Answer:
3x^2 + 3xy/2 - 7xy^2/2
Step-by-step explanation:
So we know the perimeter is 20x^2 + xy - 7y^2,
To find any perimeter you need 2l + 2w = P so,
One of the sides is 7x^2 - xy
First plug in the values,
2(7x^2-xy) + 2w = 20x^2 + xy - 7y^2
Multiply,
14x^2-2xy + 2w = 20x^2 + xy - 7y^2
Subtract,
14x^2 - 2xy - 14x^2 + 2xy + 2w = 20x^2 + xy - 7y^2 - 14x^2 + 2xy
2w = 6x^2 + 3xy - 7y^2
w = 3x^2 + 3xy/2 - 7xy^2/2
Enter an expression that is equivalent to (6x2−1)+(x2+3)−2(x2−5)−15x2, combining all like terms. Use the on-screen keyboard to type the correct polynomial in the box below.
Answer:
Its 10x^2+12
Step-by-step explanation:
Answer:
-10X^2+12
Step-by-step explanation:
A patio 20 feet wide has a slanted roof, as shown in the figure. Find the length of the roof if there is an 8-inch overhang. Show all work and round the answer to the nearest foot. Be sure to label your answer appropriately. Then write a sentence explaining your answer in the context of the problem.
Answer:
[tex]Slanted\ Roof = 20.77\ ft[/tex]
Step-by-step explanation:
The question has missing attachment (See attachment 1 for complete figure)
Given
Width, W = 20ft
Let the taller height be represented with H and the shorter height with h
H = 10ft
h = 8ft
Overhang = 8 inch
Required
Determine the length of the slanted roof
FIrst, we have to determine the distance between the tip of the roof and the shorter height;
Represent this with
This is calculated by
[tex]D = H - h[/tex]
Substitute 10 for H and 8 for h
[tex]D = 10 - 8[/tex]
[tex]D = 2ft[/tex]
Next, is to calculate the length of the slant height before the overhang;
See Attachment 2
Distance L can be calculated using Pythagoras theorem
[tex]L^2 = 2^2 + 20^2[/tex]
[tex]L^2 = 4 + 400[/tex]
[tex]L^2 = 404[/tex]
Take Square root of both sides
[tex]\sqrt{L^2} = \sqrt{404}[/tex]
[tex]L = \sqrt{404}[/tex]
[tex]L = 20.0997512422[/tex]
[tex]L = 20.10\ ft[/tex] -------Approximated
The full length of the slanted roof is the sum of L (calculated above) and the overhang
[tex]Slanted\ Roof = L + 8\ inch[/tex]
Substitute 20.10 ft for L
[tex]Slanted\ Roof = 20.10\ ft + 8\ inch[/tex]
Convert inch to feet to get the slanted roof in feet
[tex]Slanted\ Roof = 20.1\ ft + 8/12\ ft[/tex]
[tex]Slanted\ Roof = 20.10\ ft + 0.67\ ft[/tex]
[tex]Slanted\ Roof = 20.77\ ft[/tex]
Hence, the total length of the slanted roof in feet is approximately 20.77 feet
Chloe wants to wrap a present in a box for Sarah. The top and bottom of the box is 8 in. by 3 in., the sides are both 3 in by 2 in. and the front and back are 8 in by 2 in. How much wrapping
paper will Chloe need to wrap the present?
Answer:
92 inches squared
Step-by-step explanation:
T/P = 8 * 3
L/R = 3 * 2
F/B = 8 * 2
Solving for surface area!
2(24) + 2(6) + 2(16) = 92
3(x–6)=18 help plese
Answer:
x = 12
Step-by-step explanation:
3(x–6)=18
x-6 = 18:3
x-6 = 6
x = 6+6
x = 12
Answer:
x=12
Step-by-step explanation:
Choose the situation that represents a function.
A) The number of raisins in an oatmeal raisin cookie is a function of the diameter of the cookie.
B) The inches of rainfall is a function of the day’s average temperature.
C) The time it takes to cook a turkey is a function of the turkey’s weight.
D) The number of sit-ups a student can do in a minute is a function of the student’s age.
Answer:c
Step-by-step explanation:
Answer: The answer is C.
Hope this helps you!
i need help will rate you branliest
Answer:
D. the bottom one is the answer, because hyperbola is two curves that curve infinitely
Mark is buying supplies for his students. He is buying a notebook (n) and a pack of pencils for each of his 25 students. Each pack of pencils costs $1.25. If Mark's total cost is $156.25, which of the following equations can be used to find how much each notebook cost? Select TWO that apply.
Answer:
$5
Step-by-step explanation:
Note. There are no options to select.Let the notebook cost x, then Mark spent:
25x + 25*1.25 = 156.2525x + 31.25 = 156.2525x = 156.25 - 31.2525x = 125x= 125/25x= 5Notebook costs $5
Which of the following is a solution for 5 - 2x ≤ -3?
Answer:
x≥4
Step-by-step explanation:
The required solution for the inequality 5 - 2x ≤ -3 is x ≥ 4 or x ∈ [4, ∞).
What is inequality?Inequality shows relation between two expression which are not equal to each others.
The given inequality is,
5 - 2x ≤ -3.
Solve the inequality,
Add 3 to both the sides,
5 - 2x + 3 ≤ -3 + 3
8 - 2x ≤ 0
-2x ≤ -8
Multiply -1 both the sides,
2x ≥ 8
x ≥ 4
The solution for the inequality is x ≥ 4 or x ∈ [4, ∞).
To know more about Inequality on:
https://brainly.com/question/20383699
#SPJ2
Let A and B be events. The symmetric difference A?B is defined to be the set of all elements that are in A or B but not both.
In logic and engineering, this event is also called the XOR (exclusive or) of A and B.
Show that P(AUB) = P(A) + P(B)-2P(AnB), directly using the axioms of probability.
Correction:
P(AΔB) = P(A) + P(B) - 2P(AnB)
is what could be proven using the axioms of probability, and considering the case of symmetric difference given.
Answer:
P(AΔB) = P(A) + P(B) - 2P(AnB)
Has been shown.
Step-by-step explanation:
We are required to show that
P(AUB) = P(A) + P(B) - 2P(AnB)
directly using the axioms of probability.
Note the following:
AUB = (AΔB) U (AnB)
Because (AΔB) U (AnB) is disjoint, we have:
P(AUB) = P(AΔB) + P(AnB)..................(1)
But again,
P(AUB) = P(A) + P(B) - P(AnB)...............(2)
Comparing (1) with (2), we have
P(AΔB) + P(AnB) = P(A) + P(B) - P(AnB)
P(AΔB) = P(A) + P(B) - 2P(AnB)
Where AΔB is the symmetric difference of A and B.
If you invest $ 30 , 700 with an annual interest rate of 8.9 % , compounded daily, how much would you have at the end of 4 years?
Answer: $43,823.37
Step-by-step explanation:
Formula to calculate the accumulated amount earned on principal (P) at rate of interest (r) compounded daily after t years :
[tex]A=P(1+\dfrac{r}{365})^{365t}[/tex]
As per given , we have
P= $ 30,700
r= 8.9 % = 0.089
t= 4 years
[tex]A=30700(1+\dfrac{0.089}{365})^{365(4)}\\\\=30700(1+0.0002438)^{365(4)}\\\\=30700(1.0002438)^{1460}\\\\=30700(1.42747138525)\\\\=43823.3715272\approx43823.37[/tex]
Hence, the amount at the end of 4 years would be $43,823.37 .
3a-27=0
How to solve
Answer:
a = 9
Step-by-step explanation:
3a - 27 = 0
3a = 27
a = 27/3
a = 9
3*9 - 27 = 0
27 - 27 = 0
Answer:
a = 9
Step-by-step explanation:
3a-27=0
Add 27 to each side
3a = 27
Divide by 3
3a/3 = 27/3
a = 9
find the slope of the line y = 4
Answer:
Brainleist!
Step-by-step explanation:
0
there is no y=mX+b
there is no x no XXXX
that means the slope must be 0 (bc theres a y)
Sorry if my explanation is bad... let me know in comments if u need more help
the principal p is borrowed at a simple interest rate r for a period of time t. find the loan's future value g P = 700, r = 8.25, t = 3 months
Answer:
Hey there!
Simple interest formula: I=PRT
I=700(8.25)(0.25)
I=1443.75
Hope this helps :)
Answer:
Step-by-step explanation:
I = PRT
I = 700(0.0825)(1/4) = 14.44
Because the interest is usually in percentage and it's impossible to have 825% as your interest rate. So the actual interest rate has to be 0.0825.
The formula above calculated the interest, if you want the total, you will need to add 700 to that number.
[img id="5156824"][/img]Here's a small quick example of the formula that should help.
explain why the APR does not compare loans for different lengths of time
Answer:
APR does not tell you how long your rate is locked for. A 15-year loan may have a lower interest rate, but could have a higher APR, since the loan fees are amortized over a shorter period of time. It is not wise to compare a 30-year loan with a 15-year loan using their respective APRs.
Step-by-step explanation:
PLEASE HELP!!! The question is.. [tex]163-y=-5[/tex] ANSWER GETS BRAINLIEST
Answer:
y = 168Step-by-step explanation:[tex]163 -y =-5\\Collect\:Like\:terms\\163+5 = y\\Simplify\\168 =y\\\\y = 168[/tex]
Hello There!
Answer: [tex]163-168=-5[/tex]Explanation:[tex]163-y=-5[/tex]
To solve your equation, you can just change the -5 to 5 and move it to where y is. After that, change the minus sign to addition.
[tex]163+5=y[/tex]
Now all you have to do is sum it up.
[tex]163+5=168[/tex]
So y = to 168
So your answer is
[tex]163-168=-5[/tex]
Hope this Helps!
Rhombus J K L M is shown. The length of J K is 2 x + 4 and the length of J M is 3 x. What is the length of a side of rhombus JKLM? 4 units 8 units 12 units 16 units
Answer:
12 units
Step-by-step explanation:
Since all of the sides of a rhombus are congruent, JK = JM which means:
2x + 4 = 3x
-x = -4
x = 4 so 3x = 3 * 4 = 12
A sample of a radioactive substance decayed 11% over the course of 3 weeks. How many grams were in the sample originally if 30.26 grams of the substance were remaining after the 3 weeks?
Answer:
34 grams
Step-by-step explanation:
If the remaining sample has 30.26 grams of radioactive substance, and 11% of it decayed, that means that 30.26 grams is 89% of the original. Let the original be x.
30.26=0.89x
Multiply both by one hundred
3026=89x
Divide both by 89
34=x
x=original, so the original was 34 grams.
i will rate you brainliest
Answer:
D) 3/2(X-4)
Step-by-step explanation:
Invert and multiply to get:
3(x+4)/2(x²-16)
factor the bottom
3(x+4)/2(x+4)(x-4)
The (x+4)’s cancel out, and you’re left with
3/2(X-4)
[tex]\dfrac{{x+4\over2}}{{x^2-16\over3}}[/tex]
[tex]=\dfrac{3(x+4)}{2(x+4)(x-4)}=\frac{3}{2(x-4)} [/tex]
but in original fraction, denominator can't be zero so we have to exclude x=±4
do that answer is D
In the last 10 years, the population of Indonesia has grown at a rate of 1.12% per year to 258,316,051. If this rate continues, what will be the population in 10 more years? Round your answer to the nearest whole number.
Answer:
Final population after 10 years
= 288911718
Step-by-step explanation:
Present population p = 258,316,051
Rate of growth R%= 1.12%
Number of years t= 10 years
Number of times calculated n = 10
Final population A
= P(1+r/n)^(nt)
A= 258,316,051(1+0.0112/10)^(10*10)
A= 258,316,051(1+0.00112)^(100)
A= 258,316,051(1.00112)^100
A= 258,316,051(1.118442762)
A= 288911717.6
Approximately A= 288911718
Final population after 10 years
= 288911718
What is the domain of h?
Answer:
{-2, -1, 1, 5, 6}
Step-by-step explanation:
The domain includes the five x-values (inputs): {-2, -1, 1, 5, 6}
Answer:
The x-values -2, -1,1,5 and 6
Step-by-step explanation:
What are two solutions of x
Answer:
Answer is attached below :)
PLEASE HELP ASAP Madelyn drove a race car in a race. She averaged 55 mph and began the race 0.5 hours ahead of the other drivers. The variable d represents Madelyn's distance driven, in miles. The variable t represents the number of hours since the other drivers began to race. Which equation can be used to determine the distance Madelyn drove t hours into the race? d=55t−0.5 d=55(t+0.5) d=55(t−0.5) d = 55t + 0.5
Answer:
d=55(t+0.5)
Step-by-step explanation:
d=55(t+0.5)
Answer:
27.5
Step-by-step explanation:
BOND VALUATION Asiana Fashion's bonds have 10 years remaining to maturity. Interest is paid annually; they have a $1,000 par value; the coupon interest rate is 8% and thebyield to maturity is 9%.What is the bond's current market price?
Answer:
$935.76
Step-by-step explanation:
BOND VALUATION Asiana Fashion's bonds have 10 years remaining to maturity. Interest is paid annually; they have a $1,000 par value; the coupon interest rate is 8% and thebyield to maturity is 9%.What is the bond's current market price?
Step 1
We find the Present value factor of sum
The formula =
(1 + i)^n
Where
i = maturity rate = 9% = 0.09
n = number of years = 10 years
Present Value = ( 1 + 0.09)^-10
= 0.4224
Step 2
We find the present value factor of annuity
The formula is given as:
1 - (1+i)^-n / i
i = maturity rate = 9% = 0.09
n = number of years = 10 years
= 1 - (1 + 0.09)^-10 /0.09
= 1 - 0.4224 /0.09
= 0.5775 /0.09
= 6.417
Step 3
The bond's current market price is calculated as:
= PV factor of Sum × Par Value + PV factor of annuity × coupon payment
Coupon payment is calculated as:
= Coupon interest × par value
= 8% × 1000
= 80
Hence,
= 0.4224 × 1,000 + 6.417 × 80
= 422.4 + 513.36
= 935.76
In this exercise we have to use the knowledge of finance to calculate the corrective value of the market place, in this way we find that:
[tex]\$935.76[/tex]
We find the Present value factor of sum, by the formula of:
[tex](1 + i)^n[/tex]
Where:
i = maturity rate = 9% = 0.09 n = number of years = 10 years
Substituting the values in the formula as;
[tex]Present \ Value = ( 1 + 0.09)^{-10} = 0.4224[/tex]
We find the present value factor of annuity, by the formula as:
[tex]1 - (1+i)^{-n} / i[/tex]
Where:
i = maturity rate = 9% = 0.09 n = number of years = 10 years
Substituting the values in the formula as;
[tex]= 1 - (1 + 0.09)^{-10} /0.09\\= 1 - 0.4224 /0.09\\= 0.5775 /0.09\\= 6.417[/tex]
The bond's current market price is calculated as:
[tex]= PV \ factor\ of\ Sum * Par\ Value + PV\ factor\ of\ annuity * coupon\ payment[/tex]
Coupon payment is calculated as:
[tex]= Coupon\ interest * par\ value\\= 8\% * 1000= 80[/tex]
So continue the calcule;
[tex]= 0.4224 *1,000 + 6.417 * 80\\= 422.4 + 513.36\\= 935.76[/tex]
See more about market place at brainly.com/question/24518027
Find the measure of c.
Answer:
149 degrees
Step-by-step explanation:
This shape is a cyclic, so opposite angles add up to 180 degrees.
180-31 = 149
Find the work W done by a force of 7pounds acting in the direction 30 degreesto the horizontal in moving an object 7feet from (0 comma 0 )to (7 comma 0 ).
Answer:
The work done by the force is 42.4 Joules
Step-by-step explanation:
The force F = 7 pounds
angle to the horizontal that the force acts ∅ = 30°
The object is moved a distance d = 7 feet
The coordinate (0 comma 0 )to (7 comma 0 ), indicates that the movement started from the origin, and is along the x-axis.
The work done by this force = F cos ∅ x d
==> 7 cos 30° x 7
==> 7 x 0.866 x 7 = 42.4 Joules
The arc length apothem shown below is 15 feet. Part 1) State the equation that relates arc length to central angle. Part 2) Find the angle apothem in radians. Part 3) Convert your answer from Part 2 to degrees and write it to the nearest hundredth of a degree
Answer:
ans right down there
Step-by-step explanation:
Here,Part 1
if the circle has a radius r so,
15 = r theta
here, theta is in radian.
Part 2
[tex]theta = \frac{15}{6} = 2.5[/tex]
part 3
[tex]theta = \frac{2.5 \times 180}{\pi} [/tex]
or theta =
143.2394487827058021919953870352629258310136811664108038729006
name all the pairs of angles which are vertical angles , alternate interior angles , alternate exterior angles , co interior angles , co exterior angles , and corresponding angles from the given figure . (co interior - interior angles on the same side of transversal)
Answer:
Step-by-step explanation:
Since m and k are the parallel lines and a transverse 'l' is intersecting these lines at two different points.
- Opposite angles at the point of intersection of parallel lines and the transverse will be the vertical angles.
∠1 ≅ ∠3, ∠2 ≅ ∠4, ∠5 ≅ ∠8 and ∠6 ≅ ∠7 [Vertical angles]
- Pair of angles between parallel lines 'k' and 'm' but on the opposite side of the transversal are the alternate interior angles.
∠4 ≅ ∠6 and ∠3 ≅ ∠5 [Alternate interior angles]
- Angles having the same relative positions at the point of intersection are the corresponding angles.
∠2 ≅ ∠6, ∠3 ≅ ∠8, ∠4 ≅ ∠7 and ∠1 ≅ ∠5 [Corresponding angles]
- Co interior angles are the angles between the parallel lines located on the same side of the transversal.
∠4 and ∠5, ∠3 and ∠6 [Co interior angles]
- Co exterior angles are the angles on the same side of the transverse but outside the parallel lines.
∠2 and ∠8, ∠1 and ∠7 [Co exterior angles]
BRAINLEST , If y varies inversely with the square of x, and y = 26 when x = 4, find y when x = 2.
Answer:
Question 18: B. 104
Question 19: [tex] x = \frac{3}{2} [/tex]
Step-by-step Explanation:
Question 18:
Step 1: express the inverse relationship with an equation
[tex] y = \frac{k}{x^2} [/tex] ,
where k is constant
y = 26 when x = 4,
Constant, k, = [tex] y*x^2 = k [/tex]
[tex] k = 26*4^2 = 416 [/tex]
The equation would be [tex] y*x^2 = 416 [/tex]
Step 2: use the equation to find y when X = 2.
[tex] y*x^2 = 416 [/tex]
[tex] y*2^2 = 416 [/tex]
[tex] y*4 = 416 [/tex]
Divide both sides by 4
[tex] \frac{y*4}{4} = \frac{416}{4} [/tex]
[tex] y = 104 [/tex]
Question 19:
[tex] \frac{x}{3} = \frac{x + 2}{7} [/tex]
Cross multiply
[tex] x(7) = 3(x + 2) [/tex]
[tex] 7x = 3x + 6 [/tex]
Subtract 3x from both sides
[tex] 7x - 3x = 3x + 6 - 3x [/tex]
[tex] 4x = 6 [/tex]
Divide both sides by 4
[tex] \frac{4x}{4} = \frac{6}{4} [/tex]
[tex] x = \frac{3}{2} [/tex]
Answer: D.) 52
Explanation: I guessed and got it right lol
Marine ecologists estimate the reproduction curve for swordfish in a fishing ground to be f(p) = −0.01p2 + 9p, where p and f(p) are in hundreds. Find the population that gives the maximum sustainable yield, and the size of the yield.
Answer:
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is 202500 swordfishes.
Step-by-step explanation:
Let be [tex]f(p) = -0.01\cdot p^{2}+9\cdot p[/tex], the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)
First Derivative Test
[tex]f'(p) = -0.02\cdot p +9[/tex]
Let equalize the resulting expression to zero and solve afterwards:
[tex]-0.02\cdot p + 9 = 0[/tex]
[tex]p = 450[/tex]
Second Derivative Test
[tex]f''(p) = -0.02[/tex]
This means that result on previous part leads to an absolute maximum.
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is:
[tex]f(450) = -0.01\cdot (450)^{2}+9\cdot (450)[/tex]
[tex]f(450) =2025[/tex]
The maximum sustainable yield is 202500 swordfishes.
Determine the number of degrees of freedom for the two-sample t test or CI in each of the following situations. (Round your answers down to the nearest whole number.)
(a) m = 12, n = 15, s1 = 4.0, s2 = 6.0
(b) m = 12, n = 21, s1 = 4.0, s2 = 6.0
(c) m = 12, n = 21, s1 = 3.0, s2 = 6.0
(d) m = 10, n = 24, s1 = 4.0, s2 = 6.0
Answer:
a
[tex]df = 24.32[/tex]
b
[tex]df = 30.10[/tex]
c
[tex]df = 30.7[/tex]
d
[tex]df = 25.5[/tex]
Step-by-step explanation:
Generally degree of freedom is mathematically represented as
[tex]df = \frac{ [\frac{ s^2_i }{m} + \frac{ s^2_j }{n} ]^2 }{ \frac{ [ \frac{s^2_i}{m} ]^2 }{m-1 } +\frac{ [ \frac{s^2_j}{n} ]^2 }{n-1 } }[/tex]
Considering a
a) m = 12, n = 15, s1 = 4.0, s2 = 6.0
[tex]df = \frac{ [\frac{ 4^2 }{12} + \frac{ 6^2 }{15} ]^2 }{ \frac{ [ \frac{4^2}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{15} ]^2 }{15-1 } }[/tex]
[tex]df = 24.32[/tex]
Considering b
(b) m = 12, n = 21, s1 = 4.0, s2 = 6.0
[tex]df = \frac{ [\frac{ 4^2 }{12} + \frac{ 6^2 }{21} ]^2 }{ \frac{ [ \frac{4^4}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{21} ]^2 }{21-1 } }[/tex]
[tex]df = 30.10[/tex]
Considering c
(c) m = 12, n = 21, s1 = 3.0, s2 = 6.0
[tex]df = \frac{ [\frac{ 3^2 }{12} + \frac{ 6^2 }{21} ]^2 }{ \frac{ [ \frac{3^4}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{21} ]^2 }{21-1 } }[/tex]
[tex]df = 30.7[/tex]
Considering c
(d) m = 10, n = 24, s1 = 4.0, s2 = 6.0
[tex]df = \frac{ [\frac{ 4^2 }{10} + \frac{ 6^2 }{24} ]^2 }{ \frac{ [ \frac{4^2}{10} ]^2 }{10-1 } +\frac{ [ \frac{6^2}{24} ]^2 }{24-1 } }[/tex]
[tex]df = 25.5[/tex]
