Answers
Answer:
{-1/4, 1}{3/4, 6}Step-by-step explanation:
1. We can clear fractions and solve the resulting quadratic. We clear fractions by multiplying the equation by the product of the denominators.
[tex]\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}=\dfrac{8}{3}\\\\3((2x+1)^2-(2x-1)^2)=8(2x-1)(2x+1)\\\\3(8x) = 8(4x^2 -1)\\\\4x^2 -3x -1 = 0\qquad\text{factor out 8, subtract 3x}\\\\x=\dfrac{-(-3)\pm\sqrt{(-3)^2-4(4)(-1)}}{2(4)}=\dfrac{3\pm\sqrt{25}}{8}\\\\x=\dfrac{3\pm5}{8}=\left\{-\dfrac{1}{4},1\right\}[/tex]
__
2. Using the same idea here, we get ...
[tex]\dfrac{2}{x-2}+\dfrac{3}{x}=\dfrac{9}{x+3}\\\\2(x)(x+3)+3(x-2)(x+3)=9(x-2)(x)\\\\2x^2+6x+3(x^2+x-6)=9x^2-18x\\\\4x^2-27x+18=0\\\\x=\dfrac{-(-27)\pm\sqrt{(-27)^2-4(4)(18)}}{2(4)}=\dfrac{27\pm\sqrt{441}}{8}\\\\x=\dfrac{27\pm21}{8}=\left\{\dfrac{3}{4},6\right\}[/tex]
Related Questions
The athletic club at school sold raffle tickets to raise money for equipment. The club sold a total of 1050 tickets,515 to teachers and 235 tickets to staff. If the winning ticket was picked at random what is the probability of the teacher or other staff member?
Answers
Answer:
Probability of the teacher or other staff is 0.7143
Step-by-step explanation:
pr(teacher or other staff) = pr(teacher) + pr(other staff) - pr(teacher and other staff)
Total number of tickets = 1050
Number of tickets sold to teachers = 515
Number of tickets sold to other staff = 235
pr(teacher) = [tex]\frac{515}{1050}[/tex]
= 103 [tex]\frac{2}{10}[/tex]
= 0.4905
pr(other staff) = [tex]\frac{235}{1050}[/tex]
= 47 [tex]\frac{2}{10}[/tex]
= 0.2238
Since the picking of the wining ticket is mutually exclusive, then;
pr(teacher and other staff) = 0
Thus,
pr(teacher or other staff) = 0.4905 + 0.2238 - 0
= 0.7143
If a watch store paid $125 per watch for a shipment of watches, and sold all but 15 watches from the shipment for $150 per watch, then, in terms of the number of watches in the shipment, y, what function describes the watch store’s profit, P, from the sales?
A) P(y) = 125(y – 15) – 150y
B) P(y) = 15(125 – y) – 150y
C) P(y) = 150(y – 15) – 125y
D) P(y) = 15(150 – y) – 125y
Answers
Answer: C) P(y) = 150(y – 15) – 125y
Step-by-step explanation:
Hi, to answer this question we have to write an equation:
Profit = revenue - cost
Cost: a watch store paid $125 per watch for a shipment of watches
Cost = 125 y
Where y is the number of watches in the shipment
Revenue: sold all but 15 watches from the shipment for $150 per watch
Revenue = 150(y-15)
Profit(y) = 150(y – 15) – 125y
So, the correct option is:
C) P(y) = 150(y – 15) – 125y
Feel free to ask for more if needed or if you did not understand something.
Find the center and radius of x^2 – 18x + y^2 -10y = -6. part two write x2 – 18x + y2 -10y = -6 in standard form
Answers
Answer:
see explanation
Step-by-step explanation:
I will begin with part two, first.
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius.
Given
x² - 18x + y² - 10y = - 6
Using the method of completing the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(- 9)x + 81 + y² + 2(- 5)y + 25 = - 6 + 81 + 25, that is
(x - 9)² + (y - 5)² = 100 ← in standard form
with centre = (9, 5 ) and r = [tex]\sqrt{100}[/tex] = 10
A group conducted a poll of 2022
likely voters just prior to an election. The results of the survey indicated that candidate A would receive 49
%
of the popular vote and candidate B would receive 46
%
of the popular vote. The margin of error was reported to be 5
%.
The group reported that the race was too close to call. Use the concept of a confidence interval to explain what this means.
Answers
Answer:
Step-by-step explanation:
number of likely voters = 2022
candidate A = 49%
candidate B = 46%
margin of error = 5%
using the concept of a confidence interval to explain
from the result of the poll conducted candidate A scored 49% of the votes while Candidate B scored 46% therefore the difference between the two voters is 3%.
also the margin of error is 5% which is higher than the 3% difference between the candidates. this margin error means that the 5% can vote for either candidate A or candidate B .which makes the results TOO CLOSE TO CALL
Chapter 8 Written Homework 1. A hypothesis test is conducted to test the claim that the proportion of people with dark hair at Moorpark is greater than 0.8. The researchers find that the test statistic is z = 2.19. a. Using ???? = 0.05, draw a bell-shaped curve to represent the critical value approach. Be sure to label (This means find and label the critical value as well as the rejection and fail to reject regions). b. Based on your drawing would we reject of fail to reject? Explain.
Answers
Answer:
we reject H₀
Step-by-step explanation: Se annex
The test is one tail-test (greater than)
Using α = 0,05 (critical value ) from z- table we get
z(c) = 1,64
And Test hypothesis is:
H₀ Null hypothesis μ = μ₀
Hₐ Alternate hypothesis μ > μ₀
Which we need to compare with z(s) = 2,19 (from problem statement)
The annex shows z(c), z(s), rejection and acceptance regions, and as we can see z(s) > z(c) and it is in the rejection region
So base on our drawing we will reject H₀
Suppose you are interested in testing wheter the mean earning of men in the general social survey is representative of the earning of the entire U.S. Male population. If there are 372 men in the general social survey sample and approximately 128 million men in the population, calculate the degrees of freedom for this single-sample t test.
Answers
Answer:
371
Step-by-step explanation:
According to the given situation the calculation of degrees of freedom for this single-sample t test is shown below:-
Degrees of freedom is N - 1
Where N represents the number of Men
Now we will put the values into the above formula.
= 372 - 1
= 371
Therefore for calculating the degree of freedom we simply applied the above formula.
Write 4x2 + 16x - 9 in vertex form. Write 5x2 - 10x + 4 in vertex form.
Answers
Hi king,
Write [tex]4x^{2} + 16x - 9[/tex] in vertex form:
f(x)=[tex]4x^{2} + 16x - 9[/tex]
f(x)=[tex]4(x+2)^{2} -25[/tex]
Write [tex]5x^{2} - 10x + 4[/tex] in vertex form:
g(x)=[tex]5x^{2} - 10x + 4[/tex]
g(x)=[tex]5(x-1)^{2} -1[/tex]
Have a great day.
Look at picture to see question
Answers
What is m∠A? please help
Answers
Answer: 50 degrees
Step-by-step explanation:
180-85=95
180-145=35
interior angle sum for a triangle is 180 degrees, so 180=95+35+a
m of angle A is 50 degrees
. What is the solution set for
|k - 6|+17 = 30
A. (-19, 7}
B. (-7, 19)
C. (-19, 19)
D. {-41, 19)
Answers
Answer:
Hope this is correct and helpful
HAVE A GOOD DAY!
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(2,−3) B(4,−3) C(4,5) D(2,5) What is the perimeter of rectangle ABCD? please answer URGENT! :)
Answers
Answer:
21 unit square
Step-by-step explanation:
First you want to find the length and width of the rectangle using the distance formula:
d=√(x2-x1)²+(y2-y1)²
AB=√(6-3)²+ (-2 - -2)²
AB=√3² + 0
AB=√9
AB=3
BC=√(6-6)²+ (5 - -2)²
BC=√0 + 7²
BC=√49
BC=7
We can find the area by multiplying these two distances together:
A=(3)(7)
A=21 units square.
Hope it helped...... And plz mark BRAINLIEST
Tysm
A. 60
B. 15
C. 120
D. 6
Answers
Answer:
C. 120
Step-by-step explanation:
The figure shows that angles BEC and KEC are congruent. Their measures are equal.
m<KEC = m<BEC
10x = 6x + 24
4x = 24
x = 6
m<BEK = 2m<KEC
m<BEK = 2 * 10x
m<BEK = 2 * (10)(6)
m<BEK = 2 * 60
m<BEK = 120
Solve the inequality 47.75 + x Less-than-or-equal-to 50 to determine how much more weight can be added to Li’s suitcase without going over the 50-pound limit. What is the solution set?
x Less-than-or-equal-to 2.25
x Less-than-or-equal-to 2.75
x Greater-than-or-equal-to 2.25
x Greater-than-or-equal-to 2.75
Answers
Answer: x Less-than-or-equal-to 2.25
Step-by-step explanation:
The given inequality: 47.75 + x Less-than-or-equal-to 50.
To determine: How much more weight can be added to Li’s suitcase without going over the 50-pound limit.
i.e. inequality for x.
[tex]47.75+x\leq50[/tex]
Subtract 47.75 from both the sides, we get
[tex]x\leq50-47.75\\\\\Rightarrow\ x\leq2.25[/tex]
So, the solution set is "x Less-than-or-equal-to 2.25"
Hence, the correct answer is "x Less-than-or-equal-to 2.25."
Answer
A x <_ 2.25
Step-by-step explanation:
Jan wants to lay sod on this lot. How
much sod does he need?
In sq.ft.
Type in your response.
Answers
Answer:
148.5 sq. ft.
Step-by-step explanation:
Since Jan wants to lay sod on it, Sod required will be equal to area of the lot.
Lot is in trapezium shape
area of trapezium is given by = 1/2(sum of parallel sides) height
parallel sides has length 15 and 18 feet
sum of parallel sides = (15+18) = 33
height = 9 feet
thus area of lot = 1/2(33)9 = 148.5
Thus, Jan will need 148.5 sq. ft of sod.
Marta is solving the equation x2+x=3 by completing the square what number should be added to both sides of the equation to complete the square?
Answers
Answer:
C = 1/4
Step-by-step explanation:
When solving a quadratic equation, there are steps to follow and I'll highlight them here.
Assuming we have an equation
ax² + bx + c = 0
Step 1
If a is not equal to 1, divide all through by a
x² + bx + c = 0
Take c to the other side of the equation
x² + bx = c
Step 2
Add (b/2)² to both sides of the equation
x² + bx + (b/2)² = c + (b/2)²
In our original question,
We had x² + x = 3
a = 1 , b = 1 c = 3
Using step two, we would have
(b / 2)² = (½)² = ¼ (which is the answer)
Now back to the steps
Step 3
We factor our left side of the equation so as to have a perfect square
[x + (b/2)]² = c + (b/2)²
Step 4
Take the square root of both sides of the equation and solve for x
x + b/2 = ±√[c + (b/2)²]
The answer to the question is ¼
Answer:
1/4
Step-by-step explanation:
The biomass B(t) of a fishery is the total mass of the members of the fish population at time t. It is the product of the number of individuals N(t) in the population and the average mass M(t) of a fish at time t. In the case of guppies, breeding occurs continually. Suppose that at time t = 5 weeks the population is 824 guppies and is growing at a rate of 50 guppies per week, while the average mass is 1.3 g and is increasing at a rate of 0.14 g/week. At what rate is the biomass increasing when t = 5? (Round your answer to one decimal place.) B'(5) = g/week
Answers
Answer:
The rate at which the biomass is increasing when t = 5 is 180.36 g/week
Step-by-step explanation:
Given that :
t = 5 weeks
Population N(t) = 824 guppies
Growth Rate [tex]\dfrac{dN(t)}{dt}= 50 \ guppies /week[/tex]
average mass M(t) = 1.3 g
increase rate of biomass [tex]\dfrac{dM (t)}{t}[/tex]= 0.14 g/week
Therefore; the rate at which the biomass is increasing when t = 5 is:
[tex]\dfrac{dB(t)}{dt}= M(t) * \dfrac{dN(t)}{dt}+ N(t)* \dfrac{dM (t)}{t}[/tex]
[tex]\dfrac{dB(t)}{dt}=1.3 * 50+ 824* 0.14[/tex]
[tex]\dfrac{dB(t)}{dt}=65+115.36[/tex]
[tex]\mathbf{\dfrac{dB(t)}{dt}=180.36 \ g/week}[/tex]
The rate at which the biomass is increasing when t = 5 is 180.36 g/week
The rate at which the biomass is increasing when t = 5 is 180.36 g/week
Calculation of the rate:Since time = 5 weeks, Population N(t) = 824 guppies, and growth rate = 50 guppies / week, average mass = 1.3g, and the increase rate of biomass is 0.14g/week
So,
[tex]= 1.3\times 50 + 824 \times 0.14[/tex]
= 65 + 115.36
= 180.35 g/weel
Learn more about mass here: https://brainly.com/question/3943429
Complete the square to rewrite y = x2 + 8x+ 3 in vertex form, and then identify
the minimum y-value of the function.
Please answer ASAP!!!
Answers
====================================================
Work Shown:
y = x^2 + 8x + 3 is the same as y = 1x^2 + 8x + 3
It is in the form y = ax^2 + bx + c
a = 1
b = 8
c = 3
Plug the values of a and b into the formula below to get the x coordinate of the vertex (h,k)
h = -b/(2a)
h = -8/(2*1)
h = -8/2
h = -4
Plug this into the original equation to get its paired y value. This will get us the value of k
y = x^2 + 8x + 3
y = (-4)^2 + 8(-4) + 3
y = 16 - 32 + 3
y = -13
This is the smallest y output possible. Therefore it is the minimum. The minimum occurs at the vertex (h,k) = (-4, -13)
We know we are dealing with a minimum because a = 1 is positive forming a parabola that opens upward. If a < 0, then the parabola would open downward to yield a maximum.
Find the zeros of y=x^2+4x-9 by completing the square.
Answers
Answer:
[tex]\boxed{x =-2 \±\sqrt{13} }[/tex]
Step-by-step explanation:
Let y = 0
0 = x^2+4x-9
x² + 4x -9 = 0
Add 9 on both sides.
x² + 4x = 9
(b/2)² = (4/2)² = 2² = 4
Add 4 on both sides.
x² + 4x + 4 = 13
Facror left side.
(x+2)² = 13
Take the square root on both sides.
x + 2 = ±√13
Subtract 2 on both sides.
x = ±√13 - 2
Instructions: Find FS if BS=16.
Answers
Answer:
48
Step-by-step explanation:
FB:BS=2:1
[tex]\frac{FB}{BS} =\frac{2}{1} \\add~1~to~both~sides\\\frac{FB}{BS} +1=\frac{2}{1} +1=3\\\frac{FB+BS}{BS} =3\\\frac{FS}{BS} =3\\FS=3 \times~BS\\FS=3 \times~16=48[/tex]
Answer:
48
Step-by-step explanation:
Identify the type of observational study (cross-sectional, retrospective, or prospective) described below. A research company uses a device to record the viewing habits of about 25002500 households, and the data collected todaytoday will be used to determinenbsp the proportion of households tuned to a particular newsnews program.. Which type of observational study is described in the problem statement?
Answers
Answer:
Cross Sectional
Step-by-step explanation:
A cross sectional is one in which an association is developed between a risk factor or an outcome.
In the given question the device is used to record the viewing habits of about 2500 households, and the data collected today will be used to determine the proportion of households tuned to a particular news program. There will be risk factor in today's research with the future developed program which will the outcome.
For example there are 20 students in my class who cannot write. So I develop a program to help them write. But the next year there may not be any student who would require such help.So there's a risk factor associated with the outcome.
Cross sectional results are recorded in a two ways table showing do's and don'ts.
please help :) What is 96,989,200 written in scientific notation? A. 96.9892 × 10 to the 5 power B. 9.69892 × 10 to the 7 power C. 9.69892 × 10 to the 6 power D. 9.69892 × 10 to the 8 power
Answers
Answer: B. 9.69892 × 10^7
You'd have to move the imaginary decimal at the end of the number 96,989,200 seven times in order to get only one number that isn't zero before the decimal point.
Solve the following: (1 point) x + 3y = 9 3x − 3y = −13
Answers
Answer:
Step-by-step explanation:
Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.
Point Form:
(
−
1
,
10
3
)
Equation Form:
x
=
−
1
,
y
=
10
3
Tap to view steps...
image of graph
Tap to hide graph...
La trayectoria de cierto satelitese ajusta ala grafica de la funcionf(x) igual6x al cuadradomenos 12donde x representael tiempo en días y f(x9 el recorrido en kilometroscuantos kilómetros habrá recorridoel sateliteal cabo de diez días desde su lanzamiento
Answers
Answer:
588 kilómetros
Step-by-step explanation:
La función con la que estamos trabajando según la pregunta es;
F (x) = 6x ^ 2 -12
Ahora, la pregunta que simplemente nos hace es encontrar el valor de F (x) dado que x = 10
Entonces, lo simple que hacemos aquí es hacer una sustitución de x = 10 Eso sería;
F (10) = 6 (10) ^ 2 - 12 = 600-12 = 588
from the figure below identify a)Obtuse vertically opposite angles b) A pair of adjacent complementary angles c) a pair of equal supplementary angles d) a pair of unequal supplementary angles e) a pair of adjacent angles that don’t form a linear pair
Answers
Answer:
a) BOC and AOD
b) BOA and AOE
c) BOE and EOD
d) BOA and AOD
e) AOE and EOD
Step-by-step explanation:
An obtuse angle is an angle that has more than 90° and vertically opposite angles are angle formed by two lines crossed. So, Obtuse vertically opposite angles are BOC and AOD
Adjacent angles are angles in which one angle is beside the other and complementary angles are angles whose sum is equal to 90°, so, a pair of adjacent complementary angles are BOA and AOE.
Supplementary angles are angles whose sum is equal to 180°, so BOE and EOD are equal suplementary angles and BOA and AOD are unequal supplementary angles
Finally, AOE and EOD are adjacent angles that don’t form a linear pair.
26. A positive whole number is called stable if at least one of its digits has the same value
as its position in the number. For example, 78247 is stable because a
the 4th position. How many stable 3-digit numbers are there?
appears in
Answers
Answer:
OneStep-by-step explanation:
Given the value 78247 a s a stable number because at least one of its digits has the same value as its position in the number. The 4th number in the value is 4, this makes the number a stable number.
The following are the 3-digits stable numbers that appears in 78247
The first number is 824. This digits are stable numbers because 2 as a number is situated in the same place as the number (2nd position).
Hence, there are only 1 stable 3-digit numbers in the value 78247 since only a value exists as 2 in the value and there is no 1 and 3 in the value.
Please answer the following questions
Answers
Step-by-step explanation:
sorry I can only explain as there are no labels to each diagram
The first diagram is single and can solved using triangular formular given as 1/2 ×base × height
A = 1/2 × 5 × 12
A = 30cm^2..
as for the second one...it consist of 2 diagrams which will be solved separately before adding ...it can simply be done using Pythagoras theorem..
To get the smaller part ...out tita is 45degrees while our adjacent is 4 and opposite is x we are to find x which is the height...
using SOH CAH TOA...
WE HAVE TAN45= opp/adj
Tan45= x/ 4
Tan 45 =1 ...so
1 = x/ 4
and x= 4 ...
so...having our height as 4 and base as 4 ..
Area of smaller triangle become 1/2 × 4 × 4
A = 8cm^2 ...
......SOLVING FOR THE SECOND DIAGRAM ..
WE HAVE the height as ( dotted spot + undotted spot ) = 4 + 4 = 8cm
and our base can be gotten from
Tan45 = opp / adj
1 = 8/x ..
x = 8cm ....so the base is 8 and the height is 8
..
The Area becomes 1/2 × 8×8 = 32cm ...
Total area becomes 32cm + 8cm = 40cm^2
The function graphed models the profits, P(c), in thousands of dollars a store earns as a function of the number of clerks, c, working that day. Which statements are true based on the model?
Answers
Answer:
Options (1), (2) and (5)
Step-by-step explanation:
Outcomes from the quadratic function given in the graph,
1). Negative y-intercept of the graph represents the loss to the store when x = 0 Or the loss when no clerk is working.
2). Peak of the parabola represents a point (vertex) with x-coordinate as number of clerks working = 4 and y-coordinate as maximum profit earned by the store = $400,000
3). x-intercept of the graph shows the number of clerks working at store when profit earned by the store is zero.
Graph reveals that the store is in loss when number of clerks is zero and 8.
Summarizing these outcomes from the graph,
Options (1), (2), (5) are the correct options.
The function graphed models the profits, P(c), in thousands of dollars a store earns as a function of the number of clerks, c, working that day.
Which statements are true based on the model?
Help it’s urgent please
Answers
Answer:
[tex] \frac{5 {x}^{2} + 20xy + 20 {y}^{2} }{x ^{2} - xy - {6y}^{2} } [/tex]
To simplify first factorize both the numerator and the denominator
For the numerator
5x² + 20xy + 20y²
Factor 5 out
5 ( x² + 4xy + 4y²)
Using a² + 2ab + b² = ( a + b)²
The numerator is
5( x + 2y)²
For the denominator
x² - xy - 6y²
Rewrite -xy as a difference
x² + 2xy - 3xy - 6y²
Factorize
We have the denominator as
( x + 2y)( x - 3y)
So we now have
[tex] \frac{5(x + 2y)(x + 2y)}{(x + 2y)(x - 3y)} [/tex]Simplify
[tex] \frac{5(x + 2y)}{x - 3y} [/tex]We have the final answer as
[tex] \frac{5x + 10y}{x - 3y} [/tex]Hope this helps you
A randomized study compared two drugs that
are designed to lower a person's triglyceride
level. It was found that over a 1-year period,
those receiving Drug A decreased their
triglyceride level by a mean of 69. Those
receiving Drug B decreased their triglyceride
level by a mean of 45.
To determine whether the results are significant,
the data are rerandomized and the difference of
the means is shown in the dot plot.
What is the best conclusion to make based on
the data?
Answers
Answer:b
Step-by-step explanation:
2 3/8 ÷ 1 1/4
Steps
19/8 x 4/5
= 19/10
= 1 9/10
So the answer to this is B.
Move the center of the circle horizontally to the left and then to the right of the y-axis. How does the equation of the circle change as the center crosses the y-axis?
Answers
Answer:
The equation of a circle centered in the point (a, b) and with a radius R.
(x - a)^2 + (y - b)^2 = R^2
Then, if you move the circle to the left, then you are decreasing the value of b.
Where b = 0 means that the center of the circle lies on the y-axis.
When you move the graph to the right you will be increasing the value of b.
Answer:
The variable h changes as the center of the circle moves horizontally. The sign of h is negative when the center is to the left of the y-axis and positive when it is to the right of the y-axis. The sign of the variable h flips when the center moves across the y-axis.
Step-by-step explanation:
plato answer from Equation of a Circle: Tutorial :)
This link will take you to a quizlet that is on this lesson with the other answers and test question answers!!
https://quizlet.com/519491317/geometry-b-unit-7-flash-cards/#:~:text=Move%20the%20center%20of%20the%20circle%20vertically%20so%20it%20lies,of%20the%20circle%20moves%20vertically.