Answer: y = 4x/z , y = 4.
Step-by-step explanation:
Recall ; from Variation,
y ∞ x ----------------------------- 1
y ∞ ¹/z ---------------------------2
Now , combine equation 1 & 2 together, it metamorphosed to
y = kx/z -------------------------- 3
Remember, k is a constant and the value must be find first
K = yz/x
= (20 x 3) /15
= 4
To get the equation that models the relationship, we substitute for k in equation 3
y = 4x/z.
To find the value of y , substitute for the values of k, x and z
y = ( 4 x 6 )/6
= ²⁴/₆
= 4
Hey I need help adding rational numbers
Answer:
wat number
Step-by-step explanation:
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A school district has a student population of $6,734 students. If the maximum class size is 25 students. How many more teacher must the district have to supplement their staff of 217 teachers?
Answer:
53 teachers
Step-by-step explanation:
Basically, what we need to do here is to find how many teachers there need to be, first. If there are 6,734 students in the school district and if maximum class size is 25, then the number of teachers needed is:
6,734 / 25 = 269.36
Of course, it's obvious that we can't have a decimal number of teachers, so we need to find integer (269 or 270).
If we take 269 teachers and 25 students per class, we get:
269 • 25 = 6,725 students, which is not enough, since there are 6,734 students.
That means that the number of teachers needed is 270.
It is given that there are already 217 teachers, meaning that 270-217=53 teachers have to be supplemented.
52 more teachers must the district have to supplement their staff of 217 teachers.
Given that,
A school district has a student population of 6,734 students.
If the maximum class size is 25 students.
We have to determine,
How many more teachers must the district have to supplement their staff of 217 teachers?
According to the question,
Total number of students = 6,734
Maximum class size = 25 students
Then,
The number of teachers needed is,
[tex]= \dfrac{6734}{25}\\\\= 269.36[/tex]
Here, 269 teachers are needed for each group of 25 students.
Therefore,
The number of more teacher must the district have to supplement their staff of 217 teachers is,
269 - 217 = 52
Hence, 52 more teachers must the district have to supplement their staff of 217 teachers.
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Can you help me on a math problem?
Answer: -3 and +3
Step-by-step explanation:
How many liters of water must be added to 15 liters of 40 % sugar syrup to obtain 30 % sugar syrup?
Answer:
5 liters of water.
Step-by-step explanation:
Let [tex]y[/tex] be the liters of water that must be added to 15 liters of 40% sugar syrup.
Initially, we have [tex]0.4(15)=6[/tex] liters of sugar syrup, and since adding water does not add any new syrup, the amount of sugar syrup must be the same after the water has been added. After the water has been added, 30% of the solution is sugar syrup, or
[tex]Sugar\:syrup =0.3(15+y)[/tex]
And since this must equal the amount of syrup we had before:
[tex]0.3(15+y)=0.4(15)[/tex]
[tex]4.5+0.3y=6[/tex]
[tex]0.3y=1.5[/tex]
[tex]\boxed{y=5}[/tex]
Thus, 5 liters of water must be added to obtain 30% sugar syrup.
Answer:
5 liters of water
Algebra 1 WILL BE MARKED BRAINLIEST :)
(04.05 MC) Which of the following is a solution to this inequality?
y>1/2 x + 2
(1, 4)
(−1, 1)
(2, 3)
(0, 2)
What is the algebraic expression for the following word phrase: the quotient of 6 and z?
A. 6+z
B. 6z
C. 6-z
D. 6/z
Answer:
Step-by-step explanation:
the quotient is the result of division
the quotient of 6 and z...
6/z <===
** pay attention to the wording...because if it would have said : the quotient of z and 6, it would have been z/6
Use the grouping method to factor the polynomial below completely.
3x3 + 9x2 + 5x + 15
O A. (3x2 + 3)(x+5)
O B. (3x2 + 5)(x + 5)
O C. (3x2 + 3)(x+3)
O D. (3x2 + 5)(x + 3)
The correct answer is D. (3x2 + 5)(x + 3). Here’s how you can use the grouping method to factor the polynomial completely:
Group the first two terms and the last two terms: (3x3 + 9x2) + (5x + 15)
Factor out the greatest common factor from each group: 3x2(x + 3) + 5(x + 3)
Factor out the common binomial factor: (3x2 + 5)(x + 3)
So, the polynomial 3x3 + 9x2 + 5x + 15 can be factored completely as (3x2 + 5)(x + 3).
Hope it helps.
Will make brainliest if answered right
Answer:
d 10x=-3
Step-by-step explanation:
2m+4s=16
What are the values for M and S?
For this case we have the following equation:
[tex]2m + 4s = 16[/tex]
We solve for each of the variables:
For m:
We subtract 4s from both sides of the equation:
[tex]2m = 16-4s[/tex]
We divide by 2 on both sides of the equation:
[tex]m = \frac {16-4s} {2}\\m = \frac {16} {2} - \frac {4s} {2}\\m = 8-2s[/tex]
For s:
We subtract 2m from both sides of the equation:
[tex]4s = 16-2m[/tex]
We divide between 4 on both sides of the equation:
[tex]s = \frac {16} {4} - \frac {2m} {4}\\s = 4- \frac {m} {2}[/tex]
Answer:
[tex]m = 8-2s\\s = 4- \frac {m} {2}[/tex]
Without additional information or a second equation, the values for 'm' and 's' cannot be specifically determined from the equation 2m+4s=16 due to the infinite number of solutions.
Explanation:The question 2m+4s=16 asks us to find the values of m and s. However, with a single equation and two variables, there are infinite solutions. This is because without additional information or constraints, each variable can take on many different values as long as the equation balances out to 16. Therefore, we cannot determine specific values for m and s without additional equations or information.
To find the values of M and S in the equation 2M + 4S = 16, we can use algebraic methods to solve for the variables.
Step 1: Start by isolating M in the equation. Subtract 4S from both sides of the equation: 2M = 16 - 4S.
Step 2: Divide both sides by 2 to solve for M: M = (16 - 4S)/2.
Now you have an equation that expresses M in terms of S. You can substitute different values for S to find the corresponding values for M. For example, if S = 2, then M = (16 - 4(2))/2 = 4. So, when S = 2, M = 4. Repeat this process for different values of S to find the corresponding values of M.
What is 3x + 4 = x + 8
Answer:
x is equal to 2
Step-by-step explanation:
2x+4=8
2x=4
x=2
Answer:
x = 2
Step-by-step explanation:
First you must subtract x to both sides leaving you with 2x + 4=8 and you subtract 4 to both sides giving you 2x=4 and lastly to get the x by itself you divide both sides by 2 leaving you with x=2
Describe when you use a solid line or a broken line when graphing inequalities. What does each type of line mean?
Answer:
Graphing Linear Inequalities differs from graphing regular linear equations. That is it has certain rules to be followed to draw the graph.
First, rearrange the equation as y in the left and other terms in the opposite side.Check for the line: y= , y≤ and y≥ comes with straight line where as y< and y> comes with a dotted (broken) line.Shading: If y> greater than or y≥ greater than or equal is present then the space above the line has to be shaded. If y< less than or y≤ less than or equal is present then the space below the line has to be shaded.Thus if the equation has y < or y > then we use broken line and y= , y≤ and y≥ then we use solid line.
which expression is equivalent to 8/9 divided by 3/4
The expression is equivalent to 8/9 divided by 3/4 is 32/27.
What is fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is put at the upper half of the fraction above the fractional bar.We have to divide the fraction 8/9 by 3/4.
As, the fraction does not allow division then we will perform the multiplication.
So, 8/9 x 4/3
= 32 / 27
Thus, the required fraction is 32/27.
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Please help ASAP!!!!
The simplified answer is [tex]5\frac{2}{9}[/tex].
Option: C.
Step-by-step explanation:
To simply [tex]-3\frac{1}{9} - (-8\frac{1}{3} )[/tex]:
First convert this improper fraction into normal fraction.
[tex]-3\frac{1}{9}[/tex] = [tex]\frac{-28}{9}[/tex].
[tex]-8\frac{1}{3}[/tex] = [tex]\frac{-25}{3}[/tex].
Now we have to simplify [tex]-\frac{28}{9} - (-\frac{25}{3} )[/tex].
= [tex]-\frac{28}{9} + \frac{25}{3}[/tex].
After applying LCM to the denominators, Multiply the second term with 3 in both numerator and denominator.
= [tex]-\frac{28}{9} + \frac{75}{9}[/tex].
=[tex]\frac{-28+75}{9}[/tex].
=[tex]\frac{47}{9}[/tex].
Convert the answer in improper fraction form.
[tex]\frac{47}{9}[/tex] = [tex]5\frac{2}{9}[/tex].
Thus the simplified answer is [tex]5\frac{2}{9}[/tex].
The cost of 5 squash and 2 zucchini is $1.32. 3 squash and 1 zucchini cost $0.75. Find the cost of each vegetable
Is 15/18 an equivalent ratio
Answer:
no
Step-by-step explanation:
bc
15/18 cant be simplified no matter what
Answer:
No
Step-by-step explanation:
15/18 can not be simplified
During the election for class president,40% of the students voted for Gerardo,35% of the students voted for Leonardo, and 25% of the students voted for juju.70 students voted for Leonard.how many more students voted for Gerardo than for juju
Answer:
80 students
Step-by-step explanation:
Let the number of voters in the election for class president is x.
So, given that 40% of the voters voted for Gerardo,35% of the voters voted for Leonardo, and 25% of the voters voted for Juju.
So, the number of voters for Leonardo was [tex]x \times \frac{35}{100} = 0.35x[/tex]
Given that, 0.35x = 70
⇒ x = 200
Now, the number of voters for Gerardo was [tex](x \times \frac{40}{100}) = 0.4x = 0.4(200) = 80[/tex].
(Answer)
a science test is worth 100 points and has 25 questions. There are multiple-choice questions worth three points each and short essay questions worth 8 points each. How many short essay questions are on the test?
There are 5 short essay questions on test
Solution:
Let "a" be the number of multiple choice questions
Let "b" be the number of short essay questions
Worth of each multiple choice questions = 3 points
Worth of each short essay questions = 8 points
There are 25 questions in total
number of multiple choice questions + number of short essay questions = 25
a + b = 25
a = 25 - b --------- eqn 1
The test is worth 100 points. Theerefore, we frame a equation as:
number of multiple choice questions x Worth of each multiple choice questions + number of short essay questions x Worth of each short essay questions = 100
[tex]a \times 3 + b \times 8=100[/tex]
3a + 8b = 100 --------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 1 in eqn 2
3(25 - b) + 8b = 100
75 - 3b + 8b = 100
5b = 100 - 75
5b = 25
b = 5
Thus there are 5 short essay questions on test
The number of short essay questions on the test is 5.
Explanation:The science test is worth 100 points and has 25 questions. Let's represent the number of multiple-choice questions as 'x' and the number of short essay questions as 'y'. Each multiple-choice question is worth three points, so the total number of points for the multiple-choice questions is 3x. Each short essay question is worth eight points, so the total number of points for the short essay questions is 8y. We can write two equations to represent the given information:
x + y = 25 (since there are 25 questions in total)
3x + 8y = 100 (since the total points for the test is 100)
To find the number of short essay questions on the test, we need to solve these two equations. By substituting x = 25 - y into the second equation, we can solve for y.
3(25 - y) + 8y = 100
75 - 3y + 8y = 100
5y = 25
y = 5
Therefore, there are 5 short essay questions on the test.
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What are the opposites of 6, −3.4, 2.25, and 8 1/ 5 ? Enter the answers in respective order, each separated by comma.
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
6= -6, -3.4=3.4, 2.25=-2.25, 8 1/5=-81/5
Multiply the polynomials.
* (x + 4)(x2 - 5x + 3)
O
O
O
A. x2 - 5x2 - 17x+ 12
B. x3 – x2 + 3x + 12
c. x2 - 5x2 + 3x + 12
2 2 17 10
Answer:
x^3-x^2-17x+12
Step-by-step explanation:
(x+4)(x^2-5x+3)
x^3-5x^2+3x+4x^2-20x+12
x^3-5x^2+4x^2+3x-20x+12
x^3-x^2-17x+12
what is the standart dievation of 63 and 37 and what is the standart dievation of 88 and 112 this is a sample not a population
hello that is a hard question but the answer is your face
Answer:
im so sorry about the kid that said that. that was mean
Step-by-step explanation:
How to you use a unit rate to solve a rate problem for any number of units?
Answer:
Here, we have used the unit rate i.e. speed of 30 mph to get the distance traveled in 5 number of units i.e. 5 hours.
Step-by-step explanation:
We are asked the way to use a unit rate to solve a rate problem for any number of units.
Let, us assume that a car is moving at a unit rate of 30 miles per hour. And we have to calculate the distance it travels in 5 units of time i.e. 5 hours.
Now, the distance traveled in 5 hours will be given by 30 × 5 = 150 miles.
Since [tex]\textrm {Speed} = \frac{\textrm {Distance}}{\textrm {Time}}[/tex] and here, speed is 30 miles per hour and the time is 5 hours. (Answer)
Camille shaded 18/30 of a model. Write the decimal that represents the unshaded portion of the model
Answer:
The decimal that represents the unshaded portion of the model is 0.4
Step-by-step explanation:
we know that
Camille shaded 18/30 of a model
That means
The total parts of the model is equal to 30
The shaded parts of the model is 18
To find out the unshaded parts of the model subtract the shaded parts from the total parts
[tex]30-18=12[/tex]
To find out the decimal that represents the unshaded portion of the model, divide the unshaded parts of the model by the total parts of the model
so
[tex]\frac{12}{30}=0.4[/tex]
LOTS OF POINTS please help
Answer:
C
Step-by-step explanation:
Let's call the middle M. If we take triangle PMQ we see that is has a 90 degrees angle. Also both of the other corners are equal so 180=90-2x. x=45 degrees. In a triangle with two 45 degrees angles and a 90 degrees angle the following applies: Both straigth sides are 1:square root of 2 to the oblique side. That means that if say PM=4 that PQ=4sqrt2. Now we'll that to determine PM. PQ=5x so PM=5xsqrt2. The area of parallelogram PQRS then equals to 5xsqrt2×5xsqrt2=25x^2×2=50x^2. So that is C.
What is 25% of 200?
I need help pleaseeeeeeeeeeeeeee!
Answer: 50
Step-by-step explanation: 25% of 100 is equal to 25, so if we multiply that by 2, we would get 50. To fact-check your answer, always make sure that when you multiply (only for 25% problems) by 4, and you should get the whole number. 50x4=200. Or, just 200 divided by 4. It helps!
55% of 20 pages is___pages.
Answer:
11 pages
Step-by-step explanation:
55% of 20 is 11. I'm sure! Please give be brainliest.!
Answer:
11
Step-by-step explanation:
It's just 55℅ of 20 pages so 20×55℅ will give u 11
- 2X +3Y=7
5x+8y=-2
Solution=(_,_)
Answer:
The solution is the point (-2,1)
Step-by-step explanation:
we have
[tex]-2x+3y=7[/tex] ----> equation A
[tex]5x+8y=-2[/tex] ----> equation B
Solve the system of equations by graphing
Remember that the solution of the system is the intersection point both lines
using a graphing tool
The solution is the point (-2,1)
see the attached figure
9 times a number of 390
Answer:
5667
Step-by-step explanation:
Answer:
3510
Step-by-step explanation:
because you have 390 and you multiply it my 9 so you would get 3510 by 9 times
Please help!!!!! Math is very confusing and this makes no sense
A running track has the shape of a rectangle capped with a semicircle on each end, as shown below. If the track is 80 feet wide, and the rectangular portion of the track is 90 feet tall, estimate the length around the outside of the track.
The missing figure is attached down
The length around the outside of the track is about 431 feet
Step-by-step explanation:
A running track has the shape of a rectangle capped with a semicircle on each end
The track is 80 feet wideThe rectangular portion of the track is 90 feet tallWe need to estimate the length around the outside of the track
The length of the outside the track is the length of two semi-circle and two straight lengths of the rectangle
∵ The track is 80 feet wide
- From the figure the width of the track is the diameter of the
semi-circles
∴ The diameter of each semi-circle = 80 feet
∵ The radius of a circle is half its diameter
∴ The radius of each semi-circle = [tex]\frac{1}{2}[/tex] × 80 = 40 feet
∵ The length of a circle = 2πr
∴ The length of a semi-circle = πr
∴ The length of two semi-circle = 2 × πr
- Substitute r by 40
∴ The length of two semi-circle = 2 × π(40) = 80π feet
∵ The rectangular portion of the track is 90 feet tall
∴ The length of the rectangle = 90 feet
∴ The two straight parts of the track = 2 × 90 = 180 feet
- Add the length of the two semi-circles and the two straight
parts to find the length of the track
∵ Length of the track = 80π + 180
- Substitute π by 3.141
∴ Length of the track = 80(3.141) + 180
∴ Length of the track = 431.28 ≅ 431 feet
The length around the outside of the track is about 431 feet
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An online store is offering 15% off all items in your order. Before the discount is applied, the items in your cart are: shampoo for $6.35, conditioner for $6.35, granola bars for $12.50, dish soap for $13.40, and toothpaste for $2.50. What is the discounted total price for all the items, assuming no sales tax is added? Report your answer to two decimal places. Do not include the dollar sign, $, in the answer box below.
Answer:
The total discounted price is 34.93
Step-by-step explanation:
The items in the cart are:
Shampoo for $6.35Conditioner for $6.35Granola bars for $12.50Dish soap for $13.40 Toothpaste for $2.50Total cart = $ 41.10
Discount = 41.10 * 0.15 = $ 6.17
Discounted total price = 41.10 - 6.17
Discounted total price = 34.93
Answer:
34.94.
Step-by-step explanation:
First we must find the total price of all the items: =$6.35+$6.35+$12.50+$13.40+$2.50=$41.10.
Next, we can calculate the discount: =(15/100)×$41.10=$6.165.
Therefore, our discounted price is $41.10−$6.165=$34.935≈$34.94.
30 points
Which expression is equivalent to | a | ≤ 4 ?
1. a ≥ –4 and a ≤ 4
2. a ≤ –4 or a ≥ 4
3. a ≤ –4 and a ≥ 4
4. a ≥ –4 or a ≤ 4
Answer:
1. a ≥ –4 and a ≤ 4
Step-by-step explanation:
Rule : | a | ≤ 4 ⇔ -4 ≤ a ≤ 4
:)