Answer:
D) 74
Step-by-step explanation:
1c = 6p
1c = 1.5f
1f = 296
6/1.5 = 4
296/4 = 74
❊ Simplify :
1. [tex] \large{ \tt{ \frac{a + 2}{ {a}^{2} + a - 2 } + \frac{3}{ {a}^{2} - 1 } \: \: \{ANS : \frac{a + 4}{ {a}^{2} - 1 } \}}}[/tex]
2. [tex] \large{ \tt{ \frac{1}{(a - b)(b - c)} + \frac{1}{(c - b)(a - c) } \: \: \{ANS : \frac{1}{(a - b)(a - c) } \}}}[/tex]
-Show your workings! *
- Random/ Irrelevant answers will be reported!
Answer:
See Below.
Step-by-step explanation:
Problem 1)
We want to simplify:
[tex]\displaystyle \frac{a+2}{a^2+a-2}+\frac{3}{a^2-1}[/tex]
First, let's factor the denominators of each term. For the second term, we can use the difference of two squares. Hence:
[tex]\displaystyle =\frac{a+2}{(a+2)(a-1)}+\frac{3}{(a+1)(a-1)}[/tex]
Now, create a common denominator. To do this, we can multiply the first term by (a + 1) and the second term by (a + 2). Hence:
[tex]\displaystyle =\frac{(a+2)(a+1)}{(a+2)(a-1)(a+1)}+\frac{3(a+2)}{(a+2)(a-1)(a+1)}[/tex]
Add the fractions:
[tex]\displaystyle =\frac{(a+2)(a+1)+3(a+2)}{(a+2)(a-1)(a+1)}[/tex]
Factor:
[tex]\displaystyle =\frac{(a+2)((a+1)+3)}{(a+2)(a-1)(a+1)}[/tex]
Simplify:
[tex]\displaystyle =\frac{a+4}{(a-1)(a+1)}[/tex]
We can expand. Therefore:
[tex]\displaystyle =\frac{a+4}{a^2-1}[/tex]
Problem 2)
We want to simplify:
[tex]\displaystyle \frac{1}{(a-b)(b-c)}+\frac{1}{(c-b)(a-c)}[/tex]
Again, let's create a common denominator. First, let's factor out a negative from the second term:
[tex]\displaystyle \begin{aligned} \displaystyle &= \frac{1}{(a-b)(b-c)}+\frac{1}{(-(b-c))(a-c)}\\\\&=\displaystyle \frac{1}{(a-b)(b-c)}-\frac{1}{(b-c)(a-c)}\\\end{aligned}[/tex]
Now to create a common denominator, we can multiply the first term by (a - c) and the second term by (a - b). Hence:
[tex]\displaystyle =\frac{(a-c)}{(a-b)(b-c)(a-c)}-\frac{(a-b)}{(a-b)(b-c)(a-c)}[/tex]
Subtract the fractions:
[tex]\displaystyle =\frac{(a-c)-(a-b)}{(a-b)(b-c)(a-c)}[/tex]
Distribute and simplify:
[tex]\displaystyle =\frac{a-c-a+b}{(a-b)(b-c)(a-c)}=\frac{b-c}{(a-b)(b-c)(a-c)}[/tex]
Cancel. Hence:
[tex]\displaystyle =\frac{1}{(a-b)(a-c)}[/tex]
Please find attached photograph for your answer.
Hope it helps
Do comment if you have any query
if the lines shown below are perpendicular if the green line has a slope of -1/4 what is the slipped of the red line
Answer:
C; 4
Step-by-step explanation:
Mathematically, when two lines are perpendicular, the product of their slopes equal -1
in that case, we have it that;
m1 * m2 = -1
where m1 is the slope of the first line and m2 is the slope of the second line
Hence,
m2* -1/4 = -1
-m2/4 = -1
-m2 = -4
m2 = 4
I need this solve really fast.
Which sequences are geometric? Select three options.
Answer:
I guess this is the answer
Answer:
1 2 and 4 not capping like everyone else
Step-by-step explanation:
the quiz sequence
A saline solution has a weight of 1.12 kg per liter. What is the weight of the saline solution of 0.75 l?
Answer:
0.84 kg
Step-by-step explanation:
Given that :
Weight per liter = 1.12kg per liter
That is 1 Litre weighs 1.12 kilogram
The weight of saline solution of 0.75 Litre will be :
1 Litre = 1.12 kg
0.75 Litre = x
Cross multiply :
1 * x = 1.12 * 0.75
x = 0.84 kg
Hence, 0.75 Litre weighs 0.84 kg
Use the drop-down menus to choose the correct locations on the number line.
Point B is located at
The two points that are opposite are
>
Point D is located at
v is one tick mark to the left of point A.
Answer:
i) Point B is located at 0.
ii) The two points that are opposite are 5 / 5 and 10 / -5 and 5 / 5, 10 and -5, -10.
iii) Point D is located at 35.
iv) -20 is one tick mark to the left of point A.
Which of the following represents the general form of an inequality?
Ax + By 2 C
Ax + By >
Ax + By < 0
All of the choices
Answer:
Third option:
Ax + By < 0
Step-by-step explanation:
The general form of an inequality is:
(something) (symbol) (another thing).
Where the symbols can be:
> = "larger than"
< = "smaller than"
≤ = "smaller than or equal to"
≥ = "larger than or equal to"
So, a given inequality can be:
K > M
This means that K is larger than M.
From the given options, the only one that has this general form is the third option:
Ax + By < 0
This can be read as:
"A times x, plus B times y, is smaller than zero"
HELP!!!!!!!!!!!!!!!! pls
Answer: y = 25 - 2x
Step-by-step explanation:
y = mx + b
m = slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{23-25}{1-0} =\frac{-2}{1} =-2[/tex]b = y-intercept = when x = 0 = 25y = -2x + 25
PLEASE HELP! Solve the system of equations by graphing on your own paper. What is the x-coordinate of the solution?
Answer:
x = 4
Step-by-step explanation:
steps are in the pic above.
how do you discribe any opposite in a parallelogram?
Answer:
Opposite sides of a parallelogram are parallel (by definition) and so will never intersect. The area of a parallelogram is twice the area of a triangle created by one of its diagonals. The area of a parallelogram is also equal to the magnitude of the vector cross product of two adjacent sides.
Step-by-step explanation:
Of the four choices given, which two, when written as a system, have a solution of (-4,5)?
х
-1
2
3
5
y
2
-1
-2
-4
2x+y=-3
-2x+y=-3
Х
-1
2.
3
7
0
-3
4
-8
2x+y=-3 and
Х
--1
2
3
5
y
2.
-1
-2
-4
0-2x+y=-3 and
х
-1
2
3
5
у
2.
-1
-2
-4
Answer:
both choices with 2x+y = -3
Step-by-step explanation:
to have the solution (-4, 5), that point must be on both equations/functions, meaning it must be on either one.
in other words, if the point is not on at least one of the functions, it cannot be a solution for that system.
the given function
2x + y = -3
looks like for the point (-4, 5)
2×-4 + 5 = -3
-8 + 5 = -3
-3 = -3
correct.
but
-2x + y = -3
looks like for (-4, 5)
-2×-4 + 5 = -3
8 + 5 = -3
13 = -3
wrong. the point is not on this function.
as we can therefore rule out 2 of the answer options, the other 2 most be correct.
The two equations which when written as a system has a solution of (-4, 5) is; 2x + y = -3 and 2x + y = -3
Inequalities
The correct equations must have same output with the given one when we place -4 and 5 for x and y respectively.
Now, for 2x + y = -3
At x = -4, and y = 5 we have;
2(-4) + 5 = -3
Same with the right hand side.
For -2x + y = -3;
At x = -4, and y = 5 we have;
-2(-4) + 5 = 13
Not the same with the right hand side.
Thus, the two equations with 2x + y = -3 are correct
Read more about Inequalities at; https://brainly.com/question/24372553
Two cylinders are similar. The surface
area of one is 64 cm2, and the surface
area of the other is 81 cm2. Find the
scale factor between them.
Enter the smaller number first.
scale factor =
[?]:[]
solve: 28 − ≥ 7( − 4)
(show your work)
real answers only pls :(
Hi need help with this so plz help
Answer:
t > 28
Step-by-step explanation:
Which of the statements proves that the lines a and b are parallel?
Answer:
C
Step-by-step explanation:
1,2 are both supplementary
Linear Law Additional Mathematics F4
Answer:
h = 3, k = 64
Step-by-step explanation:
Given
[tex]log_{2}[/tex] y = - [tex]\frac{1}{2}[/tex] [tex]log_{2}[/tex] x + 3
In the form
y = mx + c ( m is the slope and c the y- intercept )
Then
h = 3
On the [tex]log_{2}[/tex] axis [tex]log_{2}[/tex] y = 0 then
0 = - [tex]\frac{1}{2}[/tex] [tex]log_{2}[/tex] k + 3 ( subtract 3 from both sides )
- 3 = - [tex]\frac{1}{2}[/tex] [tex]log_{2}[/tex] k ( divide both sides by - [tex]\frac{1}{2}[/tex] )
6 = [tex]log_{2}[/tex] k , then
k = [tex]2^{6}[/tex] = 64
Find the missing side of the triangle using the Pythagorean Theorem.
Answer: a^2 + b^2 = c^2
c^2 - a^2 = b^2 \/---
b^2
Step-by-step explanation: once completed you have ur answer
Answer:
[tex]\boxed {\boxed {\sf 18 \ yards}}[/tex]
Step-by-step explanation:
This triangle is a right triangle. We know this because of the small square in the corner representing a 90 degree angle. Therefore, we can use the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
In this formula a and b are the legs of the triangle and c is the hypotenuse.
In this triangle, the legs are 24 and a, because these sides form the right angle. 30 is the hypotenuse because it is opposite the right angle.
a=a b= 24 c= 30Substitute the values into the formula.
[tex]a^2+(24)^2=(30)^2[/tex]
Solve the exponents.
(24)²= 24*24=576 (30)^2= 30*30=900[tex]a^2+ 576=900[/tex]
We are solving for a, the missing side of the triangle. We must isolate the variable. 576 is being added. The inverse of addition is subtraction, Subtract 576 from both sides of the equation.
[tex]a^2+576-576=900-576\\a^2=900-576\\a^2=324[/tex]
a is being squared. The inverse of a square is a square root. Take the square root of both sides.
[tex]\sqrt{a^2}=\sqrt{324}\\a=\sqrt{324}\\a=18[/tex]
The missing side of the triangle is 18 yards.
a package is accidentally dropped from a helicopter from a height of 3,136ft. if the equation for height as a function of time is h(t) = -16t^2 + initial height where t is time in seconds and h(t) is height in feet, how many seconds will it take for the package to hit the ground?
Answer:
t = 14 seconds
Step-by-step explanation:
Given that,
A package is accidentally dropped from a helicopter from a height of 3,136ft.
The equation for height as a function of time is :
[tex]h(t) = -16t^2 + \text{initial height}[/tex]
So,
[tex]h(t) = -16t^2 +3,136[/tex]
When it hits the ground, h(t) = 0
So,
[tex]-16t^2 +3,136=0\\\\-16t^2=-3136\\\\t^2=\dfrac{3136}{16}\\\\t^2=196\\\\t=14\ s[/tex]
So, it will take 14 seconds for the package to hit the ground.
Bajo que método de inventario se usa la cuenta de compra
Answer:
Estimating the economic impact of climate change from weather variation
Step-by-step explanation:
Estimating the economic impact of climate change from weather variation:If economists are going to be able to offer clear guidance about the appropriate ambition of climate change policy, we need firmer damage estimates.This column introduces a new model that prices farmers’ ex-post and ex-ante adaptations to weather changes and forecasts. #accelerationism
-x/8-11=12
/ means fraction
Answer:
Step-by-step explanation:
-x/8=12+11=23
-x=23*8=184
x=-184
x=-184Answer:
Step-by-step explanation:
What should the follow equations is equivalent to 6.87p+9.2=-7.056
Answer:
P=-2.3662299854
Step-by-step explanation:
6.87p = - 7.056 -9.2
So 6.87p= - 16.256
P=-2.3662299854
1) Give 5 examples of a difference of two perfect squares
2) Give the factors of your examples
3) What do you call the factors of a difference of two perfect squares?
please help me
ᴀɴsᴡᴇʀ:
1.Example, x²-25 can be factored as (x+5)(x-5).
2.This method is based on the pattern (a+b)(a-b)=a²-b², which can be verified by expanding the parentheses in (a+b)(a-b).
3.When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5).
ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs!
☞︎︎︎ᴄᴀʀʀʏ ᴏɴ ʟᴇᴀʀɴɪɴɢ☜︎︎︎
What is the result of isolating x^2 in the equation below?
y^2-3x^2 = 6
Answer;
x² = 42 - 2
3
Step-by-step explanation:
#carryonlearning
Answer:
Step-by-step explanation:
y² - 3x² = 6
Subtract y² from both sides
-3x² = 6 - y²
Divide by -3
[tex]\frac{-3x^{2}}{-3}=\frac{6-y^{2}}{-3}\\\\x^{2}=\frac{y^{2}-6}{3}[/tex]
What values of x make this true?
(x^2–3x+2)/(x –1) = x – 2
Answer:
Any value of x makes the equation true. All real numbers Interval Notation: ( − ∞ , ∞ )
Hope This Helps!!!
The ratio of boys to girls in the 9th grade is 3 to 4. There are 176 girls. Set up a proportion to model this information.
Answer:
3/4=176
Step-by-step explanation:
Answer:
3/4 = b/176
Step-by-step explanation:
pls give me brainliest
3. Sarah bought 3 pounds of apples for $6. How much did each pound of apples cost?
Answer:
A
Step-by-step explanation:
6/3 = 2
Answer:
$2 each
Step-by-step explanation:
3 pounds of apples for $6
$6÷3 lbs= $2 each pound
use abc to find the value of sin b
Answer:
12/37
Step-by-step explanation:
We know ,
=> sin B = p/h
=> sin B = 12/ 37
Answer:
Step-by-step explanation:
[tex]Sin \ B = \frac{opposite \ side }{hypotenuse}\\\\Sin \ B = \frac{35}{37}\\\\[/tex]
Find the size of each of the unknown angles. Help me plz
Answer:
2a+15 = 125(being alternate angle)
or,2a = 125-15
or,2a = 110
or,a = 110÷2
,a = 55
again,2a+15+b+30=180(Being co-interior angle)
or,2×55+15+b+30=180
or,110+15+30+b=180
or,155+b=180
or,b=180-155
Therfore,b=25
in how many ways can alice distribute 12 apples to 3 children? each child has to have AT LEAST 1 apple.
Answer:
I think it would be 4 apples for each of them !
Step-by-step explanation:
its division. you had to do 12 ÷ 3
Answer:
The answer is 4 apples per child.
Step-by-step explanation:
If we have 12 apples and 3 children we write as a ratio like this:
12:3
So we have to figure out how many apples each child gets to have.
Next, we cancel out 3 from 12 and 3 which becomes:
4:1
So each child gets 4 apples.
I hope this helps!
Help me solve for 20 please ok?
Answer:
option c
Step-by-step explanation:
Quadratic function f(x) = ax² + bx +c
Here the the co-efficient of x, that is a tells if the graph is wider or narrower.
1) a < 1 that is if a is decimal less than 1, then the graph is wider.
2) a > 1, then the graph is narrow.
given g(x) = square root of x - 4 and h(x) = 2x - 8 What is g(h10))?
Step-by-step explanation:
First find h(10)
h(10)=2(10)-8
h(10)=12
Now plug in 12 as the value of x in g(x) ie.g(12)
So g(12)=√12-4=√8=2√2
