Find all values of $x$ such that
\[\frac{2x}{x + 2} = -\frac{6}{x + 4}.\]
Answers
Answer:x_1= -1 or x_2= -6
Step-by-step explanation:
In the pictures
![Find All Values Of $x$ Such That\[\frac{2x}{x + 2} = -\frac{6}{x + 4}.\]](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/mwPHIJOQBust6PV4v0Uj0PNnOgBQoaCT.jpeg)
By using factorization, [tex]\[\dfrac{2x}{x + 2} = -\dfrac{6}{x + 4}.\][/tex] , values of x are -2, 3.
What is factorization?Factorization can be defined as the process of breaking down a number into smaller numbers which when multiplied together arrive at the original number.
These numbers are broken down into factors or divisors.
For an integer, factorization is decomposition of that integer in terms of smaller integers which when multiplied with each other give back that considered number and these composing integers are called factors of that considered integers.
Given
[tex]\[\dfrac{2x}{x + 2} = -\dfrac{6}{x + 4}.\][/tex]
Cross multiplication;
2x(x + 4) = 6(x + 2)
[tex]2x^{2} + 8x = 6x + 12\\\\2x^{2} + 8x - 6x - 12 = 0\\\\2x^{2} + 2x - 12 = 0\\\\x^{2} + x - 6 = 0[/tex]
Divide above equation by 2, we get
[tex]x^{2} + x - 6 = 0[/tex]
(x +2) (x-3)
x = -2, 3
Therefore, By using factorization, [tex]\[\dfrac{2x}{x + 2} = -\dfrac{6}{x + 4}.\][/tex] , values of x are -2, 3.
Find out more information about factorization here;
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Related Questions
what is the answer of this question plzzzzzzzzzzz say fast
Answers
Answer:
[tex]1=3=70^{0} \\2=4=5=110^{0}[/tex]
Step-by-step explanation:
Given angle is 110°
Now,
[tex]4=2\,\,and\,\,4=5\,\,;[vertical\,\,angle\,\,and\,\,corresponding\,\,angle\,\,respectively ][/tex]
From the figure,
[tex]4=110^{0}\,\,;[alternate\,\,angle][/tex]
[tex]So,\,\,2=5=110^{0}[/tex]
And, as 1,2,3,4 are vertical angles and 2 = 4 = 110°
1 = 3 = 180° - 110° = 70°
Hope you have understood this.....
ask me if you have any confusion.....
if you liked it pls mark it as the brainliest
Answer:
angle 1 =70 degrees
angle 2 =110 degrees
angle 3 =70 degrees
angle 4 = 110 degrees
angle 5 =110 degrees
Step-by-step explanation:
1) 110+ angle 1=180(allied angles)
angle 1=180-110
angle 1=70 degrees
2)angle 2+ angle 1=180(angles on a straight line)
angle 2+ 70 =180
angle 2 =180-70
angle 2 =110 degrees
3)angle 3+ angle 2=180(angles on a straight line)
angle 3+ 110 =180
angle 3 =180-110
angle 3 =70 degrees
angle 3 can be taken as vertically opposite angles(70 degrees)4)angle 4 = 110 degrees (vertically opposite angles)
5)angle 5+ angle 3=180(allied angles)
angle 5+ 70 =180
angle 5 =180-70
angle 5 =110 degrees
Hope you got this .......
If you have any questions regard to this you can ask me.......
There are many ways to do these sums but the answer should be correct......
If you think this is the best answer please mark me as brainliest....
What is the volume of the following rectangula
prism?
4
units
3
23
units
4
Answers
SORRYYYYYYYYYYYYYYY I DONT KNOWWWWW
Which of the following correctly models 8 square
Answers
Answer:
A
Step-by-step explanation:
Please help me!! Find the equation of the line that is perpendicular to y=1/6x+3 and contains the point (-3,23).
Answers
Answer:
[tex]\displaystyle y = -6x + 5[/tex]
Where ? = -6.
Step-by-step explanation:
We want to find the equation of a line that is perpendicular to:
[tex]\displaystyle y = \frac{1}{6} x + 3[/tex]
And contains the point (-3, 23).
Recall that the slopes of perpendicular lines are negative reciprocals of each other.
The negative reciprocal of 1/6 is -6. Hence, the slope of the perpendicular line is -6.
We are also given that it passes through the point (-3, 23). Since we know the slope and a point, we can consider using the point-slope form:
[tex]\displaystyle y - y_1 = m(x - x_1)[/tex]
Substitute:
[tex]\displaystyle y - (23) = -6(x - (-3))[/tex]
Simplify:
[tex]\displaystyle y - 23 = -6 (x+3)[/tex]
Distribute:
[tex]\displaystyle y - 23 = -6x - 18[/tex]
And add. Hence:
[tex]\displaystyle y = -6x + 5[/tex]
In conclusion, our equation is:
[tex]\displaystyle y = -6x + 5[/tex]
Where ? = -6.
SOLVE PLEASE! (Help)
Answers
Answer:
1. [tex]\sqrt{218}[/tex]
2. [tex]\sqrt{89}[/tex]
3. [tex]2\sqrt{17}[/tex]
Step-by-step explanation:
The formula to find the distance between any two points on a coordinate plane is as follows:
[tex]D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
Where ([tex](x_1,y_1)[/tex]) and ([tex](x_2,y_2)[/tex]) are the two points one is trying to find the distance between. Substitute the points in and solve for the distance between them for each respective problem.
1.
Points: [tex](-4, 6),\ \ (3, -7)[/tex]
Substitute into the formula,
[tex]D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
[tex]D=\sqrt{((-4)-(3))^2+((6)-(-7))^2}[/tex]
Simplify,
[tex]D=\sqrt{((-4)-(3))^2+((6)-(-7))^2}[/tex]
[tex]D=\sqrt{(-4-3)^2+(6+7)^2}[/tex]
[tex]D=\sqrt{(-7)^2+(13)^2}[/tex]
[tex]D=\sqrt{49+169}[/tex]
[tex]D=\sqrt{218}[/tex]
2.
Points: [tex](-6, -5)\ \ (2,0)[/tex]
Substitute into the formula,
[tex]D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
[tex]D=\sqrt{((-6)-(2))^2+((-5)-(0))^2}[/tex]
Simplify,
[tex]D=\sqrt{((-6)-(2))^2+((-5)-(0))^2}[/tex]
[tex]D=\sqrt{(-6-2)^2+(-5-0)^2}[/tex]
[tex]D=\sqrt{(-8)^2+(-5)^2}[/tex]
[tex]D=\sqrt{64+25}[/tex]
[tex]D=\sqrt{89}[/tex]
3.
Points: [tex](-1, 4)\ \ (1,-4)[/tex]
Substitute into the formula,
[tex]D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
[tex]D=\sqrt{((-1)-(1))^2+((4)-(-4))^2}[/tex]
Simplify,
[tex]D=\sqrt{((-1)-(1))^2+((4)-(-4))^2}[/tex]
[tex]D=\sqrt{(-1-1)^2+(4+4)^2}[/tex]
[tex]D=\sqrt{(-2)^2+(8)^2}[/tex]
[tex]D=\sqrt{4+64}[/tex]
[tex]D=\sqrt{68}[/tex]
[tex]D=2\sqrt{17}[/tex]
if two points lie in a plane, then_______
Answers
Answer:
the line containing them lies in the plane.
Step-by-step explanation:
If two planes intersect, then their intersection is a line.
If two points lie in a plane, then the line containing them lies in the plane. If two planes intersect, then their intersection is a line.
I hope this answer can help you ♥️
Acme T-Shirt Company charges a $50 set-up fee plus $9 for each shirt printed. Beta T-shirt Company has no set up fee, but charges $14 per shirt. What is the minimum number of shirts for which a customer saves money by using Acme?
Answers
Answer:
Step-by-step explanation:
Acme Company:
Let the number of shirts = x
Cost = 50 + 9x
Beta Company:
Cost = 14x
50 + 9x < 14x
Subtract 9x from both sides
50 < 14x - 9x
50 < 5x
Divide both sides by 5
50/5 < x
10 < x
Minimum number of shirts for which a customer saves money by using Acme = 11 T-shirts
Divide. Write your answer as a fraction in simplest form. − 7 1/0÷2/5=
Answers
Answer:
[tex] - \frac{71}{4} [/tex]
Step-by-step explanation:
[tex] - 7 \frac{1}{10} \div \frac{2}{5} [/tex]
[tex] = - \frac{71}{10} \times \frac{5}{2} [/tex]
[tex] = - \frac{71}{2} \times \frac{1}{2} [/tex]
[tex] = - \frac{71}{4} [/tex]
help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!11
Answers
Answer:
x = 4
Step-by-step explanation:
[tex]-5(x-1)-x+1=-18\\\\-5x+5-x+1=-18\\\\-6x+6=-18\\\\-6x=-24\\\\x=4[/tex]
Answer:
x = 4
Step-by-step explanation:
-5 ( x - 1 ) -x +1 = -18
solve the brackets first
-5x + 5 - x + 1 = -18
-5x -x +5 +1 = -18
-6x + 6 = -18
-6x = -18 - 6
-6x = -24
x = -24 / -6
x = 4
A cell phone tower casts an
post
80-foot shadow. At the same time, a 6-foot fence
casts a shadow of 4 feet. What is the height of the tower?
Answers
if you buy a 5 bananas for 3 dollars how much is one
Answers
1.6667
that's the answer cause I said so
The lines shown below are perpendicular. Find the slope-intercept form of the equation of line y2.
Answers
Answer:
y = -1/3x + 4
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals of each other. The equation for line y1 is 3x - 4 The slope is the coefficient of x, which is 3. That means the slope of line y2 is -1/3, because it's the negative reciprocal. As for the y-intercept, just look for the point on the y-axis that the line intercepts. If we look closely, we can see it intercepts point (0,4) on the y-axis. Therefore, the slope-intercept form equation for line y2 is: y = -1/3x + 4.
Answer:
y=5-x/3
Step-by-step explanation:
Find the 9th term of the geometric sequence 5, -25, 125, ..
Answers
Answer:
5^9
Step-by-step explanation:
bn= b1*r^(n-1)
b9=b1*r^8
r=-25/5=-5
b9= 5*5^8=5^9
Alan has $115.78 in his savings account. He earns $15.00 cleaning out
the garage and puts $7.50 into savings. He withdrawals $35.90 to buy
a video game. He receives $20 from his grandfather and deposits $15
of it into his savings account. What is Alan's balance now?
Answers
Answer:
$137.33
Step-by-step explanation:
$115.78 + $15.00 = $130.78
$130.78 + $7.50 = $138.28
$138.28 - $35.90 = $102.33
$102.33 + $20.00 = $122.33
$122.33 + $15.00 = $137.33
Chow,...!
Please help I know it’s a lot ...?
Answers
Answer:
1. 3g - 24 = 5
2. 5y + 3 = -38
3. 2x + 4 = 45
4. 1/2n - 10 = 30
5. 5n - 6 = 5
6. 6n - 7 = 10
Step-by-step explanation:
not sure if you wanted what the variables equal if you do leave a comment
plssssssssssssss help
Answers
[tex]\frac{8}{5}[/tex] Converted to decimal is 1.6
Answer:
write 0.32 repeating as a fraction in simplest form.
Answers
Answer:
0.32 repeating as a fraction
= 32/99
Step-by-step explanation:
The fraction in simplest form that represents the repeating decimal 0.32 repeating is 32/99.
To express the repeating decimal 0.32 repeating as a fraction in simplest form, we can use the concept of geometric series.
Let's represent 0.32 repeating as x:
x = 0.323232...
Multiply both sides of the equation by 100 to shift the decimal point two places to the right:
100x = 32.323232...
Now, subtract the original equation from the shifted equation to eliminate the repeating part:
100x - x = 32.323232... - 0.323232...
Simplifying the equation:
99x = 32
Divide both sides of the equation by 99 to solve for x:
x = 32/99
Therefore, the fraction in simplest form that represents the repeating decimal 0.32 repeating is 32/99.
To learn more on Number system click:
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Nick's bank accout balance was $21. If he
writes a check for $30 and his bank charges
him $35 for overdrawing his account, find
his account balance.
Answers
Answer:
56
Step-by-step explanation:
what is the square of 18
Answers
Answer:
Square of 18 is 324
Step-by-step explanation:
[tex]18^2=18*18\\=180+80+64\\=324[/tex]
hope you have understood this...
pls mark my answer as the brainliest
How do I solve this pls help?
Answers
Answer:
a)
f(0) = 4, from the graphb)
h(11) = 15, from the tablec)
g(-9) = -2(-9)² - 4(-9) + 1 = -125, as per equationd)
f(2) = 1, from the graphe)
h(-2) = 2, from the tablef)
g(0.25) = -2(0.25)² - 4(0.25) + 1 = - 0.125, as per equationf(0) = 4
h(11) = 15
g(-9) = -2(-9)² - 4(-9) + 1 = -125
f(2) = 1
h(-2) = 2
g(0.25) = -2(0.25)² - 4(0.25) + 1 = - 0.125
2(k + 1) = -4(k - 2)
Answers
Answer:
1
Step-by-step explanation:
2(k + 1) = -4(k - 2)
2k + 2 = --4k+8
2k+4k=8-2
6k=6
k=6/6
k=1
Write the equation of the circle centered at (4, - 9) with diameter 16.
HELP A GIRL OUT
Answers
Answer:
16= (x-4)^2 +(y+9)^2
Step-by-step explanation:
hey! The formula for the equation of a circle is r^2= (x-h)^2 + (y-k)^2
r= the radius (in your case you have the diameter so you do not need to square it)
(h,k)= is the center coordinates, so your center coordinate would be (4, -9). You now have your h (h=4) and your k (k=-9) so you can plug it in the formula! :)
a nice rating would help out
how r u doing?? 1-10:D? (free pts btw)
Answers
Answer: i am good,how are you?
Step-by-step explanation:
Answer:1-10 = 9 :D
Step-by-step explanation:
please help me with this math is for my math homework
Answers
Answer:
5
Step-by-step explanation:
Step-by-step explanation:
[tex] \frac{137}{24} [/tex]
or
[tex] \frac{137}{24} or \: 5 \frac{17}{24} [/tex]
hope that helps you
Please help with steps, will give brainliest. Simplify
Answers
Answer:
=53*(54 ×^9 y^12 z^15)^1/2
=53*y^6 *z^(15/2) * x^( 9/2)* (54)^1/2
Answer:
[tex] {3x}^{4} {y}^{6} {z}^{7} \sqrt{6xz} [/tex]
Step-by-step explanation:
[tex] \sqrt{54 {x}^{9} {y}^{12} {z}^{15} } [/tex]
➡️ [tex] \sqrt{ {3}^{2} \times 6 {x}^{8 + 1} {y}^{12} {z}^{14 + 1} } [/tex]
➡️ [tex] \sqrt{ {3}^{2} \times 6 {x}^{8 } \times {x}^{1} {y}^{12} {z}^{14} \times {z}^{1} } [/tex]
➡️ [tex] \sqrt{ {3}^{2} \times 6 {x}^{8} \times {xy}^{12} {z}^{14} \times z } [/tex]
➡️ [tex] \sqrt{ {3}^{2} } \sqrt{ {x}^{8} } \sqrt {y}^{12} \sqrt{ {z}^{14} \sqrt{6xz} } [/tex]
➡️ [tex] {3x}^{4} {y}^{6} {z}^{7} \sqrt{6xz} [/tex] ✅
Find the distance of the line, then find the slope of the line using the following coordinates (-7,2) and (-4,6)?
Answers
Answer:
Distance = 5 units
Slope = [tex]\displaystyle\frac{4}{3}[/tex]
Step-by-step explanation:
Hi there!
1) Finding the distance of the line
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where two endpoints of a line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the points (-7,2) and (-4,6):
[tex]d=\sqrt{(-4-(-7))^2+(6-2)^2}\\d=\sqrt{(-4+7)^2+(6-2)^2}\\d=\sqrt{(3)^2+(4)^2}\\d=\sqrt{9+16}\\d=\sqrt{25}\\d=5[/tex]
Therefore, the length of the line/distance of the line is 5 units.
2) Finding the slope of the line
[tex]m=\displaystyle\frac{y_2-y_1}{x_2-x_1}[/tex] where two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the points (-7,2) and (-4,6):
[tex]m=\displaystyle\frac{6-2}{-4-(-7)}\\\\m=\displaystyle\frac{6-2}{-4+7}\\\\m=\displaystyle\frac{4}{3}[/tex]
Therefore, the slope of the line is [tex]\displaystyle\frac{4}{3}[/tex].
I hope this helps!
9/8(4-1/2a)=3(1/4a+5/2)
Answers
Answer:A=2 2/7
Step-by-step explanation:
Correct me if I am wrong
Sin A 4/5.
Find
COSA + tan A
Answers
Answer:
Step-by-step explanation:
The opposite side (the one not connected to A) = 4
The hypotenuse is 5
The adjacent side needs to be found for the cosine and the tangent.
a^2 + b^2 = c^2
a = opposite side = 4
b = adjacent side = ?
c = hypotenuse = 5
4^2 + x^2 = 5^2
16 + x^2 = 25
x^2 = 25 - 16
x^2 = 9
x = sqrt(9)
x = 3
cos(A) = adjacent / hypotenuse = 3/5
Tan(A) = opposite / adjacent = 4/3
cos(A) + tan(A) = 3/5 + 4/3
cos(A) + tan(A) = 9/15 + 20/15 = 29/15
To find: CosA + TanA
Solution:
16/25 + Cos²A = 1 [Sin²A + Cos²A = 1]
Cos²A = 1 - 16/25
Cos²A = 25 - 16/25
Cos²A = 9/25
CosA = 3/5
We know that TanA = SinA/CosA
TanA = (4/5)/(3/5)
TanA = 4/3
CosA + TanA = 3/5 + 4/3 = 29/15
What is the equation of the line that passes through the point (-4,-2) and has a
slope of -1/2?
Answers
Answer:
[tex]y = - \frac{1}{2} x[/tex]
someone help please :)
Answers
Answer:
its basically a Cross
the point they cross is p
and the 2 lines are AB and RS
I hope I'm correct.And yea
.hope it helps