Altogether, Abby and Annie have 2,400 coins, using the Lowest Common Multiple of 75 and 80.
What is the lowest common multiple?The lowest common multiple (LCM) of two or more numbers is the common multiple shared by the numbers.
LCM of 75 and 80 can be obtained by multiplying common prime factors of 75 and 80, and then raising them to their respective highest power, i.e. 2^4 × 3^1 × 5^2, which gives 1200.
For instance, 1,200 can be divided by both 75 and 80 evenly without a remainder. And there is no other number less than 2,000 that 75 and 80 can divide evenly without a remainder.
Abby's coins = 1,200
Annie's coins = 1,200
Total coins = 2,400
Abby's 80 coins will have 15 groups (1,200/80)
Annie's 75 coins will have 16 groups (1,200/75)
Thus, using the LCM of 80 and 75, the total number of coins held by Abby and Annie is 2,400.
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Given the inequality 4(n − 5) < 3(n + 11), determine which integer makes the inequality false.
S:{4}
S:{11}
S:{53}
S:{−8}
Answer:
C
Step-by-step explanation:
4(n-5)<3(n+11)
4n-20<3n+33
4n-3n<33+20
n<53
n is not 53 but less than 53.
Consider the function f(x) = √ x+2 and g(x) = ax+b. Find a and b, if fog (1) = 2 and g (-1)=2.
The value of a and b in the function f(x) = √ x+2 and g(x) = ax + b , is a = 0 and b = 2 .
In the question ,
it is given that ,
the function f(x) = √(x+2) and the function g(x) = ax + b
also given that
fog(1) = 2
f(g(1)) = 2
f(a + b) = 2 .... because g(1) = a + b
√(a + b +2) = 2
Squaring both the sides
a + b + 2 = 4
a + b = 2 .......(1)
also given that
g(-1) = 2
a(-1) + b = 2
-a + b = 2 .....(2)
Adding equation (1) and (2) , we get
2b = 4
b = 2
Substituting b = 2 in the a + b = 2 , we get
a + 2 = 2
a = 2 - 2
a = 0
Therefore , The value of a and b in the function f(x) = √ x+2 and g(x) = ax + b , is a = 0 and b = 2 .
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What is the solution to the system of equations
The solution of the given system of equations is (-1, -2).
Explain the method of substitution?Three steps make up the substitution technique: For each of the variables, solve one equation. Put this expression (or plug it in) into the other equation, then solve it. To identify the corresponding variable, rewrite the value's original equation.We are aware that a linear system of equations can be solved using a substitution method.
The intersection of the two lines represents the system's solution.
The given equations are-
y = 3x+1 ...eq 1
y = -2x-4 ...eq 2
Put the value of eq 1 in eq2 .
3x+1 = -2x-4
3x + 2x = -4 - 1
5x = -5
x = -5/5
x = -1
Put the x in eq 1.
y = 3(-1)+1
y = -2
Thus, the solution of the given system of equations is (-1, -2).
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The complete question is-
What is the solution to the system of equations-
y=3x+1 ;
y=-2x-4
−18 < 9x
how to solve and answer
Answer:
x> 2
Step-by-step explanation:
18< 9x Divide both sides by 9
2<x or x > 2 All the numbers greater than 2 is a solution.
Jesse and Amir were assigned the same book to read. Jesse started reading on Saturday, and he is reading 30 pages a day. Amir didn't start until Sunday, but he is reading 35 pages a day.
How many days will it take Amir to catch up to Jesse, and how many pages will they each have read?
Answer the questions to solve this problem using a system of equations.
1. Write an equation to represent the number of pages Amir has read. Use x to represent the number of days Amir has been reading and y to represent the number of pages he has read. (1 point)
2. Write an equation to represent the number of pages Jesse has read.
Using x, the number of days Amir has been reading, write an expression to represent the number of days Jesse has been reading. Remember that Jesse started reading one day before Amir. Use this expression to write an equation for the number of pages Jesse has read. Let y represent the number of pages read. (1 point)
3. Write the system of equations using your answers from questions 1 and 2.
(2 points)
5. Solve the system of equations. Show your work. (2 points)
6. Interpret your solution. How many days does it take Amir to catch Jesse? At that time, how many pages have they read? (2 points)
1. An equation representing the number of days Amir has been reading and the number of pages he has read is y = 35x.
2. An equation representing the number of days Jesse has been reading and the number of pages she has read is y = 30 + 30x.
3. The system of equations from 1 and 2 is y = 35x and y = 30 + 30x.
4. At the end of Friday, after solving the equations, both Jesse and Amir read 210 pages each, with Jesse spending 7 days and Amir 6 days.
5. For Jesse and Amir, the equation solutions are y is 210 pages and x is 6 days.
6. After solving the equations, it will take Amir 6 days to catch up with Jesse and each person must have read 210 pages or a total of 420 pages.
What is a system of equations?A system of equations involves using more than one equation solved simultaneously.
Jesse's reading rate per day = 30 pages
Amir's reading rate per day = 35 pages
The number of pages read by Jesse, y = 30 + 30x
The number of pages read by Amir, y = 35x
Where x = the number of days they have been reading
Solving the equations:y = 30 + 30x and y = 35x
35x = 30 + 30x
35x - 30x = 30
5x = 30
x = 6 (30/5)
Jesse:y = 30 + 30x
y = 30 + 30(6)
y = 210
Amir:y = 35x
y = 35(6)
y = 210
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A firm makes circular drink mats , of radius 4.5cm , that are 3mm thick . They want to produce a rectangular box to hold a pile of 12 mats. What are the minimum dimensions of the box.
Please answer with working out
Thank you
Answer:
13.5
Step-by-step explanation: that's the minimum of dimensions for the box
17 Solve the inequality. Graph the solution. 4.2y ≤ -12.6 The solution is and then where it goes on thr number line
The solution to this inequality in interval notation is {-∞, -3} and it goes to the left on the number line.
What is an inequality?In Mathematics, an inequality can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data such as integers, and variables in an equation based on any of the following inequality symbols:
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).From the information provided, we have the following inequality:
4.2y ≤ -12.6
Dividing both sides of the inequality by 4.2, we have the following:
y ≤ -12.6/4.2
y ≤ -3
In conclusion, a solution to this inequality is equal to {-∞, -3} as shown in the number line (graph) attached below.
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Word problem involving the Pythagorean Theorem
A kite is flying 8 ft off the ground. Its line is pulled taut and casts a 6-ft shadow. Find the length of the line. If necessary, round your answer to the nearest
tenth.
6
0f
x 5
The length of the line is 10ft
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse in familiar algebraic notation, a2 + b2 = c2
Given that A kite is flying 8 ft off the ground. Its line is pulled taut and casts a 6-ft shadow
We have to find a third side
By using Pythagoras' theorem. a^2+b^2=c^2
8^2+6^2=c^2
64 +36 = c^2
c^2= 100
c^2= 10
Therefore the length of the line is 10ft
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Solve for a : a+4/5= 1/ 1/2
[tex]a=\frac{6}{5}[/tex].
Step-by-step explanation:1. Write the expression.[tex]a+\frac{4}{5} =\frac{1}{\frac{1}{2} }[/tex]
2. Convert the right hand side of the equation (check attached image 1).[tex]a+\frac{4}{5} =1*\frac{2}{1} \\ \\a+\frac{4}{5} =2[/tex]
3. Subtract 4/5 from both sides of the equation.[tex]a+\frac{4}{5}-\frac{4}{5} =2-\frac{4}{5}\\ \\a=\frac{2}{1}-\frac{4}{5}\\\\a=\frac{2*5}{1*5}-\frac{4}{5}\\ \\a=\frac{10}{5}-\frac{4}{5}\\ \\a=\frac{10-4}{5} \\ \\a=\frac{6}{5}[/tex]
4. Verify your answer.[tex](\frac{6}{5} )+\frac{4}{5} =\frac{1}{\frac{1}{2} }\\ \\\frac{10}{5} =2\\ \\2=2[/tex]
5. Conclude.[tex]a=\frac{6}{5}[/tex].
In how many ways can the digits in the number 7,550,000 be arranged
The number of ways the digits of the given number can be arranged would be = 5,040
What is factorials?Factorials are mathematical expressions that are used to show the number of ways a variable can be arranged in a data set.
The number of digits found in the number 7,550,000 = 7
The number of ways the digits can be arranged would be the factorials of 7 (7!) ;
= 7×6×5×4×3×2×1
= 5,040
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A line intersects the points
(8, -4) and (-6, 10).
m = -1
Write an equation in point-slope form
using the point (8, -4).
-
y + 4 = [?] (x −
Enter
Answer:
y + 4 = -(x - 8)
Step-by-step explanation:
The point-slope form equation is y - y1 = m(x - x1)
Since we're given m and since they use the 4 from (8, -4) as y - (-4) = y+4, we simply need to plug in 8 into the RHS of the equation and you can check the math.
If you substitute 8 and -4 for y and x, you have:
-4 + 4 = -1(8 - 8)
0 = -1 * 0
0 = 0
You'd get -2 on both sides if you used -6 and 10, but having an equal equation means our math is true/accurate.
PLEASE HELP ASAP! WILL GIVE BRAINLIEST AND FIVE STAR RATING FOR ACTUAL HELP! Describe the function‘s end behavior. f(x)=−10+6x^5+4x^3
as x→ ∞, f(x)→
as x→ −∞, f(x)→
Possible answers for both are:
-∞
∞
0
an asymptote
Answer: As x approaches infinity, f(x) approaches infinity.
As x approaches -infinity, f(x) also approaches - infinity.
Step-by-step explanation:
You can either graph this function on an online graphing (such as desmos. com) calculator to see the end behavior, or you can try inputting some numbers in. You could put in the number 1,2,3 and see that the graph will keep on increasing to positive infinity, and input the numbers -1,-2,-3 to see that the numbers will decrease to negative infinity.
Ling tried to solve an equation.
12=p+6.2
12 + 6.2 = p + 6.2- 6.2 Setting up
18.2 = P Calculating
Answer:
p = 5.8
Step-by-step explanation:
12 = p + 6.2 Subtract 6.2 from both sides. Ling subtracted 6.2 from the right, but added it to the left side.
5.8 = p
change to exponential form
(4√ x5)
The graphs of f(x) and g(x) are shown below. On a coordinate plane, a straight line with negative a slope represents f (x) = negative x. The line goes through points (0, 0), (negative 6, 6) and (6, negative 6). On a coordinate plane, a straight line with a positive slope represents g (x) = 2 x. The line goes through points (negative 3, negative 6), (0, 0) and (3, 6). Which of the following is the graph of (g – f)(x)? On a coordinate plane, a straight line with a negative slope goes through points (negative 2, 6), (0, 0), and (2, negative 6) On a coordinate plane, a straight line with a negative slope goes through points (negative 6, 6), (0, 0), and (6, negative 6). On a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6).
The option that is the graph of (g – f)(x) is; On a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6).
How to Interpret Inequality Graphs?We are given the function as;
f(x) = -x
Now, the line passes through the points (0,0),(-6,6) and (6,-6) is;
The function given as; g(x) = 2x
This line passes through the points (-3,-6),(0,0) and (3,6).
Before we graph (g - f)(x), we have to first simplify it to get;
The graph of of (g - f)(x)
(g - f)(x) = g(x) - f(x)
= 2x - (-x)
= 3x
At x = 0, we have;
(g - f)(0) = 3(0) = 0
At x = 2, we have;
(g - f)(2) = 3(2) = 6
At x = -2, we have;
(g - f)(-2) = 3(-2) = -6
At x = -6, we have;
(g - f)(-6) = 3(-6) = -18
Looking at the options, option C is true
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Find a point-slope form for the line that satisfies the stated conditions. Slope 4, passing through (-8,1)
Answer: (y - 1) = 4(x + 8)
Step-by-step explanation:
The point-slope form is (y - y₁) = m(x - x₁), where:
m = slope = 4(x₁, y₁) = (-8, 1)So, the point-slope of this line would be (y - 1) = 4(x + 8).
given that M > N, determine whether the inequality M/N > N/M is always sometimes or never true
Answer:
An equation is a proposition of two expressions that are equal.
Step-by-step explanation:
The function f(x) is graphed below. How many points on the graph
represent a relative extreme value?
From the given graph of the function, the number of points on the graph representing relative extreme value are two (b and d).
As given in the question,
For the given graph of a function,
Number of points represented on the graph are 5
Points are a, b, c, d, e
Point a, c, e are on the x-axis.
Relative extreme value representing the maximum and minimum value of the graphed function.
For the given graph,
Maximum value represented by point d.
Minimum value represented by point b.
Number of points representing relative extreme values are 2 ( b and d).
Therefore, from the given graph of the function, the number of points on the graph representing relative extreme value are two (b and d).
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A local farmer had a mouse problem in his barn. He estimated there were about 800 mice to start with. He adopted some cats and noticed that the number of mice was decreasing by 8%/wk. The graph models the number of mice x weeks after the farmer adopted the cats.
Identify and interpret the key features of the exponential function modeled in terms of this situation.
Select each correct answer.
The asymptote indicates that as the number of weeks the farmer has had the cats increases, the population of mice approaches 0.
The y-intercept represents the number of mice the farmer had in the barn at the time he adopted the cats.
The line x = 0 is an asymptote of the graph.
The point (0,30) contains the x-intercept.
The line y = 0 is an asymptote of the graph.
The y-intercept is 800.
The asymptote indicates that there were never more than 800 mice in existence.
Answer:
The asymptote indicates that as the number of weeks the farmer has had the cats increases, the population of mice approaches 0.
The y-intercept represents the number of mice the farmer had in the barn at the time he adopted the cats.
The line y = 0 is an asymptote of the graph.
The y-intercept is 800.
Step-by-step explanation:
Took the test
What is the slope of the
function below?
(4,4)
(3, 3)
Slope = [?]
Answer:
slope is m=1
Step-by-step explanation:
Answer: 1
Step-by-step explanation: use the slope formula to find the slope m
Melinda needed to mail a package. She used .02 stamps and .10 stamps to mail the package. If she used 15 stamps worth .78 how many of each type of stamp did she use
The number of each type of stamp used is as follows:
9 of 0.02 stamps6 of 0.1 stampsHow to find how many of each type of stamp used?Melinda needed to mail a package. She used .02 stamps and .10 stamps to mail the package. She used 15 stamps worth 0.78. The number of each type of stamp she used can be calculated as follows:
let
x = number of 0.02 stamp
y = number of 0.10 stamp
Using system of equation,
x + y = 15
0.02x + 0.10y = 0.78
multiply equation(ii) by 50
x + y = 15
x + 5y = 39
4y = 24
y = 24 / 4
y = 6
Hence,
x = 15 - 6
x = 9
Therefore, the number of 0.02 stamps is 9 and the number of 0.10 stamp is 6.
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Solve the following expression when
t = 6 and d = 8
t + d/8-6
Answer:
1
Step-by-step explanation:
Replace the variable letter with the number.
t + d / 8 - 6
6 + 8 / 8 - 6
6 + 1 - 6
7 - 6
1
Complete the number sentence. Must show your work. Please help! I’m confused
Answer:
2 + (-10) = 12
Step-by-step explanation:
The great answers. Thank you. I hope for help to you.
PLEASE HURYYY RIGHT NOW
Answer:
Only Julia's Question.
Step-by-step explanation:
Julia: 8÷[tex]\frac{1}{4}[/tex]
Tanveer: 8*1/4
It takes 3.5 ounces of cocoa to make a cup of hot chocolate how much cocoa is needed to make 7 cups of hot chocolate
Answer: 24.5
Step-by-step explanation: 3.5 x 7 = 24.5
Answer: 24.5 ounces
Step-by-step explanation:
3.5 times 7 = 24.5 ounces
If you have trouble try
3.5 + 3.5 + 3.5 + 3.5 + 3.5 + 3.5 + 3.5
Write a linear function f with f(0)=7 and f(3)=1
y=mx+b
The linear function f with f(0) = 7 and f(3) = 1 is y = -2x + 7
How to represent linear equation?Linear equation can be represented in slope intercept form as follows:
y = mx + c
where
m = slopec = y-interceptTherefore,
f(0) = 7 and f(3) = 1
Using linear equation
7 = m(0) + b
b = 7
1 = m(3) + 7
1 - 7 = 3m
-6 = 3m
m = - 6 / 3
m = -2
Therefore, the linear function is y = -2x + 7
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The graph shows the cost of grapes at a grocery store. What is the slope of the line?
The slope of the line shown in the graph is 4.5 .
In the question ,
it is given that ,
the amount of grapes is represented on x axis . and
the cost for that grape in the grocery store is represented on y axis .
to find the slope we need two points on the line ,
from the graph we can take two points as (1 , 4.5) and (2 , 9) ,
the slope can be calculated using the formula
slope = (change in y coordinate)/(change in x coordinate)
slope = (9 - 4.5)/(2 - 1)
slope = 4.5/1
slope = 4.5 .
Therefore , The slope of the line shown in the graph is 4.5 .
The given question is incomplete , the complete question is
The graph below shows the cost of grapes at a grocery store. What is the slope of the line?
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Suppose you earned a $710,000 bonus this year and invested it at 8.25% per year. how much could you withdraw at the end of each of the next 20 years? select the correct answer.
Withdraw at the end of each of the next 20 years is [tex]710000(1.0825)^{20}[/tex]
What do you mean by simple interest and compound interest?
Simple interest can be defined as the amount that is paid back using borrowed money over a period of time.
simple interest:
Simple interest can be defined as the principal of a loan or deposit that an individual puts into a bank account.
Compound interest:
Compound interest is interest that accrues on the principal and accrues interest.
Given:
Principal, P = $710000
Rate of interest, r = 8.25%
Time period, t = 20 years
withdrawal at the end of 20 years , A = [tex]P(1+r)^{t}[/tex]
A = [tex]710000(1+8.25/100)^{20}[/tex] = [tex]710000(1+0.0825)^{20}=710000(1.0825)^{20}[/tex]
Therefore, withdraw at the end of each of the next 20 years is [tex]710000(1.0825)^{20}[/tex]
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2 3/5 divided by 9 3/5
Answer:
as decimal
0.27083333333
Answer:
2 3/5 divided by 9 3/5 is 32
A store is having a sale on walnuts and chocolate chips. For 6 pounds of walnuts and 5 pounds of chocolate chips, the total cost is $28. For 2 pounds of walnuts and 3 pounds of chocolate chips, the total cost is $14. Find the cost for each pound of walnuts and each pound of chocolate chips.
Answer:
chocolate- 2 dollars walnuts- 4
Step-by-step explanation:
2 x3=6. 14-6=8
8÷2=4