1)
[tex]\frac{d^2 - 9}{d^2 - 7d + 12} = \frac{(d - 3)(d + 3)}{(d - 3)(d - 4)} = \frac{d + 3}{d - 4}[/tex]
2)
[tex]\frac{m^2 + 2mn + n^2}{m^2 - n^2} = \frac{(m + n)(m + n)}{(m - n)(m + n)} = \frac{m + n}{m - n}[/tex]
3)
[tex]\frac{x^2 + xy - 6y^2}{x^2 - 3xy + 2y^2} = \frac{(x + 3y)(x - 2y)}{(x - y)(x - 2y)} = \frac{x + 3y}{x - y}[/tex]
1. [tex] \bf \dfrac{ {d}^{2} - 9 }{ {d}^{2} - 7d + 12 } [/tex]
[tex] \tt : \implies \dfrac{ {d}^{2} - (3)^{2} }{ {d}^{2} - 3d - 4d + 12 } [/tex]
By using identinty a² - b² = (a + b)(a - b) in numerator and splitting method in denominator :
[tex] \tt : \implies \dfrac{ (d+3)(d-3) }{ {d}^{2} - 3d - 4d + 12 } [/tex]
[tex] \tt : \implies \dfrac{ (d+3)(d-3) }{d(d - 3) - 4(d - 3)} [/tex]
[tex] \tt : \implies \dfrac{ (d+3)\cancel{(d-3)} }{\cancel{(d - 3)}(d - 4)} [/tex]
[tex] \tt : \implies \dfrac{d+3}{d - 4} [/tex]
Hence, answer is [tex] \boxed{\bf \dfrac{d+3}{d - 4} }[/tex]
________________________________
2. [tex] \bf \dfrac{ {m}^{2} + 2mn + {n}^{2} }{ {m}^{2} - {n}^{2} } [/tex]
By using identinty a² + 2ab + b² = (a + b)² in numerator and a² - n² = (a + b)(a - b) in denominator :
[tex] \tt : \implies \dfrac{(m+n)^{2}}{(m+n)(m-n)}[/tex]
[tex] \tt : \implies \dfrac{\cancel{(m+n)}(m+n)}{\cancel{(m+n)}(m-n)}[/tex]
[tex] \tt : \implies \dfrac{m+n}{m-n}[/tex]
Hence, answer is [tex] \boxed{\bf \dfrac{m+n}{m-n}}[/tex]
________________________________
3. [tex] \bf \dfrac{{x}^{2} + xy - 6{y}^{2}}{{x}^{2} - 3xy + 2{y}^{2}}[/tex]
By using splitting method in both numerator and denominator :
[tex] \tt : \implies \dfrac{{x}^{2} + 3xy - 2xy - 6{y}^{2}}{{x}^{2} - xy - 2xy + 2{y}^{2}}[/tex]
[tex] \tt : \implies \dfrac{x(x + 3y) - 2y(x + 3y)}{x(x - y) - 2y(x - y)}[/tex]
[tex] \tt : \implies \dfrac{\cancel{(x-2y)}(x + 3y)}{\cancel{(x-2y)}(x - y)}[/tex]
[tex] \tt : \implies \dfrac{x + 3y}{x - y}[/tex]
Hence, answer is [tex] \boxed{\bf \dfrac{x + 3y}{x - y}}[/tex]
This equation shows how the total number of souvenirs Mark buys is related to the number of days he spends on vacation. s = d The variable d represents the number of days he spends on vacation, and the variable s represents the total number of souvenirs he buys. How many days will Mark have to spend on vacation before he will have bought a total of 12 souvenirs?
Answer:
12 days
Step-by-step explanation:
Given:
s = d
Where,
d = number of days he spends on vacation
s = total number of souvenirs he buys
How many days will Mark have to spend on vacation before he will have bought a total of 12 souvenirs?
s = 12
Since,
s = d
Then,
12 = d
Therefore, Mark will have to spend a total of 12 days on vacation before he will have bought a total of 12 souvenirs
Name each polynomial by degree and number of terms. 1) 9x + 5
Answer:
1st degree binomial
Step-by-step explanation:
Answer:
1rst degree
binomial
Step-by-step explanation:
Which is the simplified form of p0?
Answer: 1
Step-by-step explanation:
An acute angle is less than 90°. Choose the inequality that represents the statement.
The inequality that represents the statement. "An acute angle is less than 90°"would be x < 90°.
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
WE have to find an inequality that represents the statement. "An acute angle is less than 90°".
Let x represent an acute angle.
Therefore, the inequality form as;
x < 90°
Hence, an inequality that represents the statement. "An acute angle is less than 90°"would be x < 90°.
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the product of two odd numbers
Answer:
Odd
Step-by-step explanation:
2 odd numbers will always create another odd number.
log 2 x=a then what is logx 36
Answer:
A is the answer
Step-by-step explanation:
please vote me
Simplify this expression. 17 - 12x - 18 - 5x = ??
Find the slope of (-2,1),(2,-2)
Answer:
-3/4 is the slope.
Step-by-step explanation:
Use this formula to find slope.
y2-y1/x2-x1
PLUG IN
-2 -1/2- (-2) = -3/4
The slope is -3/4
Answer:
[tex]\boxed {m = -\frac{3}{4}}[/tex]
Step-by-step explanation:
Use the Slope Formula to help you determine the slope of the two following points:
[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
(where [tex](x_{1}, y_{1})[/tex] is the first point and [tex](x_{2}, y_{2})[/tex] is the second point)
-Apply both points to the formula:
[tex](x_{1}, y_{1}) = (-2, 1)[/tex]
[tex](x_{2}, y_{2}) = (2, -2)[/tex]
[tex]m = \frac{-2 - 1}{2 + 2}[/tex]
-Solve:
[tex]m = \frac{-2 - 1}{2 + 2}[/tex]
[tex]m = \frac{-3}{4}[/tex]
[tex]\boxed {m = -\frac{3}{4}}[/tex]
Therefore, the slope is [tex]-\frac{3}{4}[/tex].
Help me doing this plzzz
Answer:
4x³+8x²-x-2=4x².(x+2)-(x+2)=(4x²-1).(x+2)=(2x-1).(2x+1).(x+2)
Gordon, Henry and Sarah share £48 in a ratio 2:3:1. How much money does each person get?
Answer: Gordon:16
Henry: 24
Sarah:1
Step-by-step explanation:
Add up the ratios and divide 48 by 6(added up ratios) and you get 8. Multiply that by individual ratios.
PLEASE HELPPPP IS ALGEBRA 1 it’s easy i guess :/
19
Tell whether the triangles are similar. Explain.
Please help!!!!!!!
Answer:
Step-by-step explanation:
Help this person she really needs help! XD
helpp me plzz i really need helppp
thanks!!!!!
Answer:
-14
Step-by-step explanation:
Someone help
5(3m-2)=20
solution :-
3m+2(m+2)=20-(2m-5)
=> 3m + (2m + 4) = 20 - (2m -5)
=> 5m + 4 = 20 -2m +5
=> 5m + 2m = 25 -4
=> 7m = 21
=> m = 3 answer
Need help with this one fast
Answer:
a ≈ 43.64
hope this helps
Evaluate the equation for the indicated value, f(n)=5n+8 for f(4),
The value of the function f(n)=5n+8 for f(4) will be 28.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given function is f(n)=5n+8. The value of the function at equal to 4 will be calculated as below:-
f(n)=5n+8
f(4) = ( 5 x 4 + 8 )
f(4) = 20 + 8
f(4) = 28
Therefore, the value of the function f(n)=5n+8 for f(4) will be 28.
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How do I solve for pie?
4x+8y=20 and -2x+y=-15
System of equations?
Answer:
a
Step-by-step explanation:
24 divided by 7872
PLEASE HELP
Answer:
328 IF its 7,872 divided 24. If it 7,872 divided by 24 then it's 0.00304878049
Step-by-step explanation: Please mark as brainlest i really need to keep me motivated.
A ball is thrown vertically upward from the top of a building 224 feet tall with an initial velocity of 80 feet per second. The distance s (in feet) of the ball from the ground after t seconds is 224 0t 6ts = +8 −1 2a) After how many seconds does the ball pass the top of the building? b) After how many seconds does the ball strike the ground?
Answer:
i dont really know
Step-by-step explanation:
You can search t up on googl nd get the answer most lieyly
translations can be moved along an vector at any time and still result in the same image true or false ?
Answer:
True................
Answer:
True
Step-by-step explanation:
Hello pls helppppppppppp
Answer:
B
Step-by-step explanation:
Answer:
For example, if we multiply the numerator and denominator of 2/3 by 4 we get. 2/3 = 2×4 / 3×4 = 8/12 which is an equivalent fraction of 2/3. t is 12/20 Simplified? - 3/5 is the simplified fraction for 12/20.least common factor of 7 3 and 5
Answer:
105
Step-by-step explanation:
3: 3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99,102,105
5: 5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100,105
7:7,14,21,28,35,42,49,56,63,70,77,84,91,98,105
What is 7/8 x 4/5 divided by 7/20
Answer: 2
Step-by-step explanation: First, multiply 7/8 by 4/5 which equals to 7/10. Then, divide 7/10 by 7/20. Finally, you should end up with a result of 2.
Alexa is using 6 pounds of apples to make pies.
How many ounces of apples is Alexa using for the pies?
Answer:
96 oz
Step-by-step explanation:
There are 16 oz in a pound, so you do 16 * 6 = 96
Student ID number consists of 6 characters. The first four
characters can be any number 1-9 without restrictions. The
last two characters are letters and cannot repeat. How
many student IDs are possible?
a) 6,760,000
b) 4,264,650
O C) 6,500,000
d) 78
Please hurry
Answer:
b. 4,264,650
Step-by-step explanation:
(9 * 9 * 9 * 9) * (26 * 25)
Can someone help please ??
Answer:
a)1 , 5 , 9 , 13 , 17, 21 , 25
An animal reserve has 20,000 elk. The population is increasing at a rate of 13% per year. How long will it take for the population to reach 60,000? If necessary, round your answer to the nearest tenth. The population will reach 60,000 in approximately years.
Write the following sentence in if-then form
“ an acute angle has a measure less than 90”
Answer:
If the angle is less than 90 degrees, it is an acute angle.
Step-by-step explanation:
question.
Contrast the plate movements that cause the stresses in diagrams B and C How did geography affect the way Greeks made their livings?
Answer:
1. Greece made most of their living from the sea.
2. They became fishers and sailors to get food.
3. On their peninsula they had many different ways to trade with other countries.
4. Greece's mountains aren't good for growing crops, although their climate was mild ,so they could grow wheat, barley, olives, and grapes.
5. Since Greece's sea's are dived from one another, it make trading fiercely independent.1. Greece made most of their living from the sea.
2. They became fishers and sailors to get food.
3. On their peninsula they had many different ways to trade with other countries.
4. Greece's mountains aren't good for growing crops, although their climate was mild ,so they could grow wheat, barley, olives, and grapes.
5. Since Greece's sea's are dived from one another, it make trading fiercely independent.
