Your equation is unclear. Do you mean the following:
(15x+21)/3=5x+7 or 3(15x+21)=5x+7
If the left equation is the correct one, the left side simplifies to 5x+7=5x+7, which must mean all real numbers are correct solutions. Thus, it has infinite real solutions.
The equation (15x + 21)³ = 5x + 7 is a cubic equation. The number of solutions can be 0, 1, 2, or 3 solutions.
Explanation:The equation is (15x + 21)³ = 5x + 7. To determine the number of solutions, we need to simplify and solve the equation.
Step 1: Expand the equation using the binomial theorem. This gives us: 3375x³ + 14175x² + 19305x + 9261 = 5x + 7.
Step 2: Combine like terms on both sides of the equation. This results in: 3375x³ + 14175x² + 19305x + 9254 = 0.
Step 3: This is a cubic equation. Cubic equations can have 3 solutions at most. However, it is not guaranteed that this equation will have 3 solutions. It can have fewer solutions or even no real solutions.
Therefore, the number of solutions for this equation is either 0, 1, 2, or 3 solutions. Further analysis or calculations may be needed to determine the exact number of solutions.
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if a car is 200 inches long, and the truck is 75% longer, how long is the truck
In a class, 8/9 of the students have blue eyes.
If 32 students have blue eyes, how many students are in the class in total?
The coffee cups can hold 7/9 of a pint of liquid. If Emily puts 2/3 of s pint of coffee into a cup, how much milk can a customer add?
1/9 pints of milk can be added by a customer
Step-by-step explanation:
We have to subtract simple fractions to find the amount of milk that can be added to a cup of coffee
Given
Total Capacity of a cup = 7/9 pints
Coffee to be added in a cup = 2/3 pints
So in order to find the amount of milk that can be added we have to subtract the amount of coffee from the total capacity of cup.
So,
[tex]Amount\ of\ milk = \frac{7}{9} - \frac{2}{3}\\=\frac{7-6}{9} = \frac{1}{9}[/tex]
Hence,
1/9 pints of milk can be added by a customer
Keywords: Fractions, addition
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Amount of milk add by customer is 1/9 pint of liquid
Given that;
Holding capacity of cup = 7/9 pint of liquid
Liquid fill by Emily = 2/3 pint of liquid
Find:
Amount of milk add by customer
Computation:
Amount of milk add by customer = Holding capacity of cup - Liquid fill by Emily
[tex]Amount\ of\ milk\ add\ by\ customer = \frac{7}{9} - \frac{2}{3}\\\\Amount\ of\ milk\ add\ by\ customer = \frac{7-6}{9}\\\\Amount\ of\ milk\ add\ by\ customer = \frac{1}{9}\\\\[/tex]
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Answer this question please. I need help!!☺️
Step-by-step explanation:
From the looks of it, it seems that you're factoring out the greatest common factor. I gotcha covered.
The square boxes are the biggest common factors in those equations. Hopefully, this helps!
Oh the other side of the balance is 4 oz and another 4 oz and on the other side is 8 oz. <— To help you find out the answer. Please I’d like some help?
A school plans the weekly reading activities. They have 18 storys books, which is 4 books more than 2 times that of science books. What is the number of science books?
Answer:
[tex]Number\ of\ science\ books=7[/tex]
Step-by-step explanation:
[tex]Let\ number\ of\ science\ books=x\\\\Story\ books=18\\\\2\times science\ books+4=Story\ books\\\\2x+4=18\\\\Subtract\ 4\ from\ both\ the\ sides\\\\2x+4-4=18-4\\\\2x=14\\\\Divide\ both\ sides\ by\ 2\\\\\frac{2x}{2}=\frac{14}{2}\\\\x=7\\\\Number\ of\ science\ books=7[/tex]
A cylindrical swimming pool has a diameter of 20 feet and a height of 3.5 feet. How many gallons of water can the pool contain? Round your answer to the nearest whole number. (1 ft3 ≈ 7.5 gal)
Answer:
The swimming pool will contain approx [tex]8243\ gal[/tex] of water.
Step-by-step explanation:
Given the swimming pool is in a cylindrical shape.
And the dimensions are [tex]20\ feet[/tex] diameter with a height of [tex]3.5\ feet.[/tex]
Also, [tex]1\ ft^3 =7.5\ gal[/tex]
First, we will find the volume of the swimming pool.
The swimming pool is in cylindrical shape.
So, the volume would be [tex]\pi r^2h[/tex]
The height [tex](h)[/tex] is given as [tex]3.5\ feet.[/tex] To calculate radius [tex](r)[/tex] we will divide the diameter by two.
The radius of the cylinder would be [tex]\frac{20}{2}=10\ feet[/tex]
Plug these values in the formula we get,
[tex]\pi r^2h\\=\pi\times 10^2\times 3.5\\=3.14\times 100\times 3.5\\=1099\ ft^3[/tex]
Now, it is given [tex]1\ ft^3 =7.5\ gal[/tex]
So, [tex]1099\ ft^3 =1099\times 7.5\ gal=8242.5\ gal[/tex]
The swimming pool will contain approx [tex]8243\ gal[/tex] of water.
To find the volume of the cylindrical pool, calculate the radius, then use the formula for the volume of a cylinder, finally convert the volume to gallons. The cylindrical swimming pool can contain approximately 8267 gallons of water.
Calculate the radius: radius = diameter / 2 = 20 ft / 2 = 10 ftCalculate the volume: volume = π * radius^2 * height = π * 10^2 * 3.5 = 350π ft^3Convert to gallons: 350π ft^3 * 7.5 gal/ft^3 ≈ 8267 gallons (rounded to the nearest whole number)
What two numbers multiplies to 16 and adds to -17?
michael breeds chicken and ducks
last month he sold 50 chickens and 30 ducks for $550. this month he sold 44 chicken's and 36 ducks for $532.
how much Does a chicken cost and how much does a duck cost?
Answer:
cost of a chicken $7.25
cost of a duck $4.25
Step-by-step explanation:
Let c represent chickens and d represent ducks
50 chicken + 3 ducks = $550 ➡ 50c + 30d = $550
44 chicken + 36 ducks = $532 ➡ 44c + 36d = $532
Now find the difference of equations
(50c + 30d) - (44c + 36d) = $550 - $532
6c - 6d = $18
6×(c-d) = $18 divide both sides by 6
c - d = $3 Now we can use this information to find the cost of a chicken and duck
50c + 30d = $550
c - d = $3 multiply second equation by 30
30 × (c-d) = $3 ➡30c - 30d = $30
Now add this new equation we found to the very first equation
30c - 30d + 50c + 30d = $550 + $30 (-30d will eliminate 30d)
80c = $580 divide both sides of the equation by 80
c = $7.25
We know that c - d = 3 so now replace c by $7.25 the price we just found
$7.25 - d = $3
$7.25 - $3 = d
$4.25 = d
Find the y-intercept of the line: 9x – 8y + 5 = 0
Answer:
-8y = -9x - 5
y = (9/8)x + 5/8
Step-by-step explanation:
y-int 5/8
The y-intercept of the given line equation 9x – 8y + 5 = 0, is 5/8, which is obtained by rearranging the equation into the slope-intercept form.
Explanation:The subject pertains to finding the y-intercept of a line from a given equation, which is a topic in Algebra.
The equation given is 9x – 8y + 5 = 0. First, we need to rearrange the equation into the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Arranging the equation, we get: -8y = -9x -5, which simplifies further to y = 9/8x + 5/8. So, the y-intercept of the line is 5/8.
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test patti green and her husband are purchasing a condominium for $123000. They have $15000 for a down payment. what is the amount of their mortgage loan?
Answer:
there amount would be 108,000
Step-by-step explanation:
um...
123,000 - 15,000
= 108,000
give me brainly :)
Albert $1000 earned 1.2% annual interest compounded monthly
$500 lost 2% over the course of the 10 years
$500 grew compounded continuously at rate of 0.8% annually
What is the balance of Albert’s $2000 after 10 years?
Answer:
$2159.07
Step-by-step explanation:
The compound interest formula is used to find the balance for the $1000 investment:
A = P(1 +r/n)^(nt)
A = 1000(1 +.012/12)^(12·10) = 1000·1.001^120 ≈ 1127.43
__
For a 2% loss, the multiplier of the investment value is 1-.02 = 0.98. The value of the first $500 investment is ...
A = 500(1 -.02) = 490.00
__
The continuous compounding formula is used for the second $500 investment.
A = Pe^(rt)
A = 500e^(.008·10) = 500e^.08 = 541.64
__
The total value of Albert's investments is ...
$1127.43 +490 +541.64 = $2159.07
The measure of CDA is 113.42°. what is the value of x?
a line passed through the point (8,9) and has a slope of -3/4. write an equation in slope intercept form.
Answer:
y = -3/4x + 3
Step-by-step explanation:
y - 9 = -3/4 (x-8)
y-9 = -3/4x -6
y = -3/4x - 6 + 9
y = -3/4x + 3
The equation of the line that passed through the point (8,9) and has a slope of -3/4 in slope-intercept form is [tex]y= -\frac{3}{4}x + 13[/tex]
The point-slope form of the equation of a line passing through the points (x₁, y₁) and with a slope m is given as:
y - y₁ = m(x - x₁)
For the line that passed through the point (8, 9) and has a slope of -3/4
x₁ = 8, y₁ = 9, and m = -3/4
Substitute these values into the equation y - y₁ = m(x - x₁)
[tex]y-9=\frac{-3}{4}(x - x_1)[/tex]
Express the equation above in the form y = mx + c
[tex]y-9=-\frac{3}{4}(x - 8)\\\\y-9= -\frac{3}{4}x + 6\\\\y= -\frac{3}{4}x + 6+9\\\\y= -\frac{3}{4}x + 13[/tex]
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my math problem dealing with fractions ask What is 1/8 of 9?
Answer:
a
Step-by-step explanation:
Answer:
1 1/8
Step-by-step explanation:
1/8 of 9
Of means multiplication
1/8 x 9
= 9/8
= 1 1/8
--x² + 5x – 8=0
What is the x
Answer:
x =(-5-√57)/2=-6.275
Step-by-step explanation:
Suppose you are choosing between two checking accounts. One account charges you $1.50 ATM
fee every time you withdraw money from a non-sponsored ATM, and the other charges you no
ATM fees and a $15 monthly fee.
How many ATM transactions are equivalent to $15 in monthly fees?
Answer:
10
Step-by-step explanation:
$15.00 / $1.50 = 10
Factorize completely
81k^2 - m^2
81k^2 - m^2 factors to
(9k + m)(9k - m)
Prove this by FOILing.
First - 81k^2
Outer - (-9km)
Inner - 9km
Last - (-m^2)
Put it into equation form
81k^2 - 9km + 9km - m^2
And combine terms to get the original equation,
81k^2 - m^2.
⭐ Answered by Hyperrspace (Ace) ⭐
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(9k+m) X (9k - m)
Step-by-step explanation:
81[tex]k^{2}[/tex] - [tex]m^{2}[/tex]
= (9k)^2 - (m)^2 ( taking the square roots)
=(9k+m) (9k - m)
here we have applied the rules of a^2 - b^2 = ( a+b) ( a -b)
here 9k is taking as a and m is taking as b
thus you get your answer.
hope it helps.
2/3xd=10/9 what is d
Answer:d=5/3x
Step-by-step explanation:
Let's solve for d.
(2/3x)(d)=10/9
Step 1: Divide both sides by (2x)/3.
2/3dx / 2x/3=10/9 / 2x/3
d=5/3x
To find the value of d in the equation 2/3 * d = 10/9, multiply both sides by the reciprocal of 2/3. The value of d is 5/3 or approximately 1.67.
Explanation:To solve the equation 2/3 * d = 10/9 for d, we can start by multiplying both sides of the equation by the reciprocal of 2/3, which is 3/2. This gives us:
d = (10/9) * (3/2) = 30/18 = 5/3
Therefore, d = 5/3 or d ≈ 1.67.
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X3-8y3+27+18xy factorise
Answer:
this expression is not factorable
Step-by-step explanation:
Write as an equation/inequality. x is less than or equal to 38.
Answer:
x[tex]\leq[/tex]38
Step-by-step explanation:
bring back the x and the 38 with a space between to decide on the symbol put back i the less than sign between both terms then put a line underneath to form the symbol less than or equal to.
Tickets to the garden show cost $6.75 for adults and $3.75 for children. By rounding to the nearest whole dollar, find an estimate of the cost for a family with 2 adults and 3 children to visit the garden show. A. $21 B. $23 C. $24 D. $26
Answer:
$26
Step-by-step explanation:
$6.75 - $7
$3.75 - $4
2 adults = 7x2= $14
3 children = 4x3= $12
$14 + $12 = $26
The answer is D. $26.
Write a word problem that can be solved by dividing 10 by 2/3 include the answer to the problem
Answer:
Step-by-step explanation:
you need to divide 10 by 2/3.
Katty has 10/1 tanks of gas fuel in his truck. He uses 2/3 of it each day.
-4x-2y=-12 4x+8y=-24
Answer:
[tex]x=6\\ \\y=-6[/tex]
Step-by-step explanation:
Given the system of two equations:
[tex]\left\{\begin{array}{l}-4x-2y=-12\\ \\4x+8y=-24\end{array}\right.[/tex]
Add these two equations (left side add to left side and right side add to right side):
[tex]-4x-2y+4x+8y=-12+(-24)\\ \\-2y+8y=-12-24\\ \\6y=-36\\ \\y=-6[/tex]
Substitute [tex]y=-6[/tex] into the first equation:
[tex]-4x-2\cdot (-6)=-12\\ \\-4x+12=-12\\ \\-4x=-12-12\\ \\-4x=-24\\ \\x=6[/tex]
If bob washed the car in 6 minutes and jack washed it in 8 minutes how long did it take them together
Answer:
14 minutes
Step-by-step explanation:
8 + 6 = 14
Two planes left simultaneously from the same airport and headed in the same direction towards another airport 3600 km away. The speed of one of the planes was 200 km/hour slower than the speed of the other plane, and so it arrived at its destination 1.5 hours after the faster plane. Find the speeds of both planes.
Answer: The speed of the faster lane is 800 km/hour and the slower plane is 600 km/hour
Step-by-step explanation:
The speed of the faster plane is 800 km/h and the speed of the slower plane is 600 km/h.
The given parameters:
Distance traveled by both planes, d = 3600 km
Let the speed of the faster plane = vThe speed of the slower plane, u = v - 200 km/hLet the time taken for the faster plane = t hoursTime taken for the slower plane to arrive = t + 1.5 hours
The distance traveled by both planes is the same;
d = u(t + 1.5) ---(1)
d = (v - 200) (t + 1.5)
3600 = vt + 1.5v - 200t - 300
d = vt ----(2)
3600 = vt
[tex]v = \frac{3600}{t}[/tex]
[tex]3600 = \frac{3600}{t} t \ +\ 1.5 (\frac{3600}{t} ) \ - \ 200 t - 300\\\\3600 = 3600 + \frac{5400}{t} - 200t - 300\\\\300 = \frac{5400}{t} - 200t\\\\300t = 5400 - 200t^2\\\\200t^2 +300t - 5400 = 0\\\\2t^2 + 3t- 54= 0\\\\(2t - 9)(t + 6)= 0\\\\t = 4.5 \ \ or \ \ -6 \ \\\\t = 4.5 \ hours[/tex]
The speed of the faster plane is calculated as;
[tex]v = \frac{3600}{t} \\\\v = \frac{3600}{4.5} \\\\v = 800 \ km/h[/tex]
The speed of the slower plane is calculated as follows;
[tex]u = v- 200\\\\u = 800 - 200\\\\u = 600 \ km/h[/tex]
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What is blank divided by 9 equals 5
Answer:
45 divided by 9 equals 5
Step-by-step explanation:
-5x = -2x - 3
What dose x equal
Answer:1
Step-by-step explanation:
-5x=-2x-3
-5x+2x=-3
-3x=-3
X=1
Answer:
X=3/7
Step-by-step explanation:
Abigail's car uses 3 2/3 gallons of gas every hour on a long distance trip. How many gallons does the car use in 8 1/2 hours?
Answer:
31.166 repeating
Step-by-step explanation:
What identity can be used to rewrite the expression 27x^3-64?
Option A:
Difference of cubes
Solution:
Given expression is [tex]27 x^{3}-64[/tex].
27 can be written as [tex]3^3[/tex].
64 can be written as [tex]4^3[/tex].
[tex]27 x^{3}-64=3^3x^3-4^3[/tex]
[tex]27 x^{3}-64=(3x)^3-4^3[/tex]
To find the identity to rewrite the given expression:
Option A: Difference of cubes
[tex]27 x^{3}-64[/tex] can be rewritten as [tex](3x)^3-4^3[/tex].
That means the difference of two cubes.
So, it is true.
Option B: Difference of squares
[tex]27 x^{3}-64[/tex] cannot be written as square terms.
So, it is false.
Option C: Sum of cubes
[tex]27 x^{3}-64[/tex] cannot be written as sum of cubes.
So, it is false.
Option D: Pythagorean Triples
[tex]27 x^{3}-64[/tex] cannot be written as Pythagorean Triples.
So, it is false.
Hence difference of cubes if the correct answer.