Answer:
[tex]\frac{463}{3}[/tex]
Step-by-step explanation:
The given geometric series is:
243-162+108.....+64/3
The first term is [tex]a=243[/tex].
The common ratio is:
[tex]r=\frac{-162}{243}=-\frac{2}{3}[/tex]
The sequence is finite, so we can generate all the terms by repeatedly multiplying by the common ratio until we get to the last term.
The complete series is
243-162+108-72+48-32+64/3
The sum is:
[tex]243+108+48+64/3-162-72-32=\frac{463}{3}[/tex]
Determine which relation is a function.
{(-4, 3), (-2,3), (-1, 2), (2,5), (3, 2)}
{(-4,1), (-2, 3), (-2, 1), (-1, 5), (3, 2)}
{(-4,1), (-2, 3), (-1, 2), (3,5), (3, 2)}
{(-4, 1), (-2, 3), (-1, 1), (-1, 5), (3, 2)}
Hello! :)
Since there is one value of y for every value of x in ( − 4 , 3 ) , ( − 2 , 3 ) , ( − 1 , 2 ) , ( 2 , 5 ) , ( 3 , 2 ) ( - 4 , 3 ) , ( - 2 , 3 ) , ( - 1 , 2 ) , ( 2 , 5 ) , ( 3 , 2 ) , this relation is a function. The relation is a function.
Hope I helped and wasn’t too late in answering!
Have fun and good luck!
~ Destiny ^_^
the correct answer is a) Function 1 only.
To determine which relations are functions from the given sets, we need to check if each element of the domain (the first number in each ordered pair) is mapped to only one element in the range (the second number in each ordered pair).
Set 1: {(-4, 3), (-2, 3), (-1, 2), (2, 5), (3, 2)}
Set 2: {(-4, 1), (-2, 3), (-2, 1), (-1, 5), (3, 2)}
Set 3: {(-4, 1), (-2, 3), (-1, 2), (3, 5), (3, 2)}
Set 4: {(-4, 1), (-2, 3), (-1, 1), (-1, 5), (3, 2)}
Analyzing each set:
Set 1 is a function because each domain value is unique and pairs with only one range value.
Set 2 is not a function because the domain value -2 is mapped to two different range values (3 and 1).
Set 3 is also not a function because the domain value 3 is mapped to two different range values (5 and 2).
Set 4 is not a function because the domain value -1 is mapped to two different range values (1 and 5).
Therefore, the correct answer is a) Function 1 only.
find the number of distinguishable permutations of the letters ZEBRA
Step-by-step Answer:
Since there are no repetitions in the five letters of the word ZEBRA, the number of permutations is 5! = 120 = 5*4*3*2*1.
Square RSTU dilates by a factor of 1\2 with respect to the origin to create square R'S'T'U'. If R'S' is 2 units, what is RS?
A.
4 units
B.
2 units
C.
0.5 units
D.
1 unit
Reset
Next
Answer: A.4 units
Step-by-step explanation:
We know that if a figure is dilated by a scale factor of k , then the measure of the corresponding image (l') of a line segment having measure 'l' is given by :-
[tex]l'=kl[/tex]
Given : Square RSTU dilates by a factor of 1\2 with respect to the origin to create square R'S'T'U'.
The measure of line segment R'S' = 2 units
The scale factor : [tex]k=\dfrac{1}{2}[/tex]
Using the above equation , we have
[tex]R'S'=\dfrac{1}{2}RS\\\\\Rightarrow\ RS= 2\times R'S'\\\\\Rightarrow\ RS= 2\times2=4[/tex]
Hence, RS = 4 units.
For which equation would n = 0 not be a solution?
n + 4 = 5
7 + n = 7
n + 12 = 12
125 + n = 125
A. n+4=5
Hope this helps
Mr. Roberts collected data to determine how many birds were at his bird feeder during different times of the day. Identify the striking deviation in his data.
A) 8-10am
B) 10am-12pm
C) 6pm-8pm
D) no striking deviation
sorry this one isnt for points this is just for help with my homework
Consider a striking deviation as an outlier (Something that stands out in a pattern, EX: 2, 3, 4, 4, 4, 5, 5, 10 where the outlier would be 10.) Because there are no outliers (Or, Striking deviations), we can conclude that the answer would be D: No striking deviation.
Determine whether the function f(x)=|x|+x2+0.001 is even , odd or neither. 10 points
the answer is even is the right answer
ANSWER
even
EXPLANATION
The given function is
[tex]f(x) = |x| + {x}^{2} + 0.001[/tex]
If f(x) is even then f(-x) =f(x).
[tex]f( - x) = | - x| + {( - x)}^{2} + 0.001[/tex]
[tex]f( - x) = | x| + {x}^{2} + 0.001[/tex]
We can see that:
[tex]f( - x) = f(x)[/tex]
Hence the given function is even.
6. Describe the end behavior and determine
whether the graph represents an
odd-degree or an even-degree polynomial function. Then state the number of real 0s
7. GEOMETRY Recall the formula for finding the area of a rectangle Define a
variable for the width and set up an equation to find the dimensions of a rectangle with an area of 144 square inches given the length is 10 inches longer than the width
Answer:
6. an odd-degree polynomial function.
f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞
7. Length =x+10=8+10=18 inches
Width=x=8 inches
Step by step explanation;
6. The graph represent an odd-degree polynomial function.
The graph enters the graphing box from the bottom and goes up leaving through the top of the graphing box.This is a positive polynomial whose limiting behavior is given by;
f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞
7.
The area of a rectangle is given by l×w, where l is length and w is the width
Let=w=x , l=x+10 and A=144 in² then;
l×w=144
(x+10) × x = 144
x²+10x =144......................complete squares on both sides
x²+10x+25=144+25
x²+10x+25=144+25................factorize
(x+5)²=169.......................square root the right-hand side
x+5= ±√169
x+5=±13.
x+5=13⇒⇒⇒x=8
x+5=-13⇒⇒⇒x= --18
x=8 inches....................value of width should be positive
Length =x+10=8+10=18 inches
Width=x=8 inches
Answer:
6. Since, by given graph,
The end behavior of the function f(x),
[tex]f(x)\rightarrow -\infty\text{ if }x\rightarrow -\infty[/tex]
[tex]f(x)\rightarrow +\infty\text{ if }x\rightarrow +\infty[/tex]
Thus, the function f(x) must has odd number of roots ( where the graph of a function intersects the x-axis )
⇒ The function must has odd number of solutions,
Again by the graph,
Graph of the function intersects the x-axis 5 times ( it touches the origin so it have the repeated root of x = 0 ),
Hence, the total number of real solution of f(x) is 5.
7. Let x represents the width of the rectangle( in inches ),
Given,
The length is 10 inches longer than the width,
⇒ Length of the rectangle = ( x + 10 ) inches
Thus, the area of the rectangle,
A = length × width = x(x+10)
According to the question,
A = 144 in²
⇒ x(x+ 10) = 144
[tex]x^2+10x=144[/tex]
[tex]x^2+10x-144=0[/tex]
[tex]x^2+18x-8x-144=0[/tex] ( Middle term splitting )
[tex]x(x+18)-8(x+18)=0[/tex]
[tex](x+18)(x-8)=0[/tex]
⇒ x = -18 or x = 8 ( By zero test property )
The width can not be negative,
Hence, the width of the rectangle would be 8 inches.
HELP!!! Use the factor Theorem to determine whether the binomial x+1 is a factor of the polynomial function f(x) =2x^3-9x^2+13x-6
A. No because f(c)=-30
B. No because f(c)=-4
C. Yes
D. No because f(c) =14
ANSWER
A. No because f(c)=-30
EXPLANATION
The given polynomial is
[tex]f(x) =2x^3-9x^2+13x-6[/tex]
If x+1 is a factor , then f(-1) must evaluate to zero.
[tex]f( - 1) =2( - 1)^3-9( - 1)^2+13( - 1)-6[/tex]
[tex]f( - 1) =2( - 1)-9( 1)+13( - 1)-6[/tex]
[tex]f( - 1) = - 2-9 - 13-6[/tex]
[tex]f( - 1) = -11 - 19[/tex]
[tex]f( - 1) = - 30[/tex]
Since f(-1) is not equal to zero, x+1 is not a factor of
[tex]f(x) =2x^3-9x^2+13x-6[/tex]
is 4, 16, 36, 64 a geometric sequence
ANSWER
No, there is no constant ratio.
EXPLANATION
We want to determine whether the sequence
4, 16, 36, 64
is geometric.
We need to find out if there is a common ratio between the consecutive terms.
[tex] \frac{16}{4} = 4[/tex]
[tex] \frac{36}{16} = \frac{9}{4} [/tex]
[tex] \frac{64}{36} = \frac{16}{9} [/tex]
Since the ratio is not the same for the consecutive terms, the sequence is not geometric.
4, 16, 36, 64 is a geometric sequence with a common ratio of 4.
Yes, 4, 16, 36, 64 is a geometric sequence.
To determine if a sequence is geometric, we need to check if there is a common ratio between consecutive terms. In this case, the common ratio is 4.A geometric sequence is one where each term after the first is found by multiplying the previous term by a constant, which is the common ratio.Write a quadratic equation to represent the circle graphed on the right
Answer:
The standard form: x² + (y + 1)² = 25The general form: x² + y² + 2y - 24 = 0Step-by-step explanation:
The equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the center (0, -1) and the radius r = 5 (look at the picture).
Substitute:
[tex](x-0)^2+(y-(-1))^2=5^2\\\\x^2+(y+1)^2=25[/tex]
use (a + b)² = a² + 2ab + b²
[tex]x^2+y^2+2y+1=25[/tex] subtract 25 from both sides
[tex]x^2+y^2+2y-24=0[/tex]
A triangle has sides that are 12, 14,
and 19. Is it acute, right, or obtuse?
Answer:
acute
Step-by-step explanation:
Find the height, in feet, of the ball after 3 seconds in the air.
By solving a system of equations, we determined the quadratic function h(x) = 33.5x^2 + 14x + 53.5 and found that the height of the ball after 3 seconds is 229.5 feet.
Certainly! Let's go through the step-by-step calculation to find the quadratic function representing the height of the ball and then determine the height after 3 seconds.
Given information:
h(1) = 91 feet
h(2) = 164 feet
We need to find the coefficients a, b, and c in the quadratic function h(x) = ax^2 + bx + c.
Step 1: Setting up Equations
We have two equations based on the given information:
a + b + c = 91 (since h(1) = a(1)^2 + b(1) + c = a + b + c = 91)
4a + 2b + c = 164 (since h(2) = a(2)^2 + b(2) + c = 4a + 2b + c = 164)
Step 2: Solving the System of Equations
We can solve the system of equations to find the values of a, b, and c.
Subtracting the first equation from the second gives: 3a + b = 73.
Let's multiply the first equation by 3 and subtract it from the second:
3(3a + b) - (a + b + c) = 3(73) - 91
Simplifying, we get 6a - c = 110.
Step 3: Substituting into the First Equation
Substitute 6a - c = 110 into the first equation:
6a - c + c = 110 + 91
Solving, 6a = 201, which implies a = 33.5.
Step 4: Finding b and c
Substitute a back into the first equation to find b + c = 91 - 33.5, and then b and c are determined as b = 14 and c = 53.5.
Step 5: Quadratic Function
Now, we have the quadratic function h(x) = 33.5x^2 + 14x + 53.5.
Step 6: Finding h(3)
Finally, substitute x = 3 into the quadratic function:
h(3) = 33.5(3)^2 + 14(3) + 53.5
Solving this yields h(3) = 229.5 feet.
Final Answer:
The height of the ball after 3 seconds is 229.5 feet.
Find the zeros of f(x) = x^2+5x-6.
A. {-2,3}
B. {-6,1}
c. {-2,-3}
D. {-6,-1}
Answer:
x^2+5x-6
a = 1 b = 5 and c = -6
Using the quadratic formula:
x = [-5 +- sq root (25 -4 * 1 *-6) ] / 2 * 1
x = [-5 +- sq root (49)] / 2
x = [-5 +- 7] / 2
x1 = 1
x2 = -6
Step-by-step explanation:
katniss divided x^3+2x^2-3x-4 by x+1. she didnt get a remainder. do you agree with her?
ANSWER
Katnis is right
EXPLANATION
We use the Remainder Theorem to check if she is right.
According to the Remainder Theorem, if the polynomial function,
[tex]p(x) = {x}^{3} + 2 {x}^{2} - 3x - 4[/tex]
is divided by x+1, then the remainder is given by
[tex]p( - 1)[/tex]
We substitute x=-1 into the function to obtain,
[tex]p( - 1) = {( - 1)}^{3} + 2 { ( - 1)}^{2} - 3( - 1) - 4[/tex]
We simplify to get:
[tex]p( - 1) = - 1+ 2 (1) + 3 - 4[/tex]
[tex]p( - 1) = 4- 4[/tex]
[tex]p( - 1) = 0[/tex]
Katnis is right because the remainder is zero
Ryan is building a tree house. It will take 85 1/4 hours to complete. He can work on the tree house 15 1/2 hours each week. To the nearest tenth, how many weeks will it take Ryan to complete the tree house
5 1/2 weeks. you divide 85 1/4 by 15 1/2 to get the answer
Ryan will take 5 weeks and 5 days to complete the tree house.
What is unitary method?'The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.'
According to the given problem,
Time taken by Ryan to complete building the tree house = 85[tex]\frac{1}{4}[/tex] hours
= [tex]\frac{341}{4}[/tex] hours
Hours he work on the tree house = 15[tex]\frac{1}{2}[/tex] hours
= [tex]\frac{31}{2}[/tex]
Weeks taken by Ryan to complete building = [tex]\frac{341}{4}[/tex] ÷ [tex]\frac{31}{2}[/tex]
= 5.5 weeks
= 5 weeks 5 days
Hence, we can conclude that Ryan is going to take 5 weeks and 5 days to complete building the tree house.
Learn more about Unitary Method here: https://brainly.com/question/24406804
#SPJ2
The expression on the left side of an equation is shown below. If the equation has an infinite number of solutions, which expression can be written in the box on the other side of the equation?
The answer is D. -2x+5.
If we simplify the left side of the equation first given, we come to the expression -2x-10.
If we solve for D., we get the same results. Thus, because an equation with all the same variable terms and constants have infinite solutions, the answer is D.
Hope this helps!
Answer:
The correct option is D) -2(x+5)
Step-by-step explanation:
Consider the provided equation.
-5(x+2)+3x=
The above equation is linear equation having one variable.
For an linear equation ax=b
a=0, b=0 in that situation the equation is in the form of 0x=0 for all value of x. Then there are infinitely many solutions.
Now solve the expression on the left side
-5(x+2)+3x
-5x-10+3x
-2x-10
-2(x+5)
Now for 0x=0 form the expression on the right side must be same as the expression on the left side for the provided equation.
Consider the options.
Option A) -5(x-3)+2x
Solve the above expression.
-5x-15+2x
-3x-15
-2(x+5)≠-3x-15
Thus the option is not correct.
Option B) -5x-10
Solve the above expression.
-5x-10
-5(x+2)
-2(x+5)≠-5(x+2)
Thus the option is not correct.
Option C) x-2x+2+3x
Solve the above expression.
x-2x+2+3x
2x+2
2(x+1)
-2(x+5)≠2(x+1)
Thus the option is not correct.
Option D) -2(x+5)
-2(x+5)=-2(x+5)
Hence, the correct option is D) -2(x+5)
Simplify Ratios 63 to 21
[tex]63:21=3:1[/tex]
Hope this helps.
r3t40
the plane that contains points C and T can also be named plane
Answer:
graph?
Step-by-step explanation:
Answer:CUB
Step-by-step explanation:
Multiply or divide as indicated (3x)^12/ (3x)^4
answer has to start with a (3
gets brainiest***
Answer:
[tex]\frac{(3x)^{12} }{(3x)^{4} } =(3x)^{8}[/tex]
Step-by-step explanation:
As we are dividing by powers, we can just subtract the powers as they have the same base. As 12-4=8 the answer would be
[tex]\frac{(3x)^{12} }{(3x)^{4} } =(3x)^{8}[/tex]
Answer:
[tex] (3 x )^ 8 [/tex]
Step-by-step explanation:
We are given the following expression which we are to multiply or divide as indicated:
[tex] \frac { ( 3 x ) ^ { 1 2 } } { ( 3 x ) ^ 4 } [/tex]
We know that if the bases are same and they are divided, then the exponent of the denominator is subtracted from the exponent of the numerator. So we get:
[tex] ( 3 x ) ^ { 1 2 - 4 } =( 3 x )^ 8 [/tex]
What is the solution to -1-7?
Answer:
-8
Step-by-step explanation:
-1-7 = -8
-8.
-1 - 7 would be adding because when subtracting negatives you always change the sign and a trick i know is that negatives are referred to as “hate” and positives are referred to as “love”. therefore if you do a negative minus a positive you will get a negative. so the answer here is -8.
I need help on this question.
Answer:
The constant of proportionality is y/x so the rate us 35
Step-by-step explanation:
Stewart has $26 dollars. He spent $12.81, including tax, to buy a new DVD. He needs to set aside $10.00 to pay for his lunch next week. If peanuts cost $0.42 per package including tax, describe the maximum number of packages that Stewart can buy?
A) p ≤ 8
B) p ≤ 7
C) p ≥ 8
D) p ≥ 7
Answer:
The answer is B,
26-12.81=13.19
13.19-10=3.19
3.19/0.42 is a little greater than 7
The sum of a number and 6 is at least 15
Answer:
x>8
Step-by-step explanation:
The number has to be bigger than 8 in order to be at least fifteen, so x is greater than 8
Ava wants to paint two walls in her room blue. Both walls are 9 feet tall and 12 feet long. One wall has a 3 foot by 2 foot window and the other wall has a 3 foot by 7 foot door. What is the combined area of the two walls Ava wants to paint?
189 ft2
210 ft2
216 ft2
243 ft2
Answer:
a
Step-by-step explanation:
it is 189ft² just trust me
Answer:
a
Step-by-step explanation:
A pyramid and a cone are both 10 centimeters tall and have the same volume. What state must be true about the two solids
Answer:
The horizontal cross-sections of the pyramid and the cone at the same height must have the same area.
Step-by-step explanation:
We are given that a pyramid and a cone are both 10 centimeters tall and have the same volume and we are to determine a statement which must be true for both the solids.
The horizontal cross-sections of the pyramid and cone at the same height must have the same area.
This is because
Answer:
Tbase area is same for both pyramid and cone
And cross section at same height the cross sectional area is same
Step-by-step explanation:
Points to remember
Volume of pyramid = (a²h)/3
Where a - side of base
h - height of pyramid
Volume of cone = (πr²h)/3
Where r - Radius of cone and
h - Height of cone
To find the correct answer
We have height of pyramid and cone is 10 cm
(a²h)/3 = (πr²h)/3
(a² * 10)/3 = (πr² * 10)/3
10a² = 10πr²
From this we get base area is same for both pyramid and cone
And cross section at same height the cross sectional area is same
pleasssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss
Answer:
Volume of prism is 60 cm^3.
Step-by-step explanation:
The volume of prism can be found using formula:
V= B*h
Where B= base area and h= height.
In the question, we are given Base area B= 10cm^2 and height h= 6cm.
Putting values in the formula:
V= B8h
V= 10* 6
V = 60 cm^3
So, volume of prism is 60 cm^3.
determine the direction that this parabola opens y=-4x^2-8x-13
Answer:
The direction that the paraboa y=-4x^2-8x-13 open is
Down
A class has 15 students; 8 females and 7 males. The teacher wants to form a group of 3
students to present the results of their class project to the Board of Education. What is the
probability that the group of three will consist of all females? You can leave your answer
as an unreduced fraction.
Answer:
8/15 chance
Step-by-step explanation:
To calculate the probability of forming an all-female group of three students from a class of 15 students, we find the total combinations of choosing three females and divide by the combinations of choosing any three students, resulting in a probability of 56/455.
The question involves calculating the probability that a group of three randomly selected students will consist of all females from a class of 15 students (8 females and 7 males). This is a problem of combinatorics and probability. We use combinations to determine the number of ways to choose three female students out of eight and divide that by the number of ways to choose any three students out of the fifteen.
First, we find the number of ways to choose three females: C(8,3) = 8! / (3! * (8-3)!) = 56. Then, we find the total number of ways to choose any three students: C(15,3) = 15! / (3! * (12!)) = 455. Therefore, the probability of choosing all females is 56/455.
WILL MARK BRAINLEST!!!
What is the difference when 5x^2 − 3x + 2 is subtracted from 4x^2 − 7x + 9?
A) x^2 − 4x + 7
B) −x^2 − 4x + 7
C) 9x^2 − 4x − 11
D) −9x^2 − 4x + 7
you answer is b) -x^2-4x+7
Answer:
B
Step-by-step explanation:
4x² - 7x + 9 - (5x² - 3x + 2) ← distribute by - 1
= 4x² - 7x + 9 - 5x² + 3x - 2 ← collect like terms
= (4x² - 5x² ) + (- 7x + 3x ) + (9 - 2)
= - x² - 4x + 7 → B
Alexandra is installing edge material around her yard. She has 400 ft of edge material to surround three sides of her rectangular yard. The fourth side will be against her deck and does not need edging. What is the maximum area that can be enclosed by the edging? Enter your answer in the box.
Answer:
The maximum area is equal to [tex]20,000\ ft^{2}[/tex]
Step-by-step explanation:
Let
x ----> the length of the rectangular yard
y ----> the width of the rectangular yard
we know that
The perimeter is equal to
[tex]400=x+2y[/tex] --> remember that the fourth side will be against her deck
isolate the variable y
[tex]y=200-0.5x[/tex] -----> equation A
The area of the rectangular yard is equal to
[tex]A=xy[/tex] ----> equation B
substitute equation A in equation B
[tex]A=x(200-0.5x)\\ \\A=200x-0.5x^{2}[/tex]
The quadratic function is a vertical parabola open downward
The vertex is a maximum
The x-coordinate of the vertex represent the length of the rectangular yard for an maximum area
The y-coordinate of the vertex represent the maximum area of the rectangular yard
Using a graphing tool
The vertex is the point (200,20,000)
see the attached figure
therefore
The length of the rectangular yard is 200 ft
The width of the rectangular yard is [tex]y=200-0.5(200)=100\ ft[/tex]
The maximum area is equal to [tex]20,000\ ft^{2}[/tex]