Answer:
30 or 52
I'm not sure. Sorry. I tried my best. Don't let the "Helping Hand" fool you. You see you said 6 forks and twice as many spoons which equals 12+6. Then "as" knives. I got confused there. I think there it's either 12 or twice as many knives as spoons. In other words, 12×2.
6 + (6 × 2) + (6 × 2) = 30
6 + (6 ×2) + (12 × 2) = 52
2y+8x=1 write in slope intercept form
Answer:
y=-4x+1/2
Step-by-step explanation:
2y+8x=1
2y=1-8x
2y=-8x+1
y=-8/2x+1/2
y=-4x+1/2
kayla is on level 12 of a new game. Every Day she completes 6 new levels. Maddy is on level 28 of the same game. Every Day she completes 2 new levels. When will they be on the same level? what level will that be?
We know that Kayla is level 12 and gains 6 levels everyday. We know that Maddy is level 28 and gains 2 levels everyday. To find which day they are both the same level we can add.
-------------------------
Day 1:
Kayla is level 12
Maddy is level 28
Day 2:
Kayla is level 18 (12 + 6)
Maddy is level 30 (28 + 2)
Day 3:
Kayla is level 24 (18 + 6)
Maddy is level 32 (30 + 2)
Day 4:
Kayla is level 30 (24 + 6)
Maddy is level 34 (32 + 2)
Day 5:
Kayla is level 36 (30 + 6)
Maddy is level 36 (34 + 2)
-------------------------
They willl be at the same level on level 36.
-------------------------
Best of luck!
Determine the point that lies on the equation y = -5x - 3.
(4, 12)
(4, -12)
(4, 23)
(4, -23)
Answer:
(4, -23)
Step-by-step explanation:
To see if a point is on the equation, substitute its "x" and "y" coordinates into the equation. The points are written as (x, y). If the left side equals the right side, the point is on the line. (LS = RS)
Try (4, 12)
y = -5x - 3
12 = -5(4) - 3
12 = -20 - 3
12 = -23
LS ≠ RS
The point is not on the line.
Try (4, -12)
y = -5x - 3
-12 = -5(4) - 3
-12 = -20 - 3
-12 = -23
LS ≠ RS
The point is not on the line.
Try (4, 23)
y = -5x - 3
23 = -5(4) - 3
23 = -20 - 3
23 = -23
LS ≠ RS
The point is not on the line.
Try (4, -23)
y = -5x - 3
-23 = -5(4) - 3
-23 = -20 - 3
-23 = -23
LS = RS
The point (4, -23) is on the line.
Is 4n+12 and 4(n+3) equivalent
yes, through distribution 4(n+3) n becomes 4n and 3 becomes 12
Final answer:
By applying the distributive property to 4(n+3), it simplifies to 4n + 12, showing that the expressions 4n+12 and 4(n+3) are indeed equivalent.
Explanation:
When we compare the two expressions 4n+12 and 4(n+3), we need to determine if they are equivalent. By applying the distributive property to 4(n+3), we multiply 4 by both n and 3, giving us 4n + 4×3, which simplifies to 4n + 12. This is exactly the same as the original expression 4n+12, thus the two expressions are equivalent.
Understanding this equivalence is crucial in algebra. It shows how the distributive property allows us to simplify or expand expressions, ensuring that we can see different forms of the same equation. This foundational skill is key to solving more complex algebraic problems, as it helps in recognizing patterns and simplifying equations.
Pls help! three arithmetic sequences are given below.
Sequence A: 5, 7, 9, 11,...
Sequence B: 34, 43, 52, 61
Sequence C: -9, -4, 1, 6..
Which of the following lists the sequences in order from least common difference to greatest common difference?
The common difference is basically the number at which the pattern increases.
A's common difference: 2
B's common difference: 9
C's common difference: 5
answer: A, C, B
Which of the following equations best describes a square root function that is reflected across the x-axis and has a vertex of (−4,2)?
A. [tex]y=\sqrt{-(x-4)} +2[/tex]
B. [tex]y= -\sqrt{x+2}-4[/tex]
C. [tex]y=-\sqrt{x+4} +2[/tex]
D. [tex]y=-\sqrt{x-4} +2[/tex]
Answer:
C
Step-by-step explanation:
Rather than picking, let's try to construct one from the description.
reflected over the x axis means -[tex]\sqrt{x}[/tex]
the vertex is usually at (0,0), now how do we move a graph? or in other words translating it.
To move left and right you use [tex]\sqrt{x-h}[/tex] where if you subtract h you move right and if you add h you move left. we go from (0,0) to (-4,2). so 0 to -4 is 4 left, so that means we add 4.
To move up and down we use [tex]\sqrt{x}+v[/tex] Here if v is positive you move up and if v is negative you move down. going from (0,0) to (-4,2) it moves up 2
So now we put them all together [tex]-\sqrt{x+4}+2[/tex] And if you look, C matches that exactly.
The correct equation is option C: y = -√(x + 4) + 2, which describes a square root function reflected across the x-axis with a vertex at (-4, 2).
We are given a square root function that is reflected across the x-axis and has a vertex at (-4, 2). Let's analyze which of the provided options fits this description step by step.
Starting with the reflection across the x-axis, the function must have a negative sign outside the square root. This eliminates option A.Next, we focus on the vertex. The general form of a square root function is y = a√(x - h) + k where (h, k) is the vertex of the graph. Here, the vertex is (-4, 2).This means our function should resemble y = -√(x + 4) + 2 because shifting x by +4 (making x + 4 = 0 when x = -4) moves the vertex to (-4, 2).Reviewing the options, purely C: y = -√(x + 4) + 2 fits this format.Thus, option C is the correct equation that describes the square root function reflected across the x-axis with a vertex at (-4, 2).
m ∠KLP+m∠PLM = _____
_______________
2. _____+m∠PLM = ______ Substitution
3. m∠PLM = _______ Algebra
4. m∠PMN=m∠P+m∠______ _______________
5. ______ = ______+180°−3x Substitution
6. x= ______ Algebra
Answer:
1. [tex]m\angle KLP+m\angle PLM=180^{\circ}[/tex]
2. [tex]3x+m\angle PLM=180^{\circ}[/tex]
3. [tex]m\angle PLM=180^{\circ}-3x[/tex]
4. [tex]m\angle PMN=m\angle P+m\angle PLM[/tex]
5. [tex]2x+72^{\circ}=x+180^{\circ}-3x[/tex]
6. [tex]x=27^{\circ}[/tex]
Step-by-step explanation:
Please find the attached diagram for the complete question.
We are supposed to complete the given blanks.
1. [tex]m\angle KLP+m\angle PLM=...[/tex]
We can see from our given diagram that angle KLP and angle PLM are linear angles, so their measure will be equal to 180 degrees. Therefore, the correct expression for blank in 1st step would be [tex]180^{\circ}[/tex].
2. [tex]...+m\angle PLM=180^{\circ}[/tex]
Now, we will substitute the measure of angle angle KLP in our equation. We can see that measure of angle angle KLP is [tex]3x[/tex]. Therefore, the correct expression for blank in 2nd step would be [tex]3x[/tex].
3. [tex]m\angle PLM=180^{\circ}...[/tex]
Our next step is to find the measure of angle PLM in terms of x by subtracting [tex]3x[/tex] from both sides as:
[tex]3x-3x+m\angle PLM=180^{\circ}-3x[/tex]
[tex]m\angle PLM=180^{\circ}-3x[/tex]
Therefore, our 3rd step would be [tex]m\angle PLM=180^{\circ}-3x[/tex].
4. [tex]m\angle PMN=m\angle P+m\angle ...[/tex]
We can see that angle PMN is an exterior angle of our given triangle, so its measure will be equal to the sum of the opposite interior angles.
We can see that angle P and angle PLM are opposite interior angle of angle PMN, so we can set an equation as:
[tex]m\angle PMN=m\angle P+m\angle PLM[/tex]
Therefore, the correct expression for blank in 4th step would be [tex]]angle PLM[/tex].
5. [tex]...=...+180^{\circ}-3x[/tex]
Our next step is to substitute the values of angle PMN and angle P as given in the diagram.
[tex]2x+72^{\circ}=x+180^{\circ}-3x[/tex]
Therefore, our 5th step would be [tex]2x+72^{\circ}=x+180^{\circ}-3x[/tex].
6. [tex]x=[/tex]
Now, we need to solve for x using algebra as:
[tex]2x+72^{\circ}=x-3x+180^{\circ}[/tex]
[tex]2x+72^{\circ}=-2x+180^{\circ}[/tex]
[tex]2x+2x+72^{\circ}=-2x+2x+180^{\circ}[/tex]
[tex]4x+72^{\circ}=180^{\circ}[/tex]
[tex]4x+72^{\circ}-72^{\circ}=180^{\circ}-72^{\circ}[/tex]
[tex]4x=108^{\circ}[/tex]
[tex]\frac{4x}{4}=\frac{108^{\circ}}{4}[/tex]
[tex]x=27^{\circ}[/tex]
Therefore, the value of x is 27 degrees.
there are five boys and ten girls in mr johnsons gym class.the simplified ratio of boys to girls is 1/2. what does this ratio mean
Answer:
This ratio means for every boy there are two girls.
There are twice as many girls as there are boys. Backwards, it's there are half as many boys as there are girl.
The simplified ratio is found by reducing the ratio to the lower terms.
5/10 = 1/2
Both sides on the unsimplified ratio are division by 5. When done, it became 1/2.
solve sin x - (3sin x-1) = 0
Answer:
[tex]\large\boxed{x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi,\ k\in\mathbb{Z}}[/tex]
Step-by-step explanation:
[tex]\sin x-(3\sin x-1)=0\\\\\sin x-3\sin x+1=0\qquad\text{subtract 1 from both sides}\\\\-2\sin x=-1\qquad\text{divide both sides by 2}\\\\\sin x=\dfrac{1}{2}\Rightarrow x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi,\ k\in\mathbb{Z}[/tex]
[tex]\text{Equation:}\\\\\sin x=a\\\\\text{has solutions}\\\\x=\theta+2k\pi\ \vee\ x=(\pi-\theta)+2k\pi\\\\\text{Why}\ 2k\pi?\\\text{Because the sine function has a period of}\ 2\pi.[/tex]
[tex]\text{look at the table}\\\\\sin x=\dfrac{1}{2}\to x=\dfrac{\pi}{6}\ \vee\ x=\pi-\dfrac{\pi}{6}=\dfrac{5\pi}{6}[/tex]
[tex]\text{Other solution:}\\\\\sin x=\dfrac{1}{2}\Rightarrow x=\sin^{-1}\dfrac{1}{2}\\\\x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi[/tex]
A population of 45 foxes in a wildlife preserve triples in size every 13 years. The function y equals 45 * 3to the x power, where x is the number of 13-year periods, models the population growth. How many foxes will there be after 39 years?
Answer:
1,215
Step-by-step explanation:
39/13=3
45*(3)^x
45*(3)^3
45*(27)
1,215
Final answer:
To find the number of foxes after 39 years, use the population growth function y = 45 *[tex]3^x[/tex]. Since 39 years corresponds to 3 periods of 13 years each, the equation becomes y = 45 * [tex]3^3,[/tex] resulting in 1215 foxes.
Explanation:
The student has asked how many foxes will there be after 39 years, given the population growth function y equals 45 times 3 to the x power, where x represents the number of 13-year periods. To solve this, we calculate the value of x by dividing the total time of population observation (39 years) by the duration of one population tripling period (13 years). This gives us:
x = 39 years / 13 years/period = 3 periods
We then substitute x into the equation and get:
y = 45 *[tex]3^3,[/tex] = 45 * 27 = 1215 foxes
Therefore, there will be 1215 foxes in the wildlife preserve after 39 years.
jason writes the following function to represent the amount of money in his account after 7 years given quarterly compounding of the $2430 initial deposit.
f(t)=2430(1.04)^28
a. rewrite the equation in the form f(t)=A(1+r/n)^nt
b. what is the annual interest rate?
Answer:
[tex]f(t) = 2430(1 + \frac{0.16}{4} )^{7 \times 4}[/tex]
The APR is 16%.
Step-by-step explanation:
Jason writes the following function to represent the amount of money in his account after 7 years given quarterly compounding of the $2430 initial deposit as
[tex]f(t) = 2430(1.04)^{28}[/tex] ......... (1)
a. If we want to rewrite the equation in the form
[tex]f(t) = A(1 + \frac{r}{n} )^{nt}[/tex] .......... (2)
Then comparing equation (1) and (2) we get, A = 2430 and t = 7
Hence, 7n = 28
⇒ n = 4
Now, [tex]1 + \frac{r}{4} = 1.04[/tex]
⇒ r = 0.16 i.e. 16%
Therefore, the expression is
[tex]f(t) = 2430(1 + \frac{0.16}{4} )^{7 \times 4}[/tex] (Answer)
b. The APR is 16%. (Answer)
what is the mean proportion between 10 and 40?
Answer:
Step-by-step explanation:
10, 20, 30, 40
Answer:25
The second side of a triangle is 7 inches more than the first side. The third side is 4 inches less than 3 times the first. The perimeter is 28 inches. Find the length of the three sides of the triangle.
Answer:
First side; 5 in
second side: 12 in
third side: 11 in
Step-by-step explanation:
A: first side B: second side C: third side
b = a + 7
c = 3a -4
a + b + c = 28
a + (a + 7) + (3a -4) =28
5a + 3 = 28
5a = 28 -3 = 25
a = 5
b = 12
c = 11
The length of the sides of a triangle is 5, 12, and 11.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.
Let's say the first second and third side of the triangle is a, b and c respectively.
Now,
The second side of a triangle is 7 inches more than the first side.
b = a + 7
The third side is 4 inches less than 3 times the first.
c = 3a - 4
Now,
Perimeter = 28
a + b + c = 28
By substituting,
a + a + 7 + 3a - 4 = 28
5a + 3 = 28
a = 5
b = 5 + 7 = 12
c = 3(5) - 4 =11
Hence "The length of the sides of a triangle is 5, 12, and 11".
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The ninth graders are hosting the next school dance. They would like to make at least a $500 profit from selling tickets. The ninth graders estimate that at most 300 students will attend the dance. They will earn $3 for each ticket purchased in advance and $4 for each ticket purchased at the door.
Answer:
I think you meant
Step-by-step explanation:
The ninth graders are hosting the next school dance. They would like to make at least a $500 profit from selling tickets. The ninth graders estimate that at most 300 students will attend the dance. They will earn $3 for each ticket purchased in advance and $4 for each ticket purchased at the door. Write a system of inequalities to represent this situation. Suppose only 30 people buy advance tickets. How many people would need to buy tickets at the door?
What is the value of this expression?
(23 — 3) + (6х9)
ОА. 300
ОВ. 234
Ос. 80
OD. 74
Answer:
Step-by-step explanation:
(23 - 3) + (6 * 9) =
20 + 54 =
74 <===
For which pair of functions is (g circle f) (a) = StartAbsoluteValue a EndAbsoluteValue minus 2?
Answer:
C
Step-by-step explanation:
The pair of functions are f(a) = 5 + a² and g(a) = √(a - 5) - 2 option third is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
(gof)(a) = |a| - 2
Let f(a) = 5 + a²
g(a) = √(a - 5) - 2
(gof)(a) = g(f(a)) = √(5 + a² - 5) - 2
(gof)(a) = |a| - 2
Thus, the pair of functions are f(a) = 5 + a² and g(a) = √(a - 5) - 2 option third is correct.
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PLEASE HELP!!
Quadrilateral ABCD is similar to Quadrilateral EFGH. Diagonal AC has length 7 and diagonal EG has length 13. What is the scale factor that describes a dilation from BC to FG? Give the exact scale factor and state whether the dilation is an expansion or a contraction.
If side AB has length 17/26 what is the length of side EF? Give the exact, un-rounded value.
If the area of ABCD is 147 square inches, what is the area of EFGH? Give the exact answer.
Answer:
13/7, 221/182 and expansion, 507 inches
Step-by-step explanation:
If the two quadrilaterals are similar, you can take the diagonal length as a similar side to find the scale factor. In this case, the scale factor would be 13/7. For simplicity, we can keep this a factor for now. Because the quadrilaterals are similar, the scale factor is the same for all sides, 13/7. Because you are going from ABCD to EFGH and the scale factor is 13/7 (otherwise the other way around would be 7/13) and so the scale factor is greater than 1, you are expanding aka expansion. So, to find EF from side AB and you have the length 17/26, just multiply that by 13/7 to get 221/182 as the length.
To find the area of EFGH, you square the scale factor 13/7 and equal it to the area of EFGH A is over the area of the ABCD (you ratio them and set them equal) so 169/49 = A/147 and solve for A which is then 49A = 169 x 147 which is then 507 inches.
Final answer:
Explaining how to find the scale factor, determine expansion/contraction, calculate side length, and find the area in similar quadrilaterals.
Explanation:
Scale factor: To find the scale factor, we compare the diagonal lengths. AC:EG = 7:13. The scale factor from BC to FG is 7/13.
Expansion or Contraction: Since the scale factor is greater than 1, this dilation is an expansion.
Side EF length: If AB is 17/26, then EF = (13/7) * (17/26) = 221/182 inches.
Area of EFGH: Since the scale factor is 7/13, the area is scaled by (7/13)^2 = 49/169 of the original area. Area of EFGH = 147 * 49/169 = 42 square inches.
Solve 7x+3y=8 and 4x-y=-9 simultaneously
Answer: x = -1 and y = 5
Step-by-step explanation:
7x + 3y = 8 ........................... equation 1
4x - y = - 9 ............................ equation 2
Solving the simultaneous linear equation by substitution method , make y the subject of the formula from equation 2 , we have
y = 4x + 9 ............................. equation 3
substitute y = 4x + 9 into equation 1 , we have;
7x + 3 ( 4x + 9 ) = 8
7x + 12x + 27 = 8
19x + 27 = 8
subtract 27 from both sides
19x = -19
divide through by 19
x = -1
substitute x = -1 into equation 3 , we have
y = 4 ( -1) + 9
y = -4 + 9
y = 5
Therefore :
x = -1 and y = 5
The perimeter of the rectangle is 76 units. Find the length of side pq
Answer: [tex]PQ=16\ units[/tex]
Step-by-step explanation:
The missing figure is attached.
The perimeter of a rectangle is:
[tex]P=2l+2w[/tex]
Where "l" is the lenght and "w" is the width.
You can identify in the figure that:
[tex]w=SR=PQ=2z+2\\\\l=QR=PS=3z+1[/tex]
Then, knowing the perimeter of the rectangle, you can make the subsitution into the formula:
[tex]76=2(3z+1)+2(2z+2)[/tex]
Now you must simplify and solve for "z"
[tex]76=6z+2+4z+4\\\\76-6=10z\\\\70=10z\\\\\frac{70}{10}=z\\\\z=7[/tex]
Finally, substituting the value of "z" into [tex]PQ=2z+2[/tex], you get:
[tex]PQ=2(7)+2=16\ units[/tex]
Ahmad is riding his bike. The distance he travels varies directly with the number of revolutions (turns) his wheels make. See the graph below.
Question 1) how far does he travel per revolution
Question 2) what is the slope?
Given that Ahmad is riding his bike. The distance he travels varies directly with the number of revolutions (turns) his wheels make. A) Ahmed travels 8 feet per revolution. B) the slope here is 8.
The slope is the measure of rate of change in y (dependent variable) due to change in x (independent variable).
In the given question, a graph is given.
On y axis we are given distance travelled, making it the dependent variable.
On x axis we are given the number of revolutions, making it the independent variable.
On reading from the graph, coordinate (2,16) clearly lies on the graph.
It implies, distance travelled in 2 revolutions = 16 feet.
By unitary method,
distance travelled in 1 revolution = [tex]\frac{16}{2} = 8[/tex] feet.
Since, distance travelled in 1 revolution is 8 feet, the change in distance travelled on unit change of revolution is 8, making the slope of the line equals to 8.
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Three workers have to do a certain job. The first worker can finish the job in 8 hours. The second worker can finish the job in 4 hours. The third worker can also finish the job in 4 hours. How long will it take the three workers to finish the job if they work together?
PLS help
Working together three workers would take 1 hour 36 minutes to finish the job
Solution:
Given that first worker can finish the job in 8 hours
So in one hour, first worker can do [tex]\frac{1}{8}[/tex] th of the work
The second worker can finish the job in 4 hours
So in one hour, second worker can do [tex]\frac{1}{4}[/tex] th of the work
The third worker can also finish the job in 4 hours
So in one hour, third worker can do [tex]\frac{1}{4}[/tex] th of the work
The three workers working together in 1 hour can do:
[tex]\frac{1}{8} + \frac{1}{4} + \frac{1}{4} = \frac{1 + 2 + 2}{8} = \frac{5}{8}[/tex]
The three worker can thus do [tex]\frac{5}{8}[/tex] th of the work in one hour
Hence the three of them together can finish the work in [tex]\frac{8}{5}[/tex] hours
[tex]\frac{8}{5} = 1\frac{3}{5}[/tex] hours
Thus working together three workers would take 1 hour 36 minutes to finish the job
According to 2015 census data, 42.7 percent of Colorado residents were born in Colorado. If a sample of 250 Colorado residents is selected at random, what is the standard deviation of the number of residents in the sample who were born in Colorado? A.6.75 B.7.82 C.10.33 D.11.97 E.61.17
Answer:
[tex]sd(X)=\sqrt{np(1-p)}=\sqrt{250*0.427*(1-0.427)}=7.82[/tex]
The best option is:
B.7.82
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Data given
[tex]p_C[/tex] represent the real population proportion for residents born in Colorado
[tex]\hat p_C =0.427[/tex] represent the estimated proportion for rsidents born in Colorado
[tex]n_C=250[/tex] is the sample size selected
Solution to the problem
Let X the random variable of interest (number of residents in the sample), on this case we now that:
[tex]X \sim Binom(n=250, p=0.427)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
The expected value is given by this formula:
[tex]E(X) = np=250*0.427=106.75[/tex]
And the standard deviation for the random variable is given by:
[tex]sd(X)=\sqrt{np(1-p)}=\sqrt{250*0.427*(1-0.427)}=7.82[/tex]
The best option is:
B.7.82
The standard deviation of the number of residents in the sample who were born in Colorado
B.7.82
hence option B is correct
Given
42.7 % of Colorado residents were born in Colorado.
If a sample of 250 Colorado residents is selected at random
We have to find out the standard deviation of the number of residents in the sample who were born in Colorado
The options are given below
A.6.75
B.7.82
C.10.33
D.11.97
E.61.17
This problem is given problem of binomial distribution is a discrete probability distribution of two independent events for the given parameters.
Number of Colorado students taken in sample = n = 250
Let, the percentage of Colorado residents that were born in Colorado be p
Let, the percentage of Colorado residents that were not born in Colorado be q
The percentage of Colorado residents that were born in Colorado = 42.7% = p = 0.427
[tex]\rm \m for \; a \; binomeal\; distribution \to p = 1-q ......(1)\\Equation \ (1)\; holds\; good[/tex]
So The percentage of Colorado residents that were not born in Colorado = q = (100-42.7) = 57.3 %
The standard deviation for binomial distribution is given by the formula as formulated in the equation number (1)
[tex]\rm \sigma = \sqrt{ n\times p\times q } .......(1)[/tex]
So we can write
Standard deviation of binomial distribution
[tex]\rm \sigma = \sqrt{ 250 \times \0.427 \times 0.573 } = 7.82[/tex]
The standard deviation of the number of residents in the sample who were born in Colorado
B.7.82
hence option B is correct
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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
100
,
80
,
64
,
.
.
.
100,80,64,...
Find the 9th term.
Find the
Answer:
The 9th term for given sequence is 16.777
Therefore the 9th term is [tex]a_{9}=16.777[/tex].
Step-by-step explanation:
Given first three terms of a sequence are 100,80,64,...
Given [tex]a_{1}=100[/tex] ,[tex]a_{2}=80[/tex] , [tex]a_{3}=64[/tex],...
Given sequence is of the form of Geometric sequence
Therefore it can be written as [tex]{\{a,ar,ar^2,...}\}[/tex]
therefore a=100 , ar=80 , [tex]ar^2=64[/tex] ,...
To find common ratio
[tex]r=\frac{a_{2}}{a_{1}}[/tex]
[tex]r=\frac{80}{100}[/tex]
[tex]r=\frac{4}{5}[/tex]
[tex]r=\frac{a_{3}}{a_{2}}[/tex]
[tex]r=\frac{64}{80}[/tex]
[tex]r=\frac{4}{5}[/tex]
Therefore [tex]r=\frac{4}{5}[/tex]
The nth term of the geometric sequence is
[tex]a_{n}=ar^{n-1}[/tex]
To find the 9th tem for the given geometric sequence is
[tex]a_{n}=ar^{n-1}[/tex]
put n=9, a=100 and [tex]r=\frac{4}{5}[/tex]
[tex]a_{9}=100(\frac{4}{5})^{9-1}[/tex]
[tex]=100(\frac{4}{5})^{8}[/tex]
[tex]=100(\frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5})[/tex]
[tex]=100(\frac{256\times 256}{625\times 625})[/tex]
[tex]=100(\frac{65536}{390625})[/tex]
[tex]=100(0.16777})[/tex]
[tex]=16.777[/tex]
Therefore [tex]a_{9}=16.777[/tex]
The 9th term is 16.777
Question 2 of 10
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Using the Properties of Equality, fill the blanks with the correct value to show the solution for y.
3(y-2) = 18
3y-_ =18
3y =
What is the value of y? |
Answer:
[tex]3y-6=18\\\\3y=24[/tex]
The value of "y" is: [tex]y=8[/tex]
Step-by-step explanation:
Given the following equation:
[tex]3(y-2) = 18[/tex]
1. You must apply the Distributive property on the left side of the equation (This is: [tex]a(b\±c)=ab\±ac[/tex]). Then:
[tex](3)(y)+(3)(-2) = 18\\\\3y-6=18[/tex]
2. Now you need to apply the Addition Property of Equality. Remember that this states that:
[tex]If\ a=b,\ then\ a+c=b+c[/tex]
So, adding 6 to both sides of the equation, you get:
[tex]3y-6+(6)=18+(6)\\\\3y=24[/tex]
3. Finally, you can apply the Division Property of Equality, which states that:
[tex]If\ a=b,\ then\ \frac{a}{c}=\frac{b}{c}[/tex]
So, dividing both sides of the equation by 3, you get:
[tex]\frac{3y}{3}=\frac{24}{3}\\\\y=8[/tex]
What is 14 divided by 19,226 with a remainder
Answer:
1373 r 4
Step-by-step explanation:
A cylinder has a base diameter of 12m and a height of 10m. What is its volume in cubic m, to the nearest tenths place?
The volume is approximately 1130.5 m³.
A cylinder's volume can be calculated using the formula
V = π r² h
Given a base diameter of 12m (radius = 6m) and a height of 10m,
we substitute these values into the formula and get the volume:
V = 3.142 × (6m)² × 10m
V = 1130.52 m³
PICTURE BELOW Consider the net of a triangular prism where each unit on the coordinate plane represents four feet. If a sheet of plywood measures 4 ft x 8 ft, how many sheets of plywood will a carpenter need to build the prism?
A) 2
B) 3
C) 4
D) 5
Answer:
The carpenter will need 2 plywood to build the prism.
Step-by-step explanation:
Given:
The size of the plywood = 4 ft x 8 ft
1 Unit = 4 feet
To Find :
Number of plywood sheets the carpenter would need = "
Solution:
Step 1: Find the area of square
Area of the square is
=>[tex]4^2[/tex]
=>[tex]16 cm^2[/tex]
Here we have 3 square, so
[tex]3 \times 16[/tex]
=>[tex]48 ft^2[/tex]
Step 2 : Area of the triangle
Area of the triangle is
=>[tex]\frac{1}{2} \times b\times h[/tex]
=>[tex]\frac{1}{2} \times 4 \times 4[/tex]
=>[tex]\frac{16}{2} [/tex]
=>[tex]8ft^2[/tex]
[tex]2 \times 8 = 16ft^2[/tex]
Step 3: Finding the plywood needed
the total area of the triangular prism is
48 + 16= [tex]64 ft^2[/tex]
Area of the plywood wood is
=> [tex]4 \times 8[/tex]
=> [tex]32 ft^2[/tex]
Number of plywood required = [tex]\frac{\text {area of the prism}}{\text{area of one plywood}}[/tex]
=> [tex]\frac{64}{32}[/tex]
=> 2
The number of square feet in the area of a square is 5 more than the number of feet in the perimeter of the square. Find the length of a side.
Answer:5
Step-by-step explanation:The area of a 5x5 square is 25, and the perimeter would be 20. A 5x5 square's area is 5 more than the perimeter.
Given f(x)=2x^2+3x-5 for what values of x is f(x) positive
Answer:
x< -2.5 or x>1
Step-by-step explanation:
Please see attached picture for full solution.
To find the values of x for which f(x) is positive, we can set f(x) greater than zero and solve for x using factoring or the quadratic formula.
Explanation:
To determine the values of x for which f(x) is positive in the quadratic function f(x) = 2x^2 + 3x - 5, we need to find the values that make the function output positive values.
First, let's set f(x) greater than zero: f(x) > 0.Next, we can factor the quadratic function to solve for the roots: 2x^2 + 3x - 5 = 0.Using factoring or the quadratic formula, we can find the roots which are x = -1 and x = 2.5.We can see that the quadratic function is positive in the intervals (-∞, -1) and (2.5, ∞).Therefore, the values of x that make f(x) positive are x < -1 and x > 2.5.
Learn more about quadratic functions here:https://brainly.com/question/35505962
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What is tan C ?
Figure shows right triangle A B C. Angle B is a right angle. Segment A B is 11 units. Segment B C is 22 units.
Express your answer as a simplified fraction.
Question 1 options:
1/2
1/4
1/3
2/1
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
In the right triangle ABC of the figure, the tangent of angle C is equal to divide the opposite side to angle C (side AB) by the adjacent side to angle C (side BC)
so
[tex]tan(C)=\frac{AB}{BC}[/tex]
substitute the given values
[tex]tan(C)=\frac{11}{22}[/tex]
simplify
[tex]tan(C)=\frac{1}{2}[/tex]