Answer:
Hi,
Step-by-step explanation:
a)
[tex]if\ \dfrac{x}{2}-3\ > \ 0\ then\ |\dfrac{x}{2}-3|=\dfrac{x}{2}-3\\\\\dfrac{x}{2}-3 > 4\\\\\dfrac{x}{2} > 7\\\\x > 14\\[/tex]
b)
[tex]if\ \dfrac{x}{2}-3\ < \0 \ then\ |\dfrac{x}{2}-3|=-(\dfrac{x}{2}-3)=-\dfrac{x}{2}+3\\\\-\dfrac{x}{2}+3\ > \ 4\\\\-\dfrac{x}{2}\ > \ 4-3\\\\-\dfrac{x}{2}\ > \ 1\\\\\dfrac{x}{2}\ < \ -1\\\\x\ < \ -2\\[/tex]
[tex]S=\{x\in\mathbb{R}\ :\ |\dfrac{x}{2}-3|\ > \ 4\}=(-\infty,-2[\ \cup\ ]14,\infty)\\[/tex]
How can the properties of linear pairs and vertical angles help to determine the angle measures created by the intersecting lines? Explain.
Step-by-step explanation:
in a management information system, the quality of information is determined by its usefulness to users, and its usefulness determines the success of the information system.
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?
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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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!
the radius of a circle measures 7 inches. a central angle of the circle measuring 4pi/15 radians cuts off a sector. what is the area of the sector? Enter your answer as simplified fraction in the box.
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=7\\ \theta =\frac{4\pi }{15} \end{cases}\implies A=\cfrac{ ~~ \frac{4\pi }{15}(7)^2}{2}\implies A=\cfrac{98\pi }{15}[/tex]
√-11
please solve this perblom
Answer:
3.31662479
Step-by-step explanation:
3.31662479
The Yasuda family bought a toy that cost t dollars and a game that cost g dollars. Both were on sale. Which of these methods could the clerk use to calculate their total bill?
The equation that the clerk can use to calculate their total bill is t + g.
How to illustrate the equation?From the information given, Yasuda family bought a toy that cost t dollars and a game that cost g dollars.
The equation to calculate their total bills will be:
= t + g
where,
t = cost of toy
g = cost of game.
In this case, the equation that the clerk can use to calculate their total bill is t + g .
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Urgent help……………………:::::::::::
Answer:
The percentage of people enjoy New years Eve only = 3%
Step-by-step explanation:
The data indicates, The percentage of people enjoy New years Eve = 28%
The percentage of people enjoy New years Eve and Memorial Day = 12%
The percentage of people enjoy New years Eve and Forth of July = 18%
The percentage of people enjoy Enjoy all the three = 5%
The percentage of people enjoy New years Eve only
= The percentage of people enjoy New years Eve
- The percentage of people enjoy New years Eve and Memorial Day
- The percentage of people enjoy New years Eve and Forth of July
+ The percentage of people enjoy Enjoy all the three
= 28% - 12% - 18% + 5%
= 3%
The average profit on each car sold was $2430, correct to the nearest $10. Calculate the lower bound for the total profit. Write down the exact answer.
The lower bound for the profit is $2425.
What is the lower bound?When a number of rounded off to the nearest $10, it means that the value of the number in the units place, if greater than 5 becomes zero and one is added to the $10 number. If the number is less than 5, there is no change in the $10 number and the units number becomes 0
The possible values of the average profit are 2425, 2426, 2427, 2428, 2429, 2430. 2431. 2432, 2433, 2434
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The weights of steers in a herd are distributed normally. The standard deviation is 200lbs and the mean steer weight is 900lbs. Find the probability that the weight of a randomly selected steer is between 1220 and 1320lbs. Round your answer to four decimal places.
Answer:
0.0369
Step-by-step explanation:
normalcdf (1220,1320,900,200) is 0.0369
How many right angles are formed by two perpendicular lines in Euclidean geometry?
A.
3
B.
8
C.
4
D.
1
Answer:
Option c 4
Step-by-step explanation:
[tex]-6 + 3x - 9x^{2}=-16[/tex]
The solution of x in -6 + 3x - 9x^2 = -16 is [tex]x = \frac{3 \pm \sqrt{369}}{18}[/tex]
How to solve the equation?The equation is given as:
-6 + 3x - 9x^2 = -16
Add 16 to both sides
10 + 3x - 9x^2 = 0
Rewrite as:
9x^2 - 3x - 10 = 0
Solve for x using the quadratic formula
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
So, we have:
[tex]x = \frac{3 \pm \sqrt{(-3)^2 - 4 * 9 * -10}}{2 * 9}[/tex]
Evaluate
[tex]x = \frac{3 \pm \sqrt{369}}{18}[/tex]
Hence, the solution of x in -6 + 3x - 9x^2 = -16 is [tex]x = \frac{3 \pm \sqrt{369}}{18}[/tex]
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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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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
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
help..and give the right reasons and statement
The triangles ΔAED and ΔCGF are similar to each other. Then angle ∠A is congruent to angle ∠C.
What is the SAS similarity theorem?ΔABC is similar to ΔDEF only if the ratio of two sides of ΔABC and the corresponding two sides of ΔDEF is equal and the angle included on both sides are congruent.
Suppose the two sides of ΔABC are AB and BC, and that of DEF is DE and EF, then for SAS similarity, we need
and
∠ABC = ∠DEF
In triangles ΔAED and ΔCGF,
AE = CF
AD = CG
∠E = ∠G = 90°
Then the triangles ΔAED and ΔCGF are similar to each other. Then angle ∠A is congruent to angle ∠C.
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please help will mark brainliest
Answer:
[tex]k > 3~~~\text{or}~~ k < -5[/tex]
Step-by-step explanation:
[tex]~~~~~|3k+3| > 12\\\\\implies 3k+3 < -12~~~~~~\text{or}~~~~~~~~~~3k+3 > 12\\\\\implies 3k < -12-3~~~~~~\text{or}~~~~~~~~~~3k > 12-3\\\\\implies 3k < -15~~~~~~~~~~~\text{or}~~~~~~~~~~3k > 9\\\\\implies k < -\dfrac{15}3~~~~~~~~~~~~\text{or}~~~~~~~~~~k > \dfrac 93\\\\\implies k < -5~~~~~~~~~~~~~~\text{or}~~~~~~~~~~k > 3[/tex]
The graph of the parent function y = x cubed is horizontally stretched by a factor of One-fifth and reflected over the y-axis. What is the equation of the transformed function?
y = (5 x) cubed
y = (negative 5 x) cubed
y = (one-fifth x) cubed
y = (negative one-fifth x) cubed
The equation of the transformed version of the function y = x³ when the transformation is horizontal stretch by a factor of 1/5, is y = (5x)³.
How does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:
Here, Horizontal shift (also called phase shift):
Left shift by c units: y = f(x + c)
Right shift by c units: y = f(x - c)
For this case, we're specified that:
Original function: y = x³
Transformation: horizontal stretch by a factor of 1/5
Assuming the horizontal axis is having input variable x, and vertical axis having output variable y = x³, and the fact that a function y = f(x) if is horizontally stretched by a factor k, becomes y = f(x/k) , we have:
y = f(x)
y = x³
y = f (5x)
y = (5x)³
Thus, The equation of the transformed version of the function y = x³ when the transformation is horizontal stretch by a factor of 1/5, is y = (5x)³.
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Answer: It's D
Step-by-step explanation:
y = [-1/5x]^3 on edge
-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]
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]
what is the percent increase of 42 from 30?
Answer:
40%
Step-by-step explanation:
your answer is *dun dun dun*
30 + 40% = 42
I need some more text apparently so that drumroll at the top and this will hopefully suffice
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
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
A distribution has the five-number summary shown below. What is the
interquartile range (IQ) of this distribution?
Answer:
tiookvgvc. jbjvth kivtcth jjvf h. bkbgv
Answer:
The IQR of the given distribution is
Step-by-step explanation:
The given distribution has the five-number
28, 34, 43, 59, 62
Divide these numbers in two equal parts.
(28, 34), 43,( 59, 62)
Now divide each parenthesis in two equal parts.
(28), (34), 43,( 59), (62)
It means first quartile is the average of 28 and 34. Third quartile is the average of 59 and 62.
The interquartile range (IQR) of this distribution is
Therefore the IQR of the given distribution is 29.5.
evalute the expression (64)1\2
Answer:
32
Step-by-step explanation:
64×1÷2
64is divided by 2 =32
and 32×1=32
how to Solve for x. -1/2 (x + 2) + 1 1/2 x = 3
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]What is the missing term?
+1 4x -3
3x 12x²?
4x - 3
Answer:
83
Step-by-step explanation:
41 plus 36 plus 36 is 83 is the answer for me
The diameter of a semicircle is 8 kilometres. What is the semicircle's perimeter?
Answer:
4pi + 8 km
Step-by-step explanation:
the circumference of teh circle is d*pi = 8pi. since this is a semicircle the circumference is 4pi. then the perimeter is 4pi + 8