Andrew has 7 dimes and 15 quarters, as obtained from the system of linear equations so formed.
What is a system of linear equations?A system of linear equations is a set of two or more linear equations. Linear equations refer to the equations that involve two or more variables in the form of "ax + b".
Given:
Number of coins = 22; only dimes and quarters.Amount of coins = $4To find: Number of dimes and quarters.
Finding:
Now, 1 dime = 10 cents and 1 Quarter = 25 centsAlso, 100 cents = $1=> By unitary method, $4 = 4(100) = 400 cents
Let the number of dimes be d and number of quarters be q.Now, According to question, a system of linear equations follows:d + q = 22 (Number of coins) => d = 22 - q (eqn1)
and 10d + 25q = 400 (amount of coins)
=> 10 ( 22 - q ) + 25q = 400
=> 220 - 10q + 25q = 400
=> 15q = 400 - 220 = 180
=> q = 12, i.e., number of quarters = 22 upon the solving of this system of linear equations.
On substituting the value of q in eqn1, we get: d = 22 - 15 = 7, i.e., number of dimes = 7.
Hence, Andrew has 7 dimes and 15 quarters, as obtained from the system of linear equations so formed.
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[tex](800)×(3×10 −1 )= ?[/tex]
The answer is 23200.
BODMAS is an acronym that stands for Bracket, Order, Division, Multiplication, Addition, Subtraction. In certain regions, a synonym for BODMAS is used: PEMDAS (parentheses, exponents, multiplication, division, addition, and subtraction). It describes the order of operations performed when solving an equation. According to the BODMAS rule, if an expression contains parentheses ((), {}, []), first break or simplify the parentheses, then "order" (meaning exponentiation, root, etc.), division, multiplication , addition and subtraction from the left.By using BODMAS , we will first simplify the bracket term.
The bracket term is [tex](3\times10-1)[/tex]
After , bracket we will operate the multiplication term which is given by
[tex]30-1[/tex]
Now , we will use the subtraction operation .
[tex]29[/tex]
On solving the bracket , we get 29 .
Now we will multiply 800 by 29 ,we get
[tex]800\times29=23200[/tex]
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The complete question is mention below :
Solve [tex]800(3\times10-1)[/tex]
i need help with this question
Answer:
x = 1 and x = -3
Step-by-step explanation:
if y = f(x) and f(x) = -5, this means y = -5
draw a horizontal line at y = -5 and see write the x values for where the line intersects with the graph.
The x values are:
x = 1 and x = -3
13. For a party, Bob's Pizza charges $12 for each
supreme pizza while Mike's Pizzeria charges based
on the equation y = 8x + 20. How many pizzas
must you order for the price to be the same?
The number of pizzas you must order for the price to be the same is 5
How many pizzas must you order for the price to be the same?Bob's Pizza charges = $12 for each supreme pizza
This can be represented as
y = 12x
For Mike's Pizzeria, we have
y = 8x + 20
Substitute y = 12x in y = 8x + 20
12x = 8x + 20
Evaluate the like terms
4x = 20
Divide by 4
x = 5
Hence, the number of pizzas you must order for the price to be the same is 5
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need help solving this
If you can't answer this question
WILL MARK
PLEASE HURRYYY
What is the rate of change of the function?
-3
-1/3
1/3
3
Answer:
-1/3
Step-by-step explanation:
To find the x-intercept from an equation, you substitute ___ for the variable ___
and solve for ___
.
To find the y-intercept from an equation, you substitute ___ for the variable __
and solve for ___
.
To find the x-intercept from an equation, you substitute 0 for the variable y
and solve for x
To find the y-intercept from an equation, you substitute 0 for the variable x
and solve for y.
How to find x-intercept and y-intercept in an equation?The x-intercept is where a line crosses the x-axis.
In other words, the x-intercept is the value of the x coordinate of a point where the value of y coordinate is equal to zero.
The y-intercept is the point where the line crosses the y-axis.
In other words, the y-intercept is the value of the y coordinate of a point where the value of x coordinate is equal to zero.
Hence,
To find the x-intercept from an equation, you substitute 0 for the variable y
and solve for x
To find the y-intercept from an equation, you substitute 0 for the variable x
and solve for y.
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Let the graph of g be a translation 4 units left followed by a horizontal shrink by a factor of 1/3 of the graph of f(x)=x²+x. Write a rule for g
The transformed function is:
g(x) = (3*(x + 4))² + (3*(x + 4))
How to write the transformed function?Here we have the function:
f(x) = x² + x
Now we want to apply a translation of 4 units to the left, followed by a horizontal shrink by a factor of 1/3.
First, the translation is written as:
g(x) = f(x + 4)
Now the shink will give:
g(x) = f( 3*(x + 4))
Replacing the actual function we will get:
g(x) = (3*(x + 4))² + (3*(x + 4))
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find ∠rqt (4x+15) (10x-3)
The measure of angle RQT is 63°
Calculating anglesFrom the question, we are to determine the measure of angle RQT.
From the diagram,
We can observe that ∠PQS and ∠SQT form a linear pair
Thus,
∠PQS + ∠SQT = 180°
(4x + 15)° + (10x - 3)° = 180°
First, determine the value of x
4x + 15 + 10x - 3 = 180
4x + 10x = 180 - 15 + 3
14x = 168
x = 168/14
x = 12
In the diagram,
∠RQT and ∠PQS are vertically opposite
From the given information,
∠PQS = (4x + 15)°
∴ ∠RQT = (4x + 15)°
Substitute the value of x
∠RQT = (4(12) + 15)°
∠RQT = (48 + 15)°
∠RQT = 63°
Hence, the measure of angle RQT is 63°
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what is the radical expression that is equivalent 27 ⅕?
Answer:
[tex]\sqrt[5]{27}[/tex]
Step-by-step explanation:
27^(1/5) = [tex]\sqrt[5]{27}[/tex]
HELP ME ASAP FOR MATHS
Answer:5 higher and 1 horizontal
Step-by-step explanation:
5 Complete the table. Rounded to the nearest 10 100 1,000 10,000 100,000 1,000,000 3,147,283 68,547 69,000 1,656,908 900,571
The completion of the table by rounding the numbers to the nearest 10, 100, 1,000, 10,000, 100,000, and 1,000,000 is as follows:
Rounded to Numbers
the nearest 3,147,283 68,547 1,656,908 900,571
10 3,147,280 68,550 1,656,910 900,570
100 3,147,300 68,500 1,656,900 900,600
1,000 3,147,000 69,000 1,657,000 901,000
10,000 3,150,000 70,000 1,660,000 900,000
100,000 3,100,000 100,000 1,700,000 900,000
1,000,000 3,000,000 0.068547 2,000,000 1,000,000
What is a rounding number?Rounding a number involves, making it simple and very close to its true value, sometimes, using zeros or scientific notations.
Rounding a number is also known as an approximation, which is an estimate before the actual calculation is carried out.
Rounded to Numbers
the nearest 3,147,283 68,547 1,656,908 900,571
10 3,147,280 68,550 1,656,910 900,570
100 3,147,300 68,500 1,656,900 900,600
1,000 3,147,000 69,000 1,657,000 901,000
10,000 3,150,000 70,000 1,660,000 900,000
100,000 3,100,000 100,000 1,700,000 900,000
1,000,000 3,000,000 0.068547 2,000,000 1,000,000
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Sketch a graph of f(x)
The graph that depicts the graphical representation of the function F(x) is attached below
This is further explained below.
What is a graph?Generally, The collection of ordered pairings where "f(x)=y" exists is the network of a function f.
These pairs are Centroid of locations in two-dimensional space and so constitute a subset of this plane in the typical situation when x and f(x) are real integers.
In conclusion, is a collection of discrete or continuous points that together form a curve or surface and each of which corresponds to a certain function's value. also known as a linear graph.
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Midpoint Find the midpoint of the line segment with the endpoints A and B. A(4,10); B(8,6) The midpoint of the line segment is. (Type an ordered pair.)
Answer:
Step-by-step explanation:
A(2,6); B(10,8)
whats the midpoint of the segment?
Bruce spent $30 on lunch. If he had $55 in his wallet, what percent of his money did he spend on lunch?
Answer:
your answer is 54%
if a+1=b+2=c+3=d+4=a+b+c+d+5 what is a+b+c+d
A rectangular garden has a length of 7 feet and a width of 6 feet what is the area of the garden
Answer:
42
Step-by-step explanation:
L*W= Area
7*6=42
Hope this helps! :)
84 x 8 + the amount of 3 =
Find the 66th term of the arithmetic sequence -10, 7, 24, ...
========================================
Explanation:
[tex]a_1[/tex] = -10 is the first term
d = 17 is the common difference. We add this amount to each term to get the next one. Eg: -10+17 = 7
We want to find the 66th term, so we'll use n = 66
Plug these values into the nth term arithmetic sequence formula below.
[tex]a_n = a_1 + d(n-1)\\\\a_{66} = -10 + 17(66-1)\\\\a_{66} = 1095\\\\[/tex]
The 66th term is 1095
Answer:
The answer is 1095.
66th term = 1095
Step-by-step explanation:
an = a1 + (n − 1)d
= -10 + (66 - 1) (17)
I did it on calculator.
It equals to = 1095
Sean decides to start a small business creating and selling outdoor yard games. It will cost Sean $50 to make each game as well as an initial cost of $300 to purchase the needed equipment and supplies. He plans to sell each game for $85. The system of equations below models the cost and revenue for Sean's outdoor yard games where x represents the number of games and y represents the amount, in dollars.
The break even point obtained for the Sean's business is (60/7, 5100/7).
How to describe the linear equation in two variables?A linear equation in 2 variables is one that is written in the form ax + by + c = 0, where a, b, and c are real numbers and thus the coefficients of x and y, i.e. a and b, are not equal to zero. For example, 12x+8y = 9 and -x+8y = 3 are two-variable linear equations.Part of the question is missing where x denotes a number of games and y denotes the monetary value.
y = 50x + 300
y = 85x
Estimate Sean's business's break-even point.
Calculate the same break even point by following method;
The functions are as follows:
The functions are given as:
Cost: y = 50x + 300 ......equation 1
Revenue: y = 85x .......equation 2
For the value at break even point;
Cost = Revenue
Thus, equating 1 and 2.
85x = 50x + 300
simplifying;
35x = 300
Dividing both sides by 35
x = 60/7
Put x = 60/7 in equation 2
y = 85 × 60/7
y = 5100/7
Therefore, the break even point are obtained as (60/7, 5100/7).
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The complete question is-
Sean decides to start a small business creating and selling outdoor yard games. It will cost Sean $50 to make each game as well as an initial cost
of $300 to purchase the needed equipment and supplies. He plans to sell each game for $85,
The system of equations below models the cost and revenue for Sean's outdoor yard games where x represents the number of games and y represents the amount, in dollars.
y = 50x + 300
y = 85
What is the surface area of a pyramid with measurements of 4cm by 4cm by 7cm
Answer:
Area of one face of pyramid equal 18.55
Step-by-step explanation:
Area of pyramid equal 18.55x4=74.2
If a population consists of 5,400,000 people and a census is taken, how many
people are sampled?
Answer: 54,000,000
Step-by-step explanation: hope this helps
3. An electrician earns $24 an hour for a regular work week (40) hours. She earns time and a half for overtime. The weekly wage function is
(24h
0
w(h) = (36(h-40)+960 h> 40
How much will she earn if she works 38.5 hours this week?
0050
She will earn $924 if she works 38.5 hours this week
How much will she earn if she works 38.5 hours this week?The function is given as
w(h) = 24h, if h < 40
w(h) = (36(h-40)+960 h> 40
If she works 38.5 hours this week, then
h < 40
So, we use
w(h) = 24h
This gives
w(38.5) = 24 * 38.5
Evaluate
w(38.5) = 924
Hence, she will earn $924 if she works 38.5 hours this week
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HII NEED HELP PLEASE! I DON'T UNDERSTAND
Answer: f(-2)=3
Step-by-step explanation:
f(-2)=(-2-1)^2+3(-2)
=9-6
=3
This is the only true statement out of the questions.
So the answer would be -2.
»
What number is equivalent to
32 +6 (14-5×2) ÷ 4
A 23/1
B 10/
C 14
D 15
The result of the given equation is 14.
This is an problem of simplification. And for simplification we need to understand the rule of BODMAS.
BODMAS means we have to first solve B for bracket, O for of, D for divide, M for multiplication, A for addition and S for subtraction.
The rule of BODMAS has to be followed in order to solve any equation in simplification method.
Here the problem is;
32+6(14-5×2)÷4
⇒32+6(14-10)÷4
⇒32+6(4)÷4
⇒32+24÷4
⇒56÷4
⇒14
So, the solution of the given equation gives 14 as the answer.
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How much of the daily value must a snack meet in order for the fda to consider it a ""good source"" of nutrients? 10 percent to 19 percent 10 percent to 19 percent 25 percent to 35 percent 25 percent to 35 percent 30 percent to 40 percent 30 percent to 40 percent 50 percent to 59 percent
10 percent to 19 percent of daily value must a snack meet in order for the FDA to consider it a ""good source"" of nutrients.
The Food Manufacturer or Distributor is responsible for ensuring their food product labeling complies with FDA regulations. FDA will not review or approve food labels. If the labels do not comply with FDA requirements, the FDA will consider the product as misbranded and may take regulatory action, including detention.
LMG's Label review service will help you confirm your product labels comply with FDA requirements. We have designed three types of label review services; you can choose the best service which fits your products.
( Food Label Compliance : FDA , Food and Drug administration)
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2/3 of the sum of nine and p
The resulting expression for 2/3 of the sum of nine and p is 2/3(9+p)
Translating expression to wordsAccording to the question, we are to write the given statement as an expression
Let the unknown variable be p such that the sum of nine and p is 9 + p
Since "of" means multiplication, hence;
2/3 of the sum of nine and p will be expressed as;
2/3 of (9 + p)
2/3 * (9 + p)
2/3(9+p)
Hence the resulting expression for 2/3 of the sum of nine and p is 2/3(9+p)
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3. Based on the graph of the function y = g(x) shown below, answer the following questions.
y
(a) Evaluate g (-2), g(0), g (3) and g (7).
hogy
Joo 1 023
(b) What values of x solve the equation g(x)=0
(c) Graph the horizontal line y = 2 on the grid
above and label.
wirb
X
(d) How many values of x solve the equation
g(x)=2?
The values of x that solve the equation g(x) = 0 are x = -3, 1, 5 and 7 and there are four values of x that solve the equation g(x) = 2
How to answer the questions based on the graph of the function y = g(x) shown?The graph represents the given parameter
(a) Evaluate g (-2), g(0), g (3) and g (7)
To do this, we take the function value at the given value of x
The function g(-2) means
x = -2
So, we have
When x = -2, g(x) = -3
This means that g(-2) = -3
The function g(0) means
x = 0
So, we have
When x = 0, g(x) = -3
This means that g(0) = -3
The function g(3) means
x = 3
So, we have
When x = 3, g(x) = 4
This means that g(3) = 3
The function g(7) means
x = 7
So, we have
When x = 7, g(x) = 0
This means that g(7) = 0
(b) What values of x solve the equation g(x) = 0On the graph, we have the following values of x at g(x) = 0
x = -3, 1, 5 and 7
Hence, the values of x that solve the equation g(x) = 0 are x = -3, 1, 5 and 7
(c) Graph the horizontal line y = 2 on the grid above and label.See attachment
(d) How many values of x solve the equation g(x)=2Using the line in (c), the line crosses the curve four times at y = 2
Hence, there are four values of x that solve the equation g(x) = 2
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now examine |a + bi| and complete the definition below. the absolute value of any complex number a + bi is the from (a, b) to (0, 0) in the complex pl
According to the given statement the absolute value of just about any complex number Ia + biI seems to be the distance between (a, b) and (0, 0) in the complex plane is √(a² + b²).
What specifically is modulus?After dividing one number by another, the modulo operation yields the remainder or signed remainder of the division. A modulo n seems to be the remainder of something like the Euclidean division on a by n, where an is the dividend and n is the divisor, given two positive numbers a and n.
What is the purpose of modulus?The modulus operator can be used in a variety of situations. It is frequently used to decrease a randomly generated number to a randomly generated number in a smaller range, and it may also rapidly tell you if one integer is a factor of another.
According to the given information:The modulus of any complex number is its absolute value, regarding which there is a modulus formula. √(a² + b²).
where a and b are integers
Please see the attached file for the complex plane of the provided points (a,b) (0,0).
The separation of two points (x1 ,y1) and (x2 ,y2) will be:
√((x1 - y1)² + (x2 - y2)²)
We need to calculate the distance between (a,b) because (0,0)
We will obtain by replacing the numbers in the distance formula.
√((0 - a)² + (0 - b)²).
The given statement the absolute value of just about any complex number a + bi seems to be the distance between (a, b) and (0, 0) in the complex plane is √(a² + b²).
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I understand that the question you are looking for is:
now examine |a + bi| and complete the definition below. the absolute value of any complex number a + bi is the from (a, b) to (0, 0) in the complex plane.
Answer: distance , positive real on edge
Step-by-step explanation:
For a certain type of computers, the length of time between charges of the battery is normally distributed with a mean of 50 hours and a standard deviation of 15 hours. john owns one of these computers and wants to know the probability that the length of time will be between 50 and 70 hours? choose one.
The probability that the length of time will be between 50 and 70 hour is 0.4082.
What is normal distribution?Height is a simple instance of an event that describes a normal distribution: most people are of medium height, the proportions of people who are taller and shorter than average are roughly equal, and a very small (but still roughly equivalent) proportion of people either are extremely tall or extremely short.
Now, as per the given question;
Let t be the variable representing the length of time (t = 50)
As a result, the mean of the battery is 50 and the standard deviation is 15.
Thus, μ = 50 (mean) σ = 15 (standard deviation)
Now, we must calculate the probability that t is between 50 & 70.
Thus, the probability P (50 < t < 70)
The z-value will be calculated as;
Z = (t – μ) / σ
Substitute the values,
Z = 50 – 50 / 15
Z = 0
Now, for the time; t = 70
Z = 70 – 50 / 15
Z = 1.33
Thus, the probability is;
P(50 < t < 70) = P(0 < z < 1.33)
So, the area to left of Z
= 1.33 – area to the left of z = 0
= 0.9082 – 0.5
P(50 < t < 70) = 0.4082
Therefore, the probability that the length of time will be between 50 and 70 hours is 0.4082.
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The MyTunes song app sells music downloads. Over the past few years, the service
has lowered its prices. The table shows the price per song and the number of songs
downloaded per day at that price.
Price per
Song
$0.89
$0.79
$0.69
$0.59
$0.49
$0.39
Number of Downloads (in
thousands)
1,212
1,704
1,760
1,877
1,944
2,011
The approximate number of downloads at a price of $0.54 per song is ______
The approximate number of downloads at a price of $0.54 per song is 1910.5
As the problem given we have The table shows the price per song and the number of songs downloaded per day at that Price per Song.
Price per song number of songs
downloaded per day at that price
$0.89 1,212
$0.79 1704
$0.69 1760
$0.59 1877
$0.49 1944
$0.39 2011
The formula for the linear interpolation process y = y1 + ((x – x1) / (x2 – x1)) * (y2 – y1), where x is the known value, y is the unknown value. x1 and y1 are the coordinates that are below the known x value, and x2 and y2 are the coordinates that are above the x value.
here x1= 0.49 y1= 1944 x2= 0.59 y2=1877 x=0.54
y=1944+((0.54-0.49)/(0.59-0.49))*(1877-1944)
y=1944-33.5=1910.5
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