domain is t ≥ 0
The range is D ≥ 0
25. Given: TE= RI, TI = RE,
Proof
LTDI and LROE are right /
Prove: TD=RO
Answer:
In triangle TEI and ERI
TI = RE ( given)
angle TDI = angle ROE ( given).
TE = RI ( given).
by side angle side criteria
both the triangles are congruent
by cpct ( corresponding parts of congruent triangles)
TD is congruent to RO
X-intercept (3,0) and y-intercept (0, -6).
Really could use help here.
Answer:
[tex]\mathsf {y =\frac{15}{7}x }[/tex] < [tex]\mathsf {y=\frac{13}{6}x }[/tex] < [tex]\mathsf {y=\frac{11}{5}x }[/tex] < [tex]\mathsf {y=\frac{21}{9}x }[/tex] < [tex]\mathsf {y= \frac{19}{8}x}[/tex]
Step-by-step explanation:
Finding the unit rate of the graph :
Take 2 points and find the slope⇒ (0,0) and (12, 25)⇒ m = 25 - 0 / 12 - 0⇒ m = 25/12The equation is : y = 25/12xNow, the equations with greater unit rates (in increasing order) are :
[tex]\mathsf {y =\frac{15}{7}x }[/tex] < [tex]\mathsf {y=\frac{13}{6}x }[/tex] < [tex]\mathsf {y=\frac{11}{5}x }[/tex] < [tex]\mathsf {y=\frac{21}{9}x }[/tex] < [tex]\mathsf {y= \frac{19}{8}x}[/tex]What is the answer for the question down below
Answer:
x = 45°Step-by-step explanation:
If AC is a supplementary line, then
x + 90° + x = 180°
solution:
2x + 90° = 180° |subtract 90° from both sides
2x = 90° |divide both sides by 2
x = 45°
Answer:
[tex] \sf \: b) \: {45}^{o} [/tex]
Step-by-step explanation:
Now we have to,
→ find the required value of x.
Forming the equation,
→ x + x + 90° = 180°
Then the value of x will be,
→ x + x + 90° = 180°
→ 2x = 180° - 90°
→ 2x = 90°
→ x = 90° ÷ 2
→ [ x = 45° ]
Hence, the value of x is 45°.
. All the students in SS3 of a named school take either Mathematics (M), or Physics (P) or Chemistry (C). 40 take Mathematics, 42 take physics, 38 take Chemistry, 20 take Mathematics and Physics, 28 take Physics and Chemistry while 25 take mathematics and chemistry.
How many take
(a) All the three subject:
(b) Mathematics, but neither Physics nor Chemistry
(c) Physics, but neither Mathematics nor Chemistry
Answer:
(a) = 13
(b) = 8
(c) = 5
Step-by-step explanation:
Addition theorems on sets are
Theorem 1 :
n(AuB) = n(A) + n(B) - n(AnB)
Theorem 2 :
n(AuBuC) : = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)
Total number of students in the school is not given
so let there are 60 students in the school
using theorem 2
n(AuBuC) : = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)
let n(A) = Mathematics, n(B) =Physics and n(C) = Chemistry
so putting values,
60 = 40 + 42 + 38 - 20 - 28 - 25 + n(AnBnC)
60 +73 -120 = n(AnBnC)
13 = n(AnBnC)
therefore, there are total 13 students who take all three subjects
Number of students who had taken only Mathematics =
n(A) - n(AnB) - n(AnC) + n(AnBnC)
40 - 20 - 25 + 13
53 - 45 = 8 students
Number of students who had taken only Physics =
n(B) - n(BnA) - n(BnC) + n(AnBnC)
42 - 20 - 28 + 13
53 - 48 = 5 students
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Which linear inequality is represented by the graph?
Step-by-step explanation:
5 because you have to round
Answer:
5
Step-by-step explanation:
because you have to round
Source: trust me bro
bear corp. has $100,000 cash in the bank restricted to repay a note payable that matures in 2 years. how should this $100,000 be reported?
It should be reported as a restricted cash in the long-term section of the company balance sheet.
What is note payable?Note payable can be defined a the money a company or an organization owes or the money they are expected to payback..
Note payable is classified as long term liabilities. Hence, the cash amount of $100,000 should be reported or recorded in the balance sheet as a restricted cash.
Therefore the $100,000 is reported as a restricted cash.
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This week, Marie trimmed 61% of the bushes in her yard. Katie trimmed 7/20 of the bushes in her yard. Who has trimmed a greater percentage of her bushes?
7d + 46 what is the answer
Answer:
i think the answer would be 53?
Step-by-step explanation:
i could be wrong
Step-by-step explanation:
the answer is d= -46/-7
or in simplest form
d= 6.57
hope this is correct...
-7mn (4m³n² + m²)
Multiply
[tex] - 7mn(4 {m}^{3} {n}^{2} + {m}^{2} ) \\ - 28 {m}^{4} {n}^{3} - 7 {m}^{3} n[/tex]
PLEASE GIVE BRAINLIEST