Answer:
Step-by-step explanation:
3r(2r^2 - 5)
6r^(2 + 1) - 5*3r
6r^3 - 15r
Find the values of c such that the area of the region bounded by the parabolas y = 4x2 − c2 and y = c2 − 4x2 is 32/3. (Enter your answers as a comma-separated list.)
Answer:
-2,2
Step-by-step explanation:
Let
[tex]y_1=4x^2-c^2[/tex]
[tex]y_2=c^2-4x^2[/tex]
We have to find the value of c such that the are of the region bounded by the parabolas =32/3
[tex]y_1=y_2[/tex]
[tex]4x^2-c^2=c^2-4x^2[/tex]
[tex]4x^2+4x^2=c^2+c^2[/tex]
[tex]8x^2=2c^2[/tex]
[tex]x^2=c^2/4[/tex]
[tex]x=\pm \frac{c}{2}[/tex]
Now, the area bounded by two curves
[tex]A=\int_{a}^{b}(y_2-y_1)dx[/tex]
[tex]A=\int_{-c/2}^{c/2}(c^2-4x^2-4x^2+c^2)dx[/tex]
[tex]\frac{32}{3}=\int_{-c/2}^{c/2}(2c^2-8x^2)dx[/tex]
[tex]\frac{32}{3}=2\int_{-c/2}^{c/2}(c^2-4x^2)dx[/tex]
[tex]\frac{32}{3}=2[c^2x-\frac{4}{3}x^3]^{c/2}_{-c/2}[/tex]
[tex]\frac{32}{3}=2(c^2(c/2+c/2)-4/3(c^3/8+c^3/28))[/tex]
[tex]\frac{32}{3}=2(c^3-\frac{4}{3}(\frac{c^3}{4}))[/tex]
[tex]\frac{32}{3}=2(c^3-\frac{c^3}{3})[/tex]
[tex]\frac{32}{3}=2(\frac{2}{3}c^3)[/tex]
[tex]c^3=\frac{32\times 3}{4\times 3}[/tex]
[tex]c^3=8[/tex]
[tex]c=\sqrt[3]{8}=2[/tex]
When c=2 and when c=-2 then the given parabolas gives the same answer.
Therefore, value of c=-2, 2
ASAP PLSSS!!!!!!!!!!1!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: i think its the last one bc if you multiply 9 and 3 in its gets you 18
Step-by-step explanation:
Answer:
V=(1/3)πr²h
v=
[tex] \frac{1}{3} \times {3}^{2} \times 9 \times \pi \\ = 27\pi[/tex]
27pi in³
27pi in³First option
Brainliest please~
The winter group provides tax advice
what? ;-;.............
One loaf of bread and six rolls cost $1.80. At the same prices, two loaves of bread and four rolls cost $2.40. How much does one loaf of bread cost. I have go the answer which is 90 cents and one roll costs 15 cents but the math Olympiad book solution does not explain it well can someone explain it better?
9514 1404 393
Answer:
loaf: $0.90; roll: $0.15
Step-by-step explanation:
Let b and r represent the cost of a loaf of bread and a roll, respectively.
The two purchases can be written in equation form as ...
b +6r = 1.80
2b +4r = 2.40
__
The usual ways to work problems like this are "substitution" or "elimination". The latter is sometimes called "addition."
SubstitutionThe way these equations are written, we can see that it is relatively easy to write an expression for b from the first equation:
b = 1.80 -6r
Substituting that into the second equation, we get ...
2(1.80 -6r) +4r = 2.40
3.60 -8r = 2.40 . . . . . . . collect terms
1.20 = 8r . . . . . . . . . . add 8r-2.40
0.15 = r . . . . . . . . . divide by 8
Then substituting this into the expression for b, we have ...
b = 1.80 -6r = 1.80 -6(0.15) = 0.90
One loaf costs $0.90; one roll costs $0.15.
__
EliminationThe idea with "elimination" is to combine the equations in such a way that one of the variables is eliminated in the process. Here, there are several ways that can be done.
We recognize that the b-coefficient in the second equation is double that in the first equation. So, we can subtract the second equation from double the first equation to make the b-terms disappear.
2(b +6r) -(2b +4r) = 2(1.80) -(2.40)
8r = 1.20 . . . . . . . simplify
r = 0.15 . . . . . . . divide by 8
Using the first equation, we can find b:
b + 6(0.15) = 1.80
b = 0.90 . . . . . . . . . subtract 0.90
One loaf costs $0.90; one roll costs $0.15.
__
Another way we can eliminate one of the variables is to rewrite the second equation without its excess factor of 2:
b +2r = 1.20
Then subtracting the first equation from 3 times this will eliminate the r variable:
3(b +2r) -(b +6r) = 3(1.20) -(1.80)
2b = 1.80 . . . . . . . . . simplify
b = 0.90
Then, using the above version of the second equation, we have ...
0.90 +2r = 1.20
2r = 0.30
r = 0.15
One loaf costs $0.90; one roll costs $0.15.
Matt and his brother will each work 13 hours this week for their dad. If Matt earns $14.00 an hour and his brother earns $17.00 an hour, how much will Matt earn by the end of the week? *
Answer:
$182.00
Step-by-step explanation:
We know that Matt will work for 13 hours, and that he will earn 14.00 an hour. We are asked how much Matt will earn by the end of the week. Because Matt's earnings are not based on his brother's earnings, we can disregard how much his brother makes.
We add 14.00 13 times, as Matt earns 14 dollars for each hour and he works for 13 dollars. This is equal to multiplying 14 by 13, resulting in 14 * 13 = 182 as our answer
Enter the letter for the function graphed below.
A) y=3^sqrt x-3
B) y=3 sqrt x -3
Answer: е) Step-by-step explanation: we know the coordinates of the points so we can easily determine which function this is To begin with, let's take any two points with an integer coordinates let these be two points with coordinates (1 ; 4) and (0 ; 3) Now let's check [tex]a) \ \displaystyle\bf 4=\sqrt[3]{1-3} \ \ wrong[/tex] and all other options except option e are incorrect because [tex]\displaystyle\ e) \sqrt[3]{1} +3=4 \ \ right[/tex]
what is the percent decrease on a Tv that has been marked down from $550 to $420? round to the nearest tenth
The percent decrease on a TV after the markdown to the nearest tenth is 23.6%.
What is the percent decrease on the TV after the markdown?The percent decrease formula can be expressed as:
Percent decrease = [( original value - new value ) / original value ] × 100%
Given the data in the question:
The original value of the TV = $550
New value after markdown = $420
Percent decrease =?
Plug the given values into the above formula and solve for the percent decrease.
Percent decrease = [( original value - new value ) / original value ] × 100%
Percent decrease = [( 550 - 420 ) / 550 ] × 100%
Percent decrease = [ 130 / 550 ] × 100%
Percent decrease = 0.2363 × 100%
Percent decrease = 23.6%
Therefore, the percent decrease is 23.6%.
Learn about Percent increase here: https://brainly.com/question/19062651
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log(x) + log(x+2) = log 3
Please find attached photograph for your answer.
Regarding the violation of multicollinearity, which of the following description is wrong?
Complete question is;
Regarding the violation of multicollinearity, which of the following description is wrong?
a. It changes the intercept of the regression line.
b. It changes the sign of the slope.
c. It changes the slope of the regression line.
d. It changes the value of F-tests.
e. It changes the value of T-tests
Answer:
a. It changes the intercept of the regression line
Step-by-step explanation:
Multicollinearity is a term used in multiple regression analysis to show a high correlation between independent variables of a study.
Since it deals with independent variables correlation, it means it must be found before getting the regression equation.
Now, looking at the options, the one that doesn't relate with multicollinearity is option A because the intercept of the regression line is the value of y that is predicted when x is 0. Meanwhile, multicollinearity from definition above does in no way change the intercept of the regression line because it doesn't predict the y-value when x is zero.
Find the common ratio for this geometric sequence.
72, 12, 2, 1/3, 1/18
OA. 1/3
ОВ. 1/6
OC. 3
OD. 6
Answer:
1/6
Step-by-step explanation:
We need to find the common ratio for the given Geometric Series . We know that ,
Geometric Series:- When a common number is multiplied to each term to obtain the next term of the Series is called Geometric Series .
Common Ratio :- The number which is multiplied to obtain the next term of the series .
Here the given series is ,
[tex]\rm\implies Series = 72 , 12 , 2 , \dfrac{1}{3},\dfrac{1}{18} [/tex]
We can find the common ratio by dividing the consecutive terms , As ,
[tex]\rm\implies Common \ Ratio (r) = \dfrac{ n \ th \ term }{ ( n - 1)th \ term } [/tex]
Substitute the respective values ,
[tex]\rm\implies Common \ Ratio (r) = \dfrac{ 12 }{ 72 } [/tex]
Simplify by dividing the term in RHS ,
[tex]\rm\implies \boxed{\blue{\rm Common \ Ratio (r) = \dfrac{ 1 }{ 6 } }}[/tex]
Hence the common ratio is 1/6 .
Find the probability of a couple having at least 1 girl among 4 children. Assume that boys and girls are
equally likely and that the gender of a child is independent of the gender of any brothers or sisters.
Answer:
15/16 (93.75%)
Step-by-step explanation:
List of Possible Combinations:
BBBB, BBBG, BBGB, BBGG, BGBB, BGBG, BGGB, BGGG, GBBB, GBBG, GBGB, GBGG, GGBB, GGBG, GGGB, GGGG
As you can see, only 1 out of 16 of the possible combinations is all boys. This means that the chance of at least 1 girl among the 4 children is 15 out of 16 (15/16) or 93.75%
For the rational function f(x)=5−xx2+5x+6, find the points on the graph at the function value f(x)=3.
Given:
The rational function is:
[tex]f(x)=\dfrac{5-x}{x^2+5x+6}[/tex]
To find:
The points on the graph at the function value [tex]f(x)=3[/tex].
Solution:
We have,
[tex]f(x)=\dfrac{5-x}{x^2+5x+6}[/tex]
Substituting [tex]f(x)=3[/tex], we get
[tex]3=\dfrac{5-x}{x^2+5x+6}[/tex]
[tex]3(x^2+5x+6)=5-x[/tex]
[tex]3x^2+15x+18=5-x[/tex]
Moving all the terms on one side, we get
[tex]3x^2+15x+18-5+x=0[/tex]
[tex]3x^2+16x+13=0[/tex]
Splitting the middle term, we get
[tex]3x^2+3x+13x+13=0[/tex]
[tex]3x(x+1)+13(x+1)=0[/tex]
[tex](3x+13)(x+1)=0[/tex]
Using zero product property, we get
[tex](3x+13)=0\text{ or }(x+1)=0[/tex]
[tex]x=-\dfrac{13}{3}\text{ or }x=-1[/tex]
Therefore, the required values are [tex]-\dfrac{13}{3},-1[/tex].
Find the perimeter of this quarter circle with radius,
r
= 38mm.
Give your answer as an expression in terms of
π
.PLEASE HELP I NEED THE ANSWER ASAP
Answer:
19[tex]\pi[/tex] + 76 mm
Step-by-step explanation:
First, use the circumference formula to find the perimeter of the entire circle:
c = 2[tex]\pi[/tex]r
c = 2[tex]\pi[/tex](38)
c = 76[tex]\pi[/tex]
Divide this by 4, since the question asks for the perimeter of the quarter circle:
76[tex]\pi[/tex]/4
= 19[tex]\pi[/tex]
19[tex]\pi[/tex] is the arc length section of the perimeter. The length of the other 2 sides of the perimeter, formed by the radius, can be found by doubling 38.
38(2) = 76
Add this to 19[tex]\pi[/tex]:
19[tex]\pi[/tex] + 76
So, the expression is 19[tex]\pi[/tex] + 76 mm
write the numeral of twelve Arab sixty core
Answer:
12600000000
Step-by-step explanation:
write the numeral of twelve Arab sixty core
The numeral of twelve Arab sixty core is
=> 12600000000
hope it is helpful to you
Step-by-step explanation:
the numeral from is 12600000000
X(1 1 -1;2 1 0;1 -1 1)=(1 -1 3;4 3 2;1 -2 5)
Step-by-step explanation:
What does the way in which Yudhishthira deals with the Yaksha’s
questions tell you about him?
Estimate the line of best using two points on the line.
Betty received $ 500,000 from a life insurance policy to be distributed to her as an annuity certain in 10 equal annual installments with the first payment made immediately. On the day she receives her third payment, she is offered a monthly perpetuity of X in lieu of the future annual payments. The first payment will be made in exactly one month. The effective annual rate of interest is 8 %. Determine the value of X.
9514 1404 393
Answer:
annual payment: $68,995.13monthly payment in perpetuity: X = $2394.76Step-by-step explanation:
a) For payments made at the beginning of the period, the annuity is called an "annuity due." The formula in the first attachment tells how to compute the payment for a given present value ($500,000), number of periods (N=10), and interest rate (i=0.08).
pmt = $500,000/(1 +(1 -(1 +i)^(-N+1))/i) = $500,000/(1 +(1 -(1.08^-9))/.08)
pmt ≈ $68,995.13 . . . . annual payment
__
b) After the first payment, the account balance is ...
$500,000 -68,995.13 = $431,004.87
After subsequent payments, the account balance will be ...
$431,004.87×1.08 -68,995.13 = $396,490.13 . . . after 2nd payment
$396,490.13×1.08 -68,995.13 = $359,214.21 . . . after 3rd payment
The payment amount that can be made in perpetuity is the amount of the monthly interest on this balance:
X = $359,214.21 × (0.08/12) = $2394.76
How does the rate of change of f(x)=3x+5 compare to the rate of change of g(x)=2x+5 ?
HELP I NEED ANSWERS
Answer:
The rate of change of f(x) is faster than the rate of change of g(x).
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
*Note:
Rate of Change is determined by slope.
Step 1: Define
f(x) = 3x + 5
↓ Compare to y = mx + b
Slope m = 3
g(x) = 2x + 5
↓ Compare to y = mx + b
Slope m = 2
Step 2: Answer
We can see that the slope of f(x) is greater than g(x).
∴ the rate of change of f(x) would be greater than g(x).
In a normally distributed data set with a mean of 19 and a standard deviation of 2.6, what percentage of the data would be between 13.8 and 24.2?a) 95% based on the Empirical Ruleb) 68% based on the histogramc) 68% based on the Empirical Ruled) 95% based on the histogram
Step-by-step explanation:
check the attachment above.
Find the x and y intercepts and graph 2x − y = −8
Answer:
-2
Step-by-step explanation:
2x-y=-8-1equation
2x=-8+y
x=-8+y -2equation
2
then, taking 1st equation;
2x-y=-8
2(-8+y/2)-y=-8
-16+2y-y=-8
4
-16+2y-4y=-8
4
-16-2y=-8*4
-2y=-32+16
y=-16/-2
y=4
for x
x=-8+y
2
x=-8+4
2
x=-4
2
x=-2
I can't figure this out, please help
1. A rectangle is formed by the intersection of the lines x = −1, y = −1, x = 5
and y = 3. What is the perimeter and area of the rectangle
Step-by-step explanation:
The length along the x-axis is 5 - (-1) = 6. The length along the y-axis is 3 - (-1) = 4. The perimeter of this rectangle can be calculated as
[tex]P = 2x + 2y = 2(6) + 2(4) = 20\:\text{units}[/tex]
The area of the rectangle can be calculated as
[tex]A = xy = (6)(4) = 24\:\text{units}^2[/tex]
If h(x) = −3x − 10, find h(−3). (1 point)
Answer:
h(- 3) = - 1
Step-by-step explanation:
Substitute x = - 3 into h(x) , that is
h(- 3) = - 3(- 3) - 10 = 9 - 10 = - 1
If anyone can please help me
Answer:
1/4
Step-by-step explanation:
5 orange + 5 mango = 10
P( mango ) = mango /total = 5/10 = 1/2
Replace
5 orange + 5 mango = 10
P(orange ) = orange /total = 5/10 = 1/2
P(mange, replace, orange) = 1/2 * 1/2 = 1/4
what is the area of this whole shape
Answer:
104 m²
Step-by-step explanation:
Area of the whole shape = area of the triangle + area of the rectangle
= ½*b*h + L*W
Where,
b = 8 m
h = 6 m
L = 10 m
W = 8 m
Plug in the values into the equation
Area of the whole shape = ½*8*6 + 10*8
= 24 + 80
= 104 m²
What is the measurement of N?
Answer:
the measurement of N is D, 81.
Step-by-step explanation:
The angle measurement of a Right Angled Triangle is 90 degrees. And based off the angle dimension given in the image above ( 9 degrees ), you need to subtract 90 ( the angle dimension of the triangle) with the angle dimension given (9 degrees) which gets you to an answer of 81 degrees.
Directions: Use the figure to write the symbol for each.
1. I ray
2. a plane
А
3. 3 points
4. 2 lines
5. 3 angles
6. 3 line segments
D
Geometry
156
Total Math Grade 6
I need help ASAP please due tomorrow 6th grade geometry
It is a total length of space between two positions
Distance traveled
It is a total length of space between two positions. The distance travelled is the path taken by a body to get from an initial point to an end point in a given period of time, at a certain velocity.
Hope it helps you! ＼(^ᴥ^)／
17. What is the solution to -7s=-35? (1 point)
Os=-6
Os=-5
Os = 5
Os=6
Answer:
(+5)=S , be the correct answer
Answer: s = +5
Step-by-step explanation: Since s is being multiplied by -7, to get s by itself, we need to divide by -7 on both sides of the equation.
So we get s = +5 which is the solution to our equation.
What type of move takes Figure A to Figure B?
Image B is on the opposite side of the Y axis and the image is upside down from what image A is.
This would be a 90 degree rotation.
Answer:
rotation of 180 degrees
Step-by-step explanation:
in this type of rotation : (x, y) --> (-x, -y)
a rice cooker was sold for $60 after a discount of 60% waht was the usual price of the rice cooker with explaination simple method for class 5
Answer:
$150
Step-by-step explanation:
So, 60 dollars is 40% of the original price. So 30 dollars is 20% of the original price, and 150 dollars is 100% of the original price. So, the original value of the rice cooker is 150 dollars.
Answer:
The price of the Rice Cooker was 150$.
Step-by-step explanation:
So if you buy an item at $150 with 60% discounts, you will pay $60 and get 90 cashback rewards ... interest per annum, dollars, pounds, coupons,60% off, 60% of price or something, we ... For example 5% of 20, which is the same thing as fraction x/100 * 20=5%. ... Formula and equation for % of something or whole numbers.
