An equivalent rational expressions with denominator (x+3), (x−4) and (x+4) is (3x²+6x-16)/(x³+3x²-16x-48).
The given denominator are (x+3), (x−4) and (x+4).
What is a rational expressions?A mathematical expression that may be rewritten to a rational fraction, an algebraic fraction such that both the numerator and the denominator are polynomials.
Here, an equivalent rational expressions is
[tex]\frac{1}{x+3}+\frac{1}{x-4} +\frac{1}{x+4}[/tex]
The LCM of denominators is (x+3)(x-4)(x+4)
= (x+3)(x²-16)
= x(x²-16)+3(x²-16)
= x³-16x+3x²-48
= x³+3x²-16x-48
Now, [tex]\frac{(x-4((x+4)+(x+3)(x+4)+(x+3)(x-4)}{x^3+3x^2-16x-48}[/tex]
= (x²-16+x²+7x+12+x²-x-12)/(x³+3x²-16x-48)
= (3x²+6x-16)/(x³+3x²-16x-48)
Hence, an equivalent rational expressions with denominator (x+3), (x−4) and (x+4) is (3x²+6x-16)/(x³+3x²-16x-48).
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what is the solution for this system of linear equations?
a. (3,1)
b. (-2,1)
c. Infinite solutions
d. No solution
Answer:
Step-by-step explanation:
hello :
d. No solution
Similar right triangles
Find the value of x.
A bottling company produces 7,200 cans of iced tea per day. How many 12-can cartons can be filled?
Answer:
600 cartons
Step-by-step explanation:
Graph y = x2 + 10x + 25.
Determine the number of solutions.
Answer:
1 solution
Step-by-step explanation:
The equation will be a horizontal parabola that has an x-intercept of (-5,0) therefore 1 solution
Answer:
vertex: (-5,0)
axis of symmetry: x=-5
some points: (-7,4)(-6,1)(-5,0)(-4,1)(-3,4)
Find the degree of the monomial.
-4a^4
Answer:
the degree is 4
Step-by-step explanation:
the exponent of the monomial of is 4 so the degree is 4
Answer:
4
Step-by-step explanation:
The degree of a monomial refers to the exponent of the term. In this case, the term is to the degree (4) because its exponent is (4).
calculate the volume of the prism by first finding the total number of half unit cubes that will fill it.There are 8 half unit cubes in every unit cube pls help guys this is my exam
Answer:
I think its C
Step-by-step explanation:
Suppose that Clayton Kershaw of the Los Angeles Dodgers throws his fastball with a mean velocity of 94 miles per hour (mph) and a standard deviation of 2 mph and that the distribution of his fastball speeds can be modeled by a Normal distribution What percent of Kershaw’s fastballs will travel at least 100 mph?
Answer:
Step-by-step explanation:
ah, probability, so the std. deviation is 2 MPH, so that means to get from the mean.. or average speed of 94, he'll have to vary by 3 std. deviations or 6 MPH to hit 100
99.7% of throws fall into that area of with in 3 std. deviations so that means
0.3% fall outside also , 1/2 of those will 3 std. deviations slow while the other half is fast
so
0.15% will be 100 or faster.... not many
0.15% is the percent of Kershaw’s fastballs will travel at least 100 mph.
What is Normal Distribution?A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
The standard deviation is 2 MPH, so that means to get from the mean.. or average speed of 94, he'll have to vary by 3 standard deviations or 6 MPH to hit 100
99.7% of throws fall into that area of with in 3 standard deviations so that means
0.3% fall outside also , 1/2 of those will 3 standard deviations slow while the other half is fast
so 0.15% will be 100 or faster
Hence 0.15 percent of Kershaw’s fastballs will travel at least 100 mph.
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how many perfect squares are there between 2 and 140
Answer:
11
Step-by-step explanation:
4, 9, 16, 25, 36, 49, 64, 81, 100, 121
There are 10 numbers who are perfect squares.
What is Square of a number?When an integer is multiplied by the same integer, the resultant number is known as a square number. For example, when we multiply 5 × 5 = 52, we get 25. Here, 25 is a square number. Square numbers are always positive, they cannot be negative because when a negative number is multiplied by the same negative number, it results in a positive number.
Properties of Square NumbersThe properties of square numbers are listed below which helps to identify them easily.
Square numbers always end with the digits 0, 1, 4, 5, 6, and 9. For example, 25, 49, 81, 100, etc are perfect squares, whereas, 37, 48, 22, etc are not considered to be perfect square numbers.The number of zeros at the end of a square number is always even. This means if a number has an odd number of zeros at the end, then the number is not a square number. For example, 400, 3600 are square numbers, whereas, 10, 250, and 360 are non-square numbers.If a number has 1 or 9 as its last digit, then its square number ends with 1. For example, the square of 9 is 81, and the square of 11 is 121.If a number has 4 or 6 as its last digit, then its square number ends with 6. For example, the square of 4 is 16, and the square of 26 is 676.The square of even numbers is always even, and the square of odd numbers is always odd. For example, the square of 12 is 144, and the square of 13 is 169.Square numbers are always positive because two negative signs multiplied by each other result in a positive sign. For example, (-6)2 = -6 × -6 = 36 . Here, the product is 36 and it is a positive square number.Given:
2 and 140
Now, the perfect squares are:
√4=2
√9=3
√16 =4
√25=5
√36=6
√49=7
√64=8
√81=9
√100=10
√121=11
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Which expression is equivalent to -8 - (-12)
8 - 12
-8 + 12
-8 - 12
-8 (8+12)
I need help with this too it’s confusing and I don’t understand it.
*PLEASE HELP ASAP ITS A TEST* How many solutions does the system of linear equations represented in the graph below have?
Answer:
0
Step-by-step explanation:
The 2 lines never intersect so there are 0 solutions
Sarah goes to dinner with two friends the total cost of dinner is $61.92 her friends pay 2/3 of the total cost exactly how much does Sarah pay
Answer:
the amount paid by Sarah is $20.64
Step-by-step explanation:
Given that
The total cost of the dinner is $61.92
And her friends pay 2 by 3
We need to find out the amount paid by Sarah
Since her friends pay 2 by 3 of the total cost
That means the remaining should be paid by Sarah i.e. 1 by 3
So, we need to multiply 1 by 3 with the total cost of the dinner i.e.
= 1 ÷3 × $61.92
= $20.64
Hence, the amount paid by Sarah is $20.64
If the population has a variance of 4.6, what is the variance of the sampling distribution of its means if the
sampling distribution was derived with sample size n = 2 and all possible samples are drawn with
replacements?
Answer:
Step-by-step explanation:
Hi
Briefly explain the roles and relationships that exists amongst the producers, consumers, and decomposers in an ecosystem such as an ocean.
The roles and relationships that exist amongst the producers, consumers, and decomposers in an ecosystem is described by the food chain.
What is an ecosystem?
The meaning of ecosystem is the complex of a community of organisms and its environment functioning as an ecological unit.
Producer is an organism that produces its own food e.g. photosynthesis in plants. Also known as the base of the food-chain.
Consumer is an organism that consumes (eats) either a producer or another consumer e.g. animals will solely eat plants (herbivore), solely animals (carnivore), or a combination of both (omnivore).
Studies are showing that most animals are omnivores. Even pre-concluded herbivores or carnivores are found to eat a small variety of both plants and animals in a pinch. E.g. a deer would eat a baby bird if it found it on the ground.
Decomposers are organisms that 'eat' and break up dying/decaying material e.g. earthworms and fungi.
All of this together is the food cycle.
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Hi
Can you help me with this ?
thank you
Have a nice day
25°>>>>>>>>>>>>>>>>>>>>
Simplify and express
[tex]2 \sqrt{2} - \frac{3}{ \sqrt{2} } + \frac{4}{ \sqrt{8} } [/tex]
as a single surd
First a few reminders:
• For a ≠ 0 and b ≥ 0, [tex]\sqrt[a]{b}=b^{\frac1a}[/tex]
• 4 = 2² and 8 = 2³
• For real numbers a, b, c, we have [tex](a^b)^c=a^{bc}[/tex]
• For any real numbers a and n (so long as both are not zero), we have [tex]\frac1{a^n}=a^{-n}[/tex]
• For any numbers a, b, c, [tex]a^b\times a^c=a^{b+c}[/tex]
So we have
[tex]\sqrt2=2^{\frac12}[/tex]
[tex]\dfrac1{\sqrt2}=2^{-\frac12}[/tex]
[tex]\dfrac1{\sqrt8}=\dfrac1{(2^3)^{\frac12}}=2^{-\frac32}[/tex]
Then the given expression can be rewritten as
[tex]2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=2\times2^{\frac12}-3\times2^{-\frac12}+2^2\times2^{-\frac32}[/tex]
[tex]2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=2^{1+\frac12}-3\times2^{-\frac12}+2^{2-\frac32}[/tex]
[tex]2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=2^{\frac32}-3\times2^{-\frac12}+2^{\frac12}[/tex]
Pull out a factor of [tex]2^{-\frac12}[/tex]:
[tex]2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=2^{-\frac12}\left(2^{\frac32+\frac12}-3+2^{\frac12+\frac12}\right)[/tex]
Simplify this:
[tex]2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=2^{-\frac12}\left(2^2-3+2^1\right)=2^{-\frac12}(4-3+2)=3\times2^{-\frac12}=\dfrac3{\sqrt2}[/tex]
Rationalize this last result to get the square root out of the denominator:
[tex]2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=\dfrac3{\sqrt2}\times\dfrac{\sqrt2}{\sqrt2}=\dfrac{3\sqrt2}{(\sqrt2)^2}=\boxed{\dfrac{3\sqrt2}2}[/tex]
Which rule describes the composition of transformations that maps triangle BCD to triangle B""C""D""?
Answer:
(d)
Step-by-step explanation:
Given
See attachment for [tex]\triangle BCD[/tex] and [tex]\triangle B"C"D"[/tex]
Required
The transformations
Using B and B"" as points of reference, we have:
[tex]B = (1,4)[/tex]
[tex]B"" = (5,-1)[/tex]
The transformation is as follows:
First, reflect across y axis.
The rule is:
[tex](x,y) \to (-x,y)[/tex]
So, we have:
[tex]B(1,4) \to B'(-1,4)[/tex]
Next, translate 6 units right.
The rule is:
[tex](x,y) \to (x + 6,y)[/tex]
So, we have:
[tex]B' (-1,4) \to B"(-1 + 6,4)[/tex]
[tex]B' (-1,4) \to B"(5,4)[/tex]
Lastly, translate 5 units down
The rule is:
[tex](x,y) \to (x,y-5)[/tex]
So, we have:
[tex]B"(5,4) \to (5,4-5)[/tex]
[tex]B"(5,4) \to (5,-1)[/tex]
Hence; (d) is correct
PLEASE HELP 50 points
Answer:
r > 7 (C)
Step-by-step explanation:
3r−7>14
Step 1: Add 7 to both sides.
3r−7+7>14+7
3r>21
Step 2: Divide both sides by 3.
3r
3
>
21
3
r>7
Hope this helps and makes sense!! Good luck and have a wonderful day! <33
Imagine this < as a alligater and itś eating the greater number!!
Answer:
C.) r ≥ 7
Step-by-step explanation:
1. Add 7 to each side to cancel it out and keep the sign the way it is to avoid confusion
3r - 7 ≥ 14
+ 7 +7
3r ≥ 21
2. Divide each side by 3 to get the variable alone
3r/3 = r
21/3 = 7
r ≥ 7
This means r is greater than or equal to 7, and it can also be written as 7 ≤ r
HELP! :))
If 35 liters of petrol cost $21.00, what is the price per liter?
Answer:
1.66$ per liter
Step-by-step explanation:
Hi there! I hope you're having a good day so far. :)
So this equation is quite simple. To write it out, you get:
35/21.00=?
All you need to do is get a calculator and put that in.
Then you will get 1.66666667, but to 'simplify' it, you just get 1.66 dollars per liter.
Therefore, the answer is 1.66$ per liter.
Helper's Message:
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-ChocoChocoCho
What is 5 11/10 simplified
Answer:
61/10 or in decimal form 6.1 or 6 1/10
Step-by-step explanation:
Anita needs to construct ten cones for a class project. How many square feet of material will she need? Use 3.14 for π. Enter your answer in the box. Th radius is 6 ft and the height is 12 ft.
Assuming that Anita needs hollow right circular cones, we are solving for its lateral surface area, which is given by the formula πr√ (h²+r²), where r is the radius and h is the height.
r = 6 ft / 2 = 3 ft
Solving for the lateral surface area of one cone:
LSA = (3.14) (3) [√ (12²+3²) ] = 116.52 sq ft.
Since she needs 10 cones:
10 * 116.52 sq. ft = 1,165.2 sq ft.
She will need 1,165.2 sq ft of material.
Hope this helps you :)
Find the area of the given figure. Show your work!
what is cooms. ......k
Answer:
The Coombs test checks your blood for antibodies that attack red blood cells. It can help prevent and diagnose problems.
ummmm
also what cu.ms out of a co.ck
lm.ao
3, 6, 9, 10, 10, 11
What is the range of the data?
What is the second quartile Q2 (or what is the median)?
What is the interquartile range? (Q1-13)
Answer:
Range : 8
Q2: 9.5
Interquartile range is 2.5
Select the expression that has a value of 13. 9 + 3 x (2 ÷ 3) + 6 (9 + 3) x 2 ÷ 3 + 6 9 − (3 x 2) ÷ 3 + 6 (9 + 3 x 2) ÷ 3 + 6
Answer:
[tex](c)\ 9 - (3 * 2) \div 3 + 6[/tex]
Step-by-step explanation:
Given
(a) to (d)
Required
Which equals 13
[tex](a):\ 9 + 3 * (2 \div 3) + 6[/tex]
Solve the bracket
[tex]9 + 3 * (2 \div 3) + 6 =9 + 3 * (\frac{2}{3}) + 6[/tex]
Open the bracket
[tex]9 + 3 * (2 \div 3) + 6 =9 +2 + 6[/tex]
[tex]9 + 3 * (2 \div 3) + 6 == 17[/tex]
[tex](b):\ (9 + 3) * 2 \div 3 + 6[/tex]
Solve the bracket
[tex](9 + 3) * 2 \div 3 + 6 =(12) * 2 \div 3 + 6[/tex]
Open bracket
[tex](9 + 3) * 2 \div 3 + 6 =24 \div 3 + 6[/tex]
Divide
[tex](9 + 3) * 2 \div 3 + 6 =8 + 6[/tex]
[tex](9 + 3) * 2 \div 3 + 6 =14[/tex]
[tex](c)\ 9 - (3 * 2) \div 3 + 6[/tex]
Solve the bracket
[tex]9 - (3 * 2) \div 3 + 6 =9 - (6) \div 3 + 6[/tex]
Remove bracket
[tex]9 - (3 * 2) \div 3 + 6 =9 - 6 \div 3 + 6[/tex]
Divide
[tex]9 - (3 * 2) \div 3 + 6 =9 - 2 + 6[/tex]
[tex]9 - (3 * 2) \div 3 + 6 =13[/tex]
[tex](d)\ (9 + 3 * 2) \div 3 + 6[/tex]
Solve the bracket (the product, first)
[tex](9 + 3 * 2) \div 3 + 6=(9 + 6) \div 3 + 6[/tex]
[tex](9 + 3 * 2) \div 3 + 6=15 \div 3 + 6[/tex]
Divide
[tex](9 + 3 * 2) \div 3 + 6=5 + 6[/tex]
[tex](9 + 3 * 2) \div 3 + 6=11[/tex]
Only (c) equals 13
Hey can you help me fast!!
(PS. I used to HATE i-ready)
factorise 5x^3-15x^2 + 25x by 5
Answer:
x^3- 3x^2+ 5x
Step-by-step explanation:
basically divide the coefficents by 5
In a lottery, the top cash prize was $615 million, going to three lucky winners. Players pick four different numbers from 1 to 59 and one number from 1 to 49 . A player wins a minimum award of $225 by correctly matching three numbers drawn from the white balls (1 through 59 ) and matching the number on the gold ball (1 through 49 ). What is the probability of winning the minimum award?
Answer:
10063571 out of 593750689 or 1.69491525424%
Step-by-step explanation:
To find probability when all variables are known, you can just multiply the numbers you need. In this case we multiply 59 * 59 * 59 *49 since these are the balls we are picking from. We can find the chance of the top prize by multiplying all the numbers. 59 * 59 * 59 * 59 * 49
Find the surface area and the volume, help me pretty please
Answer:
The surface area is 13.08 and the volume is 3.14
Step-by-step explanation:
What is the slope of the line that passes through the points (-2,-5) and (18, –5)?
Write your answer in simplest form.
Answer:
0
Step-by-step explanation:
Slope = [tex]\frac{y2-y1}{x2-x1}[/tex]
(-2,-5) = (x1,y1)
(18,-5) = (x2,y2)
Slope = [tex]\frac{-5+5}{18+2}[/tex]
= [tex]\frac{0}{20}[/tex]
= 0
find z. explain please
Answer:
13
Step-by-step explanation:
You need to use pythagorean theorem (a^2 + b^2 = c^2). In this case 5 is a, 12 is b, and z is c. 5^2 + 12^2 = z^2, this ends up as 169 = z^2. Now you find the square root of 169 which is 13.
Step-by-step explanation:
Maybe it is root 5²time 12²=60
BRAINILIEST PLEASE