Answer:
See answer below
Step-by-step explanation:
Finding the measure of each angle.
The sum of the angles in a triangle = 180°
(9x - 8) + (x + 10) + (3x + 2) = 180°
13x + 4 = 180
13x = 180 - 4
13x = 176
x = 176/13
Angle 1 = 9x - 8 Angle 2 = x + 10 Angle 3 = 3x +2
= 9(176/13) - 8 = 176/13 + 10 = 3(176/13) + 2
≈ 113.8° ≈ 23.5° ≈ 42.6°
A pool with a square bottom is to have a volume of 2000 cubic feet. The owners plan to use a fancy tile to complete the pool. The sides of the pool will cost $80 per square foot and the bottom of the pool will cost $40 per square foot. Find the pool dimensions that will minimize the cost of construction.
The pool dimensions that will minimize the cost of construction are length of square bottom = 20 ft and height of pool = 5 ft
Let l be the length of side of the square bottom of the pool and h be the height of the pool.
Its volume V = l²h
Now, the total surface area of the pool equal the area of its sides plus the area of its base.
The area of its 4 sides is 4lh.
Since the cost of the side of the pool is $80 per square foot, the total cost for the sides of the pool is C = $80 × 4lh = $ 320lh
Also, The area of its square bottom is l².
Since the cost of the side of the pool is $40 per square foot, the total cost for the square bottom of the pool is C' = $40 × l² = $ 40l²
So, the total cost of the pool is C" = C + C' = 320lh + 40l²
C" = 320lh + 40l²
Since the volume equals 2000 ft³, V = l²h
2000 = l²h
h = 2000/l²
Substituting h into C", we have
C" = 320lh + 40l²
C" = 320l × 2000/l² + 40l²
C" = 640000/l + 40l²
To find the value of l which makes C" minimum, we differentiate C" with respect to l and equate it to zero.
So, dC"/dl = d(640000/l + 40l²)/dl
dC"/dl = d(640000/l)/dl + d(40l²)/dl
dC"/dl = -640000/l² + 80l
Equating dC"/dl to zero, we have
-640000/l² + 80l = 0
-640000/l² = -80l
Cross-multiplying, we have
640000 = 80l³
Dividing through by 80, we have
l³ = 640000/80
l³ = 8000
Taking cube root of both sides, we have
l = ∛8000
l = 20 ft
We differentiate C" twice to determine if this value of l gives a minimum for C".
So, d²C"/dl² = d(-640000/l² + 80l)/dl
d²C"/dl² = d(-640000/l²)/dl + d(80l)/dl
d²C"/dl² = 640000/l³ + 80
Substituting l = 20, we have
d²C"/dl² = 640000/l³ + 80
d²C"/dl² = 640000/20³ + 80
d²C"/dl² = 640000/8000 + 80
d²C"/dl² = 80 + 80
d²C"/dl² = 160 > 0
Since d²C"/dl² = 160 > 0. So, l = 20 ft gives a minimum for C".
Since h = 2000/l²
Substituting l = 20 into the equation, we have
h = 2000/l²
h = 2000/20²
h = 2000/400
h = 5 ft
So, the pool dimensions that will minimize the cost of construction are length of square bottom = 20 ft and height of pool = 5 ft
Learn more about dimensions of a pool here:
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5 = 5+r-2r
what's the answer to this equation
Hi there!
5=5+r-2r
Combine like terms:
5=5-r
Move all the variables to the left, using the opposite operation:
r+5=5
r=5-5
r=0
r=0 is the answer
Hope it helps
~Just a gloomy gal
#CarryOnLearning
[tex]SilentNature :)[/tex]
Answer:
r = 0
Step-by-step explanation:
5 = 5 +r - 2r
5 = 5 -r
c.l.t r = 5 - 5
r = 0
simplify the ratio 4 : 0.5
Answer:
8:1
Step-by-step explanation:
-2 1/4 x -4/5
please help
Answer:
1.8
Step-by-step explanation:
-2 1/4 x -4/5 = 9/5
= 1 4/5
= 1.8
Which number is a zero of the given function?
g(x) = (x^2– 36) (x + 7)
The zeros of the function g(x) = (x² - 36)(x + 7) are x = 6 and x = -6.
To find the zeros of the function g(x) = (x² - 36)(x + 7), we need to identify the values of x that make the entire function equal to zero.
For a function to be equal to zero, at least one of its factors must be zero. Therefore, we set each factor to zero and solve for x:
Setting the first factor, x² - 36, to zero:
x² - 36 = 0
Now, add 36 to both sides of the equation:
x² = 36
Next, take the square root of both sides:
x = ±√36
x = ±6
Setting the second factor, x + 7, to zero:
x + 7 = 0
Now, subtract 7 from both sides of the equation:
x = -7
The zeros of the function g(x) = (x² - 36)(x + 7) are x = 6 and x = -6.
Learn more about zeros of the function from the link given below.
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ahh i need help with these 2 questions ill mark u as brainliest
Answer:
3. x = 96
4. x = 6
Step-by-step explanation:
Please help Please thank you
Answer: C) The student made an error in step 3.
Step-by-step explanation:
When dividing by a negative while working with inequalities, you must "flip the sign." Thus, there is an error in step 3.
N.B. The answer could very well be interpreted as B), but I believe C) is the best and most defensible answer.
Hope it helps :) and let me know if you want me to elaborate.
Answer:
nvm
Step-by-step explanation:
2+2 1,000,000,000+1,000,000,000
Answer:
22,000,000,002
Step-by-step explanation:
Hope it helps you
Answer:
Step-by-step explanation:
22,000,000,002
[tex]\sqrt{7+2\sqrt{10} } -\sqrt{7-2\sqrt{10} }[/tex]
hii I need help with this I really don't get it and I'm like, bad at Functions and stuff like that, I hope this doesn't trouble you :(
Morgan is buying packages of hotdogs and hamburgers. She is spending a total of $25. Hamburgers cost $9 and hotdogs cost $2. She bought a total of 9 packages.
Morgan wrote the following system of equation to model the scenario:
What does the variable "y" represent?
Step-by-step explanation:
I don't see the equations.
but I can build some myself :
x = number of hamburger packages
y = number of hotdogs packages
x + y = 9
9x + 2y = 25
the first equation tells us after moving y to the right side
x = -y + 9
and that we are using now in the second equation :
9(-y + 9) + 2y = 25
-9y + 81 + 2y = 25
-7y = -56
y = 8
x = -y + 9 = -8 + 9 = 1
WILL MARK BRAINLIEST IF CORRECT!
Answer:
Answer → Student A was right.
[tex]{ \tt{ \sqrt[3]{1944} = \sqrt[3]{(72 \times 27)} }} \\ \\ = { \tt{ \sqrt[3]{72} \times \sqrt[3]{27} }} \\ \\ = { \tt{ \sqrt[3]{72} \times 3}} \\ \\ = { \underline{ \tt{ \: 3 \sqrt[3]{72} } \: }}[/tex]
need help please 100 pts
Answer:
b)
Step-by-step explanation:
What is the distance between point (2,6) and (5,2)?
Answer:
5 units
Step-by-step explanation:
Distance between two points can be found by using the pythagorean theorem
The distance in y = 4
The distance in x = 3
3² + 4² = c²
9 + 16 = c²
25 = c³
c = √25
c = 5
-Chetan K
Answer:
5
Step-by-step explanation:
[tex]\mathrm{Distance \:\:Formula:}\\\\\mathrm{d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}}[/tex]
[tex]\underline{\mathrm{Plug \:the\: points:}}[/tex]
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
[tex]d = \sqrt{(5 - 2)^2 + (2-6)^2}[/tex]
[tex]\underline{\mathrm{Solve:}}[/tex]
[tex]d = \sqrt{(5 - 2)^2 + (2-6)^2}[/tex]
[tex]\sqrt{(5 - 2)^2 + (2-6)^2}[/tex]
[tex]\sqrt{3^2 + 4^2}[/tex]
[tex]3^2 = \sqrt{9+4^2} =\boxed{9}\\\\4^2=\sqrt{9+16} = \boxed{16}[/tex]
[tex]\sqrt{25}[/tex]
[tex]\sqrt{5^2}=5[/tex]
Which statement describes the sequence -9, -3, 3, 9, 15, ...?
O A.
an arithmetic sequence with common difference -9
O
B.
an arithmetic sequence with common difference 3
C.
an arithmetic sequence with common difference 6
ОО
O D. not an arithmetic sequence
Answer:
The answer is C
Step-by-step explanation:
An arithmetic sequence with common difference 6
(-3)-(-9) = 6
3 - (-3) = 6
9 - 3 = 6
15 - 9 = 6
Which ordered pair is NOT in the solution set of −2x + 3y ≥ 12?
A. (-3,5)
B. (-5,0)
C. (0,6)
D. (-5,3)
Answer:
B
Step-by-step explanation:
What is the range of function g?
Answer:
y ≥ 2
Step-by-step explanation:
Domain is x > 1 . So, range will be greater than or equal to 2
210 is the product of − 14 and x
Answer:
-14 and -15
Step-by-step explanation:
When you multiply two negative numbers together, it will equal a positive number
answer this pls!!...
help me out
-sry for my bad handwriting
Answer:
i cant read it
can u type so i can help?
Step-by-step explanation:
Compound $35.000 is invested at 5% compound interest. What is the interest at the end of three years?
Answer:
$40,516.86
Step-by-step explanation:
start by taking 35,000 and multiplying it by 0.05 to get 5% of the number. then add that number (1,750) to the original 35,000 and you should get 36,750. this would be the first year. Then multiply 36,750 by 0.05 again and add that number (1837.5) to the original 36,750 and you should get 38,587.5. Finally multiply that by 0.05 and add that number (1,929.375) to the original 38,587.5 and you should get 40516.875. Round to the hundredths since it is money.
Answer:
A = $40,516.88
Step-by-step explanation:
Assuming that interest is compounded annually:
The AMOUNT will be A = P(1 + r)^2, which here is
A = $35,000(1 + 0.05)^3, or
A = $40,516.88
2/5+3/10/−7/9pls hlp
[tex] \frac{2}{5} + \frac{3}{10} - \frac{7}{9} \\ = \frac{2 \times 18 + 3 \times 9 - 7 \times 10}{90} \\ = \frac{36 + 27 - 70}{90} \\ = \frac{ - 7}{90} [/tex]
Answer:[tex] \frac{ - 7}{90} [/tex]
Answer:
5
52
52
52 +
52 + 10
52 + 103
52 + 103
52 + 103 −
52 + 103 − 9
52 + 103 − 97
52 + 103 − 97
52 + 103 − 97
52 + 103 − 97 =
52 + 103 − 97 = 90
52 + 103 − 97 = 902×18+3×9−7×10
52 + 103 − 97 = 902×18+3×9−7×10
52 + 103 − 97 = 902×18+3×9−7×10
52 + 103 − 97 = 902×18+3×9−7×10 =
52 + 103 − 97 = 902×18+3×9−7×10 = 90
52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70
52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70
52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70
52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 =
52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90
52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7
52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7
52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7
52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7
52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7
52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7 Answer:
52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7 Answer:\frac{ - 7}{90}
52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7 Answer:\frac{ - 7}{90} 90
52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7 Answer:\frac{ - 7}{90} 90−7
52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7 Answer:\frac{ - 7}{90} 90−7
A family drove to a resort at an average speed of 30 mph and later returned over the same road at an average speed of 50 mph. Find the distance to the resort if the total driving time was 8 hours.
Answer:
150 Miles
Step-by-step explanation:
Let's say it takes x time to get there.
X x 30=(8 - 6) x 50 (The distance is the same)
30X=400 - 50X=7 X=5 hours.
So the distance is 5 x 30=150 miles.
What is the period of the trigonometric function f(t) = 3sin(t/2)?
A) 2Pie
B) 3pie
C) 4pie
D) pie/2
Find the factorization of the polynomial below. 81X2 - 18x+1
A. (18x-1)2
B. (9x-1)2
C. (9x + 1)2
D. (18x + 1)2
Answer:
B.(9 x -1)^{2}
Step-by-step explanation:
Rewrite the expression into the form of a^2\pm 2ab+b^2:(9 x)^{2} - 2 \times 9 x + 1^{2}
Factor the expression using a^{2}\pm 2ab+b^{2}=(a\pm b)^{2}:(9 x -1)^{2}
we have 81x^2 - 18x+1 = (9x)^2 -2.9x + 1 = (9x -1)^2
ok done. Thank to me :>
Slope is -4 and (6,1) is on the like the equation of the line is
Answer:
y=-4x+25
Step-by-step explanation:
If this is Point-Slope then:
y-y1=m(x-x1) m=slope
m= -4 Coordinates=(6,1)
y-1=-4(x-6)
y-1= -4x +24
y=-4x+25
I already Have the answer but can u guys show the work?
Select the correct answer.
Which equation could represent the graphed cubic function
Answer:
b
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
got it right
Julio says, “if you subtract 12 from my number and multiply the difference by -5, the result is -90” what is Julio’s number
LeAnnne has $4 in dimes and nickels. She has 10 more dimes than nickels. How many nickels does she have?
Answer:
21 she has 21 nickels
Step-by-step explanation:
Googel
The number of nickels LeAnne has 20 and the number of dimes LeAnne has 30.
Given that, LeAnnne has $4 in dimes and nickels.
Let the number of dimes be d and the number of nickels be n.
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
She has 10 more dimes than nickels.
That is, d=n+10
So, 0.05n+0.10d=4
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
5n+10(n+10)=400
5n+10n+100=400
15n=300
n=20
d=n+10
d=30
Therefore, the number of nickels LeAnne has 20.
To learn more about an equation visit:
https://brainly.com/question/14686792.
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What is the answer to the first one?
Answer:
8
Step-by-step explanation:
2(-2)^2 =10 +-2 =8