Hello studentUnion!
[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]
Solve the equation-
[tex] \frac{5}{x - 3} - \frac{4}{x + 4} = \frac{1}{x} \\ [/tex]
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex] \frac{5}{x - 3} - \frac{4}{x + 4} = \frac{1}{x} \\ [/tex]
Let's multiply both the sides of the equation by x (x - 3) & (x + 4) which is the LCM of (x - 3), (x + 4) & x. We can't solve it directly without taking the LCM first as the denominators are not equal to each other. Then do cross multiplication. After all these steps, you'll get an equation as..
[tex]x\left(x+4\right)\times 5-x\left(x-3\right)\times 4=\left(x-3\right)\left(x+4\right) \\ [/tex]
Now, use the distributive property & simplify it.
[tex]x\left(x+4\right)\times 5-x\left(x-3\right)\times 4=\left(x-3\right)\left(x+4\right) \\ \left(x^{2}+4x\right)\times 5-x\left(x-3\right)\times 4=\left(x-3\right)\left(x+4\right) \\ 5x^{2}+20x-x\left(x-3\right)\times 4=\left(x-3\right)\left(x+4\right) \\ 5x^{2}+20x-\left(x^{2}-3x\right)\times 4=\left(x-3\right)\left(x+4\right) \\ 5x^{2}+20x-\left(4x^{2}-12x\right)=\left(x-3\right)\left(x+4\right) \\ 5x^{2}+20x-4x^{2}+12x=\left(x-3\right)\left(x+4\right) \\ x^{2}+20x+12x=\left(x-3\right)\left(x+4\right) \\ x^{2}+32x=\left(x-3\right)\left(x+4\right) \\ x^{2}+32x=x^{2}+x-12 \\ x^{2}+32x-x^{2}=x-12 \\ 32x=x-12 \\ 32x-x=-12 \\ 31x=-12 \\ \boxed{ \boxed{ \bf \: x=-\frac{12}{31} }}[/tex]
The value of x is -12/31.__________________
Hope it'll help you!
ℓu¢αzz ッ
Answer:
[tex]\frac{5}{x-3} -\frac{4}{x+4} =\frac{1}{x}[/tex]
[tex]\frac{5(x+4)-4(x-3)}{(x-3)(x+4)} =\frac{1}{x} \\[/tex]
[tex]\frac{5x+20-4x+12}{(x-3)(x+4)} =\frac{1}{x}[/tex]
[tex]\frac{x+32}{(x-3)(x+4)} =\frac{1}{x}[/tex]
Use Cross multiplication
[tex]x(x+32)=(x-3)(x+4)[/tex]
[tex]x^{2} +32x = x^{2} +4x-3x-12[/tex]
[tex]x^{2} +32x=x^{2} +x-12[/tex]
[tex]x^{2} +32x-x^{2} -x=-12[/tex]
[tex]31x = -12[/tex]
[tex]\frac{31x}{31} =\frac{-12}{31} \\x = \frac{-12}{31}[/tex]
Hope this helps you.
Let me know if you have any other questions :-)
If there is a decimal in the divisor what is the rule?
Pls help asap
Answer:
Multiply
Step-by-step explanation:
You need to multiply the number by 10 or 100 or 1000 according to the number. but after multiplying it should become a whole digit. And you also need to multiply 10 or 100 or 1000 in the dividend.
Hope this has helped you.
Evaluate the expression when c=1/2 and d=1/12.
3(1/4+c^2)+2d
Enter your answer as a mixed number in simplest form in the box.
answer is
[tex]1 \times \frac{2}{3} [/tex]
Which of the following expressions are equivalent to 58 ?
5 16
52
(52)
6
O
54
52. 54
(54)
5-1.59
5-1.5-8
Answer:
(5^4)^2
Step-by-step explanation:
Through any two points, there is exactly one line.
A line segment is part of a line and is bounded by two endpoints.
If two lines intersect, then each pair of opposite angles are congruent.
postulate,
definition,
theorem.
1) Through any two points, there is exactly one line.- postulate
2) A line segment is a part of a line and is bounded by two endpoint. - Definition
3) If two lines intersect, then each pair of opposite angles are congruent. - Theorem
What are postulates?"These are statements that are assumed to be true without proof."
What is definition?"It is used to give a precise meaning to a new term."
What is theorem?"It is a statement that can be proved to be true by accepted mathematical operations and arguments"
For given question,
We have been given three statements.
We need to classify them as theorem, postulate and definition.
The first statement is 'Through any two points, there is exactly one line.'
We know that this is the fundamental postulate use in Geometry.
The second statement is 'A line segment is a part of a line and is bounded by two endpoint.'
Above statement is the definition of line segment.
The last statement is 'If two lines intersect, then each pair of opposite angles are congruent.'
We can prove above statement by using Euclid's axiom.
So, above statement is a theorem.
Therefore, 1) Through any two points, there is exactly one line.' - postulate
2) A line segment is a part of a line and is bounded by two endpoint. - Definition
3) If two lines intersect, then each pair of opposite angles are congruent. - Theorem
Learn more about postulate, theorem and definition here:
https://brainly.com/question/2725475
#SPJ2
Graph the following equation: y = -5x + 1
Answer: in your graphplot the point of the y-intercept(which in this case is 1, hence the “+1”)
Step-by-step explanation:
Next 5x is the same as -5/+1 which pretty much means you have to go down 5 times and 1 to the right in a repeated motion until you can no longer plot that point.
then you do the opposite of -5x which is -1/+5 which means you have to go up 5 times and 1 to the left in a repeated motion until you can’t
Food would be considered a fixed monthly expense. TURE OR FALSE
Answer:
True
Step-by-step explanation:
Answer:
TRUE
Step-by-step explanation:
Fixed monthly expense but not fixed expenses monthly
Can anyone help me ASAP!
Answer:
7.8
Step-by-step explanation:
the answer is
[tex] \sqrt{61} [/tex]
2p2 - 5p + 3
pliss anwered this for me
Answer:
2p²-5p+3 is the final answer as they aren't any like terms to collect in order to simply the solution further.
Step-by-step explanation:
Wishing you a splendiferous day,
stay salty...
ya'll help me w/slope, please
I got ECHA... hope it's right:)
Is the following a right triangle
Answer:
no
Step-by-step explanation:
(√17)^2+(√204)^2=218,but 15^2=225,so this triangle isn't a right triangle
12/16 which is the dividend
Answer: 12 is the dividend (sorry for the miss-conception on the question)
Step-by-step explanation:
aiden runs 5 laps around a track in 8 minutes how many laps per minute is that
Answer:
8/5 1.6 minutes per lap
5/8 0.625 lap per minutes
If a circle has a diameter of 10 cm and circumference of 31.4 cm how would you write a ratio to determine the value of pi
Which equations shows the variable terms isolated on one side and the constant terms isolated on the other side for the equation 3 x minus 5 = negative 2 x + 10? Select two options. x = 5 –15 = –5x 5x = 15 –15 = 5x x = -5
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The given expression is ~
[tex]3x - 5 = - 2x + 10[/tex][tex]3x + 2x = 10 + 15[/tex][tex]5x = 15[/tex][tex]x = 15 \div 3[/tex][tex]x = 5[/tex]So, the Correct options are ~
[tex]x = 5[/tex]and
[tex]5x = 15[/tex]Answer:
A and C
Step-by-step explanation:
factorize 2x²y⁴-6xy³
Answer:
=2xy^3x(xy-3)
Step-by-step explanation:
2x^2y4-6xy^3
=2xy^3x(xy-3)
=2xy^3x(xy-3)
IM DESPERATE FOR AN ANSWER Customers of a phone company can choose between two service plans for long distance calls. The first plan has an $18 monthly fee and charges an additional $0.13 for each minute of calls. The second plan has no monthly fee but charges $0.17 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?
Answer:
450 minutes
Step-by-step explanation:
1st plan
18 + 0.13x = y
2nd plan
0.17x = y
x is minute of calls
y is the total price customers must pay
both of them equal as y = y
y = y
18 + 0.13x = 0.17x
18 = 0.17x - 0.13x
18 = 0.04x
x = 18/0.04
x = 450 minutes
can you figure how much they should pay?
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!5
Answer:
C
Step-by-step explanation:
I may be wrong...
Sooo sorry if I am
consider the graph of f(x) = x^2 -4x +5
hope this helps :) !!
What is 28 in hexadecimal?
Emily buys a dress for £48 and adds 25% onto the price before putting it into her shop window What price does the price-tag say in the window?
PLEASE HELP I HAVE A MATHS TEST TMRW AND IM SO SCARED PLEASE SHOW ALL YOUR WORKING OUT SO I UNDERSTAND THANK YOU:)
The prism shown has a volume of 300 m3.
A prism has a length of 7.5 meters, width of w, and height of 5 meters.
What is the width of the prism?
6 m
8 m
24 m
40 m
Answer:
Your answer is 8. Divide the volume by the product of the length and height to calculate the rectangular prism's width. 7.5*5=37.5 300/37.5=8m
Step-by-step explanation:
Answer:
The answer is 8
Step-by-step explanation:
Hope this help!
Last month you spent $20 on clothing. This month you spent 180% of what you spent last month. How much did you spend this month?
Use the table to work out the values of a , b , c , and d .
Answer:
a = 16, b = 6, c = - 4, d = - 9
Step-by-step explanation:
Substitute the appropriate values of x into the equation and evaluate.
x = - 3 : y = 1 - 5(- 3) = 1 + 15 = 16 → a
x = - 1 : y = 1 - 5(- 1) = 1 + 5 = 6 → b
x = 1 : y = 1 - 5(1) = 1 - 5 = - 4 → c
x = 2 : y = 1 - 5(2) = 1 - 10 = - 9 → d
Answer:
a=16; b=6, c= -4, d= -9
Step-by-step explanation:
[tex]f(x)=1-5x\\f(-3) = 1-5(-3)=1+15=16\\f(-1) = 6\\f(1)=-4\\f(2)=-9[/tex]
7) What is the SECOND step in simplifying the equation below?
4 - 3y = 31
Answer:
subtract 4 from both sides
Step-by-step explanation:
you will then get -3y=27 as your equation then you just divide each side by -3 and your answer will be y = -9
Answer:
Step-by-step explanation:
4 - 3y = 31
Step 1: Subtract 4 from both sides
-3y = 31 -4
-3y = 27
Step 2: Divide both sides by (-3)
[tex]\dfrac{-3y}{-3}=\dfrac{27}{-3}[/tex]
y = -9
The number of hours, h, that Mr. Hampton works varies directly with the number of tasks, t, he has to perform. If he has 6 tasks to perform and works for 15 hours, what is k the constant of variation?
i think its 2.5 because 15/6= 2.5 so 2.5t=h and the equation is kt=h so 2.5 makes the most sense.
I hope this helps
Find the gradient and y-intercept in this equation:
[tex]8x+2y+9=0[/tex]
Answer:
Gradient: -4
y-intercept: [tex]-\frac{9}{2}[/tex]
Step-by-step explanation:
Step 1 - Subtract 8x from both sides to isolate the 2y + 9
[tex]8x + 2y + 9 = 0\\8x + 2y + 9 - 8x = 0 - 8x\\2y + 9 = -8x\\[/tex]
Step 2 - Subtract 9 from both sides to isolate the 2y:
[tex]2y + 9 = -8x\\2y + 9 - 9 = -8x - 9\\2y = -8x - 9[/tex]
Step 3 - Divide both sides of the equation by 2:
[tex]\frac{2y}{2} = \frac{-8x}{2} - \frac{9}{2}\\y = -4x - \frac{9}{2}[/tex]
In this form, y = mx + b, the m value is the gradient with the b value being the y-intercept. This means:
[tex]y = -4x - \frac{9}{2}\\\\m = -4\\b = -\frac{9}{2} \\\\[/tex]
Resulting in the gradient being -4 and the y-intercept being [tex]-\frac{9}{2}[/tex].
Hope this helps!
8. To make a homemade all-purpose household cleaner, you can mix the
ingredients shown in the table. Samuel has 1 cup of rubbing alcohol
and will use the entire amount. He plans to store the cleaning solution
in containers that each hold a maximum of 6 cups. How many
containers does he Need?
Answer:
Could you link the table?
Step-by-step explanation:
For all real numbers x, how many values of x are odd prime numbers less than 20 ?
Answer:
7
Step-by-step explanation:
odd prime numbers < 20 are
3, 5, 7, 11, 13, 17, 19
do any of you know what 9+10 is, and yes this is the vine
Answer: 19
9+10
19
Hope this helps! :)
Evaluate 2xy when x=−14 and y=3. Help!!!!
Answer:
-84
Step-by-step explanation:
Help is on the way! Plug in the values of x and y into the expression and then simplify with multiplication.
2(-14)(3)
-84
And you're done!
