Answers
[tex] \frac{x^2 + 5x - 36}{x^2 - 16} = \frac{(x +9)(x - 4)}{(x + 4)(x - 4)} = \frac{x+9}{x+4} [/tex]
Then you divide the numerator and the denominator by the common factor to reduce the fraction.
Related Questions
What is the image of (5,-1) under same translation?
Answers
translate 4 units left and 7 units down
so (5, -1) with 4 units left and 7 units down should be (1, -8)
answer is B. (1, -8)
The image of point (5, -1) under the same translation that maps point P to P' is (1, -8). This translation vector is obtained by subtracting the coordinates of P from P'.
To find the image of point (5, -1) under the same translation T that maps point P to P', we can calculate the vector that represents the translation from P to P' and then apply the same translation to point (5, -1).
The translation vector is given by:
Translation vector = P' - P = (-6, -4) - (-2, 3) = (-4, -7)
Now, to find the image of point (5, -1) under the same translation, we simply add this translation vector to (5, -1):
Image of (5, -1) = (5, -1) + (-4, -7) = (5 - 4, -1 - 7) = (1, -8)
So, the image of point (5, -1) under the translation T is (1, -8). Therefore, the correct answer is B. (1, -8).
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How many true conditional statements may be written using the following statements?
n is a rational number.
n is an integer.
n is a whole number.
a.
2 conditional statements
c.
4 conditional statements
b.
3 conditional statements
d.
5 conditional statements
Answers
How to calculate standard deviation given mean and sample size?
Answers
The formula for standard deviation is:
S^2 = E(X-M)^2/N-1
Here's an example:
Data set: 4,4,3,1
Mean: 3
Sample size: 4
First, put the individual scores one after the other and subtract the mean from it.
4 - 3 = 1
4 - 3 = 1
3 - 3 = 0
1 - 3 = -2
Second, square the answers you got from step 1.
1^2 = 1
1^2 = 1
0^2 = 0
-2^2 = 4
Third, plug the values from step 2 into the formula.
S^2 = (1+1+0+4)/(4-1) = 6/3 = 2
Standard deviation = 2
The length of a rectangle is 10 m less than three times the width, and the area of the rectangle is 77 m2 . find the dimensions of the rectangle
Answers
Area of a rectangle is length times width: x(3x-10)=77 => 3x^2-10x-77=0
Factor this quadratic equation: (x-7)(3x+11)=0 =.x=7 or x=-11/3
width cannot be negative, so the only answer is x=7
width is 7m, length is 11m
The length and width of the rectangle are 11 m and 7 m respectively.
What is rectangle?A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.
Given that,
Length of the rectangle is 10 m less than three times the width,
And area of rectangle = 77 m²
Let the width of rectangle is x m,
Then length of rectangle = 3x -10 m.
The area of rectangle = 77
length × width = 77
x × (3x - 10) = 77
The value of x = 7 satisfy the equation,
Therefore, the width of rectangle is x = 7 m
And length of the rectangle is 3x - 10 = 21 - 10 = 11 m
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the equation 5x+4y=20 represents a linear function in two variables. Identify the slope, x-intercept and y-intercept of this linear function
Answers
put it into y=mx+b 4y=-5x+20
to isolate y divide both sides by y=-5/4+5
to find the xi
xi is when y=0 so plug it in to the equation 4y=-5x+20 4(0)=-5x+20
0=-5x+20 subtract 20 from each side -20=-5x the negatives cancel out 20=5x
to isolate x divide each side by 5 x=20/5
20/5=4
Answers:
m=-5/4
yi=5
xi=4
How do I solve for x within a triangle?
Answers
Factor the expression 20k + 50
Answers
-----------------------------------
Work Shown:
20k+50 = 10*2k + 10*5
20k+50 = 10(2k+5)
Note how we can distribute the 10 back in to check our work
10(2k+5) = 10(2k)+10(5) = 20k+50
so that confirms we have the right answer
Another thing to notice is that 10 is the largest factor that we can pull out of 20k and 50. The value 10 is the GCF (greatest common factor) of 20 and 50.
A total of 900 tickets were sold for a game for a total of $1,150. if adult tickets sold for $2.00 and children's tickets sold for $1.00, how many of each kind of ticket were sold?
Answers
adult tickets = a
child tickets = c
a + c = 900
2a + c = 1150
Subtract c from the equation on top to get a = 900 - c
Substitute this value into the second equation 2(900 - c) = 1150
Simplify to make 1800 - 2c = 1150
Add 2c to both sides
1800 = 1150 + 2c
Subtract 1150 from each side
2c = 650
Divide by 2 so that c = 325. Therefore, 325 child tickets were sold.
To find the number of adult tickets, subtract 325 from 900
The remaining number (a = 900 - 325 = 575) is how many adult tickets were sold. 575 adult tickets were sold.
What is the least common multiple of 50, 60, and 72?
Answers
Suppose an investment of $10,000 doubles in value every 13 years. How much is the investment worth after 52 years? After 65 years?
A: $80,000; $100,000
B: $160,000; $320,000
C: $520,000; $650,000
Answers
Answer:
Step-by-step explanation:
The answer is actually B. $160,000; $320,000
The reason for this is because -
$10,000 is the constant, so let a= 10,000.
The investment doubles every 13 years, so let b=2.
Let x= the number of 13-year periods.
The value of a $10,000 investment doubling every 13 years will be $160,000 after 52 years and $320,000 after 65 years.
Explanation:To calculate the value of an investment that doubles every 13 years, you can determine the number of times the investment will double over a given period. In this case, after 52 years, the investment will have doubled 4 times (since 52 divided by 13 is 4), and after 65 years, it will have doubled 5 times (since 65 divided by 13 is 5).
The formula for the future value of an investment that doubles is: Future Value = Present Value × (2^number of doublings).
After 52 years, the investment's worth would be calculated as follows:
$10,000 × (2^4) = $10,000 × 16 = $160,000
After 65 years, the investment's worth would be:
$10,000 × (2^5) = $10,000 × 32 = $320,000
Therefore, the correct answers are $160,000 after 52 years and $320,000 after 65 years, which corresponds to choice B.
The graph of g(x) is the graph of f(x)=12x+6 compressed vertically by a factor of 13 .
Which equation describes the function g?
g(x)=12x+2
g(x)=4x+6
g(x)=4x+2
g(x)=36x+6
Answers
The volume of a rectangular prism can be computed using the formula v = lwh. what is the length of a prism that has a volume of 1344 cubic centimeters, a width of 8 centimeters, and a height of 12 centimeters?
a. 111 cm
b. 18 cm
c. 896 cm
d. 14 cm
Answers
We are given the formula:
V = l w h
and the following values:
l = ?
V = 1344 cm^3
w = 8 cm
h = 12 cm
SO rewriting the formula in terms of l:
l = V / w h
l = 1344 cm^3 / (8 cm * 12 cm)
l = 14 cm
Answer:
d
The answer would be 14
Leo is going to use a random number generator 400 times. Each time he uses it, he will get a 1 , 2 , 3 , 4 , or 5.What is the best prediction for the number of times that Leo will get an odd number?
Answers
Answer:
Close to 240 times but probably not exactly 240 times
Step-by-step explanation:
Find the square root of the fraction 64/100
Answers
Yeet! I need some help! 16 points to whoever answers!
Answers
the temperature was -3 degrees last night. it is now -4 degrees . what was the change in the temperature
Answers
If you look at -3 and -4, on a number line for example, -4 is one lower than -3, so the change is -1 degree.
(sorry that was unnecessary but it wouldn't let me post the answer unless I added more info :D)
what is the value of the function f(x)=1/4x-3 when x=12
6
1
0
-6
Answers
= 3-3=0
=0
The _____ ratio is the ratio of the length of one side of a polygon with the length of a corresponding side of a similar polygon.
Answers
The scale ratio is the ratio of the length of one side of a polygon with the length of a corresponding side of a similar polygon.
The ratio you're referring to is called the scale factor. The scale factor is the ratio of the length of one side of a polygon to the length of the corresponding side of a similar polygon. Let's denote this scale factor as ( k ).
To calculate the scale factor, you need to choose corresponding sides from the two similar polygons. Once you've chosen a pair of corresponding sides, divide the length of one side by the length of the corresponding side from the other polygon.
Let's say we have two similar polygons, Polygon A and Polygon B, and we want to find the scale factor between them. Let's denote the length of a side of Polygon A as [tex]\( L_A \)[/tex] and the length of the corresponding side of Polygon B as [tex]\( L_B \)[/tex]. Then, the scale factor, ( k ), is given by:
[tex]\[ k = \frac{L_A}{L_B} \][/tex]
This ratio will give you the scale factor between the two polygons.
Assembly Line A produces 45 units in the same time that it takes Assembly Line B to produce 37 units. If Line B produces 555 units, how many units does Line A produce during the same time?
Answers
Assembly Line A will produce 24975 units during the same time that Line B produces 555 units.
Explanation:Let's assume that the time it takes for Assembly Line A to produce 45 units is equal to the time it takes for Assembly Line B to produce 37 units. This means that the time it takes for Line A to produce 1 unit is equal to the time it takes for Line B to produce 1 unit.
Now, we can set up a proportion to find how many units Line A will produce during the same time that Line B produces 555 units:
45 units / 1 unit = x units / 555 units
Cross-multiplying, we get:
45 * 555 = x units * 1
x units = 24975 units
Therefore, Line A will produce 24975 units during the same time that Line B produces 555 units.
180 is 10 % more than witch number ?
Answers
Multiply 5x2(2x2 + 13x − 5). 10x4 + 65x3 − 25x2 10x2 + 65x − 25 7x2 + 18x − 10 7x4 + 18x3 − 10x2
Answers
Answer:
[tex]10x^4+65x^3-25x^2[/tex]
Step-by-step explanation:
Multiply 5x^2(2x^2 + 13x − 5)
[tex]5x^2(2x^2 + 13x - 5)[/tex]
Multiply 5x^2 inside the parenthesis
[tex]5x^2 * 2x^2 = 10x^4[/tex]
[tex]5x^2 * 13x = 65x^3[/tex]
[tex]5x^2 * (-5) = -25x^2[/tex]
Collect all the terms together
[tex]10x^4+65x^3-25x^2[/tex]
The function H(t) = −16t2 + 48t + 12 shows the height H(t), in feet, of a cannon ball after t seconds. A second cannon ball moves in the air along a path represented by g(t) = 10 + 15.2t, where g(t) is the height, in feet, of the object from the ground at time t seconds.
Part A: Create a table using integers 0 through 3 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points)
Part B: Explain what the solution from Part A means in the context of the problem. (4 points)
Answers
t 0 1 2 3
H(t) 12 44 44 42
g(t) 10 25 40 56
Set H(t) = g(t) yields 16t^2 -32t -2 which shows its zeroes or points of intersections are at 0.6 and 2.1 seconds
Part B
H(t) = g(t) intersect at (x,y) points (0.6 secs, 9.1 feet) and (2.1 secs, 42.1 feet)
H(t) is a parabola that opens downward which shows the cannonball arches upwards then falls downward.
g(t) is a straight linear line which slopes positive upwards and intersects G(t) in two places.
We are given a function H(t) that represents the height of a cannon ball after t seconds as:
[tex]H(t)=-16t^2+48t+12[/tex]
and a second cannon ball is represented by the function g(t) as:
[tex]g(t)=10+15.2t[/tex]
PART A:
t 0 1 2 3
H(t) 12 44 44 12
g(t) 15.2 25.2 40.4 55.6
Hence, between t= 2 seconds and t=3 seconds the ball will meet
such that H(t)=g(t)
Since, we know that the Height H(t) decreases from 44 feet to 12 feet between t=2 to t=3 seconds.
and height g(t) increases from 40.4 feet to 55.6 feet between t=2 to t=3 seconds.
Hence, the two cannon balls will definitely meet between t=2 to t=3 seconds.
and the time at which they meet is calculated by solving:
[tex]H(t)=g(t)\\\\i.e.\\\\\\-16t^2+48t+12=10+15.2t\\\\\\i.e.\\\\\\16t^2-32.8t-2=0\\\\\\i.e.\\\\\\t=-0.059\ and\ t=2.109[/tex]
As t can't be negative.
Hence, we get:
t=2.109 seconds
PART B:
The solution from PART A means that the one of the ball first reach the highest point at 44 feet and then returns back to the initial position and hence follows a parabolic path while the second cannon ball reach a greater height with the increase in time and hence in this phenomena the two balls will definitely meet.
There are 5,280 feet in 1 mile. If Riley ran 26,400 feet, how many miles did she run? [Type your answer as a number.]
Answers
Answer:
She ran 5 miles
Step-by-step explanation:
To solve this, we can easily use proportion.
The question state that there are 5,280 feet in a mile, We are ask to find the number of miles Rily run, if she ran 26,400 feet.
Using proportion;
Let x = the number of miles Rily can run
5,280 feet = 1 mile
26,400 feet = x
Cross-multiply
5280x = 26,400
To get the value of x, we will divide both-side of the equation by 5280
5280x/5280 = 26400/5280
(On the left-hand side of the equation, 5280 will cancel-out 5280 leaving us with x and on the right-hand side of the equation 26400 will divide 5280)
x = 26400 / 5280
x=5 mile
Therefore, If Rily ran 26400 feet, then she has ran 5 miles.
Apply THe ORder of operations to simplify the expression
90/ [10+(3² - 4)]
most with best answer gets brainliest please help.
Answers
90/[10+5) add the number in the parenthesis again (always do the parenthesis first) [10+5]= 15.
lastly divide 90/15 which equals to 6
always remember (PEMDAS)
The simplification form of the expression 90/ [10+(3² - 4)] is 6 the answer is 6.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
As we know, the expression can be defined as the combination of constants and variables with mathematical operators.
To begin, either multiply or divide the value in parentheses (32-4), which equals 5.
Add the number in the parentheses once more: 90/[10+5 (always do the parenthesis first) [10+5]= 15.
Finally, divide 90/15 by 6, always keeping that in mind (PEMDAS)
Thus, the simplification form of the expression 90/ [10+(3² - 4)] is 6 the answer is 6.
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The sum of twice a number and four is fourteen. find the number.
Answers
2x +4 =14
2x =10
x =5
the number is 5
Please help with these two questions thank you.
Answers
2. a=30 and b=60
Which is the correct simplified form of the expression x^1/2y^-1/3/x^1/4y^1/2
Answers
[tex]\bf \cfrac{x^{\frac{1}{2}}y^{-\frac{1}{3}}}{x^{\frac{1}{4}}y^{\frac{1}{2}}}\implies \cfrac{x^{\frac{1}{2}}x^{-\frac{1}{4}}}{y^{\frac{1}{2}}y^{\frac{1}{3}}}\implies \cfrac{x^{\frac{1}{2}-\frac{1}{4}}}{y^{\frac{1}{2}+\frac{1}{3}}}\implies \cfrac{x^{\frac{2-1}{4}}}{y^{\frac{3+2}{6}}}\implies \cfrac{x^{\frac{1}{4}}}{y^{\frac{5}{6}}}[/tex]
Answer:
(A)[tex]\frac{x^{\frac{1}{4}}}{y^{\frac{5}{6}}}[/tex]
Step-by-step explanation:
The given expression is:
[tex]\frac{x^{\frac{1}{2}}y^{\frac{-1}{3}}}{x^{\frac{1}{4}}y^{\frac{1}{2}}}[/tex]
Upon solving the given expression, we get
=[tex]{x^{\frac{1}{2}-\frac{1}{4}}{\cdot}}{y^{\frac{-1}{3}-\frac{1}{2}}}[/tex] (using the property of exponents and powers that if base is same then the powers gets added.)
=[tex]x^{\frac{1}{4}}{\cdot}y^{\frac{-5}{6}}[/tex]
=[tex]\frac{x^{\frac{1}{4}}}{y^{\frac{5}{6}}}[/tex]
which is the required simplified form of the given equation.
Hence, option A is correct.
3469131824 what would be the next number
Answers
Hope this helps!
Find the greatest common factor of 75, 8, and 21
Answers
8=2×2×2
21=3×7
there's is no common factor between them aside 1
except u typed the wrong question
Write the parametric equations x = 4 \sin^2 \theta , \quad y = 3 \cos^2 \theta in the given cartesian form.
Answers
[tex]\left{x = 4 \sin^2 \theta , \quad y = 3 \cos^2 \theta}\\\\ sin^2(\theta)= \dfrac{4}{x} , \quad cos^2(\theta)= \dfrac{3}{y} \\\\ sin^2(\theta)+cos^2(\theta)= \dfrac{4}{x} + \dfrac{3}{y} \\\\ \dfrac{3}{y}=1-\dfrac{4}{x}\\\\ y=\dfrac{3x}{x-4} [/tex]
The Cartesian form of equation is,
3x + 4y = 12
We have to given that,
The parametric equations are,
x = 4 sin² θ
y = 3 cos² θ
Now, Change the parametric equations into cartesian form as,
x = 4 sin² θ
sin² θ = x/4 .. (i)
y = 3 cos² θ
cos² θ = y/3 (ii)
Add equation (i) and (ii),
sin² θ + cos² θ = x/4 + y/3
1 = x/4 + y/3
1 = (3x + 4y)/12
12 = 3x + 4y
3x + 4y = 12
Therefore, The Cartesian form of equation is,
3x + 4y = 12
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