How can you tell from the equation of a rational function if the function has a hole in the graph ( a removable discontinuity) at x, rather than a vertical asymptote? Give an example
Consider that,
x^2+4x+4 = (x+2)(x+2)
x^2+7x+10 = (x+2)(x+5)
Dividing those expressions leads to
(x^2+4x+4)/(x^2+7x+10) = (x+2)/(x+5)
The intermediate step that happened is that we have (x+2)(x+2) all over (x+2)(x+5), then we have a pair of (x+2) terms cancel as the diagram indicates (see below). This is where the removable discontinuity happens. Specifically when x = -2. Plugging x = -2 into (x+2)/(x+5) produces an output, but it doesn't do the same for the original ratio of quadratics. So we must remove x = -2 from the domain.
A goat is tethered to a rope that is 10 ft. long. In terms of Tt, what is the maximum area the goat can graze? A) 10pi; ft? B) 25 ft2 C) 5 Ont ft2 D) 100Tt ft2
Answer: D trust me it is 100
Step-by-step explanation:
The maximum area the goat can graze is 100Tt ft2, the correct option is D.
Given
A goat is tethered to a rope that is 10 ft. long.
Area of the circleThe area of the circle is equal to the pie times of the square of the radius of the circle.
The maximum area that the goat can graze in the area of the circle that can be formed due to its circular movement.
The length of the rope represents the radius of the circle, so that;
[tex]\rm Area \ the \ goat \ can \ graze =r^2 \times Tt\\\\ Area \ the \ goat \ can \ graze =(10)2 \times Tt\\\\Area \ the \ goat \ can \ graze =100 \ Tt\\[/tex]
Hence, the maximum area the goat can graze is 100Tt ft2.
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If a box has a length of 12 inches, a width of 10 inches and a height of 6 inches, what is the surface area?
Answer:
The answer is 28.
Step-by-step explanation:
Add all of them.
(L/ length) 12.
(W/ width) 10
(H/ height) 6
12 + 10 + 6 = 28
I hope this helps
Answer:
504 inches
Step-by-step explanation:
2(lb+hb+hl)
length = 12
height = 6
width = 10
2 (120 + 60+ 72)
2( 252
= 504
4. A car is travelling 75 kilometers per hour. How many meters does the car travel in one
minute?
Answer:
1250 Meters
Step-by-step explanation:
75 kilometers divided by 60 minutes is 1.25 kilometers per minute.
1 kilometer = 1000 meters
Answer:
75km/hr =75000
60 sec =1min,60 min=1hr
75000÷60=1250m
3.15 Linear Equations and Inequalities (SHOW YOUR WORK)
1.) Use the linear graph to answer the question.
A.) Identify the quadrant in which each point lies.
Point A:_____
Point B:_____
Answer:
A- Quadrant one.
B- Quadrant three.
Step-by-step explanation:
So, the quadrants go counter-clockwise, starting at the top right which is Quadrant one. Therefore, A is in one. Using that information, we can assume that B is in Quadrant three.
I need help. URGENT
Use the information and the diagram to answer the question:
What is the area of KLM
Answer:
i think the answer might be D but im not sure
Rewrite the expression 1/x^2/3 in the form x^n
Step-by-step explanation:
Rewrite the expression 1/x^2/3 in the form x^nRewrite the expression 1/x^2/3 in the form x^n
An expression is defined as a set of numbers, variables, and mathematical operations. The given expression can be written in the form of xⁿ as x⁻⁰°⁶⁶.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression [tex]\dfrac{1}{x^{\frac23}}[/tex] can be written in the form of xⁿ using the exponential property 1/x=x⁻¹. Therefore, the expression can be rewritten as,
[tex]\dfrac{1}{x^{\frac23}}\\\\= x^{-\frac23}[/tex]
= x⁻⁰°⁶⁶
Hence, the given expression can be written in the form of xⁿ as x⁻⁰°⁶⁶.
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Evaluate the expression 8a+11−3b for a = 4 and b = 2.
Answer: 37
8(4)+11-3(2)
32+11-6
43-6
37
Which of the following is closest to the circumference of a circle whose radius is 21 m
Here Is your answer!!!!
A group of New York City residents are surveyed. They are asked if they are going to watch the New York City Marathon in person. Of the people surveyed, 68 men and 45 women will watch the marathon, while 100 men and 192 women will not watch the marathon. Place each joint and marginal relative frequency in the correct location in the two-way table.
Answer:3
Step-by-step explanation:
Find the median, mean, and range.
14, 1, 16, 6, 15, 2
Answer:
Median: 10
Mean: 9
Range: 15
Step-by-step explanation:
Have a good day :)
Graph the image of points A and B after a reflection over the x-axis.
Point B is 2,3 and Point A is 7,8
Answer:
Point A reflected = 7, -8
Point B reflected = 2, -3
Step-by-step explanation:
Help pleasee asappp sorry
Answer:
A
Step-by-step explanation:
please help me
no links please and thank you :)
The model represents an inequality. What is the solution set for the inequality?
Given:
The figure of an algebraic tiles model of an inequality.
To find:
The inequality for the given model.
Solution:
On the left hand side of the inequality sign in the model we have 8 tiles of x and 12 tiles of 1. So,
[tex]LHS=8(x)+12(1)[/tex]
[tex]LHS=8x+12[/tex]
On the right hand side of the inequality sign in the model we have 12 tiles of -1. So,
[tex]RHS=12(-1)[/tex]
[tex]RHS=-12[/tex]
Now, the inequality for the given model is:
[tex]8x+12\geq -12[/tex]
Therefore, the required inequality for the given model is [tex]8x+12\geq -12[/tex].
Forty nine minus twenty five b squared in factored form
Step-by-step explanation:
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If 36 ÷ 9 = 4, which numbers could be placed in the blanks in the order shown to create a corresponding multiplication fact? _____ × _____ = _____
A) 4, 9, 36
B) 4, 36, 9
C) 9, 36, 4
D) 36, 9, 4
Answer:
a. 4×9=36
glad to help!!
Step-by-step explanation:
The quicker I could get an answer the better because I'm soo confused
5 1/2 ÷ 3 2/3 + 1 4/5 , giving answer as a fraction in lowest terms
Answer:
6761/320
Step-by-step explanation:
[(51/2)÷32/3]+14/5
=6761/320
A piano instructor charges students a one-time fee for sheet music and an hourly rate for lessons. The graph below shows the total cost for a student who has taken x lessons.
10. Fill in the blanks so as to make the statement true:
(i) A number which can be expressed in the form m/n, where m and n are
integers and n is not equal to zero, is called a ________.
(ii) If the integers m and n have no common divisor other than 1 and n is
positive, then the rational number m/n is said to be in the ________.
(iii) Two rational numbers are said to be equal, if they have the same
________ form.
(iv) If m is a common divisor of x and y, then x/y = (x ÷ k)/______
(v) lf p and q are positive integers , then m/n is a ________ rational
number and m/-n is a ________ rational number.
(vi) The standard form of -1 is ________.
(vii) If m/n is a rational number, then n cannot be ________
(viii) Two rational numbers with different numerators are equal, if their
numerators are in the same ________ as their denominators.
Step-by-step explanation:
(I) A number which can be expressed in the form m/n, where m and n are integers and n is not equal to zero, is called a Rational Number .
(ii) If the integers m and n have no common divisor other than 1 and n is positive, then the rational number m/n is said to be in the Simplest form .
(iii) Two rational numbers are said to be equal, if they have the same Simplest form .
(iv) If m is a common divisor of x and y, then x/y = (x ÷ k)/( y ÷ k) .
(v) The standard form of -1 is -1/1
(vi) If m/n is a rational number, then n cannot be 0
(vii) Two rational numbers with different numerators are equal, if their numerators are in the same ratio as their denominators.
What is the missing length?
Answer:
16
Step-by-step explanation:
The area of a triangle is
A =1/2 bh where b is the base length and h is the height
Substitute the values in
69.6 = 1/2 ( 8.7) * p
69.6 = 4.35p
Divide each side by 4.35
69.6/4.35 = p
16 = p
The formula for the area of a triangle is: A = 1/2 * base * height.
Using this formula, let's plug in what we know.
69.6 = 1/2 * 8.7 * height
Next, we'll go ahead and get rid of that 1/2 by multiplying everything by its reciprocal, 2.
139.2 = 8.7 * height
Then, all that's left is to divide both sides by 8.7.
Height = 16 yards
Hope this helps!! :)
The equation for the line of best fit is y=–0.7x+39. In this equation, what does the y-intercept of 39 tell you?
Help me it says use the figure for 1 and 2
I need help!!! Like right now
Box 5:
Box 6:
Box 7:
Boz 8:
!!!need help please !!!
Answer:
Step-by-step explanation:
log(3) = 0.477
log(8.2) = 0.913
log(0.04) = -1.397
A marble is randomly selected from a bag containing 3 red marbles, 3 blue marbles, and 3 green marbles. what is the probability that the selected marble is green?
Answer:
1/3
Step-by-step explanation:
3x3= 9
Make 3/9 a fraction and simplify it and it would give you 1/3
a triangle has sides with lengths 9 yards 12 yards and 18yards is it a right triangle
Answer:
use Pythagorean theorem:
[tex]a^2+b^2=c^2\\9^2+12^2=18^2\\81+144=324\\225\neq 324[/tex]
it's not a right triangle
Factor 5x^2 + 16x – 16
Answer:
(x + 4)(5x - 4)
Step-by-step explanation:
[tex]5x^2 + 16x – 16 \\ = 5x^2 + 20x - 4x– 16 \\ = 5x(x + 4) - 4(x + 4) \\ = (x + 4)(5x - 4)[/tex]
Answer:
(5x - 4) • (x + 4)
Step-by-step explanation:
Multiply the coefficient of the first term by the constant 5 • -16 = -80
Find two factors of -80 whose sum equals the coefficient of the middle term, which is 16 .
Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 20
5x2 - 4x + 20x - 16
Add up the first 2 terms, pulling out like factors :
x • (5x-4)
Add up the last 2 terms, pulling out common factors :
4 • (5x-4)
Add up the four terms of step 4 :
(x+4) • (5x-4)
Which is the desired factorization