Answer:
Step-by-step explanation:
A
PLS HELP I WILL MARK BRAINILEST
Answer:
Let's assume the original price of the stock was x.
When the company announced it overestimated demand, the stock price fell by 40%.
So, the new price of the stock after the first decline was:
x - 0.4x = 0.6x
A few weeks later, when the seats were recalled, the stock price fell again by 60% from the new lower price of 0.6x.
So, the new price of the stock after the second decline was:
0.6x - 0.6(0.6x) = 0.24x
Given that the current stock price is $2.40, we can set up the equation:
0.24x = 2.40
Solving for x, we get:
x = 10
Therefore, the stock was originally selling for $10.
what is the largest integer $n$ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$?
the largest integer [tex]n $ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$ is $\boxed{62}$.[/tex]
To find the largest integer[tex]n $ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$[/tex], we need to count how many factors of 3 are in the product of the odd integers from 1 to 99.
One way to do this is to factor each odd integer into its prime factors and count how many factors of 3 are present. However, this would be quite tedious and time-consuming.
A quicker approach is to use the fact that every third odd integer is a multiple of 3. Thus, we can count how many multiples of 3 are present in the product of the odd integers from 1 to 99.
Let [tex]$m$[/tex] be the number of multiples of 3 in the range from 1 to 99. Then we have:
[tex]m = \left\lfloor \frac{99}{3} \right\rfloor = 33[/tex]
This is because there are 33 multiples of 3 in the range from 1 to 99 (namely, 3, 6, 9, ..., 96, 99).
Each multiple of 3 contributes at least one factor of 3 to the product of the odd integers. However, some multiples of 3 contribute two or more factors of 3, depending on how many factors of 3 they contain.
To count how many multiples of 3 contribute two or more factors of 3, we need to count how many multiples of 9, 27, and 81 are present in the range from 1 to 99.
There are [tex]$\left\lfloor \frac{99}{9} \right\rfloor = 11$[/tex]multiples of 9, namely 9, 18, 27, ..., 81, 90, 99. Each multiple of 9 contributes at least two factors of 3 to the product of the odd integers.
There are [tex]$\left\lfloor \frac{99}{27} \right\rfloor = 3$[/tex] multiples of 27, namely 27, 54, 81. Each multiple of 27 contributes at least three factors of 3 to the product of the odd integers.
There is only one multiple of 81 in the range from 1 to 99, namely 81, which contributes at least four factors of 3 to the product of the odd integers.
Thus, the total number of factors of 3 in the product of the odd integers from 1 to 99 is:
[tex]n = m + 2\times\text{number of multiples of 9} + 3\times\text{number of multiples of 27} + 4\times\text{number of multiples of 81}[/tex]
[tex]n = 33 + 2\times 11 + 3\times 3 + 4\times 1 = 62[/tex]
Therefore, [tex]the $ largest integer $n$ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$ is $\boxed{62}$.[/tex]
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What is the length of BC?
A) 1.7
B) 2.1
C) 3.8
D) 4.6
Answer:
B. 2.1
Step-by-step explanation:
If you draw a line from C to intersect AB perpendicularly at point D so we have 2 right triangles ACD and BCD.
For △ACD, AC is hypotenuse so sinA = CD/AC
=> CD = 5 x sin(20) = 5 x 0.342 = 1.71
then we have AB = AD + BD
Pythagorean theorem: c^2 = a^2 + b^2
for △ACD, 5^2 = 1.71^2 + AD^2
AD^2 = 5^2 - 1.71^2 = 22.0759
AD = 4.70
BD = AB - AD = 6 - 4.70 = 1.30
for △BCD, BC is hypotenuse
BC^2 = BD^2 + CD^2 = 1.30^2 + 1.71^2 = 4.61
BC = √4.61 = 2.1
Determine all real numbers s associated with the following point (x, y) on the unit circle. Write the exact radian answer in [0, 2pi) indicate remaining answers by using n to represent any integer.
If we cοnsider (x, y) tο be a pοint οn the unit circle, we get:
[tex]x^2 + y^2 = 1[/tex] (because the pοint is οn the unit circle) (since the pοint is οn the unit circle)
Hοw are real numbers determined?All real numbers must be determined in such a way that:
tan(s) = y / x
The trigοnοmetric identity can be applied:
Tan is equal tο Sin / Cοs.
We thus have:
Y/X = Tan(S), Sin(S), and Cοs (s)
Using the identity cοs(s) + sin(s) = 1, we square bοth sides tο οbtain:
[tex](y/x)^2 = sin^2(s) / cos^2(s) = 1 - cos^2(s)[/tex]
Rearranging and applying the equatiοn x2 + y2 = 1 results in:
cοs2(s) equals 1 - (y/x).
[tex]^2 = x^2[/tex]
Given that (x, y) is in the first οr fοurth quadrant and that x is pοsitive, we can take the square rοοt tο get the fοllοwing result:
cοs(s) = ± x
Sο, s is determined by:
S equals arccοs(x) + n, where n is any pοsitive integer.
The range οf x's value is limited tο [-1, 1] because it is οn the unit circle. As a result, the values οf s are prοvided by:
S = arccοs(x) + n, where n is any pοsitive integer and x is within the range [-1, 1].
The pοssible values οf s in exact radian measure in [0, 2] are as fοllοws:
S = arccοs(-1) + = S = arccοs(1) = 0
S is equal tο arccοs(0) + n + (n + 1/2)
where any integer n is used.
As n can be any integer, the pοssible pοssibilities οf s are s = 0,, and (n + 1/2).
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the cdf of a random variable is given the function on the support of , where the support of is . determine and .
The probability that X takes the value 1 is 1/4 and the probability that X takes the value 2 is 1/12.
The given CDF of a random variable X is F(X)=-*- on the support of X, where the support of X is x = 1,2,3,... The task is to determine P(X = 1) and P(X = 2).
To find P(X = 1), we need to find the probability that X takes the value 1. From the given CDF, we can see that F(1) = 1/4. Therefore, P(X = 1) = F(1) - F(1-) = 1/4 - 0 = 1/4.
To find P(X = 2), we need to find the probability that X takes the value 2. From the given CDF, we can see that F(2) = 7/12. Therefore, P(X = 2) = F(2) - F(2-) = 7/12 - 1/2 = 1/12.
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Question:-
The CDF Of A Random Variable X Is Given The Function F(X)=-*- On The Support Of X, Where The Support Of X Is X = 1,2,3,... Determine P(X = 1) And P(X = 2). 3x + X
find the value of the derivative (if it exists) at
each indicated extremum
Answer:
The value of the derivative at (2, 3) is zero.
Step-by-step explanation:
Given function:
[tex]g(x)=x+\dfrac{4}{x^2}[/tex]
To differentiate the given function, use the power rule of differentiation.
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Power Rule of Differentiation}\\\\If $y=x^n$, then $\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}$\\\end{minipage}}[/tex]
[tex]\textsf{Rewrite\;the\;function\;using\;the\;exponent\;rule\;\;$a^{-n}=\dfrac{1}{a^n}$}:[/tex]
[tex]\implies g(x)=x+4x^{-2}[/tex]
Apply the power rule:
[tex]\implies g'(x)=1+(-2) \cdot 4x^{-2-1}[/tex]
[tex]\implies g'(x)=1-8x^{-3}[/tex]
[tex]\implies g'(x)=1-\dfrac{8}{x^3}[/tex]
An extremum is a point where a function has a maximum or minimum value. From inspection of the given graph, the minimum point of the function is (2, 3).
To determine the value of the derivative at the minimum point, substitute x = 2 into the differentiated function.
[tex]\begin{aligned}\implies g'(2)&=1-\dfrac{8}{2^3}\\\\&=1-\dfrac{8}{8}\\\\&=1-1\\\\&=0\end{aligned}[/tex]
Therefore, the value of the derivative at (2, 3) is zero.
Hunter is an hourly employee, and the line that models his total pay in dollars
as it relates to the number of hours he has worked has a slope of 35 and a y
intercept of 25. Which statement is true?
O A. Hunter's wage is $35 an hour, but it appears that he received no
signing bonus.
• B. Hunter's wage is $35 an hour, and it appears that he received a
signing bonus of $25.
O C. Hunter's wage is $25 an hour, but it appears that he received no
signing bonus.
• D. Hunter's wage is $25 an hour, and it appears that he received a
signing bonus of $35.
Answer: C
Step-by-step explanation:
The correct answer is C.
The slope of the line represents the hourly wage, so Hunter's wage is $35 an hour, as given in option A and B. However, the y-intercept of the line represents the starting pay or the pay for zero hours worked. In this case, the y-intercept is 25, which means Hunter received $25 even if he did not work any hours. Hence, option C is correct as it states that Hunter's wage is $25 an hour, but it appears that he received no signing bonus.
what is the distance between the points (-9, 4)and(3,-12) ? a. 12 units b. 16 units c. 20 units d. 28 units
Answer:
20 units
Step-by-step explanation:
Point 1 (-9, 4)
Point 2 (3, -12)
Distance Formula
d=√((x2-x1)²+ (y2-y1)²)
d=√((3+9)²+ (-12-4)²)
d=√(12²+ (-16)²)
d=√(144+ 256)
d=√400
d=20
ou have five fair dice in your pocket, three are 4-sided and two are 6-sided. You randomly select two of the dice, roll them, and record the sum. a. What's the probability the sum is 6 ? b. Given that the sum of the dice is 6 , what's the probability both dice are 6 -sided? c. Given that the sum of the dice is 6 , what's the probability both dice are 4 -sided? d. Given that the sum of the dice is 6 , what's the probability one die is 4 -sided and one is 6 sided?
a) The probability the sum is 6 is equals to the 77/144.
b) The probability event that sum is 6 in case of both dice are 6 -sided is equals to the 5/36.
c) The probability event that sum is 6 in case of both dice are 4 -sided is equals to the 3/16.
d) The probability event that sum is 6 in case of one die is 4 -sided and one is 6 sided is equals to 5/24.
There are five fair dice in my pocket, three are 4-sided and two are 6-sided. Randomly select two of the dice, roll them, and record the sum. We have to determine the probabilities for different events. First, When two six-sided dice are rolled, total possible outcomes = 36
= {1,2,3,4,5,6}{1,2,3,4,5,6}
Similarly, When two four-sided dice are rolled, total possible outcomes = 16 = {1,2,3,4}{1,2,3,4}
Also, when one 4-sided and othe 6-sided faire dice are rolled, total possible outcomes = 24 = {1,2,3,4 } {1,2,3,4,5,6}
a) Let the event for sum is 6 be 'E'. The probability the sum is 6, P(E) = 5/36 + 3/16 + 5/24 = ( 20 + 27 + 30)/144
= 77/144
b) The probability that sum of the dice is 6 for both dice are 6 -sided = 5/36
c) Possible outcomes of occurrence of event E in case of both dice are 4 -sided = 3
The probability of occurrence of event E in case of both dice are 4 -sided, P(E)
= 3/16
d) Possible outcomes of occurrence of event E in case of one die is 4 -sided and one is 6 sided = 5
The probability one die is 4 -sided and one is 6 sided = 5/24
Hence, required probability is 5/24.
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Express 1.03 as a percentage
Answer:
103%
Step-by-step explanation:
1.03/1 x 100% = 103%
To convert the decimal 1.03 into a percentage, you multiply it by 100 which gives you 103%, so 1.03 is equal to 103%.
To express 1.03 as a percentage, we need to multiply the decimal by 100.
This is because the word percent in terms of mathematics means 'per hundred'. So, 1.03 multiplied by 100 equals 103.
Hence, 1.03 expressed as a percentage is 103%.
Rewrite your decimal as a fraction with a denominator of 100 to change it into a percentage.
For example, 1.03 can be written as 103/100 which translates into 103% in percentage format.
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You applied for k40 000.00 for a bank loan and you where given a flat rate interest of 9% for 2½ years. What is the amount he will pay the bank?
Answer:
The formula to calculate the amount of loan with flat rate interest is:
Amount = Principal + (Principal x Rate x Time)
Where,
Principal = the amount of loan
Rate = the interest rate per year
Time = the time period in years
Given,
Principal = K40,000.00
Rate = 9% per year
Time = 2.5 years
Substituting the values in the formula, we get:
Amount = K40,000.00 + (K40,000.00 x 0.09 x 2.5)
Amount = K40,000.00 + K9,000.00
Amount = K49,000.00
Therefore, the amount he will pay the bank is K49,000.00.
30 POINTS!!!!Carrie visited two different pet adoption centers. At the first adoption center the ratio of dogs to birds was 4:24. The ratio of dogs to birds at the second adoption center was equivalent.
Which is the ratio of dogs to birds at the second adoption center?
2:10
6:25
7:42
9:72
Answer:
7:42
Explanation: Since, the ratio was 4:24, it equals to 1:6, and the only one with a factor of 6 for the second number is C
Lionfish are considered an invasive species, with an annual growth rate of 65%. A scientist estimates there are 7,000 lionfish in a certain bay after the first year.
Part A: Write the explicit equation for f (n) that represents the number of lionfish in the bay after n years. Show all necessary math work.
Part B: How many lionfish will be in the bay after 6 years? Round to the nearest whole number and show all necessary math work.
Part C: If scientists remove 1,300 fish per year from the bay after the first year, what is the recursive equation for f (n)? Show all necessary math work.
The number of lionfish after 6 years will be 85,609. The recursive equation for [tex]f(n)[/tex] will be [tex]f(n) = 4242.42(1.65)^n - 1300n[/tex].
What is an exponent?Consider the function:
[tex]y = a (1 \pm r)^x[/tex]
Where x is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
lionfish are considered an invasive species, with an annual growth rate of 65%.
Then the equation will be
[tex]f(n) = P(1.65)^n[/tex]
[tex]\text{P = initial population}[/tex]
A scientist estimates there are 7,000 lionfish in a certain bay after the first year.
[tex]7000 = P(1.65)[/tex]
[tex]P = 4242.42[/tex]
Then the equation will be
[tex]f(n) = 4242.42(1.65)^n[/tex]
The number of lionfish after 6 years will be
[tex]f(n) = 4242.42(1.65)^6[/tex]
[tex]f(n) = 85608.58[/tex]
[tex]f(n) \cong 85,609[/tex]
If scientists remove 1,300 fish per year from the bay after the first year.
Then the recursive equation for f(n) will be
[tex]f(n) = 4242.42(1.65)^n - 1300n[/tex]
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BANK2 For 4 months, you have withdrawn $25 a month from your savings account. Your account
balance is now $75. Write an equation to represent your money(y) at any time(x).
The equation representing the money or balance (y) in your savings account any time (x) is y = z - 25x.
What is an equation?An equation is an algebraic statement showing the equality of two or more mathematical expressions.
Mathematical expressions combine variables with numbers, values, and constants without the equal symbol (=).
The monthly withdrawals = $25
The number of months (x) = 4
Account balance (y) = $75
Let z = the initial balance in the savings account.
Equation:y = z - 25x
75 = z - 25x
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choose 5 objects without replacement from 17 objects
Answer:
6188 ways
Step-by-step explanation:
there ate 5 objects to be choosen and there is no replacement of the object therefore you got
17 choices for the first selection of the object and 16 objects for the selection of the second object and so on until you get 13 objects for the last selection
totally you have 5 selections also arrangement does not matter there fore you have 17!/12!5! which is 6188
note we used 5! cause there are 5 placed objects and 12! are unplaced objects
note
that you have used one so you have to deduct one every time you use one
HELP ASAP WILL GIVE BRAINLYEST AND 100 POINTS IF YOU DON"T TRY TO ANSWER THE QUESTION RIGHT I WILL REPORT YOU
Answer:
[tex]\textsf{To\;add\;(or subtract)\;in\;Scientific\;Notation,\;you\;must\;have\;the\;same\;$\boxed{\sf power\;of\;10}$\:.}\\\textsf{Then\;you\;can\;$\boxed{\sf add\;or\;subtract}$\;the\;coefficients\;and\;$\boxed{\sf keep}$\;the\;power\;of\;10.}[/tex]
[tex]\textsf{To\;multiply\;in\;Scientific\;Notation,\; you\;must\;$\boxed{\sf multiply}$\;the\;coefficients}\\\textsf{and\;$\boxed{\sf add}$\;the\;powers\;of\;10.}[/tex]
[tex]\textsf{To\;divide\;in\;Scientific\;notation,\;you\;must\;$\boxed{\sf divide}$\;the\;coefficients}\\\textsf{and\;$\boxed{\sf subtract}$\;the\;powers\;of\;10.}[/tex]
Step-by-step explanation:
To add (or subtract) in Scientific Notation, you must have the same power of 10. Then you can add or subtract the coefficients and keep the power of 10.
Example expression:
[tex]2.3 \times 10^3 +3.2 \times 10^3[/tex]
Factor out the common term 10³:
[tex]\implies (2.3 +3.2) \times 10^3[/tex]
Add the numbers:
[tex]\implies (5.5) \times 10^3[/tex]
[tex]\implies 5.5\times 10^3[/tex]
Therefore, we have added the coefficients and kept the power of 10.
[tex]\hrulefill[/tex]
To multiply in Scientific Notation, you must multiply the coefficients and add the powers of 10.
Example expression:
[tex]2.3 \times 10^3 \times 3.2 \times 10^3[/tex]
Collect like terms:
[tex]\implies 2.3 \times 3.2 \times 10^3 \times 10^3[/tex]
Multiply the numbers (coefficients):
[tex]\implies 7.36 \times 10^3 \times 10^3[/tex]
[tex]\textsf{Apply the exponent rule:} \quad a^b \cdot a^c=a^{b+c}[/tex]
[tex]\implies 7.36 \times 10^{(3+3)}[/tex]
[tex]\implies 7.36 \times 10^{6}[/tex]
Therefore, we have multiplied the coefficients and added the powers of 10.
[tex]\hrulefill[/tex]
To divide in Scientific notation, you must divide the coefficients and subtract the powers of 10.
Example expression:
[tex]\dfrac{8.6 \times 10^6}{2.15 \times 10^2}[/tex]
Collect like terms:
[tex]\implies \dfrac{8.6}{2.15} \times \dfrac{10^6 }{10^2}[/tex]
Divide the numbers (coefficients):
[tex]\implies 4\times \dfrac{10^6 }{10^2}[/tex]
[tex]\textsf{Apply the exponent rule:} \quad \dfrac{a^b}{a^c}=a^{b-c}[/tex]
[tex]\implies 4\times 10^{(6-2)}[/tex]
[tex]\implies \implies 4\times 10^{4}[/tex]
Therefore, we have divided the coefficients and subtracted the powers of 10.
A line passes through points (5,3) and (-5,-2). Another line passes through points (-6,4) and (2,-4). Find the coordinates (ordered pairs) of the intersection of the two lines.
Step 1: Find the slope of each line
Step 2: Find the y-intercept of each line
Step 3: Write each line in slope-intercept form (y = mx + b)
Step 4: Solve for the system. Find the point of intersection for the system
Please help I will mark brainliest!!!
The point of intersection of the two lines is (-3.4, -1.2).
How to find the slope of each line?Step 1: The slope of a line passing through two points (x1,y1) and (x2,y2) can be found using the formula:
m = (y2-y1)/(x2-x1)
Using this formula, we can find the slope of the first line:
m1 = (−2−3)/(-5 -5) = −5/(-10) = 1/2
And the slope of the second line:
m2 = (−4−4)/(2 -(-6)) = -8/4 = -2
Step 2: Find the y-intercept of each line
The y-intercept of a line in slope-intercept form (y = mx + b) is the value of y when x=0. We can use one of the two given points on each line to find the y-intercept:
For the first line passing through points (5,3) and (−5,−2):
y = mx + b
3 = (1/2)(5) + b
b = 3 - 5/2
b = 1/2
So the first line can be written as y = 1/2x + 1/2
For the second line passing through points (−6,4) and (2,−4):
y = mx + b
4 = (-2)(−6) + b
b = 4 - 12
b = -8
So the second line can be written as y = -2x - 8
Step 3: Each line in slope-intercept form (y = mx + b):
First line: y = 1/2x + 1/2
Second line: y = -2x - 8
Step 4: To find the point of intersection of the two lines, we need to solve the system of equations. We can solve for x by setting the two right-hand sides equal to each other:
1/2x + 1/2 = -2x - 8
(x + 1)/2 = -2x - 8
x + 1 = -4x - 16
5x = -16 - 1
5x = -17
x = -17/5
x = -3.4
Now that we know x, we can find y by substituting x=10 into one of the two equations:
y = -2x - 8
y = -2(-3.4) - 8
y = - 1.2
Thus, the point of intersection of the two lines is (-3.4, -1.2).
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Find the error. Select choice options are step 1, 2, 3 and x-coordinates and y-coordinates
Therefore, the slope of the line that passes through (-2, 8) and (4, 6) is -1/3.
What is the slope?
In mathematics, the slope is a measure of the steepness of a line.
The solution provided involves three steps to find the slope of the line that passes through two points: (-2, 8) and (4, 6).
Step 1 involves finding the change in y-coordinates, which is the difference between the y-coordinate of the second point and the y-coordinate of the first point. In this case, the second point has a y-coordinate of 6 and the first point has a y-coordinate of 8.
Therefore, the change in y-coordinates is 6 - 8 = -2.
Step 2 involves finding the change in x-coordinates, which is the difference between the x-coordinate of the second point and the x-coordinate of the first point. In this case, the second point has an x-coordinate of 4 and the first point has an x-coordinate of -2.
Therefore, the change in x-coordinates is 4 - (-2) = 6.
Step 3 involves dividing the change in y-coordinates by the change in x-coordinates to find the slope of the line. In this case, the change in y-coordinates is -2 and the change in x-coordinates is 6, so the slope is -2/6 or -1/3.
Since all the steps are correct and properly executed, there is no error.
Therefore, the slope of the line that passes through (-2, 8) and (4, 6) is -1/3.
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3. The total number of Democrats and Republicans in the US House of Reps during the 115th
year was 434. There were 46 fewer Democrats than Reps. How many were there of each
party?
Answer:
Step-by-step explanation:
subtract 434-46
In a survey of 124 pet owners, 44 said they own a dog, and 58 said they own a cat. 14 said they own both a dog and a cat. How many owned neither a cat nor a dog?
Step-by-step explanation:
See Venn diagram below
the level of confidence of a test of hypothesis is denoted by
what is the length of h in the following composite figure? all angles are right angles. 5 m 3 m 4 m 2 m
The length of h in the attached composite figure where all the angles are right angles is equal to 4m.
In the attached diagram of composite figure,
All are right angles.
Composite figure consist two rectangles,
Upper and lower rectangles.
length of the upper rectangle is equal to 5m
Width of the upper rectangle is equal to 'h' m
Width of the lower rectangle is equal to 2m
Length of each dash '-' mark is equals to 1m.
length of 'h'm is equals
= 2 m + 2 dash marks
= 2m + 2m
= 4m
Therefore, the length of the h in the composite figure ( attached diagram ) is equals to 4m.
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The above question is incomplete, the complete question is:
What is the length of h in the following composite figure? All angles are right angles.
5 m
4 m
3 m
2 m
Diagram is attached.
Answer:
4 m is ur answer
Step-by-step explanation:
hope this helps
Write the function for the table in standard form?
I tried to work out the problem and got y = -x^2 -6x + 2 not sure if that is correct. Please see steps on the attached file.
The value of the quadratic equation in the standard form is y = -x² -6x + 2.
What is quadratic equation?y = ax² + bx + c, where a, b, and c are constants and an is not equal to 0, is a quadratic equation in standard form. A parabolic function's vertex, axis of symmetry, and intercepts with the x- and y-axes are all expressed by the quadratic equation in standard form. While the positions of the vertex and intercepts are determined by the factors b and c, the direction and form of the parabola are determined by the coefficient a. Every quadratic equation may be changed into standard form by applying the quadratic formula or the square method, which simplifies the analysis and comparison of various functions.
The standard form of the quadratic equation is given by:
y = ax² + bx + c
Substituting the values of x and y from the table we have:
For (-4, 10):
10 = a(-4)² + b(-4) + c
10 = 16a - 4b + c......(1)
For (-3, 11):
11 = a(-3)² + b(-3) + c
11 = 9a -3b + c......(2)
For (-2, 10):
10 = 4a - 2b + c .........(3)
Equation 1 can be written as follows:
10 = 16a - 4b + c
c = 10 - 16a + 4b
Substitute the value of c in equation 2 and 3:
11 = 9a -3b + c
11 = 9a - 3b + 10 - 16a + 4b
1 = - 7a + b .........(4)
And,
10 = 4a - 2b + c
10 = 4a - 2b + 10 - 16a + 4b
0 = -12a + 2b
12a = 2b
b = 6a .......(5)
Substitute the value of b in equation 4:
1 = - 7a + 6a
1 = -a
a = -1
Substitute the value of a in equation 5:
b = -6
Now, substitute the value of a and b in equation 1:
10 = 16a - 4b + c
10 = 16(-1) - 4(-6) + c
10 = -16 + 24 + c
10 = 8 + c
c = 2
Substituting the value in the quadratic equation we have:
y = -x² -6x + 2
Hence, the value of the quadratic equation in the standard form is y = -x² -6x + 2.
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6u^2+17u-10
factor please
Answer:
(2u - 1) (3u + 10)
Step-by-step explanation:
Let's Check
(2u - 1) (3u + 10)
6u² + 20u - 3u + 10
6u² + 17u + 10
So, (2u - 1) (3u + 10) is the correct answer.
X man can complete a work in 40 days.If there were 8 man more the work should be finished in 10 days less the original number of the man
Step-by-step explanation:
Original job = x men * 40 days = 40x man days to complete
now add 8 men = x+8 men
man days now is (x+8) (30) to complete job
so 40x = (x+8)(30)
40x = 30x + 240
10 x = 240
x = 24 men originally
evaluate f(0) when f(x)=5x. if it's impossible to do so, enter "dne" (with no quotes) in the answerbox.
The value of function f(0) after putting the value of x = 0 we get the value o which is not DNE.
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is often represented as y = f. (x).
Given function is
f(x)=5x
we have to find the value of the f(0)
so putting the value of 0 as x we get,
f(x)=5x
f(0) = 5(0)
f(0) = 0
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These two triangles are similar. What is the missing side measure?
X
5
O x = 9.5
0 x = 2
Ox=7
Ox=4
3.5
20
8
14
According to the given information, the missing side measure is 14.
What is triangle?
A triangle is a polygon with three sides, three angles, and three vertices. It is the simplest polygon and the fundamental shape used in geometry. A triangle can be classified based on the length of its sides and the measure of its angles.
To find the missing side measure, we can set up a proportion between the corresponding sides of the two similar triangles:
(x + 5) / x = 9.5 / 7
We can then solve for x by cross-multiplying:
7(x + 5) = 9.5x
7x + 35 = 9.5x
35 = 2.5x
x = 14
Therefore, the missing side measure is 14.
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In the diagram O is the centre of the circle. If ZOAB 32' and ZEDA-15, find: (1) ZADB and (ii) ZEAO. D 37°
Therefore, the answers are: (i) ZADB = 48.5 degrees, and (ii) ZEAO = 54 degrees.
What is angle?An angle is a geometric concept that describes the amount of rotation between two intersecting lines or planes. It is defined as the figure formed by two rays with a common endpoint, called the vertex. The two rays are called the sides of the angle, and they can be measured in degrees or radians.
In the degree measurement system, a full rotation is 360 degrees, and an angle that is one quarter of a rotation (90 degrees) is called a right angle. Angles that are less than 90 degrees are called acute angles, while angles greater than 90 degrees but less than 180 degrees are called obtuse angles. An angle that measures exactly 180 degrees is called a straight angle, and an angle that measures greater than 180 degrees, but less than 360 degrees is called a reflex angle.
by the question.
ZOAB + ZEDA = 32 + 15 = 47 degrees. Since these two angles are opposite each other, they must add up to 180 degrees (straight angle) and therefore, ZAOB + ZEDC = 180 - 47 = 133 degrees.
Angle D is given as 37 degrees, and since ZEDC is a straight line, ZEDD = 180 - 37 = 143 degrees.
ZADB = ZAOB + ZOAB + BAD. Since ZAOB + ZOAB = 180 - ZEDC = 180 - 133 = 47 degrees, we have ZADB + BAD = 37 + 47 = 84 degrees. Also, BAD is an exterior angle of triangle ABD, so it is equal to the sum of the two opposite interior angles, which are ZADB and ABD. Therefore, ZADB + ABD + BAD = 180 degrees. Substituting the value of BAD and simplifying, we get ZADB = 48.5 degrees.
ZEAO = ZEDC - ZEDA - ZOAD. We already know ZEDC and ZEDA, so we need to find ZOAD. Since ZOAB and ZOAD are opposite each other, they must add up to 180 degrees. Also, ZOAB is equal to half the central angle ZODB (since it subtends the same arc), which is equal to 2ZOAD (since it is an inscribed angle subtended by the same arc). Therefore, we have ZOAB + ZOAD = 180 and ZOAB = ZOAD/2. Substituting the value of ZOAB from the given information, we get ZOAD = 64 degrees. Substituting all the values, we get ZEAO = 54 degrees.
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1. A living room measures 4.75 m by 5.2 m. a. What is the area of the living room? 24.7m b. The area of the game room is one and a half times that of the living room. Fi the living room and the game room.
The area of the living room is 24.7 m², and the area of the game room is 37.05 m².
What is area?Area is the measure of the two-dimensional space occupied by a figure or an object. It is usually expressed in square units such as cm2, m2, or in2. It is used to measure the size of a figure or object, and can also be used to calculate the amount of material required for a project.
The area of a living room measuring 4.75 m by 5.2 m can be calculated using the formula A = l × w, where A is the area, l is the length and w is the width. In this case, A = 4.75 m × 5.2 m = 24.7 m².
To calculate the area of the game room, we must multiply the area of the living room by 1.5. Therefore, the area of the game room is 1.5 × 24.7 m² = 37.05 m².
The area of the living room is 24.7 m², and the area of the game room is 37.05 m².
The area of a room can be used to determine how much furniture can fit in the room or how much floor space is available for activities. Knowing the area of a room is also important for calculating the cost of painting, wallpapering, carpeting, and other flooring materials.
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Give an example to show that if d is not prime and n2 is divisible by d, then n need not be divisible by d.
If d is not a prime number and n^2 is divisible by d, it does not necessarily mean that n is also divisible by d, example is d = 6 and n = 3, where n^2 = 9 is divisible by 6, but n = 3 is not divisible by 6.
A prime number is a positive integer greater than 1 that has exactly two distinct factors: 1 and itself. For example, 2, 3, 5, 7, 11, 13, and 17 are all prime numbers.
If a number d is not prime, then it has at least one factor other than 1 and itself. Let's assume that d is not prime, and let p be a factor of d such that p is not equal to 1 or d. Then, by definition, p divides d evenly with no remainder.
Consider the case where d = 6 and n = 3.
Here, d is not a prime number, and n^2 = 9, which is divisible by d since 9 is a multiple of 6. However, n = 3 is not divisible by d = 6, as 6 does not divide 3 evenly.
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