Step-by-step explanation:
f(x) = -4x^2+24x-29
= -4(x^2-6x)-29
= -4(x-3)^2 -4(-9) -29
= -4(x-3)^2 +36-29
= -4(x-3)^2 +7
maximum height = 7m
A redwood tree in King’s Canyon National Park, California has a circumference of 220 inches. Tanner measured the circumference of some other redwoods that had been planted over the last 5 years. His data is recorded below. Write a rule for the data in the table.
Use your rule to predict the circumference of a tree after 50 years of growth.
Use your rule to estimate the age of the tree with a circumference of 221 inches.
Answer:
A). 101 inches
B). 110 years
Step-by-step explanation:
Years since planting Circumference Difference
1 3 -
2 5 (5 - 3) = 2
3 7 (7 - 5) = 2
4 9 (9 - 7) = 2
5 11 (11 - 9) = 2
6 13 (13 - 11) = 2
There is a difference of 2 in every successive term of the circumference.
Therefore, the given sequence is an arithmetic sequence.
Explicit formula of an arithmetic sequence is given by,
[tex]A_n=a+(n-1)d[/tex]
Here a = first term
n = number of terms
d = common difference
From the given table,
[tex]A_n=3+(n-1)2[/tex]
[tex]A_n=2n+1[/tex]
Here [tex]A_n[/tex] = circumference after 'n' years
n = Age of the plant
By this formula,
Circumference of a tree after 50 years,
[tex]A_{50}=2(50)+1[/tex]
= 101 inches
Age of tree with the circumference = 221 inches,
221 = 2n + 1
2n = 220
n = 110 years
1 last geometry problem
Which of the following is the quotient of the rational expressions shown below? Make sure your answer is in reduced form.
Answer:
The answer is B.
Step-by-step explanation:
First, you have to convert division into multiplication and cross out the common term :
[tex] \frac{3x - 6}{ {x}^{3} } \div \frac{x - 2}{2x - 1} [/tex]
[tex] \frac{3(x - 2)}{ {x}^{3} } \times \frac{2x - 1}{x - 2} [/tex]
[tex] \frac{3}{ {x}^{3} } \times (2x - 1)[/tex]
[tex] \frac{3(2x - 1)}{ {x}^{3} } [/tex]
[tex] \frac{6x - 3}{ {x}^{3} } [/tex]
The quotient of the rational expressions is [tex]\frac{6x - 3}{x^2}[/tex]
calculation:[tex]= \frac{3x - 6}{x^3}\div \frac{x-2}{2x - 1} \\\\= \frac{3(x - 2)}{x^3} \times \frac{2x-1}{x-2}\\\\ = \frac{3}{x^3} \times (2x - 1)\\\\= \frac{3(2x - 1)}{x^2}\\\\ = \frac{6x - 3}{x^2}[/tex]
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Which of the following is most likely to form when one tectonic plate is pushed with great force under another tectonic plate below the ocean? (4 points)
a
Continental rift
b
Fault
c
Mid-ocean ridge
d
Tsunami
Answer:
D I did the test on Ed.......................................
NEED HELP ASAP, WILL GIVE BRAINLIEST
Find the sum of the first 36 terms in the arithmetic series -0.2, 0.3, 0,8...
a. 318.6 b. 332.2 c. 307.8 d. 315
Answer:
b.332.2
Step-by-step explanation:
(3х – 6)(2x+2)
simplify by multiplying
PLEASE HELP
1. Is the rate of change in cost constant with respect to
the number of pencils bought? Explain.
Cost of Pencils
Number of Pencils 1
Cost ($)
0.25 1
1.75
Answer:
still need it??
Step-by-step explanation:
Elena began to solve this equation:
12x + 6(4x + 3) =2(6x + 4) – 2
----------------------
3
12x + 6(4x + 3) = 3(2(6x + 4) - 2)
12x + 6(4x + 3) = 6(6x+ 4) – 6
12x + 24x + 18 = 36x + 24 - 6
When she got to the last line she stopped and said the equation is true for all values of x. How could Elena tell?
Answer:
They have the same slope and y intercept after combining like terms, they are the same line and have infinetely many solutions.
Step-by-step explanation:
If you combine like terms it would give you 36x + 18 = 36x +18,
nThat's infinetely many solutions since they have the same slope and y-intercepts, therefore they are the same line.
The equation has infinitely many solutions. That means equation is true for all values of x.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
We have equation;
12x + 6(4x + 3) =2(6x + 4) – 2
And Elena solved,
12x + 24x + 18 = 36x + 24 - 6
Now, we will solve further,
36x + 18 = 36x + 18
That means equations are equivalent.
And there are two equations and one unknown.
So equation has infinitely many solutions.
Therefore, the equation has infinitely many solutions. That means equation is true for all values of x.
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Charis invested
$
140
$140. She earned a simple interest of
3
%
3% per year on the initial investment. If no money was added or removed from the investment, what was the amount of interest Charis received at the end of two years?
Answer:
$8.53
Step-by-step explanation:
because after 2 years she would have $148.53.
I believe the answer is $4.20
The number of people who have heard a rumor often grows exponentially. Consider a rumor that starts with 3 people and where the number of people who have heard it doubles each day. How many people would know the rumor after 20 days?
Answer:
3.9125 × 10⁵² people
Step-by-step explanation:
A rumor starts with 3 people and the number of people who heard it doubles each day.
How many people would have heard the rumor after 20 days?
To calculate exponential growth, we use the formula:
[tex]y (t) = ae^{kt}[/tex]
where;
a = value at the start =3
k = growth rate = 2×3 = 6
t = time = 20 days
y(t) = value of the population at the given time (t) =??
[tex]y(t) = 3 \times e^{6\times 20}[/tex]
y(t) = 3.9125 × 10⁵² people
Triangle A B C with centroid G is shown on an x and y-axis. Lines are drawn from each point through the centroid to the opposite side to form line segments A F, B D, and C E. Point A is at (0, 0), point D is at (c, 0), point C is at (2 c, 0), point B is at (2 a, 2 b), point F is at (a + c, b),and point E is at (a, b).
The equation of line Line A Gis y = (StartFraction b Over a + c EndFraction)x. The midpoint of BC is (a + c, b). Does the midpoint of BC lie on Line A G? Why or why not?
no, because (StartFraction b Over a + c EndFraction)b does not equal a + c
no, because (StartFraction b Over a + c EndFraction)(a + c) does not equal b
yes, because (StartFraction b Over a + c EndFraction)b = a + c
yes, because (StartFraction b Over a + c EndFraction)(a + c) = b
Answer:
Its D my friend
Step-by-step explanation:
Answer:
(D) yes, because (StartFraction b Over a + c EndFraction)(a + c) = b
Step-by-step explanation:
Triangle A B C with centroid G is shown on an x and y-axis. Lines are drawn from each point through the centroid to the opposite side to form line segments A F, B D, and C E. Point A is at (0, 0), point D is at (c, 0), point C is at (2 c, 0), point B is at (2 a, 2 b), point F is at (a + c, b),and point E is at (a, b).The equation of line Line A Gis y = (StartFraction b Over a + c EndFraction)x. The midpoint of BC is (a + c, b). Does the midpoint of BC lie on Line A G? Why or why not?
(A) no, because (StartFraction b Over a + c EndFraction)b does not equal a + c
(B) no, because (StartFraction b Over a + c EndFraction)(a + c) does not equal b
(C) yes, because (StartFraction b Over a + c EndFraction)b = a + c
(D) yes, because (StartFraction b Over a + c EndFraction)(a + c) = b
-3 x 2 x a + 5(-7b) + (12 x c x 4) in standard form?
-3ax3+48cx2+35b
Step-by-step explanation:
hope this helps
Translate 7 units to the right and 4 units up.
Then, rotate 180° about the origin.
Answer:
Add 7 to the first value, 4 to the second, then flip the signs.
Step-by-step explanation:
Well we kind of need the current coordinates but I'll help to the extent I can!
In an ordered pair the first value is the (x) and the second is the (y) .
(x, y)
(x) is always the horizontal line (left & right).
(y) is always the vertical line (up & down).
So if you translate 7 units to the right, you'd add 7 to the (x) [First value in the ordered pair].
If you translate 4 units up, you'd add 4 to the (y) [Second value in ordered pair].
Now, rotating about the origin only changes whether the number is positive or negative.
If you rotate 180° it will just flip both of the values signs.
So if it was positive it becomes negative, if it was negative it becomes positive
Since I don't have the ordered pair I can't give you an answer but I can tell you what to do to get the answer.
Assuming it's a shape, for each point on the shape you will take it's coordinates, add 7 to the (x) and 4 to the (y), then flip the value sign.
Ex: If the starting coordinate was (-6, -3) we would add 7 to the (x), 4 to the (y) and get (-2, 4), flip the signs and end up with (2, -4).
Hope this helps! If you have any questions on how I got my answer feel free to ask. Stay safe!
Unit Test Review
Active
1
leto
A triangle has side lengths measuring 2x + 2 ft, x + 3 ft,
and n ft.
COS
Which expression represents the possible values of n,
in feet? Express your answer in simplest terms.
x-1
n = 3x + 5
O n = 1 - 1
O 3x + 5
Answer:
x - 1 < n < 3x + 5
Step-by-step explanation:
If you have two sides of a triangle, the length of the third side is at least the difference between the other two sides, and at most the sum of the other two sides.
Some people advise that in very cold weather, you should keep the gas tank in your car more than half full. Irene's car had 5.5 gallons in the 14-gallon tank on the coldest day of the year. Irene filled the tank with gas that cost $3.60 per gallon. How much did Irene spend on gas?
Answer:
ok 16.5$
Step-by-step explanation:
The first 3 figures in a pattern are shown. image Which of the following functions represents f(n), the number of small squares in figure n? A. f(n) = n2 – 1 B. f(n) = 2n2 + 1 C. f(n) = (n + 1)2 + 1 D. f(n) = (n + 1)2 – 1
Answer:
A
Step-by-step explanation:
A is n= n2 -1 so thats the answer
The sum of Rayson and his brother’s age is 29. If Rayson is 4 years older than his brother 7 years ago. How old is Rayson and his brother?
Answer:
16 years, 13 years
Step-by-step explanation:
Let their ages be x, 29-x
Equation formed:-
(x - 7) + 4 = 29 - x
→ 2x = 29 + 3
→ x = 16 years
Answer: 16 years, 13 years
WILL GIVE BRAINLIEST
Answer:
x axis and y axis each end
Step-by-step explanation:
helpppppp pllzzzzzzzzz
Answer:
The length of side of largest square is 15 inches
Step-by-step explanation:
The given suares are when joined in the way as shown in picture their sides form a right agnled triangle.
Area of square 1 and perimeter of square 2 will be used to calculate the sides of the triangle.
So,
Area of square 1: 81 square inches
[tex]s^2 = A\\s^2 = 81\\\sqrt{s^2} = \sqrt{81}\\s = 9[/tex]
Perimeter of square 2: 48 inches
[tex]4*side = P\\4* side = 48\\side = \frac{48}{4}\\side = 12\ inches[/tex]
We can see that a right angled triangle is formed.
Here
Base = 12 inches
Perpendicular = 9 inches
And the side of largest square will be hypotenuse.
Pythagoras theorem can be used to find the length.
[tex](H)^2 = (P)^2+(B)^2\\H^2 = (9)^2+(12)^2\\H^2 = 81+144\\H^2 = 225\\\sqrt{H^2} = \sqrt{225}\\H = 15[/tex]
Hence,
The length of side of largest square is 15 inches
Given g(x)=-2x+3, solve for x when g(x)=-3
Answer:
g(-3)=9
Step-by-step explanation:
Replace all of the (x) with -3
So the new equation
g(-3)= -2(-3)+3
Now simplify
g(-3)= 6+3
Simplify further
g(-3)= 9
Hope this helps!
The value of x for the function g(x)=-2x+3 is 3.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
g(x)=-2x+3
Now, for g(x) = -3 we have
-2x+ 3 = -3
Now, Subtract 3 from both side
-2x + 3 - 3 = -3 -3
-2x = -6
Divide both side by (-2) we get
-2x / (-2) = -6 / (-2)
x = 3
Hence, the value of x is 3.
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Solve these plsssssssssss
Answer: B
Step-by-step explanation:
An isosceles triangle has base angles that each measure 23 degrees. Which equation can be used to find x, the measure of third angle of this isosceles triangle in degrees?
Answer:
since a triangle measures up to 180 degrees getting the value of x will be all angles added together equals to 180.
(base angles) + x = 180°
46° + x = 180°
this is what I think good luck
The measure of third angle of this isosceles triangle is 134 degrees.
What is Angle Sum Property?According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.
S = (n-2)*180° is the angle sum property formula for any polygon, where 'n' represents the number of sides in the polygon.
Given:
Two Base angles is 23 degree.
and third angle is x.
Using Angle Sum property
x + 23+ 23 =180
x +46 =180
x= 180- 46
x= 134
Hence, the third angle is 134 degree.
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A recipe calls for 3 4/5 cups of flour. However, Stacy wants to use half as much flour as the recipe calls for. How many cups of flour will Stacy use? Express your answer as a mixed number.
Explain how they are different AND the same
Proportional and linear functions are almost identical in form. The only difference is the addition of the “b” constant to the linear function. Indeed, a proportional relationship is just a linear relationship where b = 0, or to put it another way, where the line passes through the origin
Factor 5n^2 - 4n - 12 by grouping. Please show the steps.
Answer:
(n - 2)(5n + 6)
Step-by-step explanation:
Given
5n² - 4n - 12
Consider the factors of the product of the n² term and the constant term which sum to give the coefficient of the n- term
product = 5 × - 12 = - 60 and sum = - 4
The factors are - 10 and + 6
Use these factors to split the n- term
5n² - 10n + 6n - 12 ( factor the first/second and third/fourth terms )
= 5n(n - 2) + 6(n - 2) ← factor out (n - 2) from each term
= (n - 2)(5n + 6) ← in factored form
Can someone help me and show steps I’ll mark you brainliest
Answer:
y = 2x + 21
Explanation:
The slope is 2 so it would go for mx
The y-inter. for the graph is 21
your equation is y = 2x + 21
The question is jimmy scores is in the bottom 25% of the scores, but he does not have the lowest score. What is one possible value for jimmy score
Answer:
50% duhh
Step-by-step explanation:
25% is also a equation
ANSWER CORRECTLY
-2.5 - 5.5=
MUST SHOW YOUR WORK
good luck
Answer:
the answer is -7.7
Step-by-step explanation:
−2.2−5.5
−2.2+ −5.5
= --7.7
hope it helps :)
Answer:
The answer is -8
Step-by-step explanation:
-(2.5+5.5)
-8
a laptop has a listed price of $595.99 before tax. If the sales tax rate is 6.75%, find the total cost of the laptop with sales tax included. Round your answer to the nearest cent, as necessary. PLS HELP
A race follows a triangular course. The three legs of the race are, in order, 0.80 km, 2.05 km, and 2.15 km. Find the angle
between the starting leg and the last leg of the race.
Answer:
2.15 km
Step-by-step explanation:
