Answer:
D. d = 5
Step-by-step explanation:
d = d² - d¹
= 5 - 0
= 5
d = d³ - d⁴
= 10 - 5
= 5
d = dⁿ - dⁿ-¹
The common difference of the given sequence will be 5, i.e. option D.
What is Arithmetic progression?Arithmetic progression is the sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. The common difference is the value between each successive number in an arithmetic sequence
i.e. Common difference (d) = Successive term - Previous term
We have,
0, 5, 10, 15, 20, . . .
Here,
a₁ = 0
a₂ = 5
a₃ = 10
a₄ = 15
a₅ = 20
Now,
Find the common difference,
i.e.
Common difference (d) = a₂ - a₁ = 5 - 0 = 5,
Now,
Common difference (d) = a₃ - a₂ = 10 - 5 = 5
Now,
Common difference (d) = a₄ - a₃ = 15 - 10 = 5
Now,
Common difference (d) = a₅ - a₄ = 20 - 15 = 5
Now,
The Common difference is same for all i.e. 5.
Hence, we can say that the common difference of the given sequence will be 5, i.e. option D.
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What is the measure of each of the two angles formed by the bisector of the diagonal of a rhombus if the original angle measures 58 degrees?
Answer: 29 degrees is the answer
Step-by-step explanation:
The bisector is the line that divides the angle, and rhombus diagonally. So, basically you're just dividing 58 in half. Which is 29 degrees.
The measure of each of the two angles formed by the bisector of the diagonal of a rhombus will be 29 degree.
What is angle ?Angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
We have,
A Rhombus with one of its angle equal to 58°.
Now,
Bisector of an angle, divides an angle into two equal parts.
So,
From the above mentioned definition,
i.e.
[tex]=\frac{58}{2} = 29^0[/tex]
So, the measure of each angle is 29°.
Hence, we can say that the measure of each of the two angles formed by the bisector of the diagonal of a rhombus will be 29 degree.
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What is the measure of arc QR
Answer:
Could you repost your question with a picture of the arc?
The cost of performance tickets and beverages for a family of four can be modeled using the equation 4x + 12 = 48, where x
represents the cost of a ticket. How much is one ticket?
$3.00
$4.00
$9.00
$15.00
For this case we give as data the following equation:
[tex]4x + 12 = 48[/tex]
Where "x" represents the cost of a ticket.
By clearing the value of "x" of the equation we can know the cost of a ticket.
If we subtract 12 from both sides of the equation, we have:
[tex]4x = 48-12\\4x = 36[/tex]
If we divide between 4 on both sides of the equation:
[tex]x = \frac {36} {4}\\x = 9[/tex]
Therefore, the cost of a ticket is $ 9.00
Answer:
Option C
Write the equation of a line that goes through point (0, 1) and has a slope of 0.
Answer:
Equation of this line is y = 1
Step-by-step explanation:
We have to write an equation of a line passing through (0,1) and slope 0.
Standard equation of a line in slope form is y = mx + c
Where m = slope and c = y intercept.
Since m = 0
so y = c is the equation.
This line passes through (0,1)
so equation will be Y = 1
Equation of this line is y = 1
VIP at (-2,7) dropped her pass and moved to the right on a slope of -9 Where can you catch up to her to return her VIP pass
Check the picture below.
Answer:
-1,-2
Step-by-step explanation:
If you are doing this for FLVS and this helped make me the brainlist
NEED TO KNOW IMMEDIATELY the Revenue each season from tickets at the theme part is represented by t(x) = 3x the cost to pay the employees each season is represented by r(x) = (1.25)^x examine the graph of the combined function for total profit and estimate after five seasons
Answer:
r(5)=3.05 t(5)=15
Step-by-step explanation:
x=5
r(5)=(1.25)^5
r(5)=3.05
t(5)=3(5)
t(5)=15
Sam cut a pizza into 6 equal sizes slices. What is the measure of the angle formed by one of the pieces
Answer: 60
Step-by-step explanation:
A circle is 360 degrees, so 360/6 is your answer.
(02.03)Tony bought 3 tickets to a concert for $78. How much will it cost for 6 tickets to the concert if all tickets have the same unit price? Use the table below to help determine the missing value:
Number of Tickets 3 4 5 6
Cost $78 $104 $130 ?
Answer:
26$ Per ticket
missing number is 156$
Step-by-step explanation:
Find how much each ticket is by dividing 78 by 3 which is 26 the multiply 26 and 6 to find the missing number hope this helped :)
Answer:
The value of one ticket is 26 dollars, so for 6 tickets would be 156 dollars...
Step-by-step explanation:
$78 ÷ 3 tickets = $26
$26 × 6 tickets
= $156 for 6 tickets.
Helen recorded the number of tomatoes on each of her tomato plants and then arranged the numbers from smallest to largest.
The number of tomatoes on each plant were 5, 5, 5, 6, 9, 10, 10,10, 10, and 10. The mean number of tomatoes was 8.
What is the mean absolute deviation?
0.0
2.0
2.2
4.4
Answer:The last experimental design is the best of the options: 'Compare the average number of
tomatoes that are produced by 10 tomato plants that are grown in clay soil to
the average number of tomatoes that are produced by 10 tomato plants that are
grown in sandy soil''.
The first two experimental designs measure the growth of
tomato plants, which is not necessarily related to the yield of tomatoes. The
third experimental design compares the tomato yield of the two
soils with only one plant grown in each soil. Obviously, the result obtained
from this experiment would be statistically weak. The last experimental design
compares tomato yield and also uses a larger number of plants in each soil
type, so the results obtained would be of slightly greater statistical
significance.
Step-by-step explanation:
The mean absolute deviation is M = 2.2
What is Mean?The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.
Mean = Sum of Values / Number of Values
Given data ,
Let the total number of plants be n
Now , the value of n = 10
And , the number of tomatoes on each plant is given by set A
Now , the value of set A = { 5 , 5 , 5 , 6 , 9 , 10 , 10 , 10 , 10 , 10 }
So , the total number of tomatoes = 5 + 5 + 5 + 6 + 9 + 10 + 10 + 10 + 10 + 10
The total number of tomatoes = 80 tomatoes
Now , the mean number of tomatoes = 80 / 10 = 8
And , the mean deviation is M
where M = 1/10 [ ( 8 - 5 ) + ( 8 - 5 ) + ( 8 - 5 ) + ( 8 - 6 ) + | ( 8 - 9 ) | + 5( 10 - 8 )
M = ( 1/10 ) [ 3 + 3 + 3 + 2 + 1 + 5 ( 2 ) ]
M = ( 1/10 ) [ 22 ]
M = 2.2
Therefore , the value of M is 2.2
Hence , the mean deviation is 2.2
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Triangle ABC is reflected over the line y=x triangle ABC has points (-6,-1)(-2,-1) and (-5,-6) what is the C coordinate
Answer:
C' = (-6, -5)
Step-by-step explanation:
We are given that a triangle ABC is reflected over the line y = x.
Given the points of the vertices of the triangle ABC to be (-6, -1) (-2, -1) and (-5, -6) respectively, we are to determine the coordinates of C'.
When reflected over the line y = x, the x and y coordinates exchange their place.
(x, y) ---> (y, x)
Therefore, if C = (-5,-6) then C' = (-6, -5).
Answer:
[tex]\boxed{(-6,-5)}}[/tex]
Step-by-step explanation:
When you reflect a point (x, y) across the line y = x, the coordinates get interchanged. Thus,
(a,b) ⟶ (b,a)
Here are the coordinates of your triangle before and after the reflection.
[tex]\begin{array}{rcl}\textbf{Before} & & \textbf{After}\\A(-6,-1) & \longrightarrow \, & A'(-1,-6)\\B(-2,-1) & \longrightarrow \, & B'(-1,-2)\\C(-5,-6) & \longrightarrow \, & C'(-6,-5)\\\end{array}[/tex]
The diagram below shows ∆ABC with its reflection ∆A'B'C'.
[tex]\text{The coordinates of C' have become } \boxed{\mathbf{(-6,-5)}}[/tex]
What is the constant of proportionality in the equation y=5/9x
Answer:
The constant of proportionality in the equation y=5/9x is k=5/9.
Step-by-step explanation:
Equation for direct proportional function is
y = kx, where k is a constant of proportionality
so for y=5/9 x
k=5/9.
What is the vertex of x^2 -10x + 21
Answer:
(5, - 4)
Step-by-step explanation:
Given a quadratic in standard form : ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
x² - 10x + 21 ← is in standard form
with a = 1, b = - 10, so
[tex]x_{vertex}[/tex] = - [tex]\frac{-10}{2}[/tex] = 5
Substitute x = 5 into the quadratic for the corresponding value of y
y = 5² - 10(5) + 21 = 25 - 50 + 21 = - 4
vertex = (5, - 4)
If you are solving the equation by factoring, which of the following equations would you use the zero product property on? (x - 5)(x + 4) = 0 (x - 5)(x - 10) = 0 (x + 5)(x + 10) = 0
Equations would you use the zero product property on is (x-5)(x-10)=0
What is Zero product property?The zero product property states that if a⋅b=0 then either a or b equal zero.
To get the positive value we have consider those factor which have negative in their expression.
As, by the property if we equate both of them equal to zero one by one then we get the desired value.
(x-5)(x-10)= 0
if x-5=0
x=5
and if, x-10=0
x=10
Hence, equations would you use the zero product property on is (x-5)(x-10).
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Complete the proof. Below is a drag and drop geometric proof. Complete the proof in your notebook. Choose from these possible answers: Given YZ UV
Step-by-step explanation:
∠YXZ and ∠VXU are vertical angles, and therefore are congruent.
∠YXZ ≅ ∠VXU, Vertical ∠'s ≅
Next, we're given that lines YZ and UV are parallel. That means that ∠YZV and ∠UVZ are alternate interior angles, and therefore congruent.
∠YZV ≅ ∠UVZ, If lines ||, then alternate interior ∠'s ≅
If two triangles have two pairs of congruent angles, then the third pair must also be congruent, making the two triangles similar.
△XYZ ~ △XUV, AA
Since the triangles are similar, then by definition, their sides are proportional.
XY/XU = YZ/UV, Definition of Similar Polygons
YZ || UV - Given
YXZ = VXU - Vertical triangles =
YZV = UVZ - If lines ||, alternate internal triangles =
XYZ ~ XUV - AA
XY/XU = YZ/UV - Definition of Similar Polygons
If two pyramids have the same height, what must be true of the pyramids for them to also have the same volume
Answer:
If two pyramid have the same height , for volume to be the same the base area of the pyramids should be equal
Step-by-step explanation:
Volume of a pyramid is given by;
[tex]V=l*w*h /3[/tex]
where l is length of base, w is width of base, and h is height of base
If two pyramid have the same height , for volume to be the same the base area of the pyramids should be equal
The base area= l×w
For example if we have two pyramids A and B with the following properties;
A= height= x , length=l₁ and width = w₁
B= height=x, length=l₂ and width = w₂
Then the volume of the two pyramid will be the same if;
l₁*w₁=l₂*w₂
Thus
V₁= (l₁*w₁*x )/3 = (l₂*w₂*x)/3
For two pyramids with the same height to have the same volume, they must have bases with equal areas.
The volume [tex]\( V \)[/tex] of a pyramid can be calculated using the formula:
[tex]\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \][/tex]
Given that the height [tex]\( h \)[/tex] is the same for both pyramids, the volume formula simplifies to:
[tex]\[ V = \frac{h}{3} \times \text{base area} \][/tex]
For the volumes [tex]\( V_1 \)[/tex] and [tex]\( V_2 \)[/tex] of the two pyramids to be equal, the following equation must hold:
[tex]\[ \frac{h}{3} \times \text{base area}_1 = \frac{h}{3} \times \text{base area}_2 \][/tex]
Since the height [tex]\( h \)[/tex] is constant for both pyramids, it can be cancelled out from both sides of the equation:
[tex]\[ \text{base area}_1 = \text{base area}_2 \][/tex]
Therefore, the bases of the two pyramids must have equal areas to ensure that they have the same volume, given that they have the same height.
When converting from inches to feet , the measurement in inches,m, of an object varies directly with its measurement in feet, f, with the constant of variation being 12. What is the equation relating these two quantities?
Answer:
m = 12f
Or
m/12 = f
Step-by-step explanation:
The conversion from inches to feet involves a constant factor of variation which is 12. Inches is a smaller unit while feet are obtained by dividing the inches with 12.
As we know,
1 foot = 12 inches
Given in the question:
m = measurement in inches
and
f= measurement in feet
Hence the equation will be:
m = 12f
Or
m/12 = f ..
Look at the picture
↓↓↓↓↓↓↓↓↓↓
Answer:
[tex] ({ {x}^{m} )}^{3} = ( { {x}^{13} )}^{5} \times ( { {x}^{ - 8} )}^{ - 5} [/tex]
[tex] {x}^{3m} = {x}^{65} {x}^{40} [/tex]
[tex] {x}^{3m} = {x}^{105} [/tex]
[tex]3m = 105[/tex]
[tex]m = 35[/tex]
PLEASE HELP!!! Find the area
Answer:
13170
Step-by-step explanation:
We could just use heron's formula
S=(a+b+c)/2=(155+175+260)/2=295
area=sqrt(S(S-a)(S-b)(S-c))
area=sqrt(295(140)(120)(35))
area=sqrt(173460000)
area=13170 is closest whole number
you could check my work for little errors before you enter anything in if you want :p
Answer:
13170 units^2 to the nearest whole number.
Step-by-step explanation:
Use Heron's formula:
Area = √s(s-a)(s-b)(s-c)
s = the semi-perimeter
= (155 + 175 + 260) / 2
= 590/2 = 295.
Area = √ [295(295-155)(295-175(295-260)]
= √ 173460000
= 13170.42 units^2.
Jimmy can run 3.5 miles in 20 minutes. How far can he run in one hour and ten minutes?
Answer:
12.25 miles
Step-by-step explanation:
We can write a proportion to solve. Miles over time in minutes
1 hour = 60 minutes
1 hours 10 minutes = 60+10 = 70 minutes
3.5 miles x miles
--------------- = --------------
20 minutes 70 minutes
Using cross products
3.5 *70 = 20x
245 = 20x
Divide each side by 20
245/20 = 20x/20
12.25 =x
Jimmy can go 12.25 miles
Find the length of segment AC if AB is 7, BC is 12 and B is between a A and C
Step-by-step explanation:
If the B is the middle of the segment AC,
AC= AB+BC
AC=7+12= 19.
If I'm wrong, correct me please. I would be pleased.
What is the sum of the polynomials 6a²-17a-9 and -5a²+8a-2?
A) a²-9a-11
B) a²-25a-7
C) 11a²-9a-11
D) 11a²-25a-7
Answer:
Choice A) a² - 9a - 11.
Step-by-step explanation:
Separate the terms by the power of the variable, [tex]a[/tex].
Terms with power 2 on [tex]a[/tex]:
First equation: 6a²;Second equation: -5a².Terms with power 1 on [tex]a[/tex]:
First equation: -17a;Second equation: 8a.Terms with power 0 on [tex]a[/tex], which are also known as constant terms:
First equation: [tex]-9[/tex]; Second equation: [tex]-2[/tex].Apply the distributive property of multiplication in reverse. In other words, factor out terms with the same power and add the coefficients.
Terms with power 2 on [tex]a[/tex]:
[tex]6a^{2} + (-5a^{2}) = (6 + (-5))a^{2} = a^{2}[/tex].
Terms with power 1 on [tex]a[/tex]:
[tex]-17 a + 8a = ((-17) + 8)a = -9a[/tex].
Constant terms:
[tex](-9) + (-2) = -11[/tex].
Add the sum of the individual terms to find the sum of the two polynomials:
[tex]a^{2} + (- 9a) +(- 11) = a^{2}-9a -11[/tex].
ACUVIL
1) Which of the following could be the
lengths of the sides of a triangle?
B) 13, 14, 32
A) 33, 22, 55
D) 11, 15, 27
C) 16, 19, 34
Answer:
A:33,22,55
Step-by-step explanation:
If f(x) = 5x + 40, what is f(x) when x = -5?
use the substitution method
f(x)= 5x+40
f(-5)= 5(-5)+40
f(-5)= -25+40
f(-5)= 15
Answer is f(-5)= 15
What is the slope of the linear function y = 7?
The slope is 0. y = 7 makes a horizontal line, therefore there is no rise only a run.
Remember: If it creates a horizontal line the slope is zero
Hope this helped!
~Just a girl in love with Shawn Mendes
Simplify the radical expression 5/64
Answer:
40
Step-by-step explanation:
5√64 = 5 x 8 = 40
Answer:
√5
==
8
or
Sqrt5
over
8
Step-by-step explanation:
Find the product. -2 xa (-4 xb - 2 x 3 + 5 x )
Answer:
[tex]8x^{a+b}+4x^{3+a}-10x^{a+1}[/tex]
Step-by-step explanation:
We need to find the product of: [tex]-2x^{a}(-4x^{b}-2x^{3}+5x)[/tex]
We have that:
[tex]-2x^{a}(-4x^{b}-2x^{3}+5x)[/tex] = [tex]8x^{a+b}+4x^{3+a}-10x^{a+1}[/tex]
We can't simplify more the expression, therefore, the solution is:
[tex]8x^{a+b}+4x^{3+a}-10x^{a+1}[/tex].
What is the midpoint of the line segment graphed below?
(-12, 3) (5, -10)
Use the midpoint formula
(x1 + x2/2, y1 + y2/2)
Input the corresponding numbers
(-12 +5/2, 3 + -10/2)
(-7/2,-7/2)
So, the midpoint of the line segment is (-7/2,-7/2)
The midpoint of the line segment is (-3.5, -3.5)
Explanation:To find the midpoint of a line segment, we can use the midpoint formula. The formula is:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Using the coordinates (-12, 3) and (5, -10), we can substitute the values into the formula:
Midpoint = ((-12 + 5) / 2, (3 + -10) / 2)
After simplifying, the midpoint is (-3.5, -3.5).
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what is the perimeter of a triangle with vertices located at (-1,4) (2,7) and (1, 5)? Round to the nearest hundredth.
Use the distance formula to find the distance between each vertices:
Distance formula: √((x2-x1)^2 + (y2-y1)^2)
(-1,4) (2,7) = 4.24
(-1,4) (1,5) = 2.24
(2,7) (1,5) = 2.24
Perimeter = 4.24 + 2.24 + 2.24 = 8.72
Answer:
7.40 units
Step-by-step explanation:
Plssss help
A bag contains 6 red marbles, 10 white marbles, and 6 blue marbles. You draw 3 marbles out at random, without replacement.
A) What is the probability that all the marbles are red?
B) what is the probability the exactly 2 of marbles red?
C) What is the probability that none of the marbles are red?
Answer:
A) [tex]\displaystyle \frac{1}{77}[/tex].B) [tex]\displaystyle \frac{12}{77}[/tex].C) [tex]\displaystyle \frac{4}{11}[/tex].Step-by-step explanation:
All marbles here are identical. Also, the question isn't concerned about the order in which the marbles are drawn. Thus, all calculations here shall be combinations rather than permutations.
A)How many ways to choose three out of six identical red marbles without replacement?
[tex]\displaystyle _6C_3 = c(6, 3) = {6\choose 3} = 20[/tex].
Note that these three expressions are equivalent. They all represent the number of ways to choose 3 out of 6 identical items without replacement.
How many ways to choose three out of all the 6 + 10 + 6 = 22 marbles?
[tex]\displaystyle _{22} C_{3} = 1540[/tex].
The probability of choosing three red marbles out of these 22 marbles will be:
[tex]\displaystyle \frac{\text{Number of ways for choosing three out of six red marbles}}{\text{Number of ways to choose three out of 22 marbles}} = \frac{20}{1540} = \frac{1}{77}[/tex].
B)How many ways to choose two out of six identical red marbles without replacement?
[tex]\displaystyle _6 C_2 = 15[/tex].
How many ways to choose one out of 10 + 6 = 16 non-red marbles?
[tex]_{16} C_1=16 [/tex].
Choosing two red marbles does not influence the number of ways of choosing a non-red marble. Both event happen and are independent of each other. Apply the product rule to find the number of ways of choosing two red marbles and one non-red marble out of the pile of 22.
[tex]_6 C_2 \cdot _{16} C_1= 240[/tex].
Probability:
[tex]\displaystyle \frac{240}{1540} = \frac{12}{77}[/tex].
Double check that the order doesn't matter here.
C)None of the marbles are red. In other words, all three marbles are chosen out of a pile of 10 + 6 = 16 white and blue marbles. Number of ways to do so:
[tex]_{16} C_{3} = 560[/tex].
Probability:
[tex]\displaystyle \frac{560}{1540}= \frac{4}{11}[/tex].
Answer:
A) 1/77; B) 12/77; C) 4/11
Step-by-step explanation:
A) There are a total of 22 marbles. 6 of them are red.
On the first draw, the probability of getting a red marble is 6/22.
On the second draw, there's one less red marble and one less marble total, so the probability of getting another red marble is 5/21.
Similarly, on the third draw, the probability of getting a red marble is 4/20.
So the probability that all three draws are red marbles is:
P = (6/22) (5/21) (4/20)
P = 1/77
Another way this can be calculated is with combinations:
P = (ways to choose 3 red marbles from 6) / (ways to choose 3 marbles from 22)
P = ₆C₃ / ₂₂C₃
P = 20 / 1540
P = 1/77
B) The same logic can be repeated here. Using the first method, if the first two selection are red:
P = (6/22) (5/21) (16/20) = 4/77
If the first and third are red:
P = (6/22) (16/21) (5/20) = 4/77
If the last two are red:
P = (16/22) (6/21) (5/20) = 4/77
So the total probability is:
P = 4/77 + 4/77 + 4/77
P = 12/77
Using the second method:
P = (ways to choose 2 red from 6) × (ways to choose 1 non-red from 16) / (ways to choose 3 from 22)
P = ₆C₂ ₁₆C₁ / ₂₂C₃
P = 15 × 16 / 1540
P = 12/77
C)
Same logic:
P = (16/22) (15/21) (14/20)
P = 4/11
Or:
P = ₁₆C₃ / ₂₂C₃
P = 560 / 1540
P = 4/11
Using the prime factor method, find the lowest common multiple of 20 and 12.
Answer:
lcm = 4
Step-by-step explanation:
20 = 2 × 2 × 5 ← product of prime factors
12 = 2 × 2 × 3 ← product of prime factors
The lowest common multiple (lcm) = 2 × 2 × 5 × 3 = 60
Answer:
60
Step-by-step explanation:
First, break down each of the numbers into their prime factors.
20 = 2² x 5
12 = 2² x 3
To find the LCM, underline each of the prime numbers. If there is a repeated prime number, underline the one with the largest possible value. For example, if there is 3² and 3³, underline the second one. In this case, the values are the same, so just underline one.
20 = 2² x 5
12 = 2² x 3
Next, multiply all the underlined numbers.
LCM (20, 12) = 2² x 5 x 3 = 60