The simplification of the given equation is (x² + 8x - 16)/(x-4)(x+4) by the method of LCM.
What is defined as the LCM?LCM is an abbreviation for least common multiple. The smallest number which is a multiple of both numbers is the least common multiple of them.For, the given equation;
4/(x+4) + (x/x-4)
To find the common denominator, use LCM; multiply a first term by (x-4)/(x-4) and the 2nd term by (x+4)/(x+4):
= (x-4)×4/(x-4)(x+4) + x×(x+4)/(x-4)(x+4)
The following step is to disperse the 4 (x-4) and x (x+4);
So you now have;
= (4x-16 + x² + 4x)/(x-4)(x+4)
Further simplify.
= (x² + 8x - 16)/(x-4)(x+4)
As, (x² + 8x - 16) is further not factor-able. So, the simplified form of the given equation is; (x² + 8x - 16)/(x-4)(x+4).
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I don’t know this one question
Answer:
v = 13
Step-by-step explanation:
because they are supplementary angles they add up to 180
so
add them
and put them equal to 180
9v + 3 + 60 = 180
combine like terms
9v + 63 = 180
now subtract 63 to both sides
9v = 117
divide 9 to both sides
v = 13
that is your answer
Isla has $30 to spend on treats for her kindergarten class. She wants to buy her students cookies, c, and popsicles, p. Each box of cookies costs $5.50 each, and each bag of popsicles costs $3.00 each. If she must buy 3 bags of popsicles, which inequality could be used to determine the maximum number of boxes of cookies she can buy?
a
A
b
B
c
C
d
D
Answer:B
Step-by-step explanation:because she might buy more cookies but we dont know she we dont multiply it by anything but the cookies we multiply that by 3 so thats why it doesn't have p because we know how much she's getting the reason its not a is because it says greater or equal to we dont want to go over 30 we want to be equal or less than 30
hope this helps :}
Find the quotient of The quantity 30 times ten raised to the negative twenty fourth power end quantity divided by the quantity 5 times ten raised to the negative twenty fourth power end quantity.. Write the final answer in scientific notation.
6 x 1048
6 x 1024
6 x 100
6 x 10−48
The quotient of the given problem using laws of exponents is; 6 * 10⁰
How to use the law of exponents?We want to express the quotient of the quantity 30 times ten raised to the negative twenty fourth power end quantity divided by the quantity 5 times ten raised to the negative twenty fourth power end quantity.
This is;
(30 * 10⁻²⁴)/(5 * 10⁻²⁴)
Now, we can break this down into like terms to get;
(30/5) * (10⁻²⁴/10⁻²⁴)
= 6 * 1
Now, 1 can also be written as;
10⁰ = 1
Thus, the solution of the given problem is; 6 * 10⁰
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The average annual cost of living in State A, State B, and State C are displayed in the
table below.
Average Annual
Cost of Living
$44,400 =A
$62,000 = B
$55,600 = C
Suppose you were offered a job in State B that pays $117,200.
How much is this equivalent to in State A? Round your answer to the nearest whole
dollar.
The equivalent income in City A given the average annual cost of living in City A and city B is $163,658.
What is the equivalent income?The first step is to determine the ratio of the average cost of living in State A and State B. Ratio is used to show the relationship that exists between two or more values.
Cost of Living in City B / Cost of Living in City A
$62,000 / $44,400 = 1.39640
Multiply the ratio gotten in the previous step by the offered salary in State B : 1.39640 x $117,200 = $163,658
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a cat on a table 960m views a piece of meat on the ground 114.4cm away from the foot of the table. find the angle of depression of the meat from the top of the table
The angle of depression of the meat from the top of the table is 40°
This situation makes a right-angle triangle with the height of table being the perpendicular to the right-angle triangle and the distance of meat from the foot of the table becomes the base of the imaginary right-angle triangle
to know the angle of depression of the meat from the top of the table
we need to find the ratio between the perpendicular and the base of the triangle to use trigonometry.
Tan is the ratio of perpendicular and base of the triangle
which is = 96/114.4
tan Ф=0.8392
To solve for Ф , a tan would move from the left-hand side to the right-hand side and would become tan inverse.
Ф = tan-1 0.8392
Ф = 40°
The correct question is a cat on a table 96cm views a piece of meat on the ground 114.4cm away from the foot of the table. find the angle of depression of the meat from the top of the table.
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-0.75(12x+60) = -x-8x - 15.
Answer:
Step-by-step explanation:
-9x - 45 = -7x - 15 (Distribute -0.75 to (12x+60)) (x-8x = -7x)
-30 = 2x (add 15 to both sides and add 9x to both sides)
-15 = x (divide both sides by 2)
Find the compound interest and the total amount after three years if the interest is compounded half yearly. if principal is ₹1024 rate of interest 100% per annum
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1024\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{half-yearly, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &3 \end{cases}[/tex]
[tex]A=1024\left(1+\frac{1}{2}\right)^{2\cdot 3} \implies A=1024(1.5)^6\implies A = 11664~\hfill \underset{earned~interest}{\stackrel{11664~~ - ~~1024}{10640}}[/tex]
Given the function f(x) = |x+3|, find each of the following.
f(6), f(- 10), f(0)
f(6) = ?
The value of the functions f(6), f(- 10), f(0) are 9, 7 and 3 respectively.
What is a function?A function can be defined as an expression, rule or law that shows the relationship between a dependent and an independent variable.
Given the function;
f(x) = |x+3|
To determine f(6)
Substitute the value of x as 6
We have;
f(6) = | 6 + 3 |
f(6) = 9
To determine f(-10)
Substitute the value of x as - 10
We have;
f(-10) = | -10 + 3 |
f(-10) = | -7|
f(-10) = 7
To determine f(0)
Substitute the value of x as 0
We have;
f(0) = | 0 + 3|
f(0) = 3
Thus, the value of the functions f(6), f(- 10), f(0) are 9, 7 and 3 respectively.
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sorry for the blurry photo
A- -10
B- 15
C- 10
D- -15
Answer: 15
Explanation:
The length of the segment is 10 plus 5 which is fifteen because you need to know how long it is. Just ignore the negatives.
48 inches long and 36 inches wide. What is the area?
Answer:
1728
Hope this helps :)
E-7/9|12/5-6R|+50 > or equal to -30
The solution set of the inequality for R is given by [tex]-\frac{1172}{85} \leq x\leq \frac{1228}{55}[/tex] .
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. It is frequently used to compare two numbers on the number line based on their sizes. Different types of inequalities are represented by a variety of notations such as < ,> ,≤ and ≥.
The modulus function takes the absolute value of a function.
To solve the given inequality we have simplify the inequality first.
[tex]x-\frac{7}{9} |(\frac{12}{5} -6x)|+50\ge -30[/tex]
[tex]or, x-\frac{7}{9}\times \frac{6}{5} |(2-5x)|+50\ge -30\\or,x-\frac{14}{15}|2-5x|\ge-80\\[/tex]
Now we separate the inequalities:
[tex]x-\frac{14}{15}(2-5x)\ge-80[/tex] for 2x-5 ≥ 0
[tex]x-\frac{14}{15}(-(2-5x))\ge-80[/tex] for 2x-5 ≤ 0
Now we will solve the two inequalities separate and find the intersection.
[tex]x-\frac{14}{15}(2-5x)\ge-80\\or,15x-28+70x\ge-1200\\or,x\ge -\frac{1172}{85}[/tex]
Again
2x-5 ≥ 0
or, [tex]x\le\frac{2}{5}[/tex]
hence [tex]-\frac{1172}{85}\le x\le\frac{2}{5}[/tex]
Similarly solving the other inequality we get
[tex]\frac{2}{5}\le x\le\frac{1228}{55}[/tex]
Now we find the intersection of the two inequalities:
[tex]-\frac{1172}{85}\le x\le\frac{1228}{55}[/tex]
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What's the correct answer?
Answer- D = (equal sign)
Explanation-
When you see two straight lines in math | | with number inside, regardless if the number inside is positive or negative, the outcome will be positive. This is called the absolute value. After we solve our absolute value however, there is a negative on the outside, which means that 61 will become negative again. Our equation is now -61 _____ -61. Your correct choice will be the equal sign, since -61 is equal to -61.
HOPE THIS HELPS GOOD LUCK!
What two im i missing?
I’m really not understanding what the next step is or what I did wrong. if anyone could help that would be appreciated:)
The vehicle will get speed of approximately 15 mph and -210 mph.
What is speed?Science's most important concept is measurement. Many measurable quantities are measured in fundamental or base units. One such measurable quantity is speed, which is defined as the ratio of an object's distance travelled to the time required to travel that distance. Let us learn about speed in depth during this session.
The ratio of distance to time taken to cover a distance is used to calculate speed. Because it only has one direction and no magnitude, speed is a scalar quantity.
Given the equation for gas mileage = 0.02x² + 3.9x - 43 where x means speed
We have been asked to find x if gas mileage = 20 that is
0.02x² + 3.9x - 43 = 20
Lets simplify
⇒ 0.02x² + 3.9x - 43 = 20
⇒ x² /50 + 39x/10 - 63 = 0
⇒ x²/ 50 + 195x/50 - 3150 = 0
⇒ 1/50 (x + 195x - 3150 ) = 0
⇒ 1/50 (x + 210x - 15 x - 3150 ) = 0
⇒ 1/50 (x (x+210) −15 (x+210)) = 0
⇒ 1/50 (x−15)(x+210) = 0
⇒ (x−15)(x+210) = 0 × 50
⇒ (x − 15)(x + 210) = 0
⇒ x = 15, x = -210
So, try using 15 mph and -210 mph, that might work.
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Area of arrow
Find the area of the figure below
Please help
Answer:
area of the arrow is 36inches^2
Step-by-step explanation:
Area of rectangle= lw
10x3=30
Area of triangle = bh/2
3x4=12/2=6
30+6=36 inches^2
"clown juggles 12 bowling for the first 2.5 minutes then he bump it up to an average of 18 bowling pins per minute cor the last 1 1/3 minute. what is the total number if pins"
After juggling for several minutes i.e., 2.5 minutes and [tex]1\frac{1}{3}[/tex] minutes (mixed fraction), the total number of bowling pins by clown is 37 pins
As per the question statement, a clown juggles 12 bowling for the first 2.5 minutes then he bump it up to an average of 18 bowling pins per minute for the last [tex]1\frac{1}{3}[/tex] minute (Mixed Fraction form)
We are supposed to find the total number if pins by the clown.
Let's calculate the total time first that will be 2.5 minutes + [tex]1\frac{1}{3}[/tex] minutes
[tex]1\frac{1}{3} =\frac{3*1 +1}{3} =\frac{4}{3} =1.34[/tex] minutes.
Therefore total time = 3.84minutes
Given that he bumps it up to an average of 18 bowling pins per minute for the last [tex]1\frac{1}{3}[/tex] minute so, the number of pins in the last [tex]1\frac{1}{3}[/tex] minute will be = [tex]18*1.34 = 24.12 = 25[/tex] (approx.)
So total number of bowling pins = [tex]12+25 = 37[/tex] pins
Mixed Fraction: A mixed fraction is one that is represented by both of its quotient and remainder present in a single expression. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder.To learn more about such questions, click on the link given below:
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What is the 19th term of the sequence:
gn=gn−1⋅(−12) if g17=162
the sixth term is ______
This is an arithmetic sequence
The nth term of an arithmetic sequence is Tn = a + (n-1)d
a is the first term.
n is the number of terms
d is the common difference
Given that 19th term of the sequence is:
gn=gn−1⋅(−12) if g17=162
Suppose a=12
Then,
The 17th term g17=a+(n-1)d
= 12+(17-1)d
'n' means number of terms
12+(17-1)d=162 because g17=162
12+16d=162
16d=162-12
Subtract the values,
We can write,
16d=150
d=150/16
Divide the values,
We can write,
d=25
To get the sixth term g6
g6=12+(6-1)d
=12+5d
Replace with d value in above equation,
Then, g6=12+5(25)
g6=12+125
g6=137
So, the sixth term is g6=137.
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The temperature readings for 20 days at 4 AM at a local ski resort were recorded as follows: 24° −10° 9° 18° 23° 27° 8° 17° 3° 7° −2° −6° 2° −9° −8° 21° 25° 15° 10° 29° What was the average of the recorded temperatures for these 20 days? Do not round your answer.
Based on the temperature readings, the average recorded temperature in the 20 days was 10.15°
What was the average temperature?The average temperature can be found by adding all the temperatures and then dividing by the number of temperatures taken which is 20.
The average is therefore:
= 24° + (−10°) + 9° + 18° + 23° + 27° + 8° + 17° + 3° + 7° + ( −2°) + (−6°) + 2° + (−9°) + (−8°) + 21° + 25° + 15° + 10° + 29°) / 20
= 203 / 20
= 10.15°
In conclusion, the average temperature was 10.15°.
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30 POINTS Graph the solution to this inequality on the number line. 1/2 x - 3 < -1 3/8
The graphing is achieved as follows:
On the graph the third sign counting from the left is used.
This is placed on the first mark of the three marks between 3 and 4. This point equivalent to 3 1/4 or 3.25
How to find the solution of the equation
Given data
the graph
and the equation 1/2 x - 3 < -1 3/8
solving for x gives
1/2 x - 3 < -1 3/8
1/2 x < 3 -11/8
x/2 < 13/8
x < 13 / 4
x < 3 1/4
On the graph the third sign counting from the left is used.
The arrow is facing left, this is to show the sign less than.
The tail has a hollow not a solid point to show that equality sign is not included.
This is placed on the first mark after point 3 as this is the point equivalent to 3 1/4 or 3.25
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27. You are driving on the interstate with your cruise control on at a constant speed of 64 miles per hour.
Use the number lines below to determine how long it will take to drive to the next rest sop that is 16
miles away (see textbook, page 20). Explain the thinking you used to determine your answer.
The car will take 15 minutes to drive to the next stop which is 16 miles away.
As per the question statement, we are supposed to find the time taken by the car to drive to the next stop which is 16 miles away if it is driving on the interstate with cruise control on at a constant speed of 64 miles per hour.
Before solving the question, we need to know the concept of relation between time, distance and speed, which states that
[tex]speed=\frac{distance}{time}[/tex]
In the question [tex]speed = 64 mph\\distance = 16 miles\\time taken = t[/tex]
Substituting values in the formula above,
[tex]64=\frac{16}{t} \\t=\frac{16}{64} \\t=0.25 hours =0.25 *60\\t=15 minutes[/tex]
Hence the time taken by car to drive to the next stop which is 16 miles away is 15 minutes or [tex]\frac{1}{4}[/tex] hours.
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help me pleaseeeeeeeeee
Answer:
Step-by-step explanation:
x + x + 16 = 90
2x +16 = 90
2x = 74
x = 37
Solve the quadratic equation 2h^2 + 100 = 0. If there is more than one solution, separate them with commas. If there are no solutions type DNE.
Answer:
h=sqrt2*5i, h=-sqrt 2*5i
Step-by-step explanation:
Answer:
DNE
No real solutions
Step-by-step explanation:
This Quadratic Equation: 2h² + 100 = 0
Factor out the common term 2:
three answers !
please help me i need to finish this today :((
Answer:
Your answer should be 90 degrees for angle one. For angle two, 58 and angle three 32.
Step-by-step explanation:
This is because they are supplementary angles! I hope this helps. Xx
Answer: ∠1 = 90°
Step-by-step explanation:
∠1 = ∠4
∠2 = ∠5
∠3 = ∠6
reason = vertically opposite angle
∠1 = 90°
∠2 = 58°
∠3 = 32°
checking :
total angles = 360°
360° = ∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6
360° = 90° + 58° + 32° + 90° + 58° + 32°
360° = 360°
In Exercises 6-10, use the diagram.
6. Find the perimeter of AABC.
7. Find the perimeter of quadrilateral
ACDE.
8. Find the area of AABC.
9. Find the area of quadrilateral
ACDE.
10. Find the area of pentagon ABCDF.
B(-1,5) Y
A(-4, 3)
2
F(-4,-3)
-2-
N
E(-2,-3)
C(2, 3)
2 4 X
D(4,-3)
Answer: 5
Step-by-step explanation:
subtract x^2+8x from -3x^2-3x-7.
Answer: -4x²-11x-7
Step-by-step explanation:
[tex]-3x^2-3x-7-(x^2+8x)=\\-3x^2-3x-7-x^2-8x=\\-4x^2-11x-7[/tex]
Simplify 12/16 to lowest terms and find an equivalent fraction that has a denominator of 32.
10/00
O
0 / 4
[tex]\cfrac{12}{16}\implies \cfrac{4\cdot 3}{4\cdot 4}\implies \cfrac{4}{4}\cdot \cfrac{3}{4}\implies 1\cdot \cfrac{3}{4}\implies \boxed{\cfrac{3}{4}}~\hfill \cfrac{8\cdot 3}{8\cdot 4}\implies \boxed{\cfrac{24}{32}}[/tex]
A hamburger and French fries cost $13. A hamburger and two sodas cost $14. A hamburger, French fries, and a soda costs $16. Write the system of equations that describes this situation, then solve to find the price of each. (PLEASE SHOW WORK)
The cost of each hamburger is $8, the cost of each French fry is $5 while the cost of each Soda is $3.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the cost of hamburger, y represent the cost of french fries and z represent the cost of soda, hence:
x + y = 13 (1)
Also:
x + 2z = 14 (2)
And:
x + y + z = 16 (3)
From the three equations:
x = 8, y = 5, z = 3
The cost of each hamburger is $8, the cost of each French fry is $5 while the cost of each Soda is $3.
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WILL MARK BRANLIEST !!!!
For each line, determine whether the slope is positive, negative, zero, or undefined.
Answer: 1st is positive 2nd is negative 3rd and 4th are undefined or 0
Step-by-step explanation:
Answer:
1.positive
2.undefine
3.positive
4.negative
Each square of a chess board measures 57 millimeters by 57 millimeters. There are 64 squares on a chess board. What is the area of the chess board?
Answer: 207936 millimeters squared
Step-by-step explanation:
57 * 57 = 3249
3249 * 64 = 207936
Answer: 207936 millimeters^2
Step-by-step explanation: 57*57=3249
3249 64 times is 207936.
Pls help me understand this.
The area of the polygon is approximately 24.497 square units.
How to determine the area of a polygon
In accordance with the statement, we have a polygon with three vertices set on Cartesian plane, that is, a triangle. We need to find the side lengths first and later to calculate the area by Heron's formula. First, determine the lengths of each line segment by Pythagorean theorem:
JK = √[[4 - (- 3)]² + (4 - 4)²]
JK = 7
KL = √[(3 - 4)² + (- 3 - 4)²]
KL = √[(- 1)² + (- 7)²]
KL = 5√2
JL = √[[3 - (- 3)]² + (- 3 - 4)²]
JL = √85
Second, calculate the area of the triangle:
s = (JK + KL + JL) / 2
s = (7 + 5√2 + √85) / 2
s ≈ 11.645
A = √[s · (s - JK) · (s - KL) · (s - JL)]
A = √[11.645 · (11.645 - 7) · (11.645 - 5√2) · (11.645 - √85)]
A ≈ 24.497
The area of the polygon is approximately 24.497 square units.
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