The partial fraction decomposition of the given expression can be written as
[tex]\frac{(x-30)}{x2+x-30} = \frac{A}{(x-5)} +\frac{B}{(x+6)}[/tex]
What is the partial fraction and quadratic equation?
The expression which is in the form of a rational equation can be converted to multiple fractions by performing factors of the denominator equation. And later split the fraction expression into two or more simpler fractions which form a partial fraction.
A quadratic expression is a second degree polynomial equation whose coefficients are real numbers. It comes from the word “quad” which means “square”. And that is why the degree of a quadratic equation is two.
According to the question, the factors of the denominator expression which is quadratic in nature:
[tex](x^{2} +x-30)=(x-5)(x+6)[/tex]
Now, the factors of the given expression are possible. The the partial fraction can be written as:
[tex]\frac{(x-30)}{x2+x-30} = \frac{A}{(x-5)} +\frac{B}{(x+6)}[/tex]
The factors of the second equation are not possible.
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Really need help on this problem
Solving the equation s = zr - 6zc^4 for z would give you: [tex]z = \frac{s}{r - 6c^4}[/tex].
How to Solve an Equation?Given the equation, s = zr - 6zc^4, to solve the equation for z, follow the steps below:
We have to isolate the variable "z" to one side of the equation if we are to solve the equation for z.
s = zr - 6zc^4
Factor out variable z
s = z(r - 6c^4)
Divide both sides of the equation by (r - 6c^4)
s/(r - 6c^4) = z(r - 6c^4) / (r - 6c^4)
s/(r - 6c^4) = z
[tex]z = \frac{s}{r - 6c^4}[/tex]
Therefore, solving the equation s = zr - 6zc^4 for z would give you: [tex]z = \frac{s}{r - 6c^4}[/tex].
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Complete the sentence.
4ft= ____ in.
4ft = 48in or 4 feet is equivalent to 48 inches.
In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.
A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.
The sentence states an equality between units of length: feet and inches.
From there, we can say that we are asked how many inches are there in 4 feet
Converting feet to inches, we must use the conversion
1 foot = 12 inches
4ft = 4 (12 inches)
4ft = 48in
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David fills an aquarium to a depth of 3/8 meters in 3 3/5 minutes.
The unit rate in minutes per meter is 28.8 minutes per meter when David fills an aquarium to a depth of 3/8 meters in 3 3/5 minutes
The given Depth of the aquarium = 3/8 meters
Time taken to fill the aquarium = 3 3/5 minutes
To find the the unit rate in minutes per meter, we need to divide the time taken to fill the aquarium by the depth of the aquarium
So, Unit rate in minutes per meter = 3 3/5minutes ÷ 3/8 meters
= 18/5 ÷ 3/8
= 18/5 ×8/3
= 144/15
= 28.8 minutes per meter
Hence, the unit rate in minutes per meter is 28.8 minutes per meter when David fills an aquarium to a depth of 3/8 meters in 3 3/5 minutes
The correct question is David fills an aquarium to a depth of 3/8 meters in 3 3/5 minutes. What is the unit rate in minutes per meter?
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Which equation describes the line with slope -2/3 that crosses the y-axis at the point (0, 4) ?
Answer:
In slope-intercept form:
[tex]y = - \frac{2}{3} x + 4[/tex]
Edna has spent her whole life traveling. she has been to 4 different continents and to 11 countries on each continent. round to the leading digit to determine approximately how many countries edna has visited.
Edna has visited 44 countries.
For given question,
Edna has spent her whole life traveling. she has been to 4 different continents and to 11 countries on each continent.
Here each continent has 11 countries.
She visited 4 different continents.
So, the total number of countries she has visited would be given by an expression,
11 × 4
We solve above expression to determine how many countries Edna has visited.
11 × 4 = 44
Therefore, approximately 44 countries Edna has visited.
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Cheyenne is going to the store with $20.she wants buy as many bags of takis as she can. if takis are $1.50 per bag, what is the maximum number she can buy?
Cheyenne can buy a maximum of 13 bags of Takis.
We have,
To find the maximum number of bags of Takis Cheyenne can buy with $20, we need to divide the total amount of money she has by the cost per bag of Takis.
Cost per bag of Takis = $1.50
Total money Cheyenne has = $20
Maximum number of bags of Takis = Total money / Cost per bag
Maximum number of bags of Takis = $20 / $1.50
Maximum number of bags of Takis = 13.33
Since Cheyenne cannot buy a fraction of a bag, the maximum number of bags of Takis she can buy is 13.
Thus,
Cheyenne can buy a maximum of 13 bags of Takis.
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If m< EBC = 3y+10 and m< ABE = 2y-20, find m< EBF.
The value of angle m< EBF is determined as 56⁰.
What is the sum of angles in a straight line?
The sum of angles in a straight line is 180 degrees. The value of angle EBF can be determine using the concept of sum of angles in a straight line as shown below.
m< EBC + m< ABE = 180
3y + 10 + 2y - 20 = 180
5y - 10 = 180
5y = 180 + 10
5y = 190
y = 190/5
y = 38
The value of m< EBF is calculated as follows;
Assuming equal division, m< EBF = m< ABE
m< EBF = 2y - 20
m< EBF = 2(38) - 20
m< EBF = 56⁰
Thus, the value of angle m< EBF is determined as 56⁰.
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help please!!!!!!!!!!!!!!!!!!!!!
Answer:
1/8
Step-by-step explanation:
5/4 divided by 10/1 is the same as
5/4 times 1/10
5/4 * 1/10 = 5/40 = 1/8
Answer: 1/8
Step-by-step explanation:
[tex]\displaystyle\\\frac{\frac{5}{4} }{10} =\\\\\frac{5}{4}:10=\\\\\frac{5}{4} *\frac{1}{10}=\\\\ \frac{5*1}{4*10}=\\\\\frac{5}{4*5*2} =\\\\\frac{1}{4*2}=\\\\\frac{1}{8}[/tex]
TRUE OR FALSE? 0.75 is an irrational number
Answer:
FALSE
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
0.75 has a finite number of digits and can be expressed in a fraction of integers.
0.75=75/100
75/100=3/4
pay a $12 set up fee for club T-shirts plus $5 per shirt.
The math club had to
Formulate an equation. Let s represent the number of t-shirts and C the cost.
Answer:
Step-by-step explanation:
c=12+5t?
Mai-Lin measures her heart rate whenever she exercises and tries to make sure that she is staying in her target heart rate zone. The American Heart Association suggests a target heart rate of T=0.75(220-a), where T is a person's target heart rate and a is his or her age.
a. Prove that given a person's target heart rate, you can calculate his or her age using the formula a=220- T/0.75.
If the American Heart Association suggests a target heart rate of T=0.75(220-a), Proving that given a person's target heart rate, you can calculate his or her age using the formula a=220- /0.75. His/her age is 16 years.
Target heart ratea. Given:
T=0.75(220-a)
where
T =a person's target heart rate
a= his or her age
Prove:
Hence:
T=0.75(220-a)
T/0.75=220-a
T/0.75-220=a
-T/0.75+220=a
a=-T/0.75+220
a=220-T/0.75
b. How old is she:
a=220-T/0.75
where:
T=153
Substitution
a=220-153/0.75
a=220-204
a=16 years
Therefore proving that given a person's target heart rate, you can calculate his or her age using the formula a=220- /0.75. His/her age is 16 years.
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The complete question is:
Mai-Lin measures her heart rate whenever she exercises and tries to make sure that she is staying in her target heart rate zone. The American Heart Association suggests a target heart rate of T=0.75(220-a), where T is a person's target heart rate and a is his or her age.
a. Prove that given a person's target heart rate, you can calculate his or her age using the formula a=220- T/0.75.
b. If Mai-Lin’s target heart rate is 153, then how old is she? What property justifies your calculation?
Describe the meaning of a reflection. Select the two correct answers. A reflection can be done on a point, shape, or object. b A reflection is a perpendicular turn around a point. A reflection can change the measures of the angles of a figure. c A reflection flips a shape across a line. d A reflection changes the length of line segments.
Answer:
A reflection is a transformation representing a flip of a figure. Figures may be reflected in a point, a line, or a plane. When reflecting a figure in a line or in a point, the image is congruent to the preimage.A reflection maps every point of a figure to an image across a fixed line. The fixed line is called the line of reflection.
Step-by-step explanation:
Of the three types of general survivorship curves, which can be most likely expected to live closest to its maximum life expectancy?
In the given statement is :
Of the three types of general survivorship curves, which can be most likely expected to live closest to its maximum life expectancy?
In this case, In Type I Curve, organisms tend to live up to maximum life expectancy. They survive their adulthood and die when they become elderly. Humans come under this category.
Survivorship Curve:
The Survivorship Curve is used to represent the number of population that are expected to live to a certain age. There are three types of survival curves they are Type I, Type II, Type III. Each curve will show the life expectancy of a particular group of organisms.
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It took clare 100 minutes to walk the east side of garden at a constant speed. if the total distance of the east side is 2,500 feet, at what speed was she walking? feet per minute
Answer: 25 ft per min.
Step-by-step explanation:
Time= 100 min.
Distance= 2500 ft.
Speed= 2500/100 = 25 ft per min.
In the diagram, PQRS is a square. (a) Show that triangles PQU, QRV, RSW and SPT are congruent. (b) Show that TUVW is a square.
Answer:
(a)=∆PQU,∆QRV,∆RSW and ∆SPT are congruent.
Step-by-step explanation:
PQRS is square (given)
PQ=QR=RS=PS
When some software companies develop software, they do it with "planned obsolescence"
in mind. This means that they plan on the sale of the software to rise, hit a point of
maximum sales, then drop and eventually stop when they release a newer version of the
software. Suppose a graph of the curve showing the number of sales over time can be
modeled with a parabola and that the company plans on the "life span" of its product to be
6 months, with maximum sales reaching 1.5 million units. Write an equation that models
this situation.
The equation of the parabola that models the given situation is y = [tex]\frac{-1}{6}(x-3)^{2}[/tex] + 1.5.
Define parabola and its types.A parabola is a roughly U-shaped mirror-symmetrical plane curve. It corresponds to a number of seemingly unrelated mathematical descriptions that all define the same curves.
To represent a parabola algebraically in the coordinate plane, the standard equation of a parabola is used. The general equation of the parabola is given by y = [tex]a(x-h)^{2}[/tex]+ k or x = [tex]a(y-k)^2[/tex] +h, where (h,k) denotes the vertex. A regular parabola's standard equation is [tex]y^2[/tex] = 4ax.
Now, the equation of parabola for the given situation is calculated as:
y = [tex]a(x-3)^2[/tex]+ 1.5
Now, put the value of x = 0 and y = 0.
0 = [tex]a(0-3)^2[/tex]+ 1.5
0 = 9a + 1.5
-9a = 1.5
a = - 1.5/9
a = -1/6
Now, put the value of a in equation y = [tex]a(x-3)^2[/tex]+ 1.5 to obtain:
y = [tex]\frac{-1}{6}(x-3)^{2}[/tex] + 1.5.
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30 pointys!!!!!
Please tell me the answer, 30 points avaliable,
Answer:
10.97 mm
Step-by-step explanation:
Hello!
First, let's construct an altitude, as shown in the picture below. An altitude is a height from one point to another side, forming a 90° angle at that intersection.
The length of the altitude is the same as the missing length, they are both parallel.
The length from the altitude to the slant line would be 6, as found by subtracting 8 from 14.
If you look closely, we can see a right triangle, and 12.5 mm is the hypotenuse. We know the measure for another side, and we can solve for the altitude using the Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex], a and b are legs, and c is the hypotenuse.
In this case, 6 and the altitude are legs.
Solve for the Altitude[tex]a^2 + b^2 = c^2[/tex][tex]A^2 + 6^2 = 12.5^2[/tex][tex]A^2 + 36 = 156.25[/tex][tex]A^2 = 120.25[/tex][tex]A = \sqrt{120.25}[/tex][tex]A \approx 10.97[/tex]The altitude is around 10.97, so the missing length will also be 10.97 mm.
calculate the value of the expressions а) 12^9\2^15•3^7 б) ((5^8/7) ^7/4-(2^-2) ^-3/32) •(46) ^-1
Answer:
Step-by-step explanation:
0
in an election for class president,jason received 170 of the 250 votes . what percent of the vote did he receive
Answer: 68%
Step-by-step explanation:
170/250=
17/25=
0.68=
0.68 * 1=
0.68 * 100%=68%
Easy math question n
Answer: [tex]|x| \leq 5[/tex] (the last option)
Step-by-step explanation: When you plug in values from the given solution set, the number is positive because of the absolute value symbol. This causes the range of possible values to be from 0 to 5, which are all less than or equal to 5.
THIS IS EASY?? OH HELL NO-
C. C. A different class is made up of 40â% women and has 20 women in it. What is the total number of students in theâ class?
Total number of students in a class is 50.
A class has 40% of women.
Total Number of women in a class = 20 equation 1
Let total number of students in a class = x
According to the question a class has 40% of women. Mathematically we can write it as,
Total Number of women in a class = 40 % of x
Total Number of women in a class = ( (40x) / 100 ) equation 2
On equating equation 1 and equation 2, we get
20 = ( (40x) / 100 )
⇒ 40x = 2000
⇒ x = 50
Total number of students in a class is 50.
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There are green grapes and black grapes in the ratio 3:4 if there are 24 green grapes how many black grapes are there?
PLS HELP
4.8kg=_______mg
3.2kg=_______dg
mg=milligarm
dg=decigram
Answer: 4,800,000 mg
32,000 dg
Step-by-step explanation:
1 kg=1000 g
1 g=1000 mg
1 kg * 1000 g/1 kg * 1000 mg/1 g=
1*1000*1000=1,000,000 mg
1 kg=1,000,000 mg
4.8 kg=
4.8*1000000=4,800,000 mg
1 g=10 dg
3.2 kg =
3.2 kg * 1000 g/1 kg * 10 dg/1 g=
3.2*1000*10=
3.2*10,000=32,000 dg
find the distance of a speed of 15m/s for 5 minutes
15m/s * 1km/1000m*60s/1 min*60 min/1hr=
You do the calculation.
Here are the conversions used in the conversion.
1km = 1000 m, 60 seconds = 1 minute, 60 minutes = 1 hour.
When you set up the problem the 15 meters is in the numerator and 1 second is in the denominator. To convert the 15 meters to km the next conversion factor needs to have 1km in the numerator and 1000 meters in the denominator. Now the 15 m will be divided by 1000 m which cancels the meters and leaves km.
The seconds in 15 m/s is in the denominator so to convert seconds to hours multiply by 60 seconds placing it in the numerator over 1 minutes. Use the same idea to set up the conversion from minutes to hours.
Practice this conversion. It is a fundamental conversion that any middle school student should know how to do.
Please help math 100 points! Decimal Rounding
Answer:
a: 0.5 + 0.3 = 0.8
b: 2.7 + 28.2 = 30.9
c: 3.1 + 2.4 + 9.9 = 15.4
d: 15.2 + 1.4 + 0.8 = 17.4
e: 39.2 + 2.5 + 0.8 = 42.5
Step-by-step explanation:
I did the assignment and I got it right
Round 0.687 to the nearest hundredth
Answer:
0.69
Step-by-step explanation:
The 8 is in the hundredths place.
0.687 becomes 0.680, but since the leftmost digit dropped is a 7, the 8 goes up 1 to 9.
Answer: 0.69
Answer:
0.69
Step-by-step explanation:
logp(5) = x, logp(7) =y
Write logp([5p^2]/49) in terms of x and y
The expression is x+2-2y
It is given to us that logp5=x and logp7=y
Now we are required to find logp(5p^2)/49 in terms of x and y
we know that in logarithmic formulas
loga^b=b loga
logab = log a+log b
log a/b= log a- log b
Now using these formulas to find the solution,
logp 5p^2/49
= logp5+ logp p^2 -log 49
=logp5+2 logpp-2log7
we know that logpp=1,hence
= logp5+2 -2 logp7
=x+2-2y
Hence the expression is x+2-2y
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washer and a dryer cost $618 combined. the washer costs $82 less than the dryer. what is the cost of the dryer?
Answer:
$227 = washing machine cost
$391 = dryer cost
Step-by-step explanation:
$618 divided by 2 = 309
309 - 82 = 227 = cost of washing machine
618 - 227 = 391 = cost of dryer
You can double-check by,
391 + 227
= 618
$227 = washing machine cost
$391 = dryer cost
Write a subtraction sentence where the difference is positive use a positive and a negative interference
The subtraction sentence where the difference is positive which uses a positive and negative integer are written as 5 - (-3) =8.
Integers are all real , rational numbers except the decimals and fractions. There are 3 types of integers : positive negative and zero integers.
Integers include zero, a positive natural number, and a negative integer represented by a minus sign. The negative numbers are the inverse additions of the comparable positive numbers.
There are two cases;
Case 1;
when modulus of positive integer ≥ modulus of negative integer;
Example; 5 - (-3) = 5 + 3 = 8 (Here, |5| > |-3|)
Case 2;
when modulus of positive integer ≤ modulus of negative integer;
Example; 5 - (-10) = 5 + 10 = 15 (Here, |5| < |-10|)
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Which description matches the graph of the inequality y > x + 4?
The graph of the inequality y > x + 4 matches the description in Option(c)
a shaded region above a dashed boundary line.
How to graph Linear Inequalities?A linear inequality is similar to a linear equation, but instead of a =, it will have an inequality sign like >,<, or ≤,≥.Place "y" on the left and the remaining variables on the right in the equation.Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>).Shade above the line in the graph for a "greater than" (y> or y≥)or below the line in the graph for a "less than" (y< or y≤).Given function: y > x + 4
Let's plot the graph of the given function and then match it with the options to see which is the solution.
So we will Plot y = x + 4 (as a dashed line because y > )
the coordinates will be,
x = 0 , y = 4
x = -1 , y = 3
x = -2 , y = 2
x = 1 , y = 5
x = 2 , y = 6
The purple shaded region satisfies the inequality y > x + 4.
Hence the graph description is a shaded region above a dashed boundary line.
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The complete question is: "Which description matches the graph of the inequality y > x + 4?
a) a shaded region above a solid boundary line
b) a shaded region below a solid boundary line
c) a shaded region above a dashed boundary line
d) a shaded region below a dashed boundary line."