help solve these algebraic fractions please with explanation would be great <3
Answers
Answer:
7/ Ans;
[tex] \frac{x + 2}{ x + 4} \div \frac{ {x }^{2} - 2x - 8}{ {x}^{2} + 2x - 8} \\ \\ \\ \frac{x + 2}{x + 4} \times \frac{ {x}^{2} + 2x - 8 }{ {x}^{2} - 2x - 8} \\ \\ \\ \frac{x + 2}{x + 4} \times \frac{(x - 2)(x + 4)}{(x - 4)(x + 2)} \\ \\ \\ =1 \times \frac{x - 2}{x - 4} \\ \\ \\ = \frac{x - 2}{x - 4} [/tex]
___o__o__
9/Ans;
[tex] \frac{ {x}^{2} - 9}{ {x}^{2} - 6x + 9} \div \frac{x + 4}{x - 3} \\ \\ \frac{ {x}^{2} - 9 }{ {x}^{2} - 6x + 9} \times \frac{x - 3}{x + 4} \\ \\ \\ \frac{(x + 3)(x - 3)}{(x - 3)(x - 3)} \times \frac{x - 3}{x + 4} \\ \\ \\ = \frac{(x + 3)}{1} \times \frac{1}{(x + 4)} \\ \\ \\ = \frac{x + 3}{x + 4} [/tex]
__o__o__
In the two questions, we first replace the division with multiplication with flipping the fraction after the division sign, secondly we analyze any equation that needs analysis to simplify it, thirdly, to simplify the fraction by deleting the numerator and the similar denominator .
Related Questions
what fraction is at point M?
Answers
Answer:
D
Step-by-step explanation:
because 3/10 is 0.3
Hope this helps!
What is the remainder when f(x) = x³- 13x² + 40x + 18 is divided by x-7? Show your work.
Answers
Answer:
remainder = 4
Step-by-step explanation:
using the remainder theorem
when f(x) is divided by (x - a) then the remainder is f(a)
so when f(x) is divided by (x - 7) the remainder is f(7) , that is
f(7) = 7³ - 13(7)² + 40(7) + 18
= 343 - 13(49) + 280 + 18
= 343 - 637 + 298
= 4
Hence, the remainder is [tex]4[/tex].
What is the remainder value?
The remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient.
Applying the remainder theorem
In general when [tex]f(x)[/tex] is divided by [tex](x - a)[/tex] then the remainder is [tex]f(a)[/tex].
So, here when [tex]f(x)[/tex] is divided by [tex](x - 7)[/tex] the remainder is [tex]f(7)[/tex], that is
[tex]f(7)=7^3-13(7)^3+40(7)+18\\=343-13(49)+280+18\\=343-637+298\\=4[/tex]
Hence, the remainder is [tex]4[/tex].
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The quadratic function graphed has a range of y 23.
O True
False
Answers
•true
Can anybody help me with this?
Answers
Answer:
A
Step-by-step explanation:
The rate of change for the table is found using the slope formula. The rate of change for the linear function is the coefficient of x.
__
tableThe slope formula tells us the rate of change is ...
m = (y2 -y1)/(x2 -x1)
m = (-9 -(-10))/(-1 -(-4)) = 1/3
equationThe coefficient of x in the equations of the offered answer choices are 1/4 and 6.
comparisonThe relations between the various slopes are ...
1/4 < 1/3 < 6
That is, the equation with a slope of 1/4 has a rate of change less than that of the function represented by the table:
y = 1/4x +4 because ... table of values is 1/3
Which expression correctly represents "ten times the difference of a number and six"?
Answers
Answer:
10*(n-6)
Step-by-step explanation:
Break up the equation above and use words. ex.
10 (times) n (minus) 6
^
this is the difference
how do i do this could you show step by step please?
Answers
Answer:
x = 2
Step-by-step explanation:
This is a 45-45-90 special right triangle. The legs in this triangle are equal and the hypotenuse is leg multiplied with √2. Refer to the picture at the bottom.
One leg is x, the second leg is x and hypotenuse x√2.
[tex]x \sqrt{2} = 2 \sqrt{2} \\\\\text{Divide both sides with } \sqrt{2} \text{ to isolate } x.\\\frac{x \sqrt{2}}{\sqrt{2}} = \frac{2 \sqrt{2}}{\sqrt{2}}\\\\x = 2[/tex]
Find ∠ if ∠=+49, ∠=+63, and ∠=106∘.
Answers
The vslue of the angle based on the information given will be 142°.
How to calculate the angle?From the information given, it can be deduced that the shape has four sides. The total angles will be:
= (n - 2) × 180
= (4 - 2) × 180°
= 360°
The value of the last angle will be:
= 360° - (49° + 63° + 106°)
= 360° - 218°
= 142°
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The annual water usage in rockport increases at a rate of 10% every year as the town gets bigger. this year, the town used 6,740 megaliters of water. in 7 years, how much water will be used annually?
if necessary, round your answer to the nearest hundredth.
Answers
4618 mega liters of water, in 7 years, will be used annually.
What is interest?Interest is the outlay you pay to borrow money. Interest is often deliberated as an annual percentage of a loan amount.
here, we have,
I=PRT/100
=6740×10/100×7
=674×1×7
=4618
the nearest hundredth is a 4618 this is the answer.
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Answer:
13,134.35 megaliters
Step-by-step explanation:
Plug in 6,740 megaliters for the initial amount, 0.1 for the rate of increase, and 7 years for the time elapsed.
y
= a(1+r)t
y
= 6,740(1+0.1)7 Plug in values
y
= 6,740(1.1)7 Add
y
= 6,740(1.94871…) Simplify
y
= 13,134.35325… Multiply
Round to the nearest hundredth.
13,134.35325… → 13,134.35
To the nearest hundredth, Rockport will use 13,134.35 megaliters of water annually.
find the solutions(s) to 9x^2-54x+0
Answers
Answer:
x = 6
x = 0
As shown, there are 2 values for x. The question is why, which we will go over in the explanation part.Step-by-step explanation:
identify the coefficients
[tex]9x^2-54x=0\\a=9\\b=-54\\c=0[/tex]
coefficient a = 1
[tex]9x^2-54x=0\\9/9x^2-54x/9=0/9\\x^2-6x=0\\\rightarrow a=1\\\rightarrow b=-6\\\rightarrow c=0[/tex]
complete the square
[tex]b=-6\\(\frac{b}{2})^2=(\frac{-6}{2})^2\\(\frac{x}{y})^2=\frac{x^2}{y^2}\\=(\frac{-6}{2})^2=\frac{-6^2}{2^2}\\\frac{-6^2}{2^2}=\frac{36}{4}\\36 \div 4=9\\\\\downarrow\\\\x^2-6x=0\\x^2-6x+9=0+9\\x^2-6x+9=9\\\frac{b}{2}\\\frac{b}{2}=\frac{-6}{2}\\\frac{b}{2}=\frac{\left(-3\cdot 2\right)}{\left(1\cdot 2\right)}\\\frac{b}{2}=-3\\x^2-6x+9=9\\(x-3)^2=9\\[/tex]
solve for x
[tex](x-3)^2=9\\\sqrt{(x-3)^2}=\sqrt{9}\\x-3=+-\sqrt{9}\\x-3+3=3+-\sqrt{9}\\x=3+-\sqrt{9}\\x=3+-3\\x_1=6\\x_2=0[/tex]
≡ In the end, you have 2 values for x, because you can either subtract 3 by 3 or add 3 by 3 to get six or zero.
find the nature of the roots of the roots of the equation (x-705)(x-795)+800(x-750)(x-835)=0.
(A) Imaginary roots.
(B) Real and distinct.
(C) Real and equal.
(D) None.
Answers
Answer:
B
Step-by-step explanation:
If you are allowed to use a graphing calculator, this can solve a lot of time. Graphing y = (x - 705)(x - 795) + 800(x - 750)(x - 835) gets us a parabola with x-intercepts of 749.97 and 834.924.
These roots are real and distinct, or choice B.
If you aren't allowed to use a graphing calculator, you can expand and combine like terms to get 801x^2 − 1269500x + 501560475. Looking at the discriminant, we see that (−1269500)^2 - 4*801*501560475 = 4630488100 is greater than 0 and not a perfect square, so it is real and distinct, or choice B.
I hope that helps!
The type of data that contains results from other people that are of similar age and gender is known as
Answers
The type of data that contains results from other people that are of similar age and gender is known as normative data.
What is normative data?
Normative data is a type of data that is observed that contains information about the characteristics of a population of interest. For example, normative data about students in a class would contain information such as age, gender, height.
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43.7826087 rounded to the nearest tenth
Answers
Answer:
43.8
When you round look at the number after the one your rounding up to. If its greater than 5 round up. If its lower than 5 keep it the same number
Craig went bowling with $25 to spend. he rented shoes for $5.00 and paid $4.00 for each game. What was the greatest number of games he could have played?
A. 5
B. 7
C. 6
D. 4
Answers
Answer: A
Step-by-step explanation:
Given:
Budget = $25
Shoes rental = $5.00
Price per game = $4.00
To find the greatest number of games he played...
↓
First, subtract the rent for the shoes from the budget.
25 - 5 = 20
Second, divide the remaining money or budget by the price per game.
20 ÷ 4 = 5 (greatest number of games played)
Lastly, check if the expense is the same as the original amount of money.
5 (shoes) + 4(5) (number of games played)
5 + 20 = 25 (original amount of money)
Hope it helps!!! Please mark as brainliest. Thank you :D
You deposit $1600 in a bank account. Find the balance after 3 years for each of the
following situations:
The account pays 2.5% annual interest compounded monthly.
The account pays 1.75% annual interest compounded quarterly.
The account pays 4% annual interest compounded yearly.
Answers
Given the table, write an equation in slope-intercept form.
Answers
Answer:
If you plot points accordingly to the points on the table, Option A. is correct.
Bottles of water come in packages of 6. Cheese sticks come in packages of 10.
What is the least number of packages of each a person has to buy to have the same number of bottles of water and cheese sticks?
Drag and drop a number into each box to complete the statement.
That person needs to buy Response area packages of bottles water and Response area packages of cheese sticks.
Answers
Answer:
water: 5 packagescheese sticks: 3 packagesStep-by-step explanation:
The number of bottles of water and cheese sticks will be the same when both numbers are equal to the least common multiple (LCM) of 6 and 10, the numbers in each kind of package.
__
The LCM can be found by factoring out the greatest common divisor of each of the numbers:
6 = 2 × 3
10 = 2 × 5
The LCM is the product of the unique numbers here: 2 × 3 × 5 = 30.
The number of packages of bottles of water will be 30/6 = 5 packages.
The number of packages of cheese sticks will be 30/10 = 3 packages.
_____
Additional comment
You may notice that the number of packages of each kind is the unique factor in the other number.
1. Trig Function
2. Coordinate value (x, y)
3. Value in terms of sinθ and/or cosθ
sinθ = _________________
cosθ = _________________
secθ = _________________
cscθ = _________________
tanθ = _________________
cotθ = _________________
Answers
The values of the given trig functions in terms of sinθ and/or cosθ are:
sinθ = tanθ.cosθ
cosθ = sinθ/tanθ
secθ = 1/cosθ
cscθ = 1/sinθ
tanθ = sinθ/cosθ
cotθ = cosθ/sinθ
Trigonometric functionsFrom the question, we are to determine the values of the given trig functions in terms of sinθ and/or cosθ
sinθNOTE: tanθ = sinθ / cosθ
∴ sinθ = tanθ.cosθ
cosθFrom above, we can write that
cosθ = sinθ/tanθ
secθSecant is the inverse of cosine
∴ secθ = 1/cosθ
cscθ (cosecθ)Cosecant is the inverse of sine
∴ cscθ = 1/sinθ
tanθtanθ = sinθ/cosθ
cotθCotangent is the inverse of tangent
∴ cotθ = 1/tanθ
But, tanθ = sinθ/cosθ
∴ cotθ = cosθ/sinθ
Hence, the values of the given trig functions in terms of sinθ and/or cosθ are:
sinθ = tanθ.cosθ
cosθ = sinθ/tanθ
secθ = 1/cosθ
cscθ = 1/sinθ
tanθ = sinθ/cosθ
cotθ = cosθ/sinθ
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In an agricultural class, there are 17 freshmen students and 19 sophomore students. What ratio compares the number of freshmen to the number of sophomores (F:S), and what ratio compares the number of sophomores to the number of freshmen (S:F)
Answers
Answer:
Freshmen to sophomores - (17:19)
Sophomores to freshmen - (19:17)
Step-by-step explanation:
I hope this helps! Have a lovely day!! :)
what is the mean of, 50, 30, 40, 10, 20, 80, 60, 90, 10, 30, 110, 70?
Answers
Answer:
50
Step-by-step explanation:
Add all of the values together, which will equal 600, and then divide this number by how many numbers are here, which is 12.
600 / 12 = 50.
Please answer now!!!
Answers
Answer:
Step-by-step explanation:
(
81
m
6
)
1
2
Simplify the expression.
9
2
(
1
2
)
(
m
6
)
1
2
Cancel the common factor of
2
.
9
1
(
m
6
)
1
2
Simplify the expression.
9m3
Answer:
Step-by-step explanation:
Given
(81 m^6) ^ (1/2)
Solution
change 81 to 9^2
(9^2 m^6)^(1/2)
Now multiply the 1/2 by each of the powers
9^2*(1/2) m^6^1/2
Answer 9 m^3
Comment
It's hard to show this, but the 1/2 only multiplies by power. It doesn't influence the base. That's because 1/2 is a power itself.
b divided by 7-12=8
What is b?
Answers
Answer:
140
Step-by-step explanation:
b/7-12=8
b/7=8+12 add
b/7=20
b=7*20 multiply
b=140
answer is 140 it is right answer
if x= 1 y=3 satisfy the linear equation 3x - 4y +9=0
Answers
Answer:
Step-by-step explanation:
3(1) + 4(3) + 9 = 0
3 + 12 + 9 = 0
24 ≈ 0
Maria says the mean of the scores 7, 8, 3, 0, 2 is 5, because she added the scores and divided by 4. Is she correct? Explain why or why not.
Answers
Answer:
She is wrong.
Step-by-step explanation:
The mean score is
7 + 8 + 3 + 0 + 2= 20
We then divide it by the number which is 5
20/5= 4.
Therefore, Maria is wrong.
This is because she divided by 4 instead of 5, as she didn't include the rational number 0.
Given that m∠TSU = m∠SUQ, why is RT || UQ?
Answers
What is the probability that the spinner lands on an even number or on the unshaded section? one-fifth two-fifths three-fifths four-fifths
Answers
The probability that the spinner lands on an even number or on the unshaded section is; 3/5
How to find the probability?
From the spinner attached, we see that the number of sections on the spinner is 5 sections.
Now, we can also see that;
Number of even numbers section = 2
Number of shaded sections = 1
Thus, probability that the spinner lands on an even number or on the unshaded section is;
P(even number or unshaded section) = (2 + 1)/5 = 3/5
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please answer! this is my final question
Answers
Answer:
C. 103,748
Step-by-step explanation:
The one in the first number is worth 10,000
The one in the Second number is worth 100,000
11. Find the total surface area.
4 in.
6 in.
2 in.
Answers
Answer:
Appearantly, you forgot to mention the question
jeremy spends 3/4 of his check on paying bills and 15% on food if jeremy makes 500 $ how much money will he save
answer choices:
A. 375$
B. 50$
C. 125$
D. 85$
Answers
I got it by taking 15% off of 500 which is 75.
After i took off 75% and got 375. Add 375 and 75 to get 450. 500 - 450 = 50.
Therefore our answer is b, :) good luck
In 2009, a principal of $3600 was invested at 3.75% interest, compounded annually. let t be the number of years since 2008. let y be the value of investment, in dollars. Write an exponential function showing the relationship between y and t.
Answers
Answer:
3,600 x (1.0375) ^ 1
Step-by-step explanation:
Compund interest formula.
IA * (r + 1) ^t
IA = Initial amount; r = rate (as decimal); t = time (in years)
IA = 3600
r = .0375
t = 1 (2008-2009)
3,600 x (1.0375)^1
-- Gage Millar, Algebra 1/2 Tutor, (Pending Pre-Calc Tutor)
Select the correct answer from each drop-down menu.
veronica wants to cut a sheet of paper into squares with an area of 12 square inches. for the best approximation, the length of each side o
the square pieces of paper must be approximately equal to
inches. if each side were exactly this length, the area of each square
would be _____
square inches
Answers
Answer:3.46
Step-by-step explanation:i dont know the other one