Answer:
[tex]\frac{5x+2}{3x^2+4x-4}= \frac{2}{3x-2}+\frac{1}{x+2}[/tex]
Step-by-step explanation:
Ooook, step 1: write the denominator as a product, or we're not going anywhere. Can't spot any two factor by staring at it, so quadratic formula it is.
[tex]x= \frac13(-2 \pm \sqrt{4+12})=\frac13(-2\pm4) = -2;\frac23[/tex]
We got our toots, let's split the denominator now: [tex]3x^2+4x-4 = (3x-2)(x+2)\\[/tex]
Now it's all a matter of writing down what we need:
[tex]\frac{5x-2}{3x^2+4x-4}=\frac{5x-2}{(3x-2)(x+2)} = \frac{A}{3x-2}+\frac{B}{x+2} = \frac{A(x+2)+B(3x-2)}{(3x-2)(x+2)}=\frac{Ax+2A+3Bx-2B}{(3x-2)(x+2)} =\frac{(A+3B)x+(2A-2B)}{(3x-2)(x+2)}[/tex]
Here comes the fun part. Two ways: the fast and loose, and the long one.
Fast and loose: let's look only at the numerators of the 3rd to last and first step: [tex]A(x+2)+B(3x-2) = 5x+2[/tex] If we plugged a convenient value, let's say [tex]x=-2[/tex] the coeffcent of A would disappear, and we would be able to find B. Let's do it. [tex]A(-2+2) + B(3(-2)-2) = 5(-2)+2 \rightarrow -8B =-8 B=1[/tex]
At this point we have B, let's pick a different value of x, let's say 1, to get A:
[tex]A(3) + 1(1) = 7 \rightarrow 3A=6 \rightarrow A=2[/tex]
More traditional: Pick the first and last numerators: [tex]5x+2 = (A+3B)x+(2A-2B)[/tex]. Stare at them long enough and pick your favourite excuse to justify the following system (two polynomials are equal if the coefficents are equal, polynomials create a vector space of base [tex](1,x,x^2...)[/tex]
[tex]\left \{ {A+3B=5} \atop {2A-2B=2}} \right.[/tex]
Again, [tex]A=2, B=1[/tex] is a solution.
Either way, the solution is:
[tex]\frac{5x+2}{3x^2+4x-4}= \frac{2}{3x-2}+\frac{1}{x+2}[/tex]
100 points plus brainiest to right answer.
Answer:e d
Step-by-step explanation:
5.
The perimeter of a regular octagon is 88 cm.
a) Write an equation you can solve to find the side length of the octagon.
b) Solve the equation.
Answer: a) side length = perimeter ÷ 8
b) 11cm
Step-by-step explanation:
side length = the perimeter ÷ 8( there are 8 sides in an octagon)
= 88 ÷ 8
= 11cm
hope u understand
In the circle below, suppose m STQ = 102° and mZTSR=56º. Find the following.
Answer:
q
Step-by-step explanation:
1 Solve for the unknown variable:
Answer:
Approximately 6.4
Step-by-step explanation:
We can use the pythagorean thereom here, that tells us (a^2)+(b^2)=c^2. C is the hypotenuse, the side opposite from the right angle, while a and b are the other sides. We can insert 5 and 4 as a and b, and solve for c
:(5^2)+(4^2)=c^2
:25+16=c^2
:41=c^2
:sqrt(41)=6.4=c (We square rooted both sides. 6.4 is only rounded to the nearest hundredths place.) Hope this helps!
Answer:
c = 6.4
Step-by-step explanation:
To find c, we need to use Pythagoras theorem which is:
[tex]a^2 + b^2 = c^2[/tex]
Plug known variables in:
[tex]5^2 + 4^2 = c^2\\25 + 16 = c^2\\\sqrt{25 + 16} = c\\\sqrt{41} = c \\c = 6.403\\c = 6.4[/tex]
Hope this helps!
How many permutations are there of the letters APPLE, if the arrangement must begin with a
vowel and end with a consonant?
Answer:
[tex]18[/tex].
Step-by-step explanation:
Start by considering the two "[tex]\verb!P![/tex]"'s as being different from one another. That way, all five letters in this word would be distinct. With this assumption, the number of arrangements would be [tex]\left(\genfrac{}{}{0}{}{2}{1}\right) = 2[/tex] times that of the actual value.
Start by fixing the first and the last letter since they come with special requirements.
There are [tex]2[/tex] choices for the first letter (the vowel: [tex]\verb!A![/tex] and [tex]\verb!E![/tex].)
Under the assumption that the two "[tex]\verb!P![/tex]"'s are distinct, there would be [tex]3[/tex] choices for the last letter ([tex]\verb!L![/tex] and the two
After choosing the first and the last letters, there would be [tex](5 - 1 - 1) = 3[/tex] choices for the second letter, [tex](3 - 1) = 2[/tex] choices for the third, and [tex](2 - 1) = 1[/tex] for the fourth.
Thus, under the assumption that the two "[tex]\verb!P![/tex]"'s are distinct, there would be [tex](2 \times 3) \times (3 \times 2 \times 1) = 36[/tex] ways to choose the new word. Since this assumption doubles the number of arrangements, dividing the [tex]36[/tex] by [tex]\left(\genfrac{}{}{0}{}{2}{1}\right) = 2[/tex] would give the actual number of arrangements:
[tex]\begin{aligned}\frac{36}{\genfrac{(}{)}{0}{}{2}{1}} = \frac{36}{2} = 18\end{aligned}[/tex].
[tex]\begin{aligned}& 1 && \verb!APPEL!\\& 2 && \verb!APLEP!\\& 3 && \verb!APEPL!\\& 4 && \verb!APELP!\\& 5 && \verb!ALPEP!\\& 6 && \verb!ALEPP!\\& 7 && \verb!AEPPL!\\& 8 && \verb!AEPLP!\\& 9 && \verb!AELPP!\\& 10 && \verb!EAPPL!\\& 11 && \verb!EAPLP!\\& 12 && \verb!EALPP!\\& 13 && \verb!EPAPL!\\& 14 && \verb!EPALP!\\& 15 && \verb!EPPAL!\\& 16 && \verb!EPLAP!\\& 17 && \verb!ELAPP!\\& 18 && \verb!ELPAP!\end{aligned}[/tex].
Frank wants to be an astronaut when he grows up. Last weekend, the science center had an interactive space station exhibit. Frank bought a 3-day pass so he could go every day. Since he bought a multiday pass, he saved $10. Frank paid $56 in all. How much does a day at the science center normally cost?
Please help!! Picture is provided
Quad. ABCD is a trapezoid.
XY is the median
XY = 12; AB=16
Find DC
Answer:
DC = 8
Step-by-step explanation:
The median is half the sum of the parallel bases, that is
[tex]\frac{AB+DC}{2}[/tex] = XY , substitute values
[tex]\frac{16+DC}{2}[/tex] = 12 ( multiply both sides by 2 to clear the fraction )
16 + DC = 24 ( subtract 16 from both sides )
DC = 8
Answer:
DC = 8
Step-by-step explanation:
The median XY of the trapezoid ABCD is half or the sum of AB and DC.
XY = 1/2 ( AB + DC)
We need to find out DC so we can rewrite this equation isolating DC
XY = (1/2)(AB+DC), multiply both sides by 2
2XY = AB + DC, subtract from both sides AB
2XY - AB = DC, now substitute the given AB = 16 and XY = 12
2* 12 - 16 = DC , using the order of operations rules we multiply first
24 -16 = DC, subtract
8 = DC
None sense >report
I. Study the situation below:
Jose wanted to construct a rectangular garden such that its perimeter is 28mn and
its length is 6 times its width.
What are the linear equations that represents the given situation?
II. Answer the following questions:
1. How do you describe a system of linear equations in two variables?
2.
Give at least two examples of systems of linear equations in two variables.
3.
How is the system of linear equations in two variables used in solving in real
life problems and in making decisio?
Answer:
Radio waves have photons with the lowest energies. Microwaves have a little more energy than radio waves. Infrared has still more, followed by visible, ultraviolet, X-rays and gamma rays.Diya used modeling to find
2
.
82
÷
3
.
She regrouped 2 as 20 tenths and regrouped 0.8 as 7 tenths plus 10 hundredths. She divided all of the tenths and hundredths into three equal groups. Each group had 9 tenths and 4 hundredths. She decided that
2
.
82
÷
3
=
0
.
94
.
Which of the following is the correct conclusion about Diya's quotient of 0.94?
help mee
Answer:C
Step-by-step explanation: The quotient is correct because 27 tenths divided by 3 is 0.9 and 12 hundredths divided by 3 is 0.04
The quotient is correct because 27 tenths divided by 3 is 0.9 and 12 hundredths divided by 3 is 0.04.
Given that, Diya regrouped 2 as 20 tenths and regrouped 0.8 as 7 tenths plus 10 hundredths.
What are decimal numbers?Decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point. The dot present between the whole number and fractions part is called the decimal point.
According the given question, the numerical expression is
20/10 + 7/10+12/100
= 2+0.7+0.1
= 2.8
She divided all of the tenths and hundredths into three equal groups.
That is, 2.82/3
=0.94
Hence, the quotient is correct because 27 tenths divided by 3 is 0.9 and 12 hundredths divided by 3 is 0.04.
To learn more about the decimal numbers visit:
https://brainly.com/question/1578006.
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A line includes the points (7, –7) and (11, –3). What is its equation in slope-intercept form?
Emily says that the negative sign means opposite of, so -(-45) means the opposite of negative 45, which is 45. Is Emily correct?
Answer: Yes, No Submit ·
Step-by-step explanation:
What is the lowest value of the range of the function
shown on the graph?
5
4
4
©
3+
Q-2
Nw
2
0 0
14
3
-5 4 -3 -2 -1,
2
3
4/5
x
--2
3
-4+
of
Answer:
-2
Step-by-step explanation
range is just the y level, so the lowest point on the y axis that the function reaches is -2
Dija writes 7x 9 = 63 to find the
number of players on 7 baseball teams. Describe what
each of the factors represents in the multiplication equation.
Answer:
7 represents the number of teams. 9 represents the amount of players on each team. And 63 represents the total number of players.
Step-by-step explanation:
tim drives at an average of 80km
Answer:
80km --- 49.7097mi
Step-by-step explanation:
thats quite slow... but please provide context then i can solve it for you
Your visually impaired friend asked you to enlarge your notes from class so he can study. You took notes on 8.5-inch by 11-inch paper. The enlarged copy has a smaller side with a length of 10 inches. What is the scale factor of this dilation?
Find the scale factor.
Answer:FINDING A SCALE FACTOR Your visually impaired friend asked you to enlarge your notes from class so be can study. You took notes on 8.5-inch by 11-inch.
Step-by-step explanation:thank you
The scale factor is 20/17.
According to the question, you took notes on a paper with dimensions 8.5 inches × 11 inches.
the breadth of the paper is 8.5 inches
the length of the paper is 11 inches
Now, to make an enlarged copy, you used a paper that has its smaller side dimension of 10 inches.
Which means the breadth of the new paper is 10 inches.
So, if we calculate the ratio of the breadths we get the scale factor.
k = 10 / 8.5
k = 20/17 is the scale factor of dilation.
Learn more about scale factor:
https://brainly.com/question/20341092
At GameStop, there is a 30% off discount sale for a PS 5 originally priced at $600. After the sale, the discounted price of the PS5 was increased by 30%. What is the final price of the PS5 after the increase?
Answer:600-30 precent is $420 so is you increase it by 30 precent it would be
420 + (30% × 420) =
420 + 30% × 420 =
(1 + 30%) × 420 =
(100% + 30%) × 420 =
130% × 420 =
130 ÷ 100 × 420 =
130 × 420 ÷ 100 =
54,600 ÷ 100 =
546
Step-by-step explanation:
so 546 if wrong i am sorry
A similar image that is 10 times bigger write the rule
Answer:
× times 10
Step-by-step explanation:
that image times 10
3.
Use the quadratic function to predict f(x) if x equals 8.
f(x) = 25x^2 − 28x + 585
A. f(8) = 2201
B. f(8) = 2679
C. f(8) = 1614
D. f(8) = 1961
Answer:
D. f(8) = 1961
Step-by-step explanation:
i know the answer it is i think
To predict f(x) when x equals 8 we simply substitute.
So f(x) = 25x2 28x + 585
f(8) = 25 (8)^2 - 28 (8) + 585
f(8) = 25 * 64 - 224 + 585
f(8) = 1600 - 224 + 585 = 1961
Hencse f(8) = 1961
Hloo friend^_^..___
Q= f(x) = 25x2 − 28x + 585
Solution
________
f(8) = 25*(8)^2 - 28*8 + 585
= 25*64 - 224 + 585
= 1600 - 224 + 585
= 2185-224
= 1961 Ans...
So the correct ans is f(8) = 1961...
I HOPE ITS HELP U MY FRIEND..^_^
BE BRAINLY..
The length, breadth and height of a cuboid are in the ratio 6:3:5. If the total surface area is 504cm2, calculate area of 4 walls
please answer quick (i will mark as brainliest)
thank u
Step-by-step explanation:
metallic when has is equipment death of amiloride open interval a b payment to see payment payment details
Let x = √(4-√7) and y = √(4+√7), then value of (x-y/√3)² + (x²y+xy²)²+(x+y)² is -
Answer:
Refer to the attachment
A train travels 160 miles at a constant speed for 80 minutes. What is the speed of the train in mi/min
Answer:
2mi/min
Step-by-step explanation:
Speed=Distance/Time
=160mi/80min
=2mi/min
find the slope and y interceptof y=10x -1/3
with steps ( quick )
Answer:
slope = 10 , y- intercept = - [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 10x - [tex]\frac{1}{3}[/tex] ← is in slope- intercept form
with slope m = 10 and y- intercept c = - [tex]\frac{1}{3}[/tex]
The cost of a pen is 3 times the cost of a pencil. The total cost of 8 pencils and 5 pens is $11.50.
Please help me to find the costs of a pen and a pencil.
Answer:
$5.78
Step-by-step explanation:
brainliest?
3x + 9 - 2x + 1 + 5x + 11
Review the graph. On a coordinate plane, a parabola opens up and goes through (negative 2, 5), has vertex (0, 1), and goes through (2, 5). Another parabola opens to the right and goes through (8, 4), has vertex (negative 8, 0), and goes through (8, negative 4). Everything inside of the first parabola and above the second parabola within the first parabola is shaded. Which system of inequalities has the solution set shown in the graph?
Answer:
The value of h is h = -1.5
Step-by-step explanation:
The quadratic equation is represented by a parabola, the vertex form of the equation is y = a(x - h)² + k, where
(h , k) are the coordinates of its vertex point
a is the coefficient of x²
∵ The graph is a parabola opens up
∵ It has a vertex at (-1.5, 0)
∵ The vertex of the parabola is (h , k)
∴ h = -1.5 and k = 0
∵ The graph shows f(x) = (x - h)²
∵ The coordinates of the vertex are (h , k)
∵ h = -1.5 and k = 0
∴ h = -1.5
The value of h is h = -1.5
The value of h is h = -1.5
We have given that,
On a coordinate plane, a parabola opens up and goes through (negative 2, 5), has vertex (0, 1), and goes through (2, 5). Another parabola opens to the right and goes through (8, 4), has vertex (negative 8, 0), and goes through (8, negative 4).
The quadratic equation is represented by a parabola,
What is the vertex form of the parabola?The vertex form of the equation is y = a(x - h)² + k, where
(h, k) are the coordinates of its vertex point
a is the coefficient of x²
∵ The graph is a parabola that opens up
∵ It has a vertex at (-1.5, 0)
∵ The vertex of the parabola is (h , k)
∴ h = -1.5 and k = 0
∵ The graph shows f(x) = (x - h)²
∵ The coordinates of the vertex are (h, k)
∵ h = -1.5 and k = 0
∴ h = -1.5
The value of h is h = -1.5.
To learn more about the vertex form of parabola visit:
https://brainly.com/question/17987697
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Enter a digit in each box to complete the addition problem
Answer:
4.5 + 19.75 = 24.25
Find your missing digits with the equation above
Carl ordered $28 of pizza for dinner. About how much money
does he need, rounded to the nearest ten?
Answer:
30 dollars.
Step-by-step explanation:
What is 28 closer to? 20 or 30?
30.He would have to pay 30$, and would get 2 dollars back in change.
I hope this helped at all.
PLEASE hELP
Find the domain of the function shown in the graph below?
Answer:
All real numbers with vertical asymptotes at -2 and 6
Step-by-step explanation:
The domain of the function is all the possible x values of the function, so the solution is all real numbers with vertical asymptotes at -2 and 6 because the values never cross here.
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Please help mehhhhhh T^T
Answer:
Step-by-step explanation:
We can see the graph has an y intercept of 1 and from there the slope goes up one and to the right one so the slope is 1
f(x) = 2x2 + 6x + 1
=
Find f ( 6)
Answer:
so substitute x with 6
y = 4 + 36 + 1
so y or f(x) would = 41
Answer:
f(6) = 109
Step-by-step explanation:
Given polynomial:
f(x) = 2x2 + 6x + 1To Find:
f(6)Solution:
Here,in order to find f(6), substitute x = 6 onto the polynomial given:
f(x) = 2x^2 + 6x + 1f(6) = 2(6)^2 + 6(6) +1Now Simplify using PEMDAS rule.
f(6) = 2(36)+36+1f(6) = 72+36+1f(6) = 108+1f(6) = 109Hence, f(6) will be 109.