Answer:
f(x)= 2x² - 4x + 3
Step-by-step explanation:
dy/dx = 4x - 4
y = integrate dy/dx
y = 4x²/2 - 4x + c
y = 2x² - 4x + c
at (2,3)
3 = 2(2)² - 4(2) + c
3 = 8 -8 + c
c = 3
therefore f(x)= y = 2x² - 4x + 3
The graph of the function is given by f ( x ) = 2x² - 4x + 3
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the function be represented as A
Now , the value of A is
At each point (x, y) on a graph of function f, the graph has a slope equal to 4x - 4
So , dy/dx = 4x - 4
On integrating , we get
f ( x ) = 2x² - 4x + c
where the function passes through P ( 2 , 3 )
So , 3 = 2 ( 2 )² - 4 ( 2 ) + c
c = 3
Hence , the function is f ( x ) = 2x² - 4x + 3
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Find the value of x
and/or y in OA.
Can anyone please answer (show solution)
Answer:
x = 97
y = 83
Step-by-step explanation:
y = 83 (being the vertically opposite angle )
y + x = 180 (being co-interior angle)
or,
83 + x = 180
or,
x = 180 - 83
.•. x = 97
Choose the best definition for the following phrase: combining like terms (1 point)
Group of answer choices
A letter that holds the place for some unknown value in mathematics
A process where you must look for terms that have identical variable parts and then combine their coefficients
A process where if two things are equal, one can be put in the place of the other and nothing will change
Terms that have identical variable parts
Answer:
A process where you must look for terms that have identical variable parts and then combine their coefficients
Step-by-step explanation:
Combining like terms is adding or subtracting terms that have the same variable parts.
Answer: A process where you must look for terms that have identical variable parts and then combine their coefficients
Windborn company has 20,000 shares of cumulative preferred 2% stock, $150 par and 50,000 shares of $25 par common stock. the following amounts were distributed as dividends:
20y1 $120,000
20y2 24,000
20y3 180,000
determine the dividends per share for preferred and common stock for each year. round all answers to two decimal places. if an answer is zero, enter '0'.
preferred stock common stock
(dividends per share) (dividends per share)
20y1
20y2
20y3
Based on the preferred dividends, the dividends for preferred and common stock in each year are:
Preferred stock dividends:
20y1 - $3.00 per share.20y2 - $1.20 per share.20y3 - $4.80 per share.Common stock dividends:
20y1 - $1.20 per share.20y2 - $0 per share.20y3 - $1.68 per share.What are the preferred dividends?Preferred shares have a specific dividend, and as these are cumulative shares, the dividends that are not paid in one year, will be paid in the next.
Dividends per year:
= 20,000 x 2% x 150
= $60,000
20y1 dividend per share:
= 60,000 / 20,000
= $3.00 per share
20y2 dividend per share:
= 24,000 / 20,000
= $1.20 per share
20y3 dividend per share:
The remaining dividend from 20y2 will have to be paid here:
= (60,000 + (60,000 - 24,000)) / 20,000
= 96,000 / 20,000
= $4.80 per share
What are the common dividends?Preferred dividends are paid first:
Common dividends are:
= (Amount distributed as dividends - Preferred dividends) / Number of common shares
In 20y1:
= (120,000 - 60,000) / 50,000
= $1.20
In 20y2:
= (45,000 - 45,000) / 50,000
= $0 per share
In 20y3:
= (180,000 - 96,000) / 50,000
= $1.68 per share.
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Tom opens a bank account and makes an initial deposit of 500$. Then banker tells Tom that he is going to receive an annual rate of 6% on his investment. Find the bank balance assuming Tom leaves the account untouched for 15 years. (Will give brainliest to the person who has the answer correct and will shown work.)
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$500\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &15 \end{cases} \\\\\\ A=500\left(1+\frac{0.06}{1}\right)^{1\cdot 15}\implies A=500(1.06)^{15}\implies A\approx 1198.28[/tex]
Colin gets pic 'n mix when at the cinema and makes his bag up with 3 types of sweet. He picks 3 times as many cola bottles as smarties. He also picks twice as many smarties as marshmallows. What proportion of the bag of sweets are cola bottles?
Give your answer in its simplest form.
The simplest form of the proportion is 2/3
here , it is give that colin picks 3 times as many cola bottles as smarties and twice as many smarties as marshmallows. To simplify this let us suppose colin pic a number of marshmallows then number of smarties he pic will be 2a and also the number of cola bottles will be 6a.
What is proportion ?
A proportion is an equation based on the equality of two ratios.
Therefore, the proportion of the bag of sweets are cola bottles will be :
[tex]\begin{aligned}\frac{6a}{a+2a+6a}&=\frac{6}{9}\\&=\frac{2}{3}\end{aligned}[/tex]
Therefore, The simplest form of the proportion is 2/3
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If 4 more than twice a number is 8 less than three times the same number, what is the number?
[tex]\text{Let the number be x.}\\\\\text{According to the condition,}\\\\~~~~~4+2x=3x-8\\\\\implies 3x-2x = 4+8\\\\\implies x = 12\\\\\text{Hence, the number is 12.}[/tex]
Graph the lines that represent the following system of linear equations.
2s +1.5y = -60
2s + y = -50
The lines that represent the following system of linear equations.
2s +1.5y = -60
2s + y = -50
will intersect at (-15, -20)
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.
Slope is a ratio of change in y-coordinate w.r.t. change in x-coordinate. The net change in y coordinate is written as, Δy and the net change in x coordinate is written as, Δx.
Given,
System of linear equations
2s +1.5y = -60
2s + y = -50
After plotting both the graphs we can see that, point of intersection is (-15, -20)
Hence, The point of intersection is (-15, -20)
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In a word game, 1 letter is worth 1 point. this dot plot shows the scores for 20 common words.what is the median score? pointswhat is the first quartile (q1)?
points
what is the third quartile (q3)?
points
what is the interquartile range (iqr)?
The median is 6.5.
The first quartile is 5.
The third quartile is 8.
The interquartile range is 3.
What are the statistics of the data plot?The numbers in the dot plot are: 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 22
Median is the number in the middle of the dataset.
Median = 1/2 ( n + 1)
1/2 x 21 = 11.5th number = (6+ 7) / 2 = 6.5
First quartile = 1/4 x (n + 1)
1/4 x 21 = 5.25th number = 5
Third quartile = 3/4 x (n + 1)
3/4 x 21 = 15.75th number = 8
Interquartile range = 8 - 5 = 3
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19. What are equivalent statements to a + 3 = 18 and 4 b = 32?
a = 18-3 and b = 32/4
a=18/3 and b = 32/4
a = 18/3 and b = 32-4
a = 18-3 and b = 32 - 4
Answer:
The choice second . a=18/3 and b = 32/4
Step-by-step explanation:
[tex]a + 3 = 18 \\ a = 18 - 3[/tex]
[tex]4b = 32 \\ \\ b = \frac{32}{4} [/tex]
What is the polynomials of (2x^2-x+1)(x-3)
Answer:
2x^3 - 7x^2 + 4x - 3
Step-by-step explanation:
Multiply them all together.
√(2-x)-√(1-4x)=1
solve for x
Answer:
decimal form; 0.22222...
exact form; 2/9
Step-by-step explanation:
Please help !!!!!!!!!!
Answer:
the third option in the list
Step-by-step explanation:
the numbers down below qre the coefficients of the equations above
Please help me thanks!!!
Problem 9
r+h = 9
SA = 2*pi*r^2 + 2*pi*r*h = 54pi
2*pi*r^2 + 2*pi*r*h = 54pi
2pi*r(r + h) = 54pi
r(r+h) = 27
r(9) = 27
9r = 27
r = 27/9
r = 3
r+h = 9
h = 9-r
h = 9-3
h = 6
Answers: r = 3 and h = 6 are the radius and height respectively.
==========================================================
Problem 10
d = diameter = 68 mm
r = radius = d/2 = 68/2 = 34 mm
SA = surface area of a sphere
SA = 4*pi*r^2
SA = 4*pi*34^2
SA = 4264pi
Answer: 4264pi square mm
==========================================================
Problem 11
Plug V = 3000 into the sphere volume formula and isolate r.
V = (4/3)pi*r^3
3000 = (4/3)pi*r^3
(4/3)pi*r^3 = 3000
4pi*r^3 = 3*3000
4pi*r^3 = 9000
r^3 = 9000/(4pi)
r = cube root( 9000/(4pi) )
r = ( 9000/(4pi) )^(1/3)
r = 8.947002 approximately
Now we can determine the surface area of this sphere.
SA = 4pi*r^2
SA = 4*pi*( 8.947002 )^2
SA = 1005.923451
Answer: 1005.923451 square feet approximately
==========================================================
Problem 12
We'll follow the same idea as problem 11, but in reverse.
SA = 4*pi*r^2
400pi = 4pi*r^2
r^2 = (400pi)/(4pi)
r^2 = 100
r = sqrt(100)
r = 10
Luckily we get a nice whole number for the radius r. Use it to find the volume.
V = (4/3)*pi*r^3
V = (4/3)*pi*10^3
V = (4000/3)pi
Answer: (4000/3)pi cubic inches exactly
==========================================================
Problem 13
The diagram is missing. I don't have enough info to be able to answer.
A rectangular patio is 9 ft by 6 ft. when the length and width are increased by the same amount, the area becomes 88 sq ft. ginger is using the zero product property to solve the equation (6 x)(9 x) = 88. what does the value of x in her solutions represent?
Answer:
x=2
9+2=11
6+2=8
8x11+88
Step-by-step explanation:
Measure the angle shown below.
a protractor showing an angle going through the fifteenth tick mark after two hundred sixty five degrees
272°
275°
279°
280°
The measure of the angle shown is 280°
Calculating anglesFrom the question, we are to determine the measure of the angle shown
For the given protractor,
The measure between any two lines is 10°.
Also, there are 10 tick marks between any two lines.
∴ 15 tick marks will have a measure of 15°
Then,
The measure of a protractor showing an angle going through the fifteenth tick mark after two hundred sixty five degrees will be
265° + 15° = 280°
Hence, the measure of the angle shown is 280°
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Expand and simplify
4(2x + 3) + 4(3x + 2)
Answer: 20x + 20
Step-by-step explanation:
We will distribute the four into the expressions to expand, then we will simplify.
Given:
4(2x + 3) + 4(3x + 2)
Distribute:
8x + 12 + 12x + 8
Combine like terms with addition:
20x + 20
20x + 20
Zahara asked the students of her class their gymnastic scores and recorded the scores in the table shown below:
Gymnastic Scores
Score Number of Students
0 1
1 1
2 2
3 6
4 4
5 3
6 2
Based on the table, what is the mean gymnastic score? (1 point)
2.5
3.5
5.2
9.4
Answer:
B. 3.5
Step-by-step explanation:
I believe this is correct :')
We can use radicals if needed, and we need to simply.
Answer:
x = √41 which is 6.40 to the nearest hundredth.
Step-by-step explanation:
x^2 = 4^2 + 5^2 (By the Pythagoras theorem)
x^2 = 16 + 25 = 41
x = √41.
please help meeee, much appreciated!!!!!!
Answer:
expected value is $4.5
Step-by-step explanation:
expected value is $4.5
If x = 2.5, 5c = ? (Only I put decimals such as 12.7 as the answer).
Answer:
12.5
Step-by-step explanation:
x = 2.5, 5x = ?
5(2.5) = 5 x 2.5 = 12.5
Find the measures of angles a=(2x+3) and b=(2x-3),if their sum is 120 degrees
Answer:
angle A is 63 degrees,
angle B is 57 degrees
Step-by-step explanation:
first, let's create the equation. Pretty simple, because angles a and b become 120 degrees when added up, this this will become:
2x+3+2x-3=120
now, we make it simpler. In this case, just add up the numbers that we can add up. this eventually becomes:
4x=120
now, all we need to do is divide 120 by 4, which becomes 30. So, x=30.
substitute the 30 into the x in the original equation, and this becomes:
60+3+60-3=120
63+57=120
thus, angle A is 63 degrees, and angle b is 57 degrees.
If the diameter of a youth softball is 3.5 inches and the diameter of an adult softball is 3.8 inches, what is the approximate difference in their volumes? use 3.14 for pi. round to the nearest tenth of a cubic inch. recall the formula sphere volume = four-thirds pi r cubed. 6.3 cubic inches 51.1 cubic inches 67.0 cubic inches 409.2 cubic inches
Answer:
A because the volume of the adult softball is 28.7309120146 inches and the youth softball is 22.4492975038 inches and when u subtract them u get about 6.3 cubic inches :)
Step-by-step explanation:
:)
Answer: IT A!
Step-by-step explanation:
solve the quadractic formula 3x+x-3=0
Answer: x = 0.75
Step-by-step explanation:
3x+x - 3 =0
4x - 3=0
4x = 3
x = 0.75
5x^1/2
-----------
3x^1/2 -4
Solve this and ill give brainly
Answer:
(5√x) / [(3√x)-4]
Step-by-step explanation:
You cannot solve this because 5, 3, and 4 are not factors/multiples of one another
I simplified it though
when the exponent is 1/2, it is the same as taking the square root of something
5x^1/2 is the same as 5√x
3x^1/2 is the same as 3√x
24. Taylor wants to purchase an $80 purse. She has
found three stores that have the purse originally priced
at $80 but are offering 3 different sales this weekend:
1
●
Store A: off original price
• Store B: 10% off original price
Store C: $15 off original price
Which of the following is a true statement?
Answer:
we need the full question
Please help me with this PROBABILITY question! I'm really stuck and would really appreciate your help.
Please don't post nonsense answers and I'd love it if you could add working out.
Thanks :))
Answer: The probability of picking a black bead is 4/7, because there are 4 black beads out of seven. But if you took the first black bead out of the equation then the probability is now 3/7.
x/9+3<4 what is the solution to the ineqaulity
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the solution to the inequality:
[tex]\star~\large\pmb{\cfrac{x}{9}+3 < 4}[/tex]
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
First, subtract 3 from both sides, then multiply both sides by the denominator.Step 1.
[tex]\star~\large\pmb{\cfrac{x}{9} < 4-3}[/tex]
[tex]\star~\large\pmb{\cfrac{x}{9} < 1}[/tex]
Step 2.
[tex]\star~\large\pmb{\cfrac{x}{9}\times9 < 1\times9}[/tex]
Notice that on the left, the 9s cancel, and we're left with x.
Step 3.
[tex]\star~\large\pmb{x < 9}[/tex]
This is the solution.
Hope it helps you out! :D
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Answer:
x < 9
Step-by-step explanation:
Given:
[tex]\dfrac{x}{9} + 3 < 4[/tex]
1. Subtract 3 from both sides of the inequality
[tex]\dfrac{x}{9} + 3 - 3 < 4 - 3\\\\\implies\dfrac{x}{9} < 1[/tex]
2. Multiply both sides of the inequality by 9
[tex]9\left(\dfrac{x}{9}\right) < 1(9)\\\\\implies x < 9[/tex]
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given set P={3,6,9}.How many subset can be formed
Answer:
8
Step-by-step explanation:
[tex]P = \{3,6,9\}\\\\\text{Number of elements,}~ n = 3\\\\\text{Number of subset} = 2^n = 2^3 = 8[/tex]
Decrease £40 by 25%
(Hegarty maths)
Answer:
the answer to your question is 10
Step-by-step explanation:
if you divide 40 by 25% then you will get 10
. Triangle EFG has vertices E(-2, 1), F(-1, 4), and G(3, 4). Graph the figure and its image after a clockwise rotation of 90° about vertex F. Then write the coordinates of triangle E'F'G'.
Triangle EFG has vertices E(-2, 1), F(-1, 4), and G(3, 4). Graph the figure and its image after a clockwise rotation of 90° about vertex F. Then write the coordinates of triangle E'F'G'.