Answer:
[tex] \displaystyle \begin{cases} \displaystyle {x} _{1} = - p \\ \displaystyle x _{2} = - q \end{cases}[/tex]
Step-by-step explanation:
we would like to solve the following equation for x:
[tex] \displaystyle \frac{1}{p} + \frac{1}{q} + \frac{1}{x} = \frac{1}{p + q + x} [/tex]
to do so isolate [tex]\frac{1}{x}[/tex] to right hand side and change its sign which yields:
[tex] \displaystyle \frac{1}{p} + \frac{1}{q} = \frac{1}{p + q + x} - \frac{1}{x} [/tex]
simplify Substraction:
[tex] \displaystyle \frac{1}{p} + \frac{1}{q} = \frac{x - (q + p + x)}{x(p + q + x)} [/tex]
get rid of only x:
[tex] \displaystyle \frac{1}{p} + \frac{1}{q} = \frac{ - (q + p )}{x(p + q + x)} [/tex]
simplify addition of the left hand side:
[tex] \displaystyle \frac{q + p}{pq} = \frac{ - (q + p )}{x(p + q + x)} [/tex]
divide both sides by q+p Which yields:
[tex] \displaystyle \frac{1}{pq} = \frac{ -1}{x(p + q + x)} [/tex]
cross multiplication:
[tex] \displaystyle x(p + q + x) = - pq[/tex]
distribute:
[tex] \displaystyle xp + xq + {x}^{2} = - pq[/tex]
isolate -pq to the left hand side and change its sign:
[tex] \displaystyle xp + xq + {x}^{2} + pq = 0[/tex]
rearrange it to standard form:
[tex] \displaystyle {x}^{2} + xp + xq + pq = 0[/tex]
now notice we end up with a quadratic equation therefore to solve so we can consider factoring method to use so
factor out x:
[tex] \displaystyle x( {x}^{} + p ) + xq + pq = 0[/tex]
factor out q:
[tex] \displaystyle x( {x}^{} + p ) +q (x + p)= 0[/tex]
group:
[tex] \displaystyle ( {x}^{} + p ) (x + q)= 0[/tex]
by Zero product property we obtain:
[tex] \displaystyle \begin{cases} \displaystyle {x}^{} + p = 0 \\ \displaystyle x + q= 0 \end{cases}[/tex]
cancel out p from the first equation and q from the second equation which yields:
[tex] \displaystyle \begin{cases} \displaystyle {x}^{} = - p \\ \displaystyle x = - q \end{cases}[/tex]
and we are done!
Which expression represents the following algebraic statement?
Four times the difference of a number and 16.
what is the mean of 3 6 11 7 4
Solve for b.
- 28 – 6b= 8
Answer:
-6
Step-by-step explanation:
- 28 – 6b= 8
step 1 add 28 to each side
-28 + 28 cancels out
28 + 8 = 36
we now have -6b = 36
step 2 divide each side by -6
-6b / -6 = b
36 / -6 = -6
we're left with b = -6
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]b=-6[/tex]
»»————- ★ ————-««
Here’s why:
We will have to preform inverse operations to solve for 'b'.
[tex]\boxed{\text{Solving the equation for 'b':}}\\\\-28-6b=8\\\\--------\\\rightarrow-28+28-6b=8+28\\\\\rightarrow-6b=36\\\\\rightarrow\frac{-6b=36}{-6}\\\\\rightarrow \boxed{\text{b=-6}}\\\\\text{The value of 'b' is \boxed{-6}.}[/tex]
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
4.Complete each of the following BRAINIEST and 50 points its just Trigeometry
Answer:
#1:
cos a = opp/hyp = cb/ca
tan a = opp/ajd = cb/ab
sin c = adj/hyp = ab/ca
cos c = opp/hyp = ab/ca
tan c = opp/adj = ab/cb
2: *i dont have the square root symbol*
sin 60 = 3/2
cos 60 = x/2
tan 60 = 3/x
sin 30 = x/2
cos 30 = 3/2
tan 30 = x/3
3: *i dont have the square root symbol*
sin 45 = 2/x
cos 45 = x/2
tan 45 or 48 = x/y
What is the value of x in the triangle below?
Answer:
B. 5√2
Step-by-step explanation:
hey, simply use Pythagoras theorem.
h²=p²+b²
or, 10²=x²+x²
or, 100= 2x²
or, x²=50
or, x= √50
or, x= √25×√2=5√2
Someone help me with this pls
Answer:
y^6 or y^13/y^7
Step-by-step explanation:
please find the missing side of this triangle
please please please help!
AD = ___ units
Here is a rectangular prism. 2.4 in 1.5 in 8 in
1. What is the volume of the prism?
Hello!
The answer is 28.8, When finding the Volume of a shape, you multiply all numbers.
What are two numbers that multiple to -64 and add to -12
Answer:
-16,4 are the two numbers
I really really really need your help
Write an equation in slope-intercept form of the line that has a slope of -9 and a y-intercept of -4
ANSWER ASAP PLEASE!!
y=-9x-4
Slope intercept form uses the formula, y=mx+b, where m is the slope and b is the y- intercept.
I hope this helps. Have a great day!
Answer:
Y=-9x-4
Step-by-step explanation:
The formula for slope-intercept form is y=mx+b. M is the slope and b is the y-intercept. All you need to do is plug in the numbers. I hope I helped. :>
Brainliest. Brainliest WHO WANTS A BRAINLIEST
Answer:
B
Step-by-step explanation:
Answer:
1. x > -25
2. x > -16
3. x > -2
4. x [tex]\geq[/tex] 10
Give brainliest
quadratic equation: I NEED HELP- ignore the answer I pressed it's wrong
Help please I might fail…
Answer:
9 /4 which equals 2 and 1/4
Step-by-step explanation:
plugged into the calculator!
Can someone help me out my grads are bad
Answer:
50 m^2
Step-by-step explanation:
3cm = 5 m
6 cm = 10 m
5 x 10 = 50 m^2
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
50 [tex]m^{2}[/tex]
Step-by-step explanation:
3cm = 5m
6cm = 10m
5x10 = 50
If the purchase price for a house is $309,900, what is the monthly payment if you put 20% down for a 30 year loan with a fixed rate of 6%? A. $729.98 b. $912.48 c. $1,486.41 d. $1,858.01 Please select the best answer from the choices provided A B C D
Answer:
The correct answer is A. $729.98.
Step-by-step explanation:
Given that the purchase price for a house is $ 309,900, to determine what is the monthly payment if you put 20% down for a 30 year loan with a fixed rate of 6%, the following calculation must be performed:
100 - 20 = 80
(309,900 x 0.80) x 1.06 / (30x12) = X
247,920 x 1.06 / 360 = X
262,795.2 / 360 = X
729.98 = X
Therefore, the monthly payments will be $ 729.98.
Answer:
Monthly Payment = 1,486.41
Step-by-step explanation:
e d g e
Need help with school please help
Answer:
26
Step-by-step explanation:
The triangle equals 180 degrees the two measurements we already have is 90 degrees (the right angle) and 64 degrees.
90+64=154 and 180-154=26.
So 26 is your answer because 90+64+26=180
Hope this helps!
I need this please help mee
Answer:
A, 120.
Step-by-step explanation:
x-15+75=180
x+60=180
x=120.
Mahmoud is working out the height, h metres, of a tower
BT which stands on level ground.
He measures the angle TAB as 25°.
He cannot measure the distance AB and so he walks 80 m
from A to C, where angle ACB = 18° and angle ABC = 90°.
Calculate
Answer:
24.72 m
11.53 m
Step-by-step explanation:
Horizontal distance AB can be obtained from △ABC
From trigonometry :
Sin18° = opposite / hypotenus
Sin18° = AB / 80
AB = 0.3090169 * 80
AB = 24.72 m
The height BT, of tower from △ABT
From trigonometry :
Tan25° = opposite / Adjacent
Tan25° = h / 24.72m
h = Tan25 * 24.72
h = 11.527
h = 11.53 m
Hence, height of tower BT = 11.53 m
10. How do you find the product of the following? Show all your work. a. Binomial squared: (2x + 3)2 b. Binomial squared: (2x - 3)2 C. Difference of squares: (x + 5)(x - 5)
Answer:
A
Step-by-step explanation:
A because when you find the product you need to add
How many 2-digit numbers are multiples of 5 but not 4?
Answer:
14
Step-by-step explanation:
The numbers you are describing can end in 5. But there are others as well. They are t = 10 + 20*n where n goes from 0 to 4. So if n is 4 that means that t = 4*20 + 10 = 80 + 10 = 90.
Solution
15 25 35 45 55 65 75 85 95 are all divisible by 5 but not 4
10 30 50 70 90 are all divisible by 5 but not 4
Dan spent $765.00 on equipment to open a business selling bumitos. He sells the burritos for $3.50 each. The cost of the ingredients to make each burito is $0.75
Answer: 3:50b>765.00+0.75 279 Burritos
Step-by-step explanation:
A doctor compiles a numbered list of all his 350 patients. He selects every 25th patient to receive a survey after
choosing to randomly start with the seventh name on the list. Which statement correctly identifies and justifies
whether the scenario represents an SRS?
O This represents an SRS because the sample was selected with a chance process.
O This represents an SRS because there were no restrictions placed on the sample group.
This does not represent an SRS because each individual chosen does not have an equally likely chance of being
chosen.
O This does not represent an SRS because each group of patients chosen does not have an equally likely chance
of being chosen.
Answer: This does not represent an SRS because each group of patients chosen does not have an equally likely chance of being chosen.
Answer:
the answer is D. This does no represent an SRS because each group of patients chosen does not have an equally likely chance of being chosen
Step-by-step explanation:
Is algebra.
PLEASE HELP NO LINKS OR FILES.
I don't want links.
I don't want links.
I don't want links.
I don't want links.
Answer: the answer is d
Step-by-step explanation:
Find the slope of the line below:
Answer:
Step-by-step explanation:
3
8 to the power of 3
pls answer
Answer:
512
Step-by-step explanation:
8x8x8=512
pretty simple
Answer:
512
Step-by-step explanation:
8*8*8=512
A trapezoid has a height of 12 feet,
and base measurements of 15 feet and
10 feet. What is the area?
[?] square feet
Hint: The formula for the area of a traxzod is to
▬▬▬▬▬▬▬▬▬▬▬▬▬▬
Given :→ Base = 15 and 10
→ Height = 12
To Find :→ Area of trapezoid
Solution :→ Area of Trapezoid = (a + b)/2 × h
= (15 + 10)/2 × 12
= 150 ft²
∴ The area of Trapezoid is 150 ft²
▬▬▬▬▬▬▬▬▬▬▬▬▬▬
Your friend has n pennies. You have 29 pennies. You and your friend have a total of 40 pennies. Which equation could be used to find n?
Answer:
40-29=n
Step-by-step explanation:
You have 29 in total yall have 40
so to find ur friends we subtract
Answer:
Step-by-step explanation:
your pennies + your friends pennies = the total number of pennies between you two
so the equation would be :
29 + n = 40
(im not sure if you wanted it solved for n but here is the solution just in case)
29 + n = 40
n = 40 - 29
n = 11
Plz help will mark brainliest
Answer:
20
Step-by-step explanation:
First step is finding an angle in the rightmost triangle (angle K)
Using TOA we have
Tan(x)=4/8
x=26.565
which means that 90-26.565= 63.4349 will give us angle K in regards to the left triangle
Using this we can solve for JM
Tan(63.4349)=x/8
8tan(63.4349=x
x=16
So if JM = 16
and LM=4
take their sum to find JL
16+4=20