The required simplification of an expression is 2(x + 1) / (x + 4)(x + 4).
What is an expression?
An expression is any statement in mathematics written using numbers, variables and at least one operation present.
Simplification of the expression: 2x - 8 / x² - 16 . x² + 5x + 4 / x² + 8x + 16
Given an expression,
2x - 8 / x² - 16 . x² + 5x + 4 / x² + 8x + 16
On simplifying, we get,
(2x - 8).(x² + 5x + 4) / (x² - 16).(x² + 8x + 16)
For the numerator, (2x - 8).(x² + 5x + 4), we have,
= 2(x + 1)(x - 4)(x + 4)
For the denominator, (x² - 16).(x² + 8x + 16)
= (x + 4)(x - 4)(x + 4)(x + 4)
Now, (2x - 8).(x² + 5x + 4) / (x² - 16).(x² + 8x + 16)
= 2(x + 1)(x - 4)(x + 4) / (x + 4)(x - 4)(x + 4)(x + 4)
= 2(x + 1) / (x + 4)(x + 4)
The restriction to the given expression is that the denominator, x + 4 should not be 0.
Hence, the required simplification of an expression is 2(x + 1) / (x + 4)(x + 4).
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The expression 53(1+x) represents the total cost of a meal including the tip.
Answer:
53 + 53x
Step-by-step explanation:
Multiply each term in the parentheses by 53 and you get 53 + 53x
I hope that helps!!
A roll of 50 pennies has a mass of 125 grams. What is the value of 1,000 grams of pennies?
$4.00
$3.50
$5.00
$8.00
$4.50
Answer:
$4.00
Step-by-step explanation:
make a proportion
50/125=x/1000
1000(50/125)=x
8(50)=x
400=x
400pennies=$4.00
or solve like this
50/125= 0.4 pennies per gram (p/g)
0.4p/g
0.4p/g*1000g=400p=$4.00
Write
15
3
2
in surd form.
The given expression written in surd form is 15√15
From the question, we are to write the given expression in surd form
The given expression is
[tex]15^{3/2}[/tex]
To write the expression is surd form, we will apply one of the laws of indices.
From one of the laws of indices, we have that
[tex]x^{y/n} = \sqrt[n]{x^{y} }[/tex]
Then,
We can write [tex]15^{3/2}[/tex] as
[tex]15^{3/2} = \sqrt[2]{15^{3} }[/tex]
[tex]= \sqrt[]{15^{3} }[/tex]
Simplifying
[tex]\sqrt{3375}[/tex]
Further simplification
[tex]\sqrt{225 \times 15}[/tex]
= [tex]\sqrt{225} \times \sqrt{15}[/tex]
= [tex]15 \times \sqrt{15}[/tex]
= [tex]15 \sqrt{15}[/tex]
Hence, the given expression written in surd form is 15√15
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A composite figure is comprised of a semicircle, trapezoid, and 2 rectangles.
How can you decompose the composite figure to determine its area?
as a circle, three rectangles, and a triangle
as a circle, a trapezoid, and four triangles
as a semicircle, three rectangles, and a square
as a semicircle, a trapezoid, and two rectangles
The area of the composite figure is the sum of the area of a semicircle, the area of a trapezoid, and the area of two similar rectangles. Then the correct option is D.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Two rectangles, a trapezoid, and a semicircle make form a composite figure.
The diagram of the composite figure is given below.
The area of the composite figure is the sum of the area of a semicircle, the area of a trapezoid, and the area of two similar rectangles. Then the correct option is D.
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Answer:
D
Step-by-step explanation:
converting 0.000098 into scientific notation what is the missing power of 10
Answer:
9.8E^-5 (or 9.8*10^-5)
Step-by-step explanation:
0.000098 converted to scientific notation is either 9.8E^-5 or 9.8*10^-5 as they are the same, just different ways of writing it. To get this, you just count the spaces away from the decimal point the number is.
ex.) 0.98 = 9.8E^-1 as it just has to move 1 decimal
980 = 9.8E^1 as it has to move 1 decimal to the positive side
and so on.
Find the inverse of each function. Is the inverse a function?
y=x²+4
If the equation be y = x² + 4 then the inverse function be [tex]f^{-1} (x)=[/tex] ± [tex]\sqrt{x - 4[/tex].
What is meant by inverse function?An inverse function, also known as an anti function, is a function that can be reversed into another function. Simply put, if any function " f " takes x to y, then its inverse will take y to x. The inverse function is denoted by f-1 or F-1 if the function is denoted by ' f ' or ' F '.
Let the equation be y = x² + 4
then the function be f(x) = x² + 4
y = x² + 4
⇒ x = y² + 4
simplifying the above equation, we get
x - 4 = y²
√y² = √x - 4
The value of y = ± √x - 4
Therefore, the inverse function be [tex]f^{-1} (x) =[/tex] ±√x - 4
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When janelle woke up it was -3 degrees Fahrenheit outside.as the morning progressed,the temperature rose 2 degrees every hour.
W hitch line on the Garth could represent this scenario
The equation to illustrate the information regarding the temperature it the temperature rose 2 degrees every hour is -3 + 2h.
How to illustrate the information?It should be noted that an equation is used to show the relationship between the variables.
In this case, when janelle woke up it was -3 degrees Fahrenheit outside.as the morning progressed,the temperature rose 2 degrees every hour.
Let the number if hours be represented by h
Therefore, the equation to illustrate the information will be -3 + 2h
here h = number of hours.
Note that the complete information wasn't found and the equation was illustrated.
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pls help i really need it i beg
The first and third picture are the same.
1. They have 13/12 ft of lumber
2. 3/7
3. 13/12
4. It took Tim 1/4 longer to run the sprint
As a math citizen, why is it important to be able to interpret and analyze graphs?
Multiply. HELP
3/10⋅4/9
Responses
2/15
7/19
27/40
I don't know.
Two out of every five cars are red.if there are 100 cars in the parking lot, how many are red
Answer: 10 Cars!!!!
Step-by-step explanation:
determine whether descriptive or inferential statistics were used in the statement. 67% of cell phone users check their phone even though it is not ringing or vibrating. (source: pew research center)
Inferential Statistics
Inferential Statistics is the part of statistical analysis that helps you to determine or predict further steps from the data studied according to Statistical methods. It is helpful in understanding people's perspectives or analyzing data from the samples obtained from it. It can be defined as the analytical tool used to draw conclusions about a population by analyzing random samples.
Descriptive Statistics are used to describe the data and make generalizations about the studies. It is used the define the characteristics of the data obtained.
In the given situation, the statistical analysis is done and it has been inferred from the studies that 67% of people check their cell phone even when it is not ringing or vibrating.
Hence, It is a case of Inferential Statistics.
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A grocery store sells a bag of 8 oranges for $3.12. If Boubacar spent $2.34 on oranges, how many did he buy
Answer:
Step-by-step explanation:
Answer = 6 oranges
.39 x 6 = $2.34
The number of oranges Boubacar buys is 6 oranges
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The number of oranges a grocery store sells at $ 3.12 = 8 oranges
The number of oranges a grocery store sells at $ 1.00 =
The number of oranges a grocery store sells at $ 3.12 / 3.12
The number of oranges a grocery store sells at $ 1.00 = 8 / 3.12
Now ,
The number of oranges a grocery store sells at $ 2.34 = The number of oranges bought by Boubacar
The number of oranges a grocery store sells at $ 2.34 = ( 8 / 3.12 ) x 2.34
So ,
The number of oranges bought by Boubacar = ( 8 / 3.12 ) x 2.34
= 8 x 0.75
= 6 oranges
Hence , the number of oranges Boubacar buys is 6 oranges
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If the temperature has been changing at a rate of −1.5 degrees each hour, and it is currently 5 degrees, the temperature 4 hours ago was
Answer:13.33333333
Step-by-step explanation:All you have to do is 5 divided by 1.5 times 4. Your welcome random human being (or alien)
Help now please!!
I dont understand at all and need help. pls dont comment if u dont know.
Answer:
I'm pretty sure it would be B
Step-by-step explanation:
X and Y
Answer:
am pretty sure it answer b
50pts to whoever can solve this correctly
Answer:
b^2 - 4ac ==> what's inside the square root
The answer is the 2nd option
Step-by-step explanation:
b^2 - 4ac represents the number of roots in the quadratic equation. If
b^2 - 4ac>0, then there are 2 roots in the quadratic equation. If
b^2 - 4ac=0, then there is only 1 root. If b^2 - 4ac<0, then the square root of b^2 - 4ac would be invalid since the square root of a negative number has no real solution. Hence, if b^2 - 4ac<0, then there are no roots.
Answer:
The answer should be option B. b^2-4ac
Step-by-step explanation:
...
First answer gets brainliest!!!!!!!!!!!!!!!!!!!!
The following relationships between linear equations are shown below:
12 - (1 / 2) · r → [13 - (3 / 2) · r] - (1 - r) r - 13 / 6 → (7 · r - 3 / 2) - (2 / 3 + 6 · r) 13 · r + 20 → (6 · r + 7) + (13 + 7 · r) - 12 + r → (- 8 - r) + (2 · r - 4)How to match an expression with its simplified form
In this problem we find four cases of linear equations whose relationship with simplified forms, that is, linear equations of the a · r + b, where a, b are constants, must be found. Each relationship can be determined by using algebra properties. Now we proceed to present the conclusion for each case:
Choice A
(6 · r + 7) + (13 + 7 · r)
(6 · r + 7 · r) + (7 + 13)
(6 + 7) · r + 20
13 · r + 20
Choice B
[13 - (3 / 2) · r] - (1 - r)
[13 - (3 / 2) · r] + (- 1 + r)
[- (3 / 2) · r + r] + (13 - 1)
[- (3 / 2) + 1] · r + 12
(- 1 / 2) · r + 12
12 - (1 / 2) · r
Choice C
(- 8 - r) + (2 · r - 4)
(- r + 2 · r) + (- 8 - 4)
(- 1 + 2) · r - 12
r - 12
- 12 + r
Choice D
(7 · r - 3 / 2) - (2 / 3 + 6 · r)
(7 · r - 3 / 2) + (- 2 / 3 - 6 · r)
(7 · r - 6 · r) + (- 3 / 2 - 2 / 3)
r + [- (9 + 4)] / 6
r + [- 13] / 6
r - 13 / 6
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NEED CORRECT ANSWER RN PLS
PLSS HELP :((
will mark brianlist if its the correct answer ty
Solve by factoring. Check your answers. x²=-x+6
The factoring of the expression x²=-x+6 is (x-2)(x+3)
By ordering the values, we get:
x² + x - 6 = 0
To solve this exercise, we have to follow the rules of factoring:
1. Looking for the a and b number that state the following equations:
a + b = 1a * b = - 6Analyzing that (a*b) is a negative number, it means that (a) and (b) have different signs, and due to the results of (a+b) is positive the higher number has to be the positive one.
The number could be:
a = -2
b = 3
Confirming:
a + b = -2 + 3 = 1
a * b = (-2) * 3 = - 6
2. Rewriting the factored expression (x+a)(x+b) with the obtained values, we get:
(x-2)(x+3)
What is factoring?Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.
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Find the distance between C & D.
C = (8, -3) and D = (-9, -6)
Round to the nearest tenth.
Answer: 17.3
Step-by-step explanation:
13 divided by 10 5/6 in fraction
Answer:
6/5 or 1 1/5
Step-by-step explanation:
Hope this helps. Please mark me Brainliest!
describe number patterns: 1, -4, 9, 16
Answer: least to greatest is -4,1,9,16
greatest to least is 16,9,1,-4
Step-by-step explanation: it's common thinking to me
2. The official Olympic swimming pool measures about 50 m x 25 m x 2.5 m (LWH). If a
box measuring 50cm x 70cm x 25cm (LWH) can hold 315 tennis balls, then what would
be a reasonable estimate for a number of tennis balls that can fit in the swimming pool?
Answer:
the answer isssssssssssssssssss
Divide. Rationalize all denominators. ∛6 x² y⁴ / 2∛5 x⁷y
The value of the expression [tex]\frac{x^{2}y^{4}}{2\sqrt[3]{5} x^{7}y}[/tex] after rationalizing the denominator is [tex]\frac{5^{\frac{2}{3}}y^{3}}{10x^{5}}[/tex].
A finite collection of symbols that is well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.
Rationalizing the denominator is the process of shifting a root, such as a cube root or a square root, from the fraction's denominator to its numerator (numerator).
The numerator is the part of a fraction that comes before the vinculum.
The denominator of a fraction is the phrase that comes before the vinculum.
Consider the expression,
[tex]\frac{x^{2}y^{4}}{2\sqrt[3]{5} x^{7}y}[/tex]
Now, let [tex]a=\frac{x^{2}y^{4}}{2\sqrt[3]{5} x^{7}y}[/tex]
[tex]a=\frac{(x^{2}y)(y^{3})}{2\sqrt[3]{5} (x^{2}y)(x^{5})}[/tex]
[tex]a=\frac{y^{3}}{2\sqrt[3]{5} {~}x^{5} }[/tex]
To rationalize the denominator we multiply and divide the expression by ( ∛5 )².
[tex]a=\frac{y^{3}}{2\sqrt[3]{5} {~}x^{5} } \times \frac{(\sqrt[3]{5})^{2}}{(\sqrt[3]{5})^{2}}[/tex]
[tex]a=\frac{5^{\frac{2}{3}}y^{3}}{10x^{5}}[/tex]
The value of the expression when rationalized [tex]\frac{x^{2}y^{4}}{2\sqrt[3]{5} x^{7}y}[/tex] is [tex]\frac{5^{\frac{2}{3}}y^{3}}{10x^{5}}[/tex].
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I need help, thank you <3
Step-by-step explanation:
so, pre-image is then doing the opposite :
going up 2 units and left 4 units.
up/down changes y, left/right changes x.
up = positive y direction
down = negative y direction
right = positive x direction
left = negative x direction
just as indicated by the coordinate axes.
so,
going up 2 units = adding 2 to y
going left 4 units = subtracting 4 from x
giving us as pre-image point A
(4 - 4, -5 + 2) = (0, -3)
HELP!!! There is a photo please quickly!!
Answer:
∆y = 9
∆x = 6
Slope = 3/2 or 1.5
It looks like you erased it, but you had the answer correct on your paper.
Step-by-step explanation:
I am stuck. The questions are numbered so please type the number of the question by the answer. Please and thank you.
Answer:
#1 = -1/3
2# = -6/5
3# = 2/9
4# = 2
#5 = -2/3
Step-by-step explanation:
The slope formula is (y2 - y1) / x2 - x1. With (x1, x2) and (x2, y2) be points on the line.
explain why when you divide both sides of an inequality by a negative number, you must reverse the inequality sign.
What are the answers and how do you write it out
Just use a calculator.
First substitute in the numbers and make sure to use ( ) when plugging in negative values. For example, the first one says n=4, you can substitute n from the expression to 4. So n^2 + 3n + 8 will turn into 4^2 + 3(4) + 8 which is 16 + 12 + 8 = 36. You can do this with the other questions.
Number 10 is -213.
PLEASE HELP ME
look at the pic down below
Answer: (1) Deena and Eduardo, (2) (A) or cube root of 343
Step-by-step explanation:
Number 1 : Deena and Eduardo are correct,
16 x 16 = 256
4 x 4 x 4 = 64
Number 2 : (a) the cube root. of 343 will give Patel the correct answer,
h^3 = 343
cube root of both sides
so, h. = cube root of 343