Let r be the mass of a red disc and b the mass of a blue disc.
7 blues have the same mass as 1 red along with a 5 kg mass, so
7b = r + 5
7b - r = 5
2 blues and 1 red have the same mass as a 4 kg mass, so
2b + r = 4
Solve for b and r . Notice that adding the equations together eliminates r :
(7b - r) + (2b + r) = 5 + 4
9b = 9
b = 1
Then
7 • 1 - r = 5
r = 7 - 5
r = 2
So each red disc has a mass of 2 kg, and each blue disc has a mass of 1 kg.
Container A and container B have leaks. Container A has 800 ml of water, and is
leaking 6 ml per minute. Container B has 1000 ml, and is leaking 10 ml per minute.
How many minutes will it take for the two containers to have the same amount of
water?
**Write an equation to represent the situation (first blank). Use the variable m, for
minutes.
**Then solve for m (second blank).
**Finally, use your solution to determine the water level at that time (third blank).
The equation
can represent this situation. It will take
minutes for the two containers to have the same amount of water. At this time,
both containers will have ml left.
Answer:
a) 50 minutes
b) The water level at 50 minutes for Container A and B would be 500ml
Step-by-step explanation:
a) Let number of minutes at which both containers leak be represented by m.
Container A has 800 ml of water, and is leaking 6 ml per minute.
800ml - 6ml × m
800 - 6m
Container B has 1000 ml, and is leaking 10 ml per minute.
1000ml - 10ml × m
1000 - 10m
How many minutes will it take for the two containers to have the same amount of water?
Container A = Container B
800 - 6m = 1000 - 10m
Collect like terms
-6m + 10m = 1000 - 800
4m = 200
m = 200/4
m = 50 minutes
It will take 50 minutes for the two containers to have the same amount of water.
b) Finally, use your solution to determine the water level at that time.
Since m = 50 minutes
Container A = Container B
800 - 6m = 1000 - 10m
800 - 6 × 50 = 1000 - 10 × 50
800 - 300 = 1000 - 500
500 ml = 500 ml
Therefore, the water level at 50 minutes is 500 ml
Which values of X are solutions to the inequality
Answer:
The third answer choice
Step-by-step explanation:
-3(x+2) < 5x+10
-3x-6 < 5x+10
-3x-5x < 10+16
-8x < 16
x < -2
What are the solutions?
| x1 = 10
X = ?
Answer:
10
Step-by-step explanation:
The X is 10
what the slope of(-7,-4) (2,-7)
Answer:
[tex]m=\frac{-1}{3}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (-7, -4)
Point (2, -7)
Step 2: Find slope m
Substitute: [tex]m=\frac{-7+4}{2+7}[/tex]Add: [tex]m=\frac{-3}{9}[/tex]Simplify: [tex]m=\frac{-1}{3}[/tex]Find an explicit rule for the nth term of the sequence.
-4, -8, -16, -32, ...
A) an = -4 • 2n - 1
B) an = 2 • -4n + 1
C) an = 2 • -4n
D) an = -4 • 2n
Answer:
An explicit rule for the nth term of the sequence will be:
[tex]a_n=-4\cdot \:2^{n-1}[/tex]
Thus, option (A) is true.
Step-by-step explanation:
Given the sequence
[tex]-4, -8, -16, -32, ...[/tex]
A geometric sequence has a constant ratio r and is defined by
[tex]a_n=a_0\cdot r^{n-1}[/tex]
Computing the ratios of all the adjacent terms
[tex]\frac{-8}{-4}=2,\:\quad \frac{-16}{-8}=2,\:\quad \frac{-32}{-16}=2[/tex]
As the ratio 'r' is the same.
so
[tex]r=2[/tex]
as
[tex]a_1=-4[/tex]
Hence, the nth term of the sequence will be:
[tex]a_n=a_0\cdot r^{n-1}[/tex]
substituting the values [tex]r=2[/tex] and [tex]a_1=-4[/tex]
[tex]a_n=-4\cdot \:2^{n-1}[/tex]
Therefore, an explicit rule for the nth term of the sequence will be:
[tex]a_n=-4\cdot \:2^{n-1}[/tex]
Thus, option (A) is true.
The number 1,134 is divisible by all of the following except
A.3
B. 6
C. 9
D. 12
E. 14
Answer:
1,134 is not divisible by 12
Answer:
I think is: D. 12
Step-by-step explanation:
When graphing inequalities, where can the solutions be found?
Solutions will be located in the shaded region. Since this is a “less than” problem, ordered pairs on the boundary line are not included in the solution set. These values are located in the shaded region, so are solutions. (When substituted into the inequality x–y<3.
When solving systems of inequalities, the solutions are the regions where all the inequalities are true and will be represented by the intersection of the shaded areas.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
When graphing inequalities, the solutions can be found on the side of the number line or the coordinate plane where the inequality is true.
For example, if the inequality is x > 3, the solutions would be all the values of x that are greater than 3. These solutions would be represented by shading the area to the right of line x = 3 on the coordinate plane.
Similarly, if the inequality is y < 2, the solutions would be all the values of y that are less than 2. These solutions would be represented by shading the area below the line y = 2 on the coordinate plane.
It's important to note that when solving systems of inequalities, the solutions are the regions where all the inequalities are true and will be represented by the intersection of the shaded areas.
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HURRYYY HELPP!! Are the triangles below congruent by Side-Side-Side, Side-Angle-Side, or neither?
Answer:
b
Step-by-step explanation:
write a conditional statement from each given statement.
Congruent segments have equal measures.
Answer:
Our conditional statement should be written as:
'If they are congruent segments, then they have equal measures'.
Step-by-step explanation:
When we talk about conditional statements, it means we are about the statements which should contain 'if' and 'then'.
We need to recognize the hypothesis - conditions - and the conclusion - result - in the sentence. Then we should mention it as an 'if', and 'then' statement.In our example, our hypothesis must be 'if they are congruent segments' and the conclusion should be 'then they have equal measures'.
Therefore, we conclude that our conditional statement should be written as:
'If they are congruent segments, then they have equal measures'.
Which equation best describes a relationship between x and y in the table below?
Answer:
y = [tex]\frac{1}{3}[/tex] x + 5
Step-by-step explanation:
Slope m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
y = mx + b , "b" is y-intercept with coordinates (0, b)
(0, 5)
(6, 7)
m = [tex]\frac{7-5}{6-0}[/tex] = [tex]\frac{1}{3}[/tex]
y = [tex]\frac{1}{3}[/tex] x + 5
which of the following is a solution to
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]x < - 3 \: \: \: and \: \: \: x > 4[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
If (x^2 – 4) ÷ (x + 2) = x -2, which polynomial should fill in the blank below?
(x + 2) × ____= x^2 - 4
O x² – 4
O x-2
O x +2
O x² – 2
Answer:
x - 2
Step-by-step explanation:
(x + 2)(x - 2) = x^2 - 4
Seema sells two cookers for Rs.2574 each. On one she gains 10% and on the other she loses 10%.Find her gain or loss percent in the whole transaction.
Answer:
18.18%
Step-by-step explanation:
Selling price of one coker = Rs.2574
If she loose 10% on one;
%loss = Cost price - Selliing price/cost price * 100
10 =Cp-2574/Cp * 100
10/100 = Cp-2574/Cp
0.1Cp = Cp-2574
0.1Cp - Cp = -2574
-0.9Cp = -2574
Cp = 2574/0.9
Cp = Rs. 2860
Amount lost = 2860-2574 = Rs. 286
If she gains 10% on the second
%loss =Sp-Cp/Cp * 100
10 = 2574-Cp /Cp * 100
10/100 = 2574-Cp /Cp
0.1Cp = 2574-Cp
1.1Cp = 2574
Cp = 2574/1.1
Cp = Rs. 2340
Amount gained = 2340-2574 = Rs. 234
Total Loss = Amount lost - Amount gained
Total loss = 286 - 234
Total loss = Rs. 52
Total loss % = 52/286 * 100
Total loss % = 5200/286
Total loss % = 18.18%
Please help! Due tonight!
Answer:
x = square root of 119
Step-by-step explanation:
Because it is only a little bigger than the side it opposes
Could someone please answer b?
Answer:
b. The total sum of the money was $330
Step-by-step explanation:
#b
∵ A sum of money is divided among John, Paul, and Robert
∵ The ratio of the shares of John, Paul, and Robert is 2: 4: 5
→ Multiply the ratio of each share by x
∴ The share of John = 2x
∴ The share of Paul = 4x
∴ The share of Robert = 5x
→ Find their sum
∴ The sum of the money = 2x + 4x + 5x = 11x
∵ The sum of the money is divided equally among them
→ That means dividing the sum by 3 to find the share of every one
∵ The sum of the money = 11x
∴ The share of every one = [tex]\frac{11x}{3}[/tex] = [tex]\frac{11}{3}[/tex]x
∴ The share of John is larger by $50
→ That means the difference between his shares is 50
∵ [tex]\frac{11}{3}[/tex]x - 2x = 50
∴ [tex]\frac{5}{3}[/tex]x = 50
→ Divide both sides by [tex]\frac{5}{3}[/tex]
∴ x = 30
→ Substitute it in the sum of the money to find it
∵ The sum of the money = 11(30)
∴ The sum of the money = $330
∴ The total sum of the money is $330
I'm more than 9 dozen and less than the number of days in 4 months. The sum of my digits is 11.
Answer: 92 or 119
in 4 months, 2 months with 30 days per month, 2 months with 31 days per month
suppose: the number to find is X
have: 90 < X < 30.2 + 31. 2 ⇔ 90 < X < 122
if X is a number has 2 digits => X is xy
=> [tex]\left \{ {{x+y=11} \atop {90<x\leq 100}} \right.[/tex]
=> xy = 92
if X is a number has 3 digits => X is abc
we have: [tex]\left \{ {{a+b+c=11} \atop {100\leq abc<122}} \right.[/tex]
because 100 ≤ abc < 122 => a = 1; b = 0 or 1
+) if a =1 ,b = 0 but a+ b +c = 11 => c = 10 (removed because c is a 1-digit number)
+) if a = 1, b = 1 => c = 9
=> abc = 119
=> X is 92 or 119
Step-by-step explanation:
Manuel bought 9 pounds of apples. He has eaten 1.5 pounds so far and has $15
worth of apples left. Write and solve an equation to find the cost of the apples
per pound to the nearest dollar. How much did the apples cost per pound?
please answer quick
Answer:
$2 per poundStep-by-step explanation:
Let the cost of apples be x
Then we have equation:
(9 - 1.5)x = 157.5x = 15x = 15/7.5x = 2Cost of apple: $2 per pound
PLS HELP ME!
You buy 3.17 pounds of peaches, 1.15 pounds of pears, and 2.26 pounds of grapes. What is your total bill?
Answer:
Step-by-step explanation:
just add
3.17
1.15
2.26
-------
7. 48 lbs
im pretty sure
14. A satellite orbits 22, 300 miles above the equator. It completes one revolution in 24 hours. Assume that the radius of the Earth is 3, 960 miles. How far will the satellite travel in one day?
Answer:
Displacement = 0 mi
Distance = 164,996.45 mi
Step-by-step explanation:
In this case, the displacement will be zero because the satellite goes back to its starting point after one day. If there is no distance traveled between the starting point and the ending point, then the Displacement will be zero.
When it comes to the distance, we will need to calculate the perimeter of the circle the satellite describes when making one whole turn around the earth.
The perimeter of a circle is given by the equation:
[tex]p=2\pi r[/tex]
so we need to start by finding what the radius of the circle is. This radius if found by adding the radius of the earth and the distance above the equation the satellite is located at, so we get that:
[tex]r=r_{earth}+h[/tex]
where h is the height of the satellite, so the radius of the circle is:
[tex]r=22,300mi + 3,960 mi[/tex]
so
r=26,260 mi
so now we can use the perimeter equation to get:
[tex]p=2\pi r[/tex]
[tex]p=2\pi (26,260)[/tex]
So the distance traveled by the satellite in one day will be:
P=164,996.45 mi.
Plz help me with this question
10 points
9514 1404 393
Answer:
The sequence 18
Step-by-step explanation:
After Nolan brings down a zero, the dividend Nolan will be 20, the same one he started with. So, he will get the same result he has gotten so far: the first quotient digit is 1 and the second quotient digit is 8, resulting in a new dividend of 20 (after the 0 is brought down).
The digits 18 will repeat until Nolan gets tired.
-3+|n-2|>5
How would you solve this?
Answer:
3n-6>5
3n>5+6
3n>11
n>11/3
n>3.6
Answer:
n < 1/3
Step-by-step explanation:
-3(n-2) > 5
-3n + 6 > 5
-3n > 5 - 6
-3n > -1
n > -1/-3 (flip the sign of the inequality because you divided by a negative number)
Hence, n < 1/3 OR n < 0.333
Find the quotient: 189 divided by 9
1. 21
2. 22
3. 23
4. 24
The quotient is 21. the correct answer is option 1) 21.
To find the quotient of 189 divided by 9, we divide 189 by 9.
When dividing 189 by 9, we find that 9 can be subtracted from 189 a total of 21 times without going into negative values. Therefore, the quotient is 21.
So, the correct answer is option 1) 21.
When we divide 189 by 9, the result is 21, which means that 21 is the number of times that 9 can be subtracted from 189 without remainder. The quotient represents the whole number part of the division, indicating the number of groups of 9 that can be formed from 189.
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Johny and Rahul divided the benefit of the business in the ratio 7:9. If
Rahul got 4878 rupees as benefit did Johny get?
Answer:
Step-by-step explanation:
7:9 = x:4878
4878/9 times 7
3794 would be your answer
Answer:
3,794 rupees
Step-by-step explanation:
Johny got 7 parts of the benefit while Rahul got 9. This can be represented as a fraction: 7/9
To solve this problem, we can use cross multiplication, where x represents the amount of rupees Johny got:
[tex]\frac{7}{9}[/tex] = [tex]\frac{x}{4878}[/tex]
Multiply 7 by 4,878: 34,146
Multiply 9 by x: 9x
Now the equation looks like this:
9x = 34,146
Divide both sides of the equation by 9 to isolate the x:
9x/9 = 34,146/9
x = 3,794
Johny got 3,794 rupees.
Help asap cuz idk what’s going on
Answer:
The answer is the first one or 9.5
Step-by-step explanation:
This is because you need to use a^2+b^2=c^2
Plug in 9 and 3
To get 81+9
To get 90
Now find the square root of 90
It is around 9.48
Which is closest to 9.5
Which of the following statements best describes the value of the expression 5x – 4 when x = 1? A. The result is a fraction. B. The result is a prime number. C. The result is a composite number. D. The result is a whole number that is neither prime nor composite.
The statement which best describes the value of the expression at; x = 1 is; Choice D; The result is a whole number that is neither prime nor composite.
Which of the statements best describes the value of the expression 5x – 4 when x = 1?It follows from the task content that the value of the expression be determined at; x = 1 and consequently, the result be classified as a whole number, prime number or composite number.
Hence, when x = 1;
5x - 4 = 5(1) - 4.
= 5 - 4
= 1.
Hence, the result is 1 which can be classified as a whole number (integer). However, it is not a prime number and neither is it a composite number.
Therefore, Choice D is correct.
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GameStop is selling video games for $32 each. Used video games sell for $12 each. David is buying 3 new video games and x used video games. Which equation can be used to find y, the total price David must pay in dollars?
Answer:
12x plus 3x equals $32
Step-by-step explanation:
I just wrote an equation that best fits the problem
what is the value of ? pls help
3 − 3k + 7k = 5b[tex]3 − 3k + 7k = 5b[/tex]
Answer:
k=-14
Step-by-step explanation:
The 4th term of a sequence is 108. Each term after the first is three times the previous term. Write an expression that represents all 4 terms. Write an equation that represents the 4th term. What are the 4 numbers?
Answer:
First 4 terms are a, 3a, 3^2 a and 3^3 a.
The numbers are:
4, 12, 36, 108.
Step-by-step explanation:
This is a geometric sequence and we can write it as:
a, ar, ar^2, ar^3 <---- the first 4 terms.
Here the common ratio r = 3 and the 4th term is 108 so:
a(3)^3 = 108
So the first term a = 108 / 3^3
= 108/27
= 4.
So the second number = 3*4 = 12 and 3rd is 12*3 = 36.
someone please help ?!
The ratio of boys to girls in a class is 3:5. There are 32 students in the class. How many students are boys?
Answer:
12.
Step-by-step explanation:
to find a ratio, you must add the two numbers in the ratio, (3+5=8) and divide the total by that number (32÷8=4) once that is dine you can multiply the ratio number to find the amount (3×4=12) (5×4=20) so the ratio is 12:20, but the amount of boys is 12.