Answer:
[tex]\displaystyle x=-\frac{9}{2},\:x=-4[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{2}{x+6}-\frac{1}{x+3}=2\\\\\frac{2(x+3)}{(x+6)(x+3)}-\frac{(x+6)}{(x+6)(x+3)}=2\\ \\\frac{(2x+6)-(x+6)}{(x+6)(x+3)}=2\\ \\\frac{x}{(x+6)(x+3)}=2\\ \\x=2(x+6)(x+3)\\\\x=2(x^2+9x+18)\\\\x=2x^2+18x+36\\\\0=2x^2+17x+36[/tex]
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-17\pm\sqrt{(17)^2-4(2)(36)}}{2(2)}\\\\x=\frac{-17\pm\sqrt{289-288}}{4}\\\\x=\frac{-17\pm\sqrt{1}}{4}\\\\x=\frac{-17\pm1}{4}\\ \\x_1=\frac{-18}{4}=-\frac{9}{2},\: x_2=\frac{-16}{4}=-4[/tex]
If f(x)=x2−4x+4 , then f(3)=
Answer:
f(3) = 1
Step-by-step explanation:
substitute x = 3 into f(x) , that is
f(3) = 3² - 4(3) + 4 = 9 - 12 + 4 = 1
Answer:
1
Step-by-step explanation:
Substitute 3 for x in your equation leaving you with (3)^2-4(3)+4.
9-12+4
-3+4=1
Find the probability of rolling a 66 -sided dice and getting a number that is a divisor of 2020
Answer:
2/3 or 0.66 repeated
Step-by-step explanation:
Since 2022 is only divisible by 1,2,4, and 5, the probability of getting a number that is a divisor of 2020 is 4/6, simplified to 2/3 or %0.66.
Rewrite the expression (-x3 + x2 - x + 1)/(- x - 1) using the
long division method.
The solution to the expression (-x³ + x² - x + 1) / (x - 1) using long division is (x² - 2x + 3) + (4 / (-x - 1))
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the expression:
(-x³ + x² - x + 1) / (x - 1)
Using long division:
= x² + (2x² - x + 1)/(-x - 1)
= x² - 2x + (-3x + 1)/(-x - 1)
= (x² - 2x + 3) + (4 / (-x - 1))
The solution to the expression (-x³ + x² - x + 1) / (x - 1) using long division is (x² - 2x + 3) + (4 / (-x - 1))
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What is the area of the following figure if a = 13, b = 5, and c = 12?
Answer:
[tex]A(\triangle)=30\: units^2[/tex]
Step-by-step explanation:
Measures of the sides of the triangle are given as:a = 13, b = 5 and c = 12 Now, find semi perimeter (s) of the triangle, it is given as below:[tex] s=\frac{a+b+c}{2}=\frac{13+5+12}{2}=\frac{30}{2}=15[/tex]Formula for area of triangle is given as:[tex]A(\triangle)=\sqrt{s(s-a)(s-b)(s-c)}[/tex][tex]\implies A(\triangle)=\sqrt{15(15-13)(15-5)(15-12)}[/tex][tex]\implies A(\triangle)=\sqrt{15(2)(10)(3)}[/tex][tex]\implies A(\triangle)=\sqrt{900}[/tex][tex]\huge{\orange{\implies A(\triangle)=30\: units^2}}[/tex]The mass, Q, of a sample of Tritium (a radioactive isotope of Hydrogen), decays at a rate of 5.626% per year. Given a
uantity of 726 grams, determine the graph that best models the decay of this radioactive substance.
In ten years' time, the mass of tritium would become 406.87 g. That's almost half of the original mass.
The mass, Q, of a sample of Tritium (a radioactive isotope of Hydrogen), decays at a rate of 5.626% per year.
How to find the decay of the radioactive substance?To make a graph, we need to establish which is the independent and dependent variables.
The independent variable (x-axis) is time in years and the dependent variable (y-axis) is the mass of tritium in grams.
At year 1,
726(1 - 0.05626) = 685.16 g
At year 2,
685.16 (1 - 0.05626) = 646.61 g
At year 3,
646.61 g (1 - 0.05626) = 610.23 g
The final graph is shown in the attached figure.
In ten years' time, the mass of tritium would become 406.87 g. That's almost half of the original mass.
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what is a parralel line
Answer:
A parallel line is something that is equivalent on the other end. This mean if you cut a shape, a square for example, in half,the sides will be of equal length.
Answer:
a parallel line is diagonal
The universal set, &, and the sets A and B are defined below.
= {3, 4, 6, 8, 9, 12, 15, 16, 20}
A = {6, 9, 12, 15}
B = {multiples of 4}
Write down all the elements of AB'.
Answer:
wedg
Step-by-step explanation:
ed
You are trying to bulk and gain muscle. Your trainer says your daily calorie intake should increases based on hours you spend exercising and can be represented by the following equation: T=2000+500h.
a) T - Calories, 2000 - Minimum calories, 500 - Additional calories per exercise hour, b) We should consume 3500 calories to spend three hours exercising.
How to analyse a linear function of calorie gain in terms of the exercise time
In this question we have a linear function where the independent variable is the exercise time (h), in hours, and the dependent variable is the calorie gain (T), in calories. The constant "2000" is the minimum calorie consumption and the constant "500" represents the amount of additional calories per each hour of exercise.
Now we proceed to respond the questions of the part a):
(i) T - Amount of calories needed, (ii) 2000 - Minimum calorie consumption, (iii) 500 - Amount of additional calories per hour of exercise.
b) And lastly we calculate the amount of calories by evaluating the function:
T = 2000 + 500 · 3
T = 2000 + 1500
T = 3500
We should consume 3500 calories to spend three hours exercising.
Remark
The statement is incomplete, the complete form is shown below:
You are trying to bulk up and gain muscle. Your trainer says that your daily calorie intake should increase based on the hours you spend exercising and can be represented by the following equation: T = 2000 + 500 · h
a) What does each part of this expression represent? (i) T = , (ii) 2000, (iii) 500, (iv) h
b) If you spend 3 hours exercising, how many calories should you consume?
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Find x. Round your answer to the nearest tenth of a degree.
36
X
19
+
Answer: 36.9
Step-by-step explanation:
Find the fist 4 terms of a geometric series with first term of 8 and the sum to infinity of 12
Step-by-step explanation:
the sum of an infinite geriatric series with |r| < 1 is
s = a1/ (1 - r)
in our case we have
a1 = 8
12 = 8/(1 - r)
12(1 - r) = 8
1 - r = 8/12 = 2/3
-r = -1/3
r = 1/3
so, the first 4 terms (I added a5 too, just in case your teacher meant the NEXT 4 terms) are
a1 = 8
a2 = a1 × 1/3 = 8/3
a3 = a2 × 1/3 = 8/9
a4 = a3 × 1/3 = 8/27
a5 = a4 × 1/3 = 8/81
...
Answer:
[tex]8,\quad \dfrac{8}{3},\quad \dfrac{8}{9},\quad\dfrac{8}{27}[/tex]
Step-by-step explanation:
Sum to infinity of a geometric series:
[tex]S_\infty=\dfrac{a}{1-r} \quad \textsf{for }|r| < 1[/tex]
Given:
[tex]a[/tex] = 8[tex]S_\infty[/tex] = 12Substitute given values into the formula and solve for [tex]r[/tex]:
[tex]\implies 12=\dfrac{8}{1-r}[/tex]
[tex]\implies 1-r=\dfrac{8}{12}[/tex]
[tex]\implies r=1-\dfrac{8}{12}[/tex]
[tex]\implies r=\dfrac{1}{3}[/tex]
General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]
(where a is the first term and r is the common ratio)
Substitute the found values of [tex]a[/tex] and [tex]r[/tex]:
[tex]\implies a_n=8\left(\dfrac{1}{3}\right)r^{n-1}[/tex]
The first 4 terms:
[tex]\implies a_1=8\left(\dfrac{1}{3}\right)r^0=8[/tex]
[tex]\implies a_2=8\left(\dfrac{1}{3}\right)r^1=\dfrac{8}{3}[/tex]
[tex]\implies a_3=8\left(\dfrac{1}{3}\right)r^2=\dfrac{8}{9}[/tex]
[tex]\implies a_4=8\left(\dfrac{1}{3}\right)r^3=\dfrac{8}{27}[/tex]
find the slope of the line that passes through (9,-3) and (9,-8)
Answer:
The line has no slope. I hope this helps
Date:
Name:
Refocus
Directions: Solve the problems by building the figure with algebra tiles and writing an equation.
A rectangle has a length that is twice the width. The perimeter of the rectangle is 12 feet.
What is the width? What is the length?
Equation:
Width:
Length:
Answer:
Equation: 2w + 2(2w) = 12
width = 2
length = 4
Step-by-step explanation:
Width is w
Length is 2 * width = 2w
Perimeter is 2w + 2l
Substitute 2w for L.
Perimeter is now 2w + 2(2w) = 12
Distribute the 2 to the parentheses.
2w + 4w = 12
Combine Like terms
6w = 12
Divide by 6 to solve for w.
w = 2
If w = 2, then the length = 4.
Calculate the area of the alarm clock.
Given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².
What is the area of the alarm clock?Note that: Area of a circle is expressed as;
A = πr²
Where r is radius and π is constant pi ( π = 3.14 )
Given that;
Diameter d = 70cm Radius r = d/2 = 70cm/2 = 35cmArea = ?A = πr²
A = 3.14 × ( 35cm )²
A = 3.14 × 1225cm²
A = 3846.5cm²
Therefore, given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².
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A particle moves along line segments from the origin to the points (2, 0, 0), (2, 5, 1), (0, 5, 1), and back to the origin under the influence of the force field
[tex]F(x,y,z) = z^2i+5xyj+2y^2k[/tex]
Use Stokes Theorem to find the work done:
A particle moves along line segments from the origin to the points, work done is mathematically given as
W=184.5units
What is the solution of an equation that matches the model.?Considering line segments from (0,0,0)origin to (2,0,0) , (2,5,1) and (0,5,1) under the infulence of force
Generally, the equation for force is mathematically given as
F = z2i + 5xyj + 2y2k
Therefore, Considering u*v
[tex]u * v = (u_1j+u_2j+u_3k) * (v_1i+v_2j+v_3k)[/tex]
[tex]u* v = u_1v_1(i * i) + u_1v_2(i * j)+u_1v_3(i * k) + u_2v_1(j * i) + u_2v_2(j * j)+u_2_3(j* k) + u_3v_1(k * i) + u_3v_2(k * j)+u_3v_3(k * k)[/tex]
Where
[tex]i * i = j *j=k * k=0[/tex]
Hence
[tex]u* v = u_1v_2k-u_1v_3j-u_2v_1k+u_2v_3i +u_3v_1j - u_3v_2i[/tex]
[tex]u = (u_1,u_2,u_3) = (0,5,1)\\\\v = (v_1,v_2,v_3) = (-3,0,0)[/tex]
The normal equation formed
-2y + 15z = 0
z= (1/5)y
Considering the level surface and differential surface area
h(x,y,z) = -y + 5z =0
[tex]dS = |grad(h)| dA[/tex]
In terms of the x and y coordinates of (2,0,0) and (2,5,1) and (0,5,1), we can state that the ranges are 0 to 3 and 5 respectively we have
[tex]0 \leq x \leq 2 \ and \ 0 \leq y \leq 5[/tex]
Using strokes theorem to evaluate
[tex]F = z2i + 5xyj + 2y2k[/tex]
[tex]curl \ F = 4yi+2zj+5yk = (4y,2z,5y)[/tex]
[tex]curl \ F * nds= \frac{1}{5}(-2z + 25y)\ dy \ dx[/tex]
In conclusion, The work done is
[tex]W=\int _CF *dr[/tex]
[tex]\int _C F * dr = \int \int curl \ F * n ds[/tex]
[tex]\int _C F *dr = \frac{123}{2}\int_0^3 \ dx[/tex]
[tex]\int _C F * dr = \frac{123*3}{2}[/tex]
W= 184.5units
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What is the equation of the line that passes through the point (6, 1) and has a slope
of -1/2
Answer:
y = 6x + [tex]\frac{-1}{2}[/tex]
Step-by-step explanation:
I think take this with a grain of salt
At time t=0 a woman tosses an apple straight up into the air. At time t= 0.5, it begins to fall back to her hand. She catches the apple at t=1.0. Treat motion upward a positive. which of the follwong graphs could represent the motion of the apple?
The graph that could represent the motion of the apple is graph B.
What is a graph?A graph is a diagram showing the relation between variable quantities, typically of two variables, each measured along with one of a pair of axes at right angles.
Here, the speed of apple at time t is given by v=0 + at which is a straight line of slope a that passes through origin because constant is zero. At time t=0 its initial speed is 0 and it will increase constantly with time. Therefore, graph (B) is correct
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Find the circumference of a circle that has a diameter of 2 ft. Use 3.14 for pi.
5.14 ft
6.28 ft
12.56 ft
7.14 ft
Answer:
6.28 ft
Step-by-step explanation:
using the formula [tex]\pi d[/tex] to find the circumference of the circle, you substitute the numbers. 3.14(2). 3.14 x 2 = 6.28 hence the answer
A line intersects the points (3,6) and (5, -4). m=-5 write an equation in point-slope form using the point (3,6)y - [?] = __ (x -__)
Answer:
y -6 = -5(x -3)
Step-by-step explanation:
The point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
__
substituting given valuesYou have been given ...
m = -5
(h, k) = (3, 6)
Putting the given values into the point-slope form gives the equation you want:
y -6 = -5(x -3)
please answer will give brainly
Answer:
Step-by-step explanation:
The volume of a cube is given by the formula :
a³ (where a is the side length )
So now we have to cube these lengths :
Part A :
(3x²y)³ =
(3x²y)(3x²y)(3x²y) =
(9x^4y²)(3x²y) =
27x^6y³ (This is now fully simplified so our final answer for a)
Part B:
(5y²)³ =
(5y²)(5y²)(5y²) =
(25y^4)(5y²) =
125y^6 (This is now fully simplified so our final answer for b)
Hope this helped and have a good day
-28=8x+2(x+6) im so lost
[tex]\bf{Swap \ sides \ 8x+2(x+6)=-28 }[/tex]
[tex]\bf{Expand \ 2(x+6): \ \ \ \ 2x+12}[/tex]
[tex]\mathrm{Set \ the \ variables \ using: \ \ \ a(b+c)=ab+ac}[/tex]
[tex]a=2,\:b=x,\:c=6[/tex]
[tex]=2x+2\cdot \:6[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:2\cdot \:6=12[/tex]
[tex]=2x+12[/tex]
[tex]8x+2x+12=-28[/tex]
[tex]\mathrm{Add\:similar\:elements:\:8x+2x=10x}[/tex]
[tex]10x+12=-28[/tex]
[tex]\mathrm{Subtract\:}12\mathrm{\:from\:both\:sides}[/tex]
[tex]10x+12-12=-28-12[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]10x=-40[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}10[/tex]
[tex]\dfrac{10x}{10}=\dfrac{-40}{10}[/tex]
[tex]\mathrm{Simplify \ \dfrac{10x}{10}: \ \ x }[/tex]
[tex]\mathrm{Divide:}\:\dfrac{10}{10}=1[/tex]
[tex]=x[/tex]
[tex]\mathrm{Simplify \ \dfrac{-40}{10}: \ \ -4 }[/tex]
[tex]\rm{Apply \ the \ properties \ of \ fractions \ to \ fractions: \ \ \dfrac{-a}{b}=-\drac{a}{b}}[/tex]
[tex]=-\dfrac{40}{10}[/tex]
[tex]\rm{split: \ \dfrac{40}{10}=4 }[/tex]
[tex]\bf{x=-4 \ \ \to \ \ \ Answer }[/tex]
what is the volume of the rectangular prism each is 1/3
Answer:
The answer is 7
Step-by-step explanation:
To find the volume you multiply the width, height, and the length.
Length= 7/3
width= 3/3
height= 9/3
When you multiply you then have to simplify which is 7/1 or 7.
Mark this correct to help me gain!!
Find the 66th term in the following
arithmetic sequence:
-92, -85, -78, -71, ...
Answer: 363
Step-by-step explanation:
The common difference is 7, so the explicit formula is [tex]a_{n}=-92+7(n-1)[/tex].
Substituting in n=66,
[tex]a_{66}=-92+7(66-1)=\boxed{363}[/tex]
Please I really need help I’ll mark brainlist
Answer:
So, cows heart best is faster than horse.
Step-by-step explanation:
Time and heartbeats are in direct proportion.
p = kx
Where p is the beats per minute and x represents time in minutes
Now, to find the value of k, substitute p = 152 and x = 4
152 = 4k
k = 152/4
k = 38
[tex]\sf \boxed{p = 38x}[/tex]
Cow: y = 65x
So, cows heart best is faster than horse
ITS URGENT I WILL YOU GIVE BRAINLEST(if you are the first and the best)!!!
Answer:
2 Hours
Step-by-step explanation:
First you have to add up all the points which would be;
1 1/2 + 1 1/2+ 2 1/2+ 2 1/2= 8 hours
Then you have to divide by how many points to find the average;
8 hours divided by 4 points= 2 hours average
In total, she will practice 2 hours every day
Find a3, a4, and a5.
a₁ = 5
a₂ = 2
an =-2an -1 + an-2
Answer:
A1 5×3 = 15
A2 = 2×4= 8
an=I don't know that one
find the solution set. 4x^2+x=3
Answer:
[tex]x=\frac{3}{4},\:x=-1[/tex]
Keys:
For this problem, you need the quadratic formula(listed below).
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex][tex]1^a=1[/tex][tex]\sqrt[n]{a}^n=a[/tex]When you see ± in a quadratic equation, you must know there is going to be at least 2 solutions.
Step-by-step explanation:
solving for x₁ and x₂
[tex]4x^2+x=3\\4x^2+x-3=3-3\\4x^2+x-3=0\\x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot 4\left(-3\right)}}{2\cdot 4}\\[/tex]
[tex]1^2=1\\=\sqrt{1-4\cdot \:4\left(-3\right)}\\=\sqrt{1+4\cdot \:4\cdot \:3}\\=\sqrt{1+48}\\=\sqrt{49}\\=\sqrt{7^2}\\\sqrt{7^2}=7\\=7[/tex]
[tex]x_{1,\:2}=\frac{-1\pm \:7}{2\cdot \:4}\\x_1=\frac{-1+7}{2\cdot \:4},\:x_2=\frac{-1-7}{2\cdot \:4}\\[/tex]
solve for x₁
[tex]\frac{-1+7}{2\cdot \:4}[/tex]
[tex]=\frac{6}{2\cdot \:4}[/tex]
[tex]=\frac{6}{8}[/tex]
[tex]= \frac{6\div2}{8\div2}[/tex]
[tex]=\frac{3}{4}[/tex]
solve for x₂
[tex]\frac{-1-7}{2\cdot \:4}[/tex]
[tex]=\frac{-8}{2\cdot \:4}[/tex]
[tex]=\frac{-8}{8}[/tex]
[tex]=-\frac{8}{8}[/tex]
[tex]=-1[/tex]
Hope this helps!
If f(x) = 3x³ + 5x² + 5, then what is the remainder when f(x) is divided by
x - 4?
By the remainder theorem, the remainder upon dividing a polynomial [tex]p(x)[/tex] by a linear factor [tex]x - c[/tex] is exactly [tex]p(c)[/tex].
Then the remainder upon dividing [tex]f(x)[/tex] by [tex]x - 4[/tex] is
[tex]f(4) = 3\times4^3 + 5\times4^2 + 5 = \boxed{277}[/tex]
how to Solve for x. -1/2 (x + 2) + 1 1/2 x = 3
Julia can sell a certain product for $75 per unit. Total cost consists of a fixed overhead of $4000 plus production costs of $50 per unit. How many units must be sold for Julia to break even?
OK so I don't know why but I enjoy giving away points, so if anyone has the right answer then please put it in, if not please DO NOT put it in, this is for helping others, not for greed.
Lakima has a spinner divided into 5 equal sections that are labeled 1 though 5. She wants to compare the theoretical probability and the experimental probability of spinning an odd number. She spins the spinner 6 times and records the results in this list. {2, 4, 1, 5, 3, 4} Drag and drop the answers into the boxes to correctly complete the sentences. The theoretical probability of spinning an odd number is equal to . The experimental probability of spinning an odd number is equal to Response area. Therefore, the theoretical probability of spinning an odd number is the experimental probability of spinning an odd number.
The theoretical probability of getting an odd number is 0.6, but the experimental probability was 0.5.
What is the theoretical probability?Total of numbers in the spinning wheel: 5Total of odd numbers: 3 (1,3,5)Probability of getting an odd number: 3/5 = 0.6 or 60%
What is the experimental probability?Number of times the wheel was spinned: 6 timesNumber of times she got an odd number: 3 times6 times = 1003 times = xx = 3 x 100/ 6x = 50% or 0.50What can be concluded?The experimental probability is lower than the theoretical probability.
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Answer:
Answer in pic below
Step-by-step explanation: