Using the least common factor, it is found that it will take 120 days until all four buses return to the terminal on the same day.
Considering their itineraries, the number of days it will take until all four buses return to the terminal on the same day is the lcm of 6, 8, 10 and 15.To find their least common factor, we factor each number by prime numbers, hence:
6 - 8 - 10 - 15|2
3 - 4 - 5 - 15|2
3 - 2 - 5 - 15|2
3 - 1 - 5 - 15|3
1 - 1 - 5 - 5|5
1 - 1 - 1 - 1
Hence, lcm(6, 8, 10, 15) = 2³ x 3 x 5 = 8 x 15 = 120.
It will take 120 days until all four buses return to the terminal on the same day.
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Equivalent ratios
6:3 X:12 18:x
A population numbers 18,000 organisms initially and grows by 16% each year.
Answer:
The answer is 20,880
Step-by-step explanation:
This won't be a very long explanation. What I did was add 18,000 plus 16% and I got 20,880.
Hope this helps!
Have a nice day/night/afternoon.
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Is the sum of 5x⁴ + x³ and 2x³ + x² a trinomial expression. If it is true, justify your answer.
Answer:
The sum is a trinomial. It has three terms of different powers in variable "x" and three non zero constants as coefficients.
Step-by-step explanation:
(5x⁴ + x³) + (2x³ + x²) = 5x⁴ + 3x³ + x²
The sum of 5x⁴ + x³ and 2x³ + x² is a trinomial expression that is 5x⁴ + 3x³ + x²
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The sum is a trinomial. It has three terms of different powers in variable "x" and three non zero constants as coefficients.
We are given the expression as;
5x⁴ + x³ and 2x³ + x²
We need to find of the sum of the expression as;
(5x⁴ + x³) + (2x³ + x²)
= 5x⁴ + 3x³ + x²
The sum of 5x⁴ + x³ and 2x³ + x² is 5x⁴ + 3x³ + x²
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Help help help help math
Answer:
10.
Step-by-step explanation:
X is often associated with the value of "independent variable"
y=20-2(5)
y=20-10
y=10
Michael is saving money to buy a bike. So far, he
has saved $25 which is four-fifths of the total cost
of the bike. How much does the bike cost?
Let X = total cost of game
(4/5) X = $25
Multiply both sides of equation by 5/3
(5/3)(3/5) X = (5/3) $25
X = $35
find the value of x.
Answer:
25
Step-by-step explanation:
x+7 = 32 (similar triangles)
x = 25
How many times do 5 go into 32
Answer:
6 times or 6.4
3/2 x 4/3 x 5/4… x 2006/2005
Answer:
1003
Step-by-step explanation:
The problem is a classic example of a telescoping series of products, a series in which each term is represented in a certain form such that the multiplication of most of the terms results in a massive cancelation of subsequent terms within the numerators and denominators of the series.
The simplest form of a telescoping product[tex]a_{k} \ = \ \displaystyle\frac{t_{k}}{t_{k+1}}[/tex], in which the products of n terms is
[tex]a_{1} \ \times \ a_{2} \ \times \ a_{3} \ \times \ \cdots \times \ a_{n-1} \ \times \ a_{n} \ = \ \displaystyle\frac{t_{1}}{t_{2}} \ \times \ \displaystyle\frac{t_{2}}{t_{3}} \ \times \ \displaystyle\frac{t_{3}}{t_{4}} \ \times \ \cdots \ \times \ \displaystyle\frac{t_{n-1}}{t_{n}} \ \times \ \displaystyle\frac{t_{n}}{t_{n+1}} \\ \\ \-\hspace{5.55cm} = \ \displaystyle\frac{t_{1}}{t_{n+1}}.[/tex].
In this particular case, [tex]t_{1} \ = \ 2[/tex] , [tex]t_{2} \ = \ 3[/tex], [tex]t_{3} \ = \ 4[/tex], ..... , in which each term follows a recursive formula of [tex]t_{n+1} \ = \ t_{n} \ + \ 1[/tex]. Therefore,
[tex]\displaystyle\frac{t_{2}}{t_{1}} \times \displaystyle\frac{t_{3}}{t_{2}} \times \displaystyle\frac{t_{4}}{t_{3}} \times \cdots \times \displaystyle\frac{t_{n}}{t_{n-1}} \times \displaystyle\frac{t_{n+1}}{t_{n}} \ = \ \displaystyle\frac{3}{2} \times \displaystyle\frac{4}{3} \times \displaystyle\frac{5}{4} \times \cdots \times \displaystyle\frac{2005}{2004} \times \displaystyle\frac{2006}{2005} \\ \\ \-\hspace{5.95cm} = \ \displaystyle\frac{2006}{2} \\ \\ \-\hspace{5.95cm} = 1003[/tex]
Divide using polynomial long division.
2. (x² + 7x +44) = (x +4)
Answer:
the answer is given in the photo below
I MARK BRAINLIEST AND 50 points!!! find the magnitude of the resultant. forces of 92.6 lb and 118 lb act on an object. the angle between the forces is 75.2°.
a) 208 lb
b) 130 lb
c ) 168 lb
d) 150 lb
Answer:
This a vector addition problem and you need to know the law of cosines and law of sines to solve this problem.
Two vector forces of 80lbs and 70 lbs act on an object at 40 degree angle between them.
The magnitude of the resultant force can be found by applying the law of cosines:
c2 = a2 + b2 - 2abcos140°
where a = 80, b = 70 and c is the resultant force vector you are asked to find
Once you find the magnitude of the resultant force, then you can find the angle it makes wrt the 70lb force using the law of sines:
sinα/a = sin140°/c
where α is the angle opposite side a, or the angle between the resultant and the 70lb vector that you are asked to find. so it would be 140lbs
Step-by-step explanation
Nadia is a stockbroker. She earns 12% of commission each week. Last week, she sold 4,500 worth of stocks. How much did she make last week in commission? If she averages that same amount each week, how much did she make in commission in 2011?
Answer:
540 last week
52X540.=$28,080 a year
Step-by-step explanation:
What is the perimeter of the rectangle?
Answer:
6x+20 cm
Step-by-step explanation:
-formula : perimeter of rectangle=2(L+W)
L=2x+10 W=x
2(2x+10+x)
=2(3x+10) *distribute 2 on 3x ,10*
=6x+20 cm
Question:
Goofy Unlimited Lighting sells a 12 pack of lightbulbs for $8.40. Daisy Luminous Lighting sells a pack of 19 lightbulbs for
$15.35. Which store has the better deal. (3 points - 1 point showing the correct proportional relationship, 1 point
showing the unit rate, 1 point for identifying the store name)
es 0)
balo
Answer:
Goofy unlimited lighting 12 pack of light bulbs
Step-by-step explanation:
12 = 8.40/12 = .70 cents
19 = 15.35 = .81 cents
Suppose log7(10) = a and log7( 5) = b. Use the change-of-base formula along with properties of
logarithms to rewrite each expression in terms of a and b.
Step-by-step explanation:
log 10/log7=a
log10=alog7
log10=log7^a
10=7^a
log 5/log7=b
log5=blog7
log5=log7^b
5=7^b
Prove the identity.
sin(x+y) / cosxcosy = tanx+tany
[tex]\dfrac{\sin(x+y)}{\cos x \cos y}\\\\\\=\dfrac{\sin x \cos y + \sin y \cos x}{\cos x \cos y}\\\\\\=\dfrac{\tfrac{\sin x \cos y}{\cos x \cos y} + \tfrac{\sin y \cos x}{\cos x \cos y}}{\tfrac{\cos x \cos y}{\cos x \cos y}}\\\\\\=\dfrac{\tan x + \tan y}1\\\\\\= \tan x + \tan y[/tex]
Evaluate the expression for m = 45.
m|
54
Submit
[tex]|m| -54\\\\\text{When}~ m=45,\\\\|45| -54 = 45 -54 = -9[/tex]
[tex]\huge\textbf{Hey there!}\\\\\\\\\\\\\\\huge\boxed{\mathbf{|m| - 54 = }}\\\huge\boxed{\rightarrow \mathbf{|45| - 54 = }}\\\huge\boxed{\mathbf{\rightarrow 45 - 54}}\\\\\huge\text{Start at 45 and go back 54 to the left.}\\\huge\text{You should be left on \boxed{\bf -9}}\\\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{-9}}}\checkmark\\\\\\\\\\\\\\\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}\\\\\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]
which is the slope of the line that contains the point (-2,7) and (2,3)
Answer:
the slope of the line is -2.
Step-by-step explanation:
PLS HELP GIVING (BRAINLY)
Which statement shows the correct value for the exponential expression 43?
A. 3 x 3 x 3 x 3 = 81
B. 4x3 = 12
C. 4x 4x4 x 4 = 256
D. 4 x 4 x 4 = 64
Answer:
i think D. 4x4x4 = 64 is answer
Step-by-step explanation:
4³ = 4×4×4 = 64
The slope of a line running through points (6, 2) and (5, 7) is: 5. -5. 1. -1.
Answer:
-5
Step-by-step explanation:
We use the slope formula to find the slope
m = ( y2-y1)/(x2-x1)
= ( 7-2)/(5-6)
= 5/-1
= -5
A spherical solid, centered at the origin, has radius 4 and mass density(x,y,z)=6-(x^2+y^2+z^2). Set up the triple integral and find its mass.
I've attached a photo of the question.
There's something very off about this question.
In spherical coordinates,
x² + y² + z² = ρ²
so that
f(x, y, z) = 6 - (x² + y² + z²)
transforms to
g(ρ, θ, φ) = 6 - ρ²
When transforming to spherical coordinates, we also introduce the Jacobian determinant, so that
dV = dx dy dz = ρ² sin(φ) dρ dθ dφ
Since we integrate over a sphere with radius 4, the domain of integration is the set
E = {(ρ, θ, φ) : 0 ≤ ρ ≤ 4 and 0 ≤ θ ≤ 2π and 0 ≤ φ ≤ π}
so that the integral is
[tex]\displaystyle \int_{\phi=0}^{\phi=\pi} \int_{\theta=0}^{\theta=2\pi} \int_{\rho=0}^{\rho=4} (6 - \rho^2) \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi[/tex]
Computing the integral is simple enough.
[tex]\displaystyle = \int_{\phi=0}^{\phi=\pi} \int_{\theta=0}^{\theta=2\pi} \int_{\rho=0}^{\rho=4} (6 \rho^2 - \rho^4) \sin(\phi) \, d\rho \, d\theta \, d\phi[/tex]
[tex]\displaystyle = 2\pi \int_{\phi=0}^{\phi=\pi} \int_{\rho=0}^{\rho=4} (6 \rho^2 - \rho^4) \sin(\phi) \, d\rho \, d\phi[/tex]
[tex]\displaystyle = 2\pi \left(\int_{\phi=0}^{\phi=\pi} \sin(\phi) \, d\phi\right) \left(\int_{\rho=0}^{\rho=4} (6 \rho^2 - \rho^4) \, d\rho\right)[/tex]
[tex]\displaystyle = 2\pi \cdot 2 \cdot \left(-\frac{384}5\right) = \boxed{-\frac{1536\pi}5}[/tex]
but the mass can't be negative...
Chances are good that this question was recycled without carefully changing all the parameters. Going through the same steps as above, the mass of a spherical body with radius R and mass density given by
[tex]\delta(x, y, z) = k - (x^2 + y^2 + z^2)[/tex]
for some positive number k is
[tex]\dfrac{4\pi r^3}{15} \left(5k - 3r^2\right)[/tex]
so in order for the mass to be positive, we must have
5k - 3r² ≥ 0 ⇒ k ≥ 3r²/5
In this case, k = 6 and r = 4, but 3•4²/5 = 9.6.
what The Potageriterum
Answer:
Thick soup."coarse, spicy potage"A potage is a category of thick soups, stews, or porridges, in some of which meat and vegetables are boiled together with water until they form into a thick mush.Hope this helps you !!How do I verify: tan(x)+cot(x)=(2)/sin(2x)?
I always get stuck after writing out (sin^2x+cos^2x)/sin(x)cos(x)
[tex]sin^2(\theta)+cos^2(\theta)=1\qquad \qquad sin(2\theta)=2sin(\theta)cos(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]tan(x)+cot(x)=\cfrac{2}{sin(2x)} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{doing the left-hand-side}}{\cfrac{sin(x)}{cos(x)}+\cfrac{cos(x)}{sin(x)}\implies \cfrac{sin^2(x)+cos^2(x)}{\underset{\textit{using this LCD}}{sin(x)cos(x)}}} \implies \cfrac{1}{sin(x)cos(x)}[/tex]
now, let's recall that anything times 1 is just itself, namely 5*1 =5, 1,000,000 * 1 = 1,000,000, "meow" * 1 = "meow" and so on, so we can write anything as time 1.
let's recall something else, that same/same = 1, so
[tex]\cfrac{cheese}{cheese}\implies \cfrac{spaghetti}{spaghetti}\implies \cfrac{horse}{horse}\implies \cfrac{butter}{butter}\implies \cfrac{25^7}{25^7}=1[/tex]
therefore
[tex]\cfrac{1}{sin(x)cos(x)}\cdot \cfrac{2}{2}\implies \cfrac{2}{2sin(x)cos(x)}\implies \cfrac{2}{sin(2x)}[/tex]
How do I add Mixed numbers? Please explain step by step to get brainliest!
The best way to do this is to convert the mixed numbers into improper fractions. Improper fractions are when the numerator is greater than the denominator. An example of an improper fraction would be 5/4. Since 4/4 is one whole that means 5/4 as a mixed number would be 1 1/4. I'll use the expression 3 1/4 + 5 2/9 as an example.
3 1/4 is 3 wholes and 1/4 left over. We know that 4/4 is 1 whole so to find 3 holes we multiply the 1 by 3. 4 x 3 =12 so there are 12/4 in 3 holes. We then add the leftover 1/4 to get 13/4 as our first number.
For the second number, we have 5 2/9. This one is a bit harder. We know that 9/9 is in one whole, but how do we find how many are in 5 wholes? We can use multiplication. 1x 5=5. 5 x 9 =45. That means we have 45/9 in 5 holes. Add the leftover 2/9 to have 47/9 as our 2nd number.
Now that we have these two improper fractions, what do we do with them? The two numbers we are working with are 13/4 and 47/9. We need to find the common denominator. The common denominator is when both fractions have the same bottom number. If two fractions have different denominators we cannot add them.
To make the denominators the same, let's find a common multiple. A common multiple is a number that is a product of all chosen numbers. This is kind of confusing but another way to think of a common multiple is a number that is divisible by all chosen numbers. Take the two denominators and multiply them. 9x4=36. 36 is a common multiple of both 9 and 4 because both of them can go into 36 without being a decimal or a fraction.
To convert the fractions we multiply again. Whatever you do to one side you must always do to the other. In 13/4 we multiplied 4x9 to get 36. So now we multiply the numerator 13x9 to get 117. That means we have 117/36. We multiplied 9x4 to also get 36. So our numerator for our second number is 47x4=188 or 188/36.
Now we have 117/36 and 188/36. We add them together like normal and get 305/36. In some cases you'd need to simplify it, but for the example equation I used this is already the fraction's lowest form. I hope this helped! Comment if you need another example or have any questions! :)
1/2x + 4 = 10
solve the following equation algebratically. Show the work to support the answer.
Answer:
(1/2)x + 4 - 4 = 10 - 4
2(1/2)x = 6 * 2
x = 12
How can you identify the number of solutions of linear equations?
Answer:
A system of two equations can be classified as follows: If the slopes are the same but the y-intercepts are different, the system has no solution. If the slopes are different, the system has one solution. If the slopes are the same and the y-intercepts are the same, the system has infinitely many solutions.
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What is the following simplified product? Assume x 0.
(sqrt6x^2+4sqrt8x^3)(sqrt9x-xsqrt5x^5)
Answer:
c
Step-by-step explanation:
Keep in mind, whatever is inside of the square root, stays inside of the square root, and whatever is outside, stays outside, they don't multiply together. With parenthesis, exponents multiply, if there's no parenthesis, the exponents don't multiply. In this case, the exponents add.
Multiply each one together:
sqrt(6x^2) x sqrt(9x) = sqrt(54x^3)
sqrt(6x^2) x -(x sqrt(5x^5)) = -x sqrt(30x^7)
4 sqrt(8x^3) x sqrt(9x) = 4 sqrt(72x^4)
4 sqrt(8x^3) x -(x sqrt(5x^5)) = -4x sqrt(40x^8)
Then simplify:
sqrt(54x^2) = 3x sqrt(6x)
x sqrt(30x^7) = -x^4 sqrt(30x)
4 sqrt(72x^4) = 24x^2 sqrt(2)
-4x sqrt(40x^8) = -8x^5 sqrt(10)
Need answer to the question in the picture above
Answer:
solution given :
Since opposite side and side of a congruent triangle are equal.
Now
the statement which is true is:
<HDG=~ <HFE
Put the following equation of a line into slope-intercept form, simplifying all fractions.
9
x
−
3
y
=
9x−3y=12
Answer: 3y = 9x -12
Step-by-step explanation:
Which of the following situations can be modeled by the expression 5 - (-3)?
Kylie is three years younger than Tyler, and Claire is five years older than Kylie. How many years separate Tyler and Claire?
Kylie is three years younger than Tyler, and Claire is five years older than Tyler. How many years separate Kylie and Claire?
None of the above.
Kylie is three years younger than Tyler, and Claire is five years younger than Tyler. How many years separate Kylie and Claire?
Answer:the first option
Step-by-step explanation:
A tree of unknown height casts a shadow that is 18 feet long. If a person that is 5 ft 7 in casts a shadow that is 4 ft long, then how tall is the tree in feet?
Round your answer to the nearest integer. Do not include feet in your answer.
Answer:
25.
Step-by-step explanation:
5 ft 7 in = 5.583 ft.
We have 2 similar triangles here.
If h is the height of the tree, then:
h / 5.583 = 18/4
h = 18*5.583/4
h = 25.12 ft
The height of the tree is approximately 25.12 feet.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
The ratio of the shadow lengths is equal to the ratio of the object heights.
In other words, if we let H be the height of the tree in feet and h be the height of the person in feet, we have:
H/h = 18/4
We can find h by converting the person's height to feet. Since 1 inch is equal to 1/12 foot, the person's height in feet is 5 + 7/12 = 5.58 feet.
Substituting this value into the equation above and solving for H, we get:
H = (18/4) x 5.58 feet
= 25.12 feet
Therefore, the tree is around 25.12 feet tall.
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