Answers
Answer:
Step-by-step explanation:
The given equation is expressed as
(x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12
Simplifying the right hand side of the equation, it becomes
[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)
x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)
(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)
4x/(x - 1)(x + 1)
Therefore,
4x/(x - 1)(x + 1) = 7/12
Cross multiplying, it becomes
4x × 12 = 7(x - 1)(x + 1)
48x = 7(x² + x - x - 1)
48x = 7x² - 7
7x² - 48x - 7 = 0
Applying the quadratic formula,
x = - b ± √(b² - 4ac)]/2a
from our equation,
b = - 48
a = 7
c = - 7
Therefore
x = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)
x = [48 ± √(2304 + 196]/14
x = (48 ± √2500)/14
x = (48 ± 50)/14
x = (48 + 50)/14 or x = (48 - 50)/14
x = 98/14 or x = - 2/14
x = 7 or x = - 1/7
Answer: The given equation is expressed as (x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12Simplifying the right hand side of the equation, it becomes[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)4x/(x - 1)(x + 1)Therefore, 4x/(x - 1)(x + 1) = 7/12Cross multiplying, it becomes4x × 12 = 7(x - 1)(x + 1)48x = 7(x² + x - x - 1)48x = 7x² - 77x² - 48x - 7 = 0Applying the quadratic formula,x = - b ± √(b² - 4ac)]/2a from our equation, b = - 48a = 7c = - 7Thereforex = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)x = [48 ± √(2304 + 196]/14x = (48 ± √2500)/14x = (48 ± 50)/14x = (48 + 50)/14 or x = (48 - 50)/14x = 98/14 or x = - 2/14x = 7 or x = - 1/7
Step-by-step explanation:
Related Questions
Expand And Simplify
2(3a - 2b) + b
Answers
Answer:
the expansion is 6a-4b+b
the simplification is 6a-3b
Answer:Hey there...
Step-by-step explanation: 2(3a - 2b) + b
Apply Distributive property
(2*3a - 2*2b) + b
( 6a - 4b) + b
2b + b
= 3b
Hope this helps :)
The following set of ordered pairs represents a power inverse variation. Find the value of r given that k = 5.
Answers
Answer:
r=2
Step-by-step explanation:
y = k x^r is the formula for a direct variation
y = k x^ -r is the formula for a indirect variation
20= 5 (1/2)^ -r
Divide each side by 5
4 = (1/2) ^ -r
Rewriting
2^2 = 2^ -1 ^ -r
2^2 = 2 ^ r
The bases are the same so
2 =r
Answer:
r=-2
Step-by-step explanation:
because i had this questiion and i got it right
Ben and his three sisters are competing to see who gets home first from their grandmother's
house. There are four different routes from her house back to their home in Garland. Ben
chooses Route 1. What are the possible outcomes of the routes taken by the family if Ben
chooses first? Label that set S.
Answers
Answer: {Route2, Route3, Route4} (Total 3 outcomes)
Step-by-step explanation:
Given: There are 4 different routes from Ben's house back to their home in Garland.
Let Sample space for all outcomes: {Route1, Route2, Route3, Route4 }
Ben chooses Route 1.
The possible outcomes of the routes taken by the family if Ben chooses first:
{Route2, Route3, Route4}
Hence, the possible outcomes of the routes taken by the family if Ben chooses first: {Route2, Route3, Route4} (Total 3 choices)
Rosa earns $12 per hour. In 7.5 hours, she will earn x dollars. Which is a valid proportion that can be used to solve the problem? StartFraction x over 12 EndFraction = StartFraction 1 over 7.5 EndFraction StartFraction 1 over 12 EndFraction = StartFraction x over 7.5 EndFraction StartFraction 12 over 1 EndFraction = StartFraction x over 7.5 EndFraction StartFraction 12 over 1 EndFraction = StartFraction 7.5 over x EndFraction
Answers
Answer:
StartFraction x over 7.5 EndFraction = StartFraction 12 over 1 EndFraction
Step-by-step explanation:
Here, in this question, given that Rosa earns $12 in an hour, she earns x dollars in 7.5 hours. So we are interested in finding the value of x.
Let’s write this in terms of proportion;
$12 = 1 hour
$x = 7.5 hours
$12 * 7.5 hours = $x * 1 hour
So this can be rewritten as;
$x/7.5 = $12/1 hour
Answer: Start Fraction x over 7.5 End Fraction Start Fraction 12 over 1
explanation:
Help me please I need answers
Answers
Answer:
The solution of the system of equations are;
(-2, -6) and (4, 6)
Step-by-step explanation:
-2·x + y = -2...............(1)
[tex]y = -\dfrac{1}{2} \cdot x^2 + 3 \cdot x + 2[/tex]........(2)
Equation (1) gives;
y = 2·x - 2
From which we have;
[tex]2 \cdot x - 2 = -\dfrac{1}{2} \cdot x^2 + 3 \cdot x + 2[/tex]
[tex]0= -\dfrac{1}{2} \cdot x^2 + x + 4[/tex]
x² -2·x -8 = 0
(x - 4)·(x + 2) = 0
x = 4 or x = -2
The y-coordinate values are;
y = 2×(-2) - 2 = -6 and y = 2×(4) - 2 = 6
The solution points are;
(-2, -6) and (4, 6).
The points where the equation, -2·x + y = -2 and the equation [tex]y = -\dfrac{1}{2} \cdot x^2 + 3 \cdot x + 2[/tex] intersect are (-2, -6) and (4, 6).
What is the center of the circle with the equation (x+4)^2 + (y - 2)^2 = 16? a (-4, -2) b (4,2) c (-4, 2) d (4, -2)
Answers
Answer:
C) (-4, 2)
Step-by-step explanation:
Answer:
The center is ( -4,2) and the radius is 4
Step-by-step explanation:
The equation of a circle can be written as
( x-h) ^2 + ( y-k) ^2 = r^2 where ( h,k) is the center and r is the radius
(x+4)^2 + (y - 2)^2 = 16
(x- -4)^2 + (y - 2)^2 = 4^2
The center is ( -4,2) and the radius is 4
Given: Quadrilateral PQRS is isosceles trapezoid
If S=120, Q=?
30
60
120
Answers
Answer:
60
Step-by-step explanation:
60. answer degree 60120+60=180degreeThe measurement of the angle Q will be equal to 60°.
What is a isosceles trapezoid?An isosceles trapezoid is a convex quadrilateral with one pair of opposite sides bisected by a line of symmetry. It is a subset of the trapezoid. It can also be defined as a trapezoid with equal lengths for both legs and base angles.
Given that the angle S= 120. The measure of the angle Q will be calculated as:-
∠Q = ∠R = 120°
The pair of the two angles with the two parallel lines are supplementary.
∠R + ∠Q = 180
120 + ∠Q = 180
∠Q = 180 - 120 = 60
To know more about isosceles trapezoid follow
https://brainly.com/question/10644521
#SPJ5
The number of vertices a triangle has
3
6
4
5
Answers
At the beginning of year 1, Zack invests $700 at an annual compound interest
rate of 3%. He makes no deposits to or withdrawals from the account.
Which explicit formula can be used to find the account's balance at the beginning of year 5? What is the balance?
A. A(n) = 700 + (n - 1)(0.03 • 700); $784.00
B. A(n) = 700 + (0.003 • 700)^(n - 1); $719.45
C. A(n) = 700 • (1 + 0.03)^(n - 1); $787.86
D. A(n) = 700 • (1 + 0.03)^n; $811.49
Answers
Answer:
The answer is option C
The balance will be C. A(n) = 700 • (1 + 0.03)^(n - 1); $787.86.
How to calculate the compound interest amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest,
then the interest amount earned is given by:
[tex]CI = P\left(1 +\dfrac{R}{100}\right)^T - P[/tex]
The final amount becomes:
[tex]A = CI + P\\A = P\left(1 +\dfrac{R}{100}\right)^T[/tex]
The formula will become
A (n) = 700 • (1 + 0.03)^(n – 1)
Where n = 5 years
A (5) = 700 • (1 + 0.03)^(5 – 1)
A (5) = 700 • (1 + 0.03)^(4)
Thus, the account balance at the beginning of 5 years or at the end of 4 years;
A (5)=700×(1+0.03)^(4)
A (5)=787.8
Hence, The answer is C. A(n) = 700 • (1 + 0.03)^(n - 1); $787.86.
Learn more about compound interest here:
https://brainly.com/question/11897800
#SPJ2
Triangle RST was dilated with the origin as the center of dilation to create triangle R'S'T'. The triangle was dilated using a scale factor of 34. The coordinates of the vertices of triangle RST are given. You can use the scale factor to find the coordinates of the dilated image. Enter the coordinates of the vertices of triangle R'S'T' below. (Decimal values may be used.)
Answers
Answer:
Multiply every coordinate from the old one by 0.75
Step-by-step explanation:
I just did this question so I didn't need your photo. And I got it right. Hope this helps anyone else stuck on a similar question.
The rule is to multiply the old coordinates/sides by the scale factor, if its a fraction convert it to a decimal and then multiply like I did.
Answer:
x, y ----> 3/4x, 3/4y
Step-by-step explanation:
plz help, will give brainiest
(08.01, 08.02, 08.03 HC)
Create a factorable polynomial with a GCF of 3x. Rewrite that polynomial in two other equivalent forms. Explain how each form was created. (10 points)
Answers
Answer:
4x^2 + 8x + 4
4(x^2 + 2x + 1) - remove GCF of 4
4(x + 1)(x + 1) - factor
4(x + 1)^2 - collect like terms
Step-by-step explanation:
Then also expand it out by distributing:
21x^3 + 35x²
Form 1:
21x^3 + 35x² - unfactored
Form 2:
7x²(3x + 5) - factored with GCF of 7x² brought to the front
Update:
You could also multiply two binomials and make a quadratic.
Example:
(7x + 2)(3x + 5)
7x(3x + 5) + 2(3x + 5)
= 21x² + 35x + 6x + 10
= 21x² + 41x + 10
The favorable polynomial with a GCF of 3x will be 21x² + 41x + 10.
What is a polynomial?
A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
The polynomial will be solved as below:-
21x³ + 35x²
Form 1:
21x³ + 35x² - unfactored
Form 2:
7x²(3x + 5) - factored with GCF of 7x² brought to the front
You could also multiply two binomials and make a quadratic.
E = (7x + 2)(3x + 5)
E = 7x(3x + 5) + 2(3x + 5)
E = 21x² + 35x + 6x + 10
E = 21x² + 41x + 10
To know more about polynomials follow
brainly.com/question/2833285
#SPJ2
Cómo representa un diagrama de barras en una tabla de frecuencias
Answers
Answer:
Es lo mismo, la unica diferencia es que se ve differente. La tabla de frecuencia tiene dos lados igual a la de la tabla de barras.
Hi, I don't know how to do these, if you could help me answer them, that would be great
Answers
Answer:
137°Step-by-step explanation:
From the diagram, mAD lies on the line BDF. Sum of angle on a straight line is 180°. According to the line BDF; mAB + mAD = 180°
From the diagram, mAB = 43°. Substituting this value into the above equation;
mAB + mAD = 180°
43° + mAD = 180°
mAD = 180°-43°
mAD = 137°
Hence, the measure of angle mAD is 137°
2. The diagram shows a playground which is a combination
of three different shapes. TSVU is a square, SRQV is a
trapezium and PQVU is a parallelogram. Calculate the
total area of the playground.
Answers
Answer:
The diagram shows a playground which is a combination
of three different shapes. TSVU is a square, SRQV is a
trapezium and PQVU is a parallelogram. Calculate the
total area of the playground
Solve : √x+5 + √x = 15÷√x+5
Ans : 4
Answers
Answer:
x = 4
Step-by-step explanation:
The equation given is a radical equation, we will solve using the steps below:
√x+5 + √x = 15÷√x+5
√x+5 + √x = [tex]\frac{15}{\sqrt{x+5} }[/tex]
Multiply both-side of the equation by [tex]\sqrt{x+5}[/tex]
[tex]\sqrt{x+5}[/tex](√x+5 + √x) = [tex]\frac{15}{\sqrt{x+5} }[/tex] × [tex]\sqrt{x+5}[/tex] ----------------------------------(2)
Note
[tex]\sqrt{x+5}[/tex] × [tex]\sqrt{x+5}[/tex] = x +5
Also at the right-hand side of the equation [tex]\sqrt{x+5}[/tex] cancel-out [tex]\sqrt{x+5}[/tex] leaving us with just 15
so equation(2) becomes
x+5 +√x [tex]\sqrt{x+5}[/tex] = 15
subtract 5 from both-side of the equation
x+5-5 +√x [tex]\sqrt{x+5}[/tex] = 15-5
x +√x [tex]\sqrt{x+5}[/tex] = 10
subtract x from both-side of the equation
x-x +√x [tex]\sqrt{x+5}[/tex] = 10-x
√x [tex]\sqrt{x+5}[/tex] = 10-x
square both-side of the equation
(√x [tex]\sqrt{x+5}[/tex]) ² = ( 10-x)²
x (x+ 5) = ( 10-x)(10-x)
open the bracket
x² + 5x = 100 - 20x + x²
subtract x² from both-side of the equation
x² - x² + 5x = 100 - 20x + x² - x²
5x = 100 - 20x
collect like term
5x + 20x = 100
25x = 100
divide both-side of the equation by 25
25x/25 = 100 /25
x = 4
A ladder leaning against a wall makes a 35° angle with the ground. The foot of the ladder is 5 meters from the wall. What is the length of ladder?
Answers
Greetings from Brasil...
Using Cossine we will get the length L of ladder
COS 35 = 5/L
L = 6,1HELP PLS
A wine store conducted a study. It showed that a customer does not tend to buy more or fewer bottles when more samples are offered. What can we conclude?
>There is no correlation between number of bottles bought and number of samples offered.
>There is a correlation between number of bottles bought and number of samples offered. However, there is no causation. This is because there is probably an increase in the number of bottles bought with an increase in the number of samples offered.
>There is a correlation between number of bottles bought and number of samples offered. There may or may not be causation. Further studies would have to be done to determine this.
Answers
A group of dragons and sheep are randomly divided into 2 equal rows. Each animal in one row is directly opposite an animal in the other row. If 75 of the animals are dragons, and the number of sheep opposite sheep is 10 more than the number of dragons opposite dragons, find the total number of animals in the group.
Answers
Answer:
Total number of animals in the group = 170
Step-by-step explanation:
Let the number of sheep = a
Number of dragons in the group = 75
Number of dragons opposite dragons = 37
Number of sheep opposite to the dragon = 1
Number of sheep left = a - 1
Number of sheep opposite to sheep = [tex]\frac{(a-1)}{2}[/tex]
Since. number of sheep opposite to sheep is 10 more than of dragons opposite dragons,
[tex]\frac{(a-1)}{2}[/tex] = 37 + 10
[tex]\frac{(a-1)}{2}=47[/tex]
a - 1 = 94
a = 95
Then total number of animals in the group = Total number of sheep + Total number of dragons
= 95 + 75
= 170
Therefore, total number of animals in the group are 170.
what is angle and how would you know
Answers
Answer:
Angle:
When two lines/rays intersect at a point, they form an angle.
=> Angles may be in radians and degrees.
See the attached file in which two rays intersect to form an angle.
Answer:
[tex]\boxed{\mathrm{view \: explanation \: and \: attachment}}[/tex]
Step-by-step explanation:
Two lines (arms/rays) intersect at one point (vertex) creating an angle.
What is x when f(x) = 16
Answers
Answer:
A
Step-by-step explanation:
[tex]f(x) = y[/tex] (output)
[tex]y = 16\\y = 2^x\\2^x = 16\\2^x = 2^4\\x = 4[/tex]
x = number of rounds
y = number of points
In the 4th round, 16 points will be rewarded.
The value of the function at x = 4 will be 16. Then the correct option is A.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The exponent is given as
y = a(b)ˣ
The exponent function is given below.
f(x) = 2ˣ
Then the value of the variable x when the value of the function is 16.
f(x) = 16
2ˣ = 16
2ˣ = 2⁴
x = 4
The value of the function at x = 4 will be 16. Then the correct option is A.
More about the exponent link is given below.
https://brainly.com/question/5497425
#SPJ2
Which best explains why the orthocenter of an obtuse triangle is outside the triangle?
Answers
Answer: All three of the altitudes lie entirely outside the triangle.
Step-by-step explanation:
The orthocenter is the center of the triangle formed by creating all the altitudes of each side.
The altitude of a triangle is formed by creating a line from each vertex that is perpendicular to the opposite side.
In acute traingle , the orthocenter lies inside it.
In right angled triangle, the orthocenter lies on the triangle.
In obtuse triangle , the orthocenter lies outside the triangle because all the three altitudes meet outside .
So, the best explains why the orthocenter of an obtuse triangle is outside the triangle : All three of the altitudes lie entirely outside the triangle.
Answer: It’s A on edge
Solve for x in the diagram below.
Answers
Answer:
x=20
Step-by-step explanation:
3x + 2x + 80=180
5x+80=180
5x=100
x=20
Answer:
x = 20 degrees
Step-by-step explanation:
For this problem, it is important to know that the measure of a line is 180 degrees. With this in mind, let's build an equation:
3x + 80 + 2x = 180
Now that we have this equation, let's solve for x.
3x + 80 + 2x = 180
5x + 80 = 180
5x = 100
x = 20
Hence, x is 20 degrees.
Cheers.
16. Jessica was given the area and the length of the base of a triangle. A = 17.5 units, b = 5 units. She solved the formula for area for h to find the height of the triangle. Determine if Jessica solved the equation correctly and found the correct answer. If not, describe what mistake she made and solve the formula for h correctly and justify your steps.
A = 1/2bh
1/2A • b = h
1/2 (17.5)(5) = h
43.75 = h
The height of the triangle is 43.75 units.
Answers
Answer:
h = 7 units
Step-by-step explanation:
Jessica made an error with the [tex]\frac{1}{2}[/tex] in that she multiplied A by it instead of dividing.
Given
A = [tex]\frac{1}{2}[/tex] bh
with A = 17.5 and b = 5, then
17.5 = [tex]\frac{1}{2}[/tex] × h × 5 ( multiply both sides by 2 to clear the fraction )
35 = 5h ( divide both sides by 5 )
h = 7
it is wrong .
Jessica's mistake:
A = 1/2bh
1/2A • b = h >she should multiply the area with 2 not 1/2 and divide the area by b rather than multiply by b
1/2 (17.5)(5) = h
43.75 = h
correct answer:
A = 1/2bh
2A/b=h
h=2(17.5)/5
h=7
Starting at sea level, a submarine descended at a constant rate to a depth of −5/6 mile relative to sea level in 4 minutes. What was the submarine's depth relative to sea level after the first minute? Answer with a fraction :3
Answers
Answer:
-5/24 miles
Step-by-step explanation:
The submarine descends at a rate of -5/6 miles every 4 minutes.
To find the depth of the submarine relative to sea level after the first minute, we have to multiply the rate of descent by he time spent (1 minute). That is:
[tex]\frac{\frac{-5}{6} }{4} * 1[/tex]
=> D = -5 / (6 * 4) = -5/24 miles
Therefore, the submarine's depth is -5/24 miles.
Answer:
-1 1/5
Step-by-step explanation:
I took the test and this was the correct answer :D
please hellppp ......
Answers
Answer:
BC = 11.9Step-by-step explanation:
To solve for BC we use sine
sin ∅ = opposite / hypotenuse
From the question
AC is the hypotenuse
BC is the opposite
So we have
sin 58 = BC / AC
sin 58 = BC / 14
BC = 14 sin 58
BC = 11.87
BC = 11.9 to one decimal place
Hope this helps you
Answer:
[tex]\boxed{BC = 11.9 \ cm}[/tex]
Step-by-step explanation:
Sin A = [tex]\frac{opposite}{hypotenuse}[/tex]
Where A = 58°, Opposite = BC and AC = 14 cm
Sin 58 = [tex]\frac{BC}{14}[/tex]
BC = 0.848 * 14
BC = 11.9 cm
How many of the terms in the simplified expression are negative? -3x2 + 2y2 + 5xy - 2y + 5x2 - 3y2
Answers
Step-by-step explanation:
-3x² + 2y² + 5xy -2y + 5x² - 3y²
= -3x² + 5x² +2y² -3y² + 5xy -2y
= 2x² - y² +5xy -2y
2 terms
In the triangle below, Four-fifths represents which ratio?
Answers
Answer:Sin
Step-by-step explanation:
right angled triangle special trig functions can be applied
Simplify the expression 11+2/3(15-21a)
Answers
Answer:
21-14a
Step-by-step explanation:
You have to distribute the (2/3) into the (15-21a) then add it to the 11. So after distributing the (2/3) into the (15-21a) is (10-14a). Then add that to the 11
Answer:
-14a + 21
Step-by-step explanation:
11 + 2/3(15 - 21a)
Expand brackets.
11 + 2/3(15) + 2/3(-21a)
11 + 30/3 + -42/3a
Evaluate.
11 + 10 + - 14a
21 + - 14a
please help me with this
Answers
Answer:
see explanation
Step-by-step explanation:
2πr (230/360) = 2(3.142)(40) = 160.59 cm = circumference
160.59 = 2πr
base radius = 25.56 cm
Use pythagorean formula for semi-vertical height
40² = h² + 25.56²
h = 30.77 cm
volume = 1/3πr²h
V = 1/3(3.142)(25.56)²(30.77) = 21,053.98 cm³
help me with this I'm stuck I will give you branliest
Answers
Answer:
d = 9
Step-by-step explanation:
Use the slope formula to calculate m and equate to m = 3
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = A(4, 6) and (x₂, y₂ ) = B(d, 21)
m = [tex]\frac{21-6}{d-4}[/tex] = [tex]\frac{15}{d-4}[/tex] = 3 ( multiply both sides by d - 4 )
3(d - 4) = 15 ( divide both sides by 3 )
d - 4 = 5 ( add 4 to both sides )
d = 9