Answers
Answer:
[tex]\bold{x=-\dfrac23}[/tex]Step-by-step explanation:
[tex]\dfrac x{x+2}-\dfrac4{x-2}=1\qquad\qquad\qquad x\ne2\ \wedge\ x\ne-2\\\\\\ \dfrac {x(x-2)}{(x+2)(x-2)}-\dfrac{4(x+2)}{(x-2)(x+2)}=1\\\\\\ \dfrac {x^2-2x-4x-8}{x^2-4}=1\\\\ \\\dfrac {x^2-6x-8}{x^2-4}=1\quad\iff\quad x^2-6x-8=x^2-4\\\\x^2-6x-8=x^2-4\\\\-6x-8=-4\\\\-6x=4\\\\x=-\frac46\\\\x=-\frac23[/tex]
The solution to the equation is x = -2/3.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
The given equation is [tex]\frac{x}{x+2}-\frac{4}{x-2}=1[/tex].
Solve the equation as follows:
[tex]\frac{x}{x+2}-\frac{4}{x-2}=1\\\\\frac{x(x-2)-4(x+2)}{(x+2)(x-2)}=1\\\\\frac{x^2-2x-4x-8}{x^2-4}=1\\\\x^2-6x-8= x^2-4\\\\-6x = 8-4\\\\6x = -4\\\\x=-\frac{2}{3}[/tex]
Hence, the solution to the equation is x = -2/3.
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Related Questions
can someone plz help with this? geometry:)
Answers
Answer:
One property of rectangles is that the diagonals of rectangles bisect each other, meaning 2 of JN is equal to JL.
We can form an equation off of this, 2(x+3) = 3x + 1 and then solve for x
2(x+3)= 3x + 1 First, distribute the 2 to each term in x+3,
the result should be:
2x + 6 = 3x+ 1 then subtract 2x from both sides
-2x -2x
the result should be :
6 = x + 1 subtract 1 from both sides
-1 -1
the result should be x=5
plug that into the equations and JN= 5+3, JL=15+1
The two correct options are
NM = 8 ( both of the diagonals are equal to eachother )
JL = 16
.The measures of the angles of a triangle are in the extended ratio 6: 1: 5. What is the measure of the largest angle?
Answers
Answer:
90
Step-by-step explanation:
Ratio = 6 : 1 : 5
Angles are 6x ,x , 5x
Sum of all the angles of the triangle = 180
6x +x +5x = 180
12x = 180
x = 180/12
x = 15
Largest angle = 6x = 6*15 = 90
Choose the system of equations to solve the following: Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75. Determine the total number of adult and student tickets. *
A: 7.25a + 5.50s = 8 and a + s = 52.75
B: 7.25a + 5.50s = 52.75 and a + s = 52.75
C: 7.25a + 5.50s = 52.75 and a + s = 8
Answers
uMMMMMMMM I don't know
HELPPPPPPPPPPPP PLEASE
Answers
Answer: <B is congruent to <E
Step-by-step explanation:
There is no “angle,angle,angle” theorem when proving triangles are congruent.
There are 5 however that do:
ASA (angle, included side, angle)
SSS (side, side, side)
SAS (side, included angle, side)
AAS (angle,angle, non included side)
HL (hypotenuse,leg)
John and his 5 friends will share 1 1/2 pizzas if they share the pizzas equally how much pizza will each person get
Answers
Answer:
5/4
Step-by-step explanation:
Mary rides her horse 30 miles in 2 1/2 hours. What is her average speed in miles per hour?
Answers
Answer:
12 miles per hour
Step-by-step explanation:
An isosceles triangle has an angle that measures 118°. Which other angles could be in that isosceles triangle? Choose all that apply. a 69° b 31 c 118 d 54
Answers
Answer:
b. 31.
Step-by-step explanation:
The other 2 angles in the triangle are congruent so they are:
(180 - 118) / 2
= 31 degrees.
The possible measure of two similar angles in an isosceles triangle could be b. 31 °
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know in an isosceles triangle two sides are equal and angles opposite sides to the equal side are also equal.
We also know that the sum of all the interior angles in a triangle is 180°.
Let, The similar angles be 'x'.
Therefore,
x + x + 118 = 180
2x = 62.
x = 31°.
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Solve for X. Please solve all four. First person to do so will get brainliest.
Answers
Answer:
x=-12
x=10
x=-8
x=-5
Step-by-step explanation:
Answer:
1.x=-12
2.x=10
3.x=-8
4.x=-5
Step-by-step explanation:
HELP ASAP !! I have trouble with this
Answers
Answer:
x= 0.7227 in radians
x= 41.4096 in degrees
Step-by-step explanation:
cos(x) = 6/8
What is the length in centimeters of the hypotenuse of the right triangle below?
2 cm
8 cm
Answers
Answer:
Step-by-step explanation:
WASSUP
You and your friend complete video game levels at the same rate. You complete 5 levels in 45 hours. How many levels does your friend complete in 9 hours? please help!!!
Answers
Answer:
Your friend complete 1 level per 9 hours.
You complete 5 levels in 45h so you get 1 lv per 9h 45/9=5
Which graph has a slope of 4/5?
Answers
Answer: The second one
Step-by-step explanation:
f(x) = (x + 1)2, g(x) = 2x3
One way to find (f º g)(x) when x = −2 is to start by composing f(g(x)).
Find f(g(x)).
4x6 + 1
4x9 + 1
4x6 + 4x3 + 1
4x9 + 4x6 + 1
Answers
The function (f º g)(x) is 4x⁶ + 1. Option A
What is a function?A function can be defined as a law, rule or expression that shows the relationship between two variables in an equation.
These variables are called;
The independent variableThe dependent variableFrom the information given, we have the function;
f(x) = (x + 1)² g(x) = 2x³To determine the composite function, we have to substitute the value of g(x) as x in the function f(x), we have;
(f º g)(x) = (2x³ + 1)²
expand the bracket
(f º g)(x) = 4x⁶ + 1
Hence, the function is (f º g)(x) = 4x⁶ + 1
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Answer:
The first question is C: 4x^6 + 4x^3 + 1
The second question is: f(g(−2)) = 225
Step-by-step explanation:
Got it right on edg.
Explain why the product of a non-0 rational number and an irrational number is irrational?
Answers
Answer:
An irrational number is a number that can not be written as the quotient of two integer numbers.
Then if we have:
A = a rational number
B = a irrational number.
Then we can write:
A = x/y
Then the product of A and B can be written as:
A*B = (x/y)*B
Now, let's assume that this product is a rational number, then the product can be written as the quotient between two integer numbers.
(x/y)*B = (m/n)
If we isolate B, we get:
B = (m/n)*(y/x)
We can rewrite this as:
B = (m*y)/(n*x)
Where m, n, y, and x are integer numbers, then:
m*y is an integer
n*x is an integer.
Then B can be written as the quotient of two integer numbers, but this contradicts the initial hypothesis where we assumed that B was an irrational number.
Then the product of an irrational number and a rational number different than zero is always an irrational number.
We need to add the fact that the rational number is different than zero because if:
B is an irrational number
And we multiply it by zero, we get:
B*0 = 0
Then the product of an irrational number and zero is zero, which is a rational number.
Sarah and Nathan each picked a bucket of strawberries. Sarah picked 4 1/4 and Nathan picked 3 3/4. How much more did Sarah pick than Nathan?
Answers
Answer: 1/2 buckets
Step-by-step explanation:
Sarah picked 4¹/₄ buckets of grapes and Nathan picked 3³/₄ buckets.
To find out how much Sarah picked more than Nathan, simply subtract Nathan's buckets from Sarah's.
First convert the fractions to improper fractions:
4¹/₄ = 17/4
3³/₄ = 15/4
As the have the same denominator, you can directly subtract them:
= 17/4 - 15/4
= 2/4
= 1/2 buckets
6.A = 23 × 3 × 5 B = 22 × 3 × 52
Write down the highest common factor (HCF) of A and B.Required to answer. Single line text.
(1 Point)
Answers
Given:
The two numbers are
[tex]A=23\times 3\times 5[/tex]
[tex]B=22\times 3\times 52[/tex]
To find:
The highest common factor (HCF) of A and B
Solution:
We have,
[tex]A=23\times 3\times 5[/tex] ...(i)
[tex]B=22\times 3\times 52[/tex]
All the factors of A are prime but the factors of B are not prime. So, it can be written as
[tex]B=2\times 11\times 3\times 13\times 2\times 2[/tex] ...(ii)
From (i) and (ii), it is clear that 3 is the only common factor of A and B. So,
[tex]HCF(A,B) = 3[/tex]
Therefore, the highest common factor (HCF) of A and B is 3.
Find the value of y. Round your answers to the nearest tenth
Answers
Answer:
y ≈ 4.3
Step-by-step explanation:
Since the figures are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{AB}{RS}[/tex] = [tex]\frac{ED}{VU}[/tex] , substitute values
[tex]\frac{6}{4}[/tex] = [tex]\frac{8}{y+1}[/tex] ( cross- multiply )
6(y + 1) = 32
6y + 6 = 32 ( subtract 6 from both sides )
6y = 26 ( divide both sides by 6 )
y ≈ 4.3 ( to the nearest tenth )
Answer:
4.3 Is the answer like the value of X in the nearest tenth.
Write the slope-intercept form of the equation of each line.
Answers
Step-by-step explanation:
you look at how the line intersects with an integer point.
on the y-axis, the line has a value of -2 so it has a y-intercept value of -2
so the slope formula is rise/run.
As we can see on the graph, there is no line on the graph that truly lines up with a point besides (0,-2)
if we look at all of the slopes
from A,B,C, and D, and there are not any slopes besides d that are on the graph.
y=mx+b
m=slope
b=y-intercept
If we expand the graph a little bit we can see that the point (0,-2) goes up 7 and goes to the left of 4 units.
so the answer is D : y=-7/4x-2
----------------------------------------------------------------------
and since we go up and to the left or we go down and to the right that determines that the slope is negative.
If we started on a point on the y-axis, and started and went up and to the right or down and to the left.
Hope that helps :)
Please give brainliest
3. Are these figures congruent?
A Yes, they are congruent.
B) No, they are not congruent.
Answers
Answer:
B) No, they are not congruent.
One ∆ is smaller than the other & hence they are not congruent.
Answer:
B
Step-by-step explanation:
If they were to be congruent, they would have to be the same size and look the same in all aspects including angles and side lengths, but they aren't as they are similar shapes, therefore B.
Hope this helps!!
Help me it’s timed!!!
Answers
Estimate the sum by rounding each number to the nearest half or whole.
2 1/2 + 5 5/8=
O 8 1/2
O 8
O 7
O 7 1/2
Answers
(12x -2) - (-3x + 4) anyone got the answer?
Answers
Answer:
15x - 6
Step-by-step explanation:
(12x -2) -1 (3x+4)
(12x - 2 + 3x-4
12x-2+3x -4
12x -6 + 3x
15x - 6
Which is the equation of a line that passes through the point (-3, 5) with a slope
of -2/3
Answers
Decrease £843 by 91% rounded to 2 DP
Answers
Answer:
Percent (%)' means 'out of one hundred':
p% = p 'out of one hundred',
p% is read p 'percent',
p% = p/100 = p ÷ 100.
91% = 91/100 = 91 ÷ 100 = 0.91.
100% = 100/100 = 100 ÷ 100 = 1.
Decrease number by 91% of its value.
Percentage decrease = 91% × 843
New value = 843 - Percentage decrease
Calculate the New Value
New value =
843 - Percentage decrease =
843 - (91% × 843) =
843 - 91% × 843 =
(1 - 91%) × 843 =
(100% - 91%) × 843 =
9% × 843 =
9 ÷ 100 × 843 =
9 × 843 ÷ 100 =
7,587 ÷ 100 =
75.87
Calculate absolute change (actual difference)
Absolute change (actual difference) =
New value - 843 =
75.87 - 843 =
- 767.13
Proof.
Calculate percentage decrease:
Percentage decrease =
91% × 843 =
91 ÷ 100 × 843 =
91 × 843 ÷ 100 =
76,713 ÷ 100 =
767.13
Step-by-step explanation:
Hope it is helpful....
I need help ASAP!!!!!!
Answers
Answer:
1. YES 2. NO
Step-by-step explanation:
1. Since x=0.121212... and the question is asking for 100x, we need to multiply each side by 100. 0.121212... multiplied by 100 is 12.1212... So YES, 100x is still a repeating decimal.
2. 12.121212... minus 0.121212... would just be 12. This is because if we know that all the numbers behind the decimal point is 0.121212 and so on, 12.121212... minus 0.121212... the numbers behind the decimal would cancel out. So we are left with 12. So NO, the answer for 99x is NOT a repeating decimal.
How many weeks is 36 days
Answers
Answer:
about 5 weeks
Step-by-step explanation:
divide 36 by 7
Answer:
5 weeks
Step-by-step explanation:
there is 5 weeks and some days
we know 7 days= 1 week
1 day =1/7 week
36 day= 1/7)*36
=5.14 weeks
..... hope you liked it.
James travels 147 metres in 2 seconds.
Find the average speed of James during that time.
Give your answer correct to 1 decimal place where appropriate.
m/s
Answers
Answer:
73.5m/s is the average speed
Step-by-step explanation:
147/2=73.5
Solve by subsititution:
X = - 3y + 1
-3x - 3y = -15
Answers
Answer:
y=-2 x=7
Step-by-step explanation:
What does m equal?please help me.
Answers
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the inequalities.
===> -7 + 45m - 35 < 9m - 11
===> 45m - 42 < 9m - 11
===> 45m - 9m < -11 + 42
==> 36m < 31
==> m < 31/36
hence the value of m < 31/36
Answer:
m = 31/36
Step-by-step explanation:
Hope this helps you.
How do i find this slope?!?!?!
Answers
Answer:
Step-by-step explanation:
To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.
Here are the equations you can use to find the slope;
Slope. y2 - y1 / x2 - x1 = slope.
Slope Intercept form. y = mx + b.
Point slope form. y - y1 = m ( x - x1)