The simplification of the algebraic fraction equation given as 3a³ - 5b³ + (3/a) + b³ is; (3/a)(a⁴ + a) - 4b³
How to solve Algebraic Fractions?
We want to solve the algebraic fraction equation given as;
3a³ - 5b³ + (3/a) + b³
Rearranging the algebra to get;
(3a³ + (3/a)) + b³ - 5b³
Factorizing out 3/a and simplifying gives;
(3/a)(a⁴ + a) - 4b³
This is the final part for the simplification of the given algebraic fraction. Thus, we can conclude that the simplification of the algebraic fraction equation given as 3a³ - 5b³ + (3/a) + b³ is; (3/a)(a⁴ + a) - 4b³
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Help me with this math question :)
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
To prove two lines parallel, we need to check if the two angles involving the lines acts as some angle pair with defininte property.
In the given figure,
Angle 3 is congruent to Angle 19( by Alternate Exterior angle pair )
Hence, the two lines are parallel.
[tex] \qquad \large \sf {Conclusion} : [/tex]
Option C is correctThe relationship between voltage, E, current, I, and resistance, Z, is given by the equation E = IZ. If a circuit has a current I = 3 + 2i and a resistance Z = 2 – i, what is the voltage of the circuit?
4 – i
4 + i
8 + i
8 + 7i
The voltage of the circuit is 8 + i . Option C
How to determine the voltage
From the information given, we have that;
E = IZ
Where;
E is voltageI is currentZ is resistanceWe have that;
I = 3 + 2i
Z = 2 - i
Substitute into the formula
E = IZ
E = ( 3 + 2i) ( 2 - i)
Making the product of complex numbers we have:
E = ( 3 × 2 - i ) + ( 4i - 2i²)
E = ( 6 - 3i ) + ( 4i - 2 ( -1) )
E = ( 6 + 2) + ( 4 - 3 ) i
E = 8 + i
Thus, the voltage of the circuit is 8 + i . Option C
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Answer:
It's C
Step-by-step explanation:
A recipe calls for 3/4 cups of water, 2/3 cups of flour, and 1/6 cups of sugar. What is the ratio of water: flour: sugar? Express your answer reduced to the lowest terms
Answer:
9:8:2
Step-by-step explanation:
3/4 : 2/3 : 1/6 Multiply by 12.
9 : 8 : 2
. Find the perimeter of a regular pentagon with each side measuring 4.5 inches.
Answer: 22.5 inches
Step-by-step explanation:
the general formula for finding perimeter is [tex]p=s+s+s...[/tex]a pentagon contains 5 sides[tex]p=s+s+s+s+s[/tex]
note that this is a regular pentagon so it must contain 5 congruent sideseach side will be 4.5 inchesthe formula can be changed to [tex]5(s)[/tex] and solved:[tex]5(4.5 in)=p[/tex]
∴ 22.5 inches = perimeter of the pentagon
24 is what percent of 480?
Answer:
5%.
Step-by-step explanation:
That is
(24/480 * 100
Now 480 / 24 = 20 so we have
(1/20) * 100
= 100/20
= 5%.
Answer:
24 is 5% of 480
Step-by-step explanation:
24 / 480 = 0.05
Percent is "for each 100"
Then:
0.05 * 100 = 5%
1/2-1/6
Jzjzhhzhzhzhhz
Answer:
ummm the answer is very simple
The answer is 0/6
Step-by-step explanation:
[tex] \frac{1}{2 \times 3} - \frac{1}{6} [/tex]
[tex] \frac{1}{6} - \frac{1}{6} [/tex]
[tex]1 - 1 = \frac{0}{6} [/tex]
The next model of a sports car will cost 4.4% more than the current model. The current model costs $49,000. How much will the price increase in dollars? What will be the price of the next model?
Answer: $51156
Step-by-step explanation:
a = b x p%
how much will the price increase
a = 49,000 x 4.4%
= 49,000 x 0.044
= $2156
price of next model
49,000 + 2156 = $51156
Prove usin's Mathematical induction 2^n ≤(n+1)!, for n≥0
Answer:
Step-by-step explanation:
2^0 is less than or equal to 1!, because 1<= 1
if 2^n <= (n+1)!, we wish to show that 2^(n+1) <= (n+2)!, since
(n+2)! = (n+1)! * (n+2), and (n+1)!>= 2^n, then we want to prove that n+2<=2, which is always true for n>=0
Multiply each of the following(2x - 3y) and (x + 5y)
Answer:
[tex]2 {x}^{2} + 7xy - 15 {y}^{2} [/tex]
Step-by-step explanation:
We can use the rainbow expansion method to find the expression.
[tex](2x - 3y)(x + 5y) \\ = 2 {x}^{2} + 10xy - 3xy - 15 {y}^{2} \\ = 2 {x}^{2} + 7xy - 15 {y}^{2} [/tex]
Is TriangleMNL ≅ TriangleQNL? Why or why not?
Yes, they are congruent by either ASA or AAS.
Yes, they are both right triangles.
No, AngleM is not congruent to AngleNLQ.
No, there are no congruent sides.
Triangle MNL and triangle QNL are congruent to each other based on by either ASA or AAS.
What are congruent triangles?A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, equilateral, scalene and right angle triangle. Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent to each other.
From triangle MNL and triangle QNL, in triangle MNL:
∠M + ∠N + ∠L = 180° (sum of angles in a triangle)
90 + 58 + ∠L = 180
∠L = 32°
Hence Triangle MNL and triangle QNL are congruent to each other based on by either ASA or AAS.
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Fertiliser is applied at the rate of a grams per square metre. It
takes b kilograms to cover a field of area c square metres. Find a
formula for b in terms of a and c.
Step-by-step explanation:
1 kilogram (kg) = 1000 grams (g)
as "kilo" means 1000.
b = a × c / 1000
it is simple : we have "c" square meters. as we need to apply "a" grams per square meter, we need to multiply both numbers to know how many grams we need for that many square meters. hence a × c.
and to get kg, we need to divide this number of grams by 1000.
that's it.
What is 500$ invested at 8% for 6 and a half years?
Answer:
$824.56
Step-by-step explanation:
Use the compound interest formula which is A = P(1+r/n)^nt
1st using the given information we are going to find out values:
P is our initial amount of $500
r is the annual rate of interest (expressed as a decimal) 8% becomes 0.08.
n is how many times interest is compounded per year, in this case since its not stated we are going to assume its annually, so n is 1
t is how long the money is deposited (in years) so t is 6.5
A is our final amount
2nd plug in our values into the equation
Plugging all these values we get A = 500 (1 +0.08/1)^(0.08)(6.5)
A = $824.56
Complete the square -3x^2+12x-7
Answer:
[tex]-3(x-2)^2+5[/tex]
Step-by-step explanation:
First we can factor a -3 from the [tex]x^2[/tex] term and the [tex]x[/tex] term to get [tex]-3(x^2-4x)-7[/tex].
Then we want the stuff in the parentheses to have the form of [tex](x+b)^2[/tex], or equivalently, [tex](x^2+2b+b^2)[/tex] . So we can let [tex]2b = -4[/tex]. By solving it, we get [tex]b = -4/2 = -2[/tex]. Then our [tex]b^2[/tex] term should be [tex]b^2 = (-2)^2 = 4[/tex].
In order to make our [tex]b^2[/tex] term appear in the parentheses, we need to add and subtract our [tex]b^2[/tex] term, so we get [tex]-3(x^2 - 4x + 4 - 4) -7[/tex].
What we to keep inside our parentheses is [tex](x^2 - 4x + 4)[/tex] , so we can factor the [tex]-4[/tex] out of parentheses to get [tex]-3(x^2-4x+4-4)-7 = -3(x^2-4x+4)+(-3)(-4) - 7 = -3(x^2 - 4x + 4) + 12 - 7 = -3(x^2 - 4x + 4) + 5[/tex]
Finally, plugging [tex]b = -2[/tex] that we computed earlier into the equation [tex](x^2+2b+b^2) = (x+b)^2[/tex], we get [tex](x^2 - 4x + 4) = (x-2)^2[/tex].
So we have [tex]-3(x^2-4x+4)+5 = -3(x-2)^2+5[/tex].
In summary, the procedure is
[tex]-3x^2+12x-7 \\= &-3(x^2-4x) -7 \\= &-3(x^2-4x+4-4)-7 \\= -3(x^2-4x+4) + (-3)(-4)-7\\=-3(x^2-4x+4)+12-7\\= -3(x^2-4x+4)+5 \\= -3(x-2)^2+5[/tex]
Ivanna knit a scarf for each of her 9 friends. Altogether, the scarves had a total length of 41.4 ft. If each scarf was the same length, how long was each scarf? Write your answer in inches. Use the table of conversion facts as necessary, and do not round your answer. Conversion facts for length 12 inches (in) = 1 foot (ft) 3 feet (ft) = 1 yard (yd) 36 inches (in) = 1 yard (yd) 5280 feet (ft) = 1 mile (mi) 1760 yards (yd) = 1 mile (mi)
Answer: 55.2 in
Step-by-step explanation:
1ft = 12 in
41.4/9 = 4.6 ft
4.6 x 12 = 55.2 in
1-cos(6x)=___?
A. 3sin(2x)
B. 2sin^2(3x)
C. 3cos(2x)
D. 2cos^2(3x)
The solution to 1 - cos(6x) is 2sin²(x).
Hence, option B) 2sin²(x) is the correct answer.
What is solution to 1 - cos(6x)?Given that; 1 - cos(6x) = ?
First, we rewrite using trig identity
1 - cos(2 × 3x)
Using the double angle identity, { cos2(x) = 1 - 2sin²(x) }
1 - ( 1 - 2sin²(x) )
Eliminate the parentheses
1 - 1 + 2sin²(x)
2sin²(x)
The solution to 1 - cos(6x) is 2sin²(x).
Hence, option B) 2sin²(x) is the correct answer.
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A ball is launched into the sky at 54. 4 ft./s from a 268.8 m tall building. The equation for the ball’s height, h, at time t second’s is h= -3.2t^2 + 54.4t+ 268.8. When will the ball strike the ground?
Answer:
t = 21
Step-by-step explanation:
The ball strikes the groujd when h = 0.
[tex]-3.2t^2 + 54.4t+268.8=0 \\ \\ 32t^2 - 544t-2688=0 \\ \\ t^2 - 17t-84=0 \\ \\ (t-21)(t+4)=0 \\ \\ t=-4, 21[/tex]
Since time must be positive, t = 21.
I ordered a shoe a few days ago and the seller provided me with the tracking number for the hoodie but through Grailed but USPS has been stuck on "We are preparing your order for shipment" and "Delivery information will be available once the carrier has the updates." What does this mean? Also when I put my tracking number in USPS's Package Tracker, the number doesn't exist in its system. Does anyone know whats going on? Thanks!
Which of the fallowing expressions represents the distance between -4 and 1
The answer is |-4 - 1|.
If you solve this absolute value, the answer would be 5 and if you look at the number line, the distance between the two dots is 5 units.
|-4 - 1| --> |-5| --> 5
in an absolute value, there are no negative numbers so the -5 becomes 5.
What is the direction and magnitude of the following correlation coefficients
a. -0.81
b. 0.40
c. 0.15
d. -0.08
e. 0.29
-0.81 has negative direction and o.81 is the magnitude, 0.40 has positive direction and 0.40 is the magnitude, 0.15 positive direction and 0.15 is the magnitude, -0.08 has negative direction and 0.08 is the magnitude and 0.29 has positive direction and 0.29 is the magnitude
What is Vector?A quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another.
-0.81
Minus zero point eight one has negative direction and o.81 is the magnitude
0.40
zero point four zero has positive direction and 0.40 is the magnitude
0.15
Zero point one five has positive direction and 0.15 is the magnitude
-0.08
Minus zero point zero eight has negative direction and 0.08 is the magnitude
0.29
Zero point two nine has positive direction and 0.29 is the magnitude
Hence -0.81 has negative negative direction and o.81 is the magnitude, 0.40 has positive direction and 0.40 is the magnitude, 0.15 positive direction and 0.15 is the magnitude, -0.08 has negative direction and 0.08 is the magnitude and 0.29 has positive direction and 0.29 is the magnitude
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√3018+√36+√169 can you solve this for me please
Answer:
55
Step-by-step explanation:
[tex]\sqrt{3018+\sqrt{36+\sqrt{169} } }[/tex]
= [tex]\sqrt{3018+\sqrt{36+13} }[/tex]
= [tex]\sqrt{3018+\sqrt{49} }[/tex]
= [tex]\sqrt{3018+7}[/tex]
= [tex]\sqrt{3025}[/tex]
= 55
Two copies of the same Rational Function are shown below.
On the graph below draw the Horizontal Asymptote and write the equation for the horizontal asymptote underneath.
The equation for the horizontal asymptote will be y = -2.
How to illustrate the information?Since the degree of the numerator and denominator of f(x) is the same both being 1, therefore horizontal asymptote exists and is given by:
y = Leading coefficient of numerator of f(x) / Leading coefficient of denominator of f(x)
= y = -2/1
= y = -2
The vertical asymptote will be f(x) = -2x / (x + 3). To find the vertical asymptote we will equate the denominator of f(x) = 0
= x + 3 = 0
= x = -3
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y = -2(x + 5)(x + 1)
Set the factor (x + 5) = 0 and solve
Answer: [tex]x=-5[/tex]
Step-by-step explanation:
[tex]x+5=0 \implies x=-5[/tex]
please help jajajajaja
Evaluate the expression if a=2,b=-3,C=-1, and D=4
-2(b^2-5c)
Answer:
Your answer is - 28
Step-by-step explanation:
Given,
a = 2
b = - 3
c = - 1
d = 4
Now,
- 2 ( b² - 5 c )
= - 2 ( -3² - 5 ( - 1 ) )
= - 2 ( 9 + 5 )
= - 2 × 14
= - 28 ans….
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Calculating orthogonal trajectories?
The equation for the trajectories orthogonal to the family of functions of the form 5 · x² - 2 · y² = C is equal to (1 / 5) · ㏑ x + (1 / 2) · ㏑ y = C.
How to find the equation for the orthogonal trajectories of a given equation
In this problem we have a family of functions in implicit form, that is, a function of the form f(x, y, c) = 0. The equation of a orthogonal trajectory is always perpendicular to a particular form of a equation. First, we determine the first derivative of the given expression:
5 · x² - 2 · y² = C
10 · x - 4 · y · y' = 0
4 · y · y' = 10 · x
y' = (10 · x) / (4 · y)
y' = (5 · x) / (2 · y)
If f(x, y) = (5 · x) / (2 · y), then the differential equation for the orthogonal trajectories related to the family of functions is:
y' = - 1 / f(x, y)
y' = - (2 · y) / (5 · x)
dy / (2 · y) = - dx / (5 · x)
By indefinite integration we get the following solution to the ordinary differential equation:
(1 / 2) · ㏑ y = - (1 / 5) · ㏑ x + C
(1 / 5) · ㏑ x + (1 / 2) · ㏑ y = C
The equation for the trajectories orthogonal to the family of functions of the form 5 · x² - 2 · y² = C is equal to (1 / 5) · ㏑ x + (1 / 2) · ㏑ y = C.
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7
O x-3
O x-1
O x + 1
O x + 3
3
2-
What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?
3
N
3
I NEED HELP !!!!!
Answer:
x-1 gave ggs is it correct
Joey owns a small bakery and today Phoebe has ordered 100 cookies. If Joey boxes the cookies by the dozen, which of the following equations describes how many boxes of cookies Phoebe will have? Let b represent the number of boxes. (HINT: All of the cookie boxes are not necessarily full.)
Answer:
Joey needs 9 boxes.
Step-by-step explanation:
You will use the fact that a dozen is 12 cookies. You're trying to find how many dozen are in 100.
Something like:
12b = 100
or if you're studying inequalities:
12b >= 100
Divide by 12 to solve. See image. Interpret the results. See image.
Jasmine got a new puppy for her birthday. He's full of energy, so she takes him for a walk along a 1.2-mile loop in a nearby park. If they walked a total of 3.6 miles, how many loops did they do?
Answer: 3 loops
Step-by-step explanation: The loop is 1.2 miles, and the total walk is 3.6 miles. You want to find out how many laps are in the 3.6 miles. This can be found using division. 3.6/1.2= the number of 1.2 mile laps inside the 3.6 mile walk, which is 3 laps. hope this helped!
Can segments with lengths of 6, 7, and 9 form a triangle? Why or why not
Answer:
Yes
Step-by-step explanation:
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side or largest side. So, 7+6 = 13 which is greater than 9
Answer:
Yes, triangle with sides 6, 7 ,9 can be formed.
Step-by-step explanation:
The sum of any two sides of the triangle should be greater than the third side. If so, triangle can be formed.
6 + 7 = 13 > 9
7+ 9 = 16 > 6
6 +9 = 15 > 7
Add the following polynomials, then place the answer in the proper location on the grid. Write your answer in descending powers of x.
x 4 -3x + 1, 4x 2 - 2x + 8, and x 3 - 9
The addition of the polynomials x⁴ - 3x + 1, 4x² - 2x + 8, x³ - 9 in descending powers of x is x⁴ + x³ + 4x² - 5x.
Polynomialx⁴ - 3x + 14x² - 2x + 8x³ - 9Adding the polynomial
(x⁴ - 3x + 1) + (4x² - 2x + 8) + (x³ - 9)
Open parenthesis= x⁴ - 3x + 1 + 4x² - 2x + 8 + x³ - 9
Collect like terms in descending powers= x⁴ + x³ + 4x² - 3x - 2x + 1 + 8 - 9
= x⁴ + x³ + 4x² - 5x
Therefore, the addition of the polynomials x⁴ - 3x + 1, 4x² - 2x + 8, x³ - 9 in descending powers of x is x⁴ + x³ + 4x² - 5x.
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