Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form: x < 3
Interval Notation: (-∞, 3)
A chemist has three different acid solutions. The first acid solution contains 15 % acid, the second contains 35 % and the third contains 65 % . He wants to use all three solutions to obtain a mixture of 72 liters containing 45 % acid, using 2 times as much of the 65 % solution as the 35 % solution. How many liters of each solution should be used?
Answer:
18 liters 15% acid
18 liters 35% acid
36 liters 65% acid
Step-by-step explanation:
Let's say x is the volume of 15% acid, y is the volume of 35% acid, and z is the volume of 65% acid.
x + y + z = 72
z = 2y
The amounts of acid add up to the final amount.
0.15x + 0.35y + 0.65z = 0.45 (72)
Substitute the expression for z into both equations.
x + y + 2y = 72
0.15x + 0.35y + 0.65 (2y) = 0.45 (72)
Simplify:
x + 3y = 72
0.15x + 1.65y = 32.4
Solve for x in the first equation, then substitute into the second.
x = 72 − 3y
0.15 (72 − 3y) + 1.65y = 32.4
Solve for y.
10.8 − 0.45y + 1.65y = 32.4
1.2y = 21.6
y = 18
Now find x and z.
x = 72 − 3y = 18
z = 2y = 36
18 liters 15% acid, 18 liters 35% acid and 36 liters 65% acid should be used.
What is percentage?Percentage is a measurement to find the value of a given number out of a hundred.
Let x is the volume of 15% acid, y is the volume of 35% acid, and z is the volume of 65% acid.
Given that, the total mixture is 72 liters,
Implies that,
x + y + z = 72
Also,65% solution is used two times as 35% solution is used.
z = 2y
The amounts of acid add up to the final amount.
0.15x + 0.35y + 0.65z = 0.45 (72)
Substitute the value of z here,
0.15x + 0.35y + 0.65 (2y) = 0.45 (72)
Simplify
x + 3y = 72
0.15x + 1.65y = 32.4
Solve for x in the first equation, then substitute into the second.
x = 72 − 3y
0.15 (72 − 3y) + 1.65y = 32.4
Solve for y.
10.8 − 0.45y + 1.65y = 32.4
1.2y = 21.6
y = 18
Now find x and z.
x = 72 − 3y = 18
z = 2y = 36
18 liters 15% acid, 18 liters 35% acid and 36 liters 65% acid should be used.
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Joseph is making kebabs. He wants each kebab to have 3 pieces of meat and 4
pieces of vegetables.
Which of the following could Joseph use to make kebabs without any leftovers?
Answer:
Option D.
Step-by-step explanation:
From your comment, you said D was 30 pieces of meat and 40 pieces of vegetables. The starting ratio is 3:4. A true proportion is 3:4::30:40. 3 and 4 are both multiplied by 10 to get 30 and 40 therefore there would be no leftovers.
I don’t understand slopes at all! Can someone please help?Write an equation in slope-intercept form for a line that goes through the points (-3, 5) and (2, 8).
Answer:
Step-by-step explanation:
y2-y1
x2-x1=
y=mx+b
8-5
2+3=
3/5 = slope
b=0
y=3/5x
Amani is mailing packages. Each small package costs her $3.40 To send. each large package costs her $4.30. how much will it cost her to send six small packages and seven large packages?
Answer:
the answer is $50.50,
Answer:50.50
Step-by-step explanation:
f(4) if f(x)=-3+15 ?
Answer:
12
Step-by-step explanation:
f(4) means that we need to substitute 4 into x to get
f(4) = -3 + 15
and -3 + 15 = 12
Find the missing terms in each geometric sequence.
1. 3, 12, 48 __, __
2. __, __, 32, 64, 128, ...
3. 120, 60, 30, __, __
4. 5, __, 20, 40, __, __
5. __, 4, 12, 36, __, __
Lianne is saving to buy a DVD player that costs 2 1\2 times her weekly allowance. If she spends 3\4 of her allowance on other things, how long will she take to save the money for the DVD player?
Answer:
She will take 10 weeks to save the money for the DVD player
Step-by-step explanation:
Let w = Lianne's weekly allowance.
The DVD player costs 2 1/2 times her weekly allowance, thus
DVD cost = 5/2w
She gets w every week but spends 3/4w on other things, thus the remaining money is
Weekly savings =w - 3/4w = 1/4w
To know the number of weeks needed, we divide the DVD cost by the weekly savings:
[tex]\displaystyle N = \frac{\frac{5}{2}}{\frac{1}{4}}[/tex]
Operating:
[tex]\displaystyle N = \frac{5}{2}*\frac{4}{1}[/tex]
N = 10
She will take 10 weeks to save the money for the DVD player
Hi. Please I need help with these questions.
It's urgent .
No jokes. This time
Answer No 14
9514 1404 393
Answer:
21x² +20x +100 = 0
Step-by-step explanation:
We know the sum of the roots of x² +bx +c = 0 is -b, and their product is c. If the roots are α and β, then ...
α+β = -bαβ = cThe sum of the roots of the new equation will be ...
-b' = (α+1/β)+(β+1/α) = (α+β) +(1/α +1/β) = (α+β)(1 +1/(αβ))
The product of the roots of the new equation will be ...
c' = (α+1/β)(β+1/α) = αβ +2 +1/(αβ)
Using the above relations for (α+β) and αβ, we find that ...
-b' = (-b)(1 +1/c)
c' = c + 2 + 1/c
For the given equation, our definition of b and c is ...
b = 2/3
c = 7/3
so the new equation has values ...
b' = (2/3)(1 + 1/(7/3) = (2/3)(10/7) = 20/21
c' = 7/3 + 2 + 1/(7/3) = 13/3 + 3/7 = 100/21
So, the equation with the roots of interest is ...
x² +20/21x +100/21 = 0
Multiplying by 21 gives ...
21x² +20x +100 = 0
The library had 301 shelves of books. Each shelf had 13 books. Librarians checked out 807 books to students. How many books does the library have remaining
Answer:
3106 books
Step-by-step explanation:
From the question:
The library had 301 shelves of books. Each shelf had 13 books.
Hence, the total number of books in the library =
Number of shelves × Number rod books in a shelf
= 301 × 13 books
= 3913 books
The total number of books in the library is 3913 books
Librarians checked out 807 books to students.
How many books does the library have remaining?
This is calculated as:
Total number of books - Number of books checked out
= 3913 books - 807 books
= 3106 books
The library has 3106 books remaining.
dont put anything random plsi ned
Answer:
I'll go from the top row and then do the bottom row from left to right. I put the letters next to them too if that makes it any easier.
Step-by-step explanation:
First one is already done
Second one:
Slope: -3 ( letter O)
Y-intercept: (0,4) (letter N)
Third One:
Slope: 2/3 ( letter P)
Y- intercept: (0,-3) (letter J)
Fourth One:
Slope:-1/2 (letter M)
Y-intercept: (0,3) (letter F)
Fifth one: ( first one on second row)
Slope: 1 ( letter i)
Y-intercept: (0,2) (letter S)
Sixth one:
Slope: -1/3 ( letter D)
Y-intercept: (0,-2) (letter B)
seventh one:
slope: 1/4 (letter E)
y-intercept: (0,-4) (letter H)
eighth one:
Slope:2 ( letter G)
Y-intercept: (0,0) ( letter A)
Hopefully these are all correct and it's not too confusing :)
what situations can be modeled with fraction multiplication and division
A recipe calls for 6 cups of milk. If you have 4
pints of milk, how many cups will you have left
over?
1. 0.071 64 correct to 2 significant figures is
Answer:
0.07
Step-by-step explanation:
Teresa wants to buy 2 new tires for her mountain bike. She has budgeted $120 for the tires, but after researching costs, knows she may end up
spending within $25 of that amount.
Write an inequality that Teresa could use to find the cost of each tire. Use the inequality to complete this statement.
Teresa may spend at least $
and at most $
for each new tire.
Answer:
Inequality: 95 ≤ x ≤ 145
Minimum = 95
Maximum = 145
Step-by-step explanation:
Given
Budget = $120
Range = $25
Solving (a) Write an inequality to determine how much she could spend.
The range implies that she can spend less or more of the budgeted amount.
Let the amount to spend be represented by x.
If she spends more, the maximum would be
Max = Budget + Range
Max = 120 + 25
Max = 145
If she spends less, the minimum would be
Min = Budget - Range
Min = 120 - 25
Min = 95
So, this means that x could fall within the range of the minimum and the maximum.
Mathematically, this is:
Min ≤ x ≤ Max
So, the inequality would be:
95 ≤ x ≤ 145
Solving (b): The minimum and maximum.
The minimum and the maximum amount have been solved in (a) above.
Minimum = 95
Maximum = 145
Answer:
Step-by-step explanation:
Please help this is due today
ABDE is an isosceles trapezoid. Name one pair of congruent triangles that could be used to show that the diagonals of an isosceles
trapezoid are congruent.
9514 1404 393
Answer:
ΔABE, ΔBADΔAED, ΔBDEStep-by-step explanation:
Each diagonal divides the figure into two triangles. Either could be used with its counterpart to show congruence of the diagonals.
ΔABE and ΔBAD, orΔAED and ΔBDEFiona was thinking of a number. Fiona subtracts 11 from it and gets an answer of 33.9. What was the original number?
Answer: 44.9
Step-by-step explanation:
33.9+11 = 44.9
Answer:
44.9
Step-by-step explanation:
33.9+11=44.9
44.9-11=33.9
The coach took a digital photo of the new cycling team bike. She sent a 4 cm-by-6 cm photo to each team
member.
1. If the photo were enlarged to 150% of its original size, what would be its new length (long side)?
9
2. Suppose you want to make a 2 cm-by-3 cm copy of the original photo.
What percent should you use?
50%
3. What will be the measurement for each angle in the smaller photo?
Answer:
1. 9 cm
2. 50%
3. Assuming the photo is a rectangle, the answer would be 90 degrees on every angle (in a dilation, angle measurements are congruent).
Step-by-step explanation:
1. The long side is clearly the 6 cm side. multiply it by 1.5x (150%) and you get 9.
2. 2 is 50% of 4 and 3 is 50% of 6.
3. Assuming the photo is a rectangle, the answer would be 90 degrees on every angle (in a dilation, angle measurements are congruent).
HELP!! What value of y makes the equation 4x – 3y = 17 true, when x = 2?
Answer:
y= -3
Step-by-step explanation:
4(2) - 3y = 17
8-3y=17
-8 -8
-3y=9
______
-3
y=-3
Answer:
y = -3
Step-by-step explanation:
Complete the statement. Round to the nearest hundredth if necessary
14 m to ft
The answer is not 45.93 or 46.
Answer:
[tex]45.9[/tex]
Step-by-step explanation:
Remember that the hundredths place value is the second number after the decimal point and to round that number has to be greater than five in order to round up.
[tex]1m=3.28084[/tex]
[tex]3.28084\times14=45.93176[/tex]
Hundredths place value = 3
Round:
[tex]3<5[/tex]
[tex]=45.9[/tex]
Hope this helps.
please please help
Simplify (4x − 6) − (3x + 6).
Answer:
x - 12
Step-by-step explanation:
To solve the equation, you need to combine like terms.
The first pair of like terms are 4x and 3x, so 4x - 3x = x
The second pair of like terms are -6 and 6 so -6 - 6 = -12
Therefore, the answer will be x - 12
Of the 15 students in Danielle's class, 5 went to the zoo and the rest went to the aquarium. What is the ratio of the number of students who went to the aquarium to the total number of students?
Answer:
15:20=3:4
Step-by-step explanation:
What is the equation in slope-intercept form that passes through the points (-4, 47) and (2, -16)?
Answer:
y = 10.5x - 37
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Equality Properties
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
Point (-4, 47)
Point (2, -16)
Step 2: Find slope m
Substitute: [tex]m=\frac{-16-47}{2+4}[/tex]Subtract/Add: [tex]m=\frac{63}{6}[/tex]Simplify: [tex]m=\frac{21}{2}[/tex]Step 3: Find y-intercept b
Define: y = 21/2x + bSubstitute: -16 = 21/2(2) + bMultiply: -16 = 21 + bIsolate b: -37 = bRewrite: b = -37Step 4: Write linear equation
Combine all parts.
y = 21/2x - 37
y = 10.5x - 37
And we have our final answer!
Linda needs 2200 calories per day to maintain her present weight and daily activities. She wants to lose x pounds per day. Each pound of body weight lost is equivalent to 3400 calories. Write her daily calorie intake as a linear function of the number of pounds of weight lost per day. (Let y represent the calorie intake and x represent the number of pounds of weight lost per day.)
Answer:
y = - 5600x + 2200
Step-by-step explanation:
Given that:
x = number of pounds lost per day
y = calorie intake
Using the linear relation :
y = mx + c
When calorie intake = 2200, no loss or gain in weight ; x = 0 ; hence intercept c = 2200
y = 0 + 2200
Each pound of body weight lost = - 3400 calories
Hence, equation when x = 1
-3400 = m(1) + 2200
-3400 = m + 2200
-3400 - 2200 = m
-5600 = m
Hence,
y = mx + c
y = - 5600x + 2200
the price of an item has risen to 300$ today. yesterday it was 125$. Find the percentage increse.
Answer:
140
Step-by-step explanation:
Trust Me
What is the less of side a? Round to the nearest tenth of an inch.
Answer:
About 14 in the exact value is 14.38 smthn
PLS HELP I have a time limit
Answer:
THE ANWSER IS 2.7
Step-by-step explanation:
YOUR TO TAKE GRAM AND DIVE IT BY 54
Answer:
C
Step-by-step explanation:
In 2020, a town was recorded as having a population of 10,000 and is predicted to grow at 5% every year. What will be the population in 2035, to the nearest whole number? *
Answer:
20789
Step-by-step explanation:
The equation of exponential growth is y=A(1+r)^t
A=10,000
r (rate)=0.05 (5% as a decimal)
t (time)=15 (2035-2020=15)
y=10,000(1+0.05)^15
y=20789.2817
you can't have part of a person, so y=20789
Mr.morales makes a table of the number of chaperones needed for different number of students attending a field trip. the ratio of parent chaperones to students is a constant proportion. what is the missing number in Mr.morales table.
Answer:
mark brainest
Step-by-step explanation:
Answer: 48
Step-by-step explanation:
Because, its multiplying by 8.
2×8= 16
4×8=32
6×8=48
8×8=64
5. AAA Dance Shoes makes dancing shoes with leather soles. The shoes cost $29 each to
manufacture. The fixed cost for the product line is $45,000. The company has
determined their demand function to be q=-200p+30,000, where p is the price for each
pair of shoes. What is the revenue function in terms of price? S
(10 Points)
R
200p + 915,000
O R = -200p + 30,000
O R = -200p2 + 30,000
O R = 200p2 + 870,000
Answer: 200p² + 870,000
Step-by-step explanation:
Revenue is calculated as price multiplied by quantity. In this case,
Price = P
Quantity (Q) = q=-200p+30,000
Revenue = p × q
Revenue = (200p + 30,000) × p
= 200p² + 30000p
= 200p² + 30000(29)
= 200p² + 870,000
The revenue function is 200p² + 870,000
The shorter leg of a right triangle is 8 less than the hypotenuse. The longer leg
is one less than the hypotenuse.
What is the length of the hypotenuse? *
What is the perimeter of the triangle?
Answer:
b
Step-by-step explanation: