To solve this question, we need to solve an exponential equation, which we do applying the natural logarithm to both sides of the equation, getting that it will take 7.6 years for for 21 of the trees to become infected.
Model:
The exponential model for the number of infected trees after t years is given by:
[tex]f(t) = e^{0.4t}[/tex]
How many years will it take for 21 of the trees to become infected?
This is t for which:
[tex]f(t) = 21[/tex]
Thus
[tex]e^{0.4t} = 21[/tex]
Applying the natural logarithm to both sides:
[tex]\ln{e^{0.4t}} = \ln{21}[/tex]
[tex]0.4t = \ln{21}[/tex]
[tex]t = \frac{\ln{21}}{0.4}[/tex]
[tex]t = 7.6[/tex]
It will take 7.6 years for for 21 of the trees to become infected.
For another example of a problem in which an exponential equation is solved, you can check brainly.com/question/24290183.
monica has $340 in the bank and plans to save $10 per week. is this linear or exponential?
Answer:
linear. Each week adds another 10 dollars.
Step-by-step explanation:
Total = 340 + 10*w
w is the weekly amount
Suppose 5 weeks pass
Then the total amount in her bank account is
Total = 340 + 10*5
Total = 340 + 50
Total = 390
The equation is Linear.
solve
f(x)=4x5−8x4+8x2−4x
Given:
The function is:
[tex]f(x)=4x^5-8x^4+8x^2-4x[/tex]
To find:
The roots of the given equation.
Solution:
We have,
[tex]f(x)=4x^5-8x^4+8x^2-4x[/tex]
For roots, [tex]f(x)=0[/tex].
[tex]4x^5-8x^4+8x^2-4x=0[/tex]
[tex]4x(x^4-2x^3+2x-1)=0[/tex]
[tex]4x((x^4-1)+(-2x^3+2x))=0[/tex]
[tex]4x((x^2+1)(x^2-1)-2x(x^2-1))=0[/tex]
On further simplification, we get
[tex]4x(x^2+1-2x)(x^2-1)=0[/tex]
[tex]4x(x-1)^2(x+1)(x-1)=0[/tex]
[tex]4x(x+1)(x-1)^3=0[/tex]
Using zero product property, we get
[tex]4x=0[/tex]
[tex]x=0[/tex]
Similarly,
[tex]x+1=0[/tex]
[tex]x=-1[/tex]
And,
[tex](x-1)^3=0[/tex]
[tex]x=1[/tex]
Therefore, the zeroes of the given function are [tex]-1,0,1[/tex] and the factor form of the given function is [tex]f(x)=4x(x+1)(x-1)^3[/tex].
HELPPPPPPPPPPPPPPPPP PLZ
Answer:
GH = 8.4
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan J = opp side / adj side
tan J = HG / HJ
tan 40 = GH / 10
10 tan 40 = GH
8.39099=GH
Rounding to the nearest tenth
GH = 8.4
The quotient of five less than a number and six, is -4
Answer:
(a-5) / 6 = -4
or
-19
Step-by-step explanation:
(a-5) / 6 = -4
multiply by 6
a - 5 = -24
+5 +5
a = -19
Can anyone help me with this question
Answer:
60
Step-by-step explanation:
A significant figure means the most important (biggest) number.
As it just wants 1 significant figure, you count 1 to the right and round the 6 up.
Hope this helps :)
Find the equation of the line that is parallel
to the line y = 3x + 9 and passes
through the point (2,1) Write the
equation in slope-intercept form.
Answer:
y = 3x - 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + 9 ← is in slope- intercept form
with slope m = 3
Parallel lines have equal slopes, then
y = 3x + c ← is the partial equation
To find c substitute (2, 1) into the partial equation
1 = 6 + c ⇒ c = 1 - 6 = - 5
y = 3x - 5 ← equation of parallel line
The slope (m) and the y-intercept (b) of the line 2x + 3y = 12 is:
Step-by-step explanation:
[tex]2x + 3y = 12 \\ 3y = - 2x + 12 \\ y = - \frac{2}{3} x + 4[/tex]
slope is -2/3
y intercept is 4
Answer:
The slope is -2/3 and the y intercept is 4
Step-by-step explanation:
2x + 3y = 12
Slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
2x + 3y = 12
Subtract 2x from each side
2x-2x+3y = -2x+12
3y = -2x+12
Divide by 3
3y/3 = -2x/3 +12/3
y = -2/3 x +4
The slope is -2/3 and the y intercept is 4
please please please answer!! will give brainliest and extra points!
Question 10 The hypotenuse of a right triangle is I m longer than the longer leg. The other leg is 7 m shorter than the longer leg. Determine the lengths of the three sides of the triangle. (3 marks)
Answer:
5, 12, 13
Step-by-step explanation:
let x be the longer leg then x + 1 is the hypotenuse and x - 7 the shorter leg
Using Pythagoras' identity in the right triangle
x² + (x - 7)² = (x + 1)² ← expand using FOIL
x² + x² - 14x + 49 = x² + 2x + 1
2x² - 14x + 49 = x² + 2x + 1 ( subtract x² + 2x + 1 from both sides )
x² - 16x + 48 = 0 ← in standard form
(x - 4)(x - 12) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x - 12 = 0 ⇒ x = 12
x = 4 , then x - 7 = 4 - 7 = - 3 ← not possible
x = 12, then x - 7 = 12 - 7 = 5 and x + 1 = 12 + 1 = 13
The lengths of the 3 sides are
longer leg = 12 m , shorter leg = 5 m and hypotenuse = 13 m
How could Brent use a rectangle to model the factors of \large x^2-7x+6?
He could draw a diagram of a rectangle with dimensions x – 4 and x + 3 and then show the area is equivalent to the sum of x2, –4x, 3x, and half of –12.
He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x2, –x, –6x, and 6.
He could draw a diagram of a rectangle with dimensions x + 7 and x – 1 and then show the area is equivalent to the sum of x2, 7x, –x, and 6.
He could draw a diagram of a rectangle with dimensions x – 3 and x – 4 and then show the area is equivalent to the sum of x2, –3x, –4x, and half of 12.
Answer:He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x2, –x, –6x, and 6.
Step-by-step explanation:
He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x2, –x, –6x, and 6.
He could draw a diagram of a rectangle with dimensions x + 7 and x – 1 and then show the area is equivalent to the sum of x2, 7x, –x, and 6.
He could draw a diagram of a rectangle with dimensions x – 3 and x – 4 and then show the area is equivalent to the sum of x2, –3x, –4x, and half of 12.
The two cones below are similar. What is the value of x?
Cone 1
Height = 10
Radius = 3
Cone 2
Height = 3
Radius = x
A. 0.3
B. 0.9
C. 0.09
D. 0.18
Answer:
If they are similar, the ratio of 10/3 should be the same as the 3/x
then solve
10/3 = 3/x
cross multiply
10x=8
x = 9/10
so C. is the right answer
The missing value in the smaller cone is 0.9 units.
What is similarity?Similarity in math is a concept that relates to the shape and size of figures. Two figures are similar if they have the same shape, but not necessarily the same size.
Given that, two similar cones, we need to find the value of x in the smaller cone,
Since, the cones are similar, then according to the definition of similarity,
we know that the dimensions will be in equal proportion,
Let the dimensions of the big cone be H (height) and R (radius) and that of smaller cone be h (height) and r (radius)
So,
H / R = h / r
10 / 3 = 3 / x
x = 9/10
x = 0.9
Hence, the missing value in the smaller cone is 0.9 units.
Learn more about similarity, click;
https://brainly.com/question/26451866
#SPJ7
Please help
Solve for x
Answer:
X=15 since it the same
Step-by-step explanation:
X is simply equal to 15 because it an equilateral triangle
the ordered pairs model an exponential function, where w is the function name and t is the input variable.
{(1, 60), (2, 240), (3, 960), (4, 3840)}
what is the function equation in sequence notation?
wt = ____
Answer:
w = 15 (4^t)
Step-by-step explanation:
Let w be what the function is equal to
Let t be the input variable
equation :
w = k a^t
Plug in any two of the points to solve for k and a
for example, let's take (1, 60) and (2, 240):
60 = k * a^1
k = 60 / a
240 = k a^2
Substituting:
240 = 60/a (a^2)
a = 4
k = 15
The function is
w = 15 (4^t)
quadratics formula 4x^2+3x-1=0
Answer: X = 1/4 or X = -1
Step-by-step explanation:
4x2+3x−1=0
(4x−1)(x+1)=0
4x−1=0 or x+1=0
4x=1 or x=-1
Now divide 4 from both sides
like this 4x/4=1/4
now cancel out two 4's so the answer will be x=1/4
Describe the pattern in the following sequence and list the next three terms:
4, 8, 16, 32, ...
I’ll mark brainliest! Please help me
Find the measure of each angle indicated.
A) 95°
C) 26°
B) 92°
D) 20°
Answer:
D) 20°
Step-by-step explanation:
Using the triangle sum theorem, you know that every triangle's interior angles add up to 180°. Therefore the bottom triangle's missing angle can be found by giving it the variable x.
57° + 30° + x = 180°
Simplify: 87° + x =180°
x=93°
By the vertical angles theorem, the vertical angle directly across this angle is congruent to this one. Meaning that the top triangle's angle are 67°, 93°, and unknown, which we can assign y. We can use the same method from above here.
67° + 93° + y = 180°
Simplify: 160° + y = 180°
y=20°
Answer:
(C). 26°
Step-by-step explanation:
Write 1= 2x2 + 5x In standard form.
What is the value of b^2 - 4ac?
Answer:
2x^2+5x-1=0
ax^-bx+c=0
b^2-4ac = 5^2-4(2)(-1) =33
Which graph represents the function f (x) = StartFraction 2 Over x minus 1 EndFraction + 4?
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = negative 4.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = negative 4.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = 4.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4.
Answer:
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4
Step-by-step explanation:
The given function is presented as follows;
[tex]f(x) = \dfrac{2}{x - 1} + 4[/tex]
From the given function, we have;
When x = 1, the denominator of the fraction, [tex]\dfrac{2}{x - 1}[/tex], which is (x - 1) = 0, and the function becomes, [tex]\dfrac{2}{1 - 1} + 4 = \dfrac{2}{0} + 4 = \infty + 4 = \infty[/tex] therefore, the function in undefined at x = 1, and the line x = 1 is a vertical asymptote
Also we have that in the given function, as x increases, the fraction [tex]\dfrac{2}{x - 1}[/tex] tends to 0, therefore as x increases, we have;
[tex]\lim_ {x \to \infty} \dfrac{2}{(x - 1)} \to 0, and \ \dfrac{2}{(x - 1)} + 4 \to 4[/tex]
Therefore, as x increases, f(x) → 4, and 4 is a horizontal asymptote of the function, forming a curve that opens up and to the right in quadrant 1
When -∞ < x < 1, we also have that as x becomes more negative, f(x) → 4. When x = 0, [tex]\dfrac{2}{0 - 1} + 4 = 2[/tex]. When x approaches 1 from the left, f(x) tends to -∞, forming a curve that opens down and to the left
Therefore, the correct option is on a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4.
Answer:
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4
Step-by-step explanation:
The given function is presented as follows;
From the given function, we have;
When x = 1, the denominator of the fraction, , which is (x - 1) = 0, and the function becomes, therefore, the function in undefined at x = 1, and the line x = 1 is a vertical asymptote
Also we have that in the given function, as x increases, the fraction tends to 0, therefore as x increases, we have;
Therefore, as x increases, f(x) → 4, and 4 is a horizontal asymptote of the function, forming a curve that opens up and to the right in quadrant 1
When -∞ < x < 1, we also have that as x becomes more negative, f(x) → 4. When x = 0, . When x approaches 1 from the left, f(x) tends to -∞, forming a curve that opens down and to the left
Therefore, the correct option is on a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4.
Select all the expressions that represent the difference of the length to width ratios for rectangle A and rectangle B, where W is the width of rectangle A.
Answer:
w+5/w - w+1/2w
w+9/2w
Step-by-step explanation:
Answer:
A&D are corect
Step-by-step explanation:
combine like terms
What is the quotient? t +3 t +4 f+7t+12) 0 (t + 3)2 (t+4)2 1 (t-4) 1 (t + 3)?
Answer:
1
-----
(t+4)^2
Step-by-step explanation:
(t+3)
------- ÷ (t^2+7t+12)
(t+4)
Copy dot flip
(t+3) 1
------- * --------------------
(t+4) (t^2+7t+12)
Factor
(t+3) 1
------- * --------------------
(t+4) (t+4)(t+3)
Cancel
1 1
------- * --------------------
(t+4) (t+4)
1
-----
(t+4)^2
Answer:
answer is b
Step-by-step explanation:
Please hurry I will mark you brainliest
Question’s Picture included*
Answer:
when you have 32 pennies the total mass will be 185
please help asap, see attached photo. This is due in 1 hour!!! please answer both questions. Both 5 and 6
Answer:
A and C
Step-by-step explanation:
5) logx+log(x+9)=2
log(x(x+9))=2, log(x^2+9x)=2
6) log(x^2+9x)=2
(x^2+9x)=36 or 6^2
i have 17 coins. N of them are nickels and the rest are dimes. write an expression in two different ways for the amount of money that i have.(hint: one is the other simplified)
Answer:
0.05N - 0.1N + 1.7 (in dollars
1.7 - 0.05N (in dollars)
Step-by-step explanation:
Given :
Total number of coins = 17
Number of nickels = N
Number of dimes = 17 - N
1 nickel = 5 cent = $0.05
1 dime = 10 cent = $0.1
The amount of money :
(Value of nickel * number of nickels) + (value of dime * number of dime)
(0.05 * N) + (0.1 * (17-N))
0.05N + 1.7 - 0.1N
0.05N - 0.1N + 1.7
-0.05N + 1.7 = 1.7 - 0.05N
In a triangle, a segment connecting the midpoints of two sides of the triangle is
called:
Answer:
A.) Midsegment
Step-by-step explanation:
Trust me bro
Select all the points that are on the graph of the line y = −1/4 x + 3.
a. (0, -1/4)
b. (0, 3)
c. (1, 11/4)
d. (1, 3)
e. (1, 13/4)
f. (3, 0)
The points on the graph ( b , c )
I hope I helped you ^_^
Can someone help please
Answer:
[tex]10^{-3}[/tex]
Step-by-step explanation:
Answer:
https://tex.z-dn.net/?f=10%5E%7B-3%7D
Step-by-step explanation:
Which is the graph of y = RootIndex 3 StartRoot x EndRoot?
Given:
The equation is:
[tex]y=\sqrt[3]{x}[/tex]
To find:
The graph of the given equation.
Solution:
We have,
[tex]y=\sqrt[3]{x}[/tex]
The table of values is:
x y
-8 -2
-1 -1
0 0
1 1
8 8
Plot these points on a coordinate plane and connect them by a free hand curve as shown in the below graph.
Answer:
D
Step-by-step explanation:
edge 2020
Given the mean of a random variable, X, is 10 and P(X < 11) = 0.67. Find the standard deviation.
Answer:
Step-by-step explanation:
This is the problem we need to solve:
[tex]z=\frac{x_i-\bar{x}}{\sigma}[/tex] and we have everything but the z-score (which we find from a table) with our main unknown being the standard deviation.
If the probability that a random variable that is less than 11 is .67, we first have to find the z-score from the table that is closest to .67, and there are 2:
P(z < .43) = .66640 and P(z < .44) = .67003
We'll use z = .44
[tex].44=\frac{11-10}{\sigma}[/tex] and
[tex].44=\frac{1}{\sigma}[/tex] and
[tex]\sigma=\frac{1}{.44}[/tex] so
σ = 2.27 (check it; it works!)
hi pls help.you do not have to do all 3. just either one will be ok pls explain as well:) thank you
Answer:
[tex]{7a^{5}b^{5} c\\[/tex]
Step-by-step explanation:
[tex]\frac{28a^{8}b^{6} c^{3} }{4a^{3}bc^{2} }[/tex]
→ First look at the first term of each expression and see if they can be simplified, and they can
[tex]\frac{7a^{8}b^{6} c^{3} }{a^{3}bc^{2} }[/tex]
→ Now look at the a terms, since a larger one is at the top, you subtract
[tex]\frac{7a^{5}b^{6} c^{3} }{bc^{2} }[/tex]
→ Now simplify the b and c terms
[tex]{7a^{5}b^{5} c[/tex]
For a line that contains the point (3, 4) and has a slope of 4, please name another point on this line. Show the work you did to find this answer.
Answer:
y = 4x - 8
Step-by-step explanation:
y = 4x + b
4 = 4(3) + b
4 = 12 + b
-8 = b
