Answer:
Step-by-step explanation:
The general form of this equation is
[tex]A=Pe^{rt}[/tex] where P is the initial population, e is Euler's number (a constant), r is the rate of decay, and t is the time in years.
Therefore, filling in:
[tex]A=45000e^{-.02t[/tex]
1. Choose the correct algebraic equation to represent: the amount decreased by $9 is $42.
9-m=42
9-m
m-9=42
m-9
Answer:
m-9=42
Step-by-step explanation:
An amount subtracted by $9 is $42.
(an amount is unknown, so it is represented with variable, m)
m-9=42
Kathryn plants two different types of tomato plant. She records the number of tomatoes that she picks from each plant every day. Her records are shown below:
Plant A: 4, 6, 7, 3, 5, 2, 1, 3, 6, 5
Plant B: 5, 6, 7, 6, 8, 9, 6, 7, 7, 9
Which plant has the more consistent yield of tomatoes?
Answer:
plant B
Consistent means better so plant be had more better yields
a triangle has a base measuring 6 feet and a height measuring 8.3 feet. How many triangles of this area would fit inside a rectangle with a width 12 feet and a length of 33.2 feet?
Area of the triangle = 1/2 x base x height
Area of triangle = 1/2 x 6 x 8.3 = 24.9 square feet.
Area of rectangle = length x width
Area of rectangle = 33.2 x 12 = 398.4 square feet.
To find the number of triangles that can fit in the rectangle divide the area of the rectangle by the area of the triangle:
398.4 / 24.9 = 16
Answer: 16 triangles
Radio signals travel at a rate of 3x10^8 meters per second how many seconds would it take for a radio signal to travel from a satellite to the surface of the earth if the satellite is orbiting at a height of 3.6x10^7 meters
Answer:
1.2x10^-1 seconds
Step-by-step explanation:
Answer:
0.12 seconds
Step-by-step explanation:
just think - how long does it take you to travel for example 30 km, if you are going 60 km/h ?
you have to divide 30 by 60 and get 0.5 or 1/2. meaning it takes you (logically) 30 minutes or half an hour to do so.
it is the same principle for all these kinds of questions.
we only need to keep an eye on the dimension of what we are talking about. is it hours or seconds ? meters or kilometers ? and do in
we need here to focus on seconds and to calculate
3.6×10⁷ / 3×10⁸ = 3.6 / 3×10¹ = 1.2 / 10 = 0.12 seconds
or
[tex]1.2 \times {10}^{ - 1} [/tex]
seconds
find the solution for -2.5x +5 < - 2.5 on a number line
Answer:
X>3
Step-by-step explanation:
-2.5x +5 < -2.5
-2.5x < -2.5-5
-2.5x< -7.5
X> -7.5/-2.5
X>3
The graph represents a functional relationship.
Which value is an input of the function?
Iy
8
0-14
6
0-2
4
.
0 0
2
4
2
4
8 10 12 14 16 18
Х
-2
-6
-B
-10
-12
-14
By analyzing the graph we conclude that the value that is an input is x = 4.
Which value is an input of the function?
For the inputs, we need to look at the horizontal axis. In the graph we can see a closed dot at x > 0 (we can't see the exact value).
This means that the minimum of the domain is positive.
From that, we conclude that the only correct option, that we can be sure that belongs to the domain (set of the inputs), is x = 4, the third option.
If you want to learn about domains:
https://brainly.com/question/1770447
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which expression is equivalent to \root(3)(x^(5)y)
Answer:
[tex]\sqrt[3]{x^{5}y} = x^{\frac{5}{3}}y^\frac{1}{3}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt[3]{x^{5}y}[/tex]
Required
The equivalent expression
We have:
[tex]\sqrt[3]{x^{5}y}[/tex]
Rewrite as an exponent
[tex]\sqrt[3]{x^{5}y} = (x^{5}y)^\frac{1}{3}[/tex]
Open bracket
[tex]\sqrt[3]{x^{5}y} = x^{5*\frac{1}{3}}y^\frac{1}{3}[/tex]
[tex]\sqrt[3]{x^{5}y} = x^{\frac{5}{3}}y^\frac{1}{3}[/tex]
9.
A rocket is launched from the top of a 76-foot cliff with an initial velocity of 135 ft/s. a. Substitute the values into the vertical motion formula h = –16t2 + vt + c. Let h = 0. b. Use the quadratic formula to find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.
A. 0 = –16t2 + 135t + 76; 0.5 s
B. 0 = –16t2 + 76t + 135; 9 s
C. 0 = –16t2 + 76t + 135; 0.5 s
D. 0 = –16t2 + 135t + 76; 9 s
Answer:
The answer is 2.)
Step-by-step explanation:
Given initial velocity=135 ft/s
& cliff=76 foot
Given quadratic equation
⇒ (let h=0 it is given)
⇒
⇒
⇒ t=8.96≈9 s (the other root is negative)
Hence, rocket will take 9 s to hit the ground after launched.
Answer: Choice D
0 = 16t^2 + 135t + 76; 9 s
==============================================
Explanation:
The equation we start with is
[tex]h = -16t^2 + vt + c\\\\[/tex]
where v is the starting or initial velocity, and c is the starting height.
We're told that v = 135 and c = 76
We let h = 0 to indicate when the object hits the ground, aka the height is 0 ft.
That means the equation updates to [tex]0 = -16t^2 + 135t + 76\\\\[/tex]
Based on that alone, the answer is between A or D
-------------------
We'll use the quadratic formula to solve for t
We have
a = -16b = 135c = 76So,
[tex]t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\t = \frac{-135 \pm \sqrt{135^2 - 4(-16)(76)}}{2(-16)}\\\\t = \frac{-135 \pm \sqrt{23,089}}{-32}\\\\t \approx \frac{-135 \pm 151.9506}{-32}\\\\t \approx \frac{-135 + 151.9506}{-32} \ \text{ or } \ t \approx \frac{-135 - 151.9506}{-32}\\\\t \approx \frac{16.9506}{-32} \ \text{ or } \ t \approx \frac{-286.9506}{-32}\\\\t \approx -0.52971 \ \text{ or } \ t \approx 8.96721\\\\[/tex]
We ignore the negative t value because a negative time duration makes no sense.
The only practical solution here is roughly 8.96721 which rounds to 9.0 or simply 9 when we round to the nearest tenth (one decimal place).
In short, the object will hit the ground at the 9 second mark roughly. Or put another way: the object is in the air for about 9 seconds.
From this, we can see that the final answer is choice D.
Keep in mind that we aren't accounting for any wind resistance. Considering this variable greatly complicates the problem and requires much higher level mathematics. So we just assume that there is no wind at this moment.
Solve.
Sy= 2x - 6
4x – 2y = 14
Use the substitution method
Answer:
14.4 i hope it helped you
f(x) = 3+3x-1+3x^4 , g(x) = -x^3+x^2-x+2-x^4. tính f(x)+g(x) và f(x) -g(x)
Step-by-step explanation:
= 3+3x-1+3x^4 , g(x) = -x^3+x^2-x+2-x^4. tính f(x)+g(x) và f(x) -g(x)
This is for geometry, please help ASAP
Answer:
Option C,
y² = 18x, since the graph opens right
Answered by GAUTHMATH
The price of an item yesterday was 120 . Today, the price fell to 78 . Find the percentage decrease.
Answer:
65%
Step-by-step explanation:
120 * x = 78
78/120 = x
.65 = x
Answer:
35%
Step-by-step explanation:
First, set up the equation.
[tex]\frac{78-120}{120} *100=[/tex] %Then solve.
78-120 is -42.
Divide by 120. -0.35.
Multiply by 100. -35.
The negative sign means that it is decreasing, so you can take it away.
I hope this helps!
show the work please and thank you
Answer:
Option a, 13
if you solve it, you get 13 as the answer
³√(5x-1)=4
or, 5x-1=64
or, 5x=65
or, x=13
The altitude of an equilateral triangle is 6v3 units long. The length of one side of the triangle is
units.
Answer:
Side = 2 * height / sqr root 3
Side = 2 * 6 * sqr root 3 / sqr root 3
Side = 12
Step-by-step explanation:
Triangle DEF is an isosceles, so AngleDEF Is-congruent-toAngleDFE. A horizontal line has points C, F, E, G. 2 lines extend from the line at points F and E to form an isosceles triangle with point D. Angle DEF measures 75°. What is the measure of angle CFD?
Answer:
[tex]\angle CFD =105^o[/tex]
Step-by-step explanation:
Given
[tex]\angle D FE = \angle DE F = 75^o[/tex]
See attachment
Required
Determine the measure of [tex]\angle CFD[/tex]
[tex]\angle CFD[/tex] and [tex]\angle DFE[/tex] are on a straight line.
So:
[tex]\angle CFD + \angle DFE = 180^o[/tex] --- angle on a straight line
Substitute known values
[tex]\angle CFD + 75^o = 180^o[/tex]
Collect like terms
[tex]\angle CFD =- 75^o + 180^o[/tex]
[tex]\angle CFD =105^o[/tex]
One of the legs of a right triangle measures 9 cm and the other leg measures 2 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
Approximately 9.2
Step-by-step explanation:
For right triangle, if you know 2 sides, you can find the third using pythagorean theorem, a^2 + b^2 = c^2. 'a' and 'b' are the lengths of the legs, while 'c' is the hypotenuse. You can plug in what you know into this formula:
9^2 + 2^2 = c^2
81+4 = c^2
c = √85, or approximately 9.2
What is the area of the circle?
Diameter = radius x 2
So, the radius is half of the denominator.
10 / 2 = 5
A = pi x r^2
A = pi x 5^2
A = 3 x 25
A = 75 ft^2
Hope this helps!
The diagram above shows a plan for a park. ABCD is a rectangle.
APB and DQC are semicircles centred at X and Y.
Given AB = 7 cm and AC = 25 cm.
Calculate the perimeter of the park in cm.
Answer:
Perimeter of the park = 70 cm
Step-by-step explanation:
Perimeter of the park = perimeter of the 2 semicircles + 2(length of the rectangle)
Perimeter = 2πr + 2(BC)
✔️Perimeter of the 2 semicircles = 2πr
Where,
radius (r) = ½(AB) = ½(7)
r = 3.5 cm
Perimeter = 2*π*3.5 = 7*π
Perimeter of the two semicircles = 21.9911486 ≈ 22 cm
✔️Find BC using Pythagorean theorem:
Thus,
BC = √(AC² - AB²)
AC = 25
AB = 7
BC = √(25² - 7²) = √576
BC = 24
✔️Perimeter of the park = perimeter of the 2 semicircles + 2(length of the rectangle)
Perimeter of the park = 22 + 2(24)
= 22 + 48
= 70 cm
When 4x + 4x + 1 = 33 is solved, the result is:
Answer:
x = 4
Step-by-step explanation:
1. 8x+1 = 33 and the 4x together
2. 8x = 32 subtract 1 from each side
3. x = 4 Divide both sides by 8
Answer:
x=4
Step-by-step explanation:
4x+4x+1=33
Combine like (similar) terms:
8x+1=33
Rearrange terms to solve for x:
8x=33-1
8x=32
[tex]\frac{8x}{8} =\frac{32}{8}[/tex]
x=4
Therefore, x=4.
on the number line, which of the following numbers below can be found on the right of 2.26??
A.2.30
B.-2.25
C.2.25
D.1.26
Answer:
2.25
Step-by-step explanation:
The lower number will always be on the right side unless its negative numbers , So the lower number is 2.25 , Why it isn't 1.26 is because its much far from 2.26 and so cannot be counted . Thanks
three forth of a number excceed its one third by 15, find the number
The required value of x is 36
Step-by-step explanation :
Let the required number be x.
Three fourth of number = (3/4)x
One third of number = (1/3) x
According to the question ;
3x/4 = x/3 + 15
→ 3x/4-x/3 = 15
→ 9x - 4x / 12 = 15
→ 5x = 15 x 12
⇒ x = 180 / 5
⇒ x = 36
Hope this answer helps you..!!!− 96 ÷ −6 ÷ 8 =
a) 2 b) -2
Answer:
answer is 2
Step-by-step explanation:
answer is 2…………………………………
x>0, y>0, 2x+3y=8, smallest value of xy? pls help me
Answer:
where there is x in the equation we put 0
For y
=2(0)+3y=8
=0+3y=8 Group likely terms
=3y=8-0
=3y=8 Divide both sides by 3
=3y/3=8/3
Therefore y=2.6
For x
=2x+3y=8
=2x+3(0)=8
=2x+0=8 Group likely terms
=2x=8-0
=2x=8 Divide both sides by 2
=2x/2=8/2
Therefore x=4
The smallest numbers for x and y is 4 and 2.6 respectively
What is the slope of the line below is -5. Which of the following is the point-slope form of the line?
Answer:
[see below]
Step-by-step explanation:
Point slope form is:
[tex]y-y_1=m(x-x_1)[/tex]
(x1, y1) - a point
m - slope
We are given the point of (2, -7), and the slope of -5.
[tex]y-y_1=m(x-x_1)\rightarrow y-(-7)=-5(x-2)\rightarrow\boxed{y+7=-5(x-2)}[/tex]
Hope this helps.
rút gọn M=[ căn x -2/x-1- căn x +2/x+2 căn x+ 1] nhân x bình-2x+1/2 với x>0 x khác 1
Answer:
Step-by-step explanation:
What is the measure of each intercepted arc for each inscribed angle of a regular hexagon inscribed in a circle?
Answer:
Step-by-step explanation:
The inscribed angles are made up of the remote interior angles of this hexagon, of which each of them measures 120 degrees. That means that if this is measure of the inscribed angle, the arc this angle intercepts is twice the degree measure of the inscribed angle. The arcs then will all measure 240 degrees.
giai bat phuong trinh: 10x + 3 - 5x_< 14x + 12
Answer:
x>_-1
10x + 3 - 5x_< 14x + 12
-9_<9x
Answer:
Step-by-step explanation:
10x +3-5x < (nhỏ hơn hoặc bằng) 14x=12
10-14x-5x< bằng 12 -3
-9x< bằng 9
x > bằng -1
A car covers a distance of 132 km. If each tire’s diameter is 42 cm, how many rotations does each tire make in covering this distance?
Answer:
Step-by-step explanation:
Diameter (D)= 42cm
Circumference = (pie)D= (22/7)*D=(22/7)*42 = 132cm
1 circumference = 1 revolution
1 revolution = 132cm = 1.32m
for covering 5.28km no. of revolution = 5.28*1000/1.32 = 4000
Hope this answer helps you :)
Have a great day
Mark brainliest
Rhombus LMNO is shown with its diagonals.
Rhombus L M N O is shown. Diagonals are drawn from point L to point N and from point M to point O and intersect at point P. All sides are congruent.
Angle MNO measures 112°. What is the measure of angle LMN?
Answer:
hope this help
Step-by-step explanation:
Answer:
90
51
10
Step-by-step explanation:
The scale on a map is 1 inch = 10 miles.
What is the distance, in inches, on the map
between two towns that are m miles apart?
F.
m/10
G. M/5
H.5m
J.10m
K.m+10
Answer:
F. m/10.
Step-by-step explanation:
10 miles = 1 inch
1 mile = 1/10 of an inch so
m miles = m/10 inches.
