Step-by-step explanation:
6y + 2(3x + 5) + 2y + 3 = 8r + 3r² + 6r² + 2r + r
6y + 6x + 10 + 2y + 3 = 9r² + 11r
8y + 6x + 13 = 9r² + 11r
A timer is started and a few moments later a model airplane is launched from the ground. Its height (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=−(t−12)2+81
. Which of the following statements is true?
The airplane reaches its minimum height of 12 feet in 81 seconds.
The airplane reaches its maximum height of 81 feet in 12 seconds.
The airplane reaches its minimum height of 81 feet in 12 seconds.
The airplane reaches its maximum height of 12 feet in 81 seconds.
The airplane reaches its maximum height of 81 feet in 12 seconds.
Behavior of curvesIf y = [tex]x^{2}[/tex], it means that the second derivate is 2 which is positive, then there is a minimum turning point.
If y = - [tex]x^{2}[/tex], it means that the second derivative will be -2 which is negative, then there is a maximum turning point.
Analysis:
h(t) = -[tex](t - 12)^{2}[/tex] + 81
By expanding,
h(t) = -([tex]t^{2}[/tex] - 24t + 144) +81
h(t) = -[tex]t^{2}[/tex] + 24t - 144 + 81
h(t) = -[tex]t^{2}[/tex] + 24t - 63
at turning point d/dt(h(t)) = 0
d/dt (h(t)) = -2t +24
-2t +24 = 0
if we differentiate again, second derivative is -2 which is negative, so it is a maximum point.
2t = 24
t = 12 seconds
h(t) at t = 12
h(t) = [tex]-(12)^{2}[/tex] + 24(12) - 63 = 81 feet
In conclusion, the maximum height of the airplane after 12 seconds is 81 feet.
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Enter the equation of the circle described below.
Center (-3,0), radius = sqrt5
Answer: [tex](x+3)^{2}+y^{2}=5[/tex]
Which is the x-value of the solution of the system of equations? y=3x^2+15 y=5x^2-17
A. x=±1 B. x=±2
C. x=±4 D. x=±16
Answer:
C. x = ±4
Explanation:
Given two equation's:
y = 3x² + 15y = 5x² - 17Solve them simultaneously:
y = y
3x² + 15 = 5x² - 17
5x² - 3x² = 15 + 17
2x² = 32
x² = 16
x = ±√16
x = ±4
wyatt has a square garden. he adds 3 feet to one side and 1 foot to the other and now it is a rectangle with an area of 24 ft^2 what are the new dimensions of the garden
Answer:
6x4 feet
Step-by-step explanation:
6 x 4 = 24
6 - 3 = 3
4 - 1 = 3
Part A: Solve for the "h." Show all work
Answer:
2.7 m
Step-by-step explanation:
Corresponding sides of similar triangles are proportional. This figure shows similar triangles ∆ABC ~ ∆ADE.
__
The proportion that can be used to find h = DE is ...
DE/BC = DA/BA
h/(0.9 m) = (12 m+6 m)/(6 m) . . . . . filling in the values given
h = (0.9 m)(18/6) . . . . . multiply by 0.9 m
h = 2.7 m
The value of "h" is 2.7 m.
what is the name of the algebraic expression
Answer:
There are 3 main types of algebraic expressions which include: Monomial Expression. Binomial Expression. Polynomial Expression.
Based on the diagram, which expresses all possible
lengths of segment AB?
OAB = 25
27
OAB = 85
OAB< 27 or AB > 81
MEDA
The expression that expresses all possible lengths of segment AB is 27 < AB < 81. The correct option is the second option 27 < AB < 81
Properties of a triangleFrom the question, we are to determine the expression that expresses all possible lengths of segment AB
From one of the properties of a triangle,
The third side of any triangle is greater than the difference of the other two sides; and the third side of any triangle is lesser than the sum of the two other sides
Then, we can write that
AB < 27 + 54
and
AB > 54 - 27
Putting the two inequalities together, we get
54 - 27 < AB < 27 + 54
27 < AB < 81
Hence, the expression that expresses all possible lengths of segment AB is 27 < AB < 81. The correct option is the second option 27 < AB < 81
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The displacement, d, in millimeters of a tuning fork as a function of time, t, in seconds can be modeled with the equation d = 0.4 sine (1760 pi t). what is the maximum displacement of the tuning fork?
The maximum displacement of the tuning fork is 0.4 mm
What is a tuning Fork ?A tuning fork is a acoustic resonator , It is used to tune musical Instruments.
It is given in the question that the
displacement, d, in millimeters of a tuning fork as a function of time, t, in seconds can be modeled with the equation d = 0.4 sine (1760 pi t).
the maximum displacement of the tuning fork = ?
The equation for a sine function is given by
f(t) = A sin(Bt + C) + D
here A is the maximum Displacement
When this equation is compared with the given equation
d = 0.4 sine (1760 pi t).
A = 0.4
The maximum displacement of the tuning fork is 0.4 mm
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Which of these statements is true for f(x) = 2.3x?
A. The y-intercept is (0, 1).
OB. It is always decreasing.
OC. The domain is x > 0.
OD. The y-intercept is (0, 2).
Answer:D
Step-by-step explanation:when x is 0 we get y=2x3^0=2x1=2
The correct option is D.
What is a function?A function is defined as a relation between a set of inputs having one output each. a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.
Given is a function f(x) = 2·3ˣ, we need to select the correct options regarding the function,
The properties are =
y intercept: y = 2
domain: (-∞, ∞)
decreasing interval: no
Hence the correct option is D.
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Please Help if you know!
An equation that can be used to determine how much each cookie cost originally is ($13.32 + $7) / 16.
What is the equation that determines the cost of each cookie?
A coupon reduces the price of an item. Thus, the amount paid by Louis would be lower than the original price.
Original price = coupon + price paid
($13.32 + $7)
The cost per cookie, can be determined by dividing the original price by the total number of cookies bought.
($13.32 + $7) / 16
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Answer:
Step-by-step explanation:
Givens
Number of cookies = 16
Deduction = 7
Final Cost = 13.31
Equation
16c - 7 = 13.31
Solution
You are not asked for a solution but I'll put it here anyway.
16c - 7 = 13.32 Add 7 to both sides
16c -7+7 = 13.32+ 7 Combine
16c = 20.32 Divide by 16
16c/16 = 20.32/16
c = 1.27
3D TRIGONOMETRY PLS HELP ME HELP
Given the two rectangles below. Find the area of the shaded region. 4 4 9 3
Answer:
60
Step-by-step explanation:
The shaded region's area is the difference between the area of the outer rectangle and the white rectangle.
area = LW - lw
area = (4 + 4)(9 + 3) - (4)(9)
area = (8)(12) - 36
area = 96 - 36
area = 60
X/6=9/20
What is the answer?
Step-by-step explanation:
[tex] \frac{x}{6} = \frac{9}{20} \\ [/tex]
[tex]x \times 20 = 9 \times 6[/tex]
[tex]20x = 54[/tex]
[tex]x = \frac{54}{20} \\ [/tex]
[tex]x = 2.7[/tex]
A TV costs R14 000 you made a 15% deposit and pay the remainder over a 3 year period at 10% interested p.a
Calculate the deposit amount? and Determine the remainder to be paid over the 3 years
Answer:
deposited rs. 2100 of a tv and rs. 3570 paid remainder after 3 years
Over What Interval is The Function In This Graph Increasing?
The correct answer is option D.which is -4 ≤ x ≤ 1.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
in the graph, we can see that the value of x is increasing from -4 coordinate of x to the 1 coordinate of x so the interval will be given as -4 ≤ x ≤ 1.
Therefore the correct answer is option D.which is -4 ≤ x ≤ 1.
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Help my semester ends in 17 hours
i'm so confused this is all they put
Apply the Pythagorean Theorem to determine
unknown side lengths in right triangles in real
world and mathematical problems in two and
three dimensions
1. letica started an online store selling hand made blankets. she sold 92 in her first month. how did she make if each blanket cost $49
Answer:
92 x 49 = 4,508
Step-by-step explanation:
According to the texts, she sold 92 blankets in her first month, bringing her total sales to 92, and each blanket cost $49.
2. A used PlayStation 4 is on sale for 10% off the regular price of $160.00. If the sales tax rate is 9%, how much would I pay for the DVD player?
Answer:
$156.96
Step-by-step explanation:
10% off of $160.00 would be $16.00 so minus that by $160.00. Which then equals $144.00. Sales tax should be reduced to the sale price. So that would make it 144 times 0.09 for the 9% which equals $12.96 then add the $144.00 which then makes it $156.96. Hope it helps and I'm not wrong about sales tax:)
Select the correct answer from each drop-down menu.
Consider the function f(x) = 3x4 − 5x2.
This function is
1. even
2. odd
3. neither even or odd
because
1. f(x)-f(x)
2. f(x)=f(x)
3. -f(x)=f(-x)
Using the classification for even and odd functions, it is found that the function is even, because f(-x) = f(x).
How we verify if the function is even, odd, or neither?If for all values of x, f(x) = f(-x), the function is even.If for all values of x, f(-x) = -f(x), the function is odd.If neither of these statements are true, the function is neither even nor odd.Graphing the function [tex]f(x) = 3x^4 - 5x^2[/tex], for every value of x, f(x) = -f(x), that is, the function is symmetric over the y-axis, hence it is even.
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The value of x is 50% more than the value of t.
the value of y is 10% less than the value of w.
x = y
work out t/w
Answer:
To hard sorry
Step-by-step explanation:
The mean number of stereos sold per day at a store for 6 days was 13. Which statement must be true about the stereo sales at the store?
O The store sold 19 stereos for the 6 days
O The store sold 78 stereos for the 6 days
O The store sold 13 stereos on at least half of the 6 days
O The store sold 13 stereos on at least two of the days
Answer:
well I don't know the options, but I do know that 105 would have been sold in a week.
Step-by-step explanation:
thank you for this :)
find the equivalent expression of 2 to the power of 4
Answer:
16
Step-by-step explanation:
2^4=2*2*2*2=16
Answer:
16
Step-by-step explanation:
2^4=2*2*2*2=16
2 raise to the power of 4, which means 2*2*2*2
If EFG QRS, which statement is not correct
Answer:
hello how are you nice to meet you
what's the square root of 2
Answer:
The square root of 2 is 1.41421
Answer:
The square root of 2 is 1.414
Evaluate:
[tex]\bf{\sum^{20}_1\:4(\cfrac{8}{9})^{n-1}[/tex]
(find the sum of the first 20 terms of the geometric series)
Please help A.S.A.P. & show work as well.
Thank you guys!
[tex]\bigstar[/tex]
[tex]\boxed{\sf \sum _{n=1}^{20}\:4\left(\frac{8}{9}\right)^{n-1}}[/tex]
Identify the following:
First Term (a) = 4(8/9)¹⁻¹ = 4Common ratio (r) = 8/9Total Terms (n) = 20Formula Required:
[tex]\rightarrow \quad \sf S_n = \dfrac{a(r^n - 1)}{r-1}[/tex]
Insert values identified:[tex]\rightarrow \sf S_{20} = \dfrac{4(\dfrac{8}{9}^{20} - 1)}{\dfrac{8}{9} -1} \quad\overset{simplify}{\longrightarrow} \quad \dfrac{4\left(9^{20}-8^{20}\right)}{3^{38}} \quad \xrightarrow{\text{In \ Decimals} }\quad 32.58609013[/tex]
Which of the following expressions is equivalent to (x5 y3 z2) (x4 y3 z6) for all real values of x y, and z ?
a. x9y6z8
b. x9y9z8
c. x20y6z8
d. x20y9z12
e. x21y6z12
The product of the expressions (x⁵y³z²) and (x⁴y³z⁶) is equivalent to the expression x⁹y⁶z⁸. Then the correct option is A.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
The expression is given below.
(x⁵y³z²) and (x⁴y³z⁶)
Then the product of the expression will be
⇒ (x⁵y³z²) (x⁴y³z⁶)
⇒ x⁵x⁴y³y³z²z⁶
⇒ x⁵⁺⁴y³⁺³z²⁺⁶
⇒ x⁹y⁶z⁸
Then the correct option is A.
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Given quadrilateral A(2,-1) B(1,3) C(6,5) D(7,1), you want to prove that it is a parallelogram by showing opposite sides are parallel. What formula would you use?
Answer: Slope formula
Step-by-step explanation:
You could show the slopes of the opposite sides are equal, and thus they are parallel.
6. Suppose you decide to make and sell silk flower arrangements. You spend $220.00 on materials. You sell each flower arrangement for $10.50 each. How much profit would you make if you sold 23 silk flower arrangements?
The profit would you make if sold 23 silk flower arrangements be $21.5.
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
spend on materials = 220
Price for each flower =10.50
If 23 flowers are sold price would be,
= 10.50*23
=241.5
Hence, the profit would be = 241.5-220
= $21.5
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which expression is equivalent to 3 x5y ?
Answer:
2nd answer is correct
Step-by-step explanation:
We know that,
[tex]\sqrt{x} =x^{\frac{1}{2} }[/tex]
[tex]\sqrt[3]{x}=x^{\frac{1}{3} }[/tex]
By following the above, we can solve the answer to the question.
Let us solve this now
⇒ [tex]\sqrt[3]{x^5y}[/tex]
⇒ [tex]x^\frac{1}{3}^*^5y^\frac{1}{3}[/tex]
⇒ [tex]x^\frac{1*5}{3}y^\frac{1}{3}[/tex]
⇒ [tex]x^\frac{5}{3}y^\frac{1}{3}[/tex]