Answer:
[tex]a_{n}[/tex] = 100n - 78
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₁₄ = 1322 and a₃₈ = 3722 , then
a₁ + 13d = 1322 → (1)
a₁ + 37d = 3722 → (2)
subtract (1) from (2) term by term to eliminate a₁
24d = 2400 ( divide both sides by 24 )
d = 100
substitute d = 100 into either of the 2 equations and solve for a₁
substituting into (1)
a₁ + 13(100) = 1322
a₁ + 1300 = 1322 ( subtract 1300 from both sides )
a₁ = 22
then nth term formula is
[tex]a_{n}[/tex] = 22 + 100(n - 1) = 22 + 100n - 100 = 100n - 78
which statement is true of the function f(x) = -3 squared root x
Using translation concepts, it is found that the function [tex]f(x) = -3\sqrt{x}[/tex] is the function [tex]g(x) = \sqrt{x}[/tex] reflected over the x-axis and vertically stretched by a factor of 3.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, from [tex]g(x) = \sqrt{3}[/tex] to [tex]f(x) = -3\sqrt{x}[/tex], g(x) was multiplied by -3, that is, it was reflected over the x-axis(due to the multiplication by the negative number) and vertically stretched by a factor of 3.
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what is 349,001 + 209, 499?
Answer:
558, 500
Step-by-step explanation:
round 349,001 to 349,000 subtracted 1
round 209, 499 to 209, 500 added 1
349,000 + 209, 500 = 558, 500
Now, the added and subtract 1 cancel out so that is the final answer
Francisco is playing a game with 3 green, 2 yellow, 4 red, and 3 black marbles in a bag. He has calculated the probability of drawing a yellow marble, not replacing it, and then drawing a red marble. Explain the error in his solution.
The correct answer will be 2/33.
What is Probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Well, the problem is that he does not replace the first marble after he draws it.
Therefore, yes, he has a 2/12 probability of drawing a yellow marble first, but then he has a 4/11 probability of drawing a red marble second, not 4/12.
This is because there are going to only be 11 marbles left in the bag after he draws the first marble and does not replace it.
The correct answer would be:
(2/12)(4/11)
=8/132
=4/66
=2/33
Thus, the correct answer will be 2/33.
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8. How do outliers affect the mean of a data set?
OIt does not change.
It depends whether the outlier is a high outlier or a low outlier.
It decreases.
It increases.
Answer:
it depends on whether the outlier is a high outlier or a low outlier
Step-by-step explanation:
The mean of a data set is the average of the data set. So if I had the data set {5, 2, 10} the average would be (5+2+10)/3 = 5.667. Now if I added an outlier like 10,000 it would increase the mean significantly. It changes it significantly but I cannot say whether it increases or decreases it without knowing the value of the outlier, since if I had the outlier -10,000 that would decrease the mean, but I had the outlier 10,000 it would increase it. So it depends on whether the outlier is a high outlier or a low outlier
PLEASE HELP !!! which choices are equivalent to square root of -4???
Answer:
-2
Step-by-step explanation:
just a guess but it's right
1) Which statement is needed to complete this syllogism? If a quadrilateral has 4 congruent sides, then it is a rhombus. If it is a rhombus, then it’s diagonals are perpendicular. Therefore, if ________________________, then it’s diagonals are perpendicular.
A) a quadrilateral has 4 congruent sides
B) it is a rhombus
C) it is a rectangle
D) it has diagonals
Statement A is needed to complete this syllogism. its diagonals are perpendicular. Therefore, if a quadrilateral has 4 congruent sides then its diagonals are perpendicular.
What is a syllogism?A logical structure for a formal argument that includes a major, minor, and conclusion.
This syllogism cannot be concluded without Statement A. The diagonals of it are parallel. As a result, a quadrilateral's diagonals are perpendicular if it has four congruent sides.
If a quadrilateral has 4 congruent sides, then it is a rhombus. If it is a rhombus, then its diagonals are perpendicular.
Therefore, if a quadrilateral has 4 congruent sides then its diagonals are perpendicular.
Hence option A is correct.
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Answer:
a quadrilateral has 4 congruent sides
Step-by-step explanation:
Syllogisms are connected by a shared statement that connects a hypothesis to a different conclusion.
A face of a suitcase measures 24 inches long and 18 inches wide. what is the diagonal length of the face?
30 in.
25 in.
20 in.
15 in.
I think the answer is 90in.
In a case whereby the face of a suitcase measures 24 inches long and 18 inches wide the diagonal length of the face is 30 in.
How can the diagonal length be calculated?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
The suitcase measures 24 inches long and 18 inches wide
Using Pythagoras theorem,
The diagonal =[tex]\sqrt{18^{2} + 24^{2} }[/tex]
= [tex]\sqrt{900}[/tex]
=30 in.
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please help in this as well thank !!
Step-by-step explanation:
4a.
the circumference of a circle is
2×pi×r
we know, r = 6 cm.
so the whole circumference is
2×pi×6 = 12×pi = 37.69911184... cm
4b.
the arc BC is the part of the full circumference that corresponds to 120° out of the 360° of a full circle.
the arc BC is then
12×pi × 120/360 = 12×p × 1/3 = 4×pi = 12.56637061... cm
the perimeter of the shaded area (pie slice) is the arc BC plus 2 radius lengths (from the arc points to the center of the circle)
12.56637061... + 2×6 = 12.56637061... + 12 =
= 24.56637061... cm
4c.
the area of a circle is
pi×r²
in our case
pi×6² = 36pi = 113.0973355... cm²
the area of the shaded area (pie slice) is the 120° part of the full 360° circle area :
36pi × 120/360 = 36pi × 1/3 = 12pi = 37.69911184... cm²
i need help with this question (answer choices 15, 5, and 12)
Answer:
x = 15
Step-by-step explanation:
the opposite angles of a cyclic quadrilateral sum to 180° , then
6x + 20 + 3x + 25 = 180 , that is
9x + 45 = 180 ( subtract 45 from both sides )
9x = 135 ( divide both sides by 9 )
x = 15
Given: f(a)= a³ +a and g(a) = a -1 Find: (fog)(a)
Answer:
(fog)(a) = a³ - 3a² + 4a - 2
= (a - 1)×(a² - 2a + 2)
Step-by-step explanation:
Given :
g(a) = a -1
f(a)= a³ +a
…………………………
(fog)(a) = f(g(a)))
= g(a)³ + g(a)
= (a - 1)³ + (a - 1)
= (a³ - 3a² + 3a - 1) + (a - 1)
= a³ - 3a² + 3a - 1 + a - 1
= a³ - 3a² + 3a + a - 1 - 1
= a³ - 3a² + 4a - 2
Second method :
(fog)(a) = f(g(a)))
= f(a - 1)
= (a - 1)³ + (a - 1)
= (a - 1)×[(a - 1)² + 1]
= (a - 1)×[a² - 2a + 1 + 1]
= (a - 1)×(a² - 2a + 2)
y = x - 1/2, (-5, -2)
Answer:
This point is not on the line, NOT TRUE
Step-by-step explanation:
The equation of the line is written in the slope-intercept form,
y = mx + b
where m represents the slope
b represents the y-intercept
where the format of a point is (x, y)
Given: y = x - 1/2, (-5, -2)
we can plug in the point (-5, -2)
-2 = (-5) - 1/2
-2 = -5.5
-2 does not equal -5.5 so this point is not on the line
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Choose the end behavior of the graph of each polynomial function.
Options
Falls to the left and rises to the right
Rises to the left and falls to the right
Rises to the left and rises to the right
Falls to the left and falls to the right
Using limits, the end behavior of the functions are given as follows:
a. Rises to the left and falls to the right.
b. Rises to the left and rises to the right.
c. Falls to the left and rises to the right.
How to find the end behavior of a function f(x)?The end behavior of a function f(x) is given by the limit of f(x) as x goes to infinity.
In item a, we have that, respectively, to the left and to the right.
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} -5x^3 = -5(-\infty)^3 = \infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} -5x^3 = -5(\infty)^3 = -\infty[/tex]
Hence it rises to the left and falls to the right.
In item b, we have that, respectively, to the left and to the right.
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 3x^6 = 3(-\infty)^6 = \infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 3x^6 = 3(\infty)^6 = \infty[/tex]
Rises to the left and rises to the right.
In item c, we have that, respectively, to the left and to the right.
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 20x^3 = 20(-\infty)^3 = -\infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 20x^3 = 20(\infty)^3 = \infty[/tex]
Falls to the left and rises to the right.
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(08.02)How many solutions are there for the system of equations of shown on the graph?
O No solution
O One solution
O Two solutions
O Infinitely many solutions
Answer: B. One solution
Step-by-step explanation: As you see, both of these lines intersect on the point (0, 3). The point where the lines intersect is the solution. Since these lines are perpendicular, they will only intersect one time. Therefore, there is only one solution, that being (0, 3).
I hope this helps!! Pls mark brainliest :)
Select the correct answer from each drop-down menu.
The function f is given by the table of values as shown below.
Drop down box options:
The parent function of the function represented in the table is: Linear, Exponential, Quadratic
If function f was translated down 4 units, the: x- and f(x), x, or f(x)
-values would be: divided by 4, increased by 4, decreased by 4, multiplied by 4
A point in the table for the transformed function would be : (1, 52), (2,23), (4,87), (3,29)
The above Exponential function has the parent function to be F(x).
The value will decreased by 4.A point in the table for the transformed function would be : (1, 52), What is the transformation about?The difference between successive terms is: 6, 18, 54, 162. These are known to be in the powers of 2 and therefore one can say that there is an exponential increase in the parent function.
The new function is said to g(x). Translating down by 4 means that the new y-values are 4 units lower and so the answer is that the f(x)/y-values will be decreased by 4.
Therefore, looking at the above, since g(x)=f(x)-4 one need to know the value of x, the new y-value is lower by 4 from the old one. This is the case only for (1, 52) since the old function is (1, 13).
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Match each equation to the situation it represents.
Answer:
1-3
2-2
3-1
Step-by-step explanation:
ST
6
9
10
Which phrase best describes the translation from the graph y = 2x² to the graph of y = 2x² + 5?
O 5 units up
O 5 units down
O 5 units right
O 5 units left
The answer to the question is 5 units up.
If 1:w is equivalent to 1⅔: 5, find w.
Answer:
w = 3
Step-by-step explanation:
1/w = 1 2/3 / 5 cross multiply
1 2/3 (w) = 5
w = 5 / ( 1 2/3 ) = 5 / ( 5/3) = 15/5 = 3
Here is a list of numbers:7,12,16,20,27,40,56,64
Work out the difference between the two square numbers
Work out the difference between the two cube numbers
Answer:
48 and 37
Step-by-step explanation:
The 2 square numbers are 16 (4 squared) and 64 (8 squared)
So the difference between these 2 numbers: 64 - 16=48
The 2 cube numbers are 27 (3 cubed) and 64 (4 cubed)
64-27=37
answer:
48 and 37
step explanation:
The 2 square numbers are 16 (4 squared) and 64 (8 squared)
So the difference between these 2 numbers: 64 - 16=48
The 2 cube numbers are 27 (3 cubed) and 64 (4 cubed)
64-27=37
A rectangular field with sides as shown below has to be fenced all around. If fencing posts have to be fixed at 1-metre intervals, how many posts are needed?
1. 167
2. 334
3. 668
4. 6840
Step-by-step explanation:
the perimeter of a rectangle is
2×length + 2×width
so, here
2×95 + 2×72 = 190 + 144 = 334 m
so, yes, the answer 2. 334 is correct.
The solution is Option B.
The total number of posts is the total perimeter of the rectangular field and the value of N = 334 posts
What is the Perimeter of a Rectangle?
The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P = 2 ( Length + Width )
Given data ,
Let the number of posts be = N
Fencing posts have to be fixed at 1-metre intervals
The perimeter of the rectangular field = number of posts
Now , the equation will be
The length of the rectangular field = 95 m
The width of the rectangular field = 72 m
Perimeter P of the rectangle = 2 ( Length + Width )
Substituting the values in the equation , we get
Perimeter of the rectangle P = 2 ( 95 + 72 )
On simplifying the equation , we get
Perimeter of the rectangle P = 2 ( 167 )
Perimeter of the rectangle P = 334 m
Now , the number of posts = perimeter of the rectangular
So , the number of posts N = 334 posts
Therefore , the value of N is 334
Hence , the number of posts is 334 posts
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20 POINTS!! (will get brainliest)
Answer:
46. 135°
47. 225°
47. 270°
48. 3/8
49. 3/4
Step-by-step explanation:
Answer:
46) 135°
47) 225°
48) 270°
49) [tex]\frac{3}{8}[/tex] (3/8)
50) [tex]\frac{3}{4}[/tex] (3/4)
Step-by-step explanation:
{the following is if you do not understand my drawing}
There are 4 segments that we can imagine - north, south, east, and west
We can imagine that these lines all meet a circle
There are 360 degrees to a circle. So, if we divide that by 4, we know that each segment is 90 degrees.
(Also, you can probably see that the angles are right angles, or you know that straight lines are 180 degrees, you probably know this information intuitively)
This means that each smaller segment, two in both of our four segments, is 45 degrees.
These 8 sections are each 1/8 of the total circle.
How can properties of logarithms be used to change bases into equivalent bases? (to any other flvs students, this is an essential question for 05.02 of alg 2)
Answer:
We can use change of base rule
Five hundred ten of 650 high school students said that pizza was their favorite food in the school cafeteria.
what is the margin of error? round to four decimal places.
0.0005
0.0003
0.0161
0.0322
If Five hundred ten of 650 high school students said that pizza was their favorite food. The margin of error is 0.0322.
Margin of errorGiven:
Sample proportion=Five hundred ten=510
Sample size=650
Hence:
Margin of error=z×√p×(1-p)/n
Margin of error=2√510/650× (1-510/650)÷650
Margin of error=2√0.78461538×(1-0.78461538)÷650
Margin of error=2√0.78461538×0.21538462÷650
Margin of error=2√0.168994085÷650
Margin of error=2√0.0002599909
Margin of error=0.0322
Therefore the correct option is D.
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Use the diagram showing m || n, as well as the relationships between interior and exterior angles of ΔABC, to answer the questions.
The measure of angle ABC is
°.
The measure of angle BAC is
°.
The measure of angle ACB is
°.
The measure of angle ∠ACB is 70°. Then the correct option is C.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
∠ABC + ∠BCA + ∠CAB = 180°
60° + ∠BCA + 50° = 180°
∠BCA = 180° – 110°
∠BCA = 70°
Then the correct option is C.
The complete question is given below.
Use the diagram showing m || n, as well as the relationships between interior and exterior angles of ΔABC, to answer the questions.
The measure of ABC is 60
The measure of BAC is 50
The measure of ACB will be
a. 50
b. 60
c. 70
d. 120
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Answer:
Use the diagram showing m || n, as well as the relationships between interior and exterior angles of ΔABC, to answer the questions.
The measure of angle ABC is
✔ 60
°.
The measure of angle BAC is
✔ 50
°.
The measure of angle ACB is
✔ 70
°.
Step-by-step explanation:
If n= 1999 ! then [tex]\large \sf\sum\limits_{x = 1}^{1999} log_{n}(x) [/tex] is equal to
a) -1
b) 0
c) 1
d) [tex] \sf \sqrt[1999]{1999} [/tex]
Answer:
a) 1
Step-by-step explanation:
added in the picture
could someone please help me with this
Answer:
ia) center: (0, 0), the origin
ib) angle: 90°
ic) direction: CCW
ii) LM ≅ L'M', ∠L ≅ ∠L'
iii) (2, 1)
Step-by-step explanation:
A rigid transformation preserves size and shape of a figure, so the image is congruent to the original. The rigid transformations are rotation, reflection, and translation. Each has characteristics that allow one to determine the nature of the transformation(s) involved.
__
rotationangle and direction
One way to determine the angle and direction of rotation of a figure is to compare a horizontal segment on the original with the corresponding segment on the image. Here, a convenient segment is NM, which is horizontal and points to the right. Its angle relative to the direction of the +x axis is 0°.
The transformed segment N'M' points upward, at an angle relative to the +x axis of 90°. This tells you the figure was rotated 90° in the CCW direction. (This is fully equivalent to a rotation of 270° in the CW direction.)
center
Points in a rotated image always remain at the same distance from the center of rotation as the original points. In most cases, the center of rotation is the origin. We can check to see if that is the case by looking at the distances of a couple of points from the origin.
N is at coordinates (1, 1), so is √(1² +1²) = √2 from the origin
N' is at coordinates (-1, 1), so is √((-1)² +1²) = √2 from the origin
L is at coordinates (1, 3), so is √(1² +3²) = √10 from the origin
L' is at coordinates (-3, 1) so is √((-3)² +1²) = √10 from the origin
This confirms that the origin is the center of rotation.
__
Since each point and its image are on a circle centered at the center of rotation, the line between them is a chord of that circle. The perpendicular bisector of that chord goes through the center of rotation. Here, we observe that the perpendicular bisector of NN' is the y-axis. The perpendicular bisector of LL' is a line with slope -2 through (-1, 2). It will intersect the y-axis at the origin, confirming the origin as the center of rotation.
__
geometric relationshipsA rigid transformation preserves lengths and angles, so any length or angle on the rotated figure is congruent to the original:
LM ≅ L'M', MN ≅ M'N', NL ≅ N'L'
∠L ≡ ∠L', ∠M ≡ ∠M', ∠N ≡ ∠N'
__
translationThe components of a translation vector add to the corresponding coordinates of a point.
L +v = L'
(1, 3) +(1, -2) = (2, 1) . . . image of point L
PLs help answer ASAP
Answer:
The factors of the given equation are:
(11x−8)(11x+2)
Step-by-step explanation:
Since both terms are perfect squares,
Factorize using the difference of squares formula,
[tex]a^{2} -b^{2}[/tex][tex]=(a+b)(a-b)[/tex]
where a=11x−3 and b=5.
=> (11x-3+5)(11x-3-5)
=> (11x+2)(11x−8)
=>[tex](11x-3)^{2}-25[/tex]
Use the binomial theorem [tex](a-b)^{2}=a^{2} +b^{2} -2ab[/tex] to expand[tex](11x-3)^{2}-25[/tex]
=> [tex](11x^{2})+(3)^{2}- 2(11x)(3)-25[/tex]
=>[tex]121x^{2} + 9 - 66x -25[/tex]
=> [tex]121x^{2} -16+ 66x[/tex]
By the splitting method,
=> (11x−8)(11x+2)
The factors of the equation are (11x−8)(11x+2).
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How many more unit tiles must be added to the
function f(x)=x²-6x+1 in order to complete the square?
A 1
B 6
C 8
D 9
write an equation for the line that passes through the given point and has the given slope m (4,-5);m= -1/4
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y = -1/4x - 4}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Slope = -1/4, Point through = (4, -5)}[/tex]
Find: [tex]\textsf{Equation for the line that passes through the given point}[/tex]
Solution: In order to get the equation, we need to first use the point-slope form to help us sort out our information and then we solve for y.
Plug in the values
[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - (-5) = -1/4(x - 4)}[/tex]Simplify and solve for y
[tex]\textsf{y + 5 = -1/4(x - 4)}[/tex][tex]\textsf{y + 5 = -1/4x + 1}[/tex][tex]\textsf{y + 5 - 5 = -1/4x + 1 - 5}[/tex][tex]\textsf{y = -1/4x - 4}[/tex]Therefore, the final answer would be that the equation that has a slope of -1/4 and passes through (4, -5) is y = -1/4x - 4.
A trash can is in the shape of a cylinder. It has a radius of 2 feet and a height of 5 feet. What is the volume of the trash can? Round to the nearest tenth. Use 3.14 for pi
Answer: 62.8 cubic feet
Step-by-step explanation:
R is radius
H is height
R=2ft
H=5ft
V=(3.14)(2)^2(5)
V=62.8 cubic feet
3. Complete the square for the following equations:
a. y = 2x² 12x + 1
b. y = 4x² + 48x - 10
Answer:
a. y = 2(x + 3)² - 17
b. y = 4(x + 6)² - 154
Step-by-step explanation:
a. y = 2x² + 12x + 1
y = 2[(x² + 6x)] + 1
y = 2[(x + 3)² - 9] + 1
y = 2(x + 3)² - 18 + 1
y = 2(x + 3)² - 17
b. y = 4x² + 48x - 10
y = 4[(x² + 12x)] - 10
y = 4[(x + 6)² - 36)] - 10
y = 4(x + 6)² - 144 - 10
y = 4(x + 6)² - 154
