Answers
x^2 - x - 2 factors into (x - 2)(x + 1) both of which can be crossed out or canceled with the factors in the numerator. That creates very really tiny holes at x = 2 and x = - 1.
[tex] {x}^{2} - x - 2 \: = > (x + 1)(x - 2)[/tex]
Which leaves is with the equation:
[tex]y = \frac{(x - 5)(x + 1)(x - 2)}{(x + 1)(x - 2)} [/tex]
We can see that we have the common factors of (x+1) and (x-2), so these cancel out in the numerator and denominator:
[tex]y = \frac{(x - 5)}{1} [/tex]
a.k.a: y = x - 5
So if x+1 and x-2 cancel out, then the x values of the holes are:
x+1=0
x= -1
And
x-2=0
x= 2
Now we plug in each of these numbers into our simplified equation:
y = x - 5
y=(-1)-5
y= -6
This gives us the coordinate (-1,-6)
y = x - 5
y=(2)-5
y= -3
This gives us the coordinate (2,-3)
So the holes are at (-1,-6) and (2,3)
Related Questions
I need help with the attached problem. GIVING BRAINLIEST! Thank you!
Answers
First let x = the dimension of the squares and y = the congruent sides of the isosceles triangles.
To get our first equation of the system, we look at the statement regarding the perimeter of DRAGONFLIES being equal to 127.. this implies the following equation: 9x + 2y = 127
To get the second equation, we need to know that the perimeter of an isosceles triangle is defined by: P = 2(length of the congruent sides) + base side. Or in our case, 55 = 2y + x
Now our system:
9x + 2y = 127
x + 2y = 55
You can use the substitution method or linear combination to solve this system. If you have questions about how to do that, let me know.
The solution of the system is: x = 9 and y = 23
Recall x = the dimension of each square, so the area of DRAG is 81
This is my best guess at how to do the problem.. :-) Let me know if I can answer any questions.
What is the sum of 11 feet and 4 yards?
8 yards
15 feet
23 feet
8 yards, 1 foot
Answers
3 × 4 = 12
12 + 11 = 23
The answer is 23 ft.
Hope this helps!
The Sunday school teacher gave 5 Friend's Day invations to each of her 19 students to give to their friends. She had 5 left over. How much invations did the teacher start out with?
Answers
A basketball player scores 162 points in 9 games. at this rate, how many points will she score in a 24-game season? answer
Answers
162/9 = 18 points per game
18 points x 24 games = 432
In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 8m? Enter your answer in the box
Answers
The clock face in a famous clock tower has a radius of about 5 meters. What is the area of the clock face to the nearest square meter? Use 3.14 as an approximation for .
Answers
79 square meter when you round it up
Answer:
The area of the clock face is [tex]79\ m^{2}[/tex]
Step-by-step explanation:
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=5\ m[/tex]
[tex]\pi=3.14[/tex]
substitute
[tex]A=(3.14)(5^{2})=78.5\ m^{2}[/tex]
Round to the nearest square meter
[tex]78.5\ m^{2}=79\ m^{2}[/tex]
The area of a rectangular deck can be modeled by f(x) = 2x3 + 30x2 6x 90. If x + 15 represents the width, which expression represents the length?
2x^2 21
2x^2 6
2x^2 + 9
2x^2 + 45,
Answers
Y=f(x) =-2^x. Find f(x) when x=0
Answers
Answer:
f(0) = -1
Step-by-step explanation:
Any scientific or graphing calculator can help you do this. According to the Order of Operations, the exponent is evaluated first, then the sign is applied:
f(0) = -2^0 = -(2^0) = -1
Simplify: 1/3x(6x - 1) A) 5 3 x B)2x - 1 C)2x - 1 3 D)2x2 - 1 3 x
Answers
2x^2 -(1/3)x . . . . . . matches selection D
Answer is D Use the distributive property to simplify.
Evaluate: f(x) = -2x – 3 for x = -1. A. -5 B. -2 C. -1 D. 5
Answers
Write a recursive definition for the sequence 14, 10, 6, 2,… Common difference is 4 what do I do next?
Answers
a[n+1] = a[n] -4 . . . says each term is 4 less than the one before it
Since you're looking for a recursive definition, you simply need to do 2 things.
1. Define the function for some constant starting point(s).
2. Define the function in terms of itself for all other points.
For this question, I'll assume the first point is f(0). So we have f(x) = ?, with f(0) = 14
And we've handed the starting point by simply declaring that f(0) has the value of 14. Now for the recursive portion.
As you've noticed, each subsequent value is 4 less than the previous. So we can say f(x) = f(x-1) - 4. And with that, we can make the function.
f(x) = f(x-1) - 4, with f(0) = 14
As a side note, you are not restricted to just 1 starting value, nor just the immediate prior invocation of the function. For instance the definition of the Fibonacci sequence could be defined as
f(x) = f(x-1) + f(x-2), with f(0) = 0 and f(1) = 1
Plz plz help it is due in tomorrow anyone plz
Answers
2. 3/2 or an alternative 1 1/2
3. 5/33 or an alternative 1 2/3
4. 2 3/5 or an alternative 2 3/5
5. 20/3 or an alternative 6 2/3
6. 49/6 or an alternative 8 1/6
if you have any further question ask away!
hope I helped ;)
The temperature of a cup of coffee t minutes after it has been poured is described by the function C(t) = 20 + 60(0.95)^t . a. How many minutes does it take for the coffee to cool to a temperature of d degrees? b. About how fast is the temperature dropping when t = 1?
Answers
120 = 120(2 ^ 10a) + 60
2 ^ -1 = 2 ^ 10a
a = -1/10
The temperature of coffee 30 minutes after it was poured is:
F = 120 ( 2 ^ -30/10) + 60
F = 120 * 1/ 8 + 60
F = 15 + 60
F = 75
Find the simplified form of (-3)^-4
A. 12
B. -81
C. 1/81
D. -1/81
Answers
the answer is C
= 1 / (-3)^4
= 1/81
answer
C. 1/81
Roberto will save 1/6 of his allowance each day. If he gets $2.00a day, about how much money will be save each day? Round your answer to the nearest penny.
Answers
Please Help me !!Q 1,2,3
Answers
1i) (20 cm)*(12 cm) = 240 cm^2
2ii) (7 cm)*(7.5 cm) = 52.5 cm^2
3iii) 27 cm^2 = (6 cm)*h
.. h = (27 cm^2)/(6 cm) = 4.5 cm
Given that ABCD is a parallelogram, solve for k. A. 4 B. 7 C. 8 D. 11
Answers
The answer is 7 on e2020.
Aaliyah ate 7⁄8 of her mini-pizza, while James only ate 3⁄4 of his mini-pizza. How much more did Aaliyah eat
Answers
Final answer:
Aaliyah ate 1/8 more of the mini-pizza than James after converting their consumed amounts to a common denominator and subtracting James's share from Aaliyah's.
Explanation:
To calculate how much more Aaliyah ate compared to James, we need to compare the fractions of the mini-pizzas they each consumed. Aaliyah ate 7/8 of her mini-pizza, while James ate 3/4 of his mini-pizza. To make a comparison, we have to ensure both fractions have the same denominator.
Since the least common denominator for 4 and 8 is 8, we convert James's fraction from 3/4 to 6/8 by multiplying both the numerator and the denominator by 2. Now we can compare the amounts:
Aaliyah: 7/8 of a mini-pizza
James: 6/8 of a mini-pizza
To find out how much more Aaliyah ate, we subtract James's portion from Aaliyah's:
7/8 - 6/8 = 1/8
Therefore, Aaliyah ate 1/8 more of the mini-pizza than James.
Which expression is equivalent to -18a^-2 b^5/-12a^-4 b^-6? Assume a=0, b=0.
a- 2a^2 b^11/3
b-2a^2 b^30/3
c-3a^2 b^11/2
d-3a^2 b^30/2
Answers
coefficients: 18/-12 = -3/2
exponents of a: -2-(-4)=2
exponents of b: 5-(-6)=11
The required expression is (-3/2)a²b¹¹ which is equivalent to the given expression. which is the correct answer would be option (C)
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The expression is given in the question as:
-18a⁻² b⁵/-12a⁻⁴ b⁻⁶
To find the equivalent expression for -18a⁻² b⁵/-12a⁻⁴ b⁻⁶, we need to combine the constants and factors that have the same base and exponent.
You can begin by combining the constants in the fraction: -18/-12 = -3/2.
Next, you can simplify the terms involving the variables. Recall that when you divide two powers with the same base, you subtract the exponents. Therefore, you can simplify the expression as follows:
(-3/2)(a⁻² ÷ a⁻⁴ (b⁵ ÷ b⁻⁶)
= (-3/2)(a⁻⁴ a⁴) (b⁵ b⁶)
= (-3/2)(a²)(b¹¹)
= (-3/2)a²b¹¹
This is the simplified form of the given expression.
Hence, the correct answer would be option (C)
Learn more about the algebraic expression here :
brainly.com/question/21751419
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The cunninghams are moving across the country. mr. cunningham leaves 3 hours before mrs. cunningham. if he averages 55mph and she averages 75mph, how long will it take mrs. cunningham to overtake mr. cunningham?
Answers
Mrs. Cunningham travels at a speed that is 20mph faster than Mr. Cunningham. Given that Mr. Cunningham has a 165-mile head start, Mrs. Cunningham would need 8.25 hours to cover this distance and catch up with him.
Explanation:This question can be approached by analysing the relative speeds and the initial advantage Mr. Cunningham had. Mr. Cunningham travels for three hours at 55 mph before Mrs. Cunningham leaves, giving him a 165 mile head start. To determine how long it will take Mrs. Cunningham to overtake Mr. Cunningham, it's necessary to calculate how long it will take her to make up this 165-mile deficit at her faster speed.
Mrs. Cunningham travels 75mph, which is 20mph faster than Mr. Cunningham's speed. Thus, each hour, she closes the distance between them by 20 miles. To find out how many hours it takes her to close the 165 mile distance between them, divide this distance by her relative speed, so: 165miles / 20mph equals 8.25 hours.
Thus, it will take Mrs. Cunningham 8.25 hours to overtake Mr. Cunningham.
Learn more about Relative Speed here:https://brainly.com/question/14362959
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A triangle has one side that measures x, another side that measures 2x, and a third side that measures 5 less than x. The perimeter is 31 inches. Which equation would you use to find the value of x? Explain your answer
A. x + 2x + x - 5 = 31
B. x + 2x + x + 5 = 31
C. x + 2x - x - 5 = 31
D. x + 2x - x + 5 = 31
Answers
2nd side = 2x
3rd side is x-5
so x +2x + x-5 = 31
answer is A
What is the length of ST, to the nearest tenth of a yard?
Answers
Use the Law of Sines to find side b.
b / sin(B) = a / sin(A)
b / sin(59°) = 7 / sin(79°)
b = (sin(59°) x 7) / sin(79°)
b = 6.112
That is answer B.) 6.1 yards
Hope this helps!
Answer: Second Option is correct.
Step-by-step explanation:
Since we have given that
ΔSRT is a triangle with measures :
SR = 7 yd
∠T = 79°
∠R = 59°
We need to find the side ST say x.
We will use " Law of Sines " :
[tex]\frac{\sin T}{SR}=\frac{\sin R}{ST}\\\\\frac{\sin 79^\circ}{7}=\frac{\sin 59^\circ}{x}\\\\0.14=\frac{\sin 59^\circ}{x}\\\\x=\frac{\sin 59^\circ}{0.14}\\\\x=6.12\ yd[/tex]
Hence, the length of ST = 6.1 yd.
Therefore, Second Option is correct.
Use a calculator to find the approximate value of arccos(0.63).
Answers
if cos(∅)=x----------------> arccos (x)=∅
then
cos(∅)=0.63
∅=arccos(0.63)-------------> ∅=50.95°
The question does not specify in which quadrant the angle is, since the cosine function is positive, the angle must be in the first quadrant or in the fourth quadrant
if it is in the first quadrant the angle is 50.95°
and
if it is in the fourth quadrant the angle is (360°-50.95°)=309.05°
Please help me...
I think its the third graph or the last .
correct me if im wrong
Answers
I believe the answer you are looking for - is the third graph.
Hope this helps!
~Alexa
The formula for the area of a regular polygon is A=1/2ap. What is the equation solved for a?
Answers
I'm pretty sure its this a=A/(1/2p)
Answer:a=2A/p
Step-by-step explanation:
30 Points! Please Help!
Answers
Ernest is purchasing a $175,000 home and is making 20% down payment toward the cost. He is also buying 2 points in order to lower his inteest rate. The appraisal fee is $400, the title is $300, and the processing fee is $575. Including the down payment, what are his total closing costs?
Answers
Answer: 39,075 is the answer
Step-by-step explanation:
1/3 of birds egg hatch in two eggs hatch how many eggs did the bird lay
Answers
2/3 is 4.
3/3 is 6.
Hope this helped☺☺
The total number of eggs a bird laid is 6 eggs.
To solve this problem we need to break it down step by step:
Assuming 1/3 of the eggs hatch means 2 eggs hatch, so if two eggs hatch, this represents 1/3 of the total eggs laid.
To find the total number of eggs the bird laid, we need to find the equivalent of 1 whole (the total). If 1/3 is equal to 2 eggs, then the whole (3/3 or 1) would be 6 eggs.
At a sale, books are sold at $90.75 each, which is 75 percent of the original price. What is the original price
Answers
[tex] \frac{75}{100} = \frac{90.75}{x} \\ x = \frac{90.75 \times 100}{75} = \frac{9075}{75} = 121[/tex]
the answer is 121
To find the original price of the book, we can set up an equation: 0.75x = $90.75. Solving for x, we find that the original price is $121.
Explanation:To find the original price of the book, we can set up an equation. Let's denote the original price as x. The sale price is 75% of the original price, which can be expressed as 0.75x. We are given that the sale price is $90.75, so we can set up the equation:
0.75x = $90.75
To solve for x, we divide both sides of the equation by 0.75:
x = $90.75 / 0.75
Using a calculator, we can calculate that the original price of the book is $121.
what are the odds against rolling a sum of 6 with the roll of two dice?
Answers
Final answer:
The odds against rolling a sum of 6 with the roll of two dice are 31:5, as there are 5 favorable outcomes for a sum of 6 and 36 total possible outcomes when rolling two dice.
Explanation:
The question is asking about the odds against rolling a sum of 6 with two dice. To calculate this, first, we need to find all the possible combinations of two dice that sum up to 6. Those combinations are (1,5), (2,4), (3,3), (4,2), and (5,1), therefore there are 5 ways to achieve a sum of 6.
The total number of possible outcomes when rolling two dice is 6 * 6 = 36, since each die has 6 faces. So, there are 36 - 5 = 31 ways to not roll a sum of 6. The odds against rolling a sum of 6 are therefore the number of ways not to roll a 6 to the number of ways to roll a 6, which is 31:5.
Odds against rolling a sum of 6 with two dice = 31:5.