Answer:
140 ounces of water and 105 ounces of 35% salt solution.
Explanation:
Let [tex]x[/tex] be the ounces of water that need to be added and [tex]y[/tex] be the ounces of 35% solution that need to to be added.
We know that the total of ounces of water and of 35% solution must be 245 ounces:
[tex]x+y=245[/tex]
35% of [tex]x[/tex] is the salt, and since no salt is added with addition of [tex]y[/tex] liters of water, this must be equal to the amount of salt in the final 15% solution:
[tex]0.35x=0.15*245[/tex]
we solve for [tex]x[/tex] and get:
[tex]x=105[/tex]
We put this value into [tex]x+y=245[/tex] and solve for [tex]y[/tex] to get:
[tex]y=140[/tex]
Thus we have 140 ounces of water and 105 ounces of 35% solution.
To obtain a 245-ounce mixture at 15% salt concentration, the scientist needs to mix 140 ounces of water with 105 ounces of 35% salt solution by solving a system of equations that involves the total mass of the solution and the mass of the salt in the mixture.
Explanation:The student is asking for help with a mixing solution problem in algebra where they need to combine water with a 35% salt solution to create a final mixture that has a 15% salt concentration. To solve this problem, two key equations must be set up based on the mixture's total mass and the mass of the salt within the mixture. The student wants 245 ounces of the final mixture.
Let's denote X as the number of ounces of water (0% salt) and Y as the number of ounces of the 35% salt solution. The first equation is based on the total mass of the final solution: X + Y = 245. The second equation is based on the mass of the salt in the solution: 0*X + 0.35*Y = 0.15*245.
Now, we solve the system of equations. The second equation simplifies to 0.35Y = 36.75. Dividing both sides by 0.35 gives Y = 105 ounces. Substituting Y into the first equation gives X = 140 ounces. Therefore, the scientist needs to mix 140 ounces of water with 105 ounces of the 35% salt solution to achieve the desired concentration.
There is a 12-ft fence on one side of a rectangular garden. The gardener has 44 ft of fencing to the enclose the other three sides. What is the length of the gardens longer dimension?
Answer:
16 ft
Step-by-step explanation:
One of the other three sides is 12 ft. After that fence is subtracted from the total, there are 32 ft of fence left for the other two sides of the rectangle. That allows those sides to be 32 ft/2 = 16 ft long.
The rectangle can be 12 ft by 16 ft. The longer dimension is 16 ft.
The longer dimension of the rectangular garden is 16 feet. This is found by understanding the perimeter of a rectangle and subtracting the known side from the total fencing available before dividing the result by 2.
Explanation:The subject of this question is Mathematics, specifically related to the area and perimeter of rectangles. To find the length or the longer dimension of the rectangular garden, we need to understand the concept of the perimeter of a rectangle. The perimeter is the sum of all sides of the rectangle. Here, the problem provides us with one side of the rectangle to be 12 feet and the sum of the remaining three sides to be 44 feet.
Considering that the rectangular garden has two equal longer sides and two equal shorter sides, we can say the shorter side is 12 feet. Therefore, the combined length of the other two sides (the longer sides) must be 44-12=32 feet. Because these are equal, each one is 32/2 = 16 feet.
Therefore, the longer dimension of the rectangular garden is 16 feet.
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I’m not sure on how are you suppose to graph this without knowing what the x’s are and a calculator?
Answer:
The answer is shown in the plotted graph attached with the answer.
Step-by-step explanation:
i) Let y = f(x)
ii) According to the first equation we will consider x = -6, -5, -4, -3, -2, -1, 0, and
1
Therefore x and y = x + 4 for -6 ≤ x < 2
-6 -2 -5 -1 -4 0 -3 1 -2 2 -1 3 0 4 1 5iii) y = 6 when x = 2 is the second equation given for the graph
iv) x y = -x + 2 for x > 2 is the third equation given
3 -1 4 -2 5 -3 6 -4Macy doesn’t have any money in her bank account, but she saves $12.50 each week. Robby has $20 in his bank account, and he saves $7.50 each week. After how many weeks will Macy and Robby have the same amount in their accounts?
After 4 weeks, Macy and Robby will have same amount in their accounts.
Step-by-step explanation:
Given,
Amount saved by Macy each week = $12.50
Let,
x be the number of weeks.
M(x) = 12.50x
Amount saved by Robby each week = $7.50
Amount Robby already have = $20
R(x) = 7.50x + 20
For same amount;
M(x) = R(x)
[tex]12.50x=7.50x+20\\12.50x-7.50x=20\\5x=20[/tex]
Dividing both sides by 5
[tex]\frac{5x}{5}=\frac{20}{5}\\x=4[/tex]
After 4 weeks, Macy and Robby will have same amount in their accounts.
Keywords: function, division
Learn more about functions at:
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After 4weeks, Macy and Robby will have the same amount in their bank accounts.
To determine after how many weeks Macy and Robby will have the same amount in their bank accounts, we can set up an equation based on their weekly savings and initial amounts.
Let M(t) represent Macy's savings after t weeks, and R(t) represent Robby's savings after t weeks.
Macy's savings can be expressed as:
M(t) = 12.50t
Robby's saving can be expressed as:
R(t) = 20 + 7.50t
We want to find the number of weeks t such that M(t) = R(t)
Setting up the equation:
12.50t = 20 + 7.50t
To solve for t, first subtract 7.50t from both sides:
12.50t - 7.50t = 20
5t = 20
Next, divide both sides by 5 to solve for t
[tex]\[ t = \frac{20}{5} \][/tex]
t = 4
Therefore, after 4weeks, Macy and Robby will have the same amount in their bank accounts.
A recipe uses 5 cups of flour for every 2 cups of sugar. How much sugar is used for 1 cup of flour?
Answer:
0.4
Step-by-step explanation:
you have to divide 2 by 5 that gives you 0.4
Raphael Raphael Raphael Raphael
An isosceles triangle has (5 points) at least two congruent sides two sides that are perpendicular three sides with the same length two sides that are parallel
Answer:
at least two congruent sides
Step-by-step explanation:
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Question 11 of 12
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Determine if there is enough information to prove that each pair of triangles is congruent by SSS, SAS, or ASA.
Write the congruence statements to justify your reasoning.
Answer:
By ASA
Step-by-step explanation:
<SVR=<VRT (ALTERNATE ANGLES)
SIDE RV=SIDE RV (COMMON)
<SRV=<TVR (ALTERNATE ANGLES)
So by side angle side postulate both triangles are congruent
Hope u understand
Brainliest?
Step-by-step explanation:
Sorry I'm not too sure about that one, but this video might help, sorry!
https://youtu.be/JtgABYPsv7g
what percent of 80 is 48
Answer:
48 is 60% of 80.
Answer:
60%
Step-by-step explanation:
48: 80*100 =
(48*100) :80 =
4800:80 = 60
I NEED HELP!!!
CAN SOMEONE HELP ME
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The GCD and L.C.M of two numbers are 16 and 96 respectively. If the average of
the numbers is 40 then find those numbers.
Answer:
The numbers are 32 , 48
Step-by-step explanation:
Average = 40
Sum of two numbers = 40 * 2 = 80
Let one number =x
Other number = 80 - x
Product of two numbers = GCD * LCM
x*(80-x) = 16*96
80x - x² = 1536
1536 + x² - 80x = 0
x² - 80x + 1536 = 0
x² - 48x - 32x + (-32) * (-48) = 0
x (x -48x) -32 (x -48) =0
(x - 48) ( x - 32) = 0
x - 48 = 0 ; x - 32 = 0
x = 48 ; x = 32
Add the two expressions
6q + 1 and q + 11
Addition of 6q + 1 and q + 11 is 7q + 12
Solution:
Given that, we have to add the given two expressions
Given expressions are:
6q + 1 and q + 11
We have to add both the expressions
Addition of 6q + 1 and q + 11 = 6q + 1 + q + 11
Add the coefficients of same variable. Here "q" is present in two terms
Therefore, add 6q and q
Similarly, add the constants 1 and 11
Thus finally addition is done as:
[tex]6q + 1 + q + 11 = 7q +12[/tex]
Thus addition of 6q + 1 and q + 11 is 7q + 12
21 = 3x what does equally
Answer:
The x equal 7
Answer:
X = 7
Step-by-step explanation:
21 = 3x
x = 21/3
= 7
PLEASE HELP ME ...........Julie was looking at the architect's blueprint of her house. The scale on blueprint was 1/4 inch = 1 foot. On the blueprint, what are the dimensions of her bedroom if the actual dimensions of her bedroom are 12 feet by 16 feet?
Answer:
On the blueprint the dimensions are 48 inches by 64 inches.
Step-by-step explanation:
Given:
The scale on blueprint was 1/4 inch = 1 foot.
The actual dimensions of her bedroom are 12 feet by 16 feet.
Now, to find the dimensions on the blueprint.
Let the dimensions on the blueprint be [tex]x[/tex] by [tex]y.[/tex]
As, given the scale on blueprint:
[tex]\frac{1}{4}\ inch=1\ foot[/tex]
So, [tex]\frac{1}{4}\ inch[/tex] is equivalent to 1 foot.
Thus, [tex]x[/tex] is equivalent to 12 feet.
And, [tex]y[/tex] is equivalent to 16 feet.
Now, solving by cross multiplication method:
[tex]\frac{\frac{1}{4}}{1} = \frac{x}{12}[/tex]
[tex]\frac{4}{1} =\frac{x}{12}[/tex]
By cross multiplying we get:
[tex]48=x[/tex]
[tex]x=48\ inches.[/tex]
Now, again:
[tex]\frac{\frac{1}{4}}{1} =\frac{y}{16}[/tex]
[tex]\frac{4}{1} =\frac{y}{16}[/tex]
By cross multiplying we get:
[tex]64=y[/tex]
[tex]y=64\ inches.[/tex]
Therefore, on the blueprint the dimensions are 48 inches by 64 inches.
Answer:
Step-by-step explanation:
48 and 64
Two bottled waters and an order of cheese nachos costs $5.50.three bottled waters and two orders of cheese nachos costs $9.50
what does it ask for?
Answer: You might have messed up the question
Here is the answer based on your question
W (Bottled water) = 7/2$
N (Cheese Nachos) = -1/2$
Step-by-step explanation:
2W + 3N = $5.50
3W + 2N = $9.50
Find the common number and subtract them. In order to find isolate the water bottles or nachos. I will do water bottles
15 (2W + 3N = $5.50)
10 (3W + 2N = $9.50)
30w + 45N = $82.5
Minus
30W + 20N = $90
= 25N = -12.5
N = -1/2$
Substitute for N
3W + 2(-1/2) =9.5
3w -1 = 9.5
3w - 10.5
w = 7/2$
What is √2323 in simplest form as a radicand and a number outside the radicand
Since 2323 = 23*101 has no perfect square factors, this means we cannot simplify [tex]\sqrt{2323[/tex] into the form [tex]a\sqrt{b}[/tex]
It seems like your teacher may have made a typo. I would double check with them.
-----------------------------------------------------------------------
I'll show you how to simplify a different problem. Let's say we want to simplify [tex]\sqrt{232}[/tex]
Find the prime factorization of the radicand:
232 = 2^3*29
we can rewrite the "2^3" as "2^2*2" to pull out the perfect square factor, which helps us simplify as such:
[tex]\sqrt{232} = \sqrt{2^3*29}[/tex]
[tex]\sqrt{232} = \sqrt{2^2*2*29}[/tex]
[tex]\sqrt{232} = \sqrt{2^2*58}[/tex]
[tex]\sqrt{232} = \sqrt{2^2}*\sqrt{58}[/tex]
[tex]\sqrt{232} = 2*\sqrt{58}[/tex]
For the last two steps I used these square root rules
[tex]\sqrt{x*y} = \sqrt{x}*\sqrt{y}[/tex]
[tex]\sqrt{x^2} = x[/tex] where x is nonnegative
Final answer:
The square root of 2323 in simplest radical form is 29√3, where 29 is the number outside the radicand and √3 is the radicand.
Explanation:
When simplifying the square root of 2323 to its simplest radical form, the goal is to express the square root as a product of a radicand that has no perfect square factors other than 1, and a number outside the radicand, if possible. We start by finding the prime factors of 2323 and look for pairs of prime factors, as pairs will be taken out of the square root as single numbers. Upon factoring 2323, we find that it can be expressed as 2323 = 29 x 29 x 3. Taking the square root of this expression gives us:
√2323 = √(29 x 29 x 3)
Recognizing that 29 is a perfect square, we take the square root of 29 x 29, which gives us 29. The square root of 3 remains inside the radicand since it is not a perfect square:
√2323 = 29√3
Therefore, √2323 in simplest form as a radicand and a number outside the radicand is 29√3.
The length of a rectangle is 3 1/6 cm longer than the width. The perimeter of the rectangle is 15 1/3 cm. What are the width and length of this rectangle?
Answer:
[tex]Width = 2\frac{1}{4}cm[/tex]
[tex]Length=5\frac{5}{12} cm[/tex]
Step-by-step explanation:
Data from the question;
Perimeter of a rectangle is [tex]15\frac{1}{3}[/tex] cm
Length is [tex]3\frac{1}{6}[/tex] cm longer than the width
We are supposed to determine the length and the with of the rectangle;
Assuming, the width x cm
Then, the length is [tex]x+3\frac{1}{6}[/tex] cm
We need to know that the perimeter of a rectangle is given by;
Perimeter = 2 ( length + width)
Therefore;
[tex]15\frac{1}{3}= 2 ( x + (x+3\frac{1}{6}))[/tex]
[tex]15\frac{1}{3}=2(2x+3\frac{1}{6})[/tex]
Thus;
[tex]15\frac{1}{3}=4x+6\frac{1}{3}[/tex]
[tex]4x=9\\x=2\frac{1}{4}[/tex]
Therefore;
[tex]Width = 2\frac{1}{4}cm[/tex]
[tex]Length = x + 3\frac{1}{6}[/tex]
[tex]=2\frac{1}{4}+3\frac{1}{6}[/tex]
[tex]=5\frac{5}{12} cm[/tex]
Therefore; the length is [tex]5\frac{5}{12}[/tex] cm while the width is [tex]2\frac{1}{4}[/tex] cm
Find x. For problems 2 and 3
Answer:
x = 4 and x = 7
Step-by-step explanation:
Given that the segment in the triangle is parallel to the third side of the triangle and intersects the 2 sides then it divides these 2 sides in proportion, thus
[tex]\frac{x}{12}[/tex] = [tex]\frac{x+1}{15}[/tex] ( cross- multiply )
15x = 12(x + 1) ← distribute
15x = 12x + 12 ( subtract 12x from both sides )
3x = 12 ( divide both sides by 3 )
x = 4
--------------------------------------------------------------------
[tex]\frac{8}{7}[/tex] = [tex]\frac{16}{2x}[/tex] ( cross- multiply )
16x = 112 ( divide both sides by 16 )
x = 7
A square pyramid is shown below:
What is the surface area of the pyramid? (1 point)
Question 19 options:
1)
8.01 square feet
2)
2.61 square feet
3)
4.41 square feet
4)
1.71 square feet
Answer:
I do not see the picture, but if the following measurements are correct, then you have your answer!
The sides of the square base are labeled 0.9 foot. The height of one of the triangular sides is labeled 4 feet
Step-by-step explanation:
[tex]8.01 ft^{2}[/tex] or 8.01 square feetAnswer:
8.01
Step-by-step explanation:
okay this is my last question for the day please answer its about to be 11pm and thats not healthy for somebody my age to stay up this long
Step 1) Place the non-pencil part of the compass at point W and the pencil part at point X. Draw a circle. This circle has a radius of WX.
Step 2) Keep the compass the same width, place the non-pencil part at point X and the pencil part at point W. Draw a circle. This circle has the same radius.
Step 3) The two circles intersect at two other points, A and B. One point is above WX and the other is below. Connecting AB forms the perpendicular bisector.
See the diagram below.
What are the solutions to the equation x2 = 64
Answer:
x=2
Step-by-step explanation:
x2=64
Divide 2 by 2 and do the same thing to the other side 64 divided by 2. Then that leaves x=32
Answer:
x = 32
Step-by-step explanation:
x2 = x × 2
so x = 32
beacuse 64 ÷ 2 = 32
your welcome
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What is an equivalent expression for 8x+3+5(2x+6)
Answer:
18r+33
Step-by-step explanation:
The recreation department is sending out flyers for the upcoming summer sessions. Marilyn and her three friends are putting labels on each flyer. So far, they have shared the work evenly and labeled 200 total flyers. If they continue to share the work evenly, which simplified expression represents the total number of flyers each girl will label? Let f represent the number of additional flyers.
A. 100 + 4f
B. 100+ f/4
C. 200+ f/4
D. 50+ f/4
Marilyn, Sharon, and Rhonda collect earrings. Marilyn has half as many earrings as Sharon. Rhonda has 15 more earrings than Marilyn. Let x represent the number of earrings that Sharon has. Which algebraic expression represents the number of earrings Rhonda has?
A. x +15
B. 0.5x+15
C. x-15
D. 15-0.5x
Hector, Sam, Ted, and Gina are comparing their savings. Hector saved twice as much money as Sam. Ted saved $100 more than Hector. Gina saved $50 less than Ted. Let x represent the amount of money Sam has in savings. Which algebraic expression represents the amount of money Gina has?
A. 2x+50
B. 2x-50
C. x+150
D. x-50
The expressions representing the total flyers each girl will label, the number of earrings Rhonda has, and the amount of money Gina has are 50 + f/4, 0.5x + 15, and 2x + 50, respectively.
The correct answer for the following question 1) option (D), question 2) option (B) and for question 3) option (A)
To determine the number of flyers each girl will label including the additional flyers, we assume that Marilyn and her three friends will continue to share the work evenly. They have labeled 200 flyers so far, equally, which means each has labeled 200 / 4 = 50 flyers. If f represents the number of additional flyers they will label, and they continue to share this work equally, each will label f/4 more flyers. Thus, the total number each girl will label is 50 (already labeled) + f/4 (additional), represented by the expression 50 + f/4, which corresponds to option D.
For the number of earrings Rhonda has, if x represents the number of earrings that Sharon has, Marilyn has half of this amount, or 0.5x. Rhonda has 15 more than Marilyn, so the total number of earrings Rhonda has can be represented by the expression 0.5x + 15, which is option B.
In the case of the savings, if x represents the amount of money Sam has, Hector has twice this amount, so Hector has 2x. Ted has saved $100 more than Hector, leading to 2x + $100. Gina saved $50 less than Ted, which is (2x + $100) - $50, simplified to 2x + 50, and that corresponds to option A.
Drag the correct number of pieces to show how to find the area of the shaded figure in
two different ways. Pieces can be rotated to fit.
Answer:
Step-by-step explanation:
first shape = 2 pieces
Second shape 12 pieces
Answer:
First Scenario-
2 of the first ones
2 of the third ones
1 of the 5th ones
2 scenario-
2 of the 4th ones
Step-by-step explanation:
i got it right
The population of austin, texas in 1990 was 472,000 people. The population in 1980 was 346,000 people.
Answer:
SOmeOne HelP Me WiTh ThIs QuEsTioN pLz
Step-by-step explanation:
The rate of increase in population is r = 12,600 people/year.
We want to find the rate of change in the population of Austin, Texas in the years between 1980 and 1990.
We will assume that this increase in population is modelled with a linear equation, remember that a general linear equation is y = ax + b.
Where the rate of change, or slope, is a.
What is a slope formula?We know that if a line passes through two points (x₁, y₁) and (x₂, y₂) the slope is given by the formula: m=(y₂-y₁)/(x₂-x₁).
For this case we have two points, these are:
(1980, 346,000)
(1990, 472,000)
Then the slope or rate of change is (472,000-346,000)/(1990-1980)
=12,6000/10
=12,600
Therefore, the rate of increase in population is r = 12,600 people/year.
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The population of Austin, Texas in 1980 was 346,000 people. The population in 1990 was 472,000 people. What is the rate of change of the population with respect to the year for this function?
factorise the following expressions m²-9n²
Answer:
(m - 3n)(m + 3n).
Step-by-step explanation:
This is the difference of 2 squares, so we use the identity:
a^2 - b^2 = (a - b)(a + b).
So m^2 - 9n^2
(m - 3n)(m + 3n).
How many times does 9 go into 143
Answer:
15.89
Step-by-step explanation:
You would divide 149 by 9 and get 15.88.However this 8 will keep repeating so you have to round it up.
roger is buying a new pair of shoes for 25% off. if the original price of shoes was $90.00 , how much money is roger saving on shoes ???? please help ME hurry i have to finish my test !! i will give u 10 points .
Answer:
Answer: $67.50
Step-by-step explanation:
If the graph of an equation has a slope of 3 and passes through the point (1, -1). What is the equation?
3x + y = -2
3x + y = 2
3x - y = 4
3x - y = -4
Answer: The equation has a slope of 3 and passes through the point (1,-1)
is 3 x-y=4
Step-by-step explanation:
Step 1 :-
An equation having slope 'm' and passing through the point
is [tex]y-y_{1} = m(x-x_{1} )[/tex].......(1)
Step 2:-
Now given equation slope m=3 and given point is (1,-1)
substitute these values in equation(1), we get
[tex]y-(-1)=3(x-1)[/tex]
on simplification, we get
[tex]y+1 = 3 x-3[/tex]
[tex]3 x-y=4[/tex]
Given (x) - 3x-1 and g(x)=2x-3, for which value of x does g(x) = f(2)?
0910
Question:
Given f(x) = 3x-1 and g(x)=2x-3, for which value of x does g(x) = f(2)?
Answer:
The value of x is 4 for g(x) = f(2)
Solution:
Given that,
[tex]f(x) = 3x-1\\\\g(x) = 2x - 3[/tex]
We have to find the value of "x" such that g(x) = f(2)
Let us first find f(2)
Substitute x = 2 in f(x) function
[tex]f(x) = 3x-1\\\\f(2) = 3(2) - 1\\\\f(2) = 6 - 1 = 5[/tex]
Thus f(2) is 5
Now find: g(x) = f(2)
Equate given function of g(x) and f(2) which is found to be 5
[tex]g(x) = f(2)\\\\2x - 3 = 5\\\\\text{Move the constants to other side }\\\\2x = 5 + 3\\\\2x = 8\\\\\text{Divide both sides of equation by 4 }\\\\x = 4[/tex]
Thus for x = 4 , we get g(x) = f(2)
Steve said it does not matter which term is first and which term is second in a ratio, since ratios are different than fractions. Is he correct? Explain why or why not.
Ratio is a comparison of two values or two quantities.
Fraction is a another form of ratio.
The first term and the second term in the ratios are important.
It should not be changed.
The first quantity value is in first term and the second quantity value is in second term of the ratio.
Ratio and fractions are same.
Example:
The ratio of male to female in the school is 5 : 6.
5 represents male students and 6 represents female students.
The fraction form of the above ratio is [tex]\frac{5}{6} .[/tex]
Sooo I wanna know if 68 is the correct answer to this one if so how