Answers
Answer:
Step-by-step explanation:
[tex]\frac{x+6}{x+7}-\frac{x+1}{x+2}=\frac{(x+6)*(x+2)}{(x+7)*(x+2)}-\frac{(x+1)(x+7)}{(x+2)(x+7)}\\\\[/tex]
USE FOIL method
(x +6)(x + 2) = x*x + x*2 +6*x +2*6
=x² + 2x + 6x + 12 {Combine like terms}
= x² + 8x + 12
(x+ 7)(x + 2) = x*x+ x*2 +7*x + 7*2
= x² +2x+ 7x + 14
= x² + 9x + 14
(x+1)*(x +7) = x*x + x *7 + 1*x + 1*7
=x² + 7x +x + 7
=x² + 8x + 7
[tex]\frac{x+6}{x+7}-\frac{x+1}{x+2}=\frac{(x+6)*(x+2)}{(x+7)*(x+2)}-\frac{(x+1)(x+7)}{(x+2)(x+7)}\\\\\\ =\frac{(x+6)*(x+2) - [(x+1)(x+7)]}{(x+2)(x+7)}\\\\\\= \frac{x^{2}+8x+12 -[x^{2}+8x+7]}{x^{2}+9x+14}\\\\\\=\frac{x^{2}+8x+12-x^{2}-8x-7}{x^{2}+9x+14}\\\\=\frac{5}{x^{2}+9x+14}\\\\\\\\\frac{x+6}{x+7}-\frac{x+1}{x+2}=\frac{1}{3x+1}\\\\\frac{5}{x^{2}+9x+14}=\frac{1}{3x+1}\\\\[/tex]
Cross multiply,
5*(3x+1) = x² + 9x + 14
5*3x + 5*1 = x² + 9x + 14
15x + 5 = x² + 9x + 14
x² + 9x + 14 - 5x - 5 = 0
x² + 9x - 5x + 14 - 5 = 0
Combine like terms
x² + 4x + 9 = 0
a = 1 ; b = 4 ; c = 9
D = b² - 4ac
= 4² - 4*1*9
= 16 - 36
= -20
= 20i² {i² = -1}
√D = √20i² = [tex]\sqrt{2*2*5*i*i}=2i\sqrt{5}[/tex]
[tex]x = \frac{-b+\sqrt{D}}{2a} \ or \frac{-b-\sqrt{D}}{2a}\\\\\\x= \frac{-4+2i\sqrt{5}}{2} \ or \frac{-4-2i\sqrt{5}}{2}\\\\x = \frac{2*(-2+i\sqrt{5})}{2} \ or \frac{2*(-2-i\sqrt{5}}{2}\\\\x = -2 +i\sqrt{5} \ or -2-i\sqrt{5}[/tex]
Related Questions
What is the value of y?
Answers
Answer:
y =24
Step-by-step explanation:
The exterior angle is the sum of the opposite interior angles
y+18 + 3y -41 = y+49
Combine like terms
4y -23 = y+49
Subtract y from each side
4y -y -23 = y+49-y
3y -23 = 49
Add 23 to each side
3y -23+23 = 49 +23
3y = 72
Divide by 3
3y/3 = 72/3
y =24
Helppppppp please ASAP
Answers
Answer:
YW = 10 units
Step-by-step explanation:
∠Y ≅ ∠X ⇒ WX ≅ WY ⇒ YW = 10 units
The table below shows elevation of different locations in the world. List the elevations in order from greatest to least.
Answers
Answer:
C 230, 92, 75, -52, -92
Step-by-step explanation:
from greatest to least.
please tell your teacher it would correctly be called "from highest to lowest".
but he/she was only focusing on numbers. understandably. so, from the greatest value to the least value.
positive numbers get smaller in their absolute values, when we go to the smaller side, but negative numbers get "bigger" in their absolute values, when we go to the smaller side.
-2 is smaller or lower than -1
and so on.
that is the reason for the correct answer.
This Measure of Center gives you the average number.
Mean
Median
Mode
Answers
The mean is the average of all the numbers combined
the median is the number centered directly in the middle with the same number of numbers on both sides of the number in the middle
The mode is how many times a number appears
What additional piece of information is needed to prove the triangles congruent by ASA?
S
T
J
B
D
P
A. ZT ZD
B. ZJ - ZS
C
JT – SD
D. TB-DP
Answers
Answer:
option B
Step-by-step explanation:
ASA congruent triangles shall have one more angle being equal
f(x) = 3x2 – x + 5; g(x) = 2x – 3. find f(x)-g(x)
Answers
Answer:
f(x) - g(x) = 3x² - 3x + 8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
f(x) = 3x² - x + 5
g(x) = 2x - 3
Step 2: Find f(x) - g(x)
Substitute in function values: f(x) - g(x) = 3x² - x + 5 - (2x - 3)[Distributive Property] Distribute negative: f(x) - g(x) = 3x² - x + 5 - 2x + 3[Subtraction] Combine like terms (x): f(x) - g(x) = 3x² - 3x + 5 + 3[Addition] Combine like terms: f(x) - g(x) = 3x² - 3x + 8Please help!! I'm super confused
Answers
108 in^2
10x14=140
6+10=16 divided by 2 = 8
8x4=32
Answer:
Step-by-step explanation:
The top part (is a square)
Area = s^2
Area = 10 * 10
Area = 100
The bottom part is a trapezoid
h = 4
b1= 6
b2 = 10
Area = (b1 + b2) * h / 2
Area = (10 + 6 ) * 4/2
Area = 16 * 4 /2
Area = 32
Total Area = 132
Standard fom: 4x20x² 24x
what is the Leading coefficient
Explain the behavior base on the
degree and leading coefficient?
Answers
Answer:
that is behavior that coefficient
Find the perimeter of the polygon.
Answers
Explanation: To find the perimeter of any 2-D shape, simply add all the sides together:
10+24+11+7+5+19+8+16=100
Perimeter=100
Hope that helps シ
I will give u brainliest and 5 star and thanks if its correct
Answers
Answer:
1. the side length of the square is 3 when its perimeter is 12.
2. (20/21, 5/21)
Step-by-step explanation:
2. 20/21 ÷ 4 = 20/21 × 1/4 = 5/21(the side length of the square with the given perimeter of 20/21)
=> (20/21, 5/21)
The cost of 6 pounds
of coffee is $3.
Answers
Answer:
ok 2 pound per 1 doller and 1 pund per0.50 cent
Step-by-step explanation:
round to the nearest tenth what is the distance between -3,3 and 1,2
Answers
Answer:
i dont know im sorry i wish you the best bro
Step-by-step explanation:
Y is inversely proportional to the square of x. If Y = 9 when x = 2, then what is y, when x is 10?
Answers
Answer:
y = 0.36
Step-by-step explanation:
Given y is inversely proportional to x² then the equation relating them is
y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation
To find k use the condition y = 9 when x = 2 , then
9 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )
36 = k
y = [tex]\frac{36}{x^2}[/tex] ← equation of variation
When x = 10 , then
y = [tex]\frac{36}{10^2}[/tex] = [tex]\frac{36}{100}[/tex] = 0.36
What is the approximate value of sin C?
Answers
Explanation:
Sin is opposite over hypotenuse!
5/13.93 = 0.358938
Rounded to the nearest hundredth is 0.36 :)
The point (-5,3) lies on the graph of f(x). Which of the following points lies on
f-1(x)?
Answers
Answer:
(3, -5).
Step-by-step explanation:
By the definition of inverses:
[tex]\text{If $f(a) = b$, then $f^{-1}(b)=a$}[/tex]
In other words, the inverse of a function returns the input when given the output of the original function.
We know that the point (-5, 3) lies on the graph of f(x). In other words:
[tex]f(-5)=3[/tex]
Then by definition:
[tex]f^{-1}(3)=-5[/tex]
So, the point (3, -5) must lie on the graph of f⁻¹(x).
The school band has a goal of raising $800 for some new uniforms. If they have raised $512 so far, what percent of their goal have they raised?
Answers
Answer:
64%
Step-by-step explanation:
A grocery store sells apple and oranges by the pound the cost of the apples is $1.30 the cost of the oranges is $1.84 how much more is the cost for 1 and 1 half pound of oranges than the cost for 1 and 1 half pounds of apples?
Answers
Answer:
1.5 pounds of oranges cost $0.81 more than 1.5 pounds of apples
Step-by-step explanation:
1.5 pounds of apples = 1.5 × $1.30 = $1.95
1.5 pounds oforanges = 1.5 × $1.84 = $2.76
$2.76 - $1.95 = $0.81
Help down below pleaseee. I'll rlly give brainliest whoever gives me the best answer if it allows me too since I need at least 2 ppl answering.
Answers
Answer:14 dollars, 2 pounds
Step-by-step explanation:
for they first one your just rounding wich is kinda easy you just round it up to the nearest dollar wich is 1 plus 13= 14 dollars.
for the second one it would be better to specify, but since we already did rounding on the first one this might be about the same topic, meaning it might be 2 pounds. But if not 2 and 1/4 of a pound.
Answer: the answer is in simple rounding-terms, 13.55 dollars rounded to dollars is just rounding off the cents, specifically the dimes or quarters. 55 cent can also be a half-dollar, but that is not important, 0.5 can be rounded to 1 in this case, so for question 14 you would add one to 13 dollars since 0.50 cents got rounded to 1 dollar and you get 14 dollars as your answer for the first question. for the next question American cheese i would assume is the same as the cheese referenced by Mr. Marsh, so the answer would be 2.25 pounds of cheese for number 15
Step-by-step explanation: my answer.
the answer is 14, 2.25
A wildlife refuge has 200 birds when it is first established. It is so
successful that the number of birds increases by 25% every year.
Write a function to model the situation.
Find the number of birds present after 7 years.
Answers
Answer:
[tex](a)\ f(x) =200(1.25)^x[/tex]
(b) 954 birds after 7 years
Step-by-step explanation:
Given
[tex]a = 200[/tex] --- initial
[tex]r =25\%[/tex] --- rate
Solving (a): The function.
This is represented as:
[tex]f(x) =a(1+r)^x[/tex]
So, we have:
[tex]f(x) =200(1+25\%)^x[/tex]
Express percentage as decimal
[tex]f(x) =200(1+0.25)^x[/tex]
[tex]f(x) =200(1.25)^x[/tex]
Solving (b): Birds after 7 years
This implies that we calculate f(7)
[tex]f(7) =200(1.25)^7[/tex]
[tex]f(7) =953.67[/tex]
[tex]f(7) =954[/tex] --- approximated
Which ordered pair (x,y) is the solution to the given system of linear equation?
Answers
Answer:
(x, y) = (-1, 4)
Step-by-step explanation:
3x + 3y = -3 (1)
-2x + y = 2 (2)
From (2)
y = 2 + 2x
Substitute y = 2 + 2x into (1)
3x + 3y = -3 (1)
3x + 3(2 + 2x) = -3
3x + 6 + 6x = -3
9x + 6 = -3
9x = -3 - 6
9x = -9
x = -9/9
x = -1
Substitute x = -1 into (2)
-2x + y = 2 (2)
-2(-1) + y = 2
-2 + y = 2
y = 2 + 2
y = 4
(x, y) = (-1, 4)
Answer:
(-1,0)
Step-by-step explanation:
what is the dilation/scale factor?
Answers
Scale factor = (image)/(preimage)
[tex]AC=8\\\\A'C'=12[/tex]
So, the scale factor is [tex]\frac{12}{8}=\boxed{1.5}[/tex]
Please help me ASAP!!
Answers
Answer:
its b The angles need to add up to 90 degrees and this fits the formula
Answer:
B is the right answer
Step-by-step explanation:
Hope this helps you!!
What is the equation of the line?
Answers
Answer:
y = -7
Step-by-step explanation:
This is a horizontal line
The y value does not change
It is of the form y=
y = -7
Answer:
y = -7
Step-by-step explanation:
A horizontal line has an equation of the form
y = k
where k is the y-coordinate of every point on the line.
We see that every point on this line has y-coordinate -7, so the equation is
y = -7
Ram's salary is 20% more than Shyam's salary.By what percentage is shyam's salary less than that of Ram's
Answers
Which of the following results from taking the square root of a negative
number?
A. Imaginary number
B. Negative number
C. Positive number
D. Irrational number
Answers
Which of the following uses the reciprocal property to rewrite x/12 = 32/18 ?
Answers
Answer: A
Step-by-step explanation:
x/32 = 18/13
Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. Together they charged a total of $1400.
What was the rate charged per hour by each mechanic if the sum of the two rates was $165 per hour
Answers
Answer:
$115/hr The 10 hr mechanic
$50/hr The 5hr mechanic
Step-by-step explanation:
let the 10 hr mechanic charge x
then the 5 hr mechanic charges 165 - x
------------------------------
10x + 5(165 - x) = 1400
10x + 825 - 5x = 1400
5x = 575
x = 115 The 10 hr mechanic
165 - x = 50 The 5hr mechanic
can someone tell me how to do this?
Answers
Answer:
x = 10
Step-by-step explanation:
(5x + 20) = 70
5(10) + 20 = 70
Translate this sentence into an equation:
44 is the sum of 24 and Donnie's height
Answers
24 + x = 44
explanation:
24 is given and x represents donnies height so those two numbers added together equals 44
Pls help! (don't give wrong answer pls)
Decide whether the sequence is Arithmetic, Geometric or Neither.
4, 9, 16, 25, ...
Answers
Check arithmetic
t4-t3 t3-t2
25-16 16-9
=9 =7
sequence is not arithmetic bcoz t4-t3 is unequal to t4-t3
check geometric
t4÷t3 t3÷t2
25÷16 16÷9
=1.6 1.7
sequence is not geometric bcoz t4÷t3 is unequal to t3÷t2
neither