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What is the question here?
Element X is a radioactive isotope such that every 69 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 20 grams, how much of the element would remain after 30 years, to the nearest whole number?
Answer:
[tex]15\text{ grams}[/tex]
Step-by-step explanation:
Since the mass of the radioactive isotope is halved every 69 years, we want to multiply its initial mass by [tex]1/2[/tex] every 69 years.
We can model this using the following equation:
The remaining mass, [tex]f(x)[/tex], is equal to the initial mass multiplied by [tex]\frac{1}{2}^{(\frac{t}{69})}[/tex], where [tex]t[/tex] is the number of years that have passed from the initial mass. The reason why the exponent is [tex]\frac{t}{69}[/tex] is because we only want to half the mass every 69 years, so [tex]\frac{69}{69}=1[/tex] and [tex]\frac{1}{2}^1=\frac{1}{2}[/tex].
Thus, we have:
[tex]f(x)=20\cdot \frac{1}{2}^{(t/69)}[/tex]
Substituting [tex]t=30[/tex], we get:
[tex]f(x)=20\cdot \frac{1}{2}^{(30/69)}=20\cdot 0.73980522316=14.7961044632\approx \boxed{15\text{ grams}}[/tex]
The height y of a ball (in feet) is given by the function
y= -1/12^2+2+4
and x is the horizontal distance traveled by the ball. How high is the ball when it leaves the child’s hand?
Answer:
assuming that the problem was actually
-1/12 x ^ 2 + 2x + 4
height = 16
(12,16)
forty feet (40) feet
vertex = -b/2a = -2/(-1/6) = 12
f(12) = - 144/ 12 + 24 + 4 = -12+ 24 + 4 = 16
Step-by-step explanation:
The distance between the parallel lines x – 2y = 3 and 2x – 4y = 12 is
Answer:
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Step-by-step explanation:
sorry di ko po alam yung sagot pasensiya na po
Given :
Parallel lines are
x – 2y = 3 and 2x – 4y = 12
Step-by-step explanation:
Lets write the given lines in slope intercept form y=mx+b
[tex]x -2y = 3 \\-2y=-x+3\\Divide \; both \; sides \; by -2\\y=\frac{x}{2} -\frac{3}{2}[/tex]
From the above equation , y intercept of first line is [tex]\frac{-3}{2}[/tex]
Solve the second equation for y and find out y intercept
[tex]2x-4y=12\\-4y=-2x+12\\Divide \; by \; -4\\y=\frac{1}{2} x-3[/tex]
y intercept of second line is -3
To find the distance between parallel lines, we subtract the y intercepts
[tex]\frac{-3}{2} -(-3)=\frac{-3}{2} +\frac{6}{2} =\frac{3}{2} =1.5[/tex]
Answer:
The distance between the parallel lines = 1.5
Reference:
https://brainly.com/question/24145911
Pls help will mark brainliest and 30 points
1. Answer is option 3
2. Answer is option 3
Answer:
for #1 it's the 3rd one and for #2 it's the 4th one (2.8 meters)
Find the solution of the system of equations.
4x – 6y = 32
2x + 3y = 4
Answer:
(5,-2)
Step-by-step explanation:
4x – 6y = 32
2x + 3y = 4 (multiply everything by 2. This will allow for the elimination of one of the variables. In this case, the y. )
4x – 6y = 32
4x + 6y = 8 (Now add them together)
__________
8x = 40 (Divide by 8, both sides)
x = 5
4(5) - 6y = 32 ( Substitute the x value into one of the original equations)
20 - 6y = 32 (Subtract the 20 from both sides)
-6y = 12 Divide by the -6, both sides)
y = -2
Find the distance between the pair of points: (0,-8)and (0,4)
Step-by-step explanation:
the answer is in the image above
Answer:
12
Step-by-step explanation:
[tex]\sqrt{0^{2} + 12^{2} }[/tex]
12
Slopes of parallel lines
Answer:
2
Step-by-step explanation:
Parallel lines have the same slopes
If the slope of line a is 2, the slope of line b is 2
Answer:
slope of line b = 2
Step-by-step explanation:
The slopes of parallel lines are equal
Given slope of line a = 2 and parallel to line b , then
slope of line b = 2
What is the correct solution set for the following graph?
Answer: i do not see a graph
Step-by-step explanation:
PLZ ans have mocks plz
Answer:
The table will be:
x |-2 | -1 | 0 | 1 | 2
y | 1 | 4 | 5 | 4 | 2
Step-by-step explanation:
The function is:
[tex]y=5-x^{2}[/tex]
a) The x values of the table is:
x |-2 | -1 | 0 | 1 | 2
So, when x = -2, y will be:
[tex]y(-2)=5-(-2)^{2}=5-4=1[/tex]
Doing the same with the other x values we have:
[tex]y(-1)=5-(-1)^{2}=5-1=4[/tex]
[tex]y(0)=5-(0)^{2}=5[/tex]
[tex]y(1)=5-(1)^{2}=5-1=4[/tex]
[tex]y(2)=5-(2)^{2}=5-4=1[/tex]
The table will be:
x |-2 | -1 | 0 | 1 | 2
y | 1 | 4 | 5 | 4 | 1
I hope it helps you!
Which is the graph of y = |3x| – 2?
Answer:
It's the 3rd one, that you've selected in the picture.
Step-by-step explanation:
Used a graphing calculator to check,
Hope this is helpful.
for the graphed exponential equation, calculate the average rate of change from x=-2 to x= 0
Answer:
3/2
Step-by-step explanation:
Rate of change is given by
f(x2) -f(x1)
-----------------
x2 -x1
We know x2 is 0 and x1 is -2
f(x2) is -1 and f(x1) is -4
-1 - ( -4)
----------
0 - -2
-1 +4
--------
0+2
3/2
To get 400 as quotient, what number is to be divided by 16?
400+16
400 -16
400÷16
400× 16
Answer:
400×16
Step-by-step explanation:
let the number be n.
[tex] \frac{n}{16 } = 400 \\ 16 \times \frac{n}{16} = 400 \times 16\\ n = 400 \times 16[/tex]
The record for the largest scoop of ice cream was made in Wisconsin. Thebscoop of ice cream was 3,010 pounds! How many ounces of ice cream is that?
Answer:
48160
Step-by-step explanation:
Consider the series 1/4+1/6+1/9+2/27+4/81+....
Does the series converge or diverge?
Select answers from the drop-down menus to correctly complete the statements.
Answer:
The series converges as any two consecutive elements of the sum are monotonically decreasing.
Step-by-step explanation:
The series converges since the consecutive element is monotonically decreasing. That is:
[tex]\forall\,i\in \mathbb{N}\,a_{i} > a_{i+1}[/tex] (1)
Where:
[tex]a_{i}[/tex] - The i-th component of the sum.
[tex]a_{i+1}[/tex] - The (i+1)-th component of the sum.
find the solution to the system of equations
Answer: (-2,1) deduced from graph
the point where the two lines intersect is the solution
Step-by-step explanation:
Answer:
(- 2, 1 )
Step-by-step explanation:
Given a system of equations graphically then the solution is at the point of intersection of the 2 lines.
The point of intersection = (- 2, 1 ) ← solution
Can someone help me? It's urgent and thank you!
Answer:
12
Step-by-step explanation:
please help asap ill give brainliest
Answer:
is 0.24 yards in the option, becausw i am getting this as my answer
HELP PLEASEEEE!!!!!!!
Answer:
The first one with the sequence 0.25,1,4,16
Answer:
the first one
Step-by-step explanation:
I need help with this it's urgent!
Oh shucks man, I'm sorry bout that
Las calificaciones de los alumnos en un examen de Estadística han sido: 6, 4, 4, 3, 6, 10, 1, 0, 2, 6 ,6, 8, 5. Calcula su media. Seleccione una: a. 4.6 b. 6.0 c. 5.0 d. 4.7
Find the discriminant and the number of real roots for this equation.
x^2 + 3x + 8 = 0
A. 32; two real roots
B. -23; one real root
C. 32; one real root
D. -23; no real roots
I wrote it down, sorry if it’s a little bit messy.
The correct option regarding the discriminant and the number of real roots for this equation is given by:
D. -23; no real roots
What is the discriminant of a quadratic equation and how does it influence the solutions?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The discriminant is:
[tex]\Delta = b^2 - 4ac[/tex]
The solutions are as follows:
If [tex]\mathbf{\Delta > 0}[/tex], and it is a perfect square, it has 2 real solutions.If [tex]\mathbf{\Delta = 0}[/tex], it has 1 real solution.If [tex]\mathbf{\Delta < 0}[/tex], it has 0 real solutions.In this problem, the function is:
x² + 3x + 8.
Hence the coefficients are a = 1, b = 3, c = 8, and the discriminant is given by:
[tex]\Delta = b^2 - 4ac = 3^2 - 4(1)(8) = -23[/tex]
Negative discriminant, hence no real roots, and option D is correct.
More can be learned about the discriminant of a quadratic equation at https://brainly.com/question/19776811
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PLEASE HELP
What are the missing reasons in the proof?
A. Substitution; converse of diagonals theorem
B. Sum of interior angles; converse of diagonals theorem
C. Sum of interior angles; converse of opposite angles theorem
D. Substitution; converse of opposite angles theorem
Are these converses true? The answer is yes. Each of these converses can be a way to show that a quadrilateral is a parallelogram. However, the Consecutive Angles Converse can be a bit tricky, considering you would have to show that each angle is supplementary to its neighbor
(∠A
and
∠B, ∠B
and
∠C, ∠C
and
∠D
, and
∠A
and
∠D)
. We will not use this converse.
Gianna bought 6.2 pounds of berries. She used 4.8 pounds of the berries to make a pie. What equation can be used to find how many pounds of berries, b, Gianna has left over? A 6.2 + 4.8 = b
B b − 6.2 = 4.8
C 4.8 + b = 6.2
D b − 4.8 = 6.2
Sara and jo both ran an 8km race Sarah took 55 mins to run the whole race jo started the race 3 mins later than Sara but caught up when they had both travelled 6 km of Sara and jo both ran at constant speed what is jos speed in 2dp
Answer:
9.41 km/h
Step-by-step explanation:
The total distance of the race, d = 8 km
The time Sarah took to run the race, t = 55 mins
The time Jo started the race = 3 mins later than Sara
The point Jo caught up with Sarah = 6 km into the race
The rate at which Jo and Sarah ran = Constant speed
The required information = Jo's speed
From the information given, Sarah's speed, v = 8 km/(55 mins) = (8/55) km/min × 60min/h = 96/11 km/h
The time it would take Sarah to run 6 km = 6 km/(8 km/(55 mins)) = 41.25 mins
Given that Jo started 3 minutes late, and they both arrive at 6 km into the race at the same point in time, the time it took Jo to arrive at 6 km into the race = The time it took Sarah - 3 minutes
∴ The time it took Jo to run the 6 km = 41.25 minutes - 3 minutes = 38.25 minutes
Given that Jo ran at a constant speed, and speed = distance/time, we have;
Jo's speed = 6 km/(38.25 min) = 8/51 km/min × 60 min/h = (160/17) km/h ≈ 9.41 km/h.
complete each division sentence using the models provided
Answer:
honestly for division of fractions the only sentence you need to know is...
"mine is not to question why, but to invert and multiply"...
fractional division can be done with "an inverse multiplication:
5/6 ÷ 1/6 can be changed to 5/6 * 6/1 = 30/6 = 5
3/5 ÷1/10 can be changed to 3/5 * 10/1 = 30/5 = 6
Step-by-step explanation:
Pleasee help me, I might give brainliest to the best answer. I urgently need a answer
Answer:
1<1.35<2
Step-by-step explanation:
Answer:
1.35 is closer to 1 than 2
So the bag of nuts weighed about 1 pound.
Step-by-step explanation:
The decimal is closer to the whole number 1 when plotted on a number line, so it rounds to 1.
Find all solutions to the equation in the interval [0, 2pie] Enter the solutions in increasing order.
sin 2x = sin x
=============================================
Work Shown:
sin(2x) = sin(x)
sin(2x) - sin(x) = 0
2*sin(x)*cos(x) - sin(x) = 0
sin(x)*(2cos(x) - 1) = 0
sin(x) = 0 or 2cos(x)-1 = 0
sin(x) = 0 or cos(x) = 1/2
Using the unit circle, the solutions to sin(x) = 0 are x = 0, x = pi, x = 2pi
Also, the solutions to cos(x) = 1/2 are x = pi/3, x = 5pi/3
So the entire solution set on the interval [0,2pi] is {0, pi/3, pi, 5pi/3, 2pi} when written in increasing order.
All solutions to the equation in the interval [0, 2[tex]\pi[/tex]] is {0, [tex]\frac{\pi }{3}, \pi , \frac{5\pi }{3} ,2\pi[/tex]}.
What is solution to an equation?A solution is an assignment of values to the unknown variables that makes the equality in the equation true.
As sin2x = 2 sinx cosx,
sin2x = sinx is equivalent to
2 sinx cosx = sinx or 2 sinx cosx − sinx = 0 or
sinx (2cosx − 1) = 0 i.e.
either sinx = 0 and x = 0, π, 2π
or 2cosx − 1 = 0 i.e. cosx = [tex]\frac{1}{2}[/tex] i.e. x = [tex]\frac{\pi }{3} , \frac{5\pi }{3}[/tex]
Hence, solution to an equation is x = {0, [tex]\frac{\pi }{3}, \pi , \frac{5\pi }{3} ,2\pi[/tex]}
Learn more about solution to an equation here
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PQR is a triangle. PR = 13 cm, PQ = 12 cm and angle QPR = 30°
Calculate the length of QR.
Answer:
6.55 cm
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, acute, scalene, obtuse, right and equilateral triangle.
Cosine rule is used to show the relationship between sides and angles of a triangle. If a, b, and c are sides of a triangle, while A, B, and C are angles opposite to the corresponding sides. Then:
c² = a² + b² - 2ab*cos(C)
Given that PR = 13 cm, PQ = 12 cm and angle QPR = 30°, hence:
QR² = PR² + PQ² - 2(PR)(PQ)cos(∠QPR)
QR² = 13² + 12² - 2(13)(12)cos(30) = 169 + 144 - 270
QR² = 43
QR = 6.55 cm
I was doing my khan and i got stuck
6=2(y+2)
Answer:
[tex]y=1[/tex]
Step-by-step explanation:
Given:
[tex]6=2(y+2)[/tex]
Distribute the parenthesis
[tex]6=2y+4[/tex]
Subtract both sides by 4
[tex]2=2y[/tex]
Divide both sides by 2 to get [tex]y[/tex] alone
[tex]1=y[/tex]
Hope this is helpful
\frac{1}{cos^{2} x}-(3+\sqrt{3} )tanx-3+\sqrt{3} =0
Step-by-step explanation:
pls type the question
properly and I swear I will solve it