Answer:
Step-by-step explanation:
a direct variation, b/c as X goes up, so does Y
How can you tell from the equation of a rational function if the function has a hole in the graph ( a removable discontinuity) at x, rather than a vertical asymptote? Give an example
Consider that,
x^2+4x+4 = (x+2)(x+2)
x^2+7x+10 = (x+2)(x+5)
Dividing those expressions leads to
(x^2+4x+4)/(x^2+7x+10) = (x+2)/(x+5)
The intermediate step that happened is that we have (x+2)(x+2) all over (x+2)(x+5), then we have a pair of (x+2) terms cancel as the diagram indicates (see below). This is where the removable discontinuity happens. Specifically when x = -2. Plugging x = -2 into (x+2)/(x+5) produces an output, but it doesn't do the same for the original ratio of quadratics. So we must remove x = -2 from the domain.
Help me please
Point K(–5, 2) is the midpoint of line segment Y Z , with endpoint Y(1, –3). What are the coordinates of Z?
You are using the diagram below to prove that if two nonvertical lines are perpendicular, then the product of their slopes is -1
AY
9
E
р
A
H
B
7
a. Identify the slope of p and the slope of q.
mp
та
AD
DE
DE
AD
AB
BC
BC
AB
AC
5 AE
AD
DE
DE
AD
Answer: AE & AC
Step-by-step explanation:
:)
Plot the numbers
and
on the number line below.
In this number line, we marked -7/6 to the left of -1, and 4/3 to the right of 1.
To plot the numbers -1 1/6 and 4/3 on a number line, we need to find their relative positions and mark them accordingly.
Let's start with -1 1/6:
-1 1/6 can be written as a mixed number or an improper fraction. To simplify the plotting process, let's convert it to an improper fraction.
-1 1/6 = -(6/6 + 1/6) = -7/6
On the number line, we start from zero and move to the left because it is a negative number. Since -7/6 is less than -1, we will place it closer to zero but to the left of -1.
Next, let's plot 4/3:
4/3 is already in the form of an improper fraction. To plot it, we start from zero and move to the right since it is a positive number. 4/3 is greater than 1, so we will place it to the right of 1.
On this number line, we marked -7/6 to the left of -1, and 4/3 to the right of 1.
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The surface areas of to somewhere figures are 36 inches squared and 49 inches squared. If the volume of the similar figure is 640 inches cubed, what is the volume of the larger figure?
A) 1029in^3
B) 746in^3
C) 408in^3
D) 882in^3
Answer:
345
Step-by-step explanation:
What are the fourth roots of −3+33√i ?
Enter your answer by filling in the boxes. Enter the roots in order of increasing angle measure in simplest form.
Answer:
In order of increasing angle measure, the fourth roots of -3 + 3√3·i are presented as follows;
[tex]\sqrt[4]{6} \cdot \left[cos\left({-\dfrac{\pi}{12} } \right) + i \cdot sin\left(-\dfrac{\pi}{12} } \right) \right][/tex]
[tex]\sqrt[4]{6} \cdot \left[cos\left({\dfrac{5 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{5 \cdot\pi}{12} } \right) \right][/tex]
[tex]\sqrt[4]{6} \cdot \left[cos\left({\dfrac{11 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{11 \cdot\pi}{12} } \right) \right][/tex]
[tex]\sqrt[4]{6} \cdot \left[cos\left({\dfrac{17 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{17 \cdot\pi}{12} } \right) \right][/tex]
Step-by-step explanation:
The root of a complex number a + b·i is given as follows;
r = √(a² + b²)
θ = arctan(b/a)
The roots are;
[tex]\sqrt[n]{r}[/tex]·[cos((θ + 2·k·π)/n) + i·sin((θ + 2·k·π)/n)]
Where;
k = 0, 1, 2,..., n -2, n - 1
For z = -3 + 3√3·i, we have;
r = √((-3)² + (3·√3)²) = 6
θ = arctan((3·√3)/(-3)) = -π/3 (-60°)
Therefore, we have;
[tex]\sqrt[4]{-3 + 3 \cdot \sqrt{3} \cdot i \right)} = \sqrt[4]{6} \cdot \left[cos\left(\dfrac{-60 + 2\cdot k \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-60 + 2\cdot k \cdot \pi}{4} \right) \right][/tex]
When k = 0, the fourth root is presented as follows;
[tex]\sqrt[4]{6} \cdot \left[cos\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 0 \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 0 \cdot \pi}{4} \right) \right] \\= \sqrt[4]{6} \cdot \left[cos\left({-\dfrac{\pi}{12} } \right) + i \cdot sin\left(-\dfrac{\pi}{12} } \right) \right][/tex]
When k = 1 the fourth root is presented as follows;
[tex]\sqrt[4]{6} \cdot \left[cos\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 1 \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 1 \cdot \pi}{4} \right) \right] \\= \sqrt[4]{6} \cdot \left[cos\left({\dfrac{5 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{5 \cdot\pi}{12} } \right) \right][/tex]
When k = 2, the fourth root is presented as follows;
[tex]\sqrt[4]{6} \cdot \left[cos\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 2 \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 2 \cdot \pi}{4} \right) \right] \\= \sqrt[4]{6} \cdot \left[cos\left({\dfrac{11 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{11 \cdot\pi}{12} } \right) \right][/tex]
When k = 3, the fourth root is presented as follows;
[tex]\sqrt[4]{6} \cdot \left[cos\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 3 \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 3 \cdot \pi}{4} \right) \right] \\= \sqrt[4]{6} \cdot \left[cos\left({\dfrac{17 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{17 \cdot\pi}{12} } \right) \right][/tex]
Answer:
Step-by-step explanation:
Just took the test.
1) 4sqrt6 cis(pie/6)
2) 4sqrt6 cis (2pie/3)
3) 4sqrt6 cis(7pie/6)
4) 4sqrt6 cis (5pie/3)
what is 2/4 divided by 3
Answer:
0.166
Step-by-step explanation:
please help, tysm :)
Answer:
y=5x+1
i'm pretty sure...
Compute the value of the discriminant and give the number of real solutions of the quadratic equation.
- 2x^2+ 9x-1=0
Answer:
value of discriminant=73
4. A car is travelling 75 kilometers per hour. How many meters does the car travel in one
minute?
Answer:
1250 Meters
Step-by-step explanation:
75 kilometers divided by 60 minutes is 1.25 kilometers per minute.
1 kilometer = 1000 meters
Answer:
75km/hr =75000
60 sec =1min,60 min=1hr
75000÷60=1250m
Kay found four frogs on Monday and nine frogs on Tuesday in the pond by her house. Each frog has 5 warts. How many more warts are on the frogs from Tuesday than from Monday?
Answer: 25
Step-by-step explanation:
Given
Kay found 4 frogs on Monday
and 9 frogs on Tuesday by her house
each frog has 5 warts
So, total warts on Monday and Tuesday
[tex]\Rightarrow \text{Monday=}4\times 5\\\Rightarrow 20\\\\\Rightarrow \text{Tuesday =}9\times 5\\\Rightarrow 45[/tex]
The difference of warts is
[tex]\Rightarrow 45-20\\\Rightarrow 25[/tex]
Thus, there are25 more warts on frogs from Tuesday than from Monday
Frogs On Monday:
4 frogs x 5 = 20 warts
Frogs On Tuesday:
9 frogs x 5 warts = 45
Last Step:
45 (9 frogs each with 5 warts) - 20 (4 frogs each with 5 warts) =
Answer: 25
~Hope this helps!
~Hocus Pocus
The sum of the ages of Noah and Billy is 25; the sum of the ages of Noah and Ty is 20; and the sum of the ages of Billy and Ty is 31. Who is the oldest of the three and how old is he?
Answer:
the oldest is Ty and his age is 24
Step-by-step explanation:
Let us assume the billy age be x
Noah age be y
And, Ty age be z
Now according to the question
y + x = 25 ..........(1)
y + z = 20..........(2)
x + z = 31..............(3)
z = 31 - x
since
y + z = 20
y + 31 - x = 20
y - x = -11 .............(4)
Now solve (1) and (4) equation
So,
y + x = 25
y - x = -11
2y = 36
y = 18
x = 25 - 18
= 7
z = 31-7
= 24
Hence, the oldest is Ty and his age is 24
Help me it says use the figure for 1 and 2
On a test. I can't find answers anywhere else.
i think this is correct
Find the exact value of cot 330° in simplest form with a rational denominator.
Answer:
[tex]\cot 330^{\circ} = -\sqrt{3}[/tex]
Step-by-step explanation:
The cotangent function can be rewritten by trigonometric relations, that is:
[tex]\cot 330^{\circ} = \frac{1}{\tan 330^{\circ}} = \frac{\cos 330^{\circ}}{\sin 330^{\circ}}[/tex] (1)
By taking approach the periodicity properties of the cosine and sine function (both functions have a period of 360°), we use the following equivalencies:
[tex]\sin 330^{\circ} = \sin (-30^{\circ}) = -\sin 30^{\circ}[/tex] (2)
[tex]\cos 330^{\circ} = \cos (-30^{\circ}) = \cos 30^{\circ}[/tex] (3)
By (2) and (3) in (1), we have following expression:
[tex]\cot 330^{\circ} = -\frac{\cos 30^{\circ}}{\sin 30^{\circ}}[/tex]
If we know that [tex]\sin 30^{\circ} = \frac{1}{2}[/tex] and [tex]\cos 30^{\circ} = \frac{\sqrt{3}}{2}[/tex], then the result of the trigonometric expression is:
[tex]\cot 330^{\circ} = -\frac{\frac{\sqrt{3}}{2} }{\frac{1}{2} }[/tex]
[tex]\cot 330^{\circ} = -\sqrt{3}[/tex]
The exact value of cot 330° with a rational denominator is √3.
To find the exact value of cot 330°, we can first determine the reference angle. The reference angle for 330° is 30°, as it is the angle between the terminal side of 330° and the x-axis.
Cotangent (cot) is the reciprocal of the tangent function, so we need to find the tangent of the reference angle, which is tan 30°. The tangent of 30° is √3/3.
Since cot is the reciprocal of tan, the cotangent of 330° is the reciprocal of √3/3, which is 3/√3.
To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator, which is √3.
(3/√3) x (√3/√3) = 3√3/3
Simplifying further, we can cancel out the common factor of 3:
(3√3/3) = √3
Therefore, the exact value of cot 330° with a rational denominator is √3.
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5 5/6 x 1/3= and 1/3 x 6 4/5
Answer:
1 17/18 and 2 4/15
Step-by-step explanation:
5 5/6 x 1 /3 = 1 17/18
1/3 x 6 4/6 = 2 4/15
Answer: 1 17/18 and 2 4/15
Step-by-step explanation:
In the figure b and c are parallel lines select all the statements that are true
Did you ever get the answer
Answer:
Im the king of answers
Step-by-step explanation:
The answer is A, C, and E
20 is what percent of 52? Solve with an Equation
Answer:
38.46
Step-by-step explanation:
Percentage Calculator: 20 is what percent of 52? = 38.46.
Mrs. Torres wants to know how many students wear thelr uniforms. In order to gather data, she stands by the front door and records each student. Identify the data-gathering technique described above:
A. Observational Study
B. Randomized Experiment
C. Survey
D. All of the above
Answer:
Observational Study
Step-by-step explanation:
Because she stands by the front door and records each student
The data gathering technique used to know the number of students that wore their uniform is Observational study
What are data gathering technique?
Data gathering technique is the process of gathering, measuring, and analysing accurate data from a variety of relevant sources.
There are several procedure of acquiring this data, which includes the following:
Observation.Interview.Survey.Documents and record and many more.The data gathering technique used to know the number of students that wore their uniform is Observational study.
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HELPPP ME PLEASEEEEEE
Answer:
Step-by-step explanation:
[tex]y^2 = 100 + 196 = 296\\\\y = \sqrt{296} \\\\y = 17.20[/tex]
Help.
I have killed three children, the other six are locked in my basement and the cops are at my door. Do I invite them inside and poison their tea,, or do I just stab them??
P.S
Best way to get rid of bodies??
TYY!!! ^^
Answer:
Eat them. )llllllllllllllllllllllllll)
For every 2 gallons of vanilla ice cream a shop sells, they sell 11 gallons of chocolate ice cream. If they sell 16 gallons of vanilla ice cream, how many gallons of chocolate ice cream is sold?
Answer: 88 gallons
Step-by-step explanation:
Every 2 vanillas = 11 chocolates
so 16 vanillas = 88 chocolates
i did this by multiplying both numbers by 8
sorry if this is wrong
8, 9, 3, 9, 3, 8, 4,4
1)
Mean
Median
Mode
Range
Answer:
8,
4 and 8
3,4,8,9
6
Step-by-step explanation:
Solve for x and y. X= Y=
Answer:
x = 82°
y = 8°
Step-by-step explanation:
x + 98° = 180°
x = 180° - 98°
x = 82°
x + y = 90°
82° + y = 90°
y = 90° - 82°
y = 8°
5 1/2 ÷ 3 2/3 + 1 4/5 , giving answer as a fraction in lowest terms
Answer:
6761/320
Step-by-step explanation:
[(51/2)÷32/3]+14/5
=6761/320
b) A jewellery shop sells 240 necklaces in a month.
180 of the necklaces were sold via the shop's website, the rest were
sold in a high street shop.
Work out the ratio of online sales to shop sales.
Give your answer in its simplest form.
Answer:
3:1
Step-by-step explanation:
240 - 180 = 60
60:180
1:3
3:1
HELLPP ASAP!!!!
1. Find the unknown side lengths in these right triangles.
Answer:
10
Step-by-step explanation:
5x2
Which graph best represents the equation –x + 2y = 4?
Answer:
C is corrcet
Step-by-step explanation:
because the linye should be on any negtive number for x and y should be on 3
Answer:
Yes the answer is graph c
Step-by-step explanation:
Have a great day.
WHICH OF THE FOLLOWING EQUATIONS HAS INFINITELY MANY SOLUTIONS
A: b+2=b+2
B: b=-b+2
C: b+2=b-2
D: b+b=2
Answer:
A. b+2=b+2
Step-by-step explanation:
When there are two of the same things on both sides or if anything is equal to the same thing, it is infinitely many solutions.
If this has helped please mark as brainliest
10. Fill in the blanks so as to make the statement true:
(i) A number which can be expressed in the form m/n, where m and n are
integers and n is not equal to zero, is called a ________.
(ii) If the integers m and n have no common divisor other than 1 and n is
positive, then the rational number m/n is said to be in the ________.
(iii) Two rational numbers are said to be equal, if they have the same
________ form.
(iv) If m is a common divisor of x and y, then x/y = (x ÷ k)/______
(v) lf p and q are positive integers , then m/n is a ________ rational
number and m/-n is a ________ rational number.
(vi) The standard form of -1 is ________.
(vii) If m/n is a rational number, then n cannot be ________
(viii) Two rational numbers with different numerators are equal, if their
numerators are in the same ________ as their denominators.
Step-by-step explanation:
(I) A number which can be expressed in the form m/n, where m and n are integers and n is not equal to zero, is called a Rational Number .
(ii) If the integers m and n have no common divisor other than 1 and n is positive, then the rational number m/n is said to be in the Simplest form .
(iii) Two rational numbers are said to be equal, if they have the same Simplest form .
(iv) If m is a common divisor of x and y, then x/y = (x ÷ k)/( y ÷ k) .
(v) The standard form of -1 is -1/1
(vi) If m/n is a rational number, then n cannot be 0
(vii) Two rational numbers with different numerators are equal, if their numerators are in the same ratio as their denominators.