Given equation is,
\(v=-(x-3)(x+1)\)\(\begin{gathered} v=-(x-3)(x+1) \\ v=(-x+3)(x+1) \\ v=-x^2-x+3x+3 \\ v=-x^2+2x+3 \end{gathered}\)Now, let us solve the above equation.
\(\begin{gathered} v=-x^2+2x+3 \\ v=-(x^2-2x-3) \\ v=-(x^2-2x+(-1)-(-1)-3) \\ v=-((x-1)^2-(-1)^2-3) \\ v=-((x-1)^2-4 \\ v=-(x-1)^2+4 \end{gathered}\)the vertex is at (1,4)
NEED HELP!! PLS
What is the volume of the rectangular prism?
a rectangular prism with a length of eight inches, a width of four inches, and a height of three inches
96 in3
98 in3
106 in3
116 in3
Answer:
The volume of the rectangular prism is 96.
Step-by-step explanation:
Use the formula L × W × H to get your answer. Plug in the givem measurements. 8 × 4 × 3 = 96.
A dozen cheap plastic whistles cost $2.40. What is the unit rate of a whistle? Write your answer as a comparison statement.
PLEASE ANSWER ASAP
Answer:
0.2 or 0.20
Step-by-step explanation:
A dozen=12. If a dozen cheap plastic whistles cost 2.40, we divide. 2.40/12=0.2 That means that 1 whistle is 20 cents.
Suppose sam deposited 1000$ every month in the beginning for his retirement fund for 20 years at 5% compounded monthly. What is value of N
To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.
To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.
Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.
The formula to calculate the future value of a series of monthly deposits is given by:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value of the investment,
P is the monthly deposit amount,
r is the monthly interest rate, and
n is the number of deposits.
In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.
By rearranging the formula, we can solve for n:
n = log((FV * r) / (P * r + FV)) / log(1 + r)
Plugging in the values, we get:
n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)
For more such questions on future value
https://brainly.com/question/24703884
#SPJ8
Please help me with this.
Here are the correct matches to the expressions to their solutions.
The GCF of 28 and 60 is 4.
(-3/8)+(-5/8) = -4/4 = -1.
-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.
The solution of 0.5 x = -1 is x = -2.
The solution of 1/2 m = 0 is m = 0.
-4 + 5/3 = -11/3.
-2 1/3 - 4 2/3 = -10/3.
4 is not a solution of -4 < x.
1. The GCF of 28 and 60 is 4.
The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:
28 = 2 x 2 x 7
60 = 2 x 2 x 3 x 5
The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.
2. (-3/8)+(-5/8) = -1.
To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.
3. -1/6 DIVIDED BY 1/2 = -1/3.
To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.
4. The solution of 0.5 x = -1 is x = -2.
To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.
5. The solution of 1 m = 0 is m = 0.
To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.
6. -4 + 5/3 = -11/3.
To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.
7. -2 1/3 - 4 2/3 = -10/3.
To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.
8. 4 is not a solution of -4 < x.
The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.
For more such questions on GCF
https://brainly.com/question/902408
#SPJ8
Richard and Anna are saving for college.*4 points• Richard has saved $100 every year for the past 7 years in an account that has a simpleinterest rate of 12%.• Anna has saved $700 this year in cash.who has saved a greater amount of money, and why?Richard has more money in his college account, because he invested regularly over along period of time in an account that earns interest.Anna has more money in her college account, because she saved a greater amount ofmoney at one time and cash has a higher value.It is impossible to determine whether Richard or Anna have more money in theircollege accounts.Richard and Anna have the same amount in their college accounts, because they bothinvested $700.
Given:
For Richard :
\(\begin{gathered} \text{Amount saved every year = \$100} \\ \text{period = 7 years} \\ S\mathrm{}I\text{ rate = 12\%} \end{gathered}\)We can proceed to calculate the simple interest on the $100 saved yearly by Richard :
\(\begin{gathered} S\mathrm{}I\text{ = }\frac{P\text{ }\times\text{ R }\times\text{ T}}{100} \\ =\text{ }\frac{100\text{ }\times12\text{ }\times\text{ 7}}{100} \\ =\text{ \$ 84} \end{gathered}\)The total amount of money Richard has at the end of 7 years:
\(\begin{gathered} =\text{ 100 }\times\text{ 7 + 84 } \\ =\text{ \$ 784} \end{gathered}\)For Anna, she saved $700 this year only
We can conclude that :
Richard has more money in his college account, because he invested regularly over a
long period of time in an account that earns interest.
The right option is A
Calculate the distance between the points N=(-2,-1) and L=(3-4) in the coordinate plane. Give an exact answer (not a decimal approximation)
The distance between N=(-2,-1) and L=(3,-4) in coordinate plane will be √34 unit.
What is plane?
In two dimensions, a plane can continue on forever. The lack of breadth. A plane is an example of coordinate geometry. A point's location in a plane is determined by its coordinates.
A plane is a two-dimensional, flat surface that never ends in mathematics. A plane is a two-dimensional equivalent of a three-dimensional equivalent that contains three spatial dimensions, a line, and a point. Planes can resemble subspaces in some higher-dimensional situations, as if the room's walls had been substantially stretched. These walls have their own existence, exactly as in the context of Euclidean geometry.
A flat surface in three dimensions can be represented using the plane equation. There are several approaches for determining the equation for a given function.. The equation for the plane can be expressed in either cartesian form or vector form.
Hence, the general form of the equation is A(x−x1)+B(y−y1)+C(z−z1)=0
Now,
For given two points in (x1,y1),(x2,y2) in coordinate plane
distance between them will be = √((x2-x1)²+(y2-y1)²)
So, distance between N=(-2,-1) and L=(3,-4)=√((3+2)²+(-4+1)²)
=√(25+9)
=√34
hence,
The distance between N=(-2,-1) and L=(3,-4) in coordinate plane will be √34 unit.
To know more about Planes visit the link
https://brainly.com/question/29271728?referrer=searchResults
#SPJ4
3. Journalise the following transactions:
(i) Paid 2,000 in cash as wages on installation of a machine.
(ii) Sold goods to Mr. Chopra at a list price of ₹4,000. Sales
subject to 10% Trade Discount and 5% Cash discount if payment
is made immediately, Mr. Chopra availed of cash discount.
These are the two transactions that are given in the question and the journalizing of these transactions are explained with the appropriate steps and accounts.
The solution for the journalizing of the given transactions can be found below:
Journalizing refers to the recording of business transactions in the journal. In the process of journalizing, all transactions are recorded in the journal in a systematic way.
Journal is the first place where every transaction is recorded systematically.
The transaction is a business exchange in which one entity provides value to another entity in exchange for a specific item, service, or asset.
Transaction
(i) is paid Rs 2000 in cash as wages on the installation of the machine. This transaction can be journalized as follows: Journal of Transactions Date Particulars LF Amount (Dr.) Amount (Cr.) DD/MM/YYYCash a/c………………………Dr.2000To wages a/c2000 (Being cash paid as wages on the installation of the machine)Transaction
(ii) sold goods to Mr. Chopra at a list price of Rs 4,000. The sale is subject to a 10% trade discount and a 5% cash discount if the payment is made immediately, Mr. Chopra availed cash discount.
This transaction can be journalized as follows: Journal of Transactions Date Particulars LF Amount (Dr.) Amount(Cr.) DD/MM/YYYMr. Chopra a/c………………………Dr.3,420To Sales a/c4,000 (Being sales made to Mr. Chopra on a discount) To Trade Discount a/c400 (Being Trade Discount allowed to Mr. Chopra) Cash Discount a/c180 (Being cash discount allowed to Mr. Chopra) To Mr. Chopra a/c180 (Being cash received from Mr. Chopra) To CGST a/c90(Being CGST charged on sales) To SGST a/c90(Being SGST charged on sales)
For more such questions on transactions
https://brainly.com/question/1016861
#SPJ8
Calculate the next term in the geometric sequence that is calculated with a ratio of 19 if the current term is 38
Answer:
Step-by-step explanation:
The next term is going to be simply 38*19 = 722
The series is geometric which means that you multiply from one term to get to the next.
The ratio of 19, and the current term is 38. So to get to the next term, multiply 38 * 19
Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
Sung Lee invests $10,000 at age 18. He hopes the investment will be worth $30,000 when he turns 25. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Round to the nearest tenth of a percent.
Answer:
r=17%
Step-by-step explanation:
P is the investment
A is the targeted amount
t= time (25-18=7 years)
A=P(1+r)^t
30000=10000(1+r)^7
(1+r)^7=30000/10000
r=\root(7)(3)-1
r=0.16993 ≅0.17= 17%
check: A=P(1+r)^t ⇒10000(1+0.17)^7=30012≅30000
Kim's softball team was playing in the championship game. When there were 4 innings left, the team was losing by a score of 17 to 6 runs. In the last 4 innings, her team scored the same number of runs per inning, and the other team did not score any more runs. Kim's team won with the most runs. Write an inequality to determine the number of runs per inning, p, Kim's team could have scored.
The number of runs per inning that Kim's team could have scored to win the game would be greater than 11/8.
Let's suppose that in the final four innings, Kim's squad scored "p" runs on average. In that case, Kim's side would have scored a total of:
(Number of innings) x (Total runs scored by Kim's side) (Number of runs per inning)
Kim's squad scored 6 runs in the first 4 innings, so there were a total of the following runs scored by her team:
Six runs were scored by Kim's squad in the first four innings.
The total number of innings in the game would be 8, as there were still 4 innings to play. As a result, Kim's squad scored a total of runs during the entire game, which is:
Eight innings times the number of runs per inning is eight runs for Kim's team overall.
Kim's team ended up winning the game with the most runs. The total runs scored by her team must therefore be higher than the total runs scored by the opposing team. The opposing team scored 17 runs in the first four innings and none more in the following four. The total runs scored by the opposition would therefore be as follows:
The other team scored a total of 17 runs.
Combining everything, we may represent the inequality as follows:
Total runs scored by Kim's team surpasses all other teams' total runs.
8p + 6 > 17
When we reduce the inequality, we obtain:
8p > 11
When we multiply both sides by 8, we get:
p > 11/8
In order to win the game, Kim's squad would have needed to score more runs per inning than 11/8.
To know more about similar question visit:
https://brainly.com/question/28076693
#SPJ1
Answer:
6+4p>17
Kim's team scored a minimum of
3 runs per inning.
Step-by-step explanation: Khan Academy
What are the equivalent ratios of 14:6
A : 126:54
B: 91:33
C: .77:30
D: 49:21
E: 7:3
Answer:
E, and A
Step-by-step explanation:
If you divide 14/6 with 2's you get 7/3 and if you multiply 14/6 with 9 you get 126/54
Use n = 6 and p = 0.25 to complete parts (a) through (d) below.
(a) Construct a binomial probability distribution with the given parameters.
х
P(x)
0
1
2
3
4
5
6
(Round to four decimal places as needed.)
(hl somnute the mean and standard deviation of the random variable using Hy = x.P(x)] and oy =
Answer:
The binomial probability distribution is shown below.
Step-by-step explanation:
The probability mass function of X is:
\(P(X=x)={n\choose x}p^{x}(1-p)^{n-x};x=0,1,2,3..\)
It is provided that n = 6 and p = 0.25.
Construct a binomial probability distribution with the given parameters as follows:
X P (X = x)
0 \(P(X=0)={6\choose 0}(0.25)^{0}(1-0.25)^{6-0}= 0.1780\)
1 \(P(X=1)={6\choose 1}(0.25)^{1}(1-0.25)^{6-1}= 0.3560\)
2 \(P(X=2)={6\choose 2}(0.25)^{2}(1-0.25)^{6-2}= 0.2966\)
3 \(P(X=3)={6\choose 3}(0.25)^{3}(1-0.25)^{6-3}= 0.1318\)
4 \(P(X=4)={6\choose 4}(0.25)^{4}(1-0.25)^{6-4}= 0.0330\)
5 \(P(X=5)={6\choose 5}(0.25)^{5}(1-0.25)^{6-5}= 0.0044\)
6 \(P(X=6)={6\choose 6}(0.25)^{6}(1-0.25)^{6-6}= 0.0002\)
Compute the mean and standard deviation as follows:
\(\mu=np=6\times0.25=1.50\\\\\sigma=\sqrt{np(1-p)}=\sqrt{6\times 0.25\times (1-0.25)}=1.0607\)
Binomial probability distribution was constructed, and the mean and standard deviation comes to be 1.5 and 1.061 respectively.
As we know that binomial probability distribution is given by
\(P(x) = ^nC_xp^x(1-p)^{n-x}\)
What is binomial distribution?The binomial distribution is a probability distribution that depicts the likelihood that a value will take one of two independent values under a given set of parameters.
Given n=6 & p=0.25
\(P(0) = ^6C_0(0.25)^0(1-0.25)^{6-0}\) = 0.1780
\(P(1) = ^6C_1(0.25)^1(1-0.25)^{6-1}\)=0.3560
\(P(2) = ^6C_2(0.25)^2(1-0.25)^{6-2}\) = 0.2966
\(P(0) = ^6C_3(0.25)^3(1-0.25)^{6-3}\) =0.1318
\(P(0) = ^6C_4(0.25)^4(1-0.25)^{6-4}\)=0.0330
\(P(5) = ^6C_5(0.25)^5(1-0.25)^{6-5}\)=0.0044
\(P(6) = ^6C_6(0.25)^6(1-0.25)^{6-6}\)= 0.0002
Mean = np
Mean = 6*0.25
Mean = 1.5
Standard deviation σ = \(\sqrt{np(1-p)}\)
σ = \(\sqrt{6*0.25(1-0.25)}\)
σ = 1.061
Hence, binomial probability distribution was constructed, and the mean and standard deviation comes to be 1.5 and 1.061 respectively.
To get more about binomial distribution visit:
https://brainly.com/question/24756209
Decide whether the rates are equivalent. Maria saves $50 in 4 months.
Ralph saves $60 in 5 months
Answer:
The rates are not equivalent since Maria saves $0.50 more per month than Ralph.
Step-by-step explanation:
We can determine if two rates are equivalent by comparing the rates at which they save per month.
Maria's savings per month:
Both 50 and 4 can be divided by 2, which gives us 25/2. As a regular number, this becomes 12.5/1 which means Maria saves $12.5 per month.
Ralph's savings per month:
Both 60 and 5 can be divided by 5, which gives us 12. Thus, Ralph saves $12 per month.
Thus, the rates are not equivalent as Maria saves $0.50 more per month than Ralph.
Which one of the following statements is correct when the homoskedasticity assumption is violated while the rest of the OLS assumptions are correct.?
a.The beta parameter estimates can be calculated but they are wrong.
b.The beta parameter estimates are biased
c.The beta parameter estimates are unbiased because homoskedasticity assumption is not required for unbiasedness.
d.The beta parameter estimates cannot be calculated
The correct answer is option b. When the homoskedasticity assumption is violated, The beta parameter estimates are biased while the rest of the OLS assumptions are correct.
When the homoskedasticity assumption is violated, the ordinary least squares (OLS) estimator is still consistent but no longer efficient. This means that the estimates of the regression coefficients (beta parameters) are still unbiased, but they have higher variances and covariances.
In other words, the OLS estimator is no longer the best linear unbiased estimator (BLUE) and it may be biased when the errors are heteroscedastic. Therefore, option b is correct.
Learn more about homoskedasticity assumption:
https://brainly.com/question/14745756
#SPJ4
In one particular suburb, there are 28 families that own a pug. If these owners make up 80% of all dog owners in this suburb, then how many dog owners are there in this neighborhood?
Answer:
60%
Explanation:
To get percentages, take the part of a population that is being specified and divided that by the whole population and multiply that value by
100%
So there are 30 people that own boxers, this is the specific population that is being compared to the whole dog-owning population, which is comprised of 50 total families. So 30 50 can be reduced to 3 5 and that gives us 0.6
When that value is multiplied by
100%, it gives us our percentage of 0.6 ⋅ 100% = 60
which equation best describes this line?
Answer:
y=2x+8
Step-by-step explanation:
(-3,2) > (1,10)
1- -3 = 4
10-2 = 8
8/4 = 2
Mary bought 8 identical staplers at the bookshop. She paid the cashier $50 and received $12.40 in change. Find the cost of each stapler.
Answer:
$4.70
Step-by-step explanation:
so we start by subtracting with $50 and $12.40
50 - 12.4
37.6
then we divide 37.6 by 8
$4.70
Imma give 20 points and brainiest for whoever answers first and answers correctly
The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two sides (legs) is equal to the square of the hypotenuse.
Mathematically, this is expressed as: a2 + b2 = c2, where a and b are the lengths of the two sides and c is the length of the hypotenuse. To calculate the hypotenuse of a right triangle, the Pythagorean Theorem can be used. Let's say the two sides of the triangle measure 3 and 4. To calculate the hypotenuse, use the formula c2 = a2 + b2, where c is the hypotenuse, a is 3, and b is 4. So, c2 = 32 + 42. This simplifies to c2 = 9 + 16, which equals c2 = 25. The square root of 25 is 5, so the hypotenuse of the triangle with sides 3 and 4 is 5.
Learn more about Pythagoras theorem here:
https://brainly.com/question/343682
#SPJ1
Find the value of V.
From the diagram the value of v is √6
How to solve for the value of v?You should recall that Trigonometry is a branch of mathematics concerned with relationships between angles and ratios of lengths.
Using the trigonometrical ratios, we have
Tangent = opposite /adjacent
This implies that
√2/1 = 2√3/v
cross and multiplying to have
v√2 = 2√3
Rationalizing the denominator and making v the subject of the formular we have
v = 2√3/√2 *√2/√2
v = 2√2/2
Therefore the value of v is √6
Learn more about trigonometrical ratios of triangles on https://brainly.com/question/12718789
#SPJ1
Very hard must need solving
Answer:
attached
Step-by-step explanation:
if a=1 b =2and c= -3 find the value of a2b2c-2
Hello !
you made a typo with the c^-2 because otherwise it does not make a round result
\(a^{2} *b^{2} *c^{2} \\\\= 1^{2} *2^{2}* (-3)^{2} \\\\= 1*4*9\\\\\boxed{= 36}\)
Write an equation that represents the perimeter of the rectangle. The width of a rectangle is 9 less than one-third it's width, when the perimeter is 45.
Answer:
The equation that represents the perimeter of the rectangle is:
\(\text{Perimeter} = \frac{2}{3} \times [4l-27]\)
Step-by-step explanation:
The perimeter of a rectangle is given by the formula:
Perimeter = 2 × [l + w]
It is provided that the width of a rectangle is 9 less than one-third it's length.
That is:
\(w = \frac{1}{3}l-9\)
The perimeter is given as 45.
The equation that represents the perimeter of the rectangle is:
\(\text{Perimeter} = 2 \times [l + \frac{1}{3}l-9]\\\\\text{Perimeter} = 2 \times [\frac{3l+l-27}{3}]\\\\\text{Perimeter} = 2 \times [\frac{4l-27}{3}]\\\\\text{Perimeter} = \frac{2}{3} \times [4l-27]\)
Thus, the equation that represents the perimeter of the rectangle is:
\(\text{Perimeter} = \frac{2}{3} \times [4l-27]\)
Identify the missing
term(s) in the polynomial
X^3 - 95
A. Both 0x^2 and 0x
B. 0x^2
C. 0x
D. 0x4
E. There are no missing terms
The missing term in the polynomial X^3 - 95 is 0x^2.
Option A (Both 0x^2 and 0x) is the correct answer choice, as 0x represents the missing term with a degree of x (linear term) as well.
In the polynomial expression X^3 - 95, we can observe that there is a missing term with an x^2 degree.
To identify the missing term, we need to consider the standard form of a polynomial expression, which is written in descending order of exponents. In this case, the highest exponent present is x^3, followed by a constant term (-95).
To fill in the missing term, we look for the term with an x^2 degree. Since it is not present in the given expression, we can conclude that the missing term is 0x^2.
Therefore, the missing term in the polynomial X^3 - 95 is 0x^2.
Option A (Both 0x^2 and 0x) is the correct answer choice, as 0x represents the missing term with a degree of x (linear term) as well.
for such more question on polynomial
https://brainly.com/question/7297047
#SPJ8
what is 3.6 times 0.05. equal
Step-by-step explanation
Then you count how many numbers are after the decimal point(6,0,0,5) making 4. So the decimal point will be inserted by counting 4 spaces from the back.
Graph the line with the given slope m and y-intercept b.
m = 4, b = -5
Answer:
Step-by-step explanation:
What we know:
m = 4, b = -5
y = mx + b where m is the gradient/slope and b is the y-intercept
Substitute m and b values:
y = 4x + -5 which is the same as y = 4x - 5
Substitute all x values to find y coordinate:
When x = -7, y = (4 x -7) - 5 = -33
When x = -6, y = (4 x -6) - 5 = -29
When x = -5, y = …
Continue for all x values
expand 2x(3x+2y) thank you
Answer:
6x^2+4xy
Step-by-step explanation:
You distribute the 2x by multiplying it with each term
2x(3x)+ 2x(2y)
6x^2+4xy
hopes this helps please mark brainliest
In a cafeteria,
1/6of the students are eating salads , and 2/3
are eating sandwiches. There are 12 students in the cafeteria. How many students are eating lunches other than salads or sandwiches?
Answer:
2 students
Step-by-step explanation:
First, you find the number of students eating either salads and sandwiches. Then, you add the number of students eating salads and sandwiches together. Finally, you will subtract that number from the 12 total students
2/3 * 12/1 = 8 (sandwiches)1/6 * 12/1 = 2 (salads)8 + 2 = 10 (combined)12 - 10 = 2 studentsA fan of 45 kg has an unbalance that creates a harmonic force. A spring-damper system is designed to minimize the force transmitted to the base of the fan. A damper is used having the damping ratio of ζ=0.2. Calculate the required spring stiffness so that only 10% of the force is transmitted to the ground when the fan is running at 10,000 rpm.
The required spring stiffness to transmit only 10% of the maximum force to the ground is 0.00072 N/m
Let F0 = 45 kg, ω = 10000 rpm, and ζ = 0.2
The critical damping coefficient can be calculated as:
\(c = 2*sqrt(m*k) = 2*sqrt(45*k)\)
The damping ratio is given as:
\(ζ = c/(2*m*ω) = 0.2\)
Therefore,
\(k = (c^2)/(4*m*ζ^2) = (4*45*0.2^2)/(4*45*0.2^2) = 0.0045 N/m\)
The maximum force transmitted to the ground is given as:
Fmax =\((F0*ζ*ω)/sqrt(1-ζ^2) = (45*0.2*10000)/sqrt(1-0.2^2) = 36 N\)
Therefore, the required spring stiffness to transmit only 10% of the maximum force to the ground is:
\(k = (Fmax*0.1)/(F0*ω*ζ) = (36*0.1)/(45*10000*0.2) = 0.00072 N/m\)
Learn more about force here:
https://brainly.com/question/2193360
#SPJ4
A number pattern has the rule divide by 3 the fifth term of the pattern is 2 what is the second term of the pattern.