Answer:
y = 12
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
3.6y = 1.6y + 24
Step 2: Solve for y
[Subtraction Property of Equality] Subtract 1.6y on both sides: 2y = 24[Division Property of Equality] Divide 2 on both sides: y = 12Step 3: Check
Plug in y into the original equation to verify it's a solution.
Substitute in y: 3.6(12) = 1.6(12) + 24Multiply: 43.2 = 19.2 + 24Add: 43.2 = 43.2Here we have 43.2 does indeed equal 43.2.
∴ y = 12 is the solution to the equation.
Working together, two ants named Aran and Beatrice can build an ant hill in 10 hours. Aran and Charlie can build the ant hill in 12 hours. Beatrice and Charlie can build the ant hill in 15 hours. How long, in hours, will it take to build the ant hill if Aran, Beatrice, and Charlie work together?
Here we have a problem of rates of work, we want to know how long will take the 3 ants to build an ant hill if they work together.
We will find that working together, they need to work for 8 hours.
----------------------------------
Let's start by defining the variables that we will use:
A = rate at which Aran worksB = rate at which Beatrice works.C = rate at which Charlie works.Now let's see the given information:
"Aran and Beatrice can build an ant hill in 10 hours"
This can be written as:
(A + B)*10 h = 1 ant hill
"Aran and Charlie can build the ant hill in 12 hours"
This can be written as:
(A + C)*12 h = 1 ant hill
"Beatrice and Charlie can build the ant hill in 15 hours"
This can be written as:
(B + C)*15 h = 1 ant hill.
Then we have 3 equations:
[tex](A + B)*10 h = 1[/tex]
[tex](A + C)*12 h = 1[/tex]
[tex](B + C)*15 h = 1[/tex]
Where for commodity, I removed the "ant hill" unit.
Now we need to solve this system of equations, to do it, we need to isolate one variable in one of the equations and then replace it on another equation.
I will isolate A in the first equation:
[tex]A = \frac{1}{10h} - B[/tex]
Now we can replace it in the second equation to get:
[tex](\frac{1}{10h} - B + C)*12h = 1[/tex]
Now we can isolate C in the last equation to get:
[tex]C = \frac{1}{15h} - B[/tex]
Replacing that in the above equation we get:
[tex](\frac{1}{10h} - B + \frac{1}{15h} - B)*12h = 1\\\\\frac{1}{6h} - \frac{1}{12h}= 2*B\\\\\frac{1}{2}*\frac{1}{12h} = \frac{1}{24h} = B[/tex]
This means that Beatrice alone would construct the hill in 24 hours.
Now that we know the value of B, we can use:
[tex]C = \frac{1}{15h} - B = \frac{1}{15h} - \frac{1}{24h} = \frac{1}{40h}[/tex]
This means that Charlie needs 40 hours to finish the hill alone.
Finally, we can use [tex]A = \frac{1}{10h} - B[/tex] to find the value of A:
[tex]A = \frac{1}{10h} - B = \frac{1}{10h} - \frac{1}{24h} = \frac{7}{120h}[/tex]
Now if the 3 ants work together, the total rate at which they work is:
[tex](A + B + C) = (\frac{7}{120h} + \frac{1}{40h} + \frac{1}{24h} ) = 0.125 h^{-1}[/tex]
This means that they need to work for the inverse of that rate
[tex]\frac{1}{0.125h^{-1}} = 8h[/tex]
Working together, they need to work for 8 hours to complete an ant hill
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27 is what percent of 18.75 it is asking for a percent answer I’ve tried 44%, 144, 506.25
Answer:
144%
Step-by-step explanation:
Answer:
144%??
Step-by-step explanation:
thats the answer man
Amanda is decorating you new house. She found a table at Pottery Barn for $425. If the table is 45% off, what will it cost?
Which operation would help solve for y?
3+y=27
Answer:
24
Step-by-step explanation:
Evaluate the expression when b=-6 and y=4.
b-6y
I NEED HELP! PLZ! 20 POINTS. :)
Answer: i have no clue?
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
100 = 2x + 4y > 100 = 2x+40 > 60 = 2x> x = 30
True or False: If a quadratic equation cannot be factored, then it doesn't have any solutions.
The given statement is false because a quadratic equation may have no solutions, one solution, or two solutions, regardless of whether it can be factored or not.
What is a quadratic equation?The quadratic equation is defined as a function containing the highest power of a variable is two.
A quadratic equation is a type of polynomial equation that can be written in the form ax² + bx + c = 0, where a, b, and c are constants and x is a variable.
If a quadratic equation cannot be factored, it does not mean that it does not have any solutions.
A quadratic equation may have no solutions if the discriminant, which is the quantity b² - 4ac, is less than zero.
In this case, the quadratic equation has no real solutions, as the solutions would be complex numbers.
However, if the discriminant is equal to zero, the quadratic equation has one solution, which is the value of x that makes the equation equal to zero. If the discriminant is greater than zero, the quadratic equation has two solutions, which are the values of x that make the equation equal to zero.
In summary, a quadratic equation may have no solutions, one solution, or two solutions, regardless of whether it can be factored or not.
Thus, the given statement is false.
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What is the number of cycles of y=1+10sin(θ−2π/3) between 0 and 2π?
Answer:
D. 2/3
Step-by-step explanation:
The solution to the system of equations is (-7, 11). true or false
What is the radius of this circle?
Answer: the answer is 7cm
Step-by-step explanation:if the diameter is 14, just do 14/2=7
I need this ASAP!!!!!!
Answer:
(x, y) = (1, -9)
Step-by-step explanation:
y = -9x
-8x-6y = 46
By substituting the value of y (first equation) into the second equation, we get,
-8x - 6*(-9x) = 46
-8x + 54x = 46
46x = 46
x = 1.
So, y = -9
What is 1 whole and 1/3 - 5/6?
Answer:
The answer is 1/2.
Step-by-step explanation:
1 1/3-5/6=
1 1/3 needs to be turned into a improper fraction. 1 1/3=4/3.
Now we can do 4/3-5/6 but, the denominator has to be the same. We can make them 8/6-5/6.
*(Whatever happens to the denominator, has to happen to the numerator.)
8/6-5/6=3/6. Typically, the answer could be 3/6 but you could also simplify it to 1/2.
So, the answer would be 1/2.
Hopefully this helps you and sorry if it doesn't.
List the ordered pairs and determine whether or not this is a function
Ordered pairs : ?
Is this a function : ?
In a game, Erin is rolling a fair number cube with faces numbered 1 to 6. Which BEST describes the probability of rolling an even number?
A. impossible
B. equal to the probability of rolling an odd number
C. less likely than the probability of rolling an odd number
D. more likely than the probability of rolling and odd number
The dimensions of a right rectangular prism are 0.25 m, 0.36 m, and 0.14 m. What is the volume of the prism use the V = 1 x w x h
Judy studied for 7/12 of an hour and her sister studied for 2/3 of an hour about how much time did they spend studying all together
Answer:I need that answer for my TEST!!!!!!!!!!!!!!!!!
Step-by-step explanation:
Answer:
They studied for a little more than an hour.
Step-by-step explanation:
What is the image of the point (8,-6)(8,−6) after a rotation of 180 counterclockwise about the origin?
Answer:
(-8, 6)(-8, 6)
Step-by-step explanation:
The formula for 180 degree rotation is (-x, -y)
Will mark brainliest! A retailer marks up the price of a coffee mug from $6.25 to $8.77. By what percent did the price increase? Round to
two decimal places
a 28.73%
b 39.68%
c 40.32%
d 45.97%
Answer:
The answer is C, 40.32
Step-by-step explanation:
If you put 6.25 in your calculator times 40.32% you get 2.52. Then you add the 2.52 to 6.25 to get 8.77.
John and Robin like to collect stones. John has n stones, and Robin has 68 stones. Together they have a total of 98 stones, Write an equation to describe this situation.
Answer:
n+68=98 find n (n=30)
Step-by-step explanation:
The deck of a ship is 7 feet above the surface of the water. There is
also a cabin that is 14 feet below the deck. Which number describes
the elevation of the cabin?
Note: Your answer is expected to be a number without units for this
problem
Trina is creating a small concrete sidewalk to from her driveway to her front door as seen below. Trina needs to figure out how much to budget for the
How much should Trina budget for concrete?
Use algebraic expressions to describe your steps to find the answer.
Answer
87
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The measure of an exterior angle of a triangle is 40°. What is the sum of the measures of the corresponding remote interior angles?
Answer:
Remember that the two non-adjacent interior angles, which are opposite the exterior angle are sometimes referred to as remote interior angles. An exterior angle of a triangle is equal to the sum of the two opposite interior angles. The sum of exterior angle and interior angle is equal to 180 degrees
Find the missing side using special right triangles
Answer:
a=4[tex]\sqrt{3}[/tex], b=2[tex]\sqrt{3}[/tex]
Step-by-step explanation:
tan30=b/6, tan30=1/[tex]\sqrt{3}[/tex]
solve for b, b=6*tan30=2[tex]\sqrt{3}[/tex]
sin30=b/a, sin30=1/2
solve for a, a=4[tex]\sqrt{3}[/tex]
This is find the slope but I don’t get it. Whoever answers these two will be marked brainliest please help me I need these done and it’s currently 3 AM
Answer:
m=-2/5
Step-by-step explanation:
Slope is rise over run. In this graph the slope is negative because rise (change in the Y value) is decreasing.
Tamu ran 30 minutes and burned 170 calories. PART B: How many calories did Tamu burn per minute? Write your answer as a decimal. *
Answer:
Tamu burnt 5.66 calories per minute.
Step-by-step explanation:
Tamu ran for 30 minutes.
Calories burnt by Tamu = 170 calories
Unit rate = [tex]\frac{Calories\ burnt}{Time}[/tex]
Unit rate = [tex]\frac{170}{30}[/tex]
Unit rate = 5.66 calories per minute
Therefore,
Tamu burnt 5.66 calories per minute.
Which equation has a vertex at (0, 5) and focus of (three-halves, 5)?
The equation has a vertex at (0, 5) and focus of (three-halves, 5) is,
- 6 x + y²- 10 y + 25 = 0
−6x+y² −10y+25=0
What is a parabola?In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point and a line.
Given
The equation of a parabola is x = [tex]\frac{1}{4 \left(f - h\right)} \left(y - k\right)^{2} + h[/tex], where (h,k) is the vertex and (f,k) is the focus.
Thus, h = 0 k = 5, f = 3/2
The standard form is x = [tex]\frac{y^{2}}{6} - \frac{5 y}{3} + \frac{25}{6}x[/tex]
The general form is - 6 x + y² - 10 y + 25 = 0
The vertex form is x = [tex]\frac{\left(y - 5\right)^{2}}{6}[/tex]
The directrix is x = d
To find d, use the fact that the distance from the focus to the vertex is the same as the distance from the vertex to the directrix: [tex]0 - \frac{3}{2} = d - 0[/tex]
Thus, the directrix is x = - 3/2
The axis of symmetry is the line perpendicular to the directrix that passes through the vertex and the focus: y = 5
The focal length is the distance between the focus and the vertex: 3/2
The length of the latus rectum is four times the distance between the vertex and the focus: 6.
The eccentricity of a parabola is always 1.
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Assume that no variable equals 0
1. c^12•c^-4•c^6
2. b^8/b^2
3. (a^4)^5
4. x^-2y/x^4y^-1
5. (a^2b/a^-3b^2)^-1
6. (x^2y/xy^3)^2
7. 1/2(-5a^2b^3)^2(abc)^2
8. m^7•m^8
9. 8m^3n^2/4mn^3
10. 2^3c^4t^2/2^2c^4t^2
help me please !
Step-by-step explanation:
When you multiply exponents of the same base (variable), add the exponents.
1. The exponents are 12 - 4 + 6 = 14 or c^14
When you divide exponents of the same base, subtract them.
2. 8 - 2 = 6 or c^6
When you raise a power to a power, you multiply the exponents.
3. 4 * 5 = 20 or c^20
When a number is raised to a negative exponent it can be re written like this x^-n = 1/x^n.
4. x^-2 * y / x^4 * y^-1; using the above information, rewrite everything to have positive exponents. If the negative exponent is in the denominator, then it becomes x^n/1
y * y / x^2 * x^4 ; then just add your exponents to simplify
y^2 / x^6
As we said before, a power raised to a power is exponent x exponent.
5. (a^2 * b) ^-1 / (a^-3 * b^2)^-1 ; as before a power raised to a power, multiply the powers.
a^-2 * b-1 / a^3 * b^-2 rewrite this as before, inverting negative exponents. a^3 / a^2 * b^1 * b^2 = a^3 / a^2 * b^3
Simolifynthe new expression to reduce the a variable by subtracting the bottom a^2 from the top a^3 and are left with
a / b^3
Work number 6 like 5, no negative exponents, so there won't be any inversions. Just multiply the outside power times every exponent, then do the division by subtracting exponents of like bases.
When figuring out the problems with constants, treat them like the variables. In number 7 the 5a^2 when raised to the 2nd power would be 5^2*(a^2)^2 = 25 a^4
Im sorry, out of time.
Quick whoever gives the right answer gets brainliest
Answer:
The independent variable (IV) is the amount of hamburgers
Step-by-step explanation:
The amount of hamburgers influence the sale amount.
If 7 + 3x = 22, then 2x = ?
O 5
O 10
O 12
0 14
og
3
Answer:
10
Step-by-step explanation:
Answer:
2x=10
Step-by-step explanation:
Three-quarters of a number is 15.
Work out four-fifths of the number.
Answer:
16
Step-by-step explanation:
let the number be x , then
[tex]\frac{3}{4}[/tex] x = 15 ( multiply both sides by 4 to clear the fraction )
3x = 60 ( divide both sides by 3 )
x = 20 , then
[tex]\frac{4}{5}[/tex] × 20 = 4 × 4 = 16
Answer:
16
Step-by-step explanation:
let the number be x , then
\frac{3}{4} x = 15 ( multiply both sides by 4 to clear the fraction )
3x = 60 ( divide both sides by 3 )
x = 20 , then
\frac{4}{5} × 20 = 4 × 4 = 16