Step-by-step explanation:
a12 = 45 + (12-1)(-6)
= 45-66= -21
Step-by-step explanation:
yes, the other answer is correct.
just to explain a little bit more :
the sequence is clearly built by subtracting 6 from one element to the next.
in other words :
a1 = 45
a n = a n-1 - 6
in such a sequence you do the same operation/ calculation over and over again - once per new element.
the operation in this example is simple - as mentioned : subtract 6.
a1 just gives us a starting value (no operation done for for it) zu, the operation is done one time less than the running number of the element.
therefore, the general element generation algorithm/ formula is :
a n = a1 - (n-1)*6
when a number is doubled and then eight added it became 60 what is the number
Answer:
26
Step-by-step explanation:
Answer:
26
Step-by-step explanation:
Let the number be x.
Now,
2x + 8 = 60
2x = 60 - 8
x = [tex]\dfrac{52}{2}[/tex]
x = 26
Hence, the number is 26.
3.15 Linear Equations and Inequalities (SHOW YOUR WORK)
1.) Use the linear graph to answer the question.
A.) Identify the quadrant in which each point lies.
Point A:_____
Point B:_____
Answer:
A- Quadrant one.
B- Quadrant three.
Step-by-step explanation:
So, the quadrants go counter-clockwise, starting at the top right which is Quadrant one. Therefore, A is in one. Using that information, we can assume that B is in Quadrant three.
Graph the image of points A and B after a reflection over the x-axis.
Point B is 2,3 and Point A is 7,8
Answer:
Point A reflected = 7, -8
Point B reflected = 2, -3
Step-by-step explanation:
A marble is randomly selected from a bag containing 3 red marbles, 3 blue marbles, and 3 green marbles. what is the probability that the selected marble is green?
Answer:
1/3
Step-by-step explanation:
3x3= 9
Make 3/9 a fraction and simplify it and it would give you 1/3
consider the first six terms
in the sequence -11,-4, 3, 10, 17,24
Answer:
Next term is 31
Step-by-step explanation:
The numbers keep going up by 7.
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If 8 cents are needed to buy 10 pebbles, how many dollars are needed to buy 205 pebbles?
Answer:
Hello There!!
Step-by-step explanation:
If 8 cents=10 pebbles then do 205 divided by 10 which is 20.5 . So, 8×20.5=164 dollars.
(8×20.5=164) 8 cents=10 (10×20.5=205)
164 dollars=205
Therefore,the answer is 164 dollars.
hope this helps,have a great day!!
~Pinky~
Which of the binomials below is a factor of this trinomial?
4x2 + 21x + 5
A. 4x + 5
B. 4x-1
C. 4x + 1
D. 4x - 5
Answer:
c
Step-by-step explanation:
Answer:
C. 4x+1
Step-by-step explanation:
!!!need help please !!!
Answer:
Step-by-step explanation:
log(3) = 0.477
log(8.2) = 0.913
log(0.04) = -1.397
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.
To learn more about trigonometric identities;
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Rewrite the expression 1/x^2/3 in the form x^n
Step-by-step explanation:
Rewrite the expression 1/x^2/3 in the form x^nRewrite the expression 1/x^2/3 in the form x^n
An expression is defined as a set of numbers, variables, and mathematical operations. The given expression can be written in the form of xⁿ as x⁻⁰°⁶⁶.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression [tex]\dfrac{1}{x^{\frac23}}[/tex] can be written in the form of xⁿ using the exponential property 1/x=x⁻¹. Therefore, the expression can be rewritten as,
[tex]\dfrac{1}{x^{\frac23}}\\\\= x^{-\frac23}[/tex]
= x⁻⁰°⁶⁶
Hence, the given expression can be written in the form of xⁿ as x⁻⁰°⁶⁶.
Learn more about Expression here:
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A piano instructor charges students a one-time fee for sheet music and an hourly rate for lessons. The graph below shows the total cost for a student who has taken x lessons.
Which of the following is closest to the circumference of a circle whose radius is 21 m
Here Is your answer!!!!
The model represents an inequality. What is the solution set for the inequality?
Given:
The figure of an algebraic tiles model of an inequality.
To find:
The inequality for the given model.
Solution:
On the left hand side of the inequality sign in the model we have 8 tiles of x and 12 tiles of 1. So,
[tex]LHS=8(x)+12(1)[/tex]
[tex]LHS=8x+12[/tex]
On the right hand side of the inequality sign in the model we have 12 tiles of -1. So,
[tex]RHS=12(-1)[/tex]
[tex]RHS=-12[/tex]
Now, the inequality for the given model is:
[tex]8x+12\geq -12[/tex]
Therefore, the required inequality for the given model is [tex]8x+12\geq -12[/tex].
Tara picks out 4 paint colors (beige, blue, green, and gray) to paint 4 rooms in her house (living room, dining room, main bedroom, and kitchen).
What is the probability that tara first paints her bedroom green?
ASAP!!!!!
im going to guess it's [tex]\frac{1}{4}[/tex]
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
PLZ HELP I BEGG!! 100 POINTS AND BRANLIEST
Answer:
Vertical angles are opposite angles that are formed from two intersecting lines. From this, the vertical angle to 3 is 5
Answer:
Step-by-step explanation:
<3 is a right angle so its opposite angle is vertical to it. The answer is <5.
If 36 ÷ 9 = 4, which numbers could be placed in the blanks in the order shown to create a corresponding multiplication fact? _____ × _____ = _____
A) 4, 9, 36
B) 4, 36, 9
C) 9, 36, 4
D) 36, 9, 4
Answer:
a. 4×9=36
glad to help!!
Step-by-step explanation:
I need help. URGENT
Use the information and the diagram to answer the question:
What is the area of KLM
Answer:
i think the answer might be D but im not sure
Kaden works 5 days. The median number of hours he works is 3. The mean number of hours he works is 4.
Answer:
(a) 1, 2, 3, 6, 8
Step-by-step explanation:
Given
[tex]Median = 3[/tex]
[tex]Mean = 4[/tex]
Required
The sequence of hours worked each day
See attachment for options
From the question, we understand that:
[tex]Median = 3[/tex]
This means that, the middle number is 3 (when sorted)
So, we can conclude that (b) and (c) cannot be true because their middle numbers are 6 and 5 respectively
Next, is to determine the mean of (a) and (d)
The mean of a data is calculated as:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
(a)
[tex]\bar x = \frac{1+ 2+ 3+ 6+ 8}{5}[/tex]
[tex]\bar x = \frac{20}{5}[/tex]
[tex]\bar x = 4[/tex]
(d)
[tex]\bar x = \frac{1+ 2+ 3+ 4+ 5}{5}[/tex]
[tex]\bar x = \frac{15}{5}[/tex]
[tex]\bar x = 3[/tex]
Option (a) is true, because it has:
[tex]Median = 3[/tex]
[tex]Mean = 4[/tex]
G(x)=3/x find g'(x) a) by using the quotient rule: b) by first rewriting the expression using exponents and then differentiating.
Answer:
a) The quotient rule is:
if: f(x) = 1/g(x)
Then:
[tex]f'(x) = -\frac{1}{(g(x))^2}*g'(x)[/tex]
In this case, we have:
G(x) = 1/x
Then we can write this as:
G(x) = 1/h(x) with h(x) = x, and h'(x) = 1
Using the above rule we get:
G'(x) = -(1/h(x)^2)*h'(x) = -1/x^2
b) For a function like:
f(x) = x^n
we have that:
[tex]f'(x) = n*x^{n - 1}[/tex]
Here we can write G(x) = x^-1
Then we have n = -1
If we use the above rule, we get:
[tex]G'(x) = (-1)*x^{-1-1} = -1*x^{-2} = \frac{-1}{x^2}[/tex]
So we got the same result using both methods.
The formula s = StartRoot StartFraction S A Over 6 EndFraction EndRoot gives the length of the side, s, of a cube with a surface area, SA. How much longer is the side of a cube with a surface area of 480 square meters than a cube with the surface area of 270 square meters
Answer:
It's B
Step-by-step explanation:
I took the test
Answer:
B= (√30 - 2√5)
Step-by-step explanation:
Expand (p - q)(p+q).
Answer:
p^2 - q^2
Step-by-step explanation:
This is an example of "the product and difference of two squares."
The relevant formula is (a - b)(a + b) = a^2 - b^2 (no middle term).
Here,the desired product is (p - q)(p + q) = p^2 - q^2.
Answer:
(p - q)(p+q). :p²-q²....
please help me
no links please and thank you :)
PLS HURRRY PLSSS HURRYRY
Answer: 10in^2 or this
Step-by-step explanation: Hope this help :D
Answer:
29
Step-by-step explanation:
2x2=4
5x5=25
25+4=29
Sorry if this didn't help ;(
What is the missing length?
Answer:
16
Step-by-step explanation:
The area of a triangle is
A =1/2 bh where b is the base length and h is the height
Substitute the values in
69.6 = 1/2 ( 8.7) * p
69.6 = 4.35p
Divide each side by 4.35
69.6/4.35 = p
16 = p
The formula for the area of a triangle is: A = 1/2 * base * height.
Using this formula, let's plug in what we know.
69.6 = 1/2 * 8.7 * height
Next, we'll go ahead and get rid of that 1/2 by multiplying everything by its reciprocal, 2.
139.2 = 8.7 * height
Then, all that's left is to divide both sides by 8.7.
Height = 16 yards
Hope this helps!! :)
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.
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
I need help!!! Like right now
Help me it says use the figure for 1 and 2
Forty nine minus twenty five b squared in factored form
Step-by-step explanation:
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