(a)the common ratio = 2
(b)the 6th term = 64
How to find the common ratio and 6th term ?
A geometric progression, which is another name for a geometric sequence, is a series of non-zero numbers .In a G.P each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratioA geometric progression is given by a, ar, a[tex]r^{2}[/tex], a[tex]r^{3}[/tex],....Here, the common ratio = r
the first term = a = 2
(a)the common ratio
[tex]a +ar^{2} = 10\\\\2(1+r^{2} ) = 10\\\\(1+r^{2} ) = 5\\\\r^{2} =4\\\\r = 2[/tex]
The common ratio (r) = 2
(b)the 6th term
[tex]a_{n}=ar^{n-1} \\\\a_{6}=ar^{6-1} \\\\a_{6} =2(2^{5} )\\\\a_{6}=64[/tex]
Thus ,the 6th term = 64
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simplify this expression 2 (times) x (times) 3 (times) y
The first to answer I will give branliest
The simplified expression of the expression 2 x 3 x y is 6y
How to simplify the expression?From the question, we have the following statement that can be used in our computation: 2 (times) x (times) 3 (times) y
Express as numbers
So, we have
2 x 3 x y
Evaluate the products of the numbers
So, we have the following representation
2 x 3 x y = 6 x y
Evaluate the products of the number and the variable
So, we have the following representation
2 x 3 x y = 6y
The above expression cannot be further simplified
Hence, the expression is 6y
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1, 728 ÷ 32 what is the value of the expression
Result : 54
reminder = 0
[tex]1,728\div32[/tex]
Simplify the expression:
[tex]1,728\div32\\[/tex]
[tex]=54[/tex]
Hope this helps!
((1/3)x^2))-((1/9)x)-(2/9)=0
The solution of the quadratic equation (1/3)x² - (1/9)x - 2/9 = 0 are x = 1, - 2/3.
Any equation that can be written in the standard form where x stands for an unknown and a, b, and c are known quantities, with a 0, is said to be quadratic.
An assignment of values to the unknown variables that establish the equality in the equation is referred to as a solution.
Consider the expression,
(1/3)x² - (1/9)x - 2/9 = 0
Multiplying each side of the quadratic equation by 9,
9 × [ (1/3)x² - (1/9)x - 2/9 = 0 ]
3x² - x - 2 = 0
Using the quadratic formula,
[tex]x = \frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
[tex]x = \frac{1 \pm \sqrt{1+24} }{6}\\ x = \frac{1 \pm \sqrt{25} }{6}[/tex]
x = 1 and x = - 2/3
Hence, the solution of quadratic equation (1/3)x² - (1/9)x - 2/9 = 0 are x = 1, - 2/3.
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Jarrett surveyed elementary school students about their favorite animals at the zoo He displayed his results in this circle graph If 412 students chose lions as their favorite zoo animal how many total students did Jarrett survey?
Since the 40% of the students choose lion, we can use the following expression:
[tex]\begin{gathered} \text{Total of students}\cdot\frac{\text{percent}}{100}=\text{equivalent number to the percent} \\ \text{Total students}\cdot\frac{40}{100}=412 \\ \text{Isolating the variable total students:} \\ \text{Total students=}\frac{412\cdot100}{40}=\frac{41200}{40} \\ \text{Total students=1030} \end{gathered}[/tex]Jarrett survey 1030 students
Please answer :-Factorize x²+1.
The given expression is
[tex]x^2+1[/tex]We can not factorize this expression bt the normal factorizing ways
Because it is a binomial with + as a middle sign can not be distributed into 2 factors
Then there is no factorizing for the given binomial
If the sign between the two terms is (-), then we can factorize it into two same factors with different middle sign
We can use the complex numbers to factorize it
[tex]\begin{gathered} x^2=(x)(x) \\ 1=(i)(-i) \\ (x)(i)+(x)(-i)=(xi)-(xi)=0 \\ (x+i)(x-i) \end{gathered}[/tex]Then the factors are (x + i) and (x - i)
[tex]x^2+1=(x+i)(x-i)[/tex]Answer:
x^2+1
Step-by-step explanation:
The expression is not factorable with rational numbers.
The maximum load of a horizontal beam that is supported at both ends varies jointly as the width and the height and inversely as the length between the supports. A beam 6m long, 0.1m wide, and 0.06 m high supports a load of 360kg. What is the maximum load supported by a beam 16m long, 0.2m wide, and 0.08 m high?
Answer:
[tex]360kg[/tex]Explanation:
Here, we want to get the maximum load supported
From the first part of the question, we have it that:
The maximum load g, varies jointly with the width w and the height h, and inversely as the length l between the supports
Mathematically, we have that as:
[tex]g\text{ = k }\times\frac{wh}{l}[/tex]where k is the proportionality constant
Now, let us get the value of k
We substitute the first set of values as follows:
[tex]\begin{gathered} 360\text{ = }\frac{k\times0.1\times0.06}{6} \\ \\ k\text{ = 360,000 }\frac{kg}{m} \end{gathered}[/tex]Now, using this value of k, we want to get the value of g
Mathematically, we have that as:
[tex]g\text{ = }\frac{360,000\times0.2\times0.08}{16}\text{ = 360 }kg[/tex]The function shown in the graph is f(x) =
Answer:
x³-2x²-5x+6 =0
Step-by-step explanation:
x³-2x²-5x+6 =0
checking zeros
x=1 , 1-2-5+6=0, 0=0 true
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The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour plus $75 for an assistant. The committee wants to keep the total cost under $450. plssss I need stepss.
The dance committee can hire the DJ for a maximum of 3 hours keeping the cost under control
DJ charges per hour = $125
Charges for assistance = $75
Budget by the committee = $450
Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Let x represent the maximum number of hours to hire the DJ
Formulating the equation we get:
DJ charges per hour*Number of hours<= Required budget
125x + 75<=450
Solving the equation:
125x <= 375
x <=3
So, a maximum of 3 hours
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State the x and y intercepts of the given graphs.
Answer:
• x-intercept: (3, 0)
,• y-intercept: (0, -2)
Explanation:
x-intercept
The x-intercept is the point at which the graph crosses the x-axis.
From the graph, the x-intercept is at (3, 0).
y-intercept
The y-intercept is the point at which the graph crosses the y-axis.
From the graph, the y-intercept is at (0, -2).
A board game uses a spinner to determine how many spaces a player will move forward on each turn. The probability is 1/2 that the player moves forward 1 space, and moving forward 2 or 3 spaces each have 1/4 probability. What is the expected value for the number of spaces a player moves forward on a turn?
ANSWER
1.75
EXPLANATION
The expected value of an event X is the sum of the products of each value of the event and the probability of the event resulting in that value.
In this case,
[tex]E\lbrack X\rbrack=1\cdot P(1\text{ }forward)+2\cdot P(2\text{ }forward)+3\cdot P(3\text{ }forward)=1\cdot\frac{1}{2}+2\cdot\frac{1}{4}+3\cdot\frac{1}{4}[/tex]Solve,
[tex]E\lbrack X\rbrack=\frac{1}{2}+\frac{1}{2}+\frac{3}{4}=\frac{7}{4}=1.75[/tex]Hence, the expected number of spaces the player moves in a turn is 1.75.
Given f(x)= -5x^5 - x^4 + 4x^3 and g(x)= -5x^5 - 3x^3 -5x^2 +8 find and simplify f(x) - g(x).
f(x) - g(x) =
degree=
leading coefficient=
The simplified function, f(x) - g(x) is - x⁴ + 7x³ + 5x² - 8.
The degree and leading coefficient are 4 and -1 respectively.
How to simplify functions?The functions to be simplified is as follows;
f(x) = - 5x⁵ - x⁴ + 4x³
g(x) = - 5x⁵ - 3x³ -5x² + 8
Therefore, let's simplify the function,
f(x) - g(x) = - 5x⁵ - x⁴ + 4x³ - (- 5x⁵ - 3x³ -5x² + 8)
open the bracket with the negative sign
f(x) - g(x) = - 5x⁵ - x⁴ + 4x³ + 5x⁵ + 3x³ + 5x² - 8
combine like terms
f(x) - g(x) = - 5x⁵ + 5x⁵ - x⁴ + 4x³ + 3x³ + 5x² - 8
f(x) - g(x) = - x⁴ + 7x³ + 5x² - 8
Therefore,
degree of the function = 4
Leading coefficient = -1
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Write an equation and point slope for the line that passes through the giving order pairs there are two correct answers for this question Depending upon which order pair do you use for the slope for
If we label the given points to find the slope of the line, we have:
(4, 1 ) ---> x1 = 4, y1 = 1
(-2, 7) ---> x2 = -2, y2 = 7.
Then, using the formula for the slope of a line, we have:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{7-1}{-2-4}=\frac{6}{-6}\Rightarrow m=-1[/tex]Then, having this value of m, we can apply the formula for the Point-Slope Form of the line:
1. In the case we take the pair as ( 4, 1), the equation is:
[tex]y-y_1=m(x-x_1)=y-1=-1(x-4)=y-1=-(x-4)[/tex]2. In the case we take the pair as (-2, 7), we have:
[tex]y-7=-1(x-(-2)=y-7=-(x+2)[/tex]Then, we have two options:
[tex]y-1=-(x-4)[/tex][tex]y-7=-(x+2)[/tex]CuIU/u
Rebecca is playing a video game that involves planting and cutting down trees. She
moves up an energy level for each tree she plants, and she moves down a level for
each tree she cuts. If Rebecca reaches energy level 10, she will earn bonus points.
Rebecca is currently at energy level 4. The results of her next 3 turns are:
Turn 1: 6 trees cut
Turn 2: 8 trees planted
Turn 3: tree cut
Answer the questions to find out whether Rebecca earned bonus poirlts in the next 3
turns. Use the number line to help you add.
2 3 4 5 6 7 8 9 10
1. Using only addition, write an expression that represents Rebecca's score after these
three turns. (Remember that she starts at an energy level of 4.). (2 points)
By the end of her three turns, she is level 5.
The number line is what?
A number line is a visual depiction of numbers on a straight line in mathematics. A number line's numerals are arranged in a sequential manner at equal intervals along its length. It is often displayed horizontally and can extend indefinitely in any direction.
If Rebecca cuts down six trees on her next round, she drops down to level four and gains six levels. Rewriting this as -6 yields 4 + (-6) = -2. her following turn, she will plant 8 trees, increasing her level by 8. -2 + 8 = 6 In her final round, she removes one tree.
6 + (-1) = 5
4 + (-6) + 8 + (-1) = 5 in total.
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If you have a second credit card, your security deposit or spending limit prevents you from spending more than you can afford or repay
True or False?
Answer: true
Step-by-step explanation:
What is the third stage of a plant's life cycle called, when the plant is small, has only a few leaves, has a soft stem, and has small roots?
Answer:
Growing to maturity
Step-by-step explanation:
The seedling progresses to full maturity as it continues to grow. Many things are needed during the life cycle of a plant while it's growing.
I hope this helps you! Please tell me if I'm wrong.
도움이 되기를 바랍니다. 내가 틀렸다면 말해주세요.
Complete the truth table.
р
q
-
pЛ-4
P+
-(p+q)
F F
T
T
F
F
T
T T
F
T
T
חד
F
T
F
T
F
T
F
T
וד
F
וד
F
T
רד
F
F
given the function
[tex](-p\rightarrow q)\rightarrow(q\rightarrow-r)[/tex]option 1
P=T
Q=T
R=T
then
-P=F
-R=F
-P -> q=V
q ->-r= F
then
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=F[/tex]Option 2
P=T
Q=T
R=F
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=T[/tex]Option 3
P=T
Q=F
R=T
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=T[/tex]Option 4
P=T
Q=F
R=F
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=T[/tex]Option 5
P=F
Q=T
R=T
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=F[/tex]Option 6
P=F
Q=T
R=F
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=T[/tex]Option 7
P=F
Q=F
R=T
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=T[/tex]Option 8
P=F
Q=F
R=F
[tex](-p\operatorname{\rightarrow}q)\operatorname{\rightarrow}(q\operatorname{\rightarrow}-r)=T[/tex]The surface areas of two similar figures are 16 in2 and 25 in2. If the volume of the larger figure is 500 in3, what is the volume of the smaller figure?
The volume of the smaller figure is 256 in³.
Given, the surface area of two figures are 16 and 25.
volume of the larger figure is 500.
volume of smaller figure =?
Similar figures have a scale factor k, (let k be >1, so k is the ratio of a distance in the larger figure to the corresponding distance in the smaller one)
First, we calculate for the ratio of the surface areas of the given figures. From the given above, the ratio is equal to 25:16
Then, we calculate for the ratio of the perimeters or sides of the figures by getting the square root of the ratio in figure 1.
ratio of perimeter or side = 5:4
The ratio of the volumes of the figures is equal to the cube of the ratio in figure 2.
ratio of volumes = (5:4)³ = 125:64
Using this ratio and the volume of the larger figure,
500 in³/x in³ = 125/64
x in³ = 500×64/125
x in³ = 256 in³
The value of x from the equation is 256. Therefore, the volume of the smaller figure is 256 in³.
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Diamonds are weighed in carats.
A carat is gram.
5
What is the weight in grams
of the largest diamond in the world,
the 3106-carat Cullinan diamond?
plss help
Answer:
621.2 grams
Step-by-step explanation:
One carat is 0.2 grams
Multiply that by 3106 to get 621.2 grams
Which of these situations can be represented with an integer that, when combined with the opposite of 8, makes 0?
The statements below represent some possible deposits and withdrawals from Rachel's bank account. Match each statement with the total amount that Rachel's account would change. -47.50 -22.50 22.50 She deposits $35 to her account. Then spends $12.50 from her account on lunch. She withdraws $35 from her account. Then spends $12.50 from her account on lunch. She spends $35 from her account on clothes. Then she deposits $12.50 to her account. 000 OO
merlyumanzor23, this is the solution:
A. 35 - 12.50 =
Match each equation to one of the two tape diagrams. Dragon drop each card to match the equation to the correct tape diagram. - (please use ss)
First diagram:
Sum of the three parts is equal to 9: x+x+x is 9 or three times x is 9
Equations:
[tex]\begin{gathered} 3\cdot x=9 \\ 9=3\cdot x \\ x+x+x=9 \end{gathered}[/tex]Also you can write the equation 3*x=9 as follow by solving x:
[tex]x=9\div3[/tex]Second diagram:
Sum of the two parts is equal to 9: x+3 = 9
Equations:
[tex]\begin{gathered} x+3=9 \\ 3+x=9 \end{gathered}[/tex]Solving x you can write the equation:
[tex]x=9-3[/tex]Find the volume of this cylinder. Use 3 for . V = 7r2h 12 cm 5 cm V~ [?]cm Enter
Looking at the figure, the diameter of the cylinder is 12 cm and its height is 5 cm
The radius is half the diameter, so we have r = 6 cm.
Now, using the volume formula, we have:
[tex]\begin{gathered} V=\pi r^2h \\ V=3\cdot6^2\cdot5 \\ V=3\cdot36\cdot5 \\ V=540 \end{gathered}[/tex]So the volume of the cylinder is 540 cm³.
Use I = PRT to solve.
(time is in years)
| = $14,400
R = 8%
T = 30 years
Find P.
Principal is $6000.
Define simple interest.Simple Interest (S.I.) is a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest. For instance, if someone borrows $5000 at a rate of 10 p.a. for two years, they will pay S.I. on the borrowed money for those two years. Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
Given Data
Using simple interest formula,
| = $14,400
R = 8%
T = 30 years
I = [tex]\frac{PRT}{100}[/tex]
14400 = [tex]\frac{P(8)(30)}{100}[/tex]
[tex]\frac{14400(100)}{8(30)}[/tex] = P
P = 6000
Principal is $6000.
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Classify the system (options: consistent, independent consistent, inconsistent) 4x + 2y = 8y = -2x + 8
Write both equations in standard form:
[tex]ax+by=c[/tex]The first one is already written in standard form:
[tex]4x+2y=8[/tex]To write the second one in standard form, add 2x to both members of the equation:
[tex]\begin{gathered} y=-2x+8 \\ \Rightarrow y+2x=-2x+8+2x \\ \Rightarrow2x+y=8 \end{gathered}[/tex]Notice that if we divide both members of the first equation by 2, we get:
[tex]\begin{gathered} \frac{4x+2y}{2}=\frac{8}{2} \\ \Rightarrow2x+y=4 \end{gathered}[/tex]Then, the system of equations is equivalent to:
[tex]\begin{gathered} 2x+y=8 \\ 2x+y=4 \end{gathered}[/tex]For the transitive property of equality, since both left members are the same, we can conclude from that system of equations that 8=4, which is false. Then, the system is inconsistent, since it leads to a contradiction.
Therefore, the answer is:
[tex]\text{Inconsistent}[/tex]I really need help on the do you mind helping
the quation of the given graph is,
[tex]y=(x+3)^2-1[/tex]To the nearest tenth of a second, how much time would it take the penny to hit the ground?
In this problem, we want to approximate when a penny will hit the grownd after it has been dropped from the back of the bleachers.
Since we have been given a table, we can make a close estimate based on the y-values.
When the penny hits the ground, the value of y will be 0.
Notice on the table provided that the penny is going to reach 0 between the values of 0.6 and 0.7 seconds.
At 0.6 seconds, it has a distance of 0.236 meters from the ground.
At 0.7 seconds, supposing the penny went past hitting the ground, it was have a distance of
[tex]|-0.401|=0.401\text{ meters from the ground.}[/tex]Since the penny is closer to 0 at the 0.6 s mark than the 0.7 s mark, we can say 0.6 seconds is when the penny will hit the ground.
Here is a graphic model of the penny moving toward the ground:
Graph the line that contains the point (3,-6) and has a slipe of 1/2
to graph the line we first need to get its equation. The equation of a line is:
[tex]y-y_1=m(x-x_1)[/tex]Then, we have:
[tex]\begin{gathered} y-(-6)=\frac{1}{2}(x-3) \\ y+6=\frac{1}{2}x-\frac{3}{2} \\ y=\frac{1}{2}x-\frac{3}{2}-6 \\ y=\frac{1}{2}x-\frac{15}{2} \end{gathered}[/tex]Once we have the equation we can find another point on the line. If x=1 then y=-7, hence we have the point (1,-7).
Now we graph the points (1,-7) and (3,-6) and jo
In the 2.5 minutes between innings in a baseball game, a hotdog launcher launches 12 hotdogs into the crowd. Clara, a member of the mascot team, wants to know how long she has to launch each hotdog. What is the unit rate in seconds per hotdog?
The unit rate in seconds per hotdog is 12.5 seconds.
The time between the innings in a baseball game is 2.5 minutes.The hotdog launcher has to launch a total of 12 hotdogs into the crowd within the time between the innings.Clara is a member of the mascot team. She has a limited amount of time to launch each hotdog.Let us convert the time in minutes to seconds.2.5 minutes equals 2.5*60 seconds.The time is 150 seconds.The total number of hotdogs to be launched is 12.The amount of time available for each hotdog is the rate at which she can launch hotdogs into the crowd.The unit rate in seconds per hotdog is 150/12.The unit rate in seconds per hotdog is 12.5 seconds.To learn more about rate, visit :
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(Please help. Will be marked brainliest) Clifford is making a really big white cake for his sister’s birthday. The recipe calls for 1.5 times as much flour as sugar. It also calls for
1
2 as much butter as sugar. All the butter, flour, and sugar together total 7.5 cups. How much butter, sugar and flour does Clifford need?
After solving the equation, Clifford need 3.75 cups of flour, 2.5 cups of sugar and 1.25 cups of butter to make the cake.
What is an equation?Equation, also referred to as a declaration of equality between two expressions that contain variable- and/or number-based components. Since equations are essentially questions, the development of mathematics has been driven by efforts to systematically find answers to those questions.
There are many different types of equations that vary in complexity, ranging from simple algebraic equations that only call for addition or multiplication to differential equations, exponential equations that employ exponential expressions, and integral equations. They serve as an expression for many physics laws.
Let flour be f, sugar be s, and butter be b
We have given that
f = 1.5s ...1
b = 1/2(s)
= 0.5s ...2
And
F + B + S = 7.5 cups
Lets substitute the vales of f and b in F + B + S, and we get
1.5s + 0.5s + S = 7.5 cups
2S + S = 7.5
3S = 7.5
S = 7.5/3
S = 2.5 cups
Flour = (1.5)2.5
= 3.75 cups
Butter = (0.5)2.5
= 1.25 cups
Thus, Clifford need 3.75 cups of flour, 2.5 cups of sugar and 1.25 cups of butter to make the cake.
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A truck driver travels at an average speed of 65 miles per hour on a 230-mile trip to pick up a load of freight. On the return
55 miles per hour. What is the average speed for the round trip? (Round your answer to one decimal place
Answer:
60.0 miles per hour.
Step-by-step explanation:
The one-way distance is the same as the return distance, so, the average speed is obtained by averaging both speeds:
(65+55)/2 = 120/2 = 60 miles per hour
